if x-y =12 and y^2 =5 (x-2), what are two possible values of y

​

The two triangles are similar because angle C = C' and angle A = A'. The scale factor is 4/3

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent.

Also, the ratio of corresponding sides of similar triangles are equal.

Therefore to show that that the two triangles are equal;

Tan A = 4/3

Tan A = 1.333

A = 53.1°

Tan A' = 5.3/4

Tan A' = 1.33

A' = 53.1°

Therefore the two triangles are similar.

The scale factor = 4/3

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

Answer:

-3,-2,-1 is less than -4 and not greater than

Step-by-step explanation:

Answer:

I think it may be 160?

Step-by-step explanation:

400/5 is 80 there's 2 yellow so 2x80= 160 times

Sean's statement is correct. Christine's statement is incorrect when a is negative.

The value of a to the -3rd power is always less than 1 if a is positive.

For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.

The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.

For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.

Therefore, Christine's statement is incorrect when a is negative.

Learn more about the numbers here:

https://brainly.com/question/28691894

#SPJ1

The number of feet above the submarine is the shark is 23 feet.

Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.

Here, location of shark = 42-19

= 23 feet

Therefore, the number of feet above the submarine is the shark is 23 feet.

To learn more about an integers visit:

https://brainly.com/question/15276410.

#SPJ1

"Your question is incomplete, probably the complete question/missing part is:"

A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.

Answer:  the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.

Step-by-step explanation:  To solve the inequality 2(3x-1)>4x-6, we first simplify the left side by distributing the 2, which gives us 6x-2. Substituting this back into the original inequality, we get:

6x-2 > 4x-6

Next, we isolate the variable term (6x) by subtracting 4x from both sides:

2x-2 > -6

Then, we add 2 to both sides to isolate the variable term completely:

2x > -4

Finally, we divide both sides by 2 to solve for x:

x > -2

Therefore, the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.

The mean of the distribution in this problem is given as follows:

19.5625 pounds.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The dot plot shows the absolute frequency of each observation in the context of the problem.

Considering the dot plot, the sum of the observations in this problem is given as follows:

2 x 12 + 4 x 15 + 1 x 16 + 1 x 18 + 2 x 20 + 1 x 22 + 3 x 25 + 2 x 29 = 313.

The number of observations is given as follows:

2 + 4 + 1 + 1 + 2 + 1 + 3 + 2 = 16.

Hence the mean is given as follows:

313/16 = 19.5625 pounds.

The problem is given by the image presented at the end of the answer.

More can be learned about the mean of a data-set at https://brainly.com/question/1136789

#SPJ1

The equivalent value of the equation is 18x-9=72 and x=4.5

Given data ,

Let the equation be represented as A

Now , the value of A is

(3/5)(30x-15)=72

On simplifying the equation , we get

3(6x-3)=72

On further simplification , we get

18x-9=72

x=81/18

x=4.5

Hence , the equation is 18x-9=72

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The solution to the equation is x = 1.6.

Let's start by distributing the 3 on the right side of the equation:

25 + 2x = 12x + 9

Next, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side. To do this, we'll subtract 2x from both sides:

25 = 10x + 9

Then, we'll subtract 9 from both sides:

16 = 10x

Finally, we'll divide both sides by 10:

x = 1.6

So the solution to the equation is x = 1.6.

for such more question on equation

https://brainly.com/question/16983571

#SPJ11

Answer:

20 quartesrs

Step-by-step explanation:

20 quarters

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius.

Given that the sphere and the cylinder have the same radius and height, we can assume that the radius of both shapes is the same.

Let's denote the radius as 'r'. The volume of the cylinder is given as 50 ft³.

The volume of the cylinder is calculated using the formula V = πr²h, where h is the height.

Since the height of the cylinder is not given, we cannot determine the exact value of 'r' or calculate the volume of the sphere.

However, if we assume that the height of the cylinder is equal to its diameter (which is twice the radius), we can proceed with the calculation.

If the height of the cylinder is equal to 2r, the volume of the cylinder becomes:

50 = πr²(2r)

50 = 2πr³

Dividing both sides of the equation by 2π gives:

25 = πr³

Now, we can substitute this value of πr³ into the volume formula of the sphere:

V = (4/3)πr³

V = (4/3)(25)

V = 100/3

Therefore, if the height of the cylinder is equal to its diameter, the volume of the sphere would be 100/3 ft³. However, please note that this assumption might not necessarily be valid without further information about the relationship between the height and radius of the cylinder.

Answer: The Volume of the sphere is 100/3 cubic feet.

Step-by-step explanation:

It is clearly seen in the given figures, the height is two times the radius. Therefore, h is equal 2r.

We know that,

The volume of the sphere is π x r^2 x h. (r is radius and h is height)

So putting the values of height, h in the above formula, we get:

πxr^2x2r

= 2 * π * r^3.

= 2 * π * r^3 = 50

= π * r^3 = 25

We get, r^3 = 7.957747155

Therefore, r = 1.996472712

Now that we have the measure of the radius, we can find the volume of the sphere!

(4 / 3) * π * r^3

(4/3) * π * (1.996472712)^3

= (4/3) * π * 7.957747155

= (4/3) * π * (25 / π)

= (4/3) * 25

= 100/3 cubic feet.

Read more about volumes of 3-D figures,

https://brainly.com/question/21044783

Answer:

[tex]2-\sqrt{3}[/tex]

Step-by-step explanation:

Find the exact value of the expression, tan(15°).

The method I am about to show you will allow you to solve this problem without any tables or calculators. Although, memorizing the unit circle and trigonometric identities is required.

[tex]\tan(15 \textdegree)\\\\\Longrightarrow \tan(\frac{30 \textdegree}{2} )\\\\\text{Use the half-angle identity:} \ \tan(\frac{A}{2})=\pm \sqrt{\frac{1-\cos(A)}{1+\cos(A)} }=\frac{\sin(A)}{1+\cos(A)} =\frac{1-\cos(A)}{\sin(A)} \\\\\Longrightarrow\frac{1-\cos(30 \textdegree)}{\sin(30 \textdegree)} \\\\\text{From the unit circle:} \ \cos(30 \textdegree)=\frac{\sqrt{3} }{2} \ \text{and} \ \sin(30 \textdegree)=\frac{1}{2}\\[/tex]

[tex]\Longrightarrow \frac{1-\frac{\sqrt{3} }{2}}{\frac{1}{2}}\\\\\Longrightarrow 2(1-\frac{\sqrt{3} }{2})\\\\\therefore \boxed{\boxed{\tan(15 \textdegree)=2-\sqrt{3} }}[/tex]

Thus, the problem is solved.

Answer:

[tex]\tan 15^{\circ} = 2 - \sqrt{3}[/tex]

Step-by-step explanation:

To find the exact value of tan 15°, we can use trigonometric identities and the unit circle.

We know that tan(x) can be expressed as the ratio of sin(x) and cos(x). We can also write 15° as (60° - 45°).

Therefore, tan 15° can be expressed as:

[tex]\tan15^{\circ}=\tan(60^{\circ}-45^{\circ})=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}[/tex]

Now use the trigonometric angle identities to rewrite the ratio in terms of sin 60°, cos 60°, sin 45° and cos 45°.

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Angle Identities}\\\\$\sin (A - B)=\sin A \cos B - \cos A \sin B$\\\\$\cos (A - B)=\cos A \cos B + \sin A \sin B$\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\tan15^{\circ}&=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}\\\\&=\dfrac{\sin60^{\circ}\cos45^{\circ}-\cos60^{\circ}\sin45^{\circ}}{\cos 60^{\circ} \cos 45^{\circ}+ \sin 60^{\circ}\sin 45^{\circ}}\end{aligned}[/tex]

In the unit circle, the cosine of an angle is represented by the x-coordinate of a point on the circle, and the sine of an angle is represented by the y-coordinate of that same point → (x, y) = (cos θ, sin θ). Therefore, we can use the unit circle to identity the values of sin 60°, cos 60°, sin 45° and cos 45°:

[tex]\sin 60^{\circ}=\dfrac{\sqrt{3}}{2}[/tex]

[tex]\cos 60^{\circ}=\dfrac{1}{2}[/tex]

[tex]\sin 45^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]

[tex]\cos 45^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]

Substitute these into the equation and simplify:

[tex]\begin{aligned}\tan15^{\circ}&=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}\\\\&=\dfrac{\sin60^{\circ}\cos45^{\circ}-\cos60^{\circ}\sin45^{\circ}}{\cos 60^{\circ} \cos 45^{\circ}+ \sin 60^{\circ}\sin 45^{\circ}}\\\\&=\dfrac{\dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}-\dfrac{1}{2}\cdot \dfrac{\sqrt{2}}{2}}{\dfrac{1}{2}\cdot \dfrac{\sqrt{2}}{2}+ \dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}}\\\\\end{aligned}[/tex]

           [tex]\begin{aligned}&=\dfrac{\dfrac{\sqrt{2}}{2} \left(\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\right)}{\dfrac{\sqrt{2}}{2} \left(\dfrac{1}{2}+ \dfrac{\sqrt{3}}{2}\right)}\\\\&=\dfrac{\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}}{ \dfrac{1}{2}+ \dfrac{\sqrt{3}}{2}}\\\\&=\dfrac{\dfrac{\sqrt{3}-1}{2}}{\dfrac{1+\sqrt{3}}{2}}\\\\&=\dfrac{\sqrt{3}-1}{1+\sqrt{3}}\end{aligned}[/tex]

Simplify further by multiplying the numerator and denominator by the conjugate of the denominator:

           [tex]\begin{aligned}&=\dfrac{\sqrt{3}-1}{1+\sqrt{3}}\cdot \dfrac{1-\sqrt{3}}{1-\sqrt{3}}\\\\&=\dfrac{(\sqrt{3}-1)(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\&=\dfrac{\sqrt{3}-3-1+\sqrt{3}}{1-\sqrt{3}+\sqrt{3}-3}\\\\&=\dfrac{2\sqrt{3}-4}{-2}\\\\&=-\sqrt{3}+2\\\\&=2-\sqrt{3}\end{aligned}[/tex]

Therefore, the exact value of tan 15° is (2 - √3).

Okay, let's break this down step-by-step:

* The distance between Marisa's house and the post office is 720 m

* Marisa walks at an average speed of 80 m/min

* To calculate the time:

** Distance / Speed = Time

** 720 m / 80 m/min = 9 minutes

Therefore, if the distance is 720 m and Marisa's average walking speed is 80 m/min, it will take her 9 minutes to walk from her house to the post office.

There are 70,560 different ways to arrange the letters of the word "DETERRANT" so that the repeated letters do not come together.

The word "DETERRANT" has 9 letters, out of which there are 2 E's, 2 R's, and 1 T.

To determine the total number of possible arrangements, we begin with 9! (9 factorial), which counts all possible arrangements if all letters are distinct.

We must, however, account for the repeated letters. For the two E's, we divide by 2, which is the number of different ways they can be arranged without changing the overall arrangement. Likewise, we divide by 2! for the two R's.

As a result, the total number of arrangements with repeated letters that do not come together is:

9! / (2! x 2!) - 8! / (2! x 2!) = 90720 - 20160 = 70560

Therefore, there are 70,560 different ways to arrange the letters of the word "DETERRANT" so that the repeated letters do not come together.

Learn more about combinations at https://brainly.com/question/4658834

#SPJ1

The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄

There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.

Now, we are given the fraction as an improper fraction in the form of 2³₄.

Rewriting as a whole number and a fraction gives:

2 + ³/₄

Breaking down the whole number into a fraction is done as:

1 + 1 + ³/₄

= ⁴/₄ + ⁴/₄ + ³/₄

Read more about Mixed Fractions at: https://brainly.com/question/21610929

#SPJ1

Drag the solution of each inequality as shown below:

3(x - 5) + x < 13 : x<7

2(x + 8) > 4x + 2 : x<7

3x + 2(x - 8) > x : x > 4

2(x + 6) < 3x + 8 : x > 4

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

3(x - 5) + x < 13

3x -15 + x < 13

4x -15 < 13

4x < 13 + 15

4x < 28

x < 28/4

x < 7

2(x + 8) > 4x + 2

2x + 16 > 4x + 2

2x - 4x > 2 - 16

-2x > -14

x < -14/(-2)     (Note: Sign will change if you divide with negative numbers)

x < 7

3x + 2(x - 8) > x

3x + 2x -16 > x

5x - 16 > x

5x - x > 16

4x > 16

x > 16/4

x > 4

2(x + 6) < 3x + 8

2x + 12 < 3x + 8

2x - 3x < 8 - 12

-1x < -4

x > -4/(-1)

x > 4

Therefore, drag the solution of each inequality accordingly.

Learn more about inequality on:

brainly.com/question/25275758

#SPJ1

Answer:

Step-by-step explanation:

What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.

The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

To calculate the expected value for the game, we need to multiply each outcome by its respective probability and then sum them up.

Let's calculate the expected value for each outcome:

Outcome 1: Roll a 1 and receive $55.

The probability of rolling a 1 on a fair die is 1/6.

Expected value = (1/6) × $55 = $9.17

Outcome 2: Roll a 2 and receive $10.

The probability of rolling a 2 on a fair die is 1/6.

Expected value = (1/6) × $10 = $1.67

Outcome 3: Roll a 3 and win nothing.

The probability of rolling a 3 on a fair die is 1/6.

Expected value = (1/6) × $0 = $0

Outcome 4: Roll a 4 or 5 and pay Señor Rick $35.

The probability of rolling a 4 or 5 on a fair die is 2/6 or 1/3.

Expected value = (1/3) × (-$35) = -$11.67 (negative because you have to pay)

Outcome 5: Roll a 6 and pay Señor Rick $25.

The probability of rolling a 6 on a fair die is 1/6.

Expected value = (1/6) × (-$25) = -$4.17 (negative because you have to pay)

Now, let's sum up the expected values:

Expected value = $9.17 + $1.67 + $0 - $11.67 - $4.17

= -$4.00

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

for such more question on expected value

https://brainly.com/question/15858152

#SPJ11

We can actually deduce here that the major league ballpark that I identified is T-Mobile Park in Seattle, Washington.

The distance from home plate to the center field fence is 409 feet and the height of the center field fence is 8 feet.

Thus, to solve for the angle of elevation, we can use the following equation:

tan θ = (y - h) / d

Where:

θ is the angle of elevation

y is the height of the fence

h is the height of the ball

d is the distance to the fence.

tan θ = (8 - 2) / 409

tan θ = 0.602

θ =  [tex]tan^{-1}[/tex] (0.602)

θ = 0.85°

The angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground is 0.85°.

Learn more about angle of elevation on https://brainly.com/question/30738434

#SPJ1

Answer:

a = 10

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

a² + 24² = 26²

a² + 576 = 676 ( subtract 576 from both sides )

a² = 100 ( take square root of both sides )

a = [tex]\sqrt{100}[/tex] = 10

Answer: 45T + 55S +102 + 96= Combined income

Step-by-step explanation:

In this example, a positive relationship between the x- and y-values is demonstrated. This basically demonstrates that when one value increases, the other typically does too, and vice versa when one value decreases in the graph.

An x and y coordinate plane with values between -6 and +10 is displayed on the graph.

The points (2, 0), (4, 2), (6, 4), (negative 2, negative 4), and (negative 4, negative 6) are all connected by a line. The y values rise in proportion to the x values because the line has a positive slope.

In this example, a positive relationship between the x- and y-values is demonstrated. This basically demonstrates that when one value increases, the other typically does too, and vice versa when one value decreases.

Leran more about graph:

https://brainly.com/question/17267403

#SPJ1

The complete question is-

Which statement describes the relationship between the x- and y-values shown in the graph?

A coordinate plane has x-axis and y-axis with values ranging from negative 6 to 10. A positive slope passes through the points (negative 4, negative 6), (negative 2, negative 4), (2, 0), (4, 2), and (6, 4).

Answer:

Step-by-step explanation:

[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]

To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.

For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.

The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:

Number of ways = 925 * 924 * 923

Calculating this expression, we find:

Number of ways = 779,449,100

Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.

Answer: Centre: (-2,5)

Radius = 3

so

Diameter = 6

Domain: (-5,1)

Range: (2,8)

Answer:

center (-2,5)

radius =3

domain = -5< x <1

range 2 <y<8

Step-by-step explanation:

siiuu

The area of the regular polygon is 311.5 in2.

We are given that;

A polygon

Now,

To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.

To find the apothem length, we need to use some trigonometry.

The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.

To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.

A = (1/2)708.9 ≈ 311.5 in2.

Therefore, by the area the answer will be 311.5 in2.

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

Answer:

- 3 , 7 , - 13 , 5x + 2

Step-by-step explanation:

A

to evaluate f(0) substitute x = 0 into f(x)

f(0) = 5(0) - 3 = 0 - 3 = - 3

B

substitute x = 2 into f(x)

f(2) = 5(2) - 3 = 10 - 3 = 7

C

substitute x = - 2 into f(x)

f(- 2) = 5(- 2) - 3 = - 10 - 3 = - 13

D

substitute x = x + 1 into f(x)

f(x + 1)

= 5(x + 1) - 3 ← distribute each term in the parenthesis by 5

= 5x + 5 - 3 ← collect like terms

= 5x + 2

Answer:

A) -3

B) 7

C) -13

D) 5x+2

Step-by-step explanation:

For A, B, and C substitute the value stated in the parenthesis.

A) f(0) means to find the value when x=0, so we substitute 0 where x is in the function.

[tex]5(0)-3[/tex]

Then use PEMDAS and multiply first and then subtract 3 from the product.

[tex]5(0)=0\\0-3=-3[/tex]

B) Take the same steps as before with a different value. Substitute 2 for x.

[tex]5(2)-3\\5(2)=10\\10-3=7[/tex]

C) Also the same thing as the previous problems. Substitute -2 for the value of x.

[tex]5(-2)-3\\5(-2)=-10\\-10-3=-3[/tex]

D) Similar to above substitute x+1 where x is.

[tex]5(x+1)-3\\[/tex]

Then distribute 5(x+1) to get

[tex]5x+1(5)\\5x+5[/tex]

Then simplify the equation

[tex]5x+5-3=5x+2[/tex]

Answer: 7 and -4

Step-by-step explanation:

Coefficients are numbers in front of variables

6 doesn't have a variable so it's a constant

7 and -4 are the coefficients