Tonya uses the greatest common factor and the distributive property to rewrite this sum: 96 + 36
Which expression does Tonya write?
4(24 + 9)

6(16 + 6)

12(8 + 3)

18(5 + 2)

Answer:

Step-by-step explanation:

Final answer:

To simplify the given expression involving fractions and variables, multiply, divide, and subtract accordingly to obtain the simplified form. Therefore, the simplified expression is   [tex](9/4)x^2 - (1/25)y^2.[/tex]

Explanation:

The given expression is:

[tex]81/36 * x^2 - y^2/25[/tex]

To simplify this expression:

Multiply 81/36 which equals 9/4.

Then, divide [tex]x^2[/tex] by 4, and subtract [tex]y^2[/tex] divided by 25.

Therefore, the simplified expression is  [tex](9/4)x^2 - (1/25)y^2.[/tex]

Answer:

-24

Step-by-step explanation:

This is a simple multiplication problem. 8 times 3 is 24, and since one of the numbers is negative, the product (answer in multiplication) will be negative.

In multiplication and division of integers (positive and negative numbers), if the numbers have the same signs, the answer is ALWAYS positive, and if the numbers have different signs, the answer is ALWAYS negative.

Answer: -24

Step-by-step explanation: To multiply (-3)(8), it is important to understand that a negative times a positive is a negative so (-3)(8) is -24.

Answer:

≈ 12.5 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (10, - 11) and (x₂, y₂ ) = (- 1, - 5)

d = [tex]\sqrt{(-1-10)^2+(-5+11)^2}[/tex]

   = [tex]\sqrt{(-11)^2+6^2}[/tex]

   = [tex]\sqrt{121+36}[/tex]

   = [tex]\sqrt{157}[/tex] ≈ 12.5 ( to the nearest tenth )

Answer:

48000

Step-by-step explanation:

12000 students

4%

1 =annually

12×4×1= 48000

Answer:12,000

Step-by-step explanation:can’t give you one cuz I’m doing this in mathxl :p

Answer:

perpendicular bisector

Answer:

C. [tex]y^2=9[/tex]

Step-by-step explanation:

1. [tex]y^2 = 9[/tex]

2. [tex]y = \frac{+}{}\sqrt{9}[/tex]

3. Equation solutions:

[tex]y_{1} = 3\\y_{2} = -3[/tex]

Answer:ioj;i;

Step-by-step explanation:

fkuyhjgyhkuyh

Answer:

1 hour with 21 pages completed for each.

Step-by-step explanation:

First you need to list out what you know.

Tori:

Finished: 16 pgs

Rate: 5 pgs per hr

Cora:

Finished: 13 pgs

Rate: 8 pgs per hr

Now we compose Equations. In an equation we put the rate with the "X" because it is a constant rate of change. The finished amount of pages is our starting point or our y intercept we write it in this format:

y=mx+b

m being the rate of change

b being the initial amount or the starting point

For Tori the equation would be 5x+16 because 5 is our rate of change since she completes 5 pages per hour and 16 is our initial amount since she already completed them.

For Cora the equation would be 8x+13 because 8 is our rate of change since she completes 8 pages per hour and 13 is our initial amount since she already completed them.

we set these equation equal to each other:

5x+16=8x+13

eliminate the 5x on one side to leave the 16 by its self which in this case we subtract 5x to each side and get :

16=3x+13

the we subtract the 13 to leave 3x by its self and subtract 13 on both sides and get :

3=3x

lastly we divide 3 on both sides to isolate x and this would be our hours until they are both working on the same page:

1=x

this gives us 1 which means in 1 hour of working, both Cora and Tori will be working on the same page.

Substitute the 1 for each equation to get the total amount of pages completed in 1 hour:

5(1)+16

5+16

21 pages for Tori

8(1)+13

8+13

21  pages for Cora

Done

In one hour both Tori and Cora will have done 21 pages

Here's how I'm assigning a different variable to the value of each digit:

10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)

The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:

x + y = (1/5)(10x + y)

Simplify

x + y = 2x + (1/5)y

The tens digit is one less than the ones digit. Using this information, we can form the equation:

x = y - 1

Adding both sides by 1 gives

x + 1 = y

Substituting this into the y's the first equation gives:

x + x + 1 = 2x + (1/5)(x + 1)

Distribute and simplify

2x + 1 = 2x + (1/5)x + 1/5

Subtract both sides by 2x

1 = (1/5)x + 1/5

Subtract 1/5 from both sides

4/5 = (1/5)x

Multiply both sides by 5

4 = x

x = 4

Use this to solve for y

x + 1 = y

4 + 1 = y

y = 5

Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.

Let me know if you need any clarifications; this was a very interesting math problem to solve!

Answer:

x=6

Step-by-step explanation:

4x-1=2x+11

4x-2x-1=11

2x-1=11

2x=11+1

2x=12

x=12/2

x=6

Answer:

As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.

Step-by-step explanation:

[tex]2x + 2y = 14[/tex]

[tex]-x + y = 5[/tex]    Add x in both sides (Addition Property of Equality)

[tex]2x + 2y = 14[/tex]

[tex]y = x + 5[/tex]    Multiply both sides by 2

[tex]2x + 2y = 14[/tex]

[tex]2y = 2x + 10[/tex]    Subtract 2x in both sides

[tex]+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.[/tex]       ∵adding both equation

[tex]4y = 24[/tex] divide both sides by 4

[tex]y = 6[/tex]

Put the value of y = 6 to the equation [tex]-x + y = 5[/tex]

[tex]-x + 6 = 5[/tex]  Subtract 6 from both sides

[tex]-x = -1[/tex]    Change the sign

[tex]x = 1[/tex]     

Keywords: Addition property of equality, reason, proof

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Answer:

8/14 and 12/21

Step-by-step explanation:

Just multiply numerator and denominator by the same number, e.g., 2 and 3 to get above.

Answer:

8/14 and 12/21

Step-by-step explanation:

Answer: OC = πx4

Step-by-step explanation:

This question is incomplete, the correct question is

The diameter of a circle is 4 cm. Which equation can be used to find its circumference?

OC = πx2

OC= πx4

4

Answer,

Since the diameter is given as 4cm

Also,

The circumference of a circle OC = π x diameter

Therefore, OC = πx4

Answer:

He missed 14 questions

Step-by-step explanation:

Total = Right + Miss ⇒ t = r + m

Right = Miss + 12 ⇒ r = m + 12

t = 40

Since t = r + m and r = m + 12 then:

t = m + 12 + m

t = 2m + 12

40 = 2m + 12

28 = 2m

m = 14

Final answer:

Ben missed 14 questions.

Explanation:

To find the number of questions Ben missed, we can create an equation using the information given.

Let x represent the number of questions Ben missed.

We know that Ben correctly answered 12 more than he missed, so the number of questions he answered correctly can be represented as

x + 12.

Since the test had 40 questions, we can set up the equation:

x + (x + 12) = 40.

Simplifying this equation, we get

2x + 12 = 40.

Solving for x, we subtract 12 from both sides to get

2x = 28,

and then divide both sides by 2 to get

x = 14.

Therefore, Ben missed 14 questions.

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

Substitute 1 in everywhere you see 'x'

2(1)^3 - 3(1)^2 - 18(1) + 8

Solve:

f(1) = -11

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Final answer:

To evaluate the function f [tex](x) = 2x^3 - 3x^2 - 18x + 8[/tex] at x=1, substitute 1 for every instance of x in the function and simplify to get f(1) = -11.

Explanation:

The question appears to be a math problem where the student is asked to evaluate a function at a specific input. Specifically, the function given is  [tex]f(x) = 2x^3 - 3x^2 - 18x + 8[/tex] and the student has been asked to evaluate this function when x is equal to 1. To find f(1), we replace every instance of x in the function with 1.

So, f(1) = [tex]2(1)^3 - 3(1)^2 - 18(1) + 8[/tex]= 2(1) - 3(1) - 18 + 8 = 2 - 3 - 18 + 8 = -11.

Thus, f(1) evaluates to -11.

Answer:

Step-by-step explanation:

Answer:

18 feet

Step-by-step explanation:

Given:

A cat is running away from a dog.

After 5 seconds it is 16 feet away from the dog

After 11 seconds  it is 28 feet away from the dog.

Let x represent the time in seconds that have passed and y represent the

distance in feet, so there are two points are formed such as (5, 16) and (11,28).

We will find the distance between dog and cat. by using distance formula of the two points.

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Now we substitute the given value in above equation.

[tex]d=\sqrt{(11-5)^{2}+(28-11)^{2} }[/tex]

[tex]d=\sqrt{(6)^{2}+(17)^{2} }[/tex]

[tex]d=\sqrt{36+289}[/tex]

[tex]d=\sqrt{325}[/tex]

[tex]d=18.08\ feet[/tex]

18.08 ≅ 18

So [tex]d=18\ feet[/tex]

Therefore the distance between dog and cat is 18 feet.

To find the linear equation for the distance between the cat and the dog, we calculate the slope with the given points and use it with one of the points to establish the equation y = 2x + 6. A graph can be drawn with the points (5, 16) and (11, 28) to visualize the cat's path.

The linear equation describing the distance the cat is from the dog in relation to time can be determined using the two given points: (5, 16) and (11, 28), where 'x' is the time in seconds and 'y' is the distance in feet.

We first find the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values we get:

m = (28 - 16) / (11 - 5) = 12 / 6 = 2

This means for each second that passes, the cat is 2 feet further away from the dog. Next, we use one of the points and the slope to write the equation in point-slope form. Using the point (5, 16) we have:

y - 16 = 2(x - 5)

Expanding and simplifying this equation gives us:

y = 2x + 6

This is the linear equation that describes the distance of the cat from the dog over time. To draw a graph, we plot the two points given and draw the line that passes through them, which will represent the cat's path. The slope of 2 indicates that for every 1 second, the distance increases by 2 feet.

Hope it helps u..........

Answer:

[tex]\large\boxed{y=-\dfrac{3}{4}x+\dfrac{29}{4}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=================================[/tex]

[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=\dfrac{-5-(-1)}{2-5}=\dfrac{-5+1}{-3}=\dfrac{-4}{-3}=\dfrac{4}{3}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{\frac{4}{3}}=-1\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-\dfrac{3}{4}(-1)+b\\\\8=\dfrac{3}{4}+b\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\7\dfrac{1}{4}=b\to b=\dfrac{29}{4}\\\\\text{Finally:}\\\\y=-\dfrac{3}{4}x+\dfrac{29}{4}[/tex]

The sign of cos pi divided by seven is positive

Solution:

Given that we have to determine the sign of cos pi divided by seven

Let us first understand the signs of sine, cosine and tangent by quadrants

In the first quadrant, the values for sin, cos and tan are positive.

In the second quadrant, the values for sin are positive only.

In the third quadrant, the values for tan are positive only.

In the fourth quadrant, the values for cos are positive only.

Determine the sign of cos pi divided by seven

cos pi divided by seven ⇒ [tex]cos \frac{\pi}{7}[/tex]

The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant 1, Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]

In first quadrant, all trignometric functions are positive

so, [tex]\cos \frac{\pi}{7}[/tex] has positive sign.

Answer:

most likely isosceles

Step-by-step explanation:

due to the fact that two angles are congruent and the other angle is probably not it would make it all isosceles triangle

A triangle with two 45-degree angles is a special type of triangle known as an isosceles triangle.

In a triangle, if two angles are congruent, then the opposite sides of those angles are also congruent. In an isosceles triangle, two sides are equal in length, and the angles opposite those sides are congruent. Since two angles of the triangle are 45 degrees each, their opposite sides are also equal in length, making it an isosceles triangle.

Answer:

option D. 20 cm

Step-by-step explanation:

step 1

Find the volume of the water

The volume of the water is equal to

[tex]V=LWH[/tex]

we have

[tex]L=60\ cm\\W=40\ cm\\H=50\ cm[/tex]

substitute

[tex]V=(60)(40)(50)[/tex]

[tex]V=120,000\ cm^3[/tex] ---> volume of water

step 2

Find the deep of the water, if the tank is returned to its horizontal position

we have

[tex]V=120,000\ cm^3[/tex]

[tex]L=100\ cm\\W=60\ cm\\H=?\ cm[/tex]

where

H is the deep of the water

substitute in the formula of volume

[tex]120,000=(100)(60)(H)[/tex]

solve for H

[tex]120,000=6,000)(H)[/tex]

[tex]H=20\ cm[/tex]

[tex]AB=BC=CD=AD = \sqrt{10}[/tex]

As all the sides have same length, ABCD is a square

Step-by-step explanation:

To prove ABCD a square we have to find the lengths of each side

So,

the distance formula will be used to find the lengths

The distance formula is:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now,

[tex]AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]

[tex]BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]

[tex]CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]

[tex]AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]

we can see that

[tex]AB=BC=CD=AD = \sqrt{10}[/tex]

As all the sides have same length, ABCD is a square

Keywords: Distance formula, square

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Answer:

Marked price is Rs. 53333.33 and the cost price is Rs. 42333.33.

Step-by-step explanation:

Let Rs. x and Rs. y are the cost price and marked price of the mobile set respectively.

Now, the man has a loss of Rs. 8000 after giving a 15% discount on the marked price.

Therefore, 15% of y is 8000 i.e. [tex]8000 = \frac{y\times 15}{100}[/tex]

⇒ y = Rs. 53333.33

Now, the man gained Rs. 3000 by selling the mobile set allowing 15% discount on the marked price.

Therefore, the mobile set has the cost price = x = Rs. [(53333.33 - 8000) - 3000] = Rs. 42333.33 (Answer)

Answer:

The solution is the point (5,-5)

Step-by-step explanation:

we have

[tex]3x + 2y - 5 = 0[/tex] -----> equation A

[tex]x = y + 10[/tex] -----> equation B

Solve the system by substitution

substitute equation B in equation A

[tex]3(y+10) + 2y - 5 = 0[/tex]

solve for y

[tex]3y+30 + 2y - 5 = 0[/tex]

[tex]5y=-25[/tex]

[tex]y=-5[/tex]

Find the value of x

[tex]x=5+ 10[/tex]

[tex]x=5[/tex]

therefore

The solution is the point (5,-5)

Every next number is incremented by 8 from the previous number hence the sequence is arithmetic and the common difference is 8.

Hope this helps.

Answer:

The given sequence is arithmetic and common difference is 8.

Step-by-step explanation:

Given that :

            - 19, - 11, - 3, 5......

Here, a = - 19 ;  a is the first term of the series.

Now, For common difference-

d = [tex]t_{2} - t_{1}[/tex] = [tex]t_{3} - t_{2}[/tex] = [tex]t_{4} - t_{3}[/tex]

Let [tex]t_{1} = - 19,  t_{2} = - 11[/tex]

 d = - 11 - (-19)

 =  -11 + 19

  = 8

Let [tex]t_{3} = - 3,  t_{2} = - 11[/tex]

d = - 3 -(-11)

  = - 3 + 11

   = 8

Let [tex]t_{4} = 5,  t_{3} = - 3[/tex]

d = 5 - (-3)

  = 8

In each condition common difference d is same therefore the given sequence is arithmetic and common difference d = 8.

Answer:

Therefore 12.5 centimeters on the map represents an actual distance of 5 kilometers.

Step-by-step explanation:

Given:

The scale map shows that

5 centimeters =2 kilometers.

To Find:

What number of centimeters on the map represents an actual distance of 5 kilometers?

Solution:

Let 'x' cm be on the map to represent 5 kilometer.

Given:

5 centimeters = 2 kilometers.

Therefore,

x cm = 5 kilometer

Soon Equality of proportion we get

[tex]\dfrac{5}{x}= \dfrac{2}{5}\\ \\x=\dfrac{5\times 5}{2}=\dfrac{25}{2}=12.5\ cm\\\\\therefore x = 12.5\ cm[/tex]

Therefore 12.5 centimeters on the map represents an actual distance of 5 kilometers.

Answer:   The correct answer is:   [C]:  "  [tex]15^{(7/4)}[/tex] " .

____________________________________

Step-by-step explanation:

____________________________________

Note the property for square roots in exponential form:

_____________________________________

     →    [tex]\sqrt[a]{(b)^ c}[/tex]  ;  ↔  b[tex]b^{(c/a)}[/tex] ;

    { [tex]a\neq 0[/tex] ; [tex][a^{(b/c)}]\neq 0[/tex] ; [tex]c\neq 0[/tex]  .}.

_____________________________________

As such, given:

     →    [tex]\sqrt[4]{(15^7)}[/tex] ;  

  a = 15,  b = 7,  c = 4 .

     →    [tex]\sqrt[4]{(15^7)}[/tex] ;   ↔  [tex]15^{(7/4)}[/tex] ;

     →  which corresponds to:

_____________________________________

Answer choice:  [C]:  "  [tex]15^{(7/4)}[/tex] " .

_____________________________________

Hope this helps!

  Wishing you well in your academic endeavors!

_____________________________________

Answer:

The complete missing value in the solution to the equation is (-5,-8).

Step-by-step explanation:

Consider the provided equation.

[tex]-3x+7y=5x+2y[/tex]

We need to find the missing value of the coordinate; (-5__)

To find the missing value substitute x = -5 in above equation.

[tex]-3(-5)+7y=5(-5)+2y[/tex]

[tex]15+7y=-25+2y[/tex]

[tex]7y-2y=-25-15[/tex]

[tex]5y=-40[/tex]

[tex]y=-8[/tex]

Hence, the missing value is -8.

Thus, the complete missing value in the solution to the equation is (-5,-8).

Answer:

Step-by-step explanation:

-5, -8

Step-by-step explanation:

equation-

(x-3) (x-4) =

[tex] {x }^{2} - 3x - 4x + 12 = {x}^{2} - 7x + 12[/tex]

Given the roots 3 and 4 of a quadratic equation, and the leading coefficient 2, the quadratic equation can be derived as 2x^2 - 14x + 24.

To find a quadratic equation given its roots and leading coefficient, you use the factored form of a quadratic equation, x = (x - root1)(x - root2).  

Given that the roots are 3 and 4, the equation takes the form of x = (x - 3)(x - 4). When you multiply this out, you get x^2 - 7x + 12.

The problem also states that the leading coefficient is 2, so we multiply our obtained equation by 2 to get: 2x^2 - 14x + 24.

So, the requested quadratic equation is 2x^2 - 14x + 24.

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