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2 years ago

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the sum of three numbers is 131. the third number is 4 times the first. the second number is 5 more than the first. what are the

numbers

1 answer:

Sphinxa [80]2 years ago

4 0

Step-by-step explanation:

let the numbers are:

a, b, and c

the equation would be:

a+b+c = 131

c = 4a

b = a+5

=>

a + a+5 +4a = 131

6a +5 = 131

6a = 131-5

6a = 126

a= 126/6

a = 21

b = a+5 = 21+5

b = 26

c = 4a = 4(21)

c = 84

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One cube has an edge length 5 cm shorter than the edge length of the second cube. The volume of the smaller cube is 216 cm?. Wha

VLD [36.1K]

Answer:

The volume of the larger cube is $V=1,331\ cm^3$

Step-by-step explanation:

Let

x ---> the length of the smaller cube

y ---> the length of the larger cube

we know that

the volume of a cube is equal to

$V=b^3$

where

b is the length side of the cube

we have

$x=y-5$ ----> equation A

The volume of the smaller cube is 216 cm^3

so

substitute in the formula of volume

$216=x^3$

solve for x

$x=\sqrt[3]{216}\ cm$

$x=6\ cm$

<em>Find the value of y</em>

$x=y-5$

$6=y-5$

$y=6+5=11\ cm$

<em>Find the volume of the larger cube</em>

$V=y^3$

substitute the value of y

$V=11^3$

$V=1,331\ cm^3$

4 0

3 years ago

Please help me solve this question number 5

Tamiku [17]

Answer:

$(? \times \frac{?}{?} 256 = xy \times \frac{yy {j \times \frac{?}{?} }^{?} }{?}$

4 0

3 years ago

I am so confused on functions! Please help!

Gekata [30.6K]

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3 years ago

Solve the system of equations:

Sophie [7]

The solution of the system of equations is (6 , -7)

Step-by-step explanation:

There are two method to solve the system of equations

Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variable
Substitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable

Let us use the elimination method with your problem

∵ 3x + 2y = 4 ⇒ (1)

∵ 3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

∵ -3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

∴ y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

∴ x = 6

The solution of the system of equations is (6 , -7)

<em>I hope this explanation help you</em>

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

#LearnwithBrainly

3 0

2 years ago

What is the equation of the line that passes through (6, 1) and is perpendicular to the line y 3x+2? CI) At what angle do the li

Andrews [41]

Answer with explanation:

The equation of any line with slope 'm' and passing through any point $(x_1,y_1)$ is given by

$y=mx+(y_1-mx_1)$

As we know that the general equation of a line with slope 'm' is $y=mx+c$

Comparing with the given equation $y=3x+2$ we can conclude slope of the given line is $m_1=3$

Now we know that the product of slopes of perpendicular lines is -1

Mathematically we can write for perpendicular lines

$m_1\times m_2=-1$

Thus the slope of the required line is obtained from the above relation since it is given that they are perpendicular

$3\times m_{2}=-1\\\\\therefore m_{2}=\frac{-1}{3}$

Hence using the given and the obtained values the equation of the required line is

$y=-\frac{1}{3}x+(1-\frac{-1}{3}\times 6)}\\\\y=\frac{-x}{3}+3$

Part b)

The angle of intersection between 2 lines with slopes $m_{1},m_2$ is given by

$\theta =tan^{-1}(\frac{m_2-m_1}{1+m_1m_2})$

Comparing the equations of given lines

$y=6x+3\\\\y=2x+3$

with the standard equation we get

$m_{1}=6\\\\m_{2}=2$

Thus the angle of intersection becomes

$\theta =tan^{-1}(\frac{2-6}{1+2\times6})=17.10$

8 0

3 years ago