The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary.

leg: 20 m; hypotenuse: 25 m


10.5 m

8.9 m

32 m

15 m

the length of DE is 9/2 units and m<CAB is 45

The measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.

A triangle is a polygon with three angles and sides.

Given that, a right triangle ABC, right-angled at B,  

Here D and E are midpoints of AB and BC, and also AB = AC, CB = 9 units.

We need to find the measurements of DE and angle CAB in the given triangle ABC,

Since, the two sides are equal in the triangle then it is a right-isosceles triangle,

In a right-isosceles triangle, the two acutes angles are measured 45°

Therefore, ∠ CAB = ∠ ACB = 45°

Hence, ∠ CAB = 45°

Now, using the midpoint theorem, we will get. CB = 2DE

Therefore,

9 = 2DE

DE = 4.5 units

Hence, the measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.

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Answer:

x is greater than 5, so x could be anything more than 5.

Step-by-step explanation:

Hope my answer has helped you!

For this case we have that the total of the balls is 86. We know there are 8 footballs then:

Basketball: Two more than twice the number of footballs are basketballs, that is:

[tex]2 + 2 (8) = 2 + 16 = 18[/tex]

There are 18 Basketballs.

Baseballs: Four less than 5 times the number of footballs are baseballs, that is:

[tex]5 (8) -4 = 40-4 = 36[/tex]

There are 36 Baseballs.

Softballs: Six more than half of baseballs are softballs. That is to say:

[tex]6+ \frac {36} {2} = 6 + 18 = 24[/tex]

There are 24 Softballs

If we add we must get 86.

[tex]8 + 18 + 36 + 24 = 86[/tex]

ANswer:

There are 8 Footballs

There are 18 Basketballs.

There are 36 Baseballs.

There are 24 Softballs

The answer is:

The piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]

To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).

From the graph, we know that we need the following functions:

- A horizontal line, which exists from -∞ to -1, givind as input 8.

The function will be:

[tex]y=8[/tex]

Then, the piecewise function it will be:

[tex]8; x\leq -1[/tex]

- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)

The function will be:

[tex]y=x^{2}-4x+1[/tex]

Finding the y-intercept, we have:

[tex]y=0^{2}-4*80)+1[/tex]

[tex]y=1[/tex]

Finding the vertex of the parabola, we have:

[tex]x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2[/tex]

[tex]y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1[/tex]

[tex]y_{vertex}=2^{2}-4*2+1=4-8+1=-3[/tex]

The vertex of the parabola is located at the point (2,-3).

Then, for the piecewise function it will be:

[tex]x^{2} -4x+1;-1<x<5[/tex]

- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.

The function will be:

[tex]y=-x+1[/tex]

Proving that it's the correct equation by evaluating "x" equal to 5, we have:

[tex]y=-5+1[/tex]

[tex]y=-4[/tex]

It proves that the equation is correct.

Then, for the piecewise function it will be:

[tex]-x+1\geq 5[/tex]

Hence, we have that the piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]

Have a nice day!

Answer:

[tex]\large\boxed{5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}}[/tex]

Step-by-step explanation:

[tex]5(x+y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5x+5x\\\\3\left(\dfrac{y}{x}\right)=\dfrac{3y}{x}\\\\5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}[/tex]

(a): 18

(b): $792

Step-by-step explanation:

A: 900 - 576 = 324. 324/18 = 18.

18 * 18 = 324. 324 + 576 = 900.

B: 6 * 18 = 108. 900 - 108 = 792

Answer: -8 square root of 3 (choice a)

Step-by-step explanation:

You have to find 2 numbers that multiply to 48 and in the same time, 1 of these numbers is a perfect square. In this case, the numbers are 16 and 3. So -2√16*3

Then since 16 is. A perfect square, and the square root is 4, you take out the 4 and multiply it by -2 so that is -8 and now you are left with -8√3. Hopefully that helped.

ANSWER

[tex] - 8 \sqrt{3} [/tex]

EXPLANATION

We want to simplify:

[tex] - 2 \sqrt{48} [/tex]

Remove the perfect square under the radical sign.

[tex] - 2 \sqrt{16 \times 3} [/tex]

Split the radical sign for the factors under it.

[tex] - 2 \sqrt{16} \times \sqrt{3} [/tex]

Simplify:

[tex] - 2 \times 4\times \sqrt{3} [/tex]

This finally gives us:

[tex] - 8 \sqrt{3} [/tex]

The first choice is correct.

Answer:

The t-shirt cost $23.33.

Step-by-step explanation:

Answer:

$140

Step-by-step explanation:

If x was the amount of money Mr. Green had remaining, and y was the amount of money Mrs. Green had remaining, then:

x / y = 3 / 2

And, since they spent the same amount of money:

200 - x = 180 - y

We can solve this system of equations through substitution.

x = 3/2 y

200 - 3/2 y = 180 - y

20 = 1/2 y

y = 40

So Mrs. Green had $40 remaining.  Since she started with $180, she must have spent $140.  So that was the cost of the shirt.  Let's check our answer by seeing how much Mr. Green had remaining and how it compares.

$200 - $140 = $60

$60 / $40 = 3 / 2

Yep, it checks out.

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The equation of a proportional relation is of the form

y = kx,

where k is a number.

Here you have

3 - 6x = y,

which can be rewritten as

y = -6x + 3

Because of the +3, your equation is not for the form y = kx, and it is not a proportional relation.

Answer:

The temperatures were more consistent in Springville

Step-by-step explanation:

This question is on consistency of data

Generally, consistency of a data set is measured by determining the range, the variance or the standard deviation.In this case, we will use the standard deviation.

A small standard deviation means higher consistence.A lower standard deviation  will mean easy to predict a value because most of the values are closer to the average value.When the variations are less, a better analysis can be performed on a set of data.

Temperatures were more consistent in Springville that had a standard variation of 4F compared to Dakota that had a standard deviation of 6.8F

Answer:

13 min 40 sec

Step-by-step explanation:

656 copies *(1 min/48 copies)= 656 /48 min = 13  32/48 min = 13 2/3 min

2/3 min = 2/3 min * 60 sec/1 min = 40 sec

13 2/3 min = 13 min 40 sec

Answer:

44

Step-by-step explanation:

0.5 m - 0.75 n = 16

Substitute n = 8 into the equation  

0.5 m - ( 0.75 × 8 )  = 16

0.5 m - 6  = 16

( Add 6 to both sides )

0.5 m = 26

( Divide by 0.5 )

m = 52

Answer:

1000 runners

Step-by-step explanation:

Take total number of runners to be -----------x

90% of x managed to complete the marathon= 90/100 × x =0.9x

30% of those who completed the marathon were men= 30% × 0.9x

=0.3×0.9x= 0.27x

=270 men completed the marathon; this means

0.27x=270--------------------------------find x by dividing both sides by 0.27

x= 270/0.27

x=1000 runners

Answer:

1000

Step-by-step explanation:

Given : In a marathon 90% runner were managed to complete it and 30% were men.

To Find: If 270 men completed it how many total runner began the marathon.

Solution:

Let x be the number of total runners

Now we are given that 90% runner were managed to complete it

So, number of runners managed to complete = [tex]90\% \times x =\frac{90}{100}x=0.9x[/tex]

Now we are given that out of 90% , 30% were men

So, Numbers of men runners = [tex]30\% \times 0.9x=\frac{30}{100} \times 0.9x =0.27x[/tex]

Now we are given that 270 men completed it

So, [tex]0.27x=270[/tex]

[tex]x=\frac{270}{0.27}[/tex]

[tex]x=1000/tex]

Hence 1000 runners began the marathon.

Answer:

d) 18

Step-by-step explanation:

The question is on graphing linear functions

Given the table of values of x and y, plot the graph and observe the gradient of -2 and the y-intercept at (0,-5) as shown on the attached graph with blue color.

Use the given function y=7x+13 to formulate a table of values of x with corresponding values of y

x     y

-3   -8

0      13

1       20

With the above values, plot the graph of y=7x+13 and obtain the y-intercept at (0,13) as shown in the red line graph attached.

To find the distance between the y-intercepts of the two graphs we apply the expression for distance between two points;

[tex]D=\sqrt{(X2-X1)^2 +(Y2-Y1)^2 \\\\[/tex][/tex]

points are (0,-5) and (0,13)

D=√ (0-0)² + (13--5)²

D=√(18)²

D=18 units

The y-intercepts of the two functions y = 7x + 13 and y = 3x + 9 are 13 and 9 respectively. The distance between the y-intercepts is the absolute difference between them, which is 4, a result not listed among the options.

Firstly, we need to find the equation that fits the values in the table. With the given x and y values, applying a method such as 'point-slope,' we calculate the slope (m) and y-intercept (b). We find the equation is y = 3x + 9.

Then, we determine the y-intercepts of both functions. For the function y = 7x + 13, the y-intercept is 13 (the constant term). For the function y = 3x + 9, the y-intercept is 9.

The distance between the y-intercepts of the two functions is simply the absolute difference between them, which equals |13 - 9| = 4. However, none of the options a), b), c), or d) are identical to this value. There might be a mistake in the question.

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Answer:

C. 3.3 • 10^-7

Step-by-step explanation:

(1.1•10^-5)(3 •10^-2)

Multiply the numbers out front of the powers of ten, then add the exponents on the powers of 10

1.1 * 3   * 10 ^(-5+-2)

3.3 ^ (-7)

Answer:

C

Step-by-step explanation:

Answer:

135 degrees

Step-by-step explanation:

Coterminal means it ends at the same spot around the circle.

To calculate the resulting angle we need to reduce/increase the started value to arrive to a value between 0 and 359 degrees.  

If the starting angle is greater or equal to 360, we subtract 360 until we get below 360.

If the starting angle is below 0, we add 360 until we get equal or greater than 0.

So, starting with 495, we subtract 360 a first time....

A = 495 - 360 = 135

We're already in the desired range (0-359)... so we have our answer.

Answer:

22/25

Step-by-step explanation:

The overlap between the 61% and the 75% is the 48%, which means that 13% of the people are married and have no kids (61-48=13)

The 75% includes the people who have one or more kids, and the people who have one or more kids and are married.

Now all we have to do is 13% + 75% = 88% = 22/25

Using Venn probabilities, it is found that there is a 0.88 = 88% probability that a person in a survey is married or has a child.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In this question, the events are:

The probabilities are given by:

[tex]P(A) = 0.61, P(B) = 0.75, P(A \cap B) = 0.48[/tex]

Hence:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

[tex]P(A \cup B) = 0.61 + 0.75 - 0.48[/tex]

[tex]P(A \cup B) = 0.88[/tex]

0.88 = 88% probability that a person in a survey is married or has a child.

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Answer:

The answer is A. 70 in^2

Step-by-step explanation:

trust me it is right :) hope this helps! I JUST TOOK THE TEST

ANSWER

A. 70 in^2

EXPLANATION

The area of a tra-pezoid is

[tex] = \frac{1}{2} (sum \: of \: parallel \: sides) \times height[/tex]

Substitute the side lengths into the formula to obtain,

[tex] = \frac{1}{2} (8 + 14) \times 7[/tex]

Simplify the parenthesis

[tex] = \frac{1}{2} (20) \times 7[/tex]

Cancel out the common factors,

=10×7

Simplify

[tex] = 70 {in}^{2} [/tex]

The correct answer is A

Answer:

8

Step-by-step explanation:

The question is on number of subsets

Number of subset is given by 2^n

n=3 in our question, A,B,C

2^n = 2^3 =8

They are; { }, A, B, C, AB, AC, BC, ABC

Answer:

8

Step-by-step explanation:

[tex]

48=5t-7 \\

55=5t\Longrightarrow t=\frac{55}{5}=\boxed{11}

[/tex]

Answer:

Step-by-step explanation:

11

Answer:

Step-by-step explanation:

It’s is a because if you divide 4.41 divide by 3 you will get 1.47

Step-by-step explanation:

1 yard = 3 feet

So 3 yards = 9 feet

$4.41 / 9 feet = $0.49 per foot

$1.05 / 3 feet = $0.35 per foot

The second one is cheaper, so that's the better buy.

Answer:

Step-by-step explanation:

In the form ...

  ax^2 +bx +c = 0

the sum of the roots is -b/a. Here, that is -k/3. You want that value to be 3, so we have ...

  -k/3 = 3

  k = -9

__

The solution can be found by completing the square. We choose to start by making the leading coefficient be 1.

  x^2 -3x +4/3 = 0

  (x^2 -3x +9/4) + (4/3 -9/4) = 0 . . . . . . . add and subtract (3/2)^2

  (x -3/2)^2 = 11/12 . . . . . . . . . . . . . . . . . . add 11/12, write as square

  x = 3/2 ± √(11/12) = (9±√33)/6 . . . . . . . .simplify

The perimeter of tile which is 3 by 3 would be 12. If each side is 3 and the tile is a square which has four sides we can do 3 x 4 to determine the perimeter of the tile. To determine perimeter just add up all the sides. In this case since it’s a square you are able to multiply. 3 x 4 or 3 + 3 + 3 + 3 = 12

Answer:

The answer is 12

Step-by-step explanation:

Because it is lol and i just got it right

Answer:

1112

Step-by-step explanation:

Answer:

The product of x and y is 8[tex]8[/tex]

Step-by-step explanation:

If [tex]\log_{5\sqrt{5}}125=x[/tex], then the exponential form is:

[tex]125=(5\sqrt{5})^x[/tex]

[tex]\implies 5^3=(5)^{\frac{3x}{2}}[/tex]

[tex]\implies 3=\frac{3x}{2}[/tex]

[tex]\implies 6=3x[/tex]

[tex]\implies x=\frac{6}{3}=2[/tex]

Also  if, [tex]\log_{2\sqrt{2}}64=y[/tex], then the exponential form is:

[tex]64=(2\sqrt{2})^y[/tex]

[tex]\implies 2^6=(2)^{\frac{3y}{2}}[/tex]

[tex]\implies 6=\frac{3y}{2}[/tex]

[tex]\implies 12=3y[/tex]

[tex]\implies y=4[/tex]

The product of x and y is [tex]xy=2\times 4=8[/tex]

Use the fact that the co/sine functions are [tex]2\pi[/tex]-periodic and that the tangent function is [tex]\pi[/tex]-periodic. Also, recall that [tex]\cos x[/tex] is even (so that [tex]\cos(-x)=\cos x[/tex]) and [tex]\sin x[/tex] is odd (so that [tex]\sin(-x)=-\sin x[/tex].

15.

[tex]\cos\left(-\dfrac{13\pi}3\right)=\cos\dfrac{13\pi}3=\cos\left(\dfrac\pi3+4\pi\right)=\cos\dfrac\pi3=\boxed{\dfrac12}[/tex]

16.

[tex]\sin\dfrac{23\pi}4=\sin\left(\dfrac{3\pi}4+5\pi\right)=\sin\left(\dfrac{3\pi}4+\pi\right)=\sin\dfrac{7\pi}4=-\dfrac1{\sqrt2}[/tex]

[tex]\implies\csc\dfrac{23\pi}4=\boxed{-\sqrt2}[/tex]

17.

[tex]\cos\left(-\dfrac{7\pi}2\right)=\cos\dfrac{7\pi}2=\cos\left(\dfrac\pi2+3\pi\right)=\cos\left(\dfrac\pi2+\pi\right)=\cos\dfrac{3\pi}2=0[/tex]

[tex]\implies\sec\left(-\dfrac{7\pi}2\right)=\boxed{\text{undefined}}[/tex]

18.

[tex]\tan\left(-\dfrac{29\pi}6\right)=\dfrac{\sin\left(-\frac{29\pi}6\right)}{\cos\left(-\frac{29\pi}6\right)}=-\dfrac{\sin\frac{29\pi}6}{\cos\frac{29\pi}6}[/tex]

[tex]\sin\dfrac{29\pi}6=\sin\left(\dfrac{5\pi}6+4\pi\right)=\sin\dfrac{5\pi}6=-\dfrac12[/tex]

[tex]\cos\dfrac{29\pi}6=\cos\dfrac{5\pi}6=\dfrac{\sqrt3}2[/tex]

[tex]\implies\tan\left(-\dfrac{29\pi}6\right)=-\dfrac{-\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}[/tex]

[tex]\implies\cot\left(-\dfrac{29\pi}6\right)=\boxed{\sqrt3}[/tex]

Answer:

Step-by-step explanation:

The sum of the two shorter sides must be greater than the longest side.

5 + 8 = 13

13 is not greater than 14, so the three segments cannot form a triangle.

Answer: No

Step-by-step explanation:

A triangle can be formed only if the sum of 2 sides of the triangle is bigger than the length of the third side of this triangle.

In this case we have AB = 5, BC = 8 and AC = 14.

AB + AC > BC → 5 + 14 > 8 →1 9 > 8 ok!

AB + BC > AC → 5 + 8 > 14 → 13 > 14 false!

BC + AC > AB → 8 + 14 > 5 → 22 > 8 ok!

As we have that AB + BC > AC FALSE, this segments cannot form a triangle.

There are 50 degrees in angle c

Answer: A. 50°

Step-by-step explanation:

Since the measure angles of a triangle add up to 180° and the right triangle=90°, therefore when you subtract 180-90-40, you get 90-40, which then equals to 50°.

For this case we have that by definition, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees.

Now, according to the figure we have that from V to S there are 180 degrees, like this:

[tex]5x + 25x + 30 = 180[/tex]

We add similar terms:

[tex]30x + 30 = 180[/tex]

Subtracting 30 from both sides of the equation:

[tex]30x = 150[/tex]

Divide by 30 on both sides of the equation:

[tex]x = \frac {150} {30}\\x = 5[/tex]

Answer:

[tex]x = 5[/tex]

Answer:

The points corresponding to P=(3,4) and Q=(6,7), so the answer is D.

Step-by-step explanation:

Ok, in mathematics, given two sets X and Y, the collection of all the ordered pairs (X, Y), formed with a first element in X and a second element in Y, is called the Cartesian product of X and Y. The Cartesian product of sets allows define relationships and functions. In this case, it is a function that contains two points, denoted P and Q. Given, the ordered pair of each, first read the one corresponding to the X axis  and then to the Y axis.

For P: you read X and you see that it is on 3 (between 2 and 4), and then the Y axis is on 4 (between 3 and 5).

For Q: you read X and you see that it is on 6 (between 5 and 7) and then the Y axis is on 7 (between 6 and 8)