You rotate triangle ABC, with vertices A(-3, 1), B(-2, 2), and C(-3, 4), 90° counterclockwise about the origin to form triangle A′B′C′. Match each vertex of triangle A′B′C′ to its coordinates.

The values of a, b, and c are needed to write the equation's general form will be a = 1; b = -3; c = 0.Option A is corect.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given equation;

x²-3x=0

The quadratic equation in the form is;

ax² + bx + c = 0

On putting the values of the options one by one we will get the answer;

1 x²+(-3)x+0

x²-3x=0

Hence, option A is corect.

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Answer:

Answer:

1.8 hrs

Step-by-step explanation:

1.2 hr = 20 km/hr

A hr = 30 km/hr

(cross multiply)

30 x 1.2 = 20 x A

(30 x 1.2) / 20 = A

on simplifying...

1.8 = A

Therefore, it takes 1.8 hrs to travel 30 km/hr

[this is totally my method]

The statement about using the line of best fit for the given scatter plot is; False

When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.

Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.

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The value of m will be; m  = (-∞ , - 15/4) ∪ ( 1 , ∞ ).

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given: line y = mx  + 3 intersects the line 3x + 4y + 12 = 0 at two distinct points.

To find the set of values of m.

The system of equations are;

y = mx  + 3

3x + 4y + 12 = 0

The intersection point are (1, −15/4)

So, the value of m will be

m  = (-∞ , - 15/4) ∪ ( 1 , ∞ )

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Answer:

2.4 hours

Step-by-step explanation:

Because 1 hour Randy clean 1/4 of the room and Trey is 1/6. So we add both together and get that they clean 5/12 of the office in one hour. So 2.4 hours is the greatest amount of time it would take them to clean offices together

Solution 1 :-

>> -3 (3 - x) = 2x + 5

>> -3 × (3 - x) = 2x + 5

>> -9 + 3x = 2x + 5

>> 3x - 2x = 9 + 5

>> x = 14

Solution 2 :-

>> -6 - 9p = 3p

>> -9p - 3p = 6

>> -12p = 6

>> p = -1/2

Solution 3 :-

>> -5 (-4 - a) = 3a + 8

>> -5 × (-4 - a) = 3a + 8

>> 20 + 5a = 3a + 8

>> 5a - 3a = 8 - 20

>> 2a = -12

>> a = -12 / 2

>> a = -6

Solution 4 :-

>> s - 6 = -5s

>> s + 5s = 6

>> 6s = 6

>> s = 6 / 6

>> s = 1

Answer:

1) x = 14

2) p = - [tex]\frac{1}{2}[/tex]  (- 1/2)

3) a = -6

4) s = 1

work shown in image :)

hope this helps!!

Answer:

that means that the new ones contains c-14*32/100

Hope This Helps!!!

Answer:

y = 4x - 12

Step-by-step explanation:

It looks like you're saying

[tex]f(x) = ax^2 + bx + c[/tex]

and you're asked to find [tex]a,b,c[/tex] given [tex]f(0)=-4[/tex], [tex]f(1)=-1[/tex], and [tex]f(-1)=-5[/tex].

Evaluate [tex]f[/tex] at the three given points:

[tex]x=0 \implies f(0) = \boxed{c = -4}[/tex]

[tex]x=1 \implies f(1) = -1 = a + b + c \implies a+b = 3[/tex]

[tex]x=-1 \implies f(-1) = -5 = a - b + c \implies a - b = -1[/tex]

[tex](a+b) + (a-b) = 3 + (-1) \implies 2a = 2 \implies \boxed{a=2}[/tex]

[tex]a-b = -1 \implies \boxed{b=3}[/tex]

and the mapping is [tex]f(x) = 2x^2 + 3x - 4[/tex].

Option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

As we know the line of best is represented by:

y = mx + c

Here m is the slope and c is the y-intercept.

A scatter plot is made to model the amount of money left to pay on a mortgage.

Every month that passes, the amount left to pay decreases.

Plug x = 0 to get the y-intercept

y = c

The y-intercept representing the original amount of the mortgage.

Thus, option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 4x-3+5=2x+7-8x \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Simplify \ both \ sides \ of \ the \ equation. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{4x+2=-6x+7 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Add \ 6x \ to \ both \ sides.} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Subtract \ 2 \ from \ both \ sides. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Divide \ both \ sides \ by \ 10.} \end{gathered}$}[/tex]

↓

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Verification} \end{gathered}$}[/tex]

[tex]\sf{4\times\dfrac{1}{2}-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

[tex]\sf{\dfrac{4}{2}-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

[tex]\sf{2-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

Cancel 2

[tex]\sf{2-3+5=1+7-8\times\dfrac{8}{2} }[/tex]

[tex]\sf{2-3+5=1+7-\dfrac{8}{2} }[/tex]

[tex]\sf{2-3+5=1+7-4 }[/tex]

[tex]\sf{-1+5=1+7-4}[/tex]

[tex]\sf{4=1+7-4}[/tex]

[tex]\sf{4=8-4}[/tex]

[tex]\sf{4=4}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Checked} \end{gathered}$}[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

h = A / ( 1/2 a - 1/2 b)

Step-by-step explanation:

A = ½ ah - ½ bh

Factor out an h

A = h( 1/2 a - 1/2 b)

Divide each side by ( 1/2 a - 1/2 b)

A / ( 1/2 a - 1/2 b) = h ( 1/2 a - 1/2 b)/ ( 1/2 a - 1/2 b)

A / ( 1/2 a - 1/2 b) = h

h = A / ( 1/2 a - 1/2 b)

Answer:

I'm pretty sure its a since if the exponints negite they drop the the bottom and non of the others look right

Hope This Helps!!!

Answer:

1/r^7  + 1/s^12

Step-by-step explanation:

See attached image.

Answer:

[tex]\mathsf {11 \frac{1}{5} }[/tex] tons of concrete

Step-by-step explanation:

Here we need to divide fractions.

Concrete made :

Answer: 1230

Step-by-step explanation:

[tex]V=\frac{1}{3}(\pi)(r^{2)h=\frac{1}{3}(\pi)(7^{2})(24) \approx \boxed{1230 \text{ cm}^{3}}[/tex]

Answer:

Nobody likes a short, one-word-answer. Let’s make sure other people understand everything.

Step-by-step explanation:

By lisa Simpson

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4(5x-3)+12

-20x+12+12

20x+24

my answer is 20x+24.

The simplified form of the given expression -4(5x-3)+12 would be 20x+24.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

-4(5x-3)+12

Open the bracket

-20x+12+12

Solve the like terms;

20x+24

Hence, the simplified form of the given expression -4(5x-3)+12 would be 20x+24.

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There are two triangles in the figure(triangular prism) option third is correct.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

The complete question is:

How many triangles are needed to draw the net of this object?

For the figure please refer to the attached picture.

As we can see in the figure we have given a triangular prism:

The triangular prism has two triangles.

A triangle for the base of the prism and a triangle for the top of the prism.

The lateral faces of the prism are rectangular.

Thus, there are two triangles in the figure(triangular prism) option third is correct.

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Answer:

A) 9

Step-by-step explanation:

⇒ Circumference of a Circle = 2πr

[tex]36=2\pi r[/tex]

[tex]r=\frac{36}{2} \pi[/tex]

[tex]r=\frac{18}{\pi }[/tex]

Length of arc = rθ

θ = angle AC = [tex]90^o[/tex]

Convert [tex]90^o[/tex] to radian

= [tex]\frac{90\pi }{180}[/tex]

= [tex]\frac{\pi }{2}[/tex]

length of arc = 18/π x π/2

= 9

Answer: 72 cubic inches

Step-by-step explanation:

The formula for the volume of a cone: [tex]\dfrac{1}{3}\pi r^{2}h[/tex]

Formula for the volume of a cylinder: [tex]\pi r^{2}h[/tex]

We are given that a cylinder should fit exactly inside the cone

Upon comparing the two equations above, we get:

[tex]$$Volume of cone = \dfrac{1}{3}\text{Volume of cylinder}[/tex]

Since we are given the volume of cone is 24 cubic inches, we can write down the below:

[tex]24 = \dfrac{1}{3}\text{Volume of cylinder }\\ \text{Volume of cylinder = 72 cubic inches}[/tex]

Therefore, we can conclude that if the volume of the cylinder is 72 cubic inches, then the cone with volume of 24 cubic inches can fit exactly in.

Answer:

[tex]V_{cylinder}=72\:in^3[/tex]

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

Since tangent is opposite/adjacent,

Tan 40 in this case would be x/3.8 (i used x because we don't know what the value is)

So, you set it up as an algebra problem

Tan40 = x/3.8

Multiply both sides by 3.8

3.8tan40 = x, Option A

And then, angle E is 50 degrees

So tan 50 = 3.8/x

Multiply both sides by x

tan50x = 3.8

Divide both sides by tan50

x= 3.8/tan50

So, A and D are both correct

The optimal ticket price is $ 65.The amount of tickets sold is 39000 and the amount of the extra revenue will be $ 135000.

What is the objective function?

The objective function is simply an equation that represents the goal production capability that relates to maximizing profits from manufacturing.

Current revenue;

⇒ 80 × 3000 = 240000

From the given condition the price decrease by 0.5 times. So that the ticket sold will be 300 times the cost. The inequality relationship is found as;

30000+300x  49282

x≤64

The revenue value is found as;

y = ( 80 - 0.5 x )(30000+300 x)

y=-150 x²+9000 x+2400000

The value of x is found as;

[tex]\rm x= \frac{9000}{150 \times 2 }\\\\ x=30[/tex]

Hence, the optimal ticket price is $ 65.The amount of tickets sold is 39000 and the amount of the extra revenue will be $ 135000.

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Answer:

Jim:  2/9

Step-by-step explanation:

8/9-4/6

48/54-36/54          [Convert each fraction to a common denominator:  54

                              Multiply (8/9)*(6/6)=48/54;  Multiply (4/6)*(9/9) = 36/54]

 48/54-36/54 = 12/54

12/54 can be reduced to 2/9

Jim also has 2/9

Sue- 8/9-4/6=4/3 or 1 1/3:  Sue subtracted both the numerator and denominator.  This is not correct.

Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9:  Good Job Jim

Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27:  Bob converted both denominators to 54, but did not multiply the numerators by the same numbers.  Bad Bob.

Answer:

70.04 cm²

Step-by-step explanation:

Area = base x height

10.3 x 6.8 = 70.04

Hope this helps :)

Answer:

The function is even because of symmetry over x axis

Answer:

Step-by-step explanation:

Pretty sure that is the answer.

The set {(10,5), (-10,-5), (5,10), (-5,-10)} represents a function , Option D is the correct answer.

The correct option 4 is

{(10,5), (-10,-5), (5,10), (-5,-10)}

A function is a law that states relation between a dependent variable and an independent variable .

For a data to satisfy being a function ,

For every individual value of x , there should be one value of y

If there are two values for a single x then the data set doesn't represent a function but it shows a relation.

For Option 1,2 and 3 , for the same value of x there are two values of y and in only the last set the value is different.

Therefore the set {(10,5), (-10,-5), (5,10), (-5,-10)} represents a function

Option D is the correct answer.

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Answer:

x=0

Step-by-step explanation:

[tex]4 \cos(x) = - \sin {}^{2} (x) + 1[/tex]

[tex]4 \cos(x) = 1 - \sin {}^{2} (x) [/tex]

[tex]4 \cos(x) = \cos {}^{2} (x) [/tex]

[tex]4 \cos(x) - \cos {}^{2} (x) = 0[/tex]

[tex] \cos(x) (4 - \cos(x) ) = 0[/tex]

[tex] \cos(x) = 0[/tex]

[tex]x = 0[/tex]

[tex]4 - \cos(x) = 0[/tex]

[tex] \cos(x) = 4[/tex]

There is no solution here because cosine is undefined it the range is not between -1 and 1 so the only answer is 0.