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3 years ago

Please help! A car traveled 100 miles on 5 gallons of gas. How far could that same car travel on 9 gallons of gas?

Mathematics

2 answers:

Aliun [14]3 years ago

6 0

Answer:

180 miles

Step-by-step explanation:

100 (miles) ÷ 5 (gallons)= 20 miles per gallon

20 (miles) × 9 (gallons)= 180 miles

artcher [175]3 years ago

4 0

Answer: 180 miles

Step-by-step explanation:

100 divided by 5 = 20. So, the car travels 20 miles with one gallon. Then, you do 20 x 9 = 180. So, the car can travel 180 miles on 9 gallons of gas.

I hope this helps!!! :)

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arlik [135]

Given:

In a right angle triangle θ is an acute angle and $\tan\theta =\dfrac{3}{5}$ .

To find:

The value of $\cos \theta$ .

Solution:

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

We have,

$\tan\theta =\dfrac{3}{5}$

It means the ratio of perpendicular to base is 3:5. Let 3x be the perpendicular and 5x be the base.

By using Pythagoras theorem,

$Hypotenuse=\sqrt{Perpendicular^2+base^2}$

$Hypotenuse=\sqrt{(3x)^2+(5x)^2}$

$Hypotenuse=\sqrt{9x^2+25x^2}$

$Hypotenuse=\sqrt{34x^2}$

$Hypotenuse=x\sqrt{34}$

In a right angle triangle,

$\cos \theta=\dfrac{Base}{Hypotenuse}$

$\cos \theta=\dfrac{5x}{x\sqrt{34}}$

$\cos \theta=\dfrac{5}{\sqrt{34}}$

Therefore, the value of $\cos \theta$ is $\dfrac{5}{\sqrt{34}}$ .

8 0

3 years ago

A Stegosaurus eats six and two fifths big leaves for breakfast and three and one fifth big leaves for lunch. How many leaves did

Mkey [24]

Answer:

9 and 3/5

Step-by-step explanation:

Nine and Three Fifths

7 0

3 years ago

Read 2 more answers

A pole vaulter rested a 17 foot pole against a wall. If the top of the pole hit the wall 14 feet above the ground, how far from

mart [117]

Answer:

a = √93

a ≈ 9.64

Step-by-step explanation:

We can use the Pythagorean theorem for this: a² + b² = c²

c is given as the hypotenuse, which is the pole with a length of 17 ft

c² is 17²

b is a leg with a height of 14 ft

b² = 14²

We need to find the base leg, a, distance from the wall to the base of the pole.

Solve:

a² + 14² = 17²

a² + 196 = 289

a² = 93

a = √93

-Chetan K

7 0

2 years ago

Jasmine bought 3500g of flour. She used 3/7 of it to bake some tarts and 700g of it to bake a cake. Find the ratio of the amount

Serggg [28]

Answer: 15:13

Step-by-step explanation: 7/7=3500

<h2>1/7=3500÷7=500</h2><h2>500x3=1500</h2><h2>1500+700=2200</h2><h2>3500-2200=1300</h2><h2>1500:1300</h2><h2>15 : 13 (if there is a need to simplify the ratio)</h2><h2 />

6 0

3 years ago

Could somebody help me with Geometry? THANKS!!!!!!!!!!!!!!!!!!!!!

Vedmedyk [2.9K]

I'll do problem 1 to get you started.

The answer to problem 1 is <u>3400 miles</u>

============================================================

Explanation for problem 1:

We're asked to find the perimeter, which is the total distance around the exterior or outside. In other words, we need to add up the four side lengths of this quadrilateral.

We'll need the distance formula to find the lengths of the slanted sides AB and BC

----------------------------------------

Let's first find the length of segment AB

A = (x1,y1) = (0,0)

B = (x2,y2) = (400,300)

d = Length of AB

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-400)^2 + (0-300)^2}\\\\d = \sqrt{(-400)^2 + (-300)^2}\\\\d = \sqrt{160000 + 90000}\\\\d = \sqrt{250000}\\\\d = 500\\\\$

The distance from A to B is 500 miles. This is the same as saying segment AB is 500 miles long.

----------------------------------------

Now find the length of segment BC

B = (x1,y1) = (400,300)

C = (x2,y2) = (-800,800)

d = length of BC

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(400-(-800))^2 + (300-800)^2}\\\\d = \sqrt{(400+800)^2 + (300-800)^2}\\\\d = \sqrt{(1200)^2 + (-500)^2}\\\\d = \sqrt{1440000 + 250000}\\\\d = \sqrt{1690000}\\\\d = 1300\\\\$

----------------------------------------

The length of CD is fairly easy to find without needing the distance formula. This is because it is a vertical line. We subtract the y coordinates of C and D to get 800-0 = 800. So CD is 800 miles long.

Segment DA is a similar story. But we subtract the x coordinates. This only works for horizontal lines. DA is 800 miles long because |-800-0| = 800. Absolute value is used to make sure the distance is never negative.

----------------------------------------

To summarize everything so far, we found these four side lengths

AB = 500
BC = 1300
CD = 800
DA = 800

The perimeter is going to be the sum of those four sides, leading to...

perimeter = sum of sides

perimeter = AB+BC+CD+DA

perimeter = 500+1300+800+800

perimeter = 3400 miles

This is the total distance traveled if you started at city A, went to B, then to C, then to D, and then finally went back to A.

5 0

3 years ago

Read 2 more answers