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State whether the ratios are proportional.

3:5 and 1:3

6:15 and 2:5

2:3 ___ 4:1

Answer:

x = 14

Step-by-step explanation:

x + 96 + 5x = 180

6x + 96 = 180

6x = 84

x = 14

Answer:

[tex]\huge\boxed{\sf x = 14}[/tex]

Step-by-step explanation:

x + 96 + 5x = 180 (Angles on a straight line)

Combine like terms

x + 5x + 96 = 180

6x + 96 = 180

Subtract 96 to both sides

6x = 180 - 96

6x = 84

Divide both sides by 6

x = 84 / 6

x = 14

[tex]\rule[225]{225}{2}[/tex]

The solution the equation [tex]\rm log(2t+4)=log(14-3t)[/tex] is t = 2.

Considering that the logarithm function is injective then the log is removing from the both sides and solving the equation for the value of t.

Given

The equation is;

[tex]\rm log(2t+4)=log(14-3t)[/tex]

The solution of the equation is;

[tex]\rm log(2t+4)=log(14-3t)\\\\2t+4=14-3t\\\\2t+3t=14-4\\\\5t=10\\\\t=\dfrac{10}{5}\\\\t=2[/tex]

Hence, the solution the equation [tex]\rm log(2t+4)=log(14-3t)[/tex] [tex]\rm log(2t+4)=log(14-3t)[/tex] is t = 2.

To know more about logarithmic properties click the link given below.

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Answer:

y= -2x+4

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{A'C'}{AC}[/tex] = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex] = 1 [tex]\frac{1}{2}[/tex]

Answer:

A

Step-by-step explanation:

becuase the 3 is negtive and the 4/5 so it A

Answer:

[tex]a)\ y=-\frac{4}{5}x -3[/tex]

Step-by-step explanation:

Slope (m) form: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-3-1}{0-(-5)} \\\\m=\frac{-4}{0+5} \\\\m=-\frac{4}{5}[/tex]

[tex]y=mx+b\\y=-\frac{4}{5}x +b[/tex]

(-5, 1)

[tex]y=-\frac{4}{5}x +b\\1=-\frac{4}{5}(-5) +b\\1=4+b\\-4-4\\-3=b[/tex]

[tex]y=-\frac{4}{5}x -3[/tex]

Check your answer:

[tex]y=-\frac{4}{5}x -3 \\1=-\frac{4}{5}(-5) -3\\1=4-3\\1=1[/tex]

This statement is true

Hope this helps!

Answer:

Diameter = 19.33

Step-by-step explanation:

Imaging a radius line from O to the endpoints of the 7. call this line R.

Label the part of the vertical line from O to the 90 degree intersection y.

Now you have a right triangle.

Using the Pythagorean theorem:

R² = 7² + y²

also

y = R - 3

substitute for y:

R² = 49 + (R-3)²

R² = 49 + R² - 6R + 9

simplify:

0 = 58 - 6R

6R = 58

R = 9.6667

Diameter = 2(9.6667) = 19.33

Step-by-step explanation:

Given:

Theater has 15 seats

Last Row has 72 seats.

Theater has a total of 870 seats.

Unknown: Number of rows

Number of seats in each row.

Equations: Since we know the total number of seats the Theater has we can use the sum of arithmetic series

[tex]s = \frac{a _{1} + a _{n} }{2} n[/tex]

Where a1 is the first row of seats

s is total number of seats

an is last row of seats

n is number of rows.

[tex]870 = \frac{15 + 72}{2} (n)[/tex]

[tex]870 = \frac{87}{2} n[/tex]

[tex]2(870) = 87n[/tex]

[tex]20 = n[/tex]

So we have 20 rows.

To find how many seats does each row increase, we use this formula,

[tex]a _{n} = a + (n - 1)d[/tex]

Let use the 20th row as an example,

[tex]a _{20} = 15 + (19)d[/tex]

[tex]72 = 15 + (19)d[/tex]

[tex]57 = 19d[/tex]

[tex]3 = d[/tex]

So the common difference is 3.

So the seats of each row increase by 3.

Answer: 10.5

Step-by-step explanation:

Answer:

The probability of picking a 7 as the first card is 4 out of 52 or 1/13. The probability of picking a 5 as the second card is 4 out of 51. For both to happen, we multiply and get about .00603318

Thanks!

person above me is correct

Step-by-step explanation:

Answer:

$22,320

Step-by-step explanation:

1. Understanding

Mean is the average of a given set

2. Solving

We have to find the average of all of these numbers.

How do I find the average?

I add all of the numbers and divide by the number of numbers I added. Example:

(x + x + x + x)/4 or,

(x+x)/2 and examples in numbers:

(3+4)/2 or,

(9+4+8+5+7)/5

See what I mean? Dividing by the number of numbers I have.

Ok, now we know that, we can solve!

Here is the equation for this problem:

(24,600+19,000+33,000+15,000+20,000)/5 (We have 5 numbers)

We have to do Parentheses First

(24,600+19,000+33,000+15,000+20,000)/5 --> 111,600/5

111,600/5 = 22,320

22,320 is the average number of all of the numbers, which is the mean

Hope this helps :)

-jp524

Answer: red=4 blue=8 yellow=8

4:8:8

Step-by-step explanation: 1+2+2=5

20÷5=4 4×1=4 2×4=8 2×4=8

Answer:

side AB = [tex]9\sqrt{2}[/tex]

hypotenuse CB = 18

Step-by-step explanation:

with a 45-45-90 triangle, we know that the two legs (AC and AB in this picture) are the same length, so if AC is [tex]9\sqrt{2}[/tex] , then AB would have to be the same so therefore it would also be [tex]9\sqrt{2}[/tex]. We also know that the length of the hypotenuse (CB) is the length of the leg times [tex]\sqrt{2}[/tex]. So, it would be [tex](9\sqrt{2} ) *\sqrt{2}[/tex], which is the same as saying [tex]9*(\sqrt{2}) * (\sqrt{2} )[/tex]. Doing [tex](\sqrt{2}) * (\sqrt{2} )[/tex] would cancel out the square roots, leaving you with just 2, so you get 9*2, which is 18.

Step-by-step explanation:

0.32=1/f

1/0.32=f

f=3.125

Answer:

Step-by-step explanation:

∠R=90-61=29°

using sin formula

[tex]\frac{x}{\sin~29} =\frac{59}{\sin~61} \\x=\frac{\sin~29}{\sin~61} \times ~59 \approx~32.7[/tex]

Answer:

3 .62 lt

4 4300 g

5 1.78 mt

6 .0031 g

7 500 lt

8 .083 g

Answer:

see explanation

Step-by-step explanation:

note that (sinx)² = sin²x

4sin²x - 2 = 0 ( add 2 to both sides )

4sin²x = 2 ( divide both sides by 4 )

sin²x = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] ( take square root of both sides )

sinx = ± [tex]\sqrt{\frac{1}{2} }[/tex] = ± [tex]\frac{1}{\sqrt{2} }[/tex]

sinx = [tex]\frac{1}{\sqrt{2} }[/tex] ( sinx > 0 , then x is in 1st/2nd quadrants )

x = [tex]\frac{\pi }{4}[/tex] , π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3\pi }{4}[/tex]

sinx = - [tex]\frac{1}{\sqrt{2} }[/tex] ( sinx < 0 , then x is in 3rd/4th quadrants )

x = π + [tex]\frac{\pi }{4}[/tex] = [tex]\frac{5\pi }{4}[/tex] , 2π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{7\pi }{4}[/tex]

solutions are

[tex]\frac{\pi }{4}[/tex] , [tex]\frac{3\pi }{4}[/tex] , [tex]\frac{5\pi }{4}[/tex] , [tex]\frac{7\pi }{4}[/tex] in the interval [ 0, 2π )

first find perimeter and area of base

then, find tsa of triangular prism

as done in the solution above!

Note: I will be writing these in slope-intercept form.

[6] y = 2x + 4

Since the line is going from bottom left to top right, we know the slope of the line is positive.

-> The b, or y-intercept, is 4 because the line hits the y-axis at 4.

-> The slope can be found with change in y over change in x,

[tex]\frac{14-4}{5-0} =\frac{10}{5} =2[/tex]

-> The final equation is y = 2x + 4

[7] y = -3x - 5

Because the line is going from top left to bottom right, we know the slope of the line will be negative.

-> The b, or y-intercept, is -5 because the line hits the y-axis at -5.

-> The slope can be found with change in y over change in x,

[tex]\frac{4--5}{-3-0}=\frac{4+5}{-3-0}=\frac{9}{-3}=-3[/tex]

-> The final equation is y = -3x - 5

Answer:

5 adult and 3 student tickets were purchased

Step-by-step explanation:

Let x be the number of adult tickets

Then 8−x is the number of student tickets

7.25x+5.5(8−x)=52.75

7.25x+44−5.5x=52.75

1.75x=8.75

x=5

Therefore, 5 adult and 3 student tickets were purchased

Foreign Policy: Imperialism  For82622

The monthly payment for a 5-year car loan of $23,570 at 10.43% interest, compounded monthly will be $660

It is given that the monthly payment for a 5-year car loan of $23,570 at 10.43% interest, is compounded monthly.

It is required to find the monthly payment.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A=P(1+ \frac{r}{n})^n^t[/tex]

Where A = Final amount

           P = Principal amount

           r  = annual rate of interest

           n = how many times interest is compounded per year

           t = How long the money is deposited or borrowed (in years)

We have P = $23,570

               r  =  10.43% = 10.43/100 = 0.1043

               n = 12

               t = 5 years

Putting all the values in the formula, we get:

[tex]\rm A=23,570(1+\frac{0.1043}{12})^1^2^\times^5[/tex]

[tex]\rm A = 23,570\times1.680\\\rm A = 39597.6[/tex]

The monthly payment will be:

=[tex]\rm \frac{A}{t(in \ months)}[/tex]

[tex]\rm = \frac{39597.6}{60} \\\rm = 659.96\\\rm \approx 660[/tex]

Thus,  the monthly payment for a 5-year car loan of $23,570 at 10.43% interest, compounded monthly will be $660.

Learn more about the compound interest:

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Answer:

D. 505.79

Step-by-step explanation:

edge 2022

Answer:

18 units by 18 units

makes sure the square add up to 18 going across and 18 going down.

Step-by-step explanation:

Answer: Angles RLN and MLK would be vertical angles.

Step-by-step explanation:

A horizontal line has points K, L, N. A line extends from point L up and to the right to point M: Angles RLN and MLN would be vertical angles.

Based on the given information, if a horizontal line contains points K, L, and N, and a line extends from point L up and to the right to point M, then angle KLM and angle MLN are a linear pair.

Now, if Ray LR is added to the diagram opposite to Ray LM, the resulting angle RLN would be formed.

Vertical angles are formed when two lines intersect. They are opposite angles and have equal measures. Looking at the diagram, angles RLN and KLN do not share a common vertex, so they cannot be vertical angles.

Similarly, angles RLN and KLM do not share a common side or form a straight line, so they cannot be a linear pair.

Therefore, the correct statement is: Angles RLN and MLN would be vertical angles.

To know more about Angles

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#SPJ4

Answer:

the answer is 45%.

Step-by-step explanation:

if you add 5% divided by 3 = 15%.

So if you add all of those plus the 30% you will be getting 45%.

Answer:

I would say its D

Step-by-step explanation:

10:9:10 is the original ratio

It gets turned into 1:1:2, making it very distorted

The program is an illustration of loops

Loops are program statements that are used to execute repeated statements

The program, written in Java where comments are used to explain each line is as follows:

import java.util.*;

public class Main{

public static void main(String[] args) {

 Scanner input = new Scanner(System.in);

 int num;

//Get input from the user

 num = input.nextInt();

//Initialize the largest to the first input

 int maxn = num;

//This loop is repeated until a negative input is recorded

 while (num >=0){

//If the current input is greater than the previous largest

     if (num>maxn){

//Set largest to the current input

         maxn = num;      }

//Get another input from the user

     num = input.nextInt();

 }

//Print the largest

 System.out.print("Largest: "+maxn);

}

}

Read more about loops at:

https://brainly.com/question/14284157