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2 years ago

What is the slope of (4,1) and (6,-1)

Mathematics

1 answer:

schepotkina [342]2 years ago

6 0

Answer:

slope = -1

Step-by-step explanation:

you subtract the y-values (-1-1=-2) then subtract the x-values (6-4=2) then divide the sum of the y-values by the sum of the x-values

$\frac{-2}{2}$ which simplifies to a slope of -1

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Determine the missing side length:

ludmilkaskok [199]

The answer is: "3" .
_______________________________
Use the Pythagorean theorem (for right triangles):

a² + b² = c² ;

in which "a = "side length 1" (unknown; for which we which to solve);

"b" = "side length 2" = "√3" (given in the figure) ;

"c" = "length of hypotenuse" = "2√3" (given in the figure);
_____________________________________________________
a² + b² = c² ;

a² = c² − b² ;

Plug in the known values for "c" and "b" ;

a² = (2√3)² − (√3)² ;

Simplify:

(2√3)² = 2² * (√3)² = 2 * 2 * (√3√3) = 4 * 3 = 12 .

(√3)² = (√3√3) = 3 .

a² = 12 − 3 = 9 .

a² = 9

Take the "positive square root" of EACH SIDE of the equation; to isolate "a" on one side of the equation; & to solve for "a" ;

+√(a²) = +√9 ;

a = 3 .
____________________________________
The answer is: "3" .
____________________________________

3 0

3 years ago

Which ordered pairs are solutions to the inequality y−2x≤−3?

My name is Ann [436]

we will proceed to resolve each case to determine the solution

we have

$y-2x \leq -3$

$y\leq2x-3$

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

case a) $(5,-3)$

Substitute the value of x and y in the inequality

$-3\leq2*5-3$

$-3\leq7$ -------> is true

The ordered pair $(5,-3)$ is a solution

case b) $(0,-2)$

Substitute the value of x and y in the inequality

$-2\leq2*0-3$

$-2\leq-3$ -------> is False

The ordered pair $(0,-2)$ is not a solution

case c) $(-6,-3)$

Substitute the value of x and y in the inequality

$-3\leq2*-6-3$

$-3\leq-15$ -------> is False

The ordered pair $(-6,-3)$ is not a solution

case d) $(1,-1)$

Substitute the value of x and y in the inequality

$-1\leq2*1-3$

$-1\leq-1$ -------> is True

The ordered pair $(1,-1)$ is a solution

case e) $(7,12)$

Substitute the value of x and y in the inequality

$12\leq2*7-3$

$12\leq11$ -------> is False

The ordered pair $(7,12)$ is not a solution

Verify

using a graphing tool

see the attached figure

the solution is the shaded area below the line

The points A and D lies on the shaded area, therefore the ordered pairs A and D are solution of the inequality

6 0

3 years ago

Read 2 more answers

Erin has n books. She sold half of her books and then bought 16 more. Which expression represents the number of books Erin has?

Margarita [4]

Answer:

n÷2+16

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Please help with 1 and 2 :)

nordsb [41]

Answer:

1. The domain for the number of fruit cups is 0 minimum and 20 maximum.

[0 < x < 20].

2. [10 < y < 70]

Step-by-step explanation:

1. The domain is 0 to 20 because there are 20 people total who will each have a fruit cup

2. The range is $10 to $70 because the minimum price is $10 without any fruit cups and $70 when there are 20 fruit cups.

4 0

3 years ago

What is the surface area of the prism in square inches?

Kay [80]

Given:

Given that the triangular prism with height 10 inches.

The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.

We need to determine the surface area of the prism.

Surface area of the prism:

The surface area of the prism can be determined using the formula,

$SA=bh+(s_1+s_2+s_3)H$

where b is the base and h is the height of the triangle.

s₁, s₂, s₃ are the side lengths of the triangle and

H is the height of the prism.

Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;

$SA=(12)(5)+(12+5+13)(10)$

$SA=60+(30)(10)$

$SA=60+300$

$SA=360 \ in^2$

Thus, the surface area of the triangular prism is 360 square inches.

Hence, Option b is the correct answer.

8 0

3 years ago