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3 years ago

Rewrite in the simplest terms: 8k - 9(4k +4)

Mathematics

2 answers:

Assoli18 [71]3 years ago

4 0

8k - 9(4k + 4) = 8k - 36k - 36 = -28k - 36

Scrat [10]3 years ago

3 0

Let's rewrite in the simplest term,

→ 8k - 9(4k + 4)

→ 8k - 36k - 36

→ [-28k - 36]

The simplest term is -28k - 36.

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Stephanie has an aquarium that is in the shape of a right rectangular prism, 50 centimetres long, 25 centimetres wide and 30 cen

Bess [88]

To solve this, we are going to use the volume formula for a rectangular prism: $V=lwh$
where
$V$ is the volume of the prism
$l$ is the length of the prism
$w$ is the width of the prism
$h$ is the height of the prism

We are also using the volume of a sphere formula: $V= \frac{4}{3} \pi r^{3}$
where
$V$ is the volume of the sphere
$r$ is the radius of the sphere

Part A: Since she wants a layer of marbles in the bottom of the tank about 5 centimeters deep, the height of this little rectangular prism will be 5 centimeters, so $h=5$ . Since the other measures of our little rectangular prism are the same as the aquarium, $l=50$ and $w=25$ . Lets replace those values in our volume formula:
$V=lwh$
$V=(50)(25)(5)$
$V=6250 cm^{3}$
Now that we know that she wants to cover a volume of 6250 $cm^{3}$ with marbles, lets find the volume of each marble.
We know that the diameter of each marble is 1 cm. Since the radius is of a sphere is half its diameter, $r= \frac{1}{2} =0.5$ . Lets replace that value in our volume formula:
$V= \frac{4}{3} \pi r^{3}$
$V= \frac{4}{3} \pi (0.5)^{3}$
$V=0.52 cm^{3}$
Now, let $x$ the number of marbles she will need to cover a volume of 6250 $cm^{3}$ :
$0.52x=6250$
$x= \frac{6250}{0.52}$
$x=12019.23$
Since we know that each bag of marbles has 500 marbles, we are going to divide the number of marbles she will need by the number of marbles in each bag:
$\frac{12019.23}{500} =24.03$

We can conclude that to fill a layer of 5 cm with marbles, she will need 24 bags of marbles.

Part B: We know that she already have 5 cm of her aquarium filled with marbles, and that she also added water until it’s level is 3 centimeters below the top of the tank, so to find the height of this new rectangular prism, we are going to subtract 5 cm plus 3 cm from the original height of her aquarium:
 $h=30-(5+8)$
$h=30-13$
$h=17cm$
Since the other measures of our little rectangular prism are the same as the aquarium, $l=50$ and $w=25$ . Lets replace those values in our volume formula:
$V=lwh$
$V=(50)(25)(17)$
$V=21250cm^{3}$
Remember that $1litre=1000cm^{3}$ . So:
$(21250cm^3)( \frac{1litre}{1000cm^{3})} =21.25liters$

We can conclude that there are 21.25 liters of water in the tank.

6 0

3 years ago

10x - (2x + 9) = -3 (15 - 4x)

natta225 [31]

Answer:

x=9

Step-by-step explanation:

First, distribute the negative sign, changing (2x+9) to -2x-9

next, distribute. 10x+−2x+−9=(−3)(15)+(−3)(−4x)

then, combine like the like terms (10x+−2x)+(−9)=12x−45

then you get 8x+−9=12x−45, and you will subtract 12x from both sides, resulting in −4x−9=−45. To get -4x by itself, add 9 to both sides

lastly, divide both sides by -4

x=9

8 0

3 years ago

Read 2 more answers

Answer and explanation please?

nignag [31]

The answer would be A. m= -3/5 and b=-4/5
"m= -5-1 divided by 7--3
or, -6/10
or, -3/5.

to find the (B)

(-3,1). y=mx+b or 1=-3/5 × -3+b, or solving for b: b=1-(-3/5)(-3). b=-4/5.(7,-5). y=mx+b or -5=-3/5 × 7+b, or solving for b: b=-5-(-3/5)(7). b=-4/5.See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points(-3,1) and (7,-5)isy=-3/5x-4/5"
Source: webmath

5 0

3 years ago

You paint four walls. Each wall is a rectangle with a length of 20 feet and a height of 10 feet. One gallon of paint covers abou

Sphinxa [80]

Answer:

Step-by-step explanation:

20 x 10= 200 ft

1 gallon is 330 ft

paint 4 walls

200 x 4

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You would need 2.434 gallons of paint.

6 0

3 years ago

Which table represents a linear function?

Anna [14]

Answer:

Step-by-step explanation:

B. y=x+3

1=-2+3

2=-1+3

3=0+3

4=1+3

3 0

3 years ago