All categories

2 years ago

What is the slope / rate of change for 2, 5 and -3, 7

Mathematics

1 answer:

Nady [450]2 years ago

4 0

Answer:

$\displaystyle m=\frac{-2}{5}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS 

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Slope Formula: $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (2, 5)

Point (-3, 7)

Step 2: Identify

x₁ = 2, y₁ = 5

x₂ = -3, y₂ = 7

Step 3: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]: $\displaystyle m=\frac{7-5}{-3-2}$
[Slope] [Fraction] Subtract: $\displaystyle m=\frac{2}{-5}$
[Slope] [Fraction] Rewrite: $\displaystyle m=\frac{-2}{5}$

You might be interested in

Complete the equation to represent finding x, the greater integer. x(x – ) = 143

mart [117]

Answer:

x would equal -11 or 13

Step-by-step Explanation:

x(x - 2) - 143 = 0

x^2 - 2x - 143 = 0

-2x + x^2 = 143

-143 + (-2x) + x^2 = 0

(x - 13)(x + 11)

x - 13 = 0

Add 13 to both sides

x = 13

x + 11 = 0

Subtract 11 from both sides

x = -11

3 0

2 years ago

Can somebody please help me with question number 1

inysia [295]

Answer:

1a: 6.283

b: 51.313

c: 285.1

Step-by-step explanation:

Area of a sector = (angle/360)πr²

Area=(45/360)π(4²)=6.283

Area=(120/360)π(7²)=51.313

Area=(270/360)π(11²)=285.1

6 0

2 years ago

A local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle. In o

Eduardwww [97]

Answer:

(A) $H_0$ : μ = 22 ; $H_A$ : μ ≠ 22

(B) Value of the test statistic = -2.69

Step-by-step explanation:

We are given that a local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle. He takes a random sample of 65 bottles. The mean weight of the passion fruit juice in the sample is 21.54 ounces. Assume that the population standard deviation is 1.38 ounce.

We have to test the accuracy of the bottling process.

(A) Let, NULL HYPOTHESIS, $H_0$ : $\mu$ = 22 ounces {means that an average of 22 ounces of passion fruit juice is used to fill each bottle}

ALTERNATE HYPOTHESIS, $H_A$ : $\mu \neq$ 22 ounces {means that an average of 22 ounces of passion fruit juice is used to fill each bottle}

The test statistics that will be used here is One-sample z-test;

T.S. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean weight of the passion fruit juice = 21.54 ounces

$\sigma$ = population standard deviation = 1.38 ounces

n = sample of bottles = 65

(B) So, test statistics = $\frac{21.54-22}{\frac{1.38}{\sqrt{65} } }$

= -2.69

Hence, the value of test statistics is -2.69.

6 0

2 years ago

What is an equation of the line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ?

Elza [17]

Answer:

y=-2x-3

Step-by-step explanation:

Since our equation is in standard form Ax+By=C we must first manipulate the equation so that we have it in the slope-intercept form such that y=mx+b. Therefore:

$-x+2y=4\\2y=x+4\\\\y=\frac{x+4}{2}\\\\y=\frac{1}{2}x+2$

Therefore, our slope is 1/2 and our y-intercept is 2. Now in order to determine a perpendicular line to the one stated above we must then get the negative inverse of our slope meaning $\frac{1}{2}=-2$ (negative reciprocal). Now we must use the point slope formula: