Edge lengths are given in units. Find the surface area of each prism in square units.
Answers
the area of given figure made from two part Parallelogram and Triangle is 288sq cm
what is Parallelogram and Triangle?A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal in measure. Parallelograms can have various orientations, but their opposite sides will always be parallel.
A triangle, on the other hand, is a three-sided shape with three angles and three vertices. The sum of the angles in a triangle is always 180 degrees. Triangles can come in various shapes and sizes, such as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), and scalene (all sides and angles are different).
According to given informationgiven that
1st part:
Base=6cm
height=8cm
Area=1×Base×Height/2
Area=(1×6×8)cm²/2
Area=24cm²
it have two part so, Area=2×24=48sq cm
2nd part:
if we assume Parallelogram
Area=Base×Height
Area=15cm×8cm
Area=120 sq unit
it have two part so,2×120sq cm
240sq unit
total area of given figure is 48 sq cm+240sq cm=288 sq unit.
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Related Questions
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.)
Explain how to plot the point (3, -7) on the coordinate plane.
Answers
Answer:
Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).
Solids $A$ and $B$ are similar. Use the given information and scale factor $k$ from solid $A$ to solid $B$ to find the volume of solid $B$ to the nearest thousandth. Cylinder $A$ has a volume of $112\pi$ cubic meters and $k=$ $\frac{1}{4}$. The volume of solid $B$ is about
cubic meters
Answers
The volume of solid B is about 7π cubic meters, which is approximately 21.99 cubic meters when rounded to the nearest thousandth.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since solids A and B are similar, they have the same shape, but different sizes.
Let V₁ be the volume of solid A, and V₂ be the volume of solid B. The scale factor k from solid A to solid B is 1/4, which means that the dimensions of solid B are 1/4 of the dimensions of solid A.
We can find the radius and height of solid B by multiplying the radius and height of solid A by 1/4. Therefore, we have:
V₂ = π(r/4)²(h/4) = (π/16)rh²
We are given that V₁ = 112π cubic meters, so we can solve for rh²:
112π = πr²h
rh² = 112
Substituting into the formula for V₂, we get:
V₂ = (π/16)rh² = (π/16)(112) = 7π
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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!
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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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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you can use whatever math engine just help
Answers
The calculated value of the logarithmic expression log(a⁵b⁵/c⁸) is 69
Evaluating the logarithmic expressionFrom the question, we have the following parameters that can be used in our computation:
log a = 9
log b = -8
log c = -6
The expression to calculate is given as
log(a⁵b⁵/c⁸)
When the expression is expanded using product and quotient rules, we have
log(a⁵b⁵/c⁸) = loga⁵ + logb⁵ - logc⁸
Apply the power rule of logarithm to rewrite as
log(a⁵b⁵/c⁸) = 5loga + 5logb - 8logc
Substitute the known values in the above equation, so, we have the following representation
log(a⁵b⁵/c⁸) = 5 * 9 + 5 * -8 - 8 * -8
Evaluate
log(a⁵b⁵/c⁸) = 69
Hence, the value of the logarithmic expression log(a⁵b⁵/c⁸) is 69
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A line passes through the points (−4, 50) and (5, −31). What is the equation of the line in slope-intercept form?
Answers
Answer:
y = - 9x + 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )
m = [tex]\frac{-31-50}{5-(-4)}[/tex] = [tex]\frac{-81}{5+4}[/tex] = [tex]\frac{-81}{9}[/tex] = - 9 , then
y = - 9x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (5, - 31 )
- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )
14 = c
y = - 9x + 14 ← equation of line
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
I don't get it... please help thanks in advance
Answers
Answer:
Set your calculator to degree mode.
[tex] \tan( \alpha ) = \frac{23}{35} [/tex]
[tex] \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31[/tex]
The angle of elevation of the sun is about 33°.
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
Question 1 (1 point)
Given parallelogram WXYZ, where WX = 2x + 15, XY = x + 27 and YZ = 4x - 21,
determine the length of ZW, in inches.
The length of ZW=
Answers
The length of ZW is 45 inches.
What is a parallelogram?A parallelogram is a member of quadrilateral which has a pair of opposite sides to be equal, and a pair of slant opposite sides.
In the given information, we have;
WX = YZ (a pair of opposite side of a parallelogram are equal)
2x + 15 = 4x - 21
collect like terms,
21 + 15 = 4x - 2x
36 = 2x
x = 36/2
x = 18
So that;
WX = 2x + 15
= 2(18) + 15
WX = 36 + 15
= 51
XY = x + 27
= 18 + 27
= 45
Therefore,
ZW = XY (a pair of opposite sides are equal)
ZW = 45
The length of ZW is 45 inches.
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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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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 park has a large circle painted in the middle of the playground area. The circle is divided into 4 equal sections, and each section is painted a different color. The radius of the circle is 10 meters.
What is the area A of each section of the circle?
Answers
The area A of each of the section of the circle would be =78.5m²
How to calculate the area of each section of the circle given?To calculate the area of each section of the circle given, the formula for the area of circle is used which is given as follows;
Area of circle = πr²
Where;
π = 3.14
r = 10m
area = 3.14× 10×10
= 314m
But the circle is divided into 4 sections. Therefore, the area of a section = 314/4 = 78.5m²
Therefore, the area of each sector of the circle after being divided into four would be= 78.5m².
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bruce has a pet worm that fell into a well. the well is 26 feet deep. each day, the worm climbs up 8 feet, but each night, it slides back down 2 feet. how many days will it take for bruce’s worm to get to the top of the well
Answers
However, since the worm cannot complete a fraction of a day, we need to round up to the next whole day. So, it will take the worm 5 days to climb out of the well.
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 :)
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).
What is the value of line 1 and2 in y=mx+b form?Help please!!!
Answers
1. The equation of the line in graph 1 in slope-intercept form is
y = (2/3)x + 2/3.
2. The equation of the line in graph 2 is
y = (1/3)x + 4/3.
How to find the equation of the linea. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.
slope = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3
The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:
y - y1 = m(x - x1)
y - 4 = (2/3)(x - 3)
y = (2/3)x + 2/3
b. points obtained from the graph (-3, 1) and (-6, 0)
slope = (y2 - y1) / (x2 - x1)
slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3
y - y1 = m(x - x1)
y - 1 = (1/3)(x - (-3))
y = (1/3)x + 4/3
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Diners choose one salad and one main from the options given in the table.
Vegan dishes are indicated with a (V).
Salad
Main
Fish and chips
Mozzarella salad (V) Cheese pizza (V)
Chicken salad Lamb chops
Tuna salad
Aubergine curry (V)
a) Work out the fraction of all the meal combinations which have at least
one vegan option.
b) Diners also choose one of 7 desserts options.
How many different three-course meal combinations are available?
O
[3]
[2]
Answers
a) The fraction of all the meal combinations which have at least one vegan option is 1/8.
b) There are 168 different three-course meal combinations available.
What is a fraction?A fraction is a way of representing a part or a ratio of a whole, using a numerator and a denominator separated by a slash ("/") or a horizontal line. The numerator represents the number of parts being considered, and the denominator represents the total number of equal parts that make up the whole.
According to the given information:
a) To work out the fraction of all the meal combinations which have at least one vegan option, we need to count the total number of meal combinations with at least one vegan option, and then divide it by the total number of meal combinations.
The vegan options in the table are:
Mozzarella salad (V)
Cheese pizza (V)
Aubergine curry (V)
There are a total of 4 salads (including the vegan salads) and 6 mains (including the vegan mains). So the total number of meal combinations without any restriction is 4 x 6 = 24.
Now, we can calculate the total number of meal combinations without any vegan option, which is 24 - 3 = 21 (since 3 options are vegan).
So, the fraction of all the meal combinations which have at least one vegan option is (total meal combinations - meal combinations without any vegan option) divided by total meal combinations:
= (24 - 21) / 24
= 3 / 24
= 1 / 8
Therefore, the fraction of all the meal combinations which have at least one vegan option is 1/8.
b) If diners also choose one of 7 dessert options, we can simply multiply the total number of meal combinations (24) by the number of dessert options (7) to get the total number of three-course meal combinations available:
24 x 7 = 168
So, there are 168 different three-course meal combinations available.
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select all the values that are solutions to x < -4
Answers
Any value of x that is less than -4 is a solution to the inequality x < -4.
Selecting the values that are solutions to x < -4Any value of x that is less than -4 is a solution to the inequality x < -4.
Some examples of such values are:
x = -5
x = -10
x = -100
In fact, any value that is to the left of -4 on the number line is a solution to the inequality x < -4. On a number line, we represent this inequality by shading everything to the left of -4.
To understand this visually, imagine a number line with -4 as the reference point.
All the values to the left of -4 will be negative, and all the values to the right of -4 will be positive.
So, the inequality x < -4 means that x can be any value to the left of -4 on the number line.
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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.
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.
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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Suppose the ages of cars driven by employees at a company are normally distributed with a mean of 8 years and a standard deviation of 3.2 years.
What is the z-score of a car that is 6 years old?
Responses
−1.6
negative 1.6
−0.625
negative 0.625
0.625
0.625
1.6
Answers
The z-score of a car that is 6 years old is -0.625.
To find the z-score of a car that is 6 years old, we can use the formula:
z = (x - μ) / σ
where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).
Plugging in the values, we get:
z = (6 - 8) / 3.2 = -0.625
Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.
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in this experiment, you are asked to repeat the time measurements for each height a few times. why do we want to repeat these measurements? to reduce the statistical errors to reduce the systematic errors
Answers
In this experiment, we want to repeat the time measurements for each height a few times.
By repeating the measurements, we can reduce the statistical errors associated with random fluctuations in the measurement process. These fluctuations can be caused by factors such as variations in the environmental conditions or in the way the measurements are taken. By taking multiple measurements and calculating the average, we can reduce the impact of these random errors.
By reducing statistical errors, repeating the measurements can also help to reduce systematic errors, which are caused by consistent biases or inaccuracies in the measurement process. By taking multiple measurements and analyzing their differences, we can identify and correct for any systematic errors.
Hence, repeating the time measurements for each height a few times helps to increase the accuracy of the results by reducing both statistical and systematic errors.
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HELP ME PLEASE!!!!! I NEED IT
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Based on the information we can infer that the area of the figure is 464 ² units.
How to calculate the area of this figure?To calculate the area of this figure we must assume that it is a complete square and find its area as shown below:
basis = 24side = 2424 * 24 =576 units ²Now we must find the area of the non-grid regions and subtract them from the area we found previously:
4 * 12 = 48 units ²8 * 8 = 64 units ²64 + 48 = 112 units ²576 - 112 = 464 units ²
According to the above, the area of the figure is 464 units ²
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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!
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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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Find the quotient. Assume that no denominator has a value of 0.
(6x-24)÷x^2-16/6x
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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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Use point-slope form to write the equation of a line that passes through the point (16,−14) with slope 1.
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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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