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2 years ago

16 increased by twice a number is -24 what is the solution?

Mathematics

1 answer:

Lynna [10]2 years ago

3 0

Let x = the number.

"increased by" tells you we are adding.

"twice a number" tells you 2 times a number.

16 + 2x = - 24

Subtract 16 from both sides so that we have the variable on one sides and the constants on the other.

2x = - 24 - 16

2x = - 40

Divide by 2 to isolate the variable.

x = - 40/2 = - 20

Your solution is - 20.

To check your answer, plug in.

16 + 2(-20) = - 24

16 - 40 = - 24

- 24 = - 24

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-3(5x + 6) + 2 = 2(8 + 8x) - 1

bija089 [108]

So first, we multiply out the brackets.
-15x - 18 + 2 = 17 + 16x -1
Then, bring all the terms onto one side so you can solve.
-15x-18+2-17-16x+1=0
Then, we simplify this.
-31x-32=0
Then, isolate x
-31x=32
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2 years ago

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 17

yawa3891 [41]

--------------------------------------------------------
Equation Given
--------------------------------------------------------
x² + 2x = 17

--------------------------------------------------------
Add the constant to make it perfect square
--------------------------------------------------------
x² + 2x + (2/2)² - ²(2/2)² = 17

--------------------------------------------------------
Evaluate the brackets
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x² + 2x + (1)² - ²(1)² = 17

--------------------------------------------------------
Form the perfect square
--------------------------------------------------------
(x + 1)² - 1 = 17

--------------------------------------------------------
Add 1 to both sides
--------------------------------------------------------
(x + 1)² = 17 + 1
(x + 1)² = 18

--------------------------------------------------------
Square root both sides
--------------------------------------------------------
√(x + 1)² = $\pm$ √18

--------------------------------------------------------
Solve for x
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x = 4.24 - 1 or - 4.24 -1

x = 3.24 or - 5.24 (nearest hundredth)

--------------------------------------------------------
Answer: x = x = 3.24 or - 5.24
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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Help please!!

Pavel [41]

Answer:

1. Left side = 3 inches, Bottom side = 4 inches, Right side = 2 inches, Top side = 5 inches

2. A = 6 inches²

3. A = 8 inches²

4. A = 10 inches²

5. A = 12 inches²

6. A = 36 inches²

7. Left side = 5 cm, Bottom side = 12 cm, Right side = 4 cm, Top side = 13 cm

8. A = 180 cm²

Step-by-step explanation:

1. Label the dimensions of the prism:

Left side = 3 inches

Bottom side = 4 inches

Right side = 2 inches

Top side = 5 inches

2. Area of the red rectangle:

Formula:

LH = A (Length x Height = Area)

A = 3 x 2

A = 6 inches²

3. Area of the blue rectangle:

Formula:

LH = A (Length x Height = Area)

A = 4 x 2

A = 8 inches²

4. Area of the green rectangle:

Formula:

LH = A (Length x Height = Area)

A = 5 x 2

A = 10 inches²

5. (They gave the formula of the two triangles, but the question said green rectangle? They must've meant yellow triangles)

Area of the yellow triangles:

Formula:

2 (1/2 Bh) (2 (half of base x height))

A = 2(1/2 3 x 4)

A = 2(1/2 12)

A = 2(6)

A = 12 inches²

6. Total surface area of the triangular prism:

Formula:

LH + LH + LH + 2 (1/2 Bh) = Surface Area of the triangular prism (Area of the red rectangle + Area of the blue rectangle + Area of the green rectangle + Area of the yellow triangles = Total surface area of the triangular prism)

A = 6 inches² + 8 inches² + 10 inches² + 12 inches²

A = 36 inches²

7. Label the dimensions of the prism:

Left side = 5 cm

Bottom side = 12 cm

Right side = 4 cm

Top side = 13 cm

8. Total surface area of the triangular prism:

First, we can find the area of each shape, as we had previously to find the total area of the net and the surface area of the triangular prism.

Area of the red rectangle:

Formula:

LH = A (Length x Height = Area)

A = 5 x 4

A = 20 cm²

Area of the blue rectangle:

Formula:

LH = A (Length x Height = Area)

A = 12 x 4

A = 48 cm²

Area of the green rectangle:

Formula:

LH = A (Length x Height = Area)

A = 13 x 4

A = 52 cm²

Area of the yellow triangles:

Formula:

2 (1/2 Bh) (2 (half of base x height))

A = 2(1/2 5 x 12)

A = 2(1/2 60)

A = 2(30)

A = 60 cm²

Total surface area of the triangular prism:

A = 20 cm² + 48 cm² + 52 cm² + 60 cm²

A = 180 cm²

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