One of the lengths of a leg on a right angled triangle is 15 ft the length of the hypotenuse is 17 ft find the length of the other leg

Part (a)

Since we want segment AT to be an altitude, this means that point A is somewhere on segment RI such that angle TAI is 90 degrees. In other words, segments AT and RI are perpendicular. Check out the diagram below.

We'll need to find the slope of line RI, so we'll need the slope formula

R = (x1,y1) = (-2,-2)

I = (x2,y2) = (4,1)

m = slope of line RI

m = (y2-y1)/(x2-x1)

m = (1-(-2))/(4-(-2))

m = (1+2)/(4+2)

m = 3/6

m = 1/2

m = 0.5

The slope of line RI is 1/2 or 0.5

Now let's use point R(-2,-2) along with that slope we just found to find the equation of line RI.

Turn to point slope form

y - y1 = m(x - x1)

y - (-2) = 0.5(x -(-2))

y + 2 = 0.5(x + 2)

y + 2 = 0.5x + 1

y = 0.5x + 1 - 2

y = 0.5x - 1

This is the equation of line RI. We'll use it later.

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We found that the slope of line RI was 1/2.

The negative reciprocal involves us flipping the fraction and flipping the sign to get -2/1 or simply -2.

The perpendicular slope is -2. This is the slope of altitude AT.

We want line AT to go through T(-2,4), so we'll use this point along with the perpendicular slope we just found to calculate the equation of line AT.

We'll turn to the point slope form

y - y1 = m(x - x1)

y - 4 = -2(x - (-2))

y - 4 = -2(x + 2)

y - 4 = -2x - 4

y = -2x - 4 + 4

y = -2x

The equation of the line that goes through points A and T is y = -2x.

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To summarize so far, we have these two equations

Apply substitution to solve for (x,y) to find the intersection point. This will determine where point A is located.

y = 0.5x - 1

-2x = 0.5x - 1

-2x-0.5x = -1

-2.5x = -1

x = -1/(-2.5)

x = 0.4

Then we can determine y like so

y = -2x

y = -2(0.4)

y = -0.8

Therefore, point A is located at (0.4, -0.8). Both coordinate values are exact. In fraction form, we can say that the point is (2/5, -4/5), but I find decimals easier to work with in this instance.

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

Part (b)

To find the length of segment AT, we can find the distance from A to T. As you can probably guess, we'll use the distance formula.

A = (x1,y1) = (0.4, -0.8) ... found back in part (a)

T = (x2,y2) = (-2, 4) ... given

[tex]d = \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 - (-0.8))^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 + 0.8)^2 }\\\\d = \sqrt{ (-2.4)^2+(4.8)^2 }\\\\d = \sqrt{ 5.76+23.04 }\\\\d = \sqrt{ 28.8 }\\\\d \approx 5.36656\\\\d \approx 5.37\\\\[/tex]

The distance from point A to point T is approximately 5.37 units. This means that segment AT is roughly 5.37 units long.

Answer:

Step-by-step explanation:

Hello!

x² + 5x-2

6² + 5*6 -2 =

36 +30 -2 =

66 -2=

64

Answer:

96 flowers did not bloom and 12 did.

Explanation:

Total flower = 108

Number of flower that bloomed

= ⅑ of the total flowers

= ⅑ of 108

= ⅑ × 108

= 108/9

= 12

So, number of flowers that did not bloom

= Total flowers - Number of flowers that bloomed

= 108 - 12

= 96

So, 96 flowers did not bloom and 12 flowers did.

Answer:

8 hours

Step-by-step explanation:

3 1/5 cups, he drinks 2/5 cups every hour

to find the number of hours he has water for, divide the 2 numbers

3 1/5 = 16/5

16/5 divided by 2/5 is equal to 16/5 times 5/2

80/10 equals 8, so he will have water for 8 hours

Answer:

Step-by-step explanation:

I just graphed this and used the "maximum value" capability to locate the max value. It occurs at (0.363, 3).

Answer:

Step-by-step explanation:

diameter of the circle=smallest of the length and width=21 cm

r=21/2

area of the circle=πr²=22/7 ×(21/2)²=(21×441)/(7×4)=1323/4=330.75 cm²

Answer: -1

Step-by-step explanation:

Look at the patter it has

Answer:

the answer is B

Step-by-step explanation:

because only 48 is dividable by 6

Hey there! I'm happy to help!

A step function is a function that looks like stairs when you graph it. Normally the end of one line will be graphed as an open circle (less or greater than, not equal to) while the other end would be a closed circle. This allows for a new line of the function to start directly above it without it not being a function (an input cannot have two outputs)

The function f(x)=4 is just a horizontal line as it has a slope of 0 (there is no x on the right side of the equation), so this doesn't resemble a step function.

Have a wonderful day and keep learning! :D

Answer:

+ (+9) = -9  

Step-by-step explanation:

- (-9) = 9 A negative times a negative is a positive

- (+9) = -9   A negative times a positive is a negative

+ (-9) = -9  A positive times a negative is a negative

+ (+9) = -9 A positive time a positive is a positive

[tex] \large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N \: ❁}}[/tex]

[tex] \large{ \tt{❇ \: FIND \: SP \: WITHOUT \: VAT \: / \: SP\: ❇}}[/tex]

[tex] \large{ \tt{❃ \: SP \: with \: VAT= SP + VAT\% \: of \: SP}}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = SP + 13\% \: of \: SP}}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = SP + \frac{13}{100} \: sp}}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = \frac{100 \: \: SP + 13 \: SP}{100} }}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = \frac{113 \: SP}{100} }}[/tex]

[tex] \large{ \tt{⇢ \: 113 \: SP = 406800}}[/tex]

[tex] \large{ \tt{⇢ \: SP = \frac{406800}{113} }}[/tex]

[tex] \large{ \tt{⇢ \: SP = 3600}}[/tex]

[tex] \large{ \tt{✽ \: NOW , \: FIND \: THE \: MP \:✽ }}[/tex]

[tex] \large {\tt{❃ \: SP = MP - dis\% \: of \: MP}}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = x - 10\% \: of \: x}}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = x - \frac{10}{100} } \: x}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = \frac{100x - 10x}{100} }}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = \frac{90x}{100} }}[/tex]

[tex] \large{ \tt{⇾ \: 90x = 360000}}[/tex]

[tex] \large{ \tt{⇾ \: x = \frac{360000}{90} }}[/tex]

[tex] \large{ \tt{⇾ \: x = Rs \: 4000}}[/tex]

[tex] \large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER : \boxed {\tt {\: Rs \: 4000}}}}}}[/tex]

Answer:

in the pic

Step-by-step explanation:

answer A

.....

Let

ATQ

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40x+50x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 90x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=\dfrac{45000}{90}[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=500[/tex]

Now

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Rita=50x=50(500)=25000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Mina=40x=40(500)=20000[/tex]

Answer:

Square

Step-by-step explanation:

It got 4 sides like square and its form is looking like a square.

Answer:

D. Exponential growth

Step-by-step explanation:

Hope this helps

Function that is similar to exponential.

Option (A) is correct.

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula  [tex]y=a(1-b)^{x}[/tex] wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

We can observe that

First, y increases as x increases

Last it is a function that is similar to exponential.

Function is an exponential decay.

Option (A) is correct.

Find out more information about exponential decay here

https://brainly.com/question/14355665

#SPJ2

Answer:

5

Step-by-step explanation:

Use pythagorean theorem. A^2+B^2=C^2

13 is c because it is the hypotenuse and across from the right angle

a is unknown and b is 12

A^2+12^2=13^2

A^2 +144 = 169

A^2 = 169- 144

A^2= 25

now take the sq root of both side

A = 5

Answer:

17.7

Step-by-step explanation:

Answer:

B. XV and XY

Step-by-step explanation:

you can eliminate the top two options because those aren't rays. XV and XY are the only ones that end in X

Answer:

Answer is option (B)......

Answer:

x = 960

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large triangle )² = ( part of hypotenuse below it) × ( whole hypotenuse), so

x² = 576 × (576 + 1024) = 576 × 1600 = 921600 ( take square root of both sides )

x = [tex]\sqrt{921600}[/tex] = 960

Answer:

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

It is 5 because you just have to count by using a jumping math tectechnique.

Answer:

Step-by-step explanation:

Answer:

24 in^3

Step-by-step explanation:

Volume of the figure= 3 * (Volume of a cube with side 2)

Volume of the figure= 3*2^3=24 in^3

Answer:

24 cubic inches

Step-by-step explanation:

The formula for finding volume is b*h*w.

b*h*w is base multiplied my height multiplied my width. Lets use this formula to find the volume of one of cubes.

Here is the information we know about the cubes:

the base is 2 inches

the height is 2 inches

the width is 2 inches

Lets put this information into the formula to find the volume of one of the cubes. I will show the work in steps so it is easy to follow.

Step one: plug the given information into the formula.

b*h*w = 2*2*2

Step two: Solve the equation.

2*2*2 = 4*2 = 8

Now we have the volume of one on the cubes. This is 8 cubic inches. However, to find the volume of all three of the cubes we must multiply 8 by 3.

Step three: multiply 8 by 3.

8*3 = 24

And there you have it! Our final answer is 24 cubic inches.

Here is a quick review of what we did to get our answer:

2*2*2 = 8

8*3 = 24

I hope this helps!

Answer:

-x3+x2+3x+1

Step-by-step explanation:

V(x) + W(x) = -x2 + 2x - 4 + -x3 + 2x2 + x + 5= -x3+x2+3x+1

Answer:

658ft

Step-by-step explanation:

you first have to calculate the angle next to that 28°angle,if you look at the two they form a 90° so to find that angle you have to subtract 90-28=62

the x is the opposite of angle 62 and the 350 si the adjacent so you can use the tan ratio to find the answer

tan62=opposite/adjacent

tan62=y/350

y=tan62×350

=658ft

I hope this helps

Answer:

0.02

Step-by-step explanation:

either picking a green then blue;

5/22 x 1/21= 5/462

or picking a blue then green;

1/22 x 5/21= 5/462

total is 10/462 which is approximately 0.02

since there was no specific order in the question i assumed you add them both.

Answer:

Step-by-step explanation:

Scientific notation is always written as a number between 1 and 9.9999999 repeating. There follows a power of 10. I'm not sure which answer would help you see it clearer but

4.8 * 10^4 the decimal is shifted 4 places the right which is 48000 where you have no numbers, you use zeros.

2.01 * 10^6 means that you shift the decimal 6 places to the right.

2010000

So 2 million is larger than 48 thousand.

The other way to do it is just to look at the power. 6 is more than 4. 6 describes the number of places you move. So does 4. 6>4 so that's the larger number.

a right angle is 90°, or 1/4 of a circle.

3/5 * 1/4 = 3/20

radian measure is the length of the circumference of this part of the circle.

a full circumference of a circle would be 2*pi*r, also expressed as 2 rad * r

now let's multiply the full thing with the 3/20 from earlier to just get the desired fraction:

6/20 rad * r

= 3/10 rad * r

of course a solution in cm or inch still depends on the radius here, wich could be just plugged in at will

Answer:

[tex]\frac{3\pi }{10}[/tex]

Step-by-step explanation:

To express degrees in radians

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

[tex]\frac{3}{5}[/tex] of a right angle

= [tex]\frac{3}{5}[/tex] × 90° = 54° , then

radian = 54 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{54}{180}[/tex] × π = [tex]\frac{3}{10}[/tex] × π = [tex]\frac{3\pi }{10}[/tex]