The graph below represents the number of miles, y, that Jacob can drive his car for every x gallons of gas. Find the rate of change.
The slope (rate of change) of the graph shown is 31.3 miles per gallon.
What is an equation?An equation is an expression that shows the relationship between two variables and expressions.
Slope is the ratio of vertical rise to horizontal run. It is given by:
Slope = rise / run
The point passes through (10, 313) and (20, 626), hence:
Slope = rise/run
Slope = (626 - 313) / (20 - 10) = 31.3
The graph's slope is 31.3 miles per gallon.
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If n ∥ m, which of the following statements are true? Select all that apply. Line m and n are parallel lines. Point B is lies on line m. Point A and C are lies on line n. There are two lines started from point B and one line passes through point A and one line passes through point B. So there is a triangle ABC. The angle ACB is denoted by 1. The angle ABC is denoted by 3. There is an angle with line m and line AB is denoted by 2 and an angle with line m and line BC is denoted by 4. Angle 1 is alternate interior angle of angle 4. The opposite angle of angle 1 is 60 degree. Also the corresponding angle of angle 2 is 20 degree. A. m∠2 = 60° B. m∠3 = 100° C. m∠2 + m∠4 = 80° D. m∠2 + m∠3 = 80°
Based on the angle relationships formed by the parallel lines, the statements that are true are:
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
How to Apply the Angle Relationship Formed by Parallel Lines?Some of the angle relationship that applies when two parallel lines are crossed by a transversal are:
Corresponding angels that are congruent.Vertical angles that are congruent.Given the image attached below, where m and n are parallel lines, we can deduce the following measures of the numbered angles based on the angle relationships:
Measure of angle 1 = 60° [vertical angles]
Measure of angle 2 = 20° [corresponding angles]
Using the triangle sum theorem, we also have:
Measure of angle 3 = 180 - m∠CAB - m∠1
Measure of angle 3 = 180 - 20 - 60 = 100°
m∠4 = 60° [corresponding angles]
m∠2 + m∠4 = 20 + 60 = 80°
From the above, we can conclude that the statements are:
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
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Parallel lines are those straight lines that are always the same distance apart from each other.
B m∠3 = 100°
C. m∠2 + m∠4 = 80° are true
What are parallel lines?Parallel lines are those straight lines that are always the same distance apart from each other. · Parallel lines never meet no matter how much they are extended.
Given that, n||m
Point B is lies on line m.
Point A and C are lies on line n.
There are two lines started from point B and one line passes through point A and one line passes through point B forms a triangle ABC.
∠ACB=1
∠ABC=2
There is an angle with line m and line AB is denoted by 2.
Using the triangle sum theorem, we also have:
Measure of angle 3 = 180 - m∠CAB - m∠1
Measure of angle 3 = 180 - 20 - 60 = 100°
m∠4 = 60° [corresponding angles]
m∠2 + m∠4 = 20 + 60 = 80°
Hence From the above, we can conclude that the statements are:
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
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The diameter of a cylindrical pipe is 7 ft. If the pipe is 42 ft long, what is it’s volume? Use the value 3.14 for n, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
ANSWER:
1616 ft³
STEP-BY-STEP EXPLANATION:
We have that the formula to determine the volume of the cylinder is as follows:
[tex]V=\pi r^2\cdot h[/tex]The radius is equivalent to half the diameter, therefore the radius is equal to 3.5 ft (7/2) while the height, in this case, is equivalent to the length, so it is equal to 42 ft. Therefore, we replace each value and calculate the volume, like this:
[tex]\begin{gathered} V=\left(3.14\right)\left(3.5^2\right)\left(42\right) \\ \\ V=1615.53\cong1616\text{ }ft^3 \end{gathered}[/tex]The volume of the cylindrical pipe is 1616 ft³.
I need help with this question
The coordinates of B after the translation is ( 3 , -2)
What is coordinates in maths?
Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).Transformation involves changing the position of a shape.
The coordinates of B after the translation is (-4,-2)
A = ( 1, 1)
B = ( 3 , 4)
C = ( -1 , 8 )
The translation rule is given as ( x , y-6)
So, the coordinates of B' is calculated using
( x , y ) ⇒ ( x , y-6)
This gives
B = ( 3 , 4) ⇒ ( 3 , 4 - 6 )
( 3 , 4) ⇒ ( 3, -2 )
Rewrite as
B' = ( 3, -2 )
Hence, the coordinates of B after the translation is ( 3 , -2)
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a rotation of 180 degrees maps figure A onto itself. It has
Letter A doesn't show rotational symmetry of 180 degrees.
The letter 'A' has just one vertical line of symmetry.A vertical line of symmetry is that line which runs down a picture thus dividing it into two identical halves. In other words, it's a straight standing line that divides an image or shape into two identical halves.
The rotational symmetry of a shape explains that when an object is rotated on its own axis, the form of the object looks the same. Many geometrical shapes appear to be symmetrical once they are rotated 180 degrees or with some angles, clockwise or anticlockwise. A number of the examples are square, circle, hexagon, etc.
Complete Question- A rotation of 180 degrees maps figure A onto itself. It has transformation or not?
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For y = 10*0.5^x (that is read y equals ten times one half to the power of x), doesthis model exponential growth or decay? Explain how you know.
f(1)=1/2 f(2)=(1/2)^2=(1/2)*(1/2)=1/4
1/2>1/4 => f(1)>f(2) => it is decreasing, because with the grow of x the value(y) is decreasing what we have shown
Distribute property of 41×8
Using distribute property on 41×8 is 328.
What is the Distributive Property?
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.
We know that,
Distributive property is A × (B + C) = AB + AC.
So, 41 × 8 is 41 × (5 + 3 ) = 41×5 + 41×3
41 × (5 + 3 ) = 205 + 123
41 × (5 + 3 ) = 328
Hence, using distribute property on 41×8 is 328.
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The abc one is my question could I please get sum help
For this problem, we are given two sides and one angle of a triangle. We need to determine the length of the side that is opposite to the known angle.
To solve this problem, we need to use the law of cosines.
[tex]a=\sqrt{b^2+c^2-2bc\cdot\cos(m\angle A)}[/tex]Applying the given data, we have:
[tex]\begin{gathered} a=\sqrt{13^2+21^2-2\cdot13\cdot21\cdot\cos(105)}\\ \\ a=\sqrt{169+441-546\cdot(-0.2588)}\\ \\ a=\sqrt{610+141.3048}\\ \\ a=\sqrt{751.3048}=27.41 \end{gathered}[/tex]The correct answer is 27.4.
Alex buys 32oz of yogurt for $2.56. John buys a Goz yogurt for $0.48. Are the unit prices equal? Write an equation using the unit price to represent this relationship if they are equal. options: Yes, y=5.33x . Yes, y=12.5x, No, the ratios are not equivalent . Yes, y=0.08x
Answer:
Yes, y=0.08x
Explanation:
The unit price can be calculated as the price divided by the number of ozs, so the unit prices are:
[tex]\frac{\text{Price}}{\text{Ounces}}=\frac{\text{ \$2.56}}{32\text{ oz}}=\text{ \$0.08 per ounce}[/tex][tex]\frac{Price}{Ounces}=\frac{\text{ \$0.48}}{6\text{ oz}}=\text{ \$0.08 per ounce}[/tex]Therefore, the unit prices are equal, so the equation that represents the relationship is:
y = kx
Where k is the unit price, so replacing k by 0.08, we get:
y = 0.08x
So, the answer is:
Yes, y=0.08x
explain to Elena what her mistake war and what the correct solution is
Please help with math ! These are due tomorrow.
3) Alex had 20 video games at the beginning.
2) The strategy to solve the problem backward is:
The number of games Alex has now is 16 games.
The number of games he gave to his brother is 2, so add 2 to the current number of video games, 16 + 2 = 18
Now add the games he sold, which are given as 3
18 + 3 = 21
Subtract the games he traded with Hector,i.e. 6 video games
21 - 6 = 15
This obtained number is 3/4 of his games,
3/4 of the total video games = 15
Therefore, the total video games were = (15×4)/3 = 20
4) Yes the answer makes sense.
Operations in reverse order are:
The number of video games given by Alex to hector is = 1/4 of 20 = 5
Remaining video games = 20 - 5 = 15
Number of games after adding exchanged 6 video games = 15+6 = 21
Number of games after Alex sold 3 video games = 21 -3 = 18
Number of games after Alex gave 2 to his brother = 18 - 2 = 16 video games
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9-3 2 = (x) 6 what is the function family.
a. G(x) = 1/4x - 5 Since it's similar to the equation f(x)=mx + b, which is a linear
function, g(x) is a linear function.
b. f(x) = 2*(x - 1)^2 - 5 Since the degree of the polynomial is 2, we deduce it is a cuadratic function.
c. f(x) = 7 Since the degree of x is zero ( there is no x) , we deduce it is a constant function.
Which inequality is true?O A. 31 - 1<8B. + 6 < 9O c. <3D. 477 > 12
The answer is D
To solve this, we can use similar values of the ones in the problems and compare it:
With a just add one to each side:
[tex]undefined[/tex]Mr.Kermshner has 168 bandages march through June. How much is it if each bandage is 3 cents
504 bandages if it is each bandage is 3 cents.
Given,
Mr. Kermshner has 168 bandages march through June.
To find the how much is it if each bandage is 3 cents ?
Now, According to the question,
Based on the given conditions,
Formulate:
Total bandage is 168
and, each bandage is 3 cents
= 168 x 3
= 504
Alternative form = 5.04 x 10^2
Hence, 504 bandages if it is each bandage is 3 cents.
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Triangle ABC is similar to triangle DEFwhich proportion can be used to find the length of DE in centimeters?A. 4/3 = DE/9B. 5/15 = DE/4C. 4/DE = 9/3D. 9/DE = 3/5
In the given figure, Triangle ABC is similar to triangle DEF.
Applying the Similar Triangle Formula, the proportion to be used to find the length of DE is:
[tex]\frac{4\text{ cm}}{3\text{ cm}}\text{ = }\frac{DE}{9\text{ cm}}[/tex]Therefore, the answer is A.
The length of a bridge is about 6.3 meters. Which number from the list is closest to 6.3?A. 40B. 748C. 735D. 737Pls help me
The closest number to 6.3 is the number 40, because when we substract 6.3 from 40, we get the smallest number.
40 - 6.3 = 33.7
748 - 6.3 = 741.7
Fifty-two percent of realtors have a college degree. If a continuing education course enrolls a random selection of 1,600 realtors every year, what is the average number of realtors attending the course with a degree each year?
SOLUTION:
The average is given by the formula;
[tex]\begin{gathered} Mean=xP(x) \\ =0.53\times1600 \\ =848 \end{gathered}[/tex]Thus, the average number of realtors who have a degree attending the course is 848
Mr. Knox's garden is in the shape of a triangle. What is the area of Mr. Knox’s garden? __ square feet
Using the area of a triangle, the area of Mr. Knox's garden is: 58 square feet.
How to Find the Area of a Triangular Shape?The area of any triangular shape can be calculated using the formula for the area of a triangle.
The area of a triangle = 1/2(base)(height).
The shape of Mr. Knox's garden is triangular. The parameters of his triangular garden are:
Length of the base of the triangular garden = 24½ ft
Height of the triangular garden = 8 ft.
Area of the garden = 1/2(24½)(8)
Area of the garden = 1/2(29/2)(8)
Area of the garden = 1/2(232/2)
Area of the garden = 232/4
Area of the garden = 58 square feet.
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is the answer 9 im lost can you help me
Solution
Population of the town = 3000
Rate = 4%
Amount = 4700
[tex]A=P(1+r)^n[/tex][tex]\begin{gathered} 4700=3000(1+4\text{ \%\rparen}^n \\ \frac{4700}{3000}=1+0.04)^n \\ 1.567=1.04^n \end{gathered}[/tex]Find log of both side
[tex]\begin{gathered} 1.567=1.04^n \\ ln1.567=ln1.04^n \\ nln1.04=1.567 \\ n=\frac{ln1.567}{ln1.04} \\ n=11.5yrs \end{gathered}[/tex]Therefore the number of years it will take population to reach 4700 = 11.5yrs
Passing through (-4,-5) and parallel to the line whose equation is y= -3x+4
For the given values the equation of new line is y = -3x - 17
What is a line equation example?The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.
Given,
The equation of line is y= -3x+4
as the lines are parallel,
slope of lines will be same,
∴ Slope of new line = -3
The equation of line is:
y - y1 = m(x - x1)
Where x1, y1 are the given coordinates and m is the slope
⇒ y -(-5) = -3 (x - (-4))
⇒ y + 5 = -3 (x + 4)
⇒ y + 5 = -3x - 12
⇒ y = -3x - 17
∴ The equation of the line is y = -3x - 17
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There is a new fair coming to town this weekend. Tickets are selling for $10.99 for adults and $5.99 for kids. Each ride is $0.99 cents each. Make an equation for adults tickets and another equations for kids ticket. How much money would each spend if they each ride 5 rides?
Answer:
(a)Adult:10.99+0.99x, Kid: 5.99+0.99x
(b)Adult's Total cost = $15.94, Kid's Total cost =$10.94
Explanation:
Cost of a ride = $0.99
Let x be the number of rides.
Cost of an Adult Ticket = $10.99
An equation for adult tickets will therefore be: 10.99+0.99x
Similarly, the cost of a kid ticket =$5.99
An equation for adult tickets will therefore be: 5.99+0.99x
(b)If they ride 5 tickets each, the amount of money spent will be:
x=5 rides
Total cost for an adult=10.99+0.99(5)
=10.99+4.95
=$15.94
Total cost for a kid = 5.99+0.99(5)
=5.99+4.95
=$10.94
Solve the inequality and graph the solution.
−2p + 4.5 < −2.9
number line with open circle plotted at 3.7 and arrow pointing right
number line with closed circle plotted at 3.7 and arrow pointing left
number line with open circle plotted at 3.7 and arrow pointing left
number line with closed circle plotted at 3.7 and arrow pointing right
The solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality has been plotted.
The inequality is −2p + 4.5 < −2.9
Subtract 4.5 from both side
-2p + 4.5 - 4.5 <-2.9 - 4.5
-2p < -7.4
Divide both sides by -2
-2p/-2 < -7.4/-2
p > 3.7
Draw the graph using the result of the inequality
Hence, the solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality graph has been plotted.
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Answer:
number line with open circle plotted at 3.7 and arrow pointing right
Step-by-step explanation:
hope this helps :)
Write the correct inequality for the following statement and then solve for the given number of
guests.
You are in charge of planning your mother's surprise party. You have
found a hall that rents for $225 and a caterer that will charge you $15 per
guest. Write an inequality to calculate your total cost (T) based on the
number of guests (g).
If you have a total budget of $1000 how many guests can you
invite?
Step-by-step explanation:
You are in charge of planning your mother's surprise party. You have found a hall that rents for $225 and a caterer that will charge you $15 per guest. Write an inequality to calculate your total cost (T) based on the number of guests (g).
T = 15g + 225
If you have a total budget of $1000 how many guests can you
invite?
1,000 = 15g + 225
subtract 225 from both sides:
1,000 -225 = 15g + 225 - 225
775 = 15g
divide both sides by 15:
775/15 = 15g/15
g = 51.66
Because you cannot invite part of a guest round down to inviting 51 guests
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
v
Consequently, y = x + 2 is the equation for the line CD.
Points C(0, 2) and D are given (4, 6).
We must identify the equation of the line CD.
Given is the equation for the line through two points
[tex]\frac{y-y_{1} }{y_{1} - y_{2} } = \frac{x-x_{1} }{x_{1} -x_{2} }[/tex]
[tex]\frac{y-2}{6-2} = \frac{x-0}{4-0}[/tex]
y - 2 = x
x - y + 2 = 0
Consequently, y = x + 2 is the equation for the line CD.
What is the equation of the line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine if a given point lies on a line using the equation of any line.
The line's equation is a linear equation of degree one. Let's learn more about the various ways a line's equation may be expressed and how to calculate it.
The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
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Consider the following compound inequality. 7
a)The solution of the inequality is 3 < x ≤ 5
c) The solution in interval notation is (3, 5]
Step - by - Step Explanation:
What to find?
• The solution of the inequality.
,• The graph of the inequality.
,• The solution in interval notation.
Given:
7 < x +4 ≤ 9
Re-write the above inequality.
x + 4 > 7 or x + 4 ≤ 9
Solve for x in each case.
x + 4 > 7
Subtract 4 from both-side of the inequality.
x > 7 - 4
x > 3
x + 4 ≤ 9
Subtract 4 from both-side of the inequality.
x ≤ 9 - 4
x≤ 5
Combine the two solutions.
3Hence, the solution to the inequality is 3 < x ≤ 5
b) We can proceed to graph the inequality.
c) The solution in interval notation is (3, 5]
find a formula for the nth term of the arithmetic sequence the first term is 7 and the common difference is -3
The formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is - a[n] = 10 - 3n
What is an Arithmetic progression?An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -
a₁ , a₂, a₃ , a₄ ...... aₙ
will be an arithmetic progression if -
a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.
Given is the the first term equal to 7 and the common difference equal to
- 3.
We can calculate the nth term of an A.P. using the formula -
a[n] = a + (n - 1)d
a[n] = 7 + (n - 1)(- 3)
a[n] = 7 - 3n + 3
a[n] = 10 - 3n
Therefore, the formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -
a[n] = 10 - 3n
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A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)
A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2). The y-coordinates are different with the negative sign in the given transformations.
Given that,
A(-6, -2)→ A'(-6, 2) B(-3, -6) →B'(-3, 6) C(-2,-2)→ C'(-2, 2)
We have to find the difference of the transformations.
So,
First take A(-6, -2)→ A'(-6, 2)
We can see the difference is the A of y-coordinates have negative sign of the A'.
Now,
Take B(-3, -6) →B'(-3, 6)
We can see the difference is the B of y-coordinates have negative sign of the B'.
Now,
Take C(-2,-2)→ C'(-2, 2)
We can see the difference is the C of y-coordinates have negative sign of the C'.
Therefore, The y-coordinates are different with the negative sign in the given transformations.
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What the are of this parallelogram?
A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into three identical smaller rectangular plot by placing to fence is parallel to the field shorter side. Find the dimensions that maximize the enclosed area. Write your answer as a fraction reduced to lowest term
The diagram of the problem is:
S is the length of the shorter side of the fence. L is the length of the longest side of the field.
We know that the perimeter of the rectangle is 800ft. This means:
[tex]2S+2L=800[/tex]And the area:
[tex]A=SL[/tex]The smaller rectangles will have dimensions:
The area is:
[tex]a=\frac{SL}{3}[/tex]As we can see, if we maximize the area of the bigger rectangle "A", we are also maximizing the area of the smaller rectangles "a".
Then, we have two equations:
[tex]\begin{gathered} 2S+2L=800 \\ A=SL \end{gathered}[/tex]We can solve for L in the first equation:
[tex]\begin{gathered} 2S+2L=800 \\ 2L=800-2S \\ L=400-S \end{gathered}[/tex]Then substitute in the second:
[tex]A=S(400-S)[/tex]Simplify:
[tex]A=400S-S^2[/tex]This is a function of the area depending on the length of the shorter side of the rectangle:
[tex]A(S)=400S-S^2[/tex]We can find the maximum of this function if we find the value where the derivative of this function is 0.
Let's differentiate:
[tex]A^{\prime}(S)=400-2S[/tex]And now we find where A'(S) = 0:
[tex]\begin{gathered} 0=400-2S \\ 2S=400 \\ S=200 \end{gathered}[/tex]We have found that the shorter side must have a length of 200ft to maximize the area. Let's find the length of the larger side:
[tex]L=400-200=200[/tex]As expected, the quadrilateral which maximizes the area is the square. Thus, the dimensions of the field are 200ft x 200ft
Find the minimum value of the parabola y = x2 − 6.
The minimum value of the parabola is y = -6
An equation of a parabola is given as
y = x²-6
We will find its minimum value using the differentiation method.
For this first we will find the derivative with respect to x and find the value of x at which the derivative becomes zero. The derivative becomes zero only when the parabola has either a maximum or minimum value. We further check whether the parabola has a minimum or maximum at that x by finding the second derivative of the parabola at that x.
So first derivative of y with respect to x is 2x.
So 2x = 0
⇒ x =0
Now take the second derivative of y with respect to x at x = 0,
Second derivative = 2 > 0 at x = 0
Here the second derivative is greater than zero at x = 0. So y has a minimum value at x = 0
The minimum value of the parabola is,
y = 0² - 6
⇒ y = -6
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