The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to 2/3.

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and 3n + 6 = 2d + 4
5n = 3d and 4n + 4 = 3d + 6
3n = 5d and 3n + 6 = 2d + 4

Answer:

12 cm.

Step-by-step explanation:

The distance between the opposite sides is a perpendicular line so we can form a right angled triangle by drawing a perpendicular line from one corner of the parallelogram  to the opposite 24 cm side.

So  one angle of the parallelogram will have a sine of 8/16 = 1/2 so this angle =  30 degrees.

In a similar way to the above we form a right angled triangle  from the same corner by drawing a perpendicular line to the opposite 16 cm side.

This has an angle of 30 degrees (  opposite angles in a parallelogram are congruent).

So sine 30 = x / 24

1/2 = x /24

x = 12 feet.

Another way to do this is by noting that the 2 triangles are similar (because  2 corresponding angles are equal).

So  8/ 16 = x/24

16x = 192

x = 12 feet.

Final answer:

The distance between the 16 cm sides of the parallelogram is 12 cm, determined by calculating the area of the parallelogram and then using it to find the missing dimension.

Explanation:

The student in the question is dealing with a geometrical problem involving the calculation of the distance between sides of a parallelogram. To solve the problem, we must understand that the opposite sides of a parallelogram are equal in length, and the area can be calculated as the product of the base and the height (the distance between the parallel sides). The question is analogous to finding the height of a parallelogram when the area and the base are known and can be approached in a similar way to finding dimensions of scaled geometric figures.

Therefore, the distance between the 16 cm sides of the parallelogram is 12 cm.

Answer:

C.

Step-by-step explanation:

The answer is C because when you add the absolute values (distance to zero) of the two numbers, you get the number 8. Divide this by 2, and you will get 4.  Then, you add four to the lower number, -6, and you get -2.

Answer: C. -2

Step-by-step explanation:

Answer:

Option C : y = -4x+10

Step-by-step explanation:

Given equation of line is:

[tex]y = -4x-1[/tex]

Comparing it with standard form

y=mx+b

m = -4

As the slopes of parallel lines are equal, the slop of other line will also be -4.

Now, to find the value of b

[tex]2 = -4(2) + b\\2 = -8 + b\\2+8=b\\b=10[/tex]

Putting the values of b and m in standard form

[tex]y=mx+b\\y = (-4)x+10\\y= -4x+10[/tex]

Hence,

Option C is the correct answer ..

For this case we have that the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal.

So, if we have:

[tex]y = -4x-1[/tex]

A parallel line has slope [tex]m = -4[/tex]

y = -4x + b

We substitute the point (2,2) to find "b":

[tex]2 = -4 (2) + b\\2 = -8 + b\\b = 2 + 8\\b = 10[/tex]

Finally we have:

[tex]y = -4x + 10[/tex]

Answer:

Option C

Final answer:

Using the sum of the interior angles formula for a polygon, S = (n - 2) x 180 degrees, and substituting the provided sum of 2280 degrees, it is calculated that the polygon has 14 sides.

Explanation:

To solve for the number of sides n in a polygon given the sum of the interior angles, we use the formula:

S = (n - 2) × 180°

where S is the sum of the interior angles in degrees. Given that the sum of the interior angles S is 2280 degrees, we can set up the equation:

2280 = (n - 2) × 180

Divide both sides of the equation by 180:

2280 ÷ 180 = n - 2

12 = n - 2

Now, add 2 to both sides of the equation to find n:

n = 12 + 2

n = 14

So, the polygon has 14 sides.

Answer:

20°

Step-by-step explanation:

They are Vertically Opposite angles and hence are equal.

So, x + 40 = 3x.

Answer:

a. 20

Step-by-step explanation:

You are solving vertical angles. Put the measurements equal to each other:

x + 40 = 3x

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides.

x (-x) + 40 = 3x (-x)

40 = 3x - x

40 = 2x

Isolate the variable x. Divide 2 from both sides:

(2x)/2 = (40)/2

x = 40/2

x = 20

a. 20 is your answer.

~

Answer:

12x+6

Step-by-step explanation:

Multiply the like terms.

4x • 3x=12x

-1 • -6= 6

put it back into equation form

12x + 6

Hello There!

The answer would be "B"

We have to move the decimal place over for each one depending on what the power of the number is.

Answer:

your answer would be B. :)

Step-by-step explanation:

Answer:

The answer to this question is the first option:

Line segment TU is parallel to line segment RS because 32/36=40/45

Answer:

The correct option is 1.

Step-by-step explanation:

From the given figure it is clear that QT=32, TR=36, QU=40 and US=45.

The converse of side splitter theorem states that if a line divides two sides proportionally, then that line is parallel to the third side.

The ratio in which TU divides the two sides is

[tex]\frac{QT}{TR}=\frac{32}{36}=\frac{8}{9}[/tex]

[tex]\frac{QU}{US}=\frac{40}{45}=\frac{8}{9}[/tex]

[tex]\frac{QT}{TR}=\frac{QU}{US}=\frac{8}{9}[/tex]

It means the line TU divides two sides proportionally.

Using converse of side splitter theorem, Line segment TU is parallel to line segment RS because

[tex]\frac{32}{36}=\frac{40}{45}[/tex]

Therefore the correct option is 1.

Answer:

8.75 hours

Step-by-step explanation:

We can use ratios to solve.  Put the pages over the time and set them equal.

4 pages       7 pages

------------- = ---------------

5 hours        x hours

Using cross products

4 * x = 5 *7

4x =35

Divide by 4 on each side

4x/4 = 35/4

x =8.75 hours

Answer:

Step-by-step explanation:

Uploaded a pic of the answer. It’s correct

Given: We have the expression [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]

Step-1: [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]

Step-2: [tex]\left ( 875\times x^{5} \times y^{}\right )^{1/3}[/tex]                              [break the cuberoot as power [tex]1/3[/tex]]

Step-3: [tex]\left ( 125.7 \right )^{1/3}\times x^{5/3}\times y^{9/3}[/tex]                    [break [tex]875=125\times 7[/tex]]

Step-4: [tex]\left ( 5^{3} \right )^{1/3}\times 7^{1/3}\times x^{\left ( 1+2/3 \right )}\times y^{9/3}[/tex]       [ [tex]125=5^{3} \\\frac{5}{3} =1+\frac{2}{3}[/tex]]

Step-5: [tex]5^{1}\times 7^{1/3}\times x^{1}\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]] 

Step-6: [tex]5\times x\times y^{3}\left ( 7^{1/3}\times x^{2/3} \right )[/tex]

Step-7: [tex]5xy^{3}\left ( 7x^{2} \right )^{1/3}[/tex]

Step-8: [tex]5xy^{3}\sqrt[3]{7x^{2}}[/tex]

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Answer:

The answer is A. (3,5,8)

Answer:

70

Step-by-step explanation:

70 combinations of four books can be made from eight different books.

Answer:

Answers: 46, 23, and 111

Step-by-step explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

Hope this helps!

Answer:

[tex]h = \frac{3V}{\pi r^2}[/tex]

Step-by-step explanation:

Divide left and right by 1/3 π r²...

Answer:

x = 98°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle and 53° and 45° are the opposite interior angles, hence

x = 53° + 45° = 98°

Answer:

$2

Step-by-step explanation:

Step 1: Subtract the amount he had left from the amount he had to spend. 24 - 18 is 6. That's the amount spent on pencils.

Step 2: Divide the amount spent on pencils by 3. 6/3 is 2. That's the total cost of each pencil.

Answer:

Step-by-step explanation:

Look at the picture.

Coordinates of a point (x, y)

x - from x-axis

y - from y-axis

Answer:

The answer is B. the diameter of the base

Step-by-step explanation:

Just got it right on edg! Have a great day!

Answer:

[tex](x-6)(x+1)[/tex]

Step-by-step explanation:

Factoring is usually just a bit of guess and check.  [tex]x^2-5x-6[/tex] is written in the form [tex]a^2+b+c[/tex], where [tex]a=1[/tex], [tex]b=-5[/tex], and [tex]c=-6[/tex].

You need to find the two numbers that multiply together to equal [tex]-6[/tex] and can be added together to get [tex]-5[/tex].  These are [tex]-6[/tex] and [tex]1[/tex] in this case.

Now, put them together in the form [tex](x-6)(x+1)[/tex].  We will now check this answer using the FOIL method.

First term in each parentheses: [tex]x * x = x^2[/tex]

Outside terms: [tex]x * 1 = x[/tex]

Inside terms: [tex]-6 * x = -6x[/tex]

Last term in each parentheses: [tex]-6 * 1 = -6[/tex]

Now, add these together: [tex]x^2 + x - 6x - 6 = x^2 - 5x - 6[/tex]

Since we get the original expression, this is correct.

Answer:

D. 12

Step-by-step explanation:  

We have been given a diagram of a triangle. We are asked to find the value of y for our given triangle.

First of all, we will find 3rd side of larger triangle using Pythagoras theorem.

[tex]\text{3rd side}^2=16^2-8^2[/tex]

[tex]\text{3rd side}^2=256-64[/tex]

[tex]\text{3rd side}^2=192[/tex]

[tex]\text{3rd side}^2=192[/tex]  

We will use geometric mean (leg) theorem to solve our given problem.

[tex]\text{3rd side}^2=y\times 16[/tex]  

[tex]192=y\times 16[/tex]  

[tex]\frac{192}{16}=\frac{y\times 16}{16}[/tex]  

[tex]y=12[/tex]  

Therefore, the value of y is 12 and option D is the correct choice.

Hello There!

I attached an image below which explains everything and gives some examples.

Final answer:

The product rule for exponents allows you to add the exponents when multiplying two terms with the same base, simplifying the calculation. Examples include multiplying powers of the same number, or dealing with terms in scientific notation.

Explanation:

Understanding the Product Rule for Exponents

The product rule for exponents states that when you multiply two expressions with the same base, you can simply add the exponents. This rule simplifies the multiplication of exponentiated quantities.

Examples of Using the Product Rule

For instance, if you have 53 multiplied by 54, the product rule allows you to add the exponents: 53+4 = 57. Another example involves numbers in scientific notation. When you multiply 3.2 x 103 by 2 x 102, the result is 6.4 x 103+2 = 6.4 x 105.

If both terms have exponents, multiply the digit terms as usual and then add the exponents of the exponential terms. This concept also applies to logarithms, where the logarithm of a product of two numbers equals the sum of their individual logarithms.

Answer:

A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex]

Step-by-step explanation:

First, we have to turn 4x - 3y = -12 into slope-intercept form (y = mx + b). To do this, we first have to isolate 3y.

4x - 3y = -12

    +3y    +12     Add 3y to both sides and add 12 to both sides

4x + 12 = 3y

3y = 4x + 12

Isolate y by dividing 3 from both sides.

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

The graph that is parallel will have the same slope as this equation, which is [tex]\frac{4}{3}[/tex].

Therefore, A. [tex]y = \frac{4}{3} x - \frac{3}{2}[/tex] would be the correct answer.

Answer:

A

Step-by-step explanation:

Solve for y.

4x – 3y = -12

4x + 12 = 3y

y = 4/3 x + 4

The slope of the line is 4/3.  So you need another line with the same slope.  So the answer is A.

Answer:

The Answer is 1111

Step-by-step explanation:

15 = 2(7)+1

7=2(3)+1

3=2(1)+1

1=2(0)+1

look the remainder of division by 2 : 1111 in binary system​

verify : 15 = 1(2^0)+ 1(2^1)+ 1(2^2)+ 1(2^3 = 1+2+4+8=15 .....right

Answer:

your answer should be 45

Step-by-step explanation:

Answer:

15 to the third power would be 3375

Step-by-step explanation:

You start by multiplying

15 X 15 X 15

First you would get

225 X 15

Then you do the final multiplication

3375

Answer:

[tex]a=(9-10c)/b[/tex]

Step-by-step explanation:

we have

[tex]ab+10c=9[/tex]

Solve for the variable a

That means----> isolate the variable a

Subtract 10c both sides

[tex]ab+10c-10c=9-10c[/tex]

[tex]ab=9-10c[/tex]

Divide by b both sides

[tex]ab/b=(9-10c)/b[/tex]

[tex]a=(9-10c)/b[/tex]

Answer:

B. $0.30

Step-by-step explanation:

1 bar of candy = $0.20

3 bars of candy = $0.50

To solve, multiply for both:

If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:

9 x 0.20 = $1.80

If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:

9/3 = 3

3 x 0.50 = $1.50

Subtract the total cost of the individual from the pack:

$1.80 - $1.50 = $0.30

B. $0.30 is your answer.

~

Answer:

17x(1 - 2y)

Step-by-step explanation:

Given

17x - 34xy ← factor out 17x from each term

= 17x(1 - 2y) ← in factored form

Answer:

17x(1 - 2y)

Step-by-step explanation:

The percentage decrease(loss) of selling sweatshirts is 28%.

To find the percentage change of any value we need to divide by that change to the original value and then multiply by 100.

Percentage change = (change in value × 100)÷(riginal value).

Given that the selling cost of sweatshirts is $18.

The cost of the sweatshirt was $25.

Change of value

$25 - $18 = $7

By the formula

Percentage decrease = ($7)×100÷ ($25) %

Percentage decrease = 28% Hence,the percentage decreases is 28$.

To learn more about percentage change

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Answer:

f(x)  = ax + b;

f(0) = -5;

a·0 + b = -5;

b = -5;

f(1) = -3;

a·1 + (-5) = -3;

a - 5 = -3;

a = 5 - 3;

a = 2;

f(x) = 2x - 5;

Step-by-step explanation:

The linear function with the values f(0)=−5 and f(1)=−3 is f(x) = 2x - 5

The linear function can be represented as follows:

y = mx + b

where

m = slope

b = y-intercept

The y-intercept is the value of y when x = 0

Since,

f(0) = -5

Therefore,

b = -5

The equation will be as follows

f(x) = mx - 5

lets find the slope(m) using the f(1)=−3

-3 = m - 5

m = -3 + 5

m = 2

Therefore,

f(x) = 2x - 5

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