Which of the following sets could be the sides of a right triangle?{2, 3, square root of 13} {5, 5, 2, square root of 10} { 5, 12, 15 }

[tex]\bf ~\hspace{10em}\textit{Double Angle Identities}\\\\ sin(2\theta)=2sin(\theta)cos(\theta) ~\hfill cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ \boxed{\bf 2cos^2(\theta)-1} \end{cases} \\\\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}[/tex]

well, take a peek at the cos(2θ) identities.

To solve for the amount of pure silver in the alloy mixture, use the alloy mixture equation in algebra. After setting up and solving the equation, we find that roughly 22.83 ounces of pure silver are used to produce the desired alloy,

This problem can be solved using the alloy mixture equation, which is used to determine how to create a desired mixture by blending two substances of different concentrations. Let's denote the amount of pure silver used as 'x'. So, the equation can be set up as follows:

($30.48 × x + $21.35 × 52) / (x + 52) = $24.76.

After multiplying through by (x + 52) and doing algebra, you will find that x (ounces of pure silver) equals approximately 22.83 ounces.

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Answer:

The answer in the procedure

Step-by-step explanation:

we have

2x-3y=-1 ----> equation A

3x+3y=26 --> equation B

Solve the system by elimination

Adds equation A and equation B

2x-3y=-1

3x+3y=26

----------------

2x+3x=-1+26

5x=25

x=25/5

x=5

Find the value of y

substitute the value of x in equation A or equation B and solve for y

2(5)-3y=-1

10-3y=-1

3y=10+1

y=11/3

Answer:

5x=25

Step-by-step explanation:

A p e x

Answer:

$69.50

Step-by-step explanation:

First you need to know how much wall you're going to cover.

Each wall us 12 ft by 8ft

The area of a rectangle can be computed with the formula:

A = L x W

Using the given:

A = 12ft x 8 ft

  = 96 ft²

This is the area of each wall. Since all 4 walls will be covered, you multiply the area of 1 wall by 4.

96 ft² x 4 = 384 ft²

Next we subtract the area of the windows and the door because we won't be covering that.

384 ft² - 52 ft² = 332 ft²

So the total area we are covering with wall paper is 332 ft².

To get the cost of the wallpaper needed, we just need to compute first how many bolt we will need. Divide the total area to be covered by the area of one bolt of wall paper.

332 ft² ÷ 72 ft²/bolt = 4.61 bolts ≅ 5 bolts

Then we multiply it by the price per bolt:

5 bolts x $13.90/bolt = $69.50

Answer:

3/4.

Step-by-step explanation:

Total number of ways to pick 3 digits from the 4 given digits = 4P3

= 4!/ 1! = 24 ways.

The odd numbers are formed when 7 is the last digit of the 3 digits and this will be  in 6 numbers 247, 267, 427, 467, 647  and 627 . So there will be 24 - 6 = 18 even numbers.

So the probability of only even digits = 18/24 = 3/4.

Answer:

vertically stretched by a factor of 2 and moved up 5 units

Step-by-step explanation:

f(x)=x^2

f(x+5) means it moved left 5 units.

f(x-5) means it moved right 5 units.

f(x)+5 means it moved up 5 units.

f(x)-5 means it moved down 5 units.

One of the transformations we have is that it moved up 5 units.

m(x)=f(x)+5

m(x)=x^2+5

Now there is another transformation.

f(x)=x^2

a*f(x) means it is either being vertically stretched or compressed.  a also tells if we have a reflection (if a is negative) or not (if a is positive).

n(x)=2x^2 means it has been vertically stretched by a factor of 2.

Let's put it altogether.

g(x)=2x^2+5

means the parent function has been vertically stretched by a factor of 2 and moved up 5 units

The transformations applied to f(x) to create g(x) involve a vertical stretching by a factor of 2 and a vertical shift upward by 5 units. These modifications result in a parabolic curve that is steeper and shifted upwards compared to the original f(x).

To transform the function [tex]f(x) = x^2[/tex]  into [tex]g(x) = 2x^2 + 5,[/tex] several alterations are made.

First, the function is scaled vertically by a factor of 2.

This means that the output values of g(x) are twice as large as those of f(x) for any given input.

This vertical stretching increases the steepness of the parabolic curve.

Secondly, a constant term of 5 is added to g(x).

This shifts the entire graph of the function vertically upward by 5 units, creating an upward shift.

Consequently, g(x) is now centered 5 units above f(x).

For similar question on vertical stretching.

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Answer:

=63.9°

Step-by-step explanation:

To find the angle of elevation using the shadow of an object, we use the trigonometric ratio Tangent.

Tan∅=opposite/adjacent

Opposite is the height of pole while adjacent is the shadow of the pole.

The tan of the angle of elevation= height of the pole/length of shadow

Tan ∅=45/22

∅= Tan⁻¹(45/22)

=63.9°

Angle of elevation=63.9°

Answer:

Step-by-step explanation:

Step-by-step explanation:

Olivia is correct.  Each O is opposite of the angle θ, and each A is adjacent.

Paula's first triangle was correct.  But on the second triangle, she reversed the O and A.

Answer:

Answer choice C, location C

Step-by-step explanation:

If you add or subtract the standard deviation to the monthly profit, then you get $19,371.18 and $22,295.48. This shows that the deviation withholds most of the data given

The store location for which  [tex]68%[/tex]% of the data lies between $19,371.18 and $22.295.48 is location C

What is standard deviation?

Standard deviation explains the relation of data with mean.

How to find the location of the data?

For normal distributions, 68% of the data lies under one SD from the mean. Two standard deviations is within  95%, and three standard deviations would take up to 99%.

This implies that on taking (mean + SD) and (mean - SD), 68% of data would cover these two numbers.

 Add and subtract SD from the mean to check which location will give $19,371.18 and $22.295.48.

For location A, we have

M-SD=23,124.70-1553.43=21,571.27

M SD = 23,124.70 + 1,553.43 = 24,678.4

For location B, we have

M - SD = 24,842.18 - 1,617.20 = 23,224.98

M + SD = 24, 842.18 + 1,617.20 = 26,459.38

For location C, we have

M - SD = 20,833.33 - 1,462.15 = 19,371.18

M + SD = 20,833.33 + 1,462.15 = 22,295.48

This implies the store location is C

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(gºf) means solve f(x) first, then use that for g(x)

In the equation for f(x) replace x with -3:

f(x) = x +4 = -3 +4 = 1

Now replace the x in the equation for g(x) with 1

g(x) = x = 1

[tex]\sqrt{\dfrac{3}{15x}}=\sqrt{\dfrac{1}{5x}}=\dfrac{1}{\sqrt{5x}}=\dfrac{\sqrt{5x}}{5x}[/tex]

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for third angle

∠C = 180° - (50 + 75)° = 180° - 125° = 55°

∠B = 180° - (60 + 30)° = 180° - 90° = 90°

∠A = 180° - (45 + 30)° = 180° - 75° = 105°

The required measure of the angle for the given triangles is given as ∠C  = 55°, ∠B  = 90° and ∠A = 105°

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for the third angle

∠C = 180° - (50 + 75)°
     = 180° - 125°
      = 55°

Similarly,

∠B  = 90°

∠A = 105°

Thus, the required measure of the angle for the given triangles is given as ∠C  = 55°, ∠B  = 90° and ∠A = 105°

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Answer:

[tex]\frac{3}{11}=\frac{21}{y}[/tex]

Step-by-step explanation:

3 boys     ->   8 girls     -> 11 students

21 boys   ->   _____     ->  y students

This information is lined up for you to solve for your number of students, y:

Looking vertically you could say the proportion is:

[tex]\frac{3}{21}=\frac{11}{y}[/tex]

Looking horizontally you could say the proportion is:

[tex]\frac{3}{11}=\frac{21}{y}[/tex]

There are other ways to write this but this last one I wrote answers your question.

Answer:

Step-by-step explanation:

When one variable depends on another variable according to a rule it is known as function:

For example if you want an output of 2 and the input value is 4. Then you will subtract 4 from x

We have to find x f(x).

x f(x) =?

f(x) = x-4

Now input value is:  x= 3

x f(x)

3 (x-4)

3 (3-4)

3 -1

Now x= 4

x f(x)

4 (x-4)

4 (4-4)

4 0

Now x=5

x f(x)

5 (x-4)

5 (5-4)

5 1

Now x=6

x f(x)

6 (x-4)

6 (6-4)

6 2 ....

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}10x^2-y=48\\2y=16x^2+48&\text{subtracy}\ 16x^2\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}10x^2-y=48\\-16x^2+2y=48&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x^2-y=48\\-8x^2+y=24\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x^2=72\qquad\text{divide both sides by 2}\\.\qquad x^2=36\to x=\pm\sqrt{36}\\.\qquad x=\pm6\\\\\text{Put the values of}\ x\ \text{to the second equation}[/tex]

[tex]2y=16(\pm6)^2+48\\\\2y=16(36)+48\\2y=576+48\\2y=624\qquad\text{divide both sides by 2}\\y=312[/tex]

Answer:

The values of a and b are a = 11 , b = 7

Step-by-step explanation:

* Lets explain how to solve the problem

* In the exponential functions we have some rules

1-  In multiplication if they have same base we add  the power

# Ex: b^m  ×  b^n  =  b^(m + n) ⇒ b is the base , m and n are the powers

2- In division if they have same base we subtract  the power

# Ex: b^m  ÷  b^n =  b^(m – n) ⇒ b is the base , m and n are the powers

3- If we have power over power we multiply them

# Ex: (b^m)^n = b^(mn) ⇒ b is the base , m and n are the powers

* Lets solve the problem

∵ The equation is [tex](5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{a}y^{2}[/tex] ⇒ (1)

- At first multiply the coefficients

∵ -4 × 5 = -20

- Multiply the base x

∵ [tex](x^{7})(x^{4})=x^{7+4}=x^{11}[/tex]

- Multiply the base y

∵ [tex](y^{2})(y^{5})=y^{2+5}=y^{7}[/tex]

∴ [tex](5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{11}y^{7}[/tex] ⇒ (2)

- By comparing (1) and (2)

∴ a = 11 and b = 7

* The values of a and b are a = 11 , b = 7

A. X=0 Y=5

Those 2 equations are a system. You answer is the value of x and y.

13x+3y=15

y=5-4x

First, lets make each equation fit into y=mx+b

13x +3y=15 y=5-4x

-13x -13x y=-4x+5

3y= -13x +15

Let's use the elimination method to solve this.

y= -4x+ 5 multiply top by 3

3y=-13x+15

3y=-12x+15

3y=-13x+15 subtract the equations

0=x

Lets use the x we just found to solve for y.

y=4x+5

y=4(0)+5

y=5

Answer:

1/4

Step-by-step explanation:

y varies directly as x means you should translate this as y=kx.

y varies indirectly as x means you should translate this as y=k/x.

Anyways we had directly, so the equation is of the form y=kx for any point (x,y) where k is the constant.

We are given y=kx and that this equation should satisfy (x,y)=(8,2).

So let's plug in 8 for x and 2 for y giving us

2=k*8

Divide both sides by 8:

2/8=k

Simplify:

1/4=k

So k is a constant, that constant, the never changing number, for the point (x,y) is 1/4.

That means the equation is y=1/4 *x. The 1/4 is the constant of variation, also called the constant of proportionality.

The constant of variation, in this case, is found to be 1/4 using the formula y = kx.

The constant of variation in this case is 1/4.

Given that y varies directly as x and y = 2 when x = 8, we can use the formula y = kx to find the constant of variation.

By substituting the values y = 2 and x = 8 into the formula, we get 2 = k * 8, which simplifies to k = 1/4.

Answer:

7 pieces

Step-by-step explanation:

Stock that must be available at the beginning of each month = 26 yards

Since,

1 yard = 36 inches

26 yards = 26 x 36 = 936 inches

This means 936 inches of fabric must be available at beginning of each month.

Current Inventory:

4 pieces that are each 22 1/2 (or 22.5) inches long. So total length of these fabrics =  4 x 22.5 = 90 inches

3 pieces that each 33 inches long. So total length of these fabrics = 3 x 33 = 99 inches

Therefore, the total length of current inventory = 90 + 99 = 189 inches.

Length of fabric needed more:

Length of fabric that must be bought more = 936 - 189 = 747 inches

It is given that the fabric must be bought in pieces are the 3 yards long. 3 yards is equal to 108 inches.

So,  I have to buy pieces that are each 108 inches long and I need to complete 747 inches in total.

Therefore, the number of pieces that I need to buy = [tex]\frac{747}{108}=6.9[/tex]

Since, the pieces cannot be bought in fraction, I need to buy 7 complete pieces to replenish my stock.

You need to purchase 7 pieces of 3-yard fabric.

To determine how many pieces of fabric you need to buy, follow these steps:

Therefore, you need to purchase 7 pieces of fabric to replenish your stock.

Answer:

length = 11

width = 6

Step-by-step explanation:

The area of a rectangle is defined by the following formula:

[tex]A=lw[/tex]

The question content tells us this:

[tex]l=3w-7\\A=66[/tex]

If we plug these into our formula, we can find the dimensions.

[tex]66=w(3w-7)\\66=3w^2-7w\\[/tex]

Once we factor this out, we find that [tex]w=6[/tex] and [tex]w=-\frac{11}{3}[/tex]

Since a side length can't be a negative, our width is 6.

[tex]66=6l\\11=l[/tex]

Answer:

34

Step-by-step explanation:

You can use the distance formula to find the distance between any two points in the coordinate plane.

For this problem, you can use a simpler method since both points have the same x-coordinate. Two points than have the same x-coordinate are on the same vertical line. The distance between them is the absolute value of the difference between the y-coordinates.

distance = |-12 - 22| = |-34| = 34

Answer:

34

Step-by-step explanation:

By the distance formula:

[tex]D = \sqrt{[-4-(-4)]^2 + (22-(-12))^2} = \sqrt{34^2} = |34| = 34[/tex]

Answer:

* The values of x are 0 and 4

Step-by-step explanation:

* Lets explain how to solve the problem

- f(x) = x² - 2x - 4 is a quadratic function

- g(x) = 2x - 4

∵ f(x) and g(x) are intersected

∴ They meet each other in a point

- To find this point equate the two functions

∵ f(x) = g(x)

∵ f(x) = x² - 2x - 4

∵ g(x) = 2x - 4

∴ x² - 2x - 4 = 2x - 4 ⇒ subtract 2x from both sides

∴ x² - 4x - 4 = -4

- Add 4 to both sides

∴ x² - 4x = 0

- Take x as a common factor

∴ x(x - 4) = 0

- Equate each factor by 0

∴ x = 0

- OR

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∴ f(x) and g(x) intersected at x = 0 and x = 4

* The values of x are 0 and 4

Answer:

The correct option is B

Step-by-step explanation:

The equation of a line in point-slope form is:

y-y1 = m(x-x1)

where m is the slope and (x1,y1) a point on the line

here m=2 and (x1,y1)=(2,3)

substitute these values into the equation.

y-3 =2(x-2)

Thus the correct opttion is B....

Look at the picture

Carbohydrates. Carbohydrates are digested in the mouth, stomach and small intestine. Carbohydrase enzymes break down starch into sugars. The saliva in your mouth contains amylase, which is another starch digesting enzyme.

Answer:

-8x+10

Step-by-step explanation:

The expression is: -2(3x+x-5)

Step 1: Using order of operations, combine like terms

-2(4x-5)

Step 2: Distribute -2 to each term in the  parentheses:

-8x+10

Hence, the simplified expression is:

-8x+10

Answer:

-8x+10

Step-by-step explanation:

on edge

Answer:

15) Ellen is 12 years old.

16) Don't know what value you are looking for but x=(17/4) while y=(7/4) since the set of equations is 2x-2y=5 and x+y=6.

Step-by-step explanation:

15) Ellen (E) is currently twice as old as Maria (M).

Twice means to multiply by 2.

E=2M is therefore the equation for this part of the problem.

In 6 years, Maria (M) will be 2/3 as old as Ellen (E).  Keep in my Maria as aged 6 years (M+6) and Ellen as aged 6 years (E+6):

M+6=(2/3)(E+6).

So we have this system to solve:

E=2M

M+6=(2/3)(E+6).

I'm going to replace the E in the second equation with 2M since the first equation says E=2M:

M+6=(2/3)(E+6) with E=2M:

M+6=(2/3)(2M+6)

Distribute:

M+6=(4/3)M+(12/3)

Reducing 12/3 to 4:

M+6=(4/3)M+4

Subtract 4 on both sides:

M+2=(4/3)M

Subtract M on both sides:

2=(4/3)M-M

Find a common denominator:  

2=(4/3)M-(3/3)M

Combine like terms:

2=(1/3)M

Multiply both sides by the reciprocal of 1/3 which is 3:

3(2)=3(1/3)M

6=1M

6=M

M=6

Maria is six years old.

Recall E=2M.

So if M=6, then E=2(6)=12.

So currently E is twice as old as M since 6(2)=12.

In six years, M will be 12 which E will be 18.

M (12) is two-thirds as old as E (18) since 12=2/3(18)

16)

2x-2y=5

 x + y=6

Your question doesn't state which value it is looking for.

Anyways I'm going to solve the system for the point (x,y) and then you can decide which part of this answer to use.

I'm going to solve this system by elimination.  Each equation already has the same form: ax+by=c. I just need a column with the variables to be opposite or the same.

I'm going to multiply both sides of equation 2 by 2:

2x-2y=5

2x+2y=12

Now I have opposites in a column: -2y and 2y.

When you add opposites you get 0 so this is what you want to use elimination.

We are going to add the equations now:

2x-2y=5

2x+2y=12

------------------Adding!

4x+0y=17

4x      =17

Divide both sides by 4:

 x      =17/4

Now if x=17/4 and x+y=6, then we have that (17/4)+y=6.

Subtracting 17/4 on both sides gives us y=6-(17/4).

Finding a common denominaotr gives us y=(24/4)-(17/4).

Simplifying this gives us y=(7/4).

The point of intersection (the solution) is (17/4 ,  7/4)

The question is about solving two mathematical problems. The first problem is about ages, where Ellen is found to be 12 years old and Maria is six years old. The second problem is solving a linear equation system where the solution is x = 5 and y = 1.

Let's denote Maria's age as X and Ellen's age as Y. According to the problem, Ellen is twice as old as Maria, so that we can write Y = 2X. Maria will be 2/3 as old as Ellen in six years, so we can write another equation as X + 6 = 2/3 * (Y + 6). Now, we solve these equations. Substituting Y = 2X into the second equation, we get X + 6 = 2/3 * (2X + 6). Solving this, we find X = 6, so Maria is 6. Substituting X = 6 into Y = 2X, we find Y = 12, so Ellen is 12 years old.

For the second part of the problem, we solve the system of equations 2x - 2y = 5 and x + y = 6. One way is to take the second equation and solve for x: x = 6 - y. Substituting this into the first equation, we get 2*(6-y) - 2y = 5. Solving this simplifies to y = 1. Then, covering y = 1 into x + y = 6, we find x = 5.

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Answer:

-6

Step-by-step explanation:

[tex]m^2-36=0[/tex]

Adding 36 on both sides gives:

[tex]m^2=36[/tex]

Square rooting both sides:

[tex]m=\pm \sqrt{36}[/tex]

[tex]m=\pm 6[/tex]

So if square -6 , you will get 36 just like when you square 6.

That is [tex](-6)^2=6^2=36[/tex]

Answer:

-6

Step-by-step explanation:

If one solution to the problem m²-36=0 is 6, the other solution is -6.

(m + 6) • (m - 6)  = 0

Any solution of term = 0 solves product = 0 as well.

m+6 = 0  

m = -6

m-6 = 0

m = 6