One number is 3 more than 2 times another. The sum of the numbers is 15 . Find the two numbers.

1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,

[tex]x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}[/tex]

This means that the length of the hypotenuse is:

[tex]\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}[/tex]

2) (Diagram attached) We know that

[tex]\cos 51^{\circ}=\frac{x}{58}\\x=58 \cos 51^{\circ} \approx \boxed{36.5}[/tex]  (in cm)

3) From the Pythagorean identity,

[tex]\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}[/tex]

4) [tex]\frac{\pi}{6}[/tex]

The age of a tree when the diameter is 11 inches is 80.

The age of the tree increases by 10 with a 1 inch increase in the diameter of the trunk. This represents a linear increase.

The equation that can be used to represent the age of a tree given its diameter is :

age of the tree when the diameter is 4 inches + [(difference between 11 inches and 4 inches) x rate of change in age)

10 + (10 x 7)  = 80

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[tex]\text{L.H.S}\\\\=\dfrac{\sin A \tan A}{1- \cos A}\\\\\\=\dfrac{\sin A \cdot \tfrac{\sin A}{\cos A} }{ 1- \cos A}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\tan A = \dfrac{\sin A }{\cos A}\right]\\\\\\=\dfrac{\tfrac{\sin^2 A}{ \cos A}}{1- \cos A}\\\\\\=\dfrac{\sin^2 A}{\cos A(1-\cos A)}\\\\\\=\dfrac{1-\cos^2 A}{\cos A( 1- \cos A)}~~~~~~~~~~~~~~~~~~~~~~~~;[\sin^2 A + \cos^2 A = 1]\\\\\\[/tex]

[tex]=\dfrac{(1+ \cos A)(1 - \cos A)}{\cos A(1 - \cos A)}\\\\\\=\dfrac{1+ \cos A}{ \cos A}\\\\\\=\dfrac{1}{\cos A} + \dfrac{\cos A}{ \cos A}\\\\\\=\sec A + 1 \\\\\\=1+ \sec A\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

The value of the n is 64.04 after applying the tan ratio which is opposite to adjacent (TOA)

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a right angle triangle shown in the picture.

We can use SOHCAHTOA to find the unknown length.

Using the ratio of tan which is opposite to adjacent (TOA)

tan8 = 9/n

n = 64.038 ≈ 64.04

Thus, the value of the n is 64.04 after applying the tan ratio which is opposite to adjacent (TOA)

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Step-by-step explanation:

Because probability is always one(1).

Probability =

[tex]1 - \frac{2}{10} [/tex]

[tex] \frac{8}{10} [/tex]

[tex] \frac{4}{5} [/tex]

Is the probability of not choosing a red marble.

The vertex of the graph moves to a point twice as far from the y-axis.

Option B is the right answer.

The general equation of a parabola is

y = a(x-h)² + k

or

x = a(y-k)² +h

where (h,k) denotes the vertex.

It is given in the question that the value of h is doubled for the equation given

y = a(x-h)² + k

if the value of the h is doubled, the vertex of the graph shifts and shifts on the x axis away from the y axis , therefore

the vertex of the graph moves to a point twice as far from the y-axis.

Option B is the right answer.

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Answer:

its b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

On edge

Answer:

exponential growth

Step-by-step explanation:

f(x) = 4 * 2^x

This function is in the form

y = a * b^x  where a is the initial value and b is the growth or decay rate

This is  exponential form

if b > 1 then it is growth

0< b < 1 it is decay

b =2 so it is growth

Answer:

B. 3.25 p.m.

Step-by-step explanation:

[tex]20 + 30 + 45 = 96 \: minutes \\ 95 \: minutes \: = 60 \: minutes + 35 \: minutes \\ 95 \: minutes \: = 1 \: hour \: 35 \: minutes\\ 5.00 \: p.m. - 1 \: hour \: 35 \: minutes = 3.25 \: p.m.[/tex]

Answer:

7/11

Step-by-step explanation:

blue = 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7 that will be blue.

green = 1 + 1 + 1 + 1 = 4 that will be green.

So it’s going to be 7 + 4 = 11 in total then do

7/11

Is it 7/22

Mean measure of central tendency is the most affected by outliers. Then the correct option is B.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

Mean measure of central tendency is the most affected by outliers.

Then the correct option is B.

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Answer:

Step-by-step explanation:

(4x³)² (3x)⁵ = 4²(x³)² (3)⁵(x)⁵

                 = 16x⁶ (243)x⁵

                 = (16 × 243) (x⁶ × x⁵)  [commutative property]

                 = (3888) (x¹¹)   [exponent property]

                 = 3888x¹¹

Answer:

If you mean 656, then the answer is 509,712.

Edit: If you're talking about measurements, then it would be 50,893 feet and 6 inches.

Answer:

18 inches

Step-by-step explanation:

Equation is (2x-32)(x)=72, where x represents length and (2x-32) represents the width. When you simplify the equation, it ends up as 2x^2-32x-72=0. After factoring, you get 2(x-18)(x+2). Since x cannot be negative, it would therefore be 18. If you plug it back into the equation, you can see that it is right :)

The solution to the exponential equation 7^(3 – 2x) = 7^(-x) is 3

7^(3 – 2x) = 7^(-x)

3 - 2x = - x

collect like terms

3 = - x + 2x

3 = x

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Answer:

2j + 8

Step-by-step explanation:

Given:  8 more than twice Jenny's age

Let j = Jenny's age

"twice Jenny's age" means double (multiply by 2) Jenny's age  = 2j

"more than" means to add, so "8 more than" = + 8

Therefore:

"8 more than twice Jenny's age" = 2j + 8

Answer:

X=4

Step-by-step explanation:

Eveything is explained in the pic. Hope that helps ;)

[tex]y = -x^2+10x\implies y = -x^2+10x+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 10}{2(-1)}~~~~ ,~~~~ 0-\cfrac{ (10)^2}{4(-1)}\right)\implies \left( \cfrac{10}{2}~~,~~\cfrac{100}{4} \right)\implies (5~~,~~25)[/tex]

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1. The hypothesis can not be concluded.

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.

For the given problems, the Hypothesis mean is 4.5. The sample mean was 4.75 hours with a normal standard deviation of 2.0.

Now, calculating the z-score,

[tex]z = \dfrac{\bar x - \mu_o}{\dfrac{\sigma}{\sqrt n}}\\\\\\z = \dfrac{4.75-4.5}{\dfrac{2}{\sqrt{15}}}\\\\\\z = 0.48[/tex]

Now, as per the standard normal table, the p-value is 0.6844. Since the p-value is greater than the significance level, the hypothesis can not be concluded.

Hence, The hypothesis can not be concluded.

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Answer:

Y=-58

Step-by-step explanation:

Y=-2(3)^(2)-4

Y=-2(3*3*3)-4

Y=-2(27)-4

Y=-54-4

Y=-58

Answer:

[tex]y^{12} + b^{8} \\OR\\12y + 8b[/tex]

Step-by-step explanation:

If the statement is  

[tex]y^{12} + b^{16-8} \\y^{12} + b^{8} \\[/tex]this can't be more simplified

If the statement is

[tex]y{12} + b{16-8} \\y{12} + b{8} \\\\rearrange\\12y + 8b[/tex]

Answer:

Step-by-step explanation:

To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.

Answer:

A=3

B=31

Step-by-step explanation:

A)5-2=3

b)

17-10=7

10-5=5

7-5=2

2×7=14

14+17=31

Answers.