Answers
The surface area of the rectangular pyramid is 75 m².
What is surface area?Surface area is the sum of all the surfaces on each side of a three-dimensional shape.
To calculate the surface area of the rectangular pyramid, we use the formula below
Formula:
S.A = 2lh+l²............................. Equation 1Where:
S.A = Surface area of the rectangular pyramidl = Length of the base of the pyramidh = Slope height of the pyramidFrom the question,
Given:
l = 5 mh = 5 mSubstitute these values into equaation 1
S.A = 2×5×5+5²S.A = 50+25S.A = 75 m²Learn more about Surface area here: https://brainly.com/question/1297098
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Related Questions
Use the formula 6p + 3q = t to find the value of q when p = 4 and t = 24. 6
Can I have some help please
Answers
When p=4 and t=24 then substituting these values into the equation 6p + 3q = t we get q=0.
To find the value of q in the equation 6p + 3q = t when p = 4 and t = 24, you can substitute the given values into the equation and solve for q. First, replace p with 4 and t with 24
6(4) + 3q = 24
Simplify the left side of the equation
24 + 3q = 24
Subtract 24 from both sides
3q = 0
Divide both sides by 3
q = 0
Therefore, when p = 4 and t = 24, q is equal to 0.
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HELPPPPPPPPPPPP PLSSSSSSS
Answers
8.) Jesenia is standing on a pedestrian bridge that is 9.5 feet above a lake. She looks down and sees a
duck in the water. The duck is 4.5 feet away from Jesenia's position on the bridge. What is the angle of
depression from Jesenia to the duck? Round to the nearest degree.
Answers
Answer: The angle of depression from Jesenia to the duck is 25.17°. The solution has been obtained by using trigonometry.
What is trigonometry?
Right-angled triangles, their sides, angles, and connections are the main topics of the mathematical field of trigonometry.
We are given that that Jesenia is standing on a pedestrian bridge that is 9.5 feet above the lake and the duck is 4.5 feet away from jesenias position on the bridge.
This means that perpendicular is 9.5 and base is 4.5.
We know that tan θ is value of opposite side to adjacent side.
So, we get
⇒ Tan θ =
⇒ Tan θ = 0.47
⇒ θ = 25.17°
Hence, the angle of depression from Jesenia to the duck is 25.17°.
Step-by-step explanation:
Welcome!
Which line is represented by y=3/2x-3 ? A. B. C. D.
Answers
Answer:
B
Step-by-step explanation:
the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3
So, first find the graph(s) that have the y intercept of -3. The only options would be B and C.
Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point. This eliminates option C for the slope. The slope of option C is 2/3, not 3/2.
So, option B is correct. Hope this helps ;)
Answer:
B
Step-by-step explanation:
y = mx + b
y = mx (slope) + b (y-intercept)
The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).
Use point-slope form to write the equation of a line that passes through the point (16,−14) with slope 1.
Answers
The equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
What is meant by equation?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign and can include variables, constants, and mathematical operations. Equations are used to represent relationships between quantities and to solve problems in mathematics and science.
What is meant by slope?
Slope refers to the measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical distance) by the change in the x-coordinate (horizontal distance) between two points on the line.
According to the given information
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the line passes through the point (16, -14) and has a slope of 1. Plugging these values into the point-slope form, we get:
y - (-14) = 1(x - 16) y + 14 = x - 16 y = x - 30
So, the equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
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the angle of elevation to an airplane viewed from the control tower at an airport is 7. the tower is 200 feet high and the pilot reports that the altitude is 5200 feet. how far away from the control tower on a straight line is an airplane?
Answers
The distance between control room to airplane is 41027.5 feet.
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here This distance (d) from tower will be the hypotenuse of a right triangle.
The altitude is the side opposite the angle at the tower
The tower is 200' high, therefore, the altitude above the tower.
=> 5200 - 200 = 5000 feet.
Now using sine ratio then,
=> Sin 7° = AC/BC
=> BC = AC/sin 7°
=> BC = 5000/sin 7°
=> BC = d = 41027.5 feet.
Hence the distance between control room to airplane is 41027.5 feet.
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Probably basics
Playing Card problem
Needing help Please:)
It’s due in a little bit so I would deeply appreciate it
Answers
The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.
How to solveThe total number of combinations of selecting 5 cards from a deck of 52 cards is 52C5 = 5251504948/120 = 2598960.
The probability of exactly 4 of the 5 cards being Aces is 48*100/2598960 = 0.0018%.
The probability of all 5 of the cards being Spades is 1287*100/2598960 = 0.0495%.
The probability of exactly 4 of the 5 cards being face cards is 49540100/2598960 = 0.7618%.
The probability of exactly 2 Aces and exactly 2 Kings being selected is 1584*100/2598960 = 0.0609%.
The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.
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2 Bea counts the number of red pencils in 7 boxes of pencils. The list shows her
data: 22, 28, 30, 28, 35, 30, 28. The mean is 26 red pencils per box. Based on
the MAD for the data set, would it be unlikely to get a box with 31 red pencils?
Show your work. Explain your reasoning.
Answers
2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
What is the data set?To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.
Step 1: Calculate the mean of the data set
The given data set is: 22, 28, 30, 28, 35, 30, 28
The mean is calculated by adding up all the numbers and dividing by the total number of values:
Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)
Step 2: Calculate the absolute deviations
The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:
|22 - 28.71| = 6.71
|28 - 28.71| = 0.71
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
|35 - 28.71| = 6.29
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
Step 3: Calculate the MAD
The MAD is the mean of the absolute deviations:
MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)
Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.
Difference = 31 - 28.71 = 2.29
Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
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A circle has a center of (1, -1). The circumference passes through (1, 2). Find the length of the circumference of the circle. Use 3.14 for pi. Then, Find the area of the circle.
Answers
Answer:
The radius of the circle is 3, so
Circumference = 2(3)π = 6π = 18.84
Area = π(3^2) = 9π = 28.26
Expand. Your answer should be a polynomial in standard form. (-p^2+4p-3)(p^2+2)=(−p 2 +4p−3)(p 2 +2)=left parenthesis, minus, p, squared, plus, 4, p, minus, 3, right parenthesis, left parenthesis, p, squared, plus, 2, right parenthesis, equals
Answers
The expansion of the polynomial (-p²+4p-3)(p²+2) would be is -p⁴ + 4p³ - 5p² + 8p - 6
Here we need to expand the polynomial (-p²+4p-3)(p²+2)
To do so we need to multiply each of the term with the first bracketby the each term of second bracket.
So, the expansion of the polynomial (-p²+4p-3)(p²+2) would be,
(-p² + 4p - 3)(p² + 2)
= [p² × (-p² + 4p - 3)] + [2 × (-p² + 4p - 3)]
= [p² × (-p²) + p² × 4p - p² × 3] + (-2p² + 8p - 6)
= (-p⁴ + 4p³ - 3p²) + (-2p² + 8p - 6)
= -p⁴ + 4p³ - (3 + 2)p² + 8p - 6 .......(add like terms)
= -p⁴ + 4p³ - 5p² + 8p - 6
Therefore, the required polynomial is -p⁴ + 4p³ - 5p² + 8p - 6
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what is the area under the sine curve from 0 to pi?
Answers
Work Shown:
[tex]\displaystyle \int \sin(x) dx = -\cos(x)+C\\\\\displaystyle \int f(x)dx = g(x)+C\\\\\displaystyle \int_{a}^{b} f(x)dx = g(b)-g(a)\\\\\displaystyle \int_{0}^{\pi} f(x)dx = g(\pi)-g(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)-(-\cos(0))\\\\[/tex]
[tex]\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)+\cos(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -(-1)+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 1+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 2\\\\[/tex]
The area is 2 square units. You can use WolframAlpha or GeoGebra to confirm.
What is the sum and the product of x^2-9x+8
Answers
Answer:
Step-by-step explanation:
This is a trinomial quadratic equation
x^2-9x+8
= x^2 -x-8x+8
= (x-1)(x-8)
The advantage of making a stem-and-leaf display instead of a dotplot is that a stem-and-leaf display
A. is for quantitative data, while a dotplot shows categorical data.
B. none of these
C. satisfies the area principle.
D. preserves the individual data values.
E. shows the shape of the distribution better than a dotplot.
Answers
A stem-and-leaf display is a graphical representation of quantitative data that preserves the individual data values, whereas a dotplot is a graphical representation of categorical or quantitative data that shows each data point as a dot.
In a stem-and-leaf display, the data values are grouped into stems and leaves, where the stem represents the larger digits of the data values and the leaves represent the smaller digits. This allows us to see the individual data values and their distribution.
Therefore, the advantage of making a stem-and-leaf display instead of a dotplot is that it preserves the individual data values, which can be useful when analyzing the data or looking for specific patterns in the data.
You have 8 donuts to share evenly between you and your four brothers.
Which fraction describes how many donuts each of you will receive?
Answers
perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll, what is the true proportion of all local residents who are perry como fans? estimate at the 95% confidence level.
Answers
Perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll.
By use the sample proportion to estimate the true proportion of all local residents who are Perry Como fans.
Let p be the true proportion of all local residents who are Perry Como fans. Then, the sample proportion is 0.56 and the sample size is n = 982.
We construct a 95% confidence interval for p by using the formula
Sample proportion ± z*standard error
Where z is the critical value from the standard normal distribution for a 95% confidence level, which is 1.96. The standard error is the estimated standard deviation of the sample proportion which is defined as
[tex]\sqrt{p*(1-p)/n} \\}[/tex]
By putting the values we get
Standard error = [tex]\sqrt{0.56*(1-0.56)/982)[/tex] = 0.018.
95% confidence interval = 0.56 ± 1.96*0.018 = (0.525, 0.595).
Hence, we can say with 95% confidence that the true proportion of all local residents who are Perry Como fans is between 0.525 and 0.595.
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I**PLEASE HELP ME **
DONT ANSWER IF YOU DONT KNOW THE ANSWER
A contractor is building a set of stairs out of concrete. Each stair is the same length, width, and height.
A) Which solid figures can the stairs be broken into? What are the dimensions of each solid figure?
B) How much concrete will be needed to form the stairs?
Answers
Corresponding to the data, we can deduce that the stairs can be broken into a series of blockish prisms.
Which solid numbers can the stairs be broken into? What are the confines of each solid figure?The stairs can be broken into a series of blockish prisms. The confines of each blockish prism would be the same range and height as the stairs, but the length of each blockish prism would be the depth of one step.
How important concrete will be demanded to form the stairs?To determine the quantum of concrete demanded to form the stairs, you would need to calculate the total volume of all the blockish prisms that make up the stairs. This can be done by multiplying the length, range, and height of each blockish prism and also adding the volumes of all the blockish prisms together.
The formula for calculating the volume of a blockish prism is V = l x w x h, where V is the volume, l is the length, w is the range, and h is the height. So, for illustration, if each stair is 3 bases wide,1.5 bases high, and 1 bottom deep, and there are 10 stairs, also the total volume of concrete demanded would be
V = (3 x 1.5 x 1) x 10 = 45 cubic feet of concrete.
Note that this calculation assumes that there is no space between the stairs or the rectangular prisms making up the stairs. If there is any space between the stairs or the rectangular prisms, this would need to be accounted for in the calculation.
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Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answers
The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. answer is option (a).
What is a histogram?In a histogram, which is a graphical depiction of the distribution of a set of continuous or discrete data, the height of a bar above the bin on the x-axis represents the frequency or count of the data falling within each bin. On the y-axis of the histogram, the frequency or count of the data points that fall into each bin is displayed.
The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. In a histogram, bars are used to illustrate the frequency distribution of a group of continuous or discrete data points.
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A Ray's pizza party each pizza was cut into 8 slices. There were 7 groups of children. Each group ate 2\frac{1}{2} pizzas. How many pizzas were eaten at the party in all?
Answers
18 pizzas were eaten at the party in total.
What is total number?The term "total number" refers to the complete count or sum of a set of numbers or objects. It is the result of adding up all the individual numbers or objects in a set to get a final value that represents the entire set.
According to question:If each pizza was cut into 8 slices, then 2 and 1/2 pizzas is equivalent to 20 slices of pizza because:
2\frac{1}{2} \times 8 = 20
Since there were 7 groups of children, the total number of slices of pizza eaten at the party is:
20 slices/pizza x 7 groups = 140 slices
To convert this to the number of pizzas eaten, we divide the total number of slices by the number of slices per pizza:
140 slices ÷ 8 slices/pizza = 17.5 pizzas
Therefore, 17.5 pizzas were eaten at the party in total. However, since a pizza cannot be divided into fractions, we should round up to the nearest whole number, giving us a final answer of 18 pizzas.
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Is the event independent or dependent? You toss a penny and you toss a
dime.
O dependent
O independent
Answers
Answer:
the event would be independent.
Step-by-step explanation:
because the penny and dime are two seperate variables
Find the quotient. Assume that no denominator has a value of 0.
(6x-24)÷x^2-16/6x
Answers
The quotient of the expression (6x-24)÷x^2-16/6x is 36x/(x + 4)
Finding the quotient of the expressionFrom the question, we have the following parameters that can be used in our computation:
(6x-24)÷x^2-16/6x
Assume that no denominator has a value of 0, we have
(6x-24)÷x^2-16/6x = 6(x - 4) ÷ (x - 4)(x + 4)/6x
Express as products
So, we have the following representation
(6x-24)÷x^2-16/6x = 6(x - 4) * 6x/(x - 4)(x + 4)
When the factors are evaluated, we have
(6x-24)÷x^2-16/6x = 36x/(x + 4)
Hence, the solution is 36x/(x + 4)
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Need help ASAP!!!
Jordyn likes to practice dancing while preparing for a math tournament. She spends 60 minutes every day practicing dance and math. To help her concentrate better, she dances for 20 minutes longer than she works on math.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Jordyn practices math every day (x) and the number of minutes she dances every day (y). (5 points)
Part B: How much time does Jordyn spend practicing math every day? Show your work. (3 points)
Part C: Is it possible for Jordyn to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning. (2 points)
Answers
Answer:
A: x +y = 60; y = x +20
B: 20 minutes on math
C: no
Step-by-step explanation:
You have some relations and some questions about dance times and math practice times with dance times longer than math practice by 20 minutes.
A. EquationsThe given relations can be written as two equations:
x + y = 60 . . . . . total time is 60 minutes
y = x + 20 . . . . . dance time is 20 minutes longer than math time
B. SolutionWe want the value of x. We can find that by using the second equation to substitute for y in the first equation:
x + (x +20) = 60
2x = 40 . . . . . . . . . subtract 20
x = 20 . . . . . . . . divide by 2
Jordyn practices math 20 minutes every day.
C. More practiceIf Jordyn dances for 60 minutes, then she will practice math for 60 -20 = 40 minutes. That brings her total practice time to 60 +40 = 100, which is more than 80.
It is not possible to spend 80 minutes total if she spends 60 minutes dancing.
(She could spend 50 minutes dancing, 30 minutes on math, and have a total practice time of 80 minutes.)
Jordyn spends 20 minutes each day practicing math. However, if her total practice time is 80 minutes, it would not be possible for her to spend 60 minutes practicing dance.
Explanation:The total time Jordyn spends practicing both dancing and math is 60 minutes. If we establish the time she spends on math as 'x' and the time she spends dancing as 'y', we can establish the following and equations:
y = x + 20: This equation represents the fact that Jordyn dances 20 minutes longer than she works on math. x + y = 60: This equation represents the total time Jordyn spends on dancing and math combined.To solve for 'x', substitute the first equation into the second to get x + (x + 20) = 60. Simplify to get 2x + 20 = 60. Subtract 20 from each side to get 2x = 40, and finally divide by 2 to get x = 20. Therefore Jordyn spends 20 minutes practicing math each day.
To answer Part C, if Jordyn practices for a total of exactly 80 minutes and dances 20 minutes longer than she does math, it would not be possible for her to spend 60 minutes practicing dance. The most amount of time she could spend dancing is 50 minutes (80 total minutes- 30 minutes for math).
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Choose all of the two-dimensional shapes that result from a vertical, horizontal, or angled cross section of a cone.
A- Rectangle
B- Triangle
C- Circle
D- Parabola
E- Ellipse
Answers
The cross section across a conic section would produce:
Triangle, Circle and Parabola
What are the properties of conic sections?Looking at the given options, we can say that ellipse, circle and parabola are all conic sections and as such they are possible figures that can be made if we intersect a plane and a cone.
However, rectangle is not a conic section.
A cylinder which could have a rectangular cross section if the plane is perpendicular to the base or A tetrahedron could have a square cross section, which is a special case of a rectangle.
In forming a conic section , we could also form an ellipse.
Now, when we cut a cross section across a cone, we can get a circle, triangle or parabola
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Chester has 49 CDs. Tony has 1/7 as many as Chester. How many CDs does Tony have?
Answers
Answer:7
Step-by-step explanation: you divide 49 by 7 which gives you 7
Answer:
7
Step-by-step explanation:
1/7 of 49 would be equal to divided 49 by 7 to find 1 seventh of 49
49/7 = 7
so 1/7 of Chesters 49 CDS is equal to 7 CDS that Tony has.
hope this helps :)
Read the screenshot please answer this ASAP!!!!!!!! PLEASEEEEE
Answers
According to the information, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.
How to calculate the surface area and volume of this prism?Since the hexagonal bases are regular, we know that all the six triangles are congruent to each other.
Let's call the side length of the hexagon s. Then, the apothem of each triangular face is given as 9 inches, and the base of each triangular face is given as 10 inches. Using the Pythagorean theorem, we can calculate the side length of the hexagon as follows:
s^2 = (10/2)^2 + 9^2
s^2 = 25 + 81
s^2 = 106
s ≈ 10.2956 inches
The surface area of the prism can be calculated by adding up the areas of its faces. The hexagonal base has an area of:
A_base = (3√3/2) * s^2 ≈ 450.978 square inches
The area of each triangular face is:
A_tri = (1/2) * base * height = (1/2) * 10 * 9 = 45 square inches
So the total surface area of the prism is:
A_total = 2A_base + 6A_tri
A_total = 2(450.978) + 6(45)
A_total ≈ 777.868 square inches
The volume of the prism can be calculated by multiplying the area of the base by the height of the prism:
V = A_base * height
V = 450.978 * 7
V ≈ 3156.846 cubic inches
Therefore, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.
Note: This question is incomplete. Here is the complete information:
Calculate the surface area and volume of this prism.
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Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.
Please show steps and thank you in advance!
Answers
The value of cos (2tetha) is 161/289
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Therefore if tan(tetha) = -8/15, therefore opposite is 8 and adj is 15
hyp = √8²+15²
= √ 64+225
= √ 289
= 17
therefore cos (tetha) = 8/17 and since theta is in second quadrant, cos tetha will be negative
cos (tetha) = -15/17
cos²(tetha) = 225/289
sin(tetha) = 8/17
sin²(tetha) = 64/289
cos(2tetha) = cos²(tetha) -sin²(tetha)
= 225/289 - 64/289
= 161/289
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Matt is painting the trim in his living room. He leans a ladder against the wall so that it forms an angle
elevation with the floor of 56°. If it is a 12-foot ladder, how high up on the wall does it reach? Round to
the nearest tenth.
Answers
Answer:
9.9 inches
Step-by-step explanation:
Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.
Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)
Therefore, we can now set up our equation and solve. (x is the height of the wall)
sin 56 = [tex]\frac{x}{12}[/tex] Initial equation
12 sin 56 = x Multiply each side by 12 so that we get x by itself.
x ≈ 9.9 Punch 12 sin 56 into a calculator and your done!
Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)
(-4,-6) and (8,9). Slope
Answers
slope= y2 - y1/ x2 - x1 ( take (-4, -6) as 1 and (8,9) as 2 where 9 and -6 are y2 and y1 respectively and 8 and -4 as x2 and x1 respectively)
- slope = 9 - (-6) / 8 - (-4)= 9 + 6/ 8 + 4
- slope = 15 / 12 (simplify)
- slope = 5/ 4
A teacher poses this problem: I am thinking of four numbers, a, b, c, and d, where a 0, b 0, c 0, and d 0 What else do you need to know to plot the four numbers in the correct order on a number line? What two questions should you ask? Explain how the answers would help you plot the numbers on a number line
Answers
The two questions should you ask are:
What is the smallest number among the values (a, b, c, and d)What is the largest number among the values (a, b, c, and d)Why ask the question above?The given answers to the above questions, one can be able to know the ranges of values that the four numbers have, as well as their relative positions.
In the event that we know the smallest and biggest numbers, we can be ready to mark those points on the number line and after that put the other two numbers in between them agreeing to their relative positions.
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There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest angle.
The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.
The measure of the largest angle is twice the smallest angle plus 10 degrees.
The sum of the angles of a triangle can be written as x + y + z = 180.
What are the other equations that represent this system of equations?
Select each correct answer.
a.) x=2y+10
b.) x=2z+10
c.) x=40-2(y+z)
d.) x=2z+y-40
e.) 2(y+z)-40
Answers
An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.
From the given information, we have the following equations:
[tex]x = 2(y+z) - 40[/tex] (the largest angle is 40 degrees less than twice the sum of the other two angles)
[tex]x = 2z + 10[/tex] (the largest angle is twice the smallest angle plus 10 degrees)
[tex]x + y + z = 180[/tex] (the sum of the angles of a triangle is 180 degrees)
To simplify the system of equations, we can use the second equation to substitute for x in the first equation:
[tex]2z + 10 = 2(y+z) - 40[/tex]
Simplifying this equation, we get:
[tex]y = z + 25[/tex]
Now we can substitute x and y in terms of z into the third equation:
[tex]x + (z+25) + z = 180[/tex]
Simplifying this equation, we get:
[tex]x + 2z = 155[/tex]
Finally, we can substitute x in terms of z from the first equation into this last equation:
[tex]2(y+z) - 40 + 2z = 155[/tex]
Simplifying this equation, we get:
[tex]y + 3z = 97[/tex]
Therefore, the equations that represent this system are:
[tex]x = 2(y+z) - 40\\y = z + 25\\x + 2z = 155\\y + 3z = 97[/tex]
So the correct answers are:
[tex]a.) x=2y+10\\d.) x=2z+y-40\\e.) 2(y+z)-40[/tex]
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The equations that represent this system are:
a.) x=2y+10
d.) x=2z+y-40
e.) 2(y+z)-40
What is angles ?
An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.
From the given information, we have the following equations:
=> x=2(y+z)-40 (the largest angle is 40 degrees less than twice the sum of the other two angles)
=> x=2z+10 (the largest angle is twice the smallest angle plus 10 degrees)
=> x+y+z=180 (the sum of the angles of a triangle is 180 degrees)
To simplify the system of equations, we can use the second equation to substitute for x in the first equation:
=> 2z+10=2(y+z)-40
Simplifying this equation, we get:
y=z+45
Now we can substitute x and y in terms of z into the third equation:
x+z+25+z=180
Simplifying this equation, we get:
=> x+2z=155
Finally, we can substitute x in terms of z from the first equation into this last equation:
2(y+z)-40+2z=155
Simplifying this equation, we get:
y+3z=97
Therefore, the equations that represent this system are:
a.) x=2y+10
d.) x=2z+y-40
e.) 2(y+z)-40
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Which of the following is not an equation?
Answers
Answer:
Option (3)
Step-by-step explanation:
Option (3) is not an equation. It is an expression. An equation is a mathematical statement where two expressions are equal to each other connected by an equal sign. In option (1), 3+1 is equal to 4+0 so it is an equation. In option (2), x2-2x is equal to 8, so it is also an equation. In option (4), 1+3 is equal to 6, so it is an equation, though it is not a true statement. However, in option (3), there is no equal sign, so it is not an equation. It is an expression that simplifies to 8x+2.