Determine the equation of the line that is parallel to y=2/3x+4 and passes through the point (3,7)

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:

pretty sure this is right

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:

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:

z = 44

Step-by-step explanation:

26/z = 13/22

Using cross products

26 * 22 = 13*z

Divide each side by 13

26/13 * 22 = 13z/13

2 *22 =z

44 =z

Answer:

Z=44

To solve this proportion, you have to isolate z. You have to do what you do on one side of the equal sign to the other as well.

Answer:

both the equation and it's inverse are functions

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:

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:

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 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:

  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:

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:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L was drowned

3- 45000L / 50 = 900L

.. ..

Answer:

its simplest form for the question is 2:1

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:

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]c. \: \sqrt{9} . \sqrt{4} [/tex]

[tex] \\ [/tex]

Step-by-step explanation:

[tex] \sqrt{9.4} \\ = \sqrt{9} \times \sqrt{4} [/tex]

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:

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:

x=1.94

x = - 1.94

Step-by-step explanation:

8x² + 5 = 35

Subtract 5 from each side

8x² + 5-5 = 35-5

8x²  = 30

Divide each side by 8

8x² /8 = 30/8

x² = 15/4

Take the square root of each side

sqrt( x²) = ±sqrt(15/4)

x = ±sqrt(15/4)

x=1.93649

x = - 1.93649

To the nearest hundredth

x=1.94

x = - 1.94

Answer:

1.94

Step-by-step explanation:

[tex]8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\[/tex]

≈ ±1.94

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:

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:

2x⁴+x³-x²+54x+56

Step-by-step explanation:

Given the expression length of dylan room =  (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;

Area of rectangle = Length *Width

Area of the rectangle =  (x² – 2x + 8)(2x² + 5x – 7)

Area of the rectangle  = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)

= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)

expanding the bracket

= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56

Collecting the like terms;

= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56

= 2x⁴+x³-x²+54x+56

Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56

Answer:

2x^4+ x^3 - x^2 + 54x - 56 expression represents the area of Dylan’s room

Step-by-step explanation:

C on edge :)

Answer:

  x = 5 is the solution

Step-by-step explanation:

See the attachment for table values.

  f(x) = g(x) for x = 5

The solution to the equation ...

  2.5x -10.5 = 64(0.5^x)

is x = 5.

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:

(f-g)(x)= -x-4

(f.g)(x)= 2x^2 -2x-4

(f+g)(-1) = 3(-1) = -3

Step-by-step explanation:

Hi, to answer this question we have to solve the expressions:

(f-g)(x) =  x-2 -(2x+2)

(f-g)(x)= x-2 -2x-2

(f-g)(x) = -2x+x-2-2

(f-g)(x)= -x-4

(f.g)(x) =  x-2 (2x+2)

(f.g)(x)= 2x^2 +2x-4x-4

(f.g)(x)= 2x^2 -2x-4

(f+g)(x)= x-2 +2x+2

(f+g)(x) = x+2x-2+2

(f+g)(x)= 3x

(f+g)(-1) = 3(-1) = -3

Feel free to ask for more if needed or if you did not understand something.

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.

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:

[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:

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: