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3 years ago

Given the linear function with a slope of -7/3 and a y intercept of 10, what is the equation in slope intercept form?

Mathematics

1 answer:

irinina [24]3 years ago

3 0

Answer:

y = -7/3x + 10

Step-by-step explanation:

Slope Intercept form:

y = mx + b

Where m = the slope and b is the y-int.

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Simplify this complex fraction

Rufina [12.5K]

Answer:

1/4

Step-by-step explanation:

2/4 ÷ 2

Copy dot flip

2/4 * 1/2

We can cancel the 2 in the numerator and denominator

1/4 * 1/1

1/4

4 0

3 years ago

Find sin^4(a) + cos^4(a), if cos(a) + sin(a) = 1/3

Nadya [2.5K]

Answer:

49/81

Step-by-step explanation:

[cos(a) + sin(a)]^2 = (1/3)^2

(cos(a))^2 + 2sin(a)cos(a) + (sin(a))^2 = 1/9

(sin(a))^2 + (cos(a))^2 = 1

1 + 2sin(a)cos(a) = 1/9

2sin(a)cos(a) = -8/9

sin(a)cos(a) = -4/9

[cos(a) + sin(a)]^4 = (1/3)^4 = 1/81

(cos(a))^4 + 4sin(a)×(cos(a))^3 + 6×(sin(a))^2×(cos(a))^2 + 4(sin(a))^3×cos(a) + (sin(a))^4 = 1/81

(cos(a))^4 + (sin(a))^4 + 4sin(a)cos(a)((cos(a))^2 + (sin(a))^2) + 6(sin(a)cos(a))^2 = 1/81

cos(a))^4 + (sin(a))^4 + 4sin(a)cos(a)(1) + 6(sin(a)cos(a))^2 = 1/81

(cos(a))^4 + (sin(a))^4 + 4(-4/9) +6((-4/9)^2) = 1/81

(cos(a))^4 + (sin(a))^4 - 16/9 + 6(16/81) = 1/81

(cos(a))^4 + (sin(a))^4 = 1/81 + 16/9 - 6(16/81)

(cos(a))^4 + (sin(a))^4 = 49/81

3 0

3 years ago

What is the slope passing through the points (6,5) and (5,3)

Rus_ich [418]

Answer:

$m=2$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

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

Step-by-step explanation:

Step 1: Define

Point (6, 5)

Point (5, 3)

Step 2: Find slope m

Substitute [SF]: $m=\frac{3-5}{5-6}$
Subtract: $m=\frac{-2}{-1}$
Divide: $m=2$

5 0

3 years ago

a motorboat travels 371 kilometers in 7 hours going upstream. it travels 525 kilometers going downstream in the same amount of t

e-lub [12.9K]

Answer:

Speed of boat in still water = 64 km/hr

Speed of the current = 11 km/hr

Step-by-step explanation:

Let the speed of motorboat in still water = x km/hr

Let the speed of current = y km/hr

Motorboat travels 371 km in 7 hours going upstream.

Speed of motorboat while going upstream = speed of motorboat in still water - speed of current = (x-y)

=> $x-y = \frac{371}{7}$

=> $x-y = 53$ ------------------------------(1)

Motorboat travels 525 km in 7 hours going downstream.

Speed of motorboat while going downstream = speed of motorboat in still water + speed of current = (x+y)

=> $x+y = \frac{525}{7}$

=> $x+y = 75$ -----------------------------(2)

Solving for x and y from (1) and (2):

Adding (1) and (2):

2x = 128

=> x = 64

Substituting the value of x in (1), y = 11

6 0

3 years ago

Find the range 19, 21, 18, 17, 18, 22, 46

rewona [7]

Answer:

46-17=29

Step-by-step explanation:

LARGEST VALUE:46

SMALLEST VALUE: 17

7 0

3 years ago