set up an equation for your exterior angle, then use multi-step equation steps to solve for y.A. 15B. 17.4C. 5D. 10
Answers
In any triangle, the sum of the interior angles of two vertices is equal to the exterior angle of the other vertex.
Using this property, we can write the following equation:
[tex]\begin{gathered} \text{ABC+BAC=ACD}_{} \\ (4y+8)+(5y+3)=146 \\ 9y+11=146 \\ 9y=146-11 \\ 9y=135 \\ y=\frac{135}{9} \\ y=15 \end{gathered}[/tex]The value of y is equal to 15, therefore the correct option is A.
Related Questions
A. Step 1B. Step 2C. Priya did not make a mistake
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We will have the following:
[tex]\frac{f}{0.25}=16\Rightarrow f=16\cdot0.25[/tex][tex]\Rightarrow f=4[/tex]From this we can see that there was no mistaky on Priya's side. [Option 3]
katie has 5.455 apples and sadie has 10.31 how many apples do they have in all
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Katie has 5.455
Sadie has 10.31
To find how many apples they have in all add the two numbers
They have = 5.455 + 10.31
They have = 5.455 + 10.310
0 + 5 = 5
1+ 5 = 6
3 + 4 = 7
10 + 5 = 15
They have = 15.765 apples in all
You are going to paint your door on the outside. Your door is 7 feet 2 inches tall and 32inches wide. You need to know the surface area of the front of your door to determine howmuch paint to buy. The hardware store sells paint by how much covers a square foot. What isthe surface area you should report to the hardware store?
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Data
height = 7 ft 2 in
width = 32 in
1.- Convert height into inches
1 ft ------------ 12 in
7 ft ------------ x
x = 84 in
total height = 84 + 2
= 86 in
2.- Calculate the area
Area = height x width
Area = 84 x 32
Area = 2688 in 2
1 block: 11 houses = 2 blocks : ??? houses
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Determine the independent and dependent quantities in each scenario include when possible Part A: A lamp manufacturing company produces 750 lamps per shift Part B:a grocery store sells pears by the pound. A customer purchases 3 pounds by $5.07
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Here, we want to establish the independent and independent quantities in each of the parts
The independent quantities are simply the quantities that do not depend on the dependent quantity. The dependent quantity are the quantities that depend on the independent quantity
a) Here, we have 750 lamps produced per shift
This is obtained by dividing the number of lamps produced by the number of shifts it took to produce them
In this case, the number of lamps produced is dependent on the number of shifts'
Number of shifts is the independent variable while the number of lamps is the dependent variable
b) Here, the cost per pair is 5.07/3 = 1.69
So here, the cost is dependent on the number of pears
The number of pears is the independent variable while the cost of the pears is the dependent variable
Hi, can you help me answer this question please, thank you!
Answers
Given that
[tex]\begin{gathered} \mu_1=sample\text{ of soda in the coke can} \\ \mu_2=sample\text{ of soda in the pepsi can} \end{gathered}[/tex]Therefore, in the first statement, we are to test how accurate the companies package these cans.
Mathematically it can be expressed as,
[tex]H_0\colon\mu_1\leq\mu_2[/tex]In the second statement, we wish to test the claim that the mean of the amount of liquid in coke cans is greater than the amount of liquid in pepsi cans. This can be expressed mathematically as,
[tex]H_a\colon\mu_1>\mu_2[/tex]Hence, the correct option is Option 1.
Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.
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Step 1
Given;
Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.
Step 2
Find the slope of the new line based on a perpendicular relationship
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \end{gathered}[/tex][tex]\begin{gathered} 5y=2-2x \\ y=\frac{2-2x}{5} \\ y=\frac{2}{5}-\frac{2}{5}x \\ -\frac{2}{5}=-\frac{1}{m_2} \\ 2m_2=5 \\ m_2=\frac{5}{2} \end{gathered}[/tex]Thus the equation will be;
[tex]\begin{gathered} (\frac{1}{8},2) \\ y=\frac{5}{2}x+b \\ b=y-intercept \\ 2=\frac{5}{2}(\frac{1}{8})+b \\ 2=\frac{5}{16}+b \\ b=2-\frac{5}{16} \\ b=\frac{27}{16} \end{gathered}[/tex][tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]Answer;
[tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]The line M is parallel to the line y=-2x+2 and goes through the origin. Which of these points is on the line M? (-2,-4)(1,1)(2,-2)(-2,4)
Answers
Answer:
(-2,4)
Explanation:
Two lines are said to be parallel if their slopes are the same.
Comparing the line y =-2x+2 to the slope-intercept form y=mx+b, the slope of the line is -2.
Therefore, the slope of line M that is parallel to it is also - 2.
Since the line M goes through the origin, the y-intercept of line M is 0.
Therefore, the equation of line M is:
[tex]y=-2x[/tex]Therefore, the point which is on line M is the point that satisfies the equation above.
This point is (-2,4).
Check
[tex]\begin{gathered} \text{When }x=-2,y=4 \\ y=-2x \\ 4=-2(-2) \\ 4=4 \end{gathered}[/tex]True or false the function f(x) = -3(x+10)^2 has a minimum
Answers
Notice that:
[tex]\begin{gathered} f^{\prime}(x)=-6(x+10), \\ f^{\prime\prime}(x)=-6. \end{gathered}[/tex]Since for all x, f''(x)<0, by the second derivative criteria we get that f(x) reaches a maximum.
Answer: False.
How to do 2 step equations Can you solve 2x + 5=21?
Answers
Given
The equation,
[tex]2x+5=21[/tex]To find the value of x or to solve for x.
Explanation:
It is given that,
The equation is,
[tex]2x+5=21[/tex]That implies,
[tex]\begin{gathered} 2x+5=21 \\ 2x=21-5 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence, the value of x is 8.
A circle has area 36 cm². What is the diameter?
Answers
Answer:
6.77 cm
Explanation:
Given that the area of a circle = 36 cm²
We want to find the diameter of the circle.
The area of a circle of radius r is calculated using the formula:
[tex]A=\pi r^2[/tex]Substitute A=36 and π=3.14:
[tex]\begin{gathered} 36=3.14r^2 \\ \text{ Divide both sides by 3.14} \\ \frac{36}{3.14}=\frac{3.14r^2}{3.14} \\ r^2=\frac{36}{3.14} \\ \text{ Take the square root of both sides} \\ r=\sqrt{\frac{36}{3.14}} \\ r=3.3845 \end{gathered}[/tex]Finally, to get the diameter, multiply the radius by 2.
[tex]\begin{gathered} Diameter=Radius\times2 \\ =3.3845\times2 \\ =6.769 \\ Diameter\approx6.77\;cm \end{gathered}[/tex]The diameter of the circle is approximately 6.77 cm.
Solve the system of equations.y = x2 - 2y = -2x + 1A. (-3,7) and (-1,3)B. (-3,7) and (1, -1)C. (1.-1) and (3,-5)D. (-1,3) and (3, -5)
Answers
Answer
Option B is correct.
the solutions to the system of equations include
(-3, 7) and (1, -1)
Step-by-step Explanation
The question is to solve the system of equations
y = x² - 2 ..... equation 1
y = -2x + 1 ..... equation 2
To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.
y = x² - 2
y = -2x + 1
Since
y = y
x² - 2 = -2x + 1
x² + 2x - 2 - 1 = 0
x² + 2x - 3 = 0
This gives a quadratic equation which we will now solve
x² + 2x - 3 = 0
x² + 3x - x - 3 = 0
x (x + 3) - 1 (x + 3) = 0
(x - 1) (x + 3) = 0
So,
x - 1 = 0 or x + 3 = 0
x = 1 or x = -3
If x = 1,
y = x² - 2
= 1² - 2
= 1 - 2
= -1
x = 1, y = -1
If x = -3
y = x² - 2
= (-3)² - 2
= 9 - 2
= 7
x = -3, y = 7
So, the solutions to the system of equations include
x = -3, y = 7, that is, (-3, 7)
And
x = 1, y = -1, that is, (1, -1)
Hope this Helps!!!
The coordinates of the vertices of triangle RST are R(-2, -3), S(4,5), and T (8,2). List the angles of triangle RST in order from smallest to largest.
Answers
The first step is to plot the triangle RST with the given coordinates. The diagram of the triangle RST is shown below. We can see that the smallest angle is angle R, The larger angle is angle T while the largest angle is angle S
Listing the angles in order from smallest to largest., it becomes
angle R, angle T and angle S
Determine the probability of being dealt 4 Aecs of cards, from a deck of 52 playing cards, with a replacement.
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Given:
4 Aces of cards from a deck of 5 playing cards.
[tex]\begin{gathered} \text{Probability of drawing 4 Aces }=\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times4! \\ \text{Probability of drawing 4 Aces }=\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times24 \\ \text{Probability of drawing 4 Aces }=\frac{24}{28561} \end{gathered}[/tex]Solve for v. v + 4/5 = 1/3. Simplify your answer as much as possible.
Answers
Answer:
v = -7/15.
Explanation:
Given the equation:
[tex]v+\frac{4}{5}=\frac{1}{3}[/tex]To solve for v, first, subtract 4/5 from both sides of the equation:
[tex]\begin{gathered} v+\frac{4}{5}-\frac{4}{5}=\frac{1}{3}-\frac{4}{5} \\ \implies v=\frac{1}{3}-\frac{4}{5} \end{gathered}[/tex]Next, simplify the right-hand side by taking the lowest common multiple of the denominators:
[tex]\begin{gathered} v=\frac{5-3(4)}{15}=\frac{5-12}{15} \\ \implies v=-\frac{7}{15} \end{gathered}[/tex]The value of v is -7/15.
write a polynomial function in standard form with the given zeros x= -1,-2,-3,-4
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Explanation: For this question we have 4 zeros so x can be as follows
x = -1 or x = -2 or x = -3 or x = -4
We can turn the equalities above into factors as follows
[tex]\begin{gathered} x=-1\rightarrow x+1=0 \\ x=-2\rightarrow x+2=0 \\ x=-3\rightarrow x+3=0 \\ x=-4\rightarrow x+4=0 \end{gathered}[/tex]Step 1: Now that we have the factors we can build a function and simplify it as follows
[tex]\begin{gathered} y=(x+1)(x+2)(x+3)(x+4) \\ y=(x^2+2x+x+2)(x^2+4x+3x+12) \\ y=(x^2+3x+2)(x^2+7x+12) \\ y=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24 \\ y=x^4+7x^3+3x^3+12x^2+21x^2+2x^2+36x+14x+24 \\ y=x^4+10x^3+35x^2+50x+24 \end{gathered}[/tex]Final answer: So the final answer is
[tex]y=x^4+10x^3+35x^2+50x+24[/tex].
What is the y-intercept of the graph of y = 2.5x?a. 2.5b. 0c. 1d. -1
Answers
Solution
- We are asked to find the y-intercept of the graph of:
[tex]y=2.5x[/tex]- In order to find the y-intercept, we need to know the definition of the y-intercept.
- The y-intercept is the y-value where the graph crosses the y-axis.
- An implication of this definition is that whenever the graph crosses the y-axis, the x-value at that point is zero. This means that we simply need to substitute x = 0 into the equation given to us to find the y-intercept of the graph.
- The y-intercept can thus is gotten as follows:
[tex]\begin{gathered} y=2.5x \\ \text{put }x=0 \\ y=2.5(0) \\ \\ \therefore y=0 \end{gathered}[/tex]Final Answer
The y-intercept of the graph is y = 0 (OPTION B)
The minimum diameter for a hyperbolic cooling tower is 76 feet, which occurs at a height of 173 feet. The top of the cooling tower has a diameter of 93 feet, and the total height of the tower is 250 feet. Write the equation for the hyperbola that models the sides of the cooling tower assuming that the center of the hyperbola occurs at the height for which the diameter is least.Round your a and b values to the nearest hundredth if necessary.
Answers
STEP - BY - STEP EXPLANATION
What to find?
The equation for the hyperbola that models the sides of the cooling tower assuming that the center of the hyperbola occurs at the height for which the diameter is least.
Given:
Minimum diameter = 76 feet
Height = 173 feet
Diameter of the top of cooling tower = 93 feet
Total height of tower = 250 feet
Consider the general hyperbolic formula below:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]But;
2a = 76
⇒ a = 38
x=93/2 =46.5
y=250 - 173 =77
Substitute the values into the formula above and determine the value of b.
[tex]\frac{(46.5)^2}{38^2}-\frac{77^2}{b^2}=1[/tex][tex]b=109.18[/tex]Now substitute the values a= 38 and b=109.18 into the general formula
[tex]\frac{x^2}{38^2}-\frac{y^2}{109.18^2}=1[/tex]ANSWER
[tex]\frac{x^2}{38^2}-\frac{y^2}{109.18^2}=1[/tex]Find each unit price and decide which is the better buy. Assume that we are comparing sizes of the same breadFrozen orange juice $1.51 for 14 ounces $0.51 for 4 ounces Find the unit price if a frozen orange juice which cost $1.51 for 14 ounces
Answers
Unit price of a frozen orange juice which costs $1.51 for 14 ounces = $0.108 per ounce
Unit price of a frozen orange juice which costs $0.51 for 4 ounces = $0.128
The better buy is the frozen orange juice which costs $1.51 for 14 ounces
Option B
Explanations:Cost of 14 ounces of orange juice = $1.51
Cost od 4 ounces of orange juice = $0.51
Unit price of a frozen orange juice which costs $1.51 for 14 ounces
Unit price = $1.51 / 14
Unit price of a frozen orange juice which costs $1.51 for 14 ounces = $0.108 per ounce
Unit price of a frozen orange juice which costs $0.51 for 4 ounces
Unit price = $0.51 / 4
Unit price of a frozen orange juice which costs $0.51 for 4 ounces = $0.128
The better buy is the one with the lower unit price
Since the frozen orange juice which costs $1.51 for 14 ounces has the lower unit price, it is the better buy
Write the expression that can be used tofind the height of the Eiffel Tower.
Answers
First, let's picture the problem:
I have represented the height of the Effiel tower as H
Using the trigonometric ratios:
[tex]\begin{gathered} \tan 53^0\text{ = }\frac{H}{225} \\ H=225\times\tan 53^0^{} \end{gathered}[/tex]Hence the required expression is :
[tex]\begin{gathered} \text{Height of tower = d }\times\text{ tan}\phi \\ \text{if d is the distance of the base} \end{gathered}[/tex]find the value of the term in the arithmetic sequence 1,6,11,16...(8th term)
Answers
We need to find the 8th term of the following arithmetic sequence:
[tex]1,6,11,16,...[/tex]The formula to find the n-th term an of aₙ arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]where a₁ is the first term and d is the difference between two consecutive terms.
The first term of this sequence is a₁ = 1, and d is given by:
[tex]\begin{gathered} d=a_2-a_1 \\ \\ d=6-1 \\ \\ d=5 \end{gathered}[/tex]Then, for n = 8, we obtain:
[tex]\begin{gathered} a_8=1+(8-1)5 \\ \\ a_8=1+7(5) \\ \\ a_8=1+35 \\ \\ a_8=36 \end{gathered}[/tex]Answer:
The 8th term is 36.
1. Sue uses 2.59 pounds ofstrawberries and 0.65 poundof blueberries to make fruitsalad. She serves the sameamount of salad in each of 9bowls. What is the weight,in pounds, of each serving tothe nearest tenth?
Answers
Problem:
Sue uses 2.59 pounds of strawberries and 0.65 pounds of blueberries to make a fruit salad. She serves the same amount of salad in each of 9
bowls. What is the weight, in pounds, of each serving to
the nearest tenth?
Solution:
The total weight of the fruit salad is:
2.59 pounds + 0.65 pounds = 3.24 pounds.
Now, if she serves the same amount of salad in each of 9 bowls, we have that the weight in each serving is:
[tex]\frac{3.24}{9}=\text{ 0.36 pounds}[/tex]Then, we can conclude that the correct answer is:
0.36 pounds.
find all real solutions[tex](2x + 17) \div (x + 1) = x + 5[/tex]
Answers
We have the next equation
[tex]\frac{2x+17}{x+1}=x+5[/tex][tex]2x+17=(x+5)(x+1)[/tex][tex]\begin{gathered} 2x+17=x^2+x+5x+5 \\ 2x+17=x^2+6x+5 \end{gathered}[/tex]Then we sum similar terms
[tex]\begin{gathered} x^2+(6x-2x)+(5-17)=0 \\ x^2+4x-12=0 \end{gathered}[/tex]then we solve the quadratic equation
We can factorize the equation
[tex](x+6)(x-2)=0[/tex]so the solutions are
x=-6
x=2
Find the general solution to dy/dx = 2y passing through the point (5, 1)
Answers
We will have the following:
[tex]\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x[/tex][tex]\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c[/tex]Then we find "c":
[tex]\frac{\log(1)}{2}=5+c\Rightarrow c=-5[/tex]Thus, the general solution passing through (5, 1) is:
[tex]\frac{\log(y)}{2}=x-5[/tex]how do you write out this number in word 506,341,209.54
Answers
You write this number in word this way:
Five hundred six million three hundred fourty one thousand two hundred nine point fifty four.
The product of two whole numbers is 592 and their sum is 53. What are the two numbers?
Answers
To solve this problem, we have to build two equations with the given information. Using x and y to represent the two numbers:
• Equation 1
[tex]x\times y=592[/tex]• Equation 2
[tex]x+y=53[/tex]Now that we have to equations, we have to isolate one variable from one equation and replace it in the other.
[tex]x=53-y[/tex]Then, we will replace this value of x in Equation 1:
[tex](53-y)\cdot y=592[/tex]Solving for y we get:
[tex]53y-y^2=592[/tex][tex]-y^2+53y-592=0[/tex]As we got this expression, we will have to use the General Quadratic Formula. With the help of a calculator, we get both values:
[tex]y_1=16[/tex][tex]y_2=37[/tex]Finally, we have to replace these values in Equation 1 to evaluate which meets the condition:
[tex]x_1=\frac{592}{y_1}[/tex][tex]x_1=\frac{592}{16}=37[/tex][tex]x_2=\frac{592}{y_2}[/tex][tex]x_2=\frac{592}{37_{}}=16[/tex]We have to evaluate the values in each equation:
[tex]\begin{gathered} 37+16=53 \\ 53=53 \end{gathered}[/tex][tex]37\cdot16=592[/tex]The first numbers meet the condition.
Answer: 37 and 16
l A golf ball is hit in the air. The table shown describes y, the height of the ball, in feet, given the time elapsed, x, in seconds, since the time the ball was hit.Based on the information in the table, which statements are true? Select each correct statement.
Answers
Given:
y is the height of the ball in feet
x is the time in seconds
In the given table you can identify the next maximum:
x=3
y=30
The ball has height 0 when it is in the earth so it is hit at second 0 and will be back in the earth at second 6
Then, from the given statements the next are true:
The maximum height of the ball was 30 feetThe ball was in the air for only 6 secondsIn the diagram of \bigtriangleup△GKJ below, LH KJ, GL=6, LK=30, and GH=3. What is the length of GJ?
Answers
From the given figures
Since LH // KJ, then
[tex]\frac{GL}{LK}=\frac{GH}{HJ}[/tex]GL = 6, LK = 30
GH = 3, HJ = y
Substitute them in the ratio above
[tex]\frac{6}{30}=\frac{3}{y}[/tex]By using cross multiplication
[tex]\begin{gathered} 6\times y=30\times3 \\ 6y=90 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=\frac{90}{6} \\ y=15 \end{gathered}[/tex]Since GJ = GH + HJ
[tex]\begin{gathered} GJ=3+15 \\ GJ=18 \end{gathered}[/tex]The answer is 36
suppose we spin the following spinner with the first spin giving us the numerator and the second spin giving the denominator of a fraction. What is the probability that the fraction will be less than or equal to 5/6?
Answers
numerator = top number
denominator = bottom number
numerator less than or equal to 5
total numbers = 4
numbers less than or equal to 5 = 2 ( 5 and 4)
Denominator
5, 6 or 7 = 3
Possible fractions = 4/5, 4/6, 4/7, 5/6 and 5/7
5 out of 16 possible fractions
probability = 5/16
Write the expression and simplifyThe difference of -10 and the product of p and q
Answers
We start with a subtraction, where we want to subtract the second term from - 10. The second term consists in a multiplication between p and q. Writing this as a mathematical expression we have
[tex]-10-pq[/tex]This expression is already on simplest form.