A right triangle has a hypotenuse with a length 12 and a leg with
length 5. How long is the triangle's other leg?

Answer:

Step-by-step explanation:

gerald=2x

guy=x

gill= aproximately 0.3x

2x+x+0.3x=99

2.3x=99

x=43.04

The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

The equation according to the given statement will be,

The age of Gerald is 2x,

The age of the guy is x and the age of the gill is 0.33x.

So, the equation will be,

x + 2x + 0.33x = 99

3.33x = 99

x = 99/3.33

x = 29.72

Age of Gerald, 2x = 2(29.72) = 59.44 years.

Age of guy, x = 29.72 years and,

Age of gill, 0.33x = 0.33(29.72) = 9.8 years.  

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Answer:

-0.0092

Step-by-step explanation:

sin160°cos110° + sin290°cos340° + tan110°tan160°

(0.34)(-0.34) + (-0.94)(0.94) + (-2.75)(-0.36)

- 0.1156 - 0.8836 + 0.99

-0.0092

I hope this helps!

[tex]\sin 160^{\circ} \cos 110^{\circ} + \sin 290^{\circ} \cos 340^{\circ} + \tan 110^{\circ} \tan 160^{\circ}\\\\=\sin\left(2 \times 90^{\circ} - 20^{\circ} \right) \cos \left(90^{\circ} + 20^{\circ} \right) + \sin \left(3 \times 90^{\circ}+20^{\circ}\right) \cos\left(4 \times 90^{\circ}-20^{\circ \right) + 20^{\circ} \right) + \tan \left( 90^{\circ} +20^{\circ}\right) \tan\left( 2 \times 90^{\circ} - 20^{\circ} \right)\\\\[/tex]

[tex]=-\sin 20^{\circ} \sin 20^{\circ} -\cos 20^{\circ} \cos 20^{\circ}+\cot 20^{\circ} \tan 20^{\circ}\\\\=-\left(\sin^2 20^{\circ} + \cos^2 20^{\circ} \right) + \tan 20^{\circ} \cdot \dfrac 1{\tan 20^{\circ}}\\\\=-1 + 1\\\\=0[/tex]

Answer:

B. 46 ft²

Step-by-step explanation:

Two sides are rectangles 3.1 ft by 5 ft.

One side is a rectangle 5 ft by 3 ft.

area = 2(3.1 ft × 5 ft) + (5 ft × 3 ft)

area = 46 ft²

Answer:

Simple interest: 240, Final amount: 2240

hope im right

Step-by-step explanation:

Using the vertex of the quadratic equation, it is found that the stone reaches a maximum height of 221.0625 ft after 3.5625 s.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

In this problem, considering initial velocity of v(0) = 114 and an initial height of h(0) = 18, the equation is:

h(t) = -16t² + 114t + 18.

Which is a quadratic equation with coefficients a = -16, b = 114, c = 18.

Hence:

[tex]x_v = -\frac{114}{2(-16)} = 3.5625[/tex]

[tex]y_v = -\frac{114^2 - 4(-16)(18)}{4(-16)} = 221.0625[/tex]

Hence, the stone reaches a maximum height of 221.0625 ft after 3.5625 s.

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The different recital programs that are possible is 80,730 ways

Permutation has to do with arrangement while combination has to do with the selection.

According to the question, a pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces, this shows that he can select the 5 pieces in any form.

The number of ways this can be done is given as:
[tex]27C_5=\frac{27!}{(27-5)!5!}\\ 27C_5=80,730[/tex]

Hence the different recital programs that are possible is 80,730 ways

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Answer:

x = -2 & x= 1

Step-by-step explanation:

Zeroes are the x-axis value where the function crosses the x-axis!

Answer: 4,000

Step-by-step explanation:

The only logical choice there because of the rate of others

Answer: c is the answer

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Let the number be 10x+y.

So we have 2(10x+y)+2 = 10y+x, or

20x + 2y + 2 = 10y+x, or

19x=8y-2 …(1)

Try different values of x which satisfy (1) giving an integer value of y. Moreover x should be less than y. The only value of x is 2 which gives us y = 5.

So y = 5 and x = 2.

And the answer is 25.

We can prove this by simply doing the question's equation:

50(since it's the double of 25) + 2 =

50+2= 52

Hope this helps

The Total Number of socks is 10 in all, bear in mind that there is no blue socks hence it will not add to the total amount of socks

Note : 1 pais = 2 socks

Given Data

The statement " 6 times as many pairs of blue socks" is equivalent to no socks, since we have no blue socks, hence 6*0 = 0

Let us find the total socks

= 8+0+2

= 10 socks

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Answer:

9 weeks

Step-by-step explanation:

So he basically took 14 quizzes in 7 weeks.

14/7 = 2/quizzes per week

18/2 = 9 weeks

I don't know what you mean by unit rates but this is what I got.

Step-by-step explanation:

[tex]put \: x \: into \: equation \: 1[/tex]

[tex]2( - 6y + 7) - 9y = 14[/tex]

[tex] - 12y + 14 - 9y = 14[/tex]

[tex] - 21y + 14 = 14[/tex]

[tex] - 21y = 14 - 14[/tex]

[tex] - 21y = 0[/tex]

[tex] \frac{ - 21y}{12} = \frac{0}{21} [/tex]

[tex]y = 0[/tex]

[tex]put \: y = 0 \: into \: equation \: 2[/tex]

[tex]x = 6y + 7[/tex]

[tex]x = 6(0) + 7[/tex]

[tex]x = 0 + 7[/tex]

[tex]x = 7[/tex]

Answer:

y = 0

x = 7

Step-by-step explanation:

2x − 9y = 14     ⇒  ( 1 )

x = − 6y +7      ⇒ ( 2 )

First, let us find the value of y.

For that, replace x with ( - 6y + 7 ).

Let us take equation 1 for that.

2x − 9y = 14

2 ( - 6y + 7 ) - 9y = 14

-12y + 14 - 9y = 14

21y = 14 - 14

21y = 0

Divide both sides by 21.

y = 0

And now let us take equation 2 to find the value of x by replacing y with 0.

2x − 9y = 14    

2x - 9 × 0 = 14

2x - 0 = 14

2x = 14

Divide both sides by 2.

x = 7

Answer:

8√3

Step-by-step explanation:

Let a, b = the positive numbers, and the sum = s,

(1)---- ab = 192

(2)--- a + b = s

Since we want to find the minimum sum, we'll have to substitute one of the variables (either a or b) from (1) to (2), I'll choose b,

From (1), b = 192/a

Substitute b = 192/a into (2),

s = a + 192/a

Now, we are able to use a concept of calculus (maximum & minimum) to solve it, just remember 2 steps in finding the values of x in maxima minima question:

1) find dy/dx

2) Find x from dy/dx = 0

ds/da = 1 - 192/a²

When ds/da = 0,

1 - 192/a² = 0

a² = 192

a = ±√192

a = 8√3 , -8√3

Since a is positive, a = 8√3

Substitute a into (1),

b = 192/(8√3)

b = 8√3

Therefore, the two positive numbers are 8√3... and 8√3

Answer:

Period: 6, Frequency: 1/6, Equation: -4cos([tex]\frac{\pi }{3}x[/tex])-2

Step-by-step explanation:

Because the graph starts at x = 0 at a minimum/maximum, it's easiest to use cosine, so we don't have to shift the graph horizontally. cos(x)

If you take the max/min points and average them, you can use the distance between the average value and the max/min to get the total amplitude, A, which is 4.

Because this function starts at a minimum, but cosine starts at a maximum, we will flip it vertically by adding a negative coefficient to whatever the amplitude is.

We see that the same part of the graph recurres every 6 x-units, so the period is 6. The frequency of this is 1/(period), 1/6.

The coefficient of x in a sin/cos function is [tex]2\pi /Period[/tex], = [tex]\pi[/tex]/3.

The vertical shift (how much the average value of the function moved from 0 to its current position) is -2.

Put all that together, you get y = -4cos([tex]\frac{\pi }{3}x[/tex])-2

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

let's solve ~

Period :

Difference between two successive crest or trough is known as period, so here :

period = 9 - 3 = 6

Frequency

Now, we know that frequency = 1/period

So, frequency for given function is 1/6 hertz , or approximately 0.167 hertz

The required equation is ~

[tex]\qquad \sf  \dashrightarrow \:y = a \cos(bx) + k[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = - 4 \cos( \frac{ \pi}{3} x) - 2[/tex]

Answer:

multicultural

Step-by-step explanation:

Answer:

A. Multicultural

Step-by-step explanation:

It shows later in the sentence that they ate Thai noodles and Egyptian falafel those come from different cultures so it must be multicultural

Answer:

Final answer -

Area of paperboard = [tex]565.92 \: inches {}^{2} [/tex]

hope helpful :D

Answer:

powers of 10

Step-by-step explanation:

Simone examined the pattern in the table

Answer:

D

Step-by-step explanation:

4/3 (3.14) r^3 is the equation, so since the radius is 4

It's 4/3x(pi)64

256/3x(pi)

Answer:

P=90°

R=45°

Step-by-step explanation:

PQR=180°

180°-45°=135°

R=45°(iscoles triangle)

P=90°

Answer:y=4+x

Step-by-step explanation:

You are adding gallons not *,/,-,. So it's y=4+x.

The required equation is y = 4 + x. The correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Jayne stopped for gas before embarking on a road trip. There were already 4 gallons of gas in the tank.

As per the question, the required equation would be as:

y = 4 + x

This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.

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Answer:

-4 < x < -1 or x > 1 (the third option)

Step-by-step explanation:

hope this helps

Answer:

a

Step-by-step explanation:

An asteroid is a minor planet of the inner Solar System. Historically, these terms have been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail.

Answer:

$318

Step-by-step explanation:

6% x 300 = 18

300 + 18 = 318

The closer the probability is to 1, the more likely it is to occur and the closer the probability is to 0, the less likely it is to occur.

This is the likelihood that an event will occur.

So, the closer the probability is to 1, the more likely it is to occur and the closer the probability is to 0, the less likely it is to occur.

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Answer:

11 id.k i think

Step-by-step explanation:

i think that it

The function g(x) = 2f(6x) + 8 is a function transformation of the function f(x)

The function g(x) is given as:

g(x) = 2f(6x) + 8

The table is not given.

So, I will provide a general explanation

Using the following values of x:

x = 0, 1, 2, 3......

We have:

g(0) = 2f(6 *0) + 8

g(0) = 2f(0) + 8

g(1) = 2f(6 *1) + 8

g(1) = 2f(6) + 8

g(2) = 2f(6 *2) + 8

g(2) = 2f(12) + 8

g(3) = 2f(6 *3) + 8

g(3) = 2f(18) + 8

Next, we assume the following values

f(0) = 4, f(6) = 5; f(12) = 6 and f(18) = 7

The values become:

g(0) = 2f(0) + 8 = 2 * 4 + 8 = 16

g(1) = 2f(6) + 8 = 2 * 5 + 8 = 18

g(2) = 2f(12) + 8 = 2 * 6 + 8 = 20

g(3) = 2f(18) + 8 = 2 * 7 + 8 = 22

So, the table of values would be:

x     g(x)

0     16

1     18

2   20

3   22

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The exponential function that represents the number of cells present at x hours is y = 100(2)ˣ

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Let y represent the number of cells after x hours.

From the table, at point (0, 100):

100 = ab⁰

a = 100

At point (1, 200):

200 = 100b

b = 2

The exponential function is y = 100(2)ˣ

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Answer:

100(2)^h=6,400

Step-by-step explanation:

Explanation:

For an equation in the form A(b)^x=y, A represents the initial amount, and b represents the growth rate. At 0 hours, there were 100 cells, so A=100.

Between 0 hours and 1 hour, the number of cells doubled from 100 to 200, or 100(2). Between 1 and 2 hours, the number of cells again doubled from 200 to 400, or 100(2)^2. So the growth rate, or b, is 2.

The table shows that at h hours, there were 6,400 cells. Therefore, the equation that represents the number of cells at h hours is .100(2)^h=6,400

Answer:

x to the 3rd power

Step-by-step explanation:

x+x to the 2nd power = x to the 3rd power

Step-by-step explanation:

The area is the sum of three figures

A = 1*1 + 1*x + x²

   = x² + x + 1

The perimeter is the sum of border segments

P = x*4 + 1*4

  = 4x + 4