Answers
Step by step
The two “x” variable angles are supplementary so combined they will equal 180 degrees
2(5x -5) + (3x -5) = 180
Distribute
10x -10 + 3x -5 = 180
Combine
13x -15 = 180
Add 15 to both sides to isolate variable
13x -15 + 15 = 180 + 15
Combine
13x = 195
Divide both sides by 13 to solve for x
13/13 x = 195/13
x = 15
The two “y” variable angles are supplementary so combined they will equal 180 degrees
5y + 5 + 20y = 180
Combine
25y + 5 = 180
Subtract 5 from both sides to isolate y
25y +5 -5 = 180 -5
25y = 175
Divide both sides by 25 to solve for y
25/25 y = 175/25
y = 7
Related Questions
Adi is 5 inches short than Sunee. Sunee is n inches tall. What is an expression that represents Adi's height in inches?
Answers
The expression that represents the Adi's height in inches is n - 5.
Expression:
An expression is the mathematical statement which consists of numbers, variables and an arithmetic operation like addition, subtraction and division etc. between them.
Given,
Adi is 5 inches short than Sunee. Sunee is n inches tall.
Here we need to find the expression for Adi's height in inches.
Through the given question we know that,
Sunee is n inches tall.
And Adi is 5 inches lesser than Sunee.
Here we have the word short or less, that represents that we have to reduce that amount from the total.
Therefore, the expression for Adi's height in inches is,
=> n - 5.
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EB.AACB = ADCE. AB = 8 and AC = 6DE = [?]
Answers
DE will be equal to AB, then DE=8
combine the like terms to create an equivalent expression -4r - 2r + 5
Answers
Answer:8r+7-6r-5Combine the like terms=8r-6r+7-5Thenafter, simplify=2r+2
good luck
Step-by-step explanation:
6 kg of bananas cost $42. How much
would 35 kg cost?
Round the answer to the 2 decimal digit
Answers
Answer:
245
Step-by-step explanation:
6 - 42
35 - x
cross multiply
6x = 35 × 42
6x = 1470
x = 1470 ÷ 6
x = 245
6. Which of the following facts, if true, would allow you to prove that lines I and m are parallel? (1 point)
5/6
7 8
m22-m23
m27+m28=180*
Om24-m25
m26+m22=180°
1
3
4
2
m
Answers
Answer:
The first 3 answers
Step-by-step explanation:
∠2 and ∠3 are vertical angles which means they are congruent. That would then make ∠1 and ∠4 congruent.
∠7 and ∠8 = 180 means that is a straight line.
∠4 and ∠5 are alternate interior angles which make them congruent.
That would then mean ∠3 and ∠4 = 180 which is a straight line because ∠3 would then be a corresponding angle to ∠7.
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Answers
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance.
If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Enter your answer in the box
Answers
Answer:
3 months
Step-by-step explanation:
120 + 40m = 180 + 20m
Collect like terms
40m - 20m = 180 - 120
20m = 60
Divide
m = 60/20
m = 3
It will take them 3 months before Jaclyn and Pedro have saved the same amount of money.
535(-8) ??? What is the answer
Answers
Answer: the answer is -4280
Step-by-step explanation:
x+6x-5x=x+114 Please help.
Answers
Help me with this question please
Answers
Answer:
65
Step-by-step explanation:
First find the area of the triangles
a*b/2 is the equation for triangles
5*6/2 is 15
multiply 15*2 because there are two triangles
15*2=30
Now find the area of the rectangle
5*7=35
Then add.
30+35=65
:)
Given the slope of a line is -2 and it passes through the point (4,-5), write the equationof the line in standard form.
Answers
Answer:
The equation of the line is;
[tex]y=-2x+3[/tex]Explanation:
Given that
the slope of a line is -2 and it passes through the point (4,-5).
Applying the slope-intercept form of equation;
[tex]y-y_1=m(x-x_1)[/tex]Substituting the values of the slope and coordinates;
[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-2x+3[/tex]Answer:
2x + y = 3
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 )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 5 ) into the partial equation
- 5 = - 8 + c ⇒ c = - 5 + 8 = 3
y = - 2x + 3 ← in slope- intercept form
add 2x to both sides
2x + y = 3 ← equation in standard form
3potniIn a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments of equal lengths 8 cm and 2 cm. What is the length of the altitude?O 10 cm
Answers
Answer:
[tex]\text{The altitude is 4cm.}[/tex]Step-by-step explanation:
Let's illustrate the situation in a diagram to understand.
In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.
Therefore,
[tex]\begin{gathered} \frac{8}{a}=\frac{a}{2} \\ 2\cdot8=a^2 \\ 16=a^2 \\ a=\sqrt[]{16} \\ a=4\text{ cm} \end{gathered}[/tex]A person has lost a card game and is counting the points left in his hand. He announces that he has five fours and five sevens. Write this statement as a number expression.
Answers
The statement as number expression is given by the total number of points are 55.
What is Mathematical expression?
An expression is a finite combination of symbol and numbers depending on the context
We are given that A person has lost a card game and he is counting the points left in his hand.
His cards were five fours and five sevens
And we have to write this statement as number expression
Now there are five fours that is [tex]5*4=20 points[/tex]
And five sevens that is [tex]5*7=35 points[/tex]
Hence the total number of points are 20+35=55 points.
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Two similar pyramids have slant height of 4 and 6.1. Find the scale factor.2. If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?
Answers
1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:
[tex]\frac{6}{4}=\frac{3}{2}\text{ or 1.5}[/tex]So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.
2) For the Volume of the Pyramid, we can write out the formula below:
[tex]V=\frac{1}{3}\cdot Ab\cdot h[/tex]Since the scale factor is 1.5 Then we can state that
[tex]\begin{gathered} V=\frac{48}{\frac{3}{2}} \\ V=32 \end{gathered}[/tex]the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.
3) Hence, the answers are:
1.k=1.5
2. 32 m³
our football team has members, of which only are strong enough to play offensive lineman, while all other positions can be played by anyone. in how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?
Answers
By using Permutation, the total number of ways in which we can choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver is 1512.
Permutation is defined as the arrangement of items in a specific or a particular order.
Since there are 3 choices for the position of offensive lineman, and for the next position there are 9 choices, similarly 8 choices for the next position and 7 choices remain for the last position.
So we get, 3x9x8x7 =1512, by the concept of Permutation.
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the teacher wants to select 6 students from this class. the first selected student will be a media helper, the second one will be a pledge/flag helper, the third one will be a pencil sharpener, the fourth one will be attendance taker, the fifth one will be a board eraser and the sixth one will be a calendar helper. from this class of 13 students, how many different ways can this selection be done?
Answers
From this class, the teacher wishes to selected six students. 2,2,2,2,2,3 different ways are there to selected from this class of 13 students.
Given that,
From this class, the teacher wishes to selected six students. The first chosen student will assist with media, the second will assist with pledges and flags, the third will sharpen pencils, the fourth will take attendance, the fifth will wipe the board, and the sixth will assist with the calendar.
We have to find how many different ways are there to selected from this class of 13 students.
For 13 students,
We divide like 2,2,2,2,2,3.
The first 2 student will be a media helper,
The second 2 students will be a pledge/flag helper,
The third 2 students will be a pencil sharpener,
The fourth 3 students will be attendance taker,
The fifth 2 students will be a board eraser and
The sixth 2 students will be a calendar helper.
Therefore, This many ways we can selected the students.
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you are given the set of letters {a, b, c, d, e}. what is the probability that in a random five-letter string (in which each letter appears exactly once, and with all such strings equally likely) the letters a and b are next to each other?
Answers
The probability in a random 5-letter string that the letters A and B will be next to each other is 0.4
For A and B to be next to each other in the string of letters, consider the AB combination as a single letter. Then there are 4 letters AB, C, D, E.
There are 4! number of ways to arrange these 4 letters.
4!= 24 ways
We know AB can be arranged in 2 ways ( AB or BA)
Thus there are 2*4! = 2 * 24 = 48 ways of arranging the letters such that AB are next to each other in the random Five-letter string
The total number of letters in the set is 5 and hence the total number of ways the letters can be arranged without A and B necessarily being next to each other is 5!= 120
The probability that in the random five-letter string( in which each letter appears only once with all such strings equally likely) the letters A and B are next to each other= 48/120 = 0.4
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a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths. how many cubic inches are in the volume of the cube?
Answers
The volume of the cube with the shortest possible side lengths is 216 cubic inches.
If a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths, then the side lengths of the cube must be equal to the diameter of the sphere.
side length of cube = diameter of sphere
side length of cube = 2 x radius of sphere
side length of cube = 2 x 3 inches
side length of cube = 6 inches
The volume of the cube can be calculated using the formula below.
V = s³
where V = volume and s = side length of cube
V = (6 inches)³
V = 216 cubic inches
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The graph of a figure is shown below.
Which graph represents the reflection of this figure across the x-axis?
the first triangle in the photo
which is reflected on the x-axis
Answers
A graph which represents the reflection of this figure across the x-axis is: graph 5.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:
(x, y) → (x, -y) = (3, 1) → (3, -1).
(x, y) → (x, -y) = (4, 0) → (4, 0).
(x, y) → (x, -y) = (3, -1) → (3, 1).
(x, y) → (x, -y) = (4, -2) → (4, 2).
(x, y) → (x, -y) = (2, -4) → (2, 4).
(x, y) → (x, -y) = (0, -2) → (0, 2).
In conclusion, a reflection across the x-axis would transform the geometric figure to that shown in the graph attached in the image below.
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a jury pool has 22 men and 16 women, from which 12 jurors will be selected. assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of
Answers
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between f = 1/4 * c + 40 , chirps and outdoor temperature is where c is the number of chirps per minute and ƒ is the temperature in degrees Fahrenheit. a. Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature? b. If it is 75 deg * F outside, about how many chirps can we expect to hear in one minute? c. The equation is only a good model of the relationship when the outdoor temperature is at least 55 deg * F (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?
HELPPPP ME PLEASEEEEEEE
Answers
a. Using the equation of the relationship, the temperature outdoor would be 67.5 °F.
b. 140 chirps in a minute.
c. 60 chirps at that temperature is expected.
d. The graph for the relationship is given below.
e. 1/4 is the unit rate or slope = in 1/4°F per chirp.
f. 40 represents the starting or initial temperature.
What is the Graph of a Linear Equation?The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.
Given the equation, f = ¼c + 40, where:
f = temperature in degrees Fahrenheit
c = number of chirps
1/4 represents the temperature in °F per chirp
40 represents the initial temperature
a. Substitute c = 110 into the equation, f = ¼c + 40:
f = ¼(110) + 40
f = 67.5
The outdoor temperature is predicted to be 67.5 °F.
b. Substitute f = 75 into the equation, f = ¼c + 40:
75 = ¼c + 40
75 - 40 = ¼c
35 = 1/4c
4(35) = c
c = 140
140 chirps would be heard in a minute.
c. Substitute f = 55 into the equation, f = ¼c + 40:
55 = ¼c + 40
55 - 40 = ¼c
15 = c/4
4(15) = c
c = 60
Expect to hear 60 chirps at that temperature.
d. The graph for f = ¼c + 40 is in the attachment.
e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.
f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.
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Please someone help me figure out this scientific notation question
Answers
Scientific notation: 10¹
Integer: 10
The average radius of the sun is 10 times greater than the average
Explanation:The average radius of Jupiter:
[tex]R_J=4.34\times10^4miles_{}_{}[/tex]The average radius of the sun:
[tex]R_s=4.32\times10^5miles[/tex]The ratio of the two Radii
[tex]\frac{R_s}{R_J}=\frac{4.32\times10^5}{4.34\times10^4}[/tex][tex]\begin{gathered} \frac{R_s}{R_J}=0.995\times10 \\ \frac{R_s}{R_J}=9.95 \\ \frac{R_s}{R_J}=10\text{ (to the nearest integer)} \end{gathered}[/tex]The average radius of the sun is 10 times greater than the average
1) Round the number to the underlined place value.
-17.625
Answers
Question 2
help pls its hard i forgt how to do it
Answers
Answer: 52
Step-by-step explanation:
a^2+b^2=c^2
x is the hypotenuse (c). You can find the hypotenuse by finding the opposite of the right angle
48^2+20^2=2304+400=2704
√2704=52
x=52
1.64285714286
Round up the number
Answers
Answer: 1.6 or 2
Step-by-step explanation:
If you are rounding it to the nearest tenths then the answer is 1.6 but if you are rounding to the nearest whole number then its 2.
Write an integer that lies between-7.73 & -6.41, what is the answer?
Answers
As
(-7.73 + -6.41)/2 = -14.14/2 = -7.07
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A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
The ball would bounce to a height of 0.92 feet at the 7th bounce
How to determine the height of the 7th bounce of the ballThe given parameters are
Initial height = 3.75 feet
Rate of bounce = 79%
The height of the ball after n-th bounce is represented as
H(n) = A * rⁿ⁻¹
Where
A = Initial height = 3.75 feetr = Rate of bounce = 79%n = Number of bounceIn this case, we have
n = 7
So, we have
H(7) = 3.75 * (79%)⁷⁻¹
Evaluate the difference
H(7) = 3.75 * (79%)⁶
Evaluate the product
H(7) = 0.92
Hence, the height of the 7th bounce of the ball is 0.92 feet
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A book has 250 pages.how many digits have been used to print page no.s of book
Answers
Answer: 642 Digits have been used to print 250 Pages
Step-by-step explanation:
A book has 250 pages
1 - 250 Numbers will be used
Single Digit number - 9 ( 1- 9)
Two Digit Numbers 90 ( 10 - 99)
Three Digit Numbers 151 ( 100 - 250)
Number Of Digits used = 9 * 1 + 90 * 2 + 151 * 3
= 9 + 180 + 453
= 642
642 Digits have been used to print 250 Pages
A balcony at an apartment can hold up to 1,816 kilograms. How many 160-pound people can the balcony hold?
Answers
The balcony can hold 25 people of 160-pound weight.
According to the question,
We have the following information:
The maximum weight balcony can hold = 1816 kg
Weight of 1 person = 160 pound
Now, we will convert this weight into kilogram so that both the measurements have same units.
1 pound = 0.454 kg
160 pound = 160*0.454 kg
160 pound = 72.64 kg
Now, let's take the number of people balcony can hold to be x.
So, we have:
72.64x = 1816
x = 1816/72.64
x = 25
Hence, the number of people the given balcony can hold is 25.
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Find the indicated measure. Assume that all segments that appear to be tangent are tangent.
Answers
We are asked to determine the arc length of HJ. To do that we will use the following formula:
Given two secant lines that intercept outside a circle as follows:
We have the following relationship:
[tex]\angle x=\frac{1}{2}(\text{mCD-mAB)}[/tex]Substituting the values we get:
[tex]29=\frac{1}{2}(96-\text{mHJ)}[/tex]Now, we multiply both sides by 2:
[tex]58=96-mHJ[/tex]Now, we subtract 96 from both sides:
[tex]58-96=-\text{mHJ}[/tex]Solving the operations:
[tex]-38=-\text{mHJ}[/tex]Now, we multiply both sides by -1:
[tex]38=\text{mHJ}[/tex]Therefore, the measure of the arc length of HJ is 38.
