Complete the steps used to slove a system of liner equations by substituting the value of y into one of the original equations to find the value of x. What is the solution?

Answer:

At 2 drinks, the prices are equal. For 1 drink, Western Sizzlin is better since the buffet price is lower. From 3 drinks and up, Golden Corral is better.

Step-by-step explanation:

"Golden Corral charges $11 for a buffet plus $1 for each drink."

d + 11

"Western Sizzlin charges $9 for a buffet plus $2 for each drink."

2d + 9

Set the 2 cost functions equal:

2d + 9 = d + 11

d = 2

At 2 drinks, the prices are equal. For 1 drink, Western Sizzlin is better since the buffet price is lower. From 3 drinks and up, Golden Corral is better.

Answer:

64 : 216

Step-by-step explanation:

Given the ratio of the heights = a : b, then

ratio of volumes = a³ : b³

Here the ratio of heights = 4 : 6 = 2 : 3 ← in simplest form, thus

ratio of volumes = 4³ : 6³ = 64 : 216 = 8 : 27 ← in simplest form

Answer:

both the equation and it's inverse are functions

Answer:

(C)[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]

Step-by-step explanation:

The expression represented by the upper tiles is: [tex]x^2+4x-2[/tex]

The expression represented by the lower tiles is: [tex]x^2-2x+4[/tex]

Adding the two

[tex]x^2+4x-2+(x^2-2x+4)=2x^2+2x+2[/tex]

Writing it as a difference, we have:

[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]

The correct option is C.

Answer:

yeah, what newton said :]

Answer:

  C. (2, 6] hour jobs cost $100

Step-by-step explanation:

Let's consider each of these statements in view of the graph:

Answer:

(0,8) first option     and  50,100 or 200 in the second option

Step-by-step explanation:

Answer with explanation:

After dilation about the origin(0,0) with the scale factor of 'k" , the image of the original point (x,y) becomes (kx,ky)

From the given graph, the coordinates of point C = (0,6)  [Since it lies on y-axis , the x-coordinate is zero]

After a dilation about the origin(0,0) with the scale factor of [tex]\dfrac{1}{2}[/tex], the new point will be [tex](\dfrac{1}{2}\times0,\dfrac{1}{2}\times6)=(0,3)[/tex]

Now plot this point on y-axis at y=3 as given in the attachment.

Answer:

Step-by-step explanation:

A frequency table can be used to group a raw data. It shows the quantity of each variable in the data.

The required answers to the question can be found in the attachments to this answer.

Answer:

4

Step-by-step explanation:

The coordinates are: A(0,0), B(1,4), C(2,8), D(3,12), E(4,16)

Using coordinates B and D, slope = (12 - 4)/(3 - 1) = 8/2

        ∴ slope = 4

Answer:

4

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

the value of x is 6

so the answer is 6

Answer:

answer is 8

Step-by-step explanation:

Answer:

8 ft

Step-by-step explanation:

We can use ratios to solve

tree                          Otis

--------------------  = --------------

tree shadow          Otis shadow

tree                   4 ft

-------------- = ----------------

9 ft                   4.5 ft

Using cross products

4.5 tree = 4* 9

4.5 tree = 36

Divide each side by 4.5

tree = 36/4.5

tree =8

Answer:

[tex]a^{\frac{1}{3} }[/tex]

Step-by-step explanation:

Apply rule:  [tex]\displaystyle \sqrt[n]{x} =x^{\frac{1}{n}[/tex]

[tex]\sqrt[3]{a} =a^{\frac{1}{3} }[/tex]

Answer:

Step-by-step explanation:

When events are independent, the probability of some sequence of them is the product of the probabilities of the individual events in that sequence.

The probability of a child having spina bifida is 16% = 0.16, so the probability that the child will not have the condition is 1 - 0.16 = 0.84. The probability that 0 of 2 children will have spina bifida is ...

  p(0 for 2) = p(0 for 1)×p(0 for 1) = 0.84×0.84 = 0.7056

__

There are two ways that 1 of 2 children can have spina bifida: either the first one does, or the second one does. These are mutually exclusive conditions, so their probabilities add:

  p(1 for 2) = p(1 for 1)×p(0 for 1) +p(0 for 1)×p(1 for 1) = 0.16×0.84 +0.84×0.16

  p(1 for 2) = 0.2688

__

There is one way both children can have spina bifida:

  p(2 for 2) = p(1 for 1)×p(1 for 1) = 0.16×0.16 = 0.0256

__

In summary, our probability distribution is ...

  p(X=0) = 0.7056

  p(X=1) = 0.2688

  p(X=2) = 0.0256

Answer:

The first 3x^2 + 2x is a second degree polynomial, so it's a quadratic binomial (2 terms).  The second 2x^2 - 5x + 3 is a second degree trinomial (3 terms), and the third is a monomial (1 term).  Not sure if that's what you were looking for.

Step-by-step explantion:

Answer:

This means volume of the larger canister is 8 times more than volume of the smaller canister.

This means surface area of the larger canister is 4 times greater than volume of the smaller canister.

Step-by-step explanation:

Smaller canister

Diameter=9cm

Radius=diameter/2

=9/2=4.5cm

Height=12cm

Larger canister (double of the smaller canister)

Radius=4.5*2=9cm

Height=12*2=24cm

Volume=πr^2h

Surface area=2πrh + 2πr^2

Volume of smaller canister=πr^2h

=3.14*(4.5)^2*12

=3.14*20.25*12

=763.02

Surface area of the smaller canister=2πrh + 2πr^2

=2*3.14*4.5*12 + 2*3*14*(4.5)^2

=339.12 + 127.17

=466.29

Volume of larger canister=πr^2h

=3.14*(9)^2*24

=3.14*81*24

=6104.16

Surface area of larger canister=2πrh + 2πr^2

=2*3*14*9*24 + 2*3.14*(9)^2

=1356.48 + 508.68

=1865.16

Compare smaller and larger volume of the canister:

Volume if larger/volume of smaller

=6104.16/763.02

=8

This means volume of the larger canister is 8 times more than volume of the smaller canister

Compare surface area of larger and smaller canister:

Surface area of larger canister/surface area of smaller canister=1865.16/466.29

=4

This means surface area of the larger canister is 4 times greater than volume of the smaller canister

Answer:

Yeah, what she said above.

Step-by-step explanation:

Answer:

pretty sure this is right

Answer:

10a²b²6ab²

Step-by-step explanation:

Distribute the 2ab the other values

Answer:

SAS Postulate (third option)

Step-by-step explanation:

A trick that I use is that s stands for side and a for angle

the picture shows that two sides are the same which means the SS

and one angle is the same, hence the one A

Hope this helps!

Answer:

140 poles

Step-by-step explanation:

1. Convert to the same unit. Either meters to kilometers or kilometers to meters, so you can complete the computation.

2. Divide 0.06 by 8.4 (8.4/0.06 = 140).

3. 140 poles can be placed on the 8.4 km road when separated by 60 m or 0.06 km.

Answer:

[tex]\dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Step-by-step explanation:

[tex] (\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 = [/tex]

[tex] = (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3 [/tex]

[tex] = (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3 [/tex]

[tex]= (\dfrac{1}{x^{16}y^{12}z^{2}})^3[/tex]

[tex]= \dfrac{1}{x^{48}y^{36}z^{6}}[/tex]

Answer:

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Step-by-step explanation:

[tex]\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3[/tex]

[tex]\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }[/tex]

[tex]\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }[/tex]

[tex]\displaystyle \frac{x^{-48} y^{-36}}{z^6 }[/tex]

[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]

Answer:  3.2 yd

Step-by-step explanation:

Notice that TWV is a right triangle.  

Segment TU is not needed to answer this question.

∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6

[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]

Answer:

Step-by-step explanation:

Let length of the garden be ' x + 10 '

Let breath of the garden be ' x '

Area of the garden = 264 ft²

Now, let's find the breath of the garden 'x'

[tex]x(x + 10) = 264[/tex]

Distribute X through the parentheses

[tex] {x}^{2} + 10x = 264[/tex]

Move constant to left and change its sign

[tex] {x}^{2} + 10x - 264 = 0[/tex]

Write 10x as a difference

[tex] {x}^{2} + 22x - 12x - 264 = 0[/tex]

Factor out X from the expression

[tex]x(x + 22) - 12x - 264 = 0[/tex]

Factor out -12 from the expression

[tex]x(x + 22) - 12(x + 22) = 0[/tex]

Factor out X +22 from the expression

[tex](x + 22)(x - 12) = 0[/tex]

When the products of factors equals to 0 , at least one factor is 0

[tex]x + 22 = 0[/tex]

[tex]x - 12 = 0[/tex]

Solve for X

[tex]x + 22 = 0[/tex]

[tex]x = 0 - 22[/tex]

[tex]x = - 22[/tex]

Again,

[tex]x - 12 = 0[/tex]

[tex]x = 0 + 12[/tex]

[tex]x = 12[/tex]

(The dimensions can't be negative. )

So, width = 12 ft

Now, let's find the length of the garden ' X + 10 '

[tex]x + 10[/tex]

Plug the value of X

[tex]12 + 10[/tex]

Calculate the sum

[tex] = 22 \: ft[/tex]

Therefore,

Hope this helps..

Best regards!

Answer:

Yes, the ordered pair is correct.

Explanation:

You can check the if the ordered pair by substituting the values into the equation. If you substitute the ordered pair (1, 3), then you can make sure the ordered pair is correct. The equation with the substitution will be 3 = 1 + 2, which results in the true equation 3 = 3, therefore the ordered pair is correct.

Answer:

c. -1; no

Step-by-step explanation:

The inner product of 2 vector (a,b) and (c,d) is:

(a,b)(c,d) = a*c + b*d

If the inner product is equal to 0,  the vectors are perpendicular.

So, the inner product of (5,2) and (-3,7) is equal to:

 (5, 2)×(-3, 7) = 5(-3) + 2(7) = -1

The inner product is -1, it is different to 0, so the vectors are not perpendicular.

Answer:

Proved.

Step-by-step explanation:

The functions are:

1.) f(x) = 3x - 27 (* I am giving an answer using this equation. Perhaps you did't copy the question well!)

2.) g(x) = [tex]\frac{1}{3} x[/tex] + 9

If two functions are inverses of each other, then:

f(g(x)) = x and g(f(x)) = x situation must be satisfied.

f(g(x)) = 3([tex]\frac{1}{3}x + 9[/tex]) + 27

We simply it to get;

f(g(x)) = x - 27 + 27 = x (*This is correct)

g(f(x)) = [tex]\frac{1}{3}[/tex](3x - 27) + 9 = x - 9 + 9 = x (* This is also correct!)

Answer:

Step-by-step explanation:

In this problem we are going find the natural logarithmic of the numbers involved and solve for x

[tex]ln65-Ln x= 39\\[/tex]

from tables

[tex]4.17-ln x= 39\4.17-39= lnx\\-34.83=lnx\\[/tex]

taking the exponents of both sides we have

[tex]e^-^3^4^.^8^3= x\\x= 7.47[/tex]

Answer:

48 cubes

Step-by-step explanation:

A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1/2 units . how many 1/2 unit cubes does it take to fill the prism

Solution

Volume of a cube=b^3

Where,

b=side length of a cube

b=1/2 units

Volume of a cube=b^3

=(1/2)^3

=1/8 cubic units

Volume of the rectangular prism=6 cubic units

To find out the number of cubes needed to fill the prism, divide the volume of the rectangular prism by the volume of one cube

Number of cubes needed= Volume of the rectangular prism ÷ volume of a cube

=6 ÷ 1/8

=6 × 8/1

=48 cubes

Answer:

[tex]y\ =\ \left|\frac{1}{2}x-2.5\right|+3[/tex]

Step-by-step explanation:

Look at the image below ↓

Answer:

Check below the graph.

Step-by-step explanation:

Hi, for this function, check the graph below:

1) Note that in this function the value outside the brackets points how high the graph will be traced.

2) The value within the brackets, points since it's a negative expression how far to the right the graph will be traced.

Answer:

12 gallons per hour

Step-by-step explanation:

Given the following :

Start time of flight = 9:30 a.m

Arrival time of flight = 1:45p.m

Gallons of gas used during duration of flight = 51 gallons

Number of hours spent during flight:

Arrival time - start time

1:45 pm - 9:30 am = 4hours and 15minutes

4hours 15minutes = 4.25hours

If 4.25hours requires 51 gallons of gas;

Then 1 hour will require ( 51 / 4.25)gallons

= 51 / 4.25

= 12 gallons

Answer:

B C E

Step-by-step explanation:

A

P

E

X

Explanation:

Notice how the input 5 leads to the output 3 when we look at the S(x) function. The inverse will undo this. So that must mean the answer is choice A where we have the input 3 lead to the output 5. In short, the inputs and outputs swap places. This means the domain and ranges swap.