4(x+15)=640 what does x equal?

The equation of a straight line is 2y+6x=-8.find the gradient of the line

Illusion [34]

Step-by-step explanation:

Y= mx + c

2y = 3x - 8

2y = -3× - 8 ( divide all yerms by two )

y = -3 × 4

2

y = -3

2

7 0

3 years ago

The difference between the areas of the figures is less than 4.

coldgirl [10]

Answer:

1. |40 – 4x| < 4

2. 9 < x < 11

Step-by-step explanation:

We'll begin by calculating the area of each figure. This can be obtained as follow:

For triangle:

Area = ½ × base × height

Base = 8

Height = 6

Area =?

Area = ½ × 8 × 6

Area = 4 × 6

Area = 24

For Rectangle:

Area = length × breadth

Length = x – 4

Breadth = 4

Area =?

Area = (x – 4) × 4

Area = 4x – 16

Summary:

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

1. Writing an absolute value for the inequality.

From the question given above, we were told that the difference between the areas of the figures is less than 4. This can be written as:

Aₜ – Aᵣ < 4

Area of triangle (Aₜ) = 24

Area of rectangle (Aᵣ) = 4x – 16

24 – (4x – 16) < 4

Simplify

24 – (4x – 16) < 4

Clear bracket

24 – 4x + 16 < 4

24 + 16 – 4x < 4

40 – 4x < 4

Thus, we can write the absolute value for the above inequality as:

|40 – 4x| < 4

2. Determination of the solution of the inequality.

This is illustrated below:

|40 – 4x| < 4

Thus the above equation can be written as

– 4 < 40 – 4x < 4

Subtract 40 from both side

– 4 – 40 < 40 – 4x – 40 < 4 –40

– 44 < – 4x < – 36

Divide through by –4

– 44/–4 < x < – 36/–4

11 > x > 9

Note: the inequality sign changed because we divided by a negative number

Thus, 11 > x > 9 becomes 9 < x < 11

Therefore, the solution to the inequality is 9 < x < 11

3 0

4 years ago

Need help with this one

Misha Larkins [42]

The number of real solution of the system y = $3x^2$ and y = 3x - 2 is zero

The system of equations are

y = $3x^2$

y = 3x - 2

Then the equation will be

$3x^2$ = 3x - 2

Move 3x - 2 to the left hand side of the equation

$3x^2$ - 3x + 2 = 0

Find the value of $b^2$ - 4ac

Here value of a = 3

The value of b = -3

The value of c = 2

Substitute the values in the expression

= $(-3)^2$ - 4×3×2

= 9 - 24

= -15

Here the value of $b^2$ - 4ac is -15

Therefore there is no real valued solution

Hence, the number of real solution of the system y = $3x^2$ and y = 3x - 2 is zero

Learn more about real solution here

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7 0

1 year ago

The bar graph shows a company’s income and expenses over the last 5 years. Which statement is supported by the information in th

tia_tia [17]

Answer:

B

Step-by-step explanation:

Kinda hard to explain but I'm pretty sure it's B

6 0

3 years ago

Find the solutions of the following equations by extracting square roots 9x2-16=0 (z-2)2-36=0

natta225 [31]

The solutions of the equation $9x$ ² - 16 = 0is 4/3 and -4/3 and that of the equation $(z - 2)^{2} - 36 = 0$ is 8 and -4.

Solving the both quadratic equations by extracting square roots:

$9x^{2} - 16 = 0$

⇒ $9x^{2} = 16$

∴ On taking square-root of both sides, we get

$\sqrt{9x^{2} }$ = $\sqrt{16}$

⇒ $3x =$ $+4$ and $3x = -4$

⇒ $x$ = 4/3 and $x$ = -4/3

For the equation, $(z - 2)^{2} - 36 = 0$ , the solution is:

$(z - 2)^{2} - 36 = 0$

⇒ $(z - 2)^{2} = 36$

∴ On taking square-root of both sides, we get

$\sqrt{(z - 2)^{2} } = \sqrt{36}$

⇒ (z - 2) = 6 and (z - 2) = -6

⇒ z = 6 +2 and z = -6 + 2

⇒ z = 8 and z = -4

The solution of the equation $9x^{2} - 16 = 0$ is 4/3 and -4/3.

The solution of the equation $(z - 2)^{2} - 36 = 0$ is 8 and -4.

For similar equation, visit here:

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7 0

2 years ago