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ollegr [7]
3 years ago
14

What is 42= -7 × (z - 3)?

Mathematics
2 answers:
MArishka [77]3 years ago
6 0

Answer:

z=3

Step-by-step explanation:

42=−7(z−3)

Simplify both sides of the equation.

42=−7(z−3)

42=(−7)(z)+(−7)(−3)(Distribute)

42=−7z+21

Flip the equation.

−7z+21=42

Subtract 21 from both sides.

−7z+21−21=42−21

−7z=21

Divide both sides by -7.

-7z/-7=21/7

z=3

Agata [3.3K]3 years ago
3 0

Answer:

z=-3

Step-by-step explanation:

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Seven people meet and shake hands with one another. how many handshakes occur ?
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49 shakes in total. 7x7=49
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3 years ago
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4. The students in Mr. Michael’s art class are decorating a booth for Harvest Day. They have blue cloth that is 60 inches long,
MrRissso [65]

Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches.

<u>a.</u>  

As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find <u>GCF(greatest common factor) of 60, 48 and 72. </u>

First we will factor out all three numbers completely......

60=2*2*3*5\\ \\ 48=2*2*2*2*3\\ \\ 72=2*2*2*3*3

The common factors are: 2, 2 and 3

Thus the GCF = 2*2*3=12

So, the greatest possible length of the pieces without having any cloth left over will be 12 inches.

<u>b. </u>  

For finding the number of pieces for each color cloth, we will just <u>divide the length of each cloth by 12</u>. So...

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Number of pieces for white cloth =\frac{72}{12}=6

4 0
3 years ago
|9x-7|=|6x+3| Solve the inequality
dexar [7]

Answer:

x = 4/15 and x= 10/3

Step-by-step explanation:

|9x-7|=|6x+3|

There are two solutions, one positive and one negative.

(9x-7)=6x+3                   - (9x-7)=6x+3

We will take the positive one first

(9x-7)=6x+3

Subtract 6x from each side

(9x-6x-7)=6x-6x+3

3x -7=3

Add 7 to each side

3x-7+7 = 3+7

3x = 10

Divide by 3x/3 = 10/3

x = 10/3


Now we will take the negative solution

- (9x-7)=6x+3

Distribute the negative sign

-9x+7 = 6x+3

Add 9x to each side

-9x+9x+7 = 6x+9x+3

7 = 15x+3

Subtract 3 from each side

7-3 = 15x +3-3

4 = 15x

Divide by 15 on each side

4/15 =15x/15

4/15 =x

8 0
3 years ago
an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a
viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  \mathbf{\dfrac{dh}{dt}  = \dfrac{-25}{100  \pi} \  \ ft/s}

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

\dfrac{h}{r}= \dfrac{20}{8}    ( similar triangle property)

\dfrac{h}{r}= \dfrac{5}{2}

\dfrac{h}{r}= 2.5

h = 2.5r

r = \dfrac{h}{2.5}

The volume of the water in the tank is represented by the equation:

V = \dfrac{1}{3} \pi r^2 h

V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h

V = \dfrac{1}{18.75} \pi \ h^3

The rate of change of the water depth  is :

\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\  \dfrac{dh}{dt}

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

\dfrac{dv}{dt}= - 4  \ ft^3/sec

Therefore,

-4 = \dfrac{\pi r^2}{6.25}\  \dfrac{dh}{dt}

the rate of change of the water at depth h = 10 ft is:

-4 = \dfrac{ 100 \ \pi }{6.25}\  \dfrac{dh}{dt}

100 \pi \dfrac{dh}{dt}  = -4 \times 6.25

100  \pi \dfrac{dh}{dt}  = -25

\dfrac{dh}{dt}  = \dfrac{-25}{100  \pi}

Thus, the rate of change of the water depth when the water depth is 10 ft is;  \mathtt{\dfrac{dh}{dt}  = \dfrac{-25}{100  \pi} \  \ ft/s}

4 0
3 years ago
Rewrite the expression in the form a^n
Marianna [84]

Answer:

a7/5

Step-by-step explanation:

3 0
2 years ago
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