Of the 800 participants in a marathon, 120 are running to raise money for a cause. How

A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of

Elanso [62]

How many miles did the cars go? You can’t solve the question without that.

6 0

3 years ago

Read 2 more answers

Find the equation of the line that is perpendicular to the given line and passes through the given point. Enter the right side o

disa [49]

$Let\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\ k:y=\dfrac{3x-12}{2}=\dfrac{3x}{2}-\dfrac{12}{2}=\dfrac{3}{2}x-6\to m_1=\dfrac{3}{2}\\\\l:y=mx+b\to\dfrac{3}{2}m=-1\qquad|\cdot\dfrac{2}{3}\\\\m=-\dfrac{2}{3}\\\\l:y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (9, 9) to the equation of the line}\ l:\\\\9=-\dfrac{2}{3}(9)+b\\\\9=-2(9)+b\\\\9=-18+b\qquad|+18\\\\b=27\\\\y=-\dfrac{2}{3}x+27\to y=-\dfrac{2x}{3}+\dfrac{27\cdot3}{3}\to\boxed{y=\dfrac{-2x+81}{3}}$

3 0

3 years ago

What is the measure of SQ? 1. 95 2. 190 3. 265 4. 360

Vesnalui [34]

Answer:

The measure of arc SQ is 95° ⇒ (1)

Step-by-step explanation:

The measure of any circle is 360°

The measure of the subtended arc to an inscribed angle is twice the measure of this angle

In the given circle

∵ S lies on the circumference of the circle

∴ ∠QSR is an inscribed angle

∵ ∠QSR is subtended by arc QR

→ By using the 2nd rule above

∴ m arc QR = 2 × m∠QSR

∵ m∠QSR = 95°

∴ m arc QR = 2 × 95

∴ m arc QR = 190°

→ By using the 1st rule above

∵ m of the circle = m arc QR + m arc SQ + m arc SR

∵ m arc SR = 75° and m arc QR = 190°

→ Substitute them in the equation above

∴ 360 = 190 + m arc SQ + 75

→ Add the like term in the right side

∴ 360 = 265 + m arc QS

→ Subtract 265 from both sides

∵ 360 - 265 = 265 - 265 + m arc SQ

∴ 95° = m arc SQ

∴ The measure of arc SQ is 95°

7 0

3 years ago

A plane flies at x miles per hour in still air. Flying with a tailwind, its speed is 485 miles per hour. Against the wind, its a

Svetradugi [14.3K]

Answer:20mph

Step-by-step explanation:

speed of plane = x mph

Speed of plane with wind = 485 mph

So therefore, speed of wind =

485 - x

Speed of plane against wind = 445 mph

So therefore, speed of wind =

x - 445

So therefore, equating the 2 equations of speed of wind

485 - x = x - 445

Collect like terms

485 + 445 = x + x

930 = 2x

2x = 930

x = 930/2 = 465 mph

Speed of wind = x = 465mph

So we put this value on any of the equations for speed of wind

Speed of wind = x - 445 = 465 - 445

= 20 mph

So therefore, speed of wind = 20mph

7 0

3 years ago

The air temperature is -6 degrees celsius every hour for several hours. The air temperature after x hours is represented by the

andreyandreev [35.5K]

Answer:

x-intercept is (2,0) [The x-intercept means that it takes 2 hours for the temperature to reach 0°C]

y-intercept is (0, -6) [The y-intercept represents the temperature at sunrise, -6°C]

Step-by-step explanation:

Complete Question:

The air temperature is -6 degrees celcius at sunrise and rises 3 degree celcius every hour for several hours. The air temperature after x hours is represented by the function f(x) = 3x - 6. Find the x-intercept and y-intercept and interpret their meaning.

The x-intercept is the x-axis cutting point found by setting y = 0 [function = 0]
The y-intercept is the y-axis cutting point found by setting x = 0

Lets find x-intercept first:

f(x) = 3x - 6

0 = 3x - 6

3x = 6

x = 6/3

x = 2

x-intercept is (2,0)

Now, lets find y-intercept:

f(x) = 3x - 6

f(x) = 3(0) - 6

f(x) = -6

y-intercept is (0, -6)

The x-intercept means that it takes 2 hours for the temperature to reach 0°C

The y-intercept represents the temperature at sunrise, -6°C

3 0

3 years ago