Cindy recycles 54 pounds of paper. She recycles 9 times as many pounds of paper Monica recycles. How can I solve the equation to find the number of pounds of paper Monica recycled?

Answer:   5

Step-by-step explanation:

[tex]\sqrt{4x+5}-\sqrt{x-1}=\sqrt{x+4}\\\\(\sqrt{4x+5}-\sqrt{x-1})^2=(\sqrt{x+4})^2\\\\4x+5-2\sqrt{(4x+5)(x-1)}+x-1=x+4\\\\5x+4-2\sqrt{(4x+5)(x-1)}=x+4\\\\4x=2\sqrt{(4x+5)(x-1)}\\\\2x=\sqrt{(4x+5)(x-1)}\\\\(2x)^2=(\sqrt{(4x+5)(x-1)})^2\\\\4x^2=(4x+5)(x-1)\\\\4x^2=4x^2+x-5\\\\0=x-5\\\\5=x\\\\\\Check:\\\sqrt{4(5)+5}-\sqrt{(5)-1}=\sqrt{(5)+4}\\\\\sqrt{25}-\sqrt{4}=\sqrt9\\\\5-2=3\ \checkmark[/tex]

Answer:   A. Line segment

Step-by-step explanation:

A line is a one-dimensional geometric straight -undefined figure which has no thickness or depth . It extends infinitely in both directions.  

A line segment is a part of a line having end-points on both the sides.

It has only length therefore, it is one dimensional.

Thus , the objects is considered to be one-dimensional because it has length but no width or height is a line segment.

The triangle is 2-dimensional , point has no-dimensions,  and cube  is 3-dimensional.

A line segment is the correct answer, as in mathematics it is considered one-dimensional because it only has length but no width or height. It extends in one direction, unlike a triangle and a cube, which have more dimensions. The point does not have length.

In mathematics, a line segment is considered to be one-dimensional as it only possesses a property of length but no width or height. This means it only extends in one direction, often represented on a number line. In comparison, other options presented such as a triangle, point or cube have other dimensions involved. Specifically, a triangle falls in two dimensions as it has both length and width; a cube is a three-dimensional object possessing length, width, and height; and a point, though it lacks all three dimensions, is not accurate as it doesn't have length, which is the key criterion in the question.

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Answer:

Plane = 441 mi/h; wind =  63 mi/h

Step-by-step explanation:

distance = rate × time

 Let p = the plane's speed in still air

and w = the wind speed . Then,

p + w = speed with wind

 p - w = speed against wind

We have two conditions:

(1)  756 = (p - w) × 2

(2) 756 = (p + w) × 1.5

Distribute the constants                  (3)    756 = 2p - 2w

                                                          (4)   756 = 1.5p + 1.5 w  

Multiply Equation (3) by 3                (5) 2268 = 6p  -  6w

Multiply Equation (4) by 4                (6) 3024 = 6p + 6w

Add Equations (5) and (6)                     5292 = 12p

Divide each side by 12                     (7)        p = 441 mi/h

Substitute (7) into Equation(3)                 756 = 882 - 2w

Add 2w to each side                      2w + 756 = 882

Subtract 756 from each side                    2w = 126

Divide each side by 2                                 w = 63 mph

The plane's speed in still air is 441 mi/h.

The wind speed is 63 mph.

Check:

(1) 756 = (441 - 63) × 2     (2) 756 = (441 + 63) × 1.5

   756 = 378 × 2                   756 = 504 × 1.5

   756 = 756                         756 = 756

The speed of the plane in still air is 420 miles per hour and the wind speed is 84 miles per hour.

To solve Dave and Sandy Hartranft's problem, we set up two equations for flying into and with the wind. For Dave and Sandy flying into the wind, we use the formula speed equals distance over time: P - W = 756 miles / 2 hours. This represents the plane's speed minus the wind speed equaling the distance traveled divided by the time taken. We denote P as plane's speed and W as wind speed.

On the return trip, with the wind behind them, we calculate plane's speed plus the wind speed based on the same formula: P + W = 756 miles / 1.5 hours. Solving these two equations, you get: P = 420 miles per hour (plane's speed in still air) and W = 84 miles per hour (wind speed).

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Answer:

5

Step-by-step explanation:

There are 9 friends with 4 or 5 pets so, you subtract 9-4 because there are 4 friends with 2 or 3 = 5 because the question is asking how many more.

Answer:

28 miles per gallon

Step-by-step explanation:

you divide 420 by 15 to see how many miles per gallon and

420 divided by 15= 28 (gallons)

28 miles I think I’m not sure but just divide 15 into 420 and you should get the answer.

Answer:

Yes

Step-by-step explanation:

Yes, that is possible because whenever one number is a factor of the other one, it's their greatest common factor. Here are some examples.

2 and 200

10 and 100

13 and 52

one thousand and one million

Answer:

m<2 = 63

m<3 = 117

Step-by-step explanation:

<1 and <2 are alternate interior angles and are therefore equal. M<1 = 63 degrees,  so m<2 must be the same thing.

<2 and <3 are on the same straight line.

They are supplementary.

Therefore they equal 180 degrees.

63 + m<3 = 180                  Subtract 63 from both sides.

63 - 63 +m<3 = 180 - 63   Collect like terms

m<3 = 117

Answer:

The answer is C, 220 units.

Answer:

[tex]x \geq -56[/tex]

Step-by-step explanation:

You can solve inequalities the same way as equations as long as whenever you multiply or divide by a negative number, or flip fractions, you change the direction of the sign.

We don't have to do that here, here is the worked solution:

[tex]-12 \leq 44 + x[/tex]

[tex]-56 \leq x[/tex]

[tex]x \geq -56[/tex]

Answer:

x ≥ -56

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Hope this helps,

Davinia.

Answer:

multiple 6 with numbers inside paranthesis:

12x - 66 + 15 = 21

add 66 fhen substrack 15 from both sides :

12x = 72 divide both sides with 12:

x = 6

Step-by-step explanation:

In his answer above he didn’t add 81 to both sides. (Somebody correct me if I’m wrong)

Answer:

Although variables wouldn't really fit for this problem, if you were to graph it, the pizza types would be on the x axis and the cost would be on the y axis since the cost of the pizzas technically "depend" on the type of pizza.

It’s the second one from the right

Since there’s a - behind x it means it has to be facing down so it’s either 2 or 4

Now it’s x-2 and we know that x moves the opposite so it needs to move 2 to the right so the answer is 2

Answer:

c)Q3

Step-by-step explanation:

In the third quadrant, tangent and cotangent are positive while cosine and thus secant are negative. Therefore, the solution is C. Q3

Answer: (-1, -4) and (4, 6)

Step-by-step explanation:

The pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equations:

y = 2x - 2

y = x² - x - 6

Equate both equations:

2x - 2 = x² - x - 6

x² - 3x - 4 = 0

Solving using the quadratic formula:

[tex]\rm x_{1,\:2}=\dfrac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]

x = 4, -1

y = 6, -4

Thus, the pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

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Answer:

C

Step-by-step explanation:

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ x=-2, no explanation

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

There always needs to be an explanation so you understand it!

Follow this step by step.

#1. Remove all -1 on both sides.

You are left with 2(x+3)+x=0.

#2. Expand the equation.

2x+6+x=0.

#3. Simplify 2x + 6 + x to 3x + 6.

3x+6=0

#4. Subtract 6 from each side.

3x=−6.

#5. Divide both sides by 3.

x = -6/3.

#6. Simplify 6/3 to 2.

x = 2.

Therefore, you get [tex]\fbox{x = 2}[/tex].

Answer:

C.) -33

Step-by-step explanation:

2/3 (x+6) = -18

x+6 = -27

x = -33

Answer:

B

Step-by-step explanation:

2/3*(x + 6) = -18

Multiply by 3

2(x + 6) = -18*3

2(x + 6) = -54    

Remove the brackets

2x + 12 = - 54

Subtract 12 from both sides

2x+12-12 = - 54 - 12

Combine like terms

2x = -66

Divide by 2

2x/2 = -66/2

x = -33

Answer B

Answer:

[tex]\large\boxed{D.\ y=-\dfrac{1}{5}x+\dfrac{32}{5}}[/tex]

Step-by-step explanation:

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

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

m - slope

b - y-intercept

We have the slope m = -1/5. Substitute:

[tex]y=-\dfrac{1}{5}x+b[/tex]

Put the coordinates of the given point (-3, 7) to the equation:

[tex]7=-\dfrac{1}{5}(-3)+b[/tex]

[tex]7=\dfrac{3}{5}+b[/tex]            subtract 3/5 from both sides

[tex]6\dfrac{2}{5}=b\to b=\dfrac{6\cdot5+2}{5}=\dfrac{32}{5}[/tex]

?

Step-by-step explanation:

first you have to add the PIC to have us answer

Answer:

That is it's simplest form

Step-by-step explanation:

There is no coefficients that are the same

North Carolina = 3 * Utah

North Carolina = 2 * Oregon

Arkansas = Oregon - 1,000,000

North Carolina + Utah + Oregon + Arkansas = 27,000,000

North Carolina = 3 * Utah

Utah = 1/3 * North Carolina

Utah = 1/3 * (2 * Oregon)

(2 * Oregon) + (1/3 * (2 * Oregon)) + Oregon + (Oregon - 1,000,000) = 27,000,000

2O + (1/3 * 2O) + O + O - 1,000,000 = 27,000,000

2O + 2/3O + O + O - 1,000,000 = 27,000,000

4 2/3 O - 1,000,000 = 27,000,000

4 2/3 O = 28,000,000

O = 6,008,584

NC = 2O

NC = 2(6,008,584)

NC = 12,017,167

A = O - 1,000,000

A = 6,008,584 - 1,000,000

A = 5,008,584

NC = 3U

12,017,167 = 3U

U = 4,005,722

The populations of the four states are as follows:

- Utah has a population of 4 million.

- Oregon has a population of 6 million.

- North Carolina has a population of 12 million.

- Arkansas has a population of 5 million.

Let's denote the population of Utah, Oregon, and Arkansas as U, O, and A, respectively. According to the information given:

1. North Carolina has three times the population of Utah: [tex]\( NC = 3U \).[/tex]

2. North Carolina has twice the population of Oregon: [tex]\( NC = 2O \).[/tex]

3. Arkansas has 1 million people fewer than Oregon: [tex]\( A = O - 1 \).[/tex]

4. The total population of these four states is 27 million: [tex]\( U + O + A + NC = 27 \).[/tex]

From equations (1) and (2), we can equate the populations of Utah and Oregon since both are related to the population of North Carolina:

[tex]\( 3U = 2O \) or \( O = \frac{3}{2}U \).[/tex]

Now, substitute the value of O from equation (3) into the total population equation (4):

[tex]\( U + \frac{3}{2}U + ( \frac{3}{2}U - 1 ) + 3U = 27 \).[/tex]

Combine like terms:

[tex]\( U + \frac{3}{2}U + \frac{3}{2}U - 1 + 3U = 27 \),[/tex]

[tex]\( U + 3U + 3U - 1 = 27 \),[/tex]

[tex]\( 7U - 1 = 27 \).[/tex]

Now, solve for U:

[tex]\( 7U = 27 + 1 \),[/tex]

[tex]\( 7U = 28 \),[/tex]

[tex]\( U = \frac{28}{7} \),[/tex]

[tex]\( U = 4 \)[/tex] million.

Now that we have the population of Utah, we can find the populations of the other states:

[tex]\( O = \frac{3}{2}U = \frac{3}{2} \times 4 = 6 \)[/tex] million,

[tex]\( NC = 2O = 2 \times 6 = 12 \)[/tex] million,

[tex]\( A = O - 1 = 6 - 1 = 5 \)[/tex] million.

C is the one you're looking for

The solution to the number 8000 in scientific notation is 8  * 10³

From the question, we have the following parameters that can be used in our computation:

Number = 8000

Multiply the number by 1

So, we have

Number = 8000 * 1

Express 1 as 1000/1000

So, we have the following representation

Number = 8000 * 1000/1000

Next, we have

Number = 8 * 1000

Express 1000 as 10³

So, we have

Number = 8 * 10³

Hence, the solution is 8  * 10³

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Answer:

[tex]90cm^2[/tex]

Step-by-step explanation:

The side length AB of triangle ABC corresponds to side length of PQ of triangle PQR.

The scale factor from ABC to PQR is [tex]k=\frac{6}{4}=1.5[/tex]

The area of triangle PQR will change by [tex]k^2=1.5^2=2.25[/tex] centimeters square.

Since we know the area of triangle ABC to be [tex]40cm^2[/tex], the area of triangle PQR [tex]=2.25\times 40=90cm^2[/tex]

Answer:

The area of the triangle PQR is 90 cm^2.

Step-by-step explanation:

We are given two triangles, ABC and PQR, which are similar to each other.

If two triangles are similar, then the ratio of their areas is the square of the ratio of their sides.

Given that area of the triangle ABC is [tex]40cm^2[/tex], we are to find the area of the triangle PQR.

Finding the scale factor [tex]k=\frac{6}{4} =1.5[/tex]

So square of this scale factor will be [tex]k^2=(1.5)^2=2.25[/tex]

Area of triangle PQR = [tex]2.25 \times 40[/tex] = 90cm^2

The student did not solve it correctly. They forgot to add the 5 foot height to the value of x.

The correct height is  23.4 feet, I know because I added 5 to the value of x.

Answer:

The wall is 3 ft high and 5 ft long.

Step-by-step explanation:

Recall:  Area of the rectangular wall is A = (length)(height).

Let the height be represented by h.  Then the length is represented by h + 2.

The formula A = (length)(height) then becomes A = h(h+2) = 15 ft², which, written in the standard form of a quadratic equation, is h² + 2h - 15 = 0.

Let's solve this last equation for h using completing the square:

h² + 2h - 15 = 0 becomes h² + 2h + 1 -1 - 15 = 0, or (h + 1)² = 16.  Taking the square root of both sides, we get:

h + 1 = ±4, which is equivalent to h = 3 and h = -5.  Discard the negative result.  Then h = 3 and w = 3+2 = 5.

The wall is 3 ft high and 5 ft long.  Its area is (3 ft)(5 ft) = 15 ft²

The height and the length of the rectangular wall is 3 feet and 5 feet respectively.

Area of a rectangle = 15 square feet

Length = x feet

Height = (x - 2) feet

Area of a rectangle = height × length

15 = x × (x - 2)

15 = x² - 2x

set to quadratic equation

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x(x - 5) + 3(x - 5) = 0

(x + 3)(x - 5) = 0

x + 3 = 0 or x - 5 = 0

x = -3 or x = 5

The length of a rectangle cannot be negative

Therefore,

Length = x feet

= 5 feet

Height = (x - 2) feet

= 5 - 2

= 3 feet

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Answer:

your answer would be: x=1±√11 all divided by 2

Hope this helps

~QueenSupreme AKA Trinity

Answer:   [tex]\bold{\dfrac{1\pm \sqrt{11}}{2}}[/tex]

Step-by-step explanation:

[tex]x^2-x-\frac{5}{2}=0\quad \text{multiply by 2 to get:}\\\\2x^2-2x-5=0\quad \rightarrow \quad a=2,\ b=-2,\ c=-5\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(2)(-5)}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{40}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{44}}{2(2)}\\\\\\.\ =\dfrac{2\pm 2\sqrt{11}}{2(2)}\\\\\\.\ =\boxed{\dfrac{1\pm \sqrt{11}}{2}}[/tex]

Answer: B: 23 3/4

Step-by-step explanation:

You have to multiply 4 3/4 by 5 in order to get your answer. Turn 4 3/4 into an improper fraction which would be 19/4. Then multiply it by 5; 19/4 times 5 equals 95/4. You then divide 95 by 4 which equals 23 3/4.

Answer:

Your answer is 23 3/4

Step-by-step explanation:

Answer:

The answer is 0.42525 TONS (METRIC)