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3 years ago

The points (-9, -10) and (-2,-5) form a proportional relationship. Find the slope of the

Mathematics

1 answer:

kondaur [170]3 years ago

8 0

Answer:

$m=\frac{5}{7}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (-9, -10)

Point (-2, -5)

Step 2: Find slope m

Substitute: $m=\frac{-5+10}{-2+9}$
Add: $m=\frac{5}{7}$

And we have our final answer!

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Kyra has a rock collection. When she puts her rocks into 2 equal plies, there are no rocks left over. When she puts her rocks in

Nat2105 [25]

Step-by-step explanation:

According to this description we need a number that can be divided by 2,3 and 4 since the amount of rocks can be described by a natural number. However if a number is divided by 4 it is divided by 2 as well since 2*2=4.

$\frac{x}{4} = \alpha \\ \frac{x}{2} = 2 \alpha$

If α is a natural number then 2*α is a natural number as well as the product of two natural numbers.

Which means that we need a number devided by 3 and 4.

The smallest number that fulfills this demand is 3*4=12.

Also any product of 12 with any natural number can be devided by 3, 4 and 2.

If the exercise asks for the numbers that are divided only by 2,3 and 4 these are:

${3}^{ \alpha } \times 12 \: and \: {4}^{ \alpha } \times 12 \: \\ where \: \alpha \: belongs \: to \: the \: set \: of \: all \: \\ natural \: numbers$

8 0

3 years ago

Name the binomial you can multiply by (x + 9) to get the product x^2 + 5x- 36

SpyIntel [72]

If you would like to solve (x^2 + 5x - 36) / (x + 9), you can do this using the following steps:

a = ?
(x + 9) * (x + a) = (x^2 + 5x - 36)
x^2 + ax + 9x + 9a = x^2 + 5x - 36
ax + 9x = 5x
a + 9 = 5
a = 5 - 9
a = - 4

The correct result would be x - 4.

5 0

3 years ago

A kid traveled a distance of 9 km by bike, and then walked a distance of km.

vichka [17]

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question;

A kid traveled a distance of 9 km by bike, and then walked a distance of x km.

a.Find the total distance traveled in terms of x

b. If the total distance was less than 30 km, form an inequality in x, and

then solve it!

a) Total distance = distance travelled by bike + distance walked

Total distance = 9km + xkm

Total distance = (9+x)km

b) If the total distance was less than 30 km, the inequality representing this is;

9+x < 30

Subtract 9 from both sides;

9+x-9 < 30-9

x < 21

hence the solution to the inequality is x< 21

3 0

3 years ago

ted runs two-thirds as fast as frank. in 2hr frank runs 8mi farther than ted. how fast does each run?

charle [14.2K]

Answer:

In 2 hr Frank runs 8 mi farther than Ted

Step-by-step explanation:

7 0

3 years ago

Use a graphing calculator and a system of equations to find the roots of the equation. x4 − 4x3 = 6x2 − 12x From least to greate

iren [92.7K]

Answer:

The roots are -2 , 0 , (3 - √3) , (3 + √3)

The integral roots are -2 , 0

Step-by-step explanation:

∵ x^4 - 4x³ = 6x² - 12x

∴ x^4 - 4x³ - 6x² + 12x = 0

∴ x(x³ - 4x² - 6x + 12) = 0

∴ x = 0

∴ x³ - 4x² - 6x + 12 = 0

∵ f(-2) = (-2)³ - 4(-2)² - 6(-2) + 12 = -8 - 16 + 12 + 12 = 0

∴ (x + 2) is a factor of the equation x³ - 4x² - 6x + 12 = 0

∴ (x³ - 4x² - 6x + 12) ÷ (x + 2) = (x² - 6x + 6)(x + 2)

∴ (x² - 6x + 6)(x + 2) = 0

∴ x + 2 = 0 ⇒ ∴ x = -2

∴ x² - 6x + 6 = 0 ⇒ quadratic equation (ax² + bx + c = 0)

∵ a = 1 , b = -6 , c = 6

∵ $x=\frac{-b+\sqrt{b^{2}-4ac}}{2a}=\frac{6+\sqrt{36-24}}{2}=\frac{6+2\sqrt{3}}{2}=3+\sqrt{3}$

∴ x = 3 + √3 and x = 3 - √3

∴ The roots are -2 , 0 , (3 - √3) , (3 + √3)

6 0

3 years ago

Read 2 more answers