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3 years ago

There is a discount of sale of 20% off of a $450 pair of skis how much is the discount ?

Mathematics

2 answers:

Reika [66]3 years ago

6 0

Answer:

Step-by-step explanation:

20% of something is 1/5 and 1/5 of 450 is 90

450/5=90

g100num [7]3 years ago

5 0

Answer:

360

Step-by-step explanation:

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A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,corr

lina2011 [118]

Answer:

(a) the new angle the ladder makes with the ground is $32.7^o$

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

$sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m$

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

$sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o$

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

$cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m$

Now fro the new position of the bottom of the ladder relative to the wall:

$cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m$

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

4 0

3 years ago

Hey there can you please help me posted picture of question

mash [69]

We can use quadratic formula to determine the roots of the given quadratic equation.

The quadratic formula is:

$x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a}$

b = coefficient of x term = 12
a = coefficient of squared term = 4
c = constant term = 9

Using the values, we get:

$x= \frac{-12+- \sqrt{144-4(4)(9)} }{2(4)} \\ \\ 
x= \frac{-12+-0}{8} \\ \\ 
x= \frac{-3}{2}$

So, the correct answer to this question is option B

5 0

3 years ago

Find the value of each expression. show your work. 9^P3 and 10^C4

Komok [63]

⁹P₃=9×8×7=504; ¹⁰C₄=10×9×8×7÷(4×3×2×1)=210.

3 0

3 years ago

Slope = ; y-intercept = -3

Goshia [24]

Question is incomplete Let assume the Slope = 2

Answer:

Therefore the Equation of line is

$y=2x -3$

Step-by-step explanation:

Given:

Slope = 2 ( Assumption )

y-intercept = -3

To Find:

Equation of Line in Slope-intercept form

Solution:

Equation of Line in Slope-intercept Form is given as

$y=mx+c$

Where,

$m=Slope\\c=y-intercept$

So, substituting Slope =2 and y-intercept = -3 in above we get

$y=2\times x -3$ Which is the Required Equation of line

Therefore the Equation of line is

$y=2x -3$

8 0

3 years ago

A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "One-half of my cats plus two."

mixer [17]

I got ten. Here's the equation.

x = 1/2x + 5

Subtract 1/2x from both sides to get all x's on one side 

x - 1/2x = 1/2x - 1/2x + 5 

1/2x = 5 

Now multiple the left by 2 to get x, but since it's an equation, you need to also multiply the right by 2 to keep it =. 

2 * 1/2x = 2 * 5 

x = 10 cats

4 0

3 years ago

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