Answer:
Angle 1 = 51.6°
Angle 2 = 38.4°
Step-by-step explanation:
All complimentary angles add up to 90°.
If two complimentary angles were congruent then their measures would both be 45°.
Since one angle's measure is 6.6° more than the other's measure, it's measure is 6.6° more than 45°
Vice versa for the second angle, its measure will be 6.6° less than 45°
Write a numerical pattern that represents the rule y=x+0 starting with x=0
The pattern represents a straight line that passes through the origin with a slope of 1.
What are linear equations in two variables?The form Ax + By + C = 0 is a two-variable linear equation, where A and B are the coefficients, C is a constant term, and x and y are the two variables, with each having a degree of 1.
The numerical pattern that represents the rule y = x + 0, starting with x = 0, is:
x y
0 0
1 1
2 2
3 3
4 4
... ...
This example shows that when x increments by 1, y additionally increments by 1. Since the rule for y is y = x + 0, we can see that adding 0 to x doesn't change its value, so y is just the same as x. As a result, x and y have a linear relationship with a slope of 1 and a y-intercept of 0.
To put it another way, the pattern is a straight line with a slope of one that runs through the origin.
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Riley is saving up to buy a new television. She needs a total of $1,290.78. Riley has saved $200.73 already and earns $83.85 pe
week at her job. How many weeks does Riley need to work to save enough money to buy the new television? PLEASE HELP ASAP EXTRA POINTS!!
Considering the definition of an equation and the way to solve it, the correct answer is option C: Riley need to work 13 weeks to save enough money to buy the new television.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Weeks that Riley need to workBeing "x" the number of weeks Riley need to work, and knowing that:
The total amount that Riley requires = $1,290.78The amount of savings Riley already has = $200.73Riley's earnings per week = $83.85the equation in this case is:
200.73 + 83.85x= 1290.78
Solving:
83.85x= 1290.78 - 200.73
83.85x= 1090.05
x= 1090.05 ÷ 83.85
x=13
Finally, Riley need to work 13 weeks.
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determina el volumen cuyo diametro es de 8 y su altura de 15 cm
Answer:
3016 centímetros cúbicos.
Step-by-step explanation:
El radio del cilindro es de 8 cm y la altura es de 15 cm. Sustituya 8 por r y 15 por h en la fórmula . Simplifique. Por lo tanto, el volumen del cilindro es de alrededor de 3016 centímetros cúbicos.
A restaurant raises the price of its signature dish by 15%
The new price of the dish is 14.50
What was the original price of the dish?
Answer:
Therefore, the original price of the dish was $12.61.
Step-by-step explanation:
Let the original price of the dish be "x".
After raising the price by 15%, the new price becomes:
x + 0.15x = 1.15x
We know that the new price is $14.50, so we can set up the equation:
1.15x = 14.5
To solve for x, we can divide both sides by 1.15:
x = 14.5 / 1.15
x = 12.61 (rounded to two decimal places)
Please HELPP IM IN URGE
I'll Give BRAINLIEST
The measure of arc angle QT is determined as 142 ⁰.
The measure of m∠STR is determined as 23⁰.
What is the measure of arc angle QT?The measure of angle subtended by the arc QT is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
The measure of m∠STR is calculated as;
m∠STR = ¹/₂( arc SR )
m∠STR = ¹/₂ x 46⁰
m∠STR = 23⁰
The measure of arc QT is calculated as;
m∠QST = ¹/₂( arc QT )
arc QT = 2 (m∠QST)
arc QT = 2 x 71⁰
arc QT = 142⁰
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PLS HELP ME!!!!!
The line plot has ______ dots plotted on it.
Answer:
Step-by-step explanation:
Okay but seriously though, you would have to write the whole question down.
Un deportista se ejercita y recorre 350 metros, retrocede 125 metros avanza 80 metros. Si el punto de partida es su casa a que distancia de la misma se encuentra
The sportsman has a final distance with respect to his home equal to 305 meters.
How to determine the distance of a sportsman with respect to a home
In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:
X = ∑ xₙ, for n = {1, 2, 3, ..., N}
Where the sportsman goes far away for his home for x > 0, in meters.
Now we proceed to determine the final distance:
X = + 350 m - 125 m + 80 m
X = + 305 m
The final distance of the sportsman with respect to his home is 305 meters.
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A 20 litre solution is 85% paint and 15% thinner. Five litres of thinner is added to this solution.
What percentage of the new solution is PAINT?
Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%
Step-by-step explanation:
help me quick and right answers only. algebra
The function that has a range of all real numbers is given as follows:
f(x) = -x + 2.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.Hence the range for each function in the context of this problem is given as follows:
f(x) = -x + 2 -> all real values.f(x) = -x²: y ≤ 0.f(x) = 2^x + 1: y ≥ 1.More can be learned about domain and range at brainly.com/question/26098895
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If you have a piece of round cake that has an area of 100 square inches, and you know the piece sweeps out an angle of 50, find the radius of the cake.
If piece of cake has area of 100 in² and sweeps angle of 50°, then the radius of the cake is 15.13 inches.
The area of the piece of cake is given as 100 square inches and
The piece of cake sweeps out an angle of 50 degrees, we have to find the radius of the cake;
We know that "Area" of a sector of a circle is given as : A = (θ/360)πr²,
where A = area of the sector, θ is = angle swept by sector, and r is radius of circle,
We know that area of "piece-of-cake" is = 100 square inches and
The "angle-swept' by the piece is = 50 degrees.
Substituting the values in area of sector formula,
We get,
⇒ 100 = (50/360)πr²,
⇒ r² = (100 × 360)/(50π)
⇒ r ≈ 15.13,
Therefore, the radius of the cake is approximately 15.13 inches.
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There are spiders and dogs in Veronica's backyard. Veronica sees 240 legs in total. The total number of animals (spiders and dogs) is 3 times the amount of spiders. How many spiders are in the backyard?
There are 15 spiders in the backyard. The correct option is D
To solve this problemLet's begin by resolving the issue using algebra. Let's use "s" for the quantity of spiders and "d" for the quantity of dogs in the backyard.
As a result of the difficulty, we know that there are 3 times as many animals as there are spiders.
s + d = 3s
Simplifying this equation, we get:
d = 2s
We also know that there are 240 legs in the backyard, with each dog having 4 legs and each spider having 8. Thus, we can create the following equation:
8s + 4d = 240
Substituting d = 2s, we get:
8s + 4(2s) = 240
Simplifying and solving for s, we get:
16s = 240
s = 15
Therefore, there are 15 spiders in the backyard.
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which diagram represents the expression |-5|
A diagram that represents the expression |-5| include the following: A. graph A.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Since the absolute value of -5 or |-5|, an inequality that matches this graph is represented by the first diagram.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
34. What are the coordinates of the information
center? Explain.
Generally, coordinates are a way of specifying the position of something in space, usually using a system of latitude and longitude or x, y, and z axes.
What informs the coordinates of an information center?The coordinates of a physical location that serves as a hub for information, such as a data center or a library, then the answer will depend on the specific location you have in mind. To find the coordinates of such a place, you would need to use a mapping tool or geographic information system (GIS) to locate the facility and determine its latitude and longitude.
On the other hand, if you're asking about the "coordinates" of information in a more abstract sense, then this could refer to the ways in which information is organized or classified.
For example, a database might use a system of fields and tables to arrange information in a structured way, while a search engine might use algorithms to determine the relevance and ranking of different pieces of information based on factors like keywords, backlinks, and user behavior.
In conclusion, the coordinates of an information center is dependent on its nature in terms of its structural formation and the set goals to be accomplished by determining such coordinates.
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Please help if you can calculate it!
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
How to construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change.(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.
(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:
Sampling error = z*(standard deviation/square root of sample size)
Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.
Substituting the values, we get:
Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%
Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.
(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:
Confidence interval = point estimate ± (z*standard error)
Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.
Substituting the values, we get:
Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)
Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.
(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:
New sample mean = 0.96 * 550 = 528
The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.
To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:
Confidence interval = sample mean ± (t*standard error)
Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.
The standard error can be calculated as follows:
Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31
Substituting the values, we get:
Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)
Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
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Question 3: 13 of the 20 students in Mr Davidson's class are girls. Two students are chosen at random. 2nd student (a) Copy and complete the tree diagram (b) Work out the probability of two boys being selected. (c) Work out the probability of two girls being selected. CORBETTMATHS 2018 1st student boy girl boy girl boy girl outcome BB BG GB GG probability
Answer:
answer int he photos
Step-by-step explanation:
Answer:
This is a product rule and probablity question. b) 49/400
c) 169/400
Step-by-step explanation:
the amount of money an hourly employee makes, m for working h hours can be represented by the equation m = 12.80h . what is the constant of propportionality of the equation?
The constant of proportionality of the equation would be = 12.80.
What is constant of proportionality of an equation?The constant of proportionality of an equation is the figure that represents the ratio that exists between two different variables that has direct proportional relationship.
The amount of money made by an employee is directly proportional to the number of hours they worked.
That is m directly proportional to h
The equation = m = k h. where k = 12.80 = constant of proportionality.
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what is the surface area if the radius is 8 units and a height of 5 units
The total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.
What is surface area?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area. A three-dimensional shape with height, breadth, and depth is referred to as having three dimensions, and surface area is a measurement of the total area that the surface of that shape occupies. In other terms, the surface area is the sum of the areas of all an object's sides.
Here, we have
Given:
Radius of cylinder = 8 units
Height of cylinder = 5 units
Thus:
Total Surface Area of a cylinder = 2 × 3.14 × 8 (8 + 5)
Total Surface Area of a cylinder = 50.24(13) = 653.12 sq. units.
Hence, the total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.
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Which list shows all the factors of 48?
Answer:
Step-by-step explanation:
1,2,3,4,6,8,12,16,24,48
hope i helped
help me pls I’ll give brainliest
The equation is expanding Pascal's triangle and the Binomial theorem
(x + 0.5)³ = x³/8 + 3x²/4 + 3x/2 + 1/8
(s + 4t)⁶ = s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶
(3a - 3b)⁴ = 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴
(3m - 2n)⁵ = 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵
(a-4)⁵ = a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024
What is the binomial theorem formula?The binomial theorem formula for any positive integer n.
(x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn x.
11) Using the Binomial Theorem, we have:
(x + 0.5)³ = C(3,0) x³(0.5)⁰ + C(3,1) x²(0.5)¹ + C(3,2) x¹(0.5)² + C(3,3) x⁰(0.5)³
= x³/2³ + 3x²/2² + 3x/2 + 1/2³
= x³/8 + 3x²/4 + 3x/2 + 1/8
12) Using Pascal's Triangle, we have:
(s + 4t)⁶ = C(6,0) s⁶(4t)⁰ + C(6,1) s⁵(4t)¹ + C(6,2) s⁴(4t)² + C(6,3) s³(4t)³ + C(6,4) s²(4t)⁴ + C(6,5) s(4t)⁵ + C(6,6) (4t)⁶
= s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶
13) Using Pascal's Triangle, we have:
(3a - 3b)⁴ = C(4,0) (3a)⁴(-3b)⁰ + C(4,1) (3a)³(-3b)¹ + C(4,2) (3a)²(-3b)² + C(4,3) (3a)(-3b)³ + C(4,4) (-3b)⁴
= 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴
14)Using Pascal's Triangle, we have:
(3m - 2n)⁵ = C(5,0) (3m)⁵(-2n)⁰ + C(5,1) (3m)⁴(-2n)¹ + C(5,2) (3m)³(-2n)² + C(5,3) (3m)²(-2n)³ + C(5,4) (3m)(-2n)⁴ + C(5,5) (-2n)⁵
= 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵
15) Using Pascal's Triangle, we have:
(a-4)⁵ = C(5,0) a⁵(-4)⁰ + C(5,1) a⁴(-4)¹ + C(5,2) a³(-4)² + C(5,3) a²(-4)³ + C(5,4) a(-4)⁴ + C(5,5) (-4)⁵
= a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024
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The equation is expanding Pascal's triangle and the Binomial theorem ,
[tex](x + 0.5)^3= x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]
[tex](s + 4t)^6 = s^6+ 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4+ 6s(4t)^5 + 4t^6[/tex]
[tex](3a - 3b)^4 = 81a^4 - 324a^3b + 486a^2b^2- 324ab^3 + 81b^4[/tex]
[tex](3m - 2n)^5 = 243m^5 - 810m^4n + 1080m^3n^2- 720m^2n^3 + 240mn^4- 32n^5[/tex]
[tex](a-4)^5= a^5 - 20a^4 + 160a^3 - 640a^2+ 1280a - 1024[/tex]
What is the binomial theorem formula?
The binomial theorem formula for any positive integer n.
[tex](x + y)^n = nC_0 x^n + nC_1x^{n-1} y+ nC_2 x^{n-2} y_2 + … + nC_{n-1} x y^{n-1} + nC_n x.[/tex]
11) Using the Binomial Theorem, we have:
[tex](x + 0.5)^3 = C(3,0) x^3(0.5)^0 + C(3,1) x^2(0.5)^1 + C(3,2) x^1(0.5)^2 + C(3,3) x^0(0.5)^3[/tex]
=[tex]x^3/2^3 + 3x^2/2^2 + 3x/2 + 1/2^3[/tex]
= [tex]x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]
12) Using Pascal's Triangle, we have:
[tex](s + 4t)^6 = C(6,0) s^6(4t)^0+ C(6,1) s^5(4t)^1+ C(6,2) s^4(4t)^2 + C(6,3) s^3(4t)^3 + C(6,4) s^2(4t)^4+ C(6,5) s(4t)^5 + C(6,6) (4t)^6[/tex]
= [tex]s^6 + 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4 + 6s(4t)^5 + 4t^6[/tex]
13) Using Pascal's Triangle, we have:
[tex](3a - 3b)^4 = C(4,0) (3a)^4(-3b)^0 + C(4,1) (3a)^3(-3b)^1 + C(4,2) (3a)^2(-3b)^2 + C(4,3) (3a)(-3b)^3 + C(4,4) (-3b)^4[/tex]
= [tex]81a^4 - 324a^3b + 486a^2b^2 - 324ab^3 + 81b^4[/tex]
14)Using Pascal's Triangle, we have:
[tex](3m - 2n)^5= C(5,0) (3m)^5(-2n)^0 + C(5,1) (3m)^4(-2n)^1 + C(5,2) (3m)^3(-2n)^2+ C(5,3) (3m)^2(-2n)^3 + C(5,4) (3m)(-2n)^4 + C(5,5) (-2n)^5[/tex]
= [tex]243m^5- 810m^4n + 1080m^3n^2 - 720m^2n^3 + 240mn^4 - 32n^5[/tex]
15) Using Pascal's Triangle, we have:
[tex](a-4)^5= C(5,0) a^5(-4)^0+ C(5,1) a^4(-4)^1 + C(5,2) a^3(-4)^2 + C(5,3) a^2(-4)^3 +C(5,4) a(-4)^4 + C(5,5) (-4)^5[/tex]
= [tex]a^5 - 20a^4 + 160a^3 - 640a^2 + 1280a - 1024[/tex]
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A number cube with the numbers 1 through 6 is rolled. What is the probability of the number cube showing a 3 or an odd number?
You need a 60% alcohol solution. On hand, you have a 130 mL of a 55% alcohol mixture. You also
have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired
solution?
Therefore , the solution of the given problem of unitary method comes out to be 70% alcohol combination with 130 mL of the 55% alcohol mixture.
What is a unitary method?Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.
Here,
Let x represent the required amount (in mL) of the 70% alcohol mixture.
The total amount of alcohol in the final mixture would be equal to the desired 60% alcohol solution since it would be the sum of the alcohol in the 55% alcohol mixture and the alcohol in the 70% alcohol mixture.
=> 0.55 * 130 + 0.70 * x = 0.60 * (130 + x)
=> 71.5 + 0.70x = 78 + 0.60x
=> 0.10x = 6.5
=> x = 65
Therefore, to create a 60% alcohol solution, you would need to combine 65 mL of the 70% alcohol combination with 130 mL of the 55% alcohol mixture.
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Felix exercises by spending 12 minutes warming up and then running for 20 minut
He has exercised a total of 240 minutes this month.
Felix has spent a total time of 11.4 hours (or 684 minutes) running this month.
HOW CAN WE CALCULATE TOTAL TIME?we can calculate the total time Felix has spent running this month.
Given:
Warm-up time: 12 minutes
Running time: 20 minutes
Total exercise time in a month: 240 minutes
Step 1: Calculate the total time spent running
Let x be the total time spent running in minutes.
According to the given information, Felix spends 12 minutes on warm-up and 20 minutes on running.
So, the equation would be:
12 + 20x = 240
Step 2: Solve for x
Subtract 12 from both sides of the equation:
20x = 240 - 12
20x = 228
Divide both sides by 20:
x = 228 / 20
x = 11.4
So, Felix has spent a total of 11.4 hours (or 684 minutes) running this month.
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3x + 3 = 3y + 6
What is the value of x?
A : x=3y + 9
B : x= y + 1
C : x= y + 3
D : x= 3y + 3
The value of x in the expression is y + 3
How to calculate the value of x?The expression given is written as
3x + 3= 3y + 6
collect the like terms
3x - 3y= 6-3
3x - 3y= 3
3x= 3 + 3y
x= 3 + 3y/3
x= 3 + y
x= y + 3
Hence the value of x in the expression is y + 3
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2x^2-5x-3=0 what values of x make the equation true?
x=
x=
in buying ground beef for hamburgers, there are several packages from which to choose, as shown in the table below. If johannes needs 5 pounds of beef for his barbeque, what will he pay?
Johannes will need to pay $8.61 for 5 pounds of ground beef
What is the cost of the beef?Since Johannes needs 5 pounds of ground beef, and the available pounds are 1.5, 2, 3, and 3.75 pounds.
To reduce the cost, he need to select the package with the lowest cost per pound.
The cost per pound for each package is:
Package 1: $5.58 / 1.5
= $3.72 per pound
Package 2: $7.44 / 2
= $3.72 per pound
Package 3: $1.16 / 3
= $0.39 per pound
Package 4: $13.95 / 3.75
= $3.72 per pound
Therefore, the package with the lowest cost per pound is Package 3 and package 2 which will give us 5 pounds
So he can do it as:
$1.16 + $7.44
= $8.6
Or
(1 package of 3 pounds x $0.39 per pound) + (1 package of 2 pounds x $3.72 per pound)
= $1.17 + $7.44
= $8.61
Therefore, Johannes will need to pay $8.61 for 5 pounds of ground beef.
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equation of line perpendicular to y = -4x + 3 with point 8, 1
The equation of a line that is perpendicular to the line y = –4x + 3 and passes through the point (8, 1) is y = 1/4(x) - 1
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the equation of this line is perpendicular to the line y = –4x + 3, the slope is given by;
Slope, m = -4
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
Slope, m₂ = 1/4
At data point (8, 1) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 1/4(x - 8)
y = 1/4(x) - 1
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The value 3pi/4 is a solution for the equation 3√2 sec theta +7 = 1.
A. True
B. False
Answer:
False
Step-by-step explanation:
3√2 sec(theta) + 7 = 1
3√2 sec(theta) = -6
sec(theta) = -2/√2
sec(theta) = -√2
theta = arcsec(-√2)
However, the range of secant function is [-∞, -1] U [1, ∞]. Since -√2 is not within this range, we cannot take the arcsecant of -√2. Therefore, there is no real value of theta that satisfies the equation, including 3π/4.
Therefore, the statement "The value 3π/4 is a solution for the equation 3√2 sec(theta) + 7 = 1" is False.
I hope it helps you
Which ordered pair is not included in a graph of y= 2 x + 5
Mimi chose A (0,0) how did she get that answer? and is she correct.
The Diaz family is driving at a constant
speed on the highway so their distance
varies directly with their speed. They
traveled 17.5 miles in 15 minutes. How
far did they travel in 2 hours?
A 50 miles
B 70 miles
C 140 miles
D 262.5 miles
(17.5 times 15)
Answer:
To solve this problem, we can use the concept of direct variation, which states that two quantities vary directly with each other if they can be expressed as y = kx, where y is the dependent variable, x is the independent variable, and k is a constant of variation.
In this case, the distance traveled is the dependent variable and the speed is the independent variable. We are given that the distance traveled is 17.5 miles when the time (or speed) is 15 minutes.
So, we can set up the proportion:
distance / time = constant
17.5 miles / 15 minutes = k
Solving for k, we get:
k = 17.5 / 15
k = 1.16667 (rounded to 5 decimal places)
Now that we have the constant of variation k, we can use it to find the distance traveled in 2 hours (which is equivalent to 2 hours * 60 minutes/hour = 120 minutes).
distance = k * time
distance = 1.16667 * 120
distance = 139.99964 miles (rounded to 5 decimal places)
So, the correct answer is C) 140 miles, as it is the closest rounded value to the calculated distance of 139.99964 miles.
What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9
To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.
What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9?3/9 = 1/3, which is not a multiple of 1/9
4/9 cannot be simplified further and is therefore a multiple of 1/9
9/12 can be simplified to 3/4, which is not a multiple of 1/9
9/10 cannot be simplified further and is therefore a multiple of 1/9
2/9 cannot be simplified further and is therefore a multiple of 1/9
9/9 = 1, which is not a multiple of 1/9
Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.
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