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3 years ago

10

Each afternoon she goes to the track and divides her time between running and jogging. she spends a total of 2 hours exercising

and does a total of 10 miles. if she runs at 5 miles per hour and jogs at 2.5 miles per hour, how long did she spend on each type exercise?

1 answer:

katrin [286]3 years ago

3 0

I think the spent about an hour and 15 min on running and 45 min on jogging

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In a right triangle, Sin (30 + x) º = Cos (3x) º. What is the value of x?

pogonyaev

Answer:

$x=15^\circ$

Step-by-step explanation:

In a right triangle:

$\sin \theta =cos(90^\circ-\theta) $ (Complementary angles)$

Therefore, given:

$Sin (30 + x) \º = Cos (3x) \º\\30+x+3x=90^\circ\\30+4x=90^\circ\\4x=90^\circ-30^\circ\\4x=60^\circ\\$Divide both sides by 4\\x=15^\circ$

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3 years ago

Write an equation for a function that has vertical asymptotes at x=3 & x=-10

stepan [7]

Answer:

$\frac{5}{ {x}^{2} + 7x - 30}$

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

$0 - x = 3$

$0 - x = - 10$

$0 - ( - 3) = = 3$

$0 - 10 = 10$

So we would represent that's as

$x - 3$

and

$x + 10$

Multiply the two binomial together.

$(x - 3)(x + 10) = {x}^{2} + 7x - 30$

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

$\frac{5}{ {x}^{2} + 7x - 30 }$

7 0

3 years ago

What is the answer to this solution. -7r−4≥ 4r+2

tia_tia [17]

Answer:

The solution is:

$-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}$

Please check the attached line graph below.

Step-by-step explanation:

Given the expression

$-7r-4\ge \:4r+2$

Add 4 to both sides

$-7r-4+4\ge \:4r+2+4$

Simplify

$-7r\ge \:4r+6$

Subtract 4r from both sides

$-7r-4r\ge \:4r+6-4r$

Simplify

$-11r\ge \:6$

Multiply both sides by -1 (reverses the inequality)

$\left(-11r\right)\left(-1\right)\le \:6\left(-1\right)$

Simplify

$11r\le \:-6$

Divide both sides by 11

$\frac{11r}{11}\le \frac{-6}{11}$

Simplify

$r\le \:-\frac{6}{11}$

Therefore, the solution is:

$-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}$

Please check the attached line graph below.

7 0

3 years ago

How to solve this question? Please help me

Maurinko [17]

Answer:

≈ 82 feet

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to calculate distance (d)

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

Here the hypotenuse is the distance (d) between the 2 poles, hence

d² = 80² + 45² = 6400 + 2025 = 8425 ( take the square root of both sides )

d = $\sqrt{8425}$ ≈ 82 feet ( to the nearest foot )

8 0

3 years ago

Help me please, you gonna be my hero

Lisa [10]

The rate of change of the relationship is 6/5

<h3>Rate of change of a line</h3>

The rate of change of a line is also known as the slope of the line. The formula for calculating the slope of a line is expressed as:

Slope =y2-y1/x2-x1

Given the coordinate points (-3,-2) and (2, 4). On substituting;

Slope = 4-(-2)/2-(-3)

Slope =4+2/2+3

Slope = 6/5

Hence the rate of change of the relationship is 6/5

Learn more on rate of change here: brainly.com/question/25184007

#SPJ1

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2 years ago