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3 years ago

What is the solution to the equation 7(a – 10) = 13 – 2(2a 3)?

Mathematics

2 answers:

geniusboy [140]3 years ago

7 0

7(a - 10) = 13 - 2(2a + 3)
7a - 70 = 13 - 4a - 6 = 7 - 4a
7a + 4a = 7 + 70
11a = 77
a = 77/11 = 7
a = 7.

valina [46]3 years ago

3 0

Answer:

$a=7$

Step-by-step explanation:

we have

$7(a-10)=13-2(2a+3)$

Solve for a

$7a-70=13-4a-6$

Group terms that contain the same variable and move the constants to the other side

$7a+4a=13-6+70$

Combine like terms

$11a=77$

Divide by $11$ both sides

$a=7$

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Jackson used the process of completing the square to solve the equation 2x2−12x=−6.

Nikolay [14]

Answer:

$x=3-\sqrt{6},x=3+\sqrt{6}$

Step-by-step explanation:

we are given equation as

$2x^2-12x=-6$

Since, we have to solve it by using complete square

so, firstly we will complete square

and then we can solve for x

step-1:

Factor 2 from both sides

$2(x^2-6x)=-3\times 2$

step-2:

Simplify it

$x^2-6x=-3$

step-3:

Add both sides 3^2

$x^2-6x+3^2=-3+3^2$

now, we can complete square

$(x-3)^2=6$

step-4:

Take sqrt both sides

$(x-3)=-\sqrt{6},(x-3)=\sqrt{6}$

step-5:

Add both sides by 3

we get

$x=3-\sqrt{6},x=3+\sqrt{6}$

3 0

3 years ago

Solve the following equation system by graphing X-Y=4 X+Y=2 What is the solution?

AfilCa [17]

X-Y=4,
X+Y=2
-------------add
2x = 6
x = 3

X - Y =4
3 - Y = 4
Y = 3 - 4
Y = -1

solution (3 , -1)

4 0

3 years ago

A spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. The arrows are congrue

tekilochka [14]

Answer:

Option (c) is correct.

The approximate total area of the plastic triangles on the spinner is 2 × 3.9 square centimeters = 7.7 square centimeters

Step-by-step explanation:

Given:A spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. The arrows are congruent isosceles triangles connected at their bases.

also, Given: The base of each triangle measures 2 centimeters and the perimeter of each triangle is 10 centimeters.

We have to find the approximate total area of the plastic triangles on the spinner.

Perimeter of triangle is the sum of sides.

Since given the triangle to be isosceles .

Let the two equal side be x cm, then,

Perimeter of given triangle = 1 0

⇒ x + x + 2 = 1 0

⇒ 2x = 8

⇒ x = 4

Thus, side of triangle is 4 cm.

Now we find the area of isosceles triangle.

We first find the height, using Pythagoras theorem,

$(AC)^2=(AD)^2+(DC)^2$

Putting values, we get,

$(4)^2=(AD)^2+(1)^2$

Solving we get,

$AD=3.87$

Thus, area of one isosceles triangle $A=\frac{1}{2} bh$

area of one isosceles triangle $A=\frac{1}{2} \times 2 \times 3.87$

On solving we get,

Approximate area of one plastic triangles on the spinner is 3.9 square centimeters.

Thus, the approximate total area of the plastic triangles on the spinner is 2 × 3.9 square centimeters = 7.7 square centimeters

Option (c) is correct.

7 0

3 years ago

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aleksandr82 [10.1K]

Answer:

$\frac{1}{125}$

Step-by-step explanation:

$5^{-3}= \frac{1}{5^{3}} =\frac{1}{125}$

6 0

3 years ago

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xxMikexx [17]

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3 years ago