Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest radical form. In your video include whether you would use SAAS or HYLLS to solve (and WHY), the proportion you would set up, how you would solve for the missing side, and how you know your answer is in simplest radical form.

Answer:

180 miles

Step-by-step explanation:

distance = rate x time

t = time

1st car:

distance = 40t

2nd car:

distance = 60(t - 1,5)

When the car catch up to each other the distances will be the same, so set the equation equal to each other.  Calculate the time and then put the time back into either equation and solve for the distance.

40t = 60(t-1.5)  Distribute the 60

40t = 60t -(60)1.5

40t = 60t - 90  Subtract 60t from both sides of the equation

-20t = -90  Divide both sides by -20

t = 4.5

Now that we know the time, substitue that back into either equaiton and solve for the time

distance = 40 (4.5)

180 miles

Solution

We have the following integral:

We can use the substitution u= 4 +3x² and we have du= 6x dx, then we have this:

Answer:

14.73%

Step-by-step explanation:

firstly let's divide the phone price into 7 equal parts. by this equation 219.00/7=31.28

So Alec needs to save $31.28 but we want the percentage.

by equation x%*212.34=31.28

x=(31.28*100)/212.34=3128/212.34=14.73

so Alec needs to save 14.73% of 212.34 each week.

Answer:

24.0 cm

Explanation:

To find the value of a, we will use the Law of sines, so

So, replacing A = 150°, B = 12°, and b = 10 cm, we get:

Now, we need to solve for a. First, cross multiply

Then, divide by sin12

Therefore, a = 24.0 cm

you have the following equation:

3x - 2 = 2(x+1)

You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:

1. 3x - 2 = 2(x + 1) given

2. 3x - 2 = 2x + 2 distribution prop

3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop

x - 2 = 2

4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop

x = 4

Since the probability of Cheetah is 0.4

Since the probability of Tiger is 0.7

Since the probability of Cheetah or Tiger or both is 0.5

Let us draw a figure to show this information

Then we need to find both animals (x)

Since

Add x to both sides and subtract 0.5 from both sides

Divide both sides by 2 to find x

a) The probability of both animals is 0.3

Since the total of probability is 1, then to find the neither subtract (0.4 + 0.7 - 0.3) from 1

b) the probability of neither is 0.2

Events A and B are independent if the equation P(A∩B) = P(A) · P(B)

Since

Since P(Ch) . P(T) = 0.4 x 0.7 = 0.28

Then

c) The events are not independent

First let's find the amount Sonia puts in her account each week.

To do so, let's find the amount increased between weeks 5 and 10:

The account increased $25 in 5 weeks, so for each week, we have:

So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:

So the initial amount is $20.

Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:

So the correct option is the third one.

         A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

Response: C

        A node of a graph, or one of the points on which the graph is defined and which may be connected by graph edges, is referred to as a "vertex" in computing.

For instance, a rectangle's four sides result in its four vertices.

   Response:  C . The coordinates are obtained by first subtracting 1 from 4 to obtain 3 and then adding 3 to -2 to obtain 1. (3, 1)

       The vertex is the collective endpoint. Vertex, on the other hand, refers to the common terminal point where two rays converge to make an angle. In a similar manner, we must understand an angle's arm. The term "arm of an angle" refers to the two rays that unite to make an angle.

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Answer: 35.8

Step-by-step explanation: 40x?=1432

40x35.8=1432

Answer:

[tex](y+6)=\frac{2}{8} (x+2)[/tex]

Step-by-step explanation:

First, find the slope

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

-4+6=2

6+2=8

m=2/8

With the slop, you have everything you need to stick one of your points in point-slope form.  I chose (-2,-6)

[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]

Really, that's all you need as it is not an equation of a line.  Not the most useful form, but works as an answer.

Answer:

After tax interest expenses = Interest expenses x (100 - Tax Rate) 

= 70000 x (100 - 30)% 

= 70000 x 70% 

= $49,000.00

Step-by-step explanation:

The number divisible by 5 is 670.

Numbers divisible by 5 have their last digits as 0 or 5

Answer : 670

Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

So, tiles needed to cover the wall:

Calculate the area of a tile as follows:

Now, calculate the area of the wall as follows:

Then, tiles needed to cover the wall:

Which means: 80½

Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

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Let's say x is going to be the number meters of the width of the room:

x: width

Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:

1.8x: lenght

We know that the perimeter of a rectangle is given by

Perimeter = 2· (width + lenght)

We know that the perimeter is 29 meters, then

Perimeter = 29

↓

29 = 2· (width + lenght)

We do know an expression for its width and lenght, we replace them:

29 = 2· (width + lenght)

↓

29 = 2· (x + 1.8x)

Since x + 1.8x = 2.8x:

29 = 2· (x + 1.8x)

↓

29 = 2· (2.8x)

↓ 2· 2.8 = 5.6

29 = 5.6x

↓ dividing both sides by 5.6

29/5.6 = 5.6x/5.6

5.2 = x

Since

x: width

then

Width = 5.2 meters

Since

1.8x: lenght

then

Lenght = 1.8 · 5.2 meters = 9.36 meters

EXPLANATION

we are asked to use the long division method to solve the division

We will have

To find the solution to the system of equation

we will use the elimination method

3x - y = - 5 ----------------------------(1)

2x + 3y = 4 -------------------------------(2)

We will eliminate y and solve for x

multiply equation (1) through by 3

9x - 3y = - 15 ------------------------------------(3)

add equation (2) and equation (3)

11x = -11

divide both-side of the equation by 11

x = -1

substitute x = -1 in equation (1) and solve for y

3x - y = - 5

3(-1) - y = -5

-3 - y = -5

add 3 to both-side of the equation

- y = -5 +3

-y = -2

multiply through byb -1

y = 2

Hence, the correct option is B

The value of the trigonometric function is;  sin(A) =√51/10.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given that  angle A lies in Quadrant IV and cos(A)= 7/10 then;

cos(A)= 7/10

Hence, base = 7

hypotenuse = 10

Therefore, perpendicular

h² = b² + p²

10² = 7² + p²

100 = 49 + p²

p = √51

Then  sin(A = perpedicular/ hypotenuse

sin(A) = √51/10

Hence, the value of the trigonometric function is;  sin(A) =√51/10.

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Given,

Multiplying equation (ii) by 2 as it make the coefficent of x in both equation equal.

Substracting equation (i) from equation (iii) then we get,

The value of y is -2.

Substituting the value of y in equation (i) then,

Hence, the solution of the linear pair (x, y) is (3, -2).

f(7) gives 5 1/2.

the position is the 7th term

Explanation:

f(1)= 8 1/2

f(n)= f(n-1) - 1/2

we are looking for the function that gives 5 1/2

We have been given f(1), this means n = 1

f(1) = f(1-1) - 1/2

8 1/2 = f(0) - 1/2

f(0) = 8 1/2 + 1/2

f(0) = 8 + 1 = 9

when n = 2

f(2) = f(2-1) - 1/2

f(2) = f(1) - 1/2

f(2) = 8 1/2 - 1/2

f(2) = 8

when n = 3

f(3) = f(3-1) - 1/2

f(3) = f(2) - 1/2

f(3) = 8 - 1/2

f(3) = 7 1/2

when x = 4

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

f(4) = f(3) - 1/2

f(4) = 7 1/2 - 1/2

f(4) = 7

when n = 5

f(5) = f(5-1) - 1/2

f(5) = f(4) - 1/2

f(5) = 7 - 1/2

f(5) = 6 1/2

f(6) = f(6-1) - 1/2

f(6) = f(5) - 1/2

f(6) = 6 1/2 - 1/2 = 6

when n = 7

f(7) = f(7-1) - 1/2

f(7) = f(6) - 1/2

f(7) = 6 -1/2 = 5 1/2

f(7) gives 5 1/2.

Hence, the position is the 7th term

In this case,

This difference is made this way:

-2 - (-6) =

-2 +6 = 4

So there we have this identity. The minus before the parentheses turns the minus into plus sign.

0.0404

Repeating decimal (periodic)

1) Let's proceed with the long division of 4 by 99:

1.1) Since 4 is way smaller than 99 let's add one zero to the dividend and another for the quotient followed by a dot.

But 40 is still lesser than 99, so let's add another zero after the dot to make it 400. Now we can divide 400 by 99

1.2) Again to proceed with that division we'll need to write a zero at that 4 and another one in the quotient.

As and we can see already this a repeating decimal or periodic. This division will yield 0.0404040404.....

2) Hence, the answer is 0.0404

Percent is given by the expression:

So, he is paying 74% more using the quarterly rate

The Hooke's law is given by:

F = k*x

Where:

F = force

k = constant factor

x = distance

If F = 20 and x = 20

20 = k*20

Solving for k:

20/20 = k

k = 1

So: how far will a 29 pound mass stretch the spring?

29 = 1* x

Solving for x:

29/1 = x

x = 29 in

Given the sum of the functions expressed as:

Collecting the like terms:

Group the terms based on their degrees

Simplify the result to determine the final answer:

Hence the required sum of the functions is x^2 - 3x + 7

Explanation

We are required to determine the value of the following:

This is achieved thus:

We know that the combination formula is given as:

Therefore, we have:

Hence, the answer is:

The total of students that study for 3 to 4 h is 147

The total of students that study for 5 to 6 h is 107

Then, the statement: "more students study for 3 to 4 hours than for 5 to 6 hours" is true because 147 students study for 3 to 4 hours and 107 students study for 5 to 6 hours.

Notice that the number of students that got a grade below 80 is:

and the total number of students is:

Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:

Finally, we get that 7 represents the

of 20.

Answer:

The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.

The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.

Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:

Hence, the correct option is option B

Let's do the mutiplications:

(3a)(5a) = 15a²

(5p)(2p) = 10p²

(3 inches)(5 inches) = 15 inches²

(5 feet)(2 feet) = 10 feet²mutiplic

The first complement of the binary addition is 00011111.

The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0.

Given that, the addition of the given number

  00011101 + 11111101

In the binary addition,

0+1 = 1

1+0 = 1

1+1 = 0

00011101 + 11111101 = 11100000

Then inverse code means first complement of the answer.

In the first complement, 0 is the inverse of 1 and 1 is inverse of 0.

11100000 = 00011111

Hence, The first complement of the binary addition is 00011111.

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