Given the value of the hypotenuse c for a 30°-60°-90° triangle, write the equations to represent sides a and b in terms of c. Assume a is the shorter leg.

Answer:

y:  13, 22, 25, 28

ordered pairs: (3, 13)  (6, 22)  (7, 25)  (8, 28)

Step-by-step explanation:

Given:

To find the y-values, substitute the x-values into the function and solve.

when x = 3

y = 3(3) + 4

  = 9 + 4

  = 13

when x = 6

y = 3(6) + 4

   = 18 + 4

   = 22

when x = 7

y = 3(7) + 4

   = 21 + 4

   = 25

when x = 8

y = 3(8) + 4

  = 24 + 4

  = 28

Therefore, the ordered pairs are;  (3, 13)  (6, 22)  (7, 25)  (8, 28)

Answer:

volume = 527.52 in³

volume increased by 30% = 685.776 in³

Step-by-step explanation:

Volume of a cone

[tex]V=\dfrac13\pi r^2h[/tex]

(where r is the radius and h is the height)

Given:

[tex]\implies V=\dfrac13 \cdot 3.14 \cdot 6^2 \cdot 14[/tex]

[tex]\implies V=527.52 \ \sf in^3[/tex]

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If the volume increases by 30% then it will now be 130% of the original volume.

130% as a decimal = 130/100 = 1.3

Therefore, to find the new volume, multiply the original volume by 1.3.

[tex]\implies V=527.52 \cdot 1.3[/tex]

[tex]\implies V=685.776 \ \sf in^3[/tex]

Answer:

⅙

Step-by-step explanation:

it could be 6 and 1, 5 and 2, 4 and 3, 3 and 4, 2 and 5 or 1 and 6.

It is 2 fair dice, so all together, the probability is 36.

6/36 can be simplified to ⅙

Answer:

have a good day

Step-by-step explanation:

rump 2020

The geometric mean of 18 and 30 is the product of 18 and 30 square rooted, so:

      [tex]\sqrt{18*30} =\sqrt{540} =\sqrt{9*4*15} =\sqrt{36*15} =6\sqrt{15}[/tex]

Hope that helps!

Answer:

8490.56 yd^2

Step-by-step explanation:

find radius by dividing 104 by 2

we get 52 yd

now the area of circle is [tex]\pi r^{2}[/tex]

we use 3.14 for pi

so 3.14 times 52*52

3.14 times 2704

8490.56

24

Explanation:

R = D + 12 (1)

D = B + 6 (2)

R = 2*B (3)

Put (3) into (1): 2*B = D + 12 (4)

Rewrite (2) as B = D - 6 and put this into (4): 2*(D - 6) = D + 12

So: 2D - 12 = D + 12

Subtract D from both sides and add 12 to both sides to get: D = 24

(not suree)

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

The surface area of the hexagonal prism is calculated using:

A = 6al + 3[tex]\sqrt[/tex]3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]

Divide both sides by 0.04

275 = 24l + 48[tex]\sqrt[/tex]3

Subtract 48[tex]\sqrt[/tex]3 from both sides

24l = 275 - 48[tex]\sqrt[/tex]3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Read more about surface areas at:

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Answer:

275, 7.99

Step-by-step explanation:

i got it right

and please get me too branliest

Answer:

Step-by-step explanation:

The last one.

A would be a quadratic if the leading coefficient was anything but 0. 0 eleminates the x^2. Not A

B has no x^2 term to begin with. B is not the answer.

C is in exponential form. C is not the answer

D has an x^2 term. There is nothing using x that is higher. D is the answer.

Answer:

a. 7 by 21

b. a(-12, 2), b(-12, -5), c(9, -5)

Step-by-step explanation:

AD is 3 times the length of AB. X can be the length of AB. Then 3x would be the length of AD. The perimeter is 56, which would also be 3x + x + 3x + x which is 8x. This gives us 8x = 56, meaning that x is 7, or the length of AB is 7. Because AD is 3 times the length of AB (which is 7), AD = 21. Therefore, the dimensions of the rectangle ABCD is 7 by 21.

Coordinates of A have to be 21 units away from D since AD = 21. It goes in the left direction, meaning that 21 is subtracted from 9 (since this is a horizontal edge involving x coordinates) while the y value remains the same. The result is (-12, 2). For coordinate B, it has to be 7 units away from A downwards since AB = 7. This means that you subtract 7 from 2 (involving only the y coordinates), resulting in (-12, -5). For coordinate C, it has to be 21 units from B since BC = AD = 21.  Because C is right compared to B, you have to add 21 to -12 (involving only the x coordinate) resulting in (9, -5).

Answer:

1. 392 in², 2. 94.99 cm², 3. 145.2 ft², 4. 161.5 m², 5. 17 ft and 81 cm

Step-by-step explanation:

1. A = 16 x 19

A = 304

A = 1/2(11x16)
A = 1/2(176)
A = 88
304 + 88 = 392 in²

2. A = πr²
A = 3.14*5.5²
A = 3.14*30.25
A = 94.985
A = 94.99 cm²

3. A = 1/2(bh)
A = 1/2(11x26.4)
A = 1/2(290.4)
A = 145.2 ft²

4. A = bh
A = 9.5*17
A = 161.5 m²

5. part 1
A = (1/2) · (p + q) · h

112 = (1/2)(11+q)(8)
112 = 4(11+q)
112 = 44 + 4q
68 = 4q
17 = q

17 ft

5. part 2
A = lw
364.5 = 27w
13.5 = w
P = 2l + 2w
P = 2(27) + 2(13.5)
P = 54 + 27
P = 81
81 cm

Hope this helps :)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's see ~

[tex]\qquad \sf  \dashrightarrow \:j + j + 2k[/tex]

[tex]\qquad \sf  \dashrightarrow \:2j + 2k[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(j + k)[/tex]

・．━━━━━━━━━━†━━━━━━━━━━━━．・

Answer:

y - 2 = 6 (x - 1)

Step-by-step explanation:

Slope intercept form equations look like this:

y - y1 = m (x - x1)

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

Using the point (1,2), we know that x1 = 1 and y1 = 2. Let's sub these values into the slope intercept equation:

y - 2 = m (x - 1)

To complete this equation, we need to find slope. Pick out another point on the graph and plug into the slope equation. We can use point (2,8), where (1,2) = Point 1 and (2,8) = Point 2.

[tex]\frac{y2-y1}{x2-x1}=\frac{8-2}{2-1} =\frac{6}{1} =6[/tex]

Now that we know m = 6, let's plug that back into the original equation to get our final answer:

y - 2 = 6 (x - 1)            

I hope this helps!

What is 2/5 of 15?

Want to quickly learn or show students how to convert 2/5 of 15? Play this very quick and fun video now!

How to Calculate the Fraction of a Whole Number

  How to Calculate the Fraction of a Whole Number

You probably know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.

Here's a little tip for you. Any number can be converted to fraction if you use 1 as the denominator:

15

1

So now that we've converted 15 into a fraction, to work out the answer, we put the fraction 2/5 side by side with our new fraction, 15/1 so that we can multiply those two fractions.

That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:

2 x 15

5 x 1

=

30

5

In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.

You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 30 and 5 is 5.

We can now divide both the new numerator and the denominator by 5 to simplify this fraction down to its lowest terms.

30/5 = 6

5/5 = 1

When we put that together, we can see that our complete answer is:

6

1

The complete and simplified answer to the question what is 2/5 of 15 is:

6

hope this helps

Missing number is 6

Set up the proportion

[tex] \frac{2}{5} = \frac{x}{15} [/tex]

Cross multiply to get 5x=30.

Divide both sides by 30 to get the answer

5x÷5=30÷5

x=6

Answer:

the volume is 210

Step-by-step explanation:

length x width x height

length=6

width=5

height=7

6 x 5 = 30

30 x 7 = 210

Answer:

x = 16.71m

Step-by-step explanation:

KL² = KX² + LX² - 2KX × LX × cos(KXL)

x² = 26² + 20² - 2 × 26 × 20 × cos(40°)

x = 16.713m ≈ 16.71m

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer:

2.082.

Step-by-step explanation:

Solution,

Given,

Area ( A ) = 26.025 m².

Length ( L ) = 12.5 m.

Now,

Breadth ( B ) = Area ÷ Length.

= 26.025 ÷ 12.5

= 2.082.

Thus, The breadth of the room is 2.082 m.

Answer:

x=140(corresponding angle)

Corresponding angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal

The 140° angle on line m and the x° angle on line n are corresponding angles.

The value of x is 140°

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

The figure is given,

Line m and Line n are parallel.

t line is the transversal line on the two parallel lines, line m and line n.

We see that,

140° angle on line m is corresponding to the x° angle on line n.

Corresponding angles are equal.

So,

140° = x°

x° = 140°

Thus,

The 140° angle on line m and the x° angle on line n are corresponding angles.

The value of x is 140°

Learn more about corresponding angles here:

https://brainly.com/question/1597341

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Answer:

Step-by-step explanation:

3^(n-1) * (n(n+1)/2 = 20412

The n(n +1)/2 is a factorial which is defined for integers so we are looking for a whole number solution.

We could draw a graph manually or using software and get the solution where the graph cuts the  x axis.

Also we could find the prime  factors of 20412:

20412 = 2^2 * 3^6  * 7

and try substituting 2, 3 and 7 into the equation

Using this method we see that one solution is n = 7.

I could have tried  n = 7 first because  3^n-1 = 3^6!!

Answer:

3419.46 mm3

Step-by-step explanation:

volume of cylinder = area of circle x heoight

A of circle  = pie r sqy = 3.14 x 11 x 11 = 379.94

379.94 x 9 = 3419.46

Answer:

C

Step-by-step explanation:

There are 4 aces and 4 sixes. 4 + 4 is 8 (since it says or) so the chance is 8 / 52. 8 / 52 simplified, divide both sides by 4 and you get 2 / 13.

Answer:

C

Step-by-step explanation:

there are 4 aces and 4 sixes in a deck of 52 cards.

"And" means a probability * another probability

"Or" means a probability + another probability.

In this case, it is (probability of picking an ace) + (probability of picking an six).

[tex]\frac{4}{54} + \frac{4}{54} = \frac{8}{54} = \frac{2}{13}[/tex]

Please pick as brainliest!

The measure of angle A in the kite before cutting the fabric is 42 degrees.

A kite is a quadrilateral with four sides and four angles. Adjacent sides are equal, and the diagonals bisect each other at 90 degrees.

Also, there is a pair of equal opposite angles.

From the diagram:

110 + (6x + 4) + (4x + 26) = 180 (sum of angles in a straight line)

10x + 30 = 70

x = 4

∠A = 4(4) + 26 = 42°

The measure of angle A in the kite before cutting the fabric is 42 degrees.

Find out more on kite at: https://brainly.com/question/386327

Answer: Here, this should help ya out :

With graphing lines and slopes use desmos graphing calulator dont worry, its safe ;)

Answer:

See below ↓

Step-by-step explanation:

Step 1 : Mark the y-intercept.

Step 2 : Draw the slope.