60% of the 50 students in Jessie’s gym class are 12 years old. How many students in Jessie’s class are 12 years old?

Answer:

Step-by-step explanation:

setup a proportion

                               Big Triangle             Small Triangle

corresponding              15                              3

corresponding               x                               6

so you are trying to solve 15/x=3/6

cross multiply 6(15)=3(x)

last step divide both sides by 3 giving x=30 ft

If the triangles are similar, value of x in the drawings is Option(B) 30 ft.

Similar triangles are triangles that have the same shape, but their sizes may vary. If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

The given two triangles are similar .

In the diagram, it is mentioned that one side is 3 and its corresponding other side of the similar triangle is 15 .

Thus the proportion is 15/3 = 5

Therefore if the other side of the same triangle is 6 then its corresponding other side of the similar triangle will be 6*5 = 30

Thus x = 30 ft.

Therefore, if the triangles are similar, value of x in the drawings is Option(B) 30 ft.

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f(-2) means replace x in the equation with -2, then solve:

-2^2 +5(-2)

Simplify:

4 + -10

Add:

-6

Answer:

[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = - 8x + 4 ( add 8x to both sides )

8x + y = 4 ( subtract y from both sides )

8x = 4 - y ( divide both sides by 8 )

x = [tex]\frac{4-y}{8}[/tex]

Change y back into terms of x

[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]

Answer:

The height of the lighthouse is [tex]742.5\ ft[/tex]

Step-by-step explanation:

Let

h -----> the height of the lighthouse

we know that

The tangent of angle of 68 degrees is equal to divide the height of the lighthouse by the horizontal distance from the buoy to the base of lighthouse

so

[tex]tan(68\°)=\frac{h}{300}[/tex]

Solve for h

[tex]h=(300)tan(68\°)=742.5\ ft[/tex]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept (0, b)

We have the slope m = -3/2 and the y-intercept b = 3.

Substitute:

y = -3/2x + 3

The x-intercept is for y = 0. Substitute:

0 = -3/2x + 3           add 3/2x to both sides

3/2x = 3     multiply both sides by 2

3x = 6           divide both sides by 3

x = 2

Answer:

Step-by-step explanation:

Notice that for each unit increase in x, y increases by 1 unit.  Thus, the parent function is y = x.

Answer:

f(x)=x

Step-by-step explanation:

We are given with a table, Lets look at the value of x  and y

The value of y is constantly increasing and the value of x is also increasing constantly. So it is a table for a linear equation.

the value of x  and y are same, so the equation of the line is

y=x

when x=-2  the value of y=-2

when x=1 the value of y=1

Hence , the parent function is  [tex]f(x)=x[/tex]

Answer:

Length =12

Width= 10

Step-by-step explanation:

The difference between two consecutive integers is 2.

Thus the difference between the length and the width of the rectangle also differ by 2.

width- x

length- x+2

AREA=L×W

120=x(x+2)

x²+2x-120=0

Factorizing:

x² - 10x + 12x - 120=0

x(x-10) + 12( x-10)=0

(x-10)(x+12)=0

either x-10=0 or x+12=0

x=10 0r -12

We consider positive roots only. thus x=10

width = 10

length = 10+2 =12

Answer:

C.) 5.1

Step-by-step explanation:

First, solve for J's angle of degrees

180 - (120 + 40) = 20

Second, fill in all the information that you know in the equation

sin(20) / 2 and sin(120) / k

Third, cross multiply

k x sin(20) = 2 x sin(120)

Fourth, solve for k

k x sin(20) / sin(20) = [2 x sin(120)] / sin(20)

k = [2 x sin(120)] / sin(20)

k = 5.0641777.....

Fifth, round to the nearest tenth

k = 5.1

Answer:

its 5.1 on edg

Step-by-step explanation:

Because this expression is a difference of squares, meaning both terms have square roots, the factors would be 12+7x and 12-7x

Answer:12+7x and 12-7x

Answer:

-15/2

Step-by-step explanation:

False.

[tex]\sec{\dfrac{\pi}{2}}=undefined[/tex]

Hope this helps.

r3t40

Answer:

TRUE APEX dont trust the other guy!!!

Step-by-step explanation:

The answer for AB is 5.

To find this answer, you would use Pythagorean Theorem. The equation would be a² + 12² = 13². First, square 12 and 13, to get the equation to say a² + 144 = 169. Next, subtract 144 from both sides. This leaves a² = 25. Finally, square root  both sides to a = 5. Thus meaning 5 is the answer.

Here is an image to show how this answer is found. I hope this helps!

Answer:

0.75 and n-6= 0.75(t-8)

Step-by-step explanation:

To find the average speed of Ava's car, divide the total distance traveled by the total time taken. Ava travels 6 miles in 8 minutes, so the average speed is 0.75 miles per minute. The equation of the line representing the number of mile markers passed as a function of time is n = (3/4)t.

To find the average speed of Ava's car in miles per minute, we can use the formula:

Average speed = total distance / total time

First, we need to find the total distance traveled. Ava travels from mile marker 0 to mile marker 6, which is a distance of 6 miles.

Next, we need to find the total time it took Ava to travel this distance. Ava notes that 8 minutes have passed when she reaches mile marker 6, but it took her 4 minutes to travel from mile marker 0 to mile marker 3. This means it took her 4 minutes to travel 3 miles. Therefore, it would take her an additional 4 minutes to travel the remaining 3 miles from mile marker 3 to mile marker 6.

So, the total time taken by Ava to travel 6 miles is 4 minutes + 4 minutes = 8 minutes.

Now, we can use the formula to calculate the average speed:

Average speed = total distance / total time = 6 miles / 8 minutes = 0.75 miles per minute.

Equation of the line:

To find the equation of the line that represents the number of mile markers passed as a function of time, we can use the equation:

n = mt + b

Here, 'n' represents the number of mile markers passed, 't' represents time in minutes, 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this scenario, Ava starts checking her car's clock at mile marker 0, which means the y-intercept is 0. We also know that Ava takes 4 minutes to travel from mile marker 0 to mile marker 3, which means she passes 3 mile markers in 4 minutes. Therefore, the slope of the line is 3/4.

So, the equation of the line is: n = (3/4)t.

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Answer:

the ordered pair is (2,-1)

Step-by-step explanation:

We need to solve the system of equations using elimination method

12x - y = 25     eq(1)

9x + y = 17      eq(2)

Adding eq(1) and eq(2)

12x - y = 25

9x + y = 17

___________

21x = 42

x = 42/21

x= 2

Now, putting value of x in equation 1

12x - y = 25

12(2) -y = 25

24 -y = 25

Adding -24 on both sides

24 -y-24 = 25-24

-y = 25-24

-y = 1

Multiply both sides by -1

y = -1

the value of x = 2 and y = -1

So, the ordered pair is (2,-1)

Answer:

The solution is: (2, -1)

Step-by-step explanation:

I have the following system of equations

[tex]12x - y = 25[/tex]

[tex]9x + y =17[/tex]

Note that if we add both equations, the variable y is "eliminated".

So add the first equation to the second and solve for the variable x

[tex]12x - y = 25[/tex]

[tex]9x + y =17[/tex]

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

[tex]21x=42[/tex]

[tex]x=\frac{42}{21}\\\\x=2[/tex]

Now substitute the value of x in any of the two equations and solve for the variable y

[tex]9(2) + y =17[/tex]

[tex]18 + y =17[/tex]

[tex]y =17-18[/tex]

[tex]y =-1[/tex]

The solution is: (2, -1)

Answer:

B.

Step-by-step explanation:

Let's find g(f(x)) for each choice for fun and so you can have more examples:

A) f(x)=3x and g(x)=sqrt(x)+1

so g(f(x))=g(3x)=sqrt(3x)+1

So definitely not this choice

B) f(x)=x+1 and g(x)=sqrt(3x)

so g(f(x))=g(x+1)=sqrt(3(x+1))

So this one works! :)

C) f(x)=sqrt(x)+1 and g(x)=3x

so g(f(x))=g(sqrt(x)+1)=3(sqrt(x)+1)

Not this one!

D) f(x)=sqrt(3x) and g(x)=1

g(f(x))=g(sqrt(3x))=1

Answer:

263.99 m3 (i tried my best)

Step-by-step explanation:

diameter > radius= 12/2

=6 m

v. of cone: 1/3 x 22/7 x r² x h

1/3 x 22/7 x 6² x 7

=263.99 m3

Answer:84piem^3

Step-by-step explanation:AP3X

Slope formula = y2-y1/x2-x1

Plug in.

4 - 7/-1 - 3 = -3/-4 = 3/4

Answer: 3/4 or Choice A

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y< 8[/tex]

The solution is the interval -----> (-∞,8)

[tex]y\geq3[/tex]

The solution is the interval -----> [3,∞)

The solution of the system is equal to

[3,∞)∩ (-∞,8)-------> [3,8)

All real numbers greater than or equal to 3 and less than 8

The graph in the attached figure

Answer:

Equation of line: y=3x-18

Step-by-step explanation:

Point: (5,7) and slope=-13

y-7=-13(x-5)

y=-13x+72

Answer:

the value  of the digit 1 in the no. 13 is 10

Step-by-step explanation:

cuz it's in the tens place

tens    ones

hope u understood

and helps u

and ur welcm

:D

The value of digit 1 in the number 13 is 10 because it is located in the 'tens' place.

The value of the digit 1 in the number 13 corresponds to its place value in the number. In the number 13, 1 is in the 'tens' place, thus its value is 10. Place value is determined by the position of a digit in a number. It shows the mathematical worth of each digit at their respective places. Zeroes play a significant role in deciding the place value of digits in a number, acting as placeholders that help identify decimal points.

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Answer:

16 quarters 2 dimes

Step-by-step explanation:

16 quarters is 4 dollars

2 dimes is 20 cents

Step-by-step explanation:

If D is number of dimes and Q is number of quarters:

D + Q = 21

10D + 25Q = 420

Solve the system of equations through either substitution or elimination.

10D + 25(21 - D) = 420

10D + 525 - 25D = 420

105 = 15D

D = 7

Q = 14

There are 7 dimes and 14 quarters.

Answer:

420

Step-by-step explanation:

Each of the 7 appetizers can be paired with one of 10 entrees, and each entree can be paired with one of 6 desserts.  So the number of combinations is:

7 × 10 × 6 = 420

By combination property, there are a total of 420 different lunch specials that are possible.

The combination property is defined as the selection of items from a set that has distinct members, such that the order of selection does not matter.

It is given that a restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts.

Thus, there are 3 different items which quantities are also mentioned. '

Thus by combination property, the total number of lunch specials that are possible -

7 * 10 * 6 = 420 .

Therefore, by combination property, there are a total of 420 different lunch specials that are possible.

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Answer:

Yep the answer is C bro. I very much appreciate your help :D

congruency statement applies to the trapezoids is CDEF ≅ NMOP.

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid

From question, we have

Hence, Trapezoid CDEF and trapezoid NMOP are congruent.

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Answer:

B.  9/4 <x <= 4

Step-by-step explanation:

5x - 19 <= 1

5x <= 20

 x <= 4

-4x + 3 < - 6

-4x < - 9

  x > 9/4

Answer

9/4 <x <= 4

Answer:

x ≤ 4

Step-by-step explanation:

1. 5x - 19 ≤ 1

Add: 5x ≤ 20

Divide: x ≤ 4

2. -4x + 3 > -6

Subtract: -4x > -9

Divide: x < ⁹/₄

3. Or means the union of the two sets, or all values that are in either set.

x ≤ 4 ∪ x < ⁹/₄ is x ≤ 4, since they both inequality signs point left, and 4 is larger than ⁹/₄, so x ≤ 4 also includes x < ⁹/₄.

I see here that x ≤ 4 is not one of the options. I'm not sure what to do then.

Answer:  -1x-11

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$1040\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases} \\\\\\ 1040=1000(1+0.04t)\implies \cfrac{1040}{1000}=1+0.04t\implies \cfrac{26}{25}=1+0.04t \\\\\\ \cfrac{26}{25}-1=0.04t\implies \cfrac{~~\frac{26}{25}-1~~}{0.04}=t\implies \cfrac{~~\frac{1}{25}~~}{0.04}=t\implies 1=t[/tex]

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\left( \frac{\pi }{3} \right)\implies s=2\pi \implies \stackrel{\textit{rounded up}}{s=6.3}[/tex]

Answer: [tex]arc\ length=6.3\ ft[/tex]

Step-by-step explanation:

You  need to use the following formula for calculate the arc lenght:

[tex]arc\ length=r\theta[/tex]

Where  "r" is the radius and [tex]\theta[/tex] is the central angle in radians.

You know that the central angle in radians s:

[tex]\theta=\frac{\pi }{3}[/tex]

And the radius is:

[tex]r=6\ ft[/tex]

Therefore, the final step is to substitute the values into the formula. Then you get:

[tex]arc\ length=(6\ ft)(\frac{\pi }{3})[/tex]

[tex]arc\ length=6.3\ ft[/tex]

Answer:

The correct answer is (-5,-5)

Step-by-step explanation:

1. Both of the equations are in standard form, so first you set them equal to each other.

2. Solve for x as a normal algebraic equation.

3. Back substitute your answer for x into one of the original equations. (back substitution is just putting the x back into the equation and solving for y.)

4. Now you have your x and y coordinates, and the point of intersection of the two lines.

The ordered pair represents the solution to the system is (-5, -5), and the correct option is A.

A pair of numbers that are written in a particular order, enclosed in brackets are known as ordered pairs.

The given system of equation is;

y = 3x + 10

y = 5x +20

Subtraction equation 1 from 2

y - y = 3x + 10 - 5x -20

0 = -2x -10

2x = -10

x = -10/2

x = -5

Substitute the value of x in equation 1

y = 3x + 10

y = 3(-5) +10

y = -15 +10

y = -5

Hence, the ordered pair represents the solution to the system is (-5, -5), and the correct option is A.

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Final answer:

Lily's budget scenario with her sister's charm bracelet is translated into the inequality statement 12 + 1.50c ≤ 25, where c represents the number of charms she can buy. Solving this inequality will show how many charms Lily can afford without exceeding her $25 budget.

Explanation:

The question involves translating a real-life situation into an inequality statement concerning budget and expenses. Lily has $25 to spend on her sister's birthday gift, which is a charm bracelet. The cost structure for the bracelet is $12 for the bracelet itself plus $1.50 for each charm. We let the number of charms she plans to buy be represented by c. The total cost for these charms would be $1.50c, and when added to the initial $12 for the bracelet, the sum should not exceed Lily's budget of $25.

Therefore, the inequality that represents this situation is 12 + 1.50c ≤ 25.

To find the maximum number of charms Lily can afford, we would solve for c in the inequality. This step involves subtracting 12 from both sides and then dividing by 1.50.

Answer: y=3x+8

Step-by-step explanation:

The slope will be the same as the original equation, so 3. And to make the line go the points (0,8), you can plug in 0 into the original equation to find what needs to change. Hope this helps!

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be 3

y = 3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(0, 8)

8 = 3(0) + b

8 = 0 + b

8 = b

y = 3x + 8

Hope this helped!

~Just a girl in love with Shawn Mendes