Terrence is folding paper cranes at a constant rate. The table below shows the amount of time he needs to fold cranes.
Number of cranes Total time (minutes)
555 17.517.517, point, 5
888 282828
121212 424242
Write an equation to describe the relationship between ccc, the number of cranes, and ttt, the total time in minutes.

Points [tex]X(-2,1)[/tex] and [tex](-4,-3)[/tex] are defined therefore we have all data we need to construct equation.

Linear function has a form of,

[tex]y=ax+b[/tex]

First calculate the slope a.

[tex]a=\dfrac{dy}{dx}=\dfrac{-3-1}{-4-1}=\dfrac{-4}{-5}=\dfrac{4}{5}[/tex]

Now plug in the coordinates of either one of the points into the linear function. I'll pick point X.

[tex]y=ax+b\Longrightarrow1=\dfrac{4}{5}\cdot(-2)+b[/tex]

Now just solve for b.

[tex]1=-\dfrac{8}{5}+b\Longrightarrow b=\dfrac{13}{5}[/tex]

The equation is therefore,

[tex]\boxed{y=\dfrac{4}{5}x+\dfrac{13}{5}}[/tex]

Hope this helps.

r3t40

Answer: A. 1.55 repeating.

Step-by-step explanation: Since 5/9 is not going to end as .5, the answer would be 1.55 repeating. 5/10 would make the answer be 1.5.

The mixed fraction number 1  5/9 is equal to the decimal number 1.55.... Then the correct option is A.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

The mixed fraction number is given below.

⇒ 1  5/9

Convert the mixed fraction number into the fraction number. Then we have

1  5/9 = 14 / 9

Convert the fraction number into a decimal number, then we have

⇒ 14/9

⇒ 1.55......

The mixed fraction number 1  5/9 is equal to the decimal number 1.55.... Then the correct option is A.

More about the Algebra link is given below.

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Answer:

a

Step-by-step explanation:

We are looking for an exponential function [tex]y=a(r)^x[/tex] where r is less than 1.

a works because it is in the form [tex]y=a(r)^x[/tex] where r is less than 1.

b is in the form [tex]y=a(r)^x[/tex] but r is more than 1.

c. and d. are not even exponential functions.

c. is a polynomial

d. is a constant polynomial (no variable)

Answer:

y ≤ ¼x + 1

Step-by-step explanation:

Starting from the y-intercept of course, use rise\run until you hit another endpoint [finding the rate of change (slope)]. That means me we go up north one block, then go over four blocks east, and since the slope is already simplified, we do not need to go any further. Now all we have left is to determine the correct inequality symbol, and since we know that the bottom portion of the graph is shared, we automatically know it is less than, but to check this, we need to do what is called a zero-interval test [do not recall the actual term], meaning that we plug in 0 for both y and x, getting 0 < 1, which is a GENUINE statement, so the bottom portion stays shaded, otherwise we would have had to shade the top portion if it were a false statement. Finally, we have to determine if we have to add an equivalence line under the inequality symbol, and we DO because as you can see, the line is SOLID BLACK. If it were DASHED BLACK, then it would stay "<" instead of "≤".

I am joyous to assist you anytime.

Answer:

G !!! Have a good day BLOODY

Answer:

8x+1

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

7x−5(x+6)

=7x+(−5)(x)+(−5)(6)

=7x+−5x+−30

=7x+−5x+−30

=(7x+−5x)+(−30)

=2x+−30

-2x=-30

x=15

Answer:

See attachment

Step-by-step explanation:

We want to graph [tex]f(x)=|x|-12[/tex] on the interval -10 to 10.

Let [tex]g(x)=|x|[/tex] be the parent absolute value function.

We can easily graph [tex]f(x)=|x|-12[/tex], if we use translation.

When the parent function is shifted downwards by 12 units, we obtain the graph of [tex]f(x)=|x|-12[/tex].

The parent function is a v-shaped graph with vertex at the origin.

We shift the parent function down so that its vertex is now at (0,-12) to get the graph of [tex]f(x)=|x|-12[/tex] .

See attachment for the graph of [tex]f(x)=|x|-12[/tex]  on the specified interval.

Answer:

Which of the following did you include in your response?

No, you will not see the graph.

When x is 0, y is –12, which is outside the viewing window.

Because the function has been reflected, it opens down.

From x = –10 to x =10, the y-values range from –22 to –12.

Step-by-step explanation:

Answer:

[tex]\large\boxed{6y+52}[/tex]

Step-by-step explanation:

In this question, we're going to simplify the expression.

We would do this by distributing and solving after.

Solve:

[tex]6(2y + 8) - 2(3y - 2)\\\\\text{Distribute the 6 to the 2y and 8}\\\\12y+48- 2(3y - 2)\\\\\text{Distribute the -2 to the 3y and -2}\\\\12y+48-6y+4\\\\\text{Combine like terms}\\\\6y+48+4\\\\\boxed{6y+52}[/tex]

When you're done solving, you should get 6y+52

This means that the simplified version would be 6y+52

Answer:

53.4 and 62.6

Step-by-step explanation:

Answer:

53.4 and 62.6

Step-by-step explanation:

Got it right :/

[tex]\bf r=2sec(\theta )\qquad \begin{cases} x=rcos(\theta )\\ \frac{x}{r}=cos(\theta ) \end{cases}\qquad \implies r=2\cdot \cfrac{1}{cos(\theta )}\implies r=\cfrac{2}{~~\frac{x}{r}~~} \\\\\\ r=\cfrac{\frac{2}{1}}{~~\frac{x}{r}~~}\implies r=\cfrac{2r}{x}\implies x=\cfrac{2~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies x=2[/tex]

Answer:

121

Step-by-step explanation:

THIS IS BECAUSE 11*11 = 121

Answer:

121

Step-by-step explanation:

121= 11x11, that is the only option

140 has no square

168 is close, but still isn't a square

195 is 1 away from a square, but not a square

Answer:

Lara's share = 25000

Step-by-step explanation:

Partnership's income = 50,000

Lara's guaranteed payment = 20,000

As the Income 50,000 is larger than Lara's guaranteed payment i.e 20,000. Since Lara is 50% partner so she will receive half the amount of the partnership's income.

Partnership's Income = 50,000  

Half of Partnership's income = 50,000/2

                                                = 25,000

Therefore, Lara's distributive share is 25,000.

!!

Answer:3x+y=3 is the red line.

6x+y=-4 is the blue line.

Step-by-step explanation:I answer it on the test it is right..

Step-by-step explanation:

Look at the picture.

All rhombuses are

parallelograms

quadrilaterals

Answer:

a) The length of the diagonal is 17.71 feet

b)  The area of the trapezoid is 123.14 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- Look to the attached figure

- ABCD is an isosceles trapezoid

∵ DC is the longer base with length 18 feet

∵ AD and BC are the two non-parallel sides with length 8 feet

∵ ∠ ADC and ∠ BCD are the bases angles with measure 75°

- AE and BF are ⊥ DC

# In Δ BFC

∵ m∠BFC = 90° ⇒ BF ⊥ CD

∵ m∠C = 75°

∵ BC = 8

∵ sin∠C = BF/BC

∴ sin(75) = BF/8 ⇒ multiply both sides by 8

∴ BF = 8 × sin(75) = 7.73

∵ cos∠C = CF/BC

∴ cos(75) = CF/8 ⇒ multiply both sides by 8

∴ CF = 8 × cos(75) = 2.07

# In Δ BFD

∵ m∠BFD = 90°

∵ DF = CD - CF

∴ DF = 18 - 2.07 = 15.93

∵ BD = √[(DF)² + (BF)²] ⇒ Pythagoras Theorem

∴ BD = √[(15.93)² + (7.73)²] = 17.71

a)

∵ BD is the diagonal of the trapezoid

* The length of the diagonal is 17.71 feet

b)

- The area of any trapezoid is A = 1/2 (b1 + b2) × h, where b1 and b2

  are the barallel bases and h is the height between the two bases

∵ b1 is CD

∴ b1 = 18

∵ b2 is AB

∵ AB = CD - (CF + DE)

∵ ABCD is an isosceles trapezoid

∴ CF = DE

∴ AB = 18 - (2.07 + 2.07) = 13.86

- BF is the perpendicular between AB and CD

∴ BF = h

∴ h = 7.73

∵ A = 1/2 (18 + 13.86) × 7.73 = 123.14

* The area of the trapezoid is 123.14 feet²

Answer:

b=3/8a

Step-by-step explanation:

Have a good night/day<3

To find the equation describing the proportional relationship between A and B, we divide B by A and find that the constant of proportionality is 3/8. Thus, the equation is B = (3/8)A.

To find the equation that describes the proportional relationship between A and B, we can start by examining the given pairs of values. For A = 8, B = 3; for A = 24, B = 9; and for A = 40, B = 15. We observe that as A increases, B increases at a constant rate. This suggests a direct proportionality between A and B.

To determine the constant of proportionality (the rate at which B changes with respect to A), we can divide the values of B by the corresponding values of A. Doing so, we find:

All these ratios reduce to 3/8, which is the constant of proportionality. Therefore, B is 3/8 times A, which we can express as:

B = (3/8)A

This equation represents the proportional relationship between A and B, with the constant of proportionality being 3/8.

Final answer:

The notation h(40)=1820 means that the function h produces an output of 1820 when the input is 40, although additional context is needed to determine what h represents specifically in this scenario.

Explanation:

The expression h(40)=1820 typically means that a function h is being evaluated at the input value of 40, and the output is 1820. This could represent a variety of contexts, such as the height of a rocket in meters at 40 seconds after launch, the amount of money saved after 40 weeks, or any other situation described by a function where the variable h depends on the number 40. Without additional context, it's impossible to say precisely what 1820 refers to, but it is the result of the function h when the input is 40.

Answer:

-28

Step-by-step explanation:

[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]

We going to use PE(MD)(AS).

So P means ( ).

We do have operations to perform in the ( ).

We have [tex]2-2^3[/tex] in the first set of ( ) and (-2) in the second set of ( ).

There are no operations in the second  set containing -2.

So we are just focusing on the [tex]2-2^3[/tex] right now.

You have subtract and exponent here.

Exponents come first in PE(MD)(AS) so we will perform that first.

[tex]2-2^3=2-8=-6[/tex]

Let's go back to the original problem now.

[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]

[tex]-(-6)^2-4 \cdot(-2)[/tex]

Now there are no longer any operations grouped together by use of ( ).

It on to the rest of PE(MD)(AS).

So now we are doing the E part, the exponents.

[tex]-(36)-4 \cdot(-2)[/tex]

Now there is multiplication and subtraction left.

(MD) comes before (AS) so we do the multiplication and then the subtraction.  So I'm going to do 4(-2) now:

[tex]-(36)-(-8)[/tex]

Subtraction is addition of the opposite so you could write:

[tex]-(36)+8[/tex]

We don't really need ( ) around the first number:

[tex]-36+8[/tex]

36-8 is 28 but since 36>8 and 36 has a negative sign on it, the answer is -28.

Answer:

The correct option is A.

Step-by-step explanation:

We need to find the cheapest per month over all.

Assume a month has 30 days.

In option A:

Rent = 11.95 a day

Monthly rent = 11.95 × 30 = 358.5

Total renting amount is 358.5.

In option B:

Lease = 149.00 a month 3180 due at signing

Total amount = 149 + 3180 = 3329

Total leasing amount is 3329.

In option C:

Buying = 16,000

In option D:

Finance = 389.00 /month

The cheapest amount for a month is 358.5 .Therefore the correct option is A.

Answer: renting a car

Step-by-step explanation:

To find the volume of a rectangular prism, multiply the length by the width by the height.

Volume = 2.2 x 3.1 x 1.2 = 8.184 cm^3

All the dimensions are one decimal place, so if you round the answer to one decimal place it would be 8.2 cm^3

To find the volume of a rectangular prism, multiply the length by the width by the height.Volume = 2.2 x 3.1 x 1.2 = 8.184 cm^3All the dimensions are one decimal place, so if you round the answer to one decimal place it would be 8.2 cm^3

Answer:

[tex]\large\boxed{\frac{1}{1}\,\text{or}\,1}[/tex]

Step-by-step explanation:

In this question, we're trying to find the slope with the given points.

To find the slope, we're going to need to sue the slope formula.

Slope formula:

[tex]\text{Slope}=\frac{y2-y1}{x2-x1}[/tex]

You would plug in the coordinates to its right spot.

Plug in -2 to x1, 3 in y1, 2 in x2, and 7 in y2.

Your equation should look like this:

[tex]\text{Slope}=\frac{7-3}{2-(-2)}[/tex]

Now, you will solve:

[tex]\text{Slope}=\frac{7-3}{2-(-2)}\\\\\text{Slope}=\frac{4}{2-(-2)}\\\\\text{Carry the minus sign over to the -2, turning it to a positive 2}\\\\\text{Slope}=\frac{4}{2+2}\\\\\text{Slope}=\frac{4}{4}\\\\\text{Divide}\\\\\text{Slope}=\frac{1}{1}=1[/tex]

When you're done solving, you should get 1.

This means that the slope of the line is 1/1 or 1

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =7\\y_{1} =3\\x_{2} =2\\x_{1} =-2[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{7-3}{2 - (-2)}[/tex]

[tex]\frac{4}{4}[/tex]

^^^This can be further simplified down to...

1

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

f(-5) = -33

Step-by-step explanation:

f(x) = {-x^2+2x+2 if  x ≤  - 5

        {-3/4x+3 if   x > 1

find what f(-5) = ​

If x=-5, we use the first equation

f(-5) =  -x^2+2x+2  since it has the equal to part

       = - (-5)^2 +2(-5) +2

        =  -25 -10+2

        = -35+2

         =-33

Answer:

10.5 units

Step-by-step explanation:

Since M is the centre of the circle. The measure to the edge is the radius.

Which in this case is 10.5 units

Answer: A. 10.5 units

Step-by-step explanation: The answer would be 10.5 units because the radius is equal to half the circle. MS is a radius, and MR is a radius. A radius has one point in the center, and one point on the circle.

Answer:

If the width of the rectangle is x than the length is 4x because 4x*x is 4x^2

Step-by-step explanation:

Answer:

[tex]x_1 = 9[/tex] and [tex]x_2 = 11[/tex].

Step-by-step explanation:

Start by adding 1 to both sides of this equation.

[tex](x - 10)^{2} = 1[/tex].

The square of what number or numbers will lead to the number "1"? It turns out that not only [tex]1^{2} = 1[/tex], but [tex](-1)^{2}= 1[/tex] as well. In other words, the value [tex](x - 10)[/tex] can be either 1 or -1. Either way, the equation is still going to hold. That's the reason why there are two solutions to this equation.

Consider the case when [tex]x - 10 = 1[/tex]. Add 10 to both sides of the equation. [tex]x = 11[/tex].

Now, consider the case when [tex]x - 10 = -1[/tex]. Again, add 10 to both sides of the equation, [tex]x = 9[/tex].

Order the two solutions in an increasing order:

Answer:

22 feet below sea level

Step-by-step explanation:

If she goes down by 20 and back up by 7 the overall effect is going down by 13 and then going down 9 more feet makes it a total of 22 feet.

Answer:22

Step-by-step explanation:

-20+7-9= -22 ft, or 22 ft below sea level

B -median

Hypotenuse is only right triangles and legs are sides of a triangle. A bisector divides something in half evenly . Altitude is height of a triangle and median is the same segment

:

The altitude of an isosceles triangle is the same segment in the triangle as the bisector.

The bisector is a line that divides a line or an angle into two equivalent parts. The bisector of a segment always contains the midpoint of the segment.

In an isosceles triangle,

Bisector of vertex angle = midline of base side = altitude

The altitude of an isosceles triangle is the same segment in the triangle as the bisector.

Option C is correct.

Find out more information about bisector here

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To solve the system of equations x + 3y = 5 and x - 3y = -1, we add both equations to get 2x = 4, solve for x to find x = 2, and then substitute x back into one of the equations to find y = 1, resulting in the solution (2, 1).

The solution of the system of linear equations given by x + 3y = 5 and x - 3y = -1 involves manipulating the equations to find the values of x and y that satisfy both equations simultaneously. One common method to solve these is to add or subtract the equations, which eliminates one variable, making it possible to solve for the other.

Starting with the addition method, we align the equations and add them together:

x + 3y = 5

x - 3y = -1

Adding these equations, we get 2x = 4, and solving for x gives us x = 2. We can substitute x = 2 back into one of the original equations to find the value of y, yielding y = 1.

The solution to the system is the intersection point of the two lines represented by the equations, which is the point (2, 1).

Answer: -1/7

Step-by-step explanation: The reciprocal of -7 is -1/7. Flip -7 to get the answer. -7 is the same as -7/1, so flip the numbers to find the reciprocal.

Answer:

y = - 3x + 10

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 slope m = - 3, hence

y = - 3x + c ← is the partial equation

To find c substitute (4, - 2) into the partial equation

- 2 = - 12 + c ⇒ c = - 2 + 12 = 10

y = - 3x + 10 ← equation of line

Answer:   [tex]y=-3x+10[/tex]

Step-by-step explanation:

The equation of a line in intercept form: [tex]y=mx+c[/tex]

The equation of a line passing through (a,b) and has slope m is given by :_

[tex](y-b)=m(x-a)[/tex]

Similarly, the  equation in slope-intercept form that describes a line through (4, -2) with slope -3 will be :_

[tex](y-(-2))=-3(x-4)\\\\\Rightarrow\ y+2=-3x+12\\\\\Rightarrow\ y=-3x+12-2\\\\\Rightarrow\ y=-3x+10\ \ \text{In intercept form}[/tex]

Hence, the equation in slope-intercept form that describes a line through (4, -2) with slope -3 = [tex]y=-3x+10[/tex]