Use the Pythagorean’s Theorem to find the missing side of each triangle

Step-by-step explanation:

4x -24=-y

-24-4x=y

then do calculation

Answer:

infinite solutions

Step-by-step explanation:

substitute y in the first equation

4x+(-4x+24)=24

4x and -4x cancel out

24/24=1

or solve for x, you should also get 1

therefore, infinite solutions. you can also try using a graphing calculator

Answer:

= 7

Step-by-step explanation:

switch sides

v+5/3 =4

multiply both sides by 3

3(v+5)/3=4 times 3

simplify

v+5=12

subtract 5 from both sides

v+5-5=12-5

simplify

v=7

Answer:

The values of [tex]r_{2}[/tex] and [tex]\alpha_{2}[/tex] are 2 and 150º.

Step-by-step explanation:

The complete statement is:

Find [tex]\alpha_{2}[/tex] and [tex]r_{2}[/tex] such that  [tex]\sin \theta - \sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos (\theta - \alpha_{2})[/tex].

We proceed to use the following trigonometric identity:

[tex]\cos (\theta - \alpha_{2}) = \cos \theta \cdot \cos \alpha_{2} +\sin \theta \cdot \sin \alpha_{2}[/tex] (1)

[tex]\sin \theta -\sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos \theta \cdot \cos \alpha_{2}+r_{2}\cdot \sin \theta \cdot \sin \alpha_{2}[/tex]

By direct comparison we derive these expressions:

[tex]r_{2}\cdot \sin \alpha_{2} = 1[/tex] (2)

[tex]r_{2}\cdot \cos \alpha_{2} = -\sqrt{3}[/tex] (3)

By dividing (2) by (3), we have the following formula:

[tex]\tan \alpha_{2} = -\frac{1}{\sqrt{3}}[/tex]

[tex]\tan \alpha_{2} = -\frac{\sqrt{3}}{3}[/tex]

The tangent function is negative at second and fourth quadrants. That is:

[tex]\alpha_{2} = \tan^{-1} \left(-\frac{\sqrt{3}}{3} \right)[/tex]

There are at least two solutions:

[tex]\alpha_{2,1} = 150^{\circ}[/tex], [tex]\alpha_{2,2} = 330^{\circ}[/tex]

And the value of [tex]r_{2}[/tex]:

[tex]r_{2}^{2}\cdot \sin^{2}\alpha_{2} + r_{2}^{2}\cdot \cos^{2}\alpha_{2} = 4[/tex]

[tex]r_{2}^{2} = 4[/tex]

[tex]r_{2} = 2[/tex]

The values of [tex]r_{2}[/tex] and [tex]\alpha_{2}[/tex] are 2 and 150º.

Answer:

G. 477.75

Step-by-step explanation:

Answer:

The missing angle I believe is 25%.

Step-by-step explanation:

180-130=50

Divide 50 by 2 and it equals 25. 25 degrees for each angles.

Answer:25

Step-by-step explanation:

alright so the triangle theorem states that all of the angles of a triangle add up to 180. we already of 130 so we take away 130 from 180 to get 50. If you see the two little lines on the triangles sides opposite of the two angles that we are missing then you can tell by those lines that the angles opposite of them are equal to each other. So you divide 2 from 50 to get 25 which is the value of x. Hope you understand this (:

Answer:

G.

Step-by-step explanation:

It doesn't matter if you switch what is inside the parentheses, as long as you don't put it outside or switch around the equation.

(hope this helps!)

Answer: 42

Step-by-step explanation:

First you have to subtract 450 from 6750 to get 6300

Second you have to figure out how many tax returns you have to make by dividing 6300 by 14 to get 450

Third you have to do 6300 / 42 to get 150 so if you times 150x 42 equals 6300.

Answer:

3a+33

Step-by-step explanation:

Add 2a+1 to a+32

Answer:

a = 3, b = 1, c = - 3

Step-by-step explanation:

Substitute n = 1, 2, 3 into the n th term

a + b + c = 1 → (1)

4a + 2b + c = 11 → (2)

9a + 3b + c = 27 → (3)

Subtract (1) from (2) term by term to eliminate c

Subtract (2) from (3) term by term to eliminate c

3a + b = 10 → (4)

5a + b = 16 → (5)

Subtract (4) from (5) term by term to eliminate b

2a = 6 ( divide both sides by 2 )

a = 3

Substitute a = 3 into (4) and evaluate for b

3(3) + b = 10

9 + b = 10 ( subtract 9 from both sides )

b = 1

Substitute a = 3, b = 1 into (1) and evaluate for c

3 + 1 + c = 1

4 + c = 1 ( subtract 4 from both sides )

c = - 3

Then a = 3, b = 1 and c = - 3

The measure of a, b and c is  3, 1 and - 3 respectively.

A quadratic sequence is a sequence whose nth term is given by the general formula -

A{n} = an² + bn + c.

Given are the 4 terms of the quadratic sequence as 1, 11, 27 and 49.

Now, we can the following equations as -

A{1} = a + b + c = 1

a + b + c = 1

c = 1 - a - b              ........ Eq[1]

A{2} = 4a + 2b + c = 11

4a + 2b + c = 11

c = 11 - 4a - 2b           ........ Eq[2]

A{3} = 9a + 3b + c = 27

9a + 3b + c = 27

c = 27 - 9a - 3b               ........ Eq[3]

A{4} = 16a + 4b + c = 49

16a + 4b + c = 49

c = 49 - 16a - 4b             ........ Eq[4]

Equate Eq[1] and Eq[2] -

1 - a - b  =  11 - 4a - 2b  

1 - 11 = - 4a - 2b + a + b

- 10 = - 3a - b

3a + b = 10                ........... Eq[5]

Equate Eq[3] and Eq[4] -

27 - 9a - 3b = 49 - 16a - 4b  

- 9a - 3b + 16a + 4b = 49 - 27

7a + b = 22          .......... Eq[6]

We can write -

7a + 10 - 3a = 22

4a + 10 = 22

4a = 12

a = 3

and

b = 10 - 3a

b = 10 - 9

b = 1

At last -

c = 1 - a - b

c = 1 - 3 - 1

c = - 3

Therefore, the measure of a, b and c is  3, 1 and - 3 respectively.

To solve more questions on quadratic sequence, visit the link below -

https://brainly.com/question/22412845

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Answer:

for ac I got 11

ab i got 14

I'm not quite sure tho

but you could use SOH CAH TOA to find ab then use Pythagoras theorem to find AB

Answer:

AB = 11.6 inches

AC = 7.3 inches

m∠B = 39°

Step-by-step explanation:

To calculate side AB (c) put b (9 inches) over the sine of β (51°).

c = 9/sin(51)

The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). This would be about 0.777.

c = 9/0.777

I recommend using a fraction here. 0.777 becomes 777/1000. Find the reciprocal (1000/777). Switch the sign to multiplication.

c = 9/1 * 1000/777

Cross cancel if needed.

c = 3/1 * 1000/259

Now multiply.

c = 3000/259

Divide 3000 by 259.

c ≈ 11.5830116 inches ≈ 11.6 inches

Now we know AB. To find AC, find the square root of AB² - BC².

AC = √(11.6² - 9²)

Square both 11.6 and 9.

AC = √(134.56 - 81)

Add 134.56 and 81 to get 53.56

AC = √53.56

Find the square root of 53.56

AC ≈ 7.31846979 ≈ 7.3 inches.

Finding the measure of angle B is comparatively simple. Subtract 51 from 90 to get 39° for angle B.

Answer:

8.

Step-by-step explanation: Start at 8 and go up until 15. boom, you hit the dot at 15. Simple.

The solution is, The geometric mean of 45 and 15​ is 25.98.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

here, we have,

We are given two numbers as 45 and 15​.

Formula for geometric mean is

G.M = √x₁ × ... × xₐ  

So, using this we get

⇒G.M = √45 × 15

⇒G.M = √675

⇒G.M = 25.98

Hence, the geometric mean of 45 and 15​ is 25.98.

Learn more about geometric mean from the given link

brainly.com/question/28562725

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Answer:

x=0

Step-by-step explanation:

We can first add 49 to both sides to get (x+7)^2=49

We can then take the square root of both sides and get x+7=7

Subtract 7 to both sides and you get x=0

Answer:

[tex]x=-14\text{ and } x=0[/tex]

Step-by-step explanation:

We are given:

[tex](x+7)^2-49=0[/tex]

And we want to solve for x.

First, we can add 49 to both sides:

[tex](x+7)^2=49[/tex]

Now, we can take the square root of both sides. Since we are taking an even root, we will need plus-minus. Hence:

[tex]x+7=\pm\sqrt{49}[/tex]

Evaluate:

[tex]x+7=\pm7[/tex]

Subtract 7 from both sides:

[tex]x=-7\pm7[/tex]

So, we have two solutions:

[tex]x=-7+7\text{ and } x=-7-7[/tex]

Evaluate:

[tex]x=0\text{ and } x=-14[/tex]

So, from least to greatest, our solutions are:

[tex]x=-14\text{ and } x=0[/tex]

Answer:

B

Step-by-step explanation:

Answer:

90 degree counter clockwise rotation.

Answer:

90 degree counter-clockwise rotation.

Answer:

$60

Step-by-step explanation:

The computation of the money saved each month is shown below:

= Spending per month × decrease office supply percentage

= $375 × 16%

= $60

The office supplies after given percentage is

= $375 - $60

= $315

So the money that saved each month is $60

Answer:

D

Step-by-step explanation:

When in doubt choose D

Answer:

D

Step-by-step explanation:

The other dude is wrong, you have to plug in the domain to find the range.

Answer:

3/9

Step-by-step explanation:

15*4= 60 so 15/60 is equivalent to 1/4.

1/16 is just a smaller equivalent of 2/8 which is just a smaller equivaent of 1/4.

3/9 simplified is 1/3. I/s is bigger than 1/4.

Hope this helps

Answer:

3/9

Step-by-step explanation:

[tex]\frac{1}{4}\cdot\frac{4}{4}=\frac{4}{16}\\\\\frac{1}{4}\cdot\frac{2}{2}=\frac{2}{8}\\\\\frac{1}{4}\cdot\frac{15}{15}=\frac{15}{60}[/tex]

We can turn 1/4 into all of the first three fractions by multiplying it by some version of 1, but we can't do the same for 3/9: trying to multiply 1/4 by 3/3 will get us a different fraction: 3/12. Additionally, 3/9 in lowest form is 1/3, and 1/3 is clearly not equal to 1/4.

Answer:

Kindly check explanation

Step-by-step explanation:

Give the line of best fit :

y = 1.62x + 18 ; where ;

y = wait time ; x = number of staffs available

If slope of the line is -1.62.

The slope of linear graph represents the ratio of change in the y variable and the x variable. With a slope value of - 1.62, the rate of change is negative and thus an increase in x will lead to a decrease in y. This means that for every unit increase in the number of staffs, the wait time reduces at a rate of 1.62 per unit.

Answer:

[tex]4[/tex]

[tex]75.96^{\circ}[/tex]

Step-by-step explanation:

La función es

[tex]f(x)=x^2-8x+16[/tex]

La derivada de la ecuación nos da la tangente

[tex]f'(x)=2x-8[/tex]

El punto es [tex](6,4)[/tex]

Entonces en [tex]x=6[/tex]

[tex]f'(6)=2\times 6-8=4[/tex]

La pendiente de la tangente es [tex]4[/tex].

El ángulo de la pendiente está dado por

[tex]\tan\theta=m\\\Rightarrow \theta=\tan{-1}m\\\Rightarrow \theta=\tan^{-1}4\\\Rightarrow \theta=75.96^{\circ}[/tex]

El ángulo que forma la tangente con el eje x positivo es [tex]75.96^{\circ}[/tex]

Answer:

2770

Step-by-step explanation:

Answer:

1: corresponding

2: supplementary

3: complementary

4: vertical

Step-by-step explanation:

Answer:

1: corresponding

2: supplementary

3: complementary

4: vertical

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

you try to get x by itself in this case I devided x/2 and -2/2

Answer:

infinitely many solutions

Step-by-step explanation:

12t-5t=7t-7t=0=-4t=-4, 4+-4=0 so 0=0

The answer will be 1/10. First you will change the denominator to the same number because you can’t mutiply fractions if the denominator is different. 5x2=10 and 2x5=10. So both of the denominator will turn into a 10. Now you’ll have to find the numerator. For the first one, multiply it by 2 because that how much the number need to turn equalvilant for the denominator. 1x2=2. So now you know that the first fraction is 2/10. Then you multiply 1 with 5 which is 5. Now the numbers all have the same denominator. Multiply 2/10 and 5/10 which is 1/10.

Answer:

D.) 75 meters

Step-by-step explanation:

1 minute is 60 seconds

So, you divide 60 divided by 40=1.5

1.5 times 50=75

75 meters

D.)

Hope this helped!! :)

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