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Nikolay [14]
3 years ago
15

Solve the equation: 3(x - 5) = x + 21 ( please help me )

Mathematics
1 answer:
Alex787 [66]3 years ago
5 0

Answer:x=18

Step-by-step explanation:

3(x-5)=x+21

Distribute the 3

3x-15=x+21

Add 15 to each side

3x=x+36

Subtract x from each side

2x=36

Divide each side by 2

x=18

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What is the volume of a prism if the area of its cross-section is 2 m² and its length is 7 m?
DerKrebs [107]

Answer:

14m^3

Step-by-step explanation:

Volume of the prism = base area * height

Given

Area of the cross section = 2m^2

Length = 7m

Substitute

Volume of the prism = 2 * 7

Volume of the prism = 14m^3

Hence the volume of the prism is 14m^3

5 0
3 years ago
Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). Select all the possible coordi
Radda [10]

(1, \sqrt{27})  and (1, - \sqrt{27})

Step-by-step explanation:

Step 1 :

The co ordinates of the given equilateral triangle are A(-2,1) and B(4,1)

The distance between these 2 points is the length of the given triangle

Distance between the 2 points is  \sqrt{(x2-x1)^{2}+ (y2-y1)^{2}} = sqrt (sq(4-(-2)) + sq(1-1)) = 6

Hence the given triangle has 3 equal side of length 6 unit.

Step 2:

The length of the other side should be 6. Let (x,y) be the co-ordinate of the point C

We have then x = 1 (because the perpendicular from C to AB bisects AB we have the point C to have the x co-ordinate as 1)

Also we have the distance between the point B(4,1) and C(1,y) to be 6 as this is an equilateral triangle

Hence \sqrt{(4-1)^{2} + (1-y)^{2 } = 6

=> 9 + 1 + y^{2} -2 y = 6

=> y^{2}-2 y - 26 = 0

=> y = 2± sqrt(4+104) / 2 = 1 ± sqrt(27)

Hence the possible co ordinates of C are (1, \sqrt{27})  and (1, - \sqrt{27})

3 0
4 years ago
Abox in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12
IRISSAK [1]

Answer:

48

Step-by-step explanation:

You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).

6 0
3 years ago
Write this sentence as an equation? <br><br> Six less than 4 times a number gives 18
agasfer [191]

Answer:

6-4 times x=18

btw x=9

4 0
3 years ago
Read 2 more answers
Option 2:<br><br> Find m &lt; C. Show all work.
maksim [4K]

Answer:

m∠C = 28.1°

Explanation:

angle m∠C has opposite angle of 16 and hypotenuse of 34

using sine rule:

\boxed{  sin(C) = \frac{opposite}{hypotenuse}}

sin(C)=\frac{16}{34}

C = sin^{-1}(\frac{16}{34} )

C = 28.07248°

C = 28.1°

5 0
3 years ago
Read 2 more answers
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