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3 years ago

Four times the sum of three consecutive integers is 156.Write and solve an equation that will find the smallest integer.

Mathematics

1 answer:

Burka [1]3 years ago

3 0

Answer:

4(x+x+1+x+2)=156, x=12

Step-by-step explanation:

let the numbers be x, x+1 and x+2.

Now,

4(x+x+1+x+2)=156

4(3x+3)=156

divide both side by 4

3x+3=156/4=39

subtract 3 from both sides

3x=39-3

3x=36

divide both sides by 3

x=36/3=12

x=12

Hence, the smallest of the integers is 12.

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3 years ago

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Answer:

The Area of Δ ABC = 219.13

Step-by-step explanation:

The hard part about this problem is finding the area without the height

The formula to do this is Area = $\sqrt{S(S-A)(S-B)(S-C)}$

A, B, C represent the sides

S represents $\frac{1}{2}$ (A + B + C)

In this equation, we will make the base be A, and the other two sides will be B and C

Sides B and C are the same length because they meet at a 90° angle

Lets plug the numbers into the variables

A = 28

B= 21

C= 21

Remember: S represents $\frac{1}{2}$ (A + B + C)

S = $\frac{1}{2}$ (28 + 21 + 21)

S = $\frac{1}{2}$ (70)

S = 35

Lets plug the numbers into the Area Formula now!

Area = $\sqrt{35(35 - 28)(35 - 21)(35 - 21)}$

According to the order of operations, we need to do the calculations in parentheses first

35 - 28 = 7

35 - 21 = 14

14 x 14 x 7 = 1372

1372 x 35 = 48020

$\sqrt{48020}$ = 219.13

The Area of Δ ABC = 219.13

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3 years ago

What is the value of y when x = 43 A. 87 B. 85 C. 49 D. 45

BartSMP [9]

Answer:

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−

Step-by-step explanation:

−

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2 years ago

Fine Floors can install 15 square yards of carpeting in 4 hours and 30 minutes. At this rate, how long would it take to install

AnnZ [28]

D is your awnser here

3 0

3 years ago

Read 2 more answers

Rewrite each equation in vertex form by completing the square. Then identify the vertex.

ioda

ANSWER

Vertex form;

$y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}$

Vertex

$V( - \frac{3}{2} , - \frac{35}{4} )$

EXPLANATION

Given:

$f(x) = 3 {x}^{2} + 9x - 2$

We complete the square as follows:

$y = 3( {x}^{2} + 3x) - 2$

$y = 3( {x}^{2} + 3x + \frac{9}{4} ) - 2 - 3 \times \frac{9}{4}$

The vertex form is:

$y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}$

The vertex is

$V( - \frac{3}{2} , - \frac{35}{4} )$

6 0

3 years ago

Read 2 more answers