Freshman Algebra, I need to simplify it

[tex] \frac{ - 1}{4} (v {q}^{4} )( - 8 {v}^{3} q {)}^{2} [/tex]
​

Answer:

Part 1) The system of equations is equal to

12x+y=66.75

3x+10y=82.50

Part 2) The cost of one drink is $5

Step-by-step explanation:

Part 1) Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn

Let

x----> the price of one drink

y ----> the price of one bag of popcorn

we know that

Jason

12x+y=66.75 -----> equation A

Henry

3x+10y=82.50 -----> equation B

Part 2) Using these equations, determine and state the price of a drink, to the nearest cent

12x+y=66.75 -----> equation A

3x+10y=82.50 -----> equation B

Solve the system of equations by elimination

Multiply the equation A by -10 both sides

-10*(12x+y)=66.75*(-10)

-120x-10y=-667.5 -----> equation C

Adds equation B and C and solve for x

3x+10y=82.50

-120x-10y=-667.5

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

3x-120x=82.50-667.5

120x-3x=667.50-82.50

117x=585

x=5

therefore

The cost of one drink is $5

Answer:

7.5 ab and cd

4 bd and ac

Step-by-step explanation:

Answer:

i believe the answer is 7.5 ab and cd, 4 bd and ac

Answer:

Skewed to the right

Step-by-step explanation:

As we can see in the table, the first three intervals have smaller frequency and last 4 intervals have higher frequency values. When the class intervals and frequency will be plotted on graph while taking class intervals on x-axis and frequency at y-axis, the graph will be skewed to the right because of the larger frequency values in the last intervals..

Answer:

x ≈ 9.2

Step-by-step explanation:

When 2 chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

5x = 9 × 5.1 = 45.9 ( divide both sides by 5 )

x ≈ 9.2

If you divide any number by 1, the answer is itself. The answer is 7 and 1/2.

Hope this helps!

Answer:

7 1/2

Step-by-step explanation:

Take it like the following scenario.

There are 7 1/2 M&M's left in a bag.

Neither of your friends want any so you get to have all of them.

So, the 7 1/2 M&M's divided by one person is 7 12 since all of the M&M's go to you.

[Rememember that any number you divide by 1, the answer is itself

Ex: 4 divided by 1 = 4]

I hope this helps!

Answer:

$16,384

Step-by-step explanation:

The amount of money Nadir saves increases exponentially by a factor of 2. If you keep multiplying each previous number by 2 until you get to the 15th number, (2*2, 4*2, 8*2, 16*2), you will get 16,384.

Answer:

$16,384

Step-by-step explanation:

Let's find the general equation for his savings:

The first day he saves $1 = [tex]2^{0}[/tex]

The second day, $2 = 1*2 = [tex]2^{1}[/tex]

The third day, $4 = 1*2*2 = [tex]2^{2}[/tex]

The fourth day, $8 = 1*2*2*2 = [tex]2^{3}[/tex]

In general, in the n-th day, he saves [tex]2^{n-1}[/tex]

With this, we can calculate the amount that he will save on the fifteenth day:

[tex]2^{15-1} = 2^{14} = \$16,384[/tex]  

ANSWER

The explicit formula is :

[tex]a_n = 8+ 3(n - 1)[/tex]

EXPLANATION

The given sequence is

8,11,14,17,20,23,26,...

The first term is

[tex]a_1=8[/tex]

The common difference is

d=11-8

d=3

The explicit formula is given by:

[tex]a_n = a_1 + d(n - 1)[/tex]

We substitute the values to get,

[tex]a_n = 8+ 3(n - 1)[/tex]

Answer:

Leah has 48 marbles.

Step-by-step explanation:

Represent the number of marbles that each person has by L and D.

Leah has 28 more marbles than Dan:  L = D + 28.

Then (1/3)L = (4/5)D.  Here the LCD is 15, and so multiplying this equation by 15 will remove the fractions:  15(1/3)L = 15(4/5)D.  

Therefore, 5L = 12D, and D = 5L/12.

Then, since L = D + 28,        L = (5/12)L + 28, or

12L = 5L + 336, or

7L = 336, or

L = 336/7 = 48.

Leah has 48 marbles.  That means that Dan has 20 marbles.

The number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

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.

It is given that:

Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

Let x be the number of marbles Leah has.

Let y be the number of marbles Dan has.

Leah has 28 more marbles than Dan:  

x = y + 28

(1/3)x = (4/5)y

Solving above two linear equation, we get:

5x = 12y

5(y + 28) = 12y

5y + 140 = 12y

12y - 5y = 140

7y = 140

y = 140/7 = 20

x = 20 + 28 = 48

Thus, the number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

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Answer:

A. 2x^5y^8 and 12xy^7

Step-by-step explanation:

The question is on laws of indices

when we have x^a × x^b = x^(a+b)

Given in the question 24x^6y^15

24 could be 2×12............for the length and width

Then x^6 = x^1 × x^5 = x^(1+5) = x^6

And  y^15 = y^8 ×y^7 = y^(8+7) = y^(15)

Answer:

The correct answer is :[tex]l=2x^5y^8,w = 12xy^7[/tex]

Step-by-step explanation:

Let the dimension of the rectangle be l and w.

A = [tex]24x^6y^{15}[/tex]

[tex]24x^6y^{15}=l\times w[/tex]

A) If the dimension are :

[tex]l=2x^5y^8,w = 12xy^7[/tex]

Area of the rectangle

[tex]= 2x^5y^8\times 12xy^7=24x^6y^{15}=A[/tex]

B) If the dimension are :

[tex]l=6x^2y^3,w = 4x^3y^5[/tex]

Area of the rectangle

[tex]= 6x^2y^3\times 4x^3y^5=24x^5y^{8}\neq A[/tex]

C) If the dimension are :

[tex]l=10x^6y^{15},w = 14x^6y^{15}[/tex]

Area of the rectangle

[tex]= 10x^6y^{15}\times 14x^6y^{15}=140x^{12}y^{30}\neq A[/tex]

D) If the dimension are :

[tex]l=9x^4y^{11},w = 12x^2y^4[/tex]

Area of the rectangle

[tex]= 9x^4y^{11}\times 12x^2y^4=108x^6y^{15}\neq A[/tex]

Answer:

The equation of the hyperbola is x²/16 - y²/9 = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

- The length of the transverse axis is 2a

- The coordinates of the vertices are (±a , 0)

- The length of the conjugate axis is 2b

- The coordinates of the co-vertices are (0 , ±b)

- The coordinates of the foci are (± c , 0),  

- The distance between the foci is 2c where c² = a² + b²

- The distance between the vertex and the focus in-front of it is c - a

* Now lets solve the problem

- The distance from a vertex to the center of the mirror

∵ The vertex of the mirror is (a , 0)

∵ The distance between a vertex and the center of the mirror

  is 4 inches

∴ a = 4

∵ The distance between the vertex and a focus in front of  the surface

  of the mirror is 1

∵ The distance between the vertex and the focus in-front of it is c - a

∴ c - a = 1

∴ c - 4 = 1 ⇒ add 4 to the both sides

∴ c = 5

- The mirror has a horizontal transverse axis and the hyperbola is

 centered at (0, 0)

∴ The equation of the hyperbola is x²/a² - y²/b² = 1

- Lets find b from a and c

∵ c² = a² + b²

∵ c = 5 and a = 4

∴ (5)² = (4)² + b²

∴ 25 = 16 + b² ⇒ subtract 16 from both sides

∴ 9 = b² ⇒ take √ for both sides

∴ b = ±3

- Lets write the equation

∴ x²/(4)² - y²/(3)² = 1

∴ x²/16 - y²/9 = 1

* The equation of the hyperbola is x²/16 - y²/9 = 1

The distance of the focus from the center is the sum of the distance from

the focus to the surface and the vertex distance.

Correct response:

Given:

Distance of the vertex from the center = 4 inches

Distance of the focus from the mirror surface = 1 inches

Coordinates of the center of the mirror = (0, 0)

Required:

To write the equation of the hyperbola that can be used to model the mirror

Solution:

The equation of an hyperbola having an horizontal transverse axis is presented as follows;

Where;

(h, k) = The coordinate of the center

a = Center to vertex distance

b² = c² - a²

Where;

c = The from the center to the vertex

Therefore;

a = 4

(h, k) = (0. 0)

c = 4 + 1 = 5

b² = 5² - 4² = 9

b = √9 = 3

The equation of the hyperbola is therefore;

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Answer: The line that passes through the points  (0,1) and  (-7,0). Observe the graph attached.

Step-by-step explanation:

By definition, a line intersects the y-axis when the value of "x" is zero ([tex]x=0[/tex]), then if the y-intercept  is 1, then the point where the line intersects the y-axis is:

(0,1)

By definition, a line intersects the x-axis when the value of "y" is zero ([tex]y=0[/tex]), then if the x-intercept  is -7, then the point where the line intersects the x-axis is:

(-7,0)

Therefore, now you know this, you can graph a line that passes through the points  (0,1) and  (-7,0). Observe the graph attached.

Answer:

Check the attached graph

Step-by-step explanation:

Given that y-intercept is 1.

That means graph passes through the point (0,1).

Given that x-intercept is -7.

That means graph passes through the point (-7,0).

Now we need to graph the line using above information. So begin by graphing both points .

Now draw a line joining both points to get the final graph.

Answer:

68 - C = m

If he completes 33 it means :

c = 33

Substituting this in the equation we have :

m > 68 - 33

m > 35

Answer:

I think the first one is 68-c=m and the 2nd one is 35

Step-by-step explanation:

Jeez i hope im right i had to think really hard for some reason. I havent done this is a while >.<

A. Traffic on the side with the broken yellow line. The dashes signify the “openness” of the ability that the drivers on that side have to pass.

Answer:

A). Traffic on the side with broken yellow line

Step-by-step explanation:

A solid yellow line used in two lane roadways where passing or crossing is strictly prohibited. It is dangerous and may lead to serious accidents while violating this.

                             On the other hand, broken yellow line on the roadways indicates that vehicles moving can pass or cross the road when only it is safe to cross the lane.

Therefore, when the center line is one solid yellow line and one broken yellow line, then the vehicles on the side of the broken lines may cross the line to pass only when it is safe to cross.

The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,

⇒ {36, 1, 16}

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable

Given that;

The function is,

⇒ f (x) = (x - 1)²

And, domain is {-5,0,5}.

Now, We can find the value of range as;

Put x = - 5 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = (- 5 - 1)²

⇒ f (x) = (- 6)²

⇒ f (x) = 36

Put x = 0 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = (0 - 1)²

⇒ f (x) = (- 1)²

⇒ f (x) = 1

Put x =  5 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = ( 5 - 1)²

⇒ f (x) = ( 4)²

⇒ f (x) = 16

Thus, The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,

⇒ {36, 1, 16}

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[tex] \frac{8}{t} + 5 = t - \frac{3}{t} + 5 + \frac{1}{3} \\ \\ 1. \: \frac{8}{t} = - \frac{3}{t} + \frac{1}{3} \\ \\ 2. \: 24 = 3t^{2} - 9 + t \\ \\ 3. \: 24 - 3t^{2} + 9 - t = 0 \\ \\ 4. \: 33 - 3t ^{2}- t = 0 \\ \\ 5. \: t = \frac{1 + \sqrt{397} }{ - 6} \: \frac{1 - \sqrt{397} }{ - 6} \\ \\ 6. \: t = - \frac{1 + \sqrt{397} }{6} \: - \frac{1 - \sqrt{397} }{6} [/tex]

Answer:

Final answer is t=7.

Step-by-step explanation:

[tex]\frac{8}{t+5}=\frac{t-3}{t+5}+\frac{1}{3}[/tex]

[tex]=\frac{8}{t+5}\cdot3\left(t+5\right)=\frac{t-3}{t+5}\cdot3\left(t+5\right)+\frac{1}{3}\cdot3\left(t+5\right)[/tex]

[tex]8\cdot3=3\left(t-3\right)+\left(t+5\right)[/tex]

[tex]24=3t-9+t+5[/tex]

[tex]24=4t-9+5[/tex]

[tex]24=4t-4[/tex]

[tex]24+4=4t[/tex]

[tex]28=4t[/tex]

[tex]\frac{28}{4}=t[/tex]

[tex]7=t[/tex]

[tex]t=7[/tex]

Hence final answer is t=7.

Answer: The height of the container is 10 centimeters. If its diameter and height were both doubled, the container's capacity would be 8 times its original capacity.

Step-by-step explanation:

The volume of a cone can be calculated with this formula:

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

Where "r" is the radius and "h" is the height.

We know that the radius is half the diameter. Then:

[tex]r=\frac{12cm}{2}=6cm[/tex]

We know the volume and the radius of the conical container, then we can find "h":

[tex]120\pi cm^3=\frac{\pi (6cm)^2h}{3}\\\\(3)(120\pi cm^3)=\pi (6cm)^2h\\\\h=\frac{3(120\pi cm^3)}{\pi (6cm)^2}\\\\h=10cm[/tex]

The diameter and height doubled are:

[tex]d=12cm*2=24cm\\h=10cm*2=20cm[/tex]

Now the radius is:

[tex]r=\frac{24cm}{2}=12cm[/tex]

And the container capacity is

[tex]V=\frac{\pi (12cm)^2(20cm)}{3}=960\pi cm^3[/tex]

Then, to compare the capacities, we can divide this new capacity by the original:

 [tex]\frac{960\pi cm^3}{120\pi cm^3}=8[/tex]

Therefore,  the container's capacity would be 8 times its original capacity.

Answer:

i can’t see others answers

Answer:

The best possible answer is A

Step-by-step explanation:

Answer:

Option A is correct that is Surface Area of the Cylinder is 1659 in.²

Step-by-step explanation:

Given:

Radius of the Cylinder , r = 11 in.

Height of the Cylinder , h = 13 in.

We have to find the Surface Area of Cylinder to the nearest Whole number.

We know that,

Surface Area of the Cylinder = 2πr(r+h)

                                                 = 2 × 22/7 × 11 ( 11 + 13 )

                                                 = 2 × 22/7 × 11 × 24

                                                 = 1659.42 in.²

                                                 = 1659 in.²  (nearest whole number)

Therefore, Option A is correct that is Surface Area of the Cylinder is 1659 in.²

Answer:

Step-by-step explanation:

[tex]30x^2-26x+4=0\\\\30x^2-20x-6x+4=0\\\\10x(3x-2)-2(3x-2)=0\\\\(3x-2)(10x-2)=0\iff3x-2=0\ \vee\ 10x-2=0\\\\3x-2=0\qquad\text{add 2 to both sides}\\\\3x=2\qquad\text{divide both sides by 3}\\\\x=\dfrac{2}{3}\\\\10x-2=0\qquad\text{add 2 to both sides}\\\\10x=2\qquad\text{divide both sides by 10}\\\\x=\dfrac{2:2}{10:2}\\\\x=\dfrac{1}{5}[/tex]

Answer:

The reflection is across the x-axis

Step-by-step explanation:

* Lets revise the reflection

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

* Now lets solve the problem

∵ The endpoints of a line segment are (3 , 2) and (2 , -3)

∵ The image of the endpoints after the reflection are (3 , -2) and (2 , 3)

* Lets study the change

# The x-coordinates of the points are 3 and 2

# The x-coordinates of the images are 3 and 2

# The y-coordinates of the points are 2 and -3

# The y-coordinates of the images are -2 and 3

- The change is in the signs of the y-coordinates

∴ The reflection is across the x-axis

Answer:

$106,147

Step-by-step explanation:

The price of the house is $160,000. The value of the house is going down by 5% each year, and we need to find the price of the value after 8 years.

Year 0:

$160,000

Year 1:

$160,000×0.95 = $152,000

Year 2:

$152,000×0.95 = $144,400

Year 3:

$144,400×0.95 = $137,180

Year 4:

$137,180×0.95 = $130,321

Year 5:

$130,321×0.95 = $123,804.95

Year 6:

$123,804.95×0.95 = $117,614.7025

Year 7:

$117,614.7025×0.95 = $111,733.967375

Year 8:

$111,733.967375×0.95 = $106,147.26900625  ≈  $106,147

Therefore, the correct answer is the second ONE. ✔️✔️

Answer:

1.8, -2.8

Step-by-step explanation:

1.8, -2.8 in decimal form rounded to the nearest tenth.

In quadratic form its originally [tex]x=\frac{-1+\sqrt{21} }{2} ,\frac{-1-\sqrt{21} }{2}[/tex]

Hope this helps

Answer:

slope m=0.5, y-intercept b=5, the price of a 0 page book starts off at 5 and increases 0.5 every 50 pages

Step-by-step explanation:

point slope formula

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

choose a point on the line, I chose (2.00,6.00)

and b is the y-intercept at (0,5)

then plug those numbers in

[tex]6.00 = m2.00 + 5.00[/tex]

simplify & isolate the variable

[tex]6.00 - 5.00 = m2.00 + 5.00 - 5.00 [/tex]

[tex]1 = m2[/tex]

[tex]1 \div 2 = m2 \div 2[/tex]

solve for m

[tex]0.1 = m[/tex]

the y intercept is were the line crosses the y axis.

the y axis represents cost in dollars, the x axis represents number of pages

Answer:

One point:  (2/3, 0)

Step-by-step explanation:

The fastest way to determine this is to find the discriminant, b^2-4ac:

discriminant = (-12)^2 - 4(9)(4) = 144 - 144 = 0

The rule here states that if the discriminant is 0, the function has two real, equal roots.  Those roots are

       -(-12) ± √0

x =   ---------------- = 12/18, or 2/3.

             2(9)

The graph touches the x-axis at x = 2/3, but does not cross it.  In other words, the graph intersects the x-axis at only one x value:  2/3.

x = ------------------

The graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of a parabola.

We have,

y = 9x² - 12x + 4

Now,

So, to get the x-intercept,

Put y = 0,

i.e.

0 = 9x² - 12x + 4

Now,

Using the mid term splitting method,

0 = 9x² - 12x + 4

0 = 9x² - 6x - 6x + 4

0 = 3x(3x - 2) -23(x - 2)

i.e.

0 = (3x - 2) (3x - 2)

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex]

And,

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex] ,

So,

The x -intercept is only at one point, i.e. [tex]x = \frac{2}{3}[/tex].

Hence, we can say that the graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

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To factor the expression 3x^4 - 3x^3 - 18x^2 completely, factor out the GCF 3x^2, then factor the quadratic expression inside the parentheses (x^2 - x - 6) into (x - 3)(x + 2).

To factor the expression 3x^4 - 3x^3 - 18x^2 completely, we can first factor out the greatest common factor (GCF), which in this case is 3x^2. This gives us 3x^2(x^2 - x - 6). To factor the quadratic expression inside the parentheses, we can use the quadratic formula or factor by grouping. The quadratic expression x^2 - x - 6 can be factored as (x - 3)(x + 2).

Therefore, the completely factored expression is 3x^2(x - 3)(x + 2).

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Solve the equation by replacing x with -7 and then -1.

Then subtract the two to find the difference and divide that by the difference between -7 and -1.

f(-7) = -7^2 + 2(-7) -8 = 49 -14 -8 = 27

f(-1) = -1^2 + 2(-1) -8 = 1 -2 - 8 = -9

Difference between 27 and -9 = -36

Difference between -1 and -7 = -6

Rate of change = -36 /-6 = 6

ANSWER

[tex]3 \frac{1}{4} [/tex]

EXPLANATION

We want to find the distance between

[tex] - 3 \frac{1}{4} [/tex]

and

[tex] - 6 \frac{1}{2} [/tex]

This numbers can be located on the number line.

The distance between them is the absolute value of the difference between the two numbers.

[tex] | - 6 \frac{1}{2} - - 3 \frac{1}{4} | [/tex]

[tex] | - \frac{13}{4} | [/tex]

[tex] = \frac{13}{4} [/tex]

[tex] = 3 \frac{1}{4} [/tex]

Altitude is how high or low you are in relation to sea level, while temperature is how hot or cold it is. Altitude often effects the temperature. As high altitude places are usually get cold.

Hope this helps!

Answer:

Second option: [tex]x + x + 18[/tex]

Step-by-step explanation:

You know that "x" represents the Avery's weigth (in pounds).

Let be "y" the weight of Jada in pounds.

Since Jada weighs 18 pounds more than Avery, you can write this expression:

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

The weight of them together is:

[tex]weight\ together=x+y[/tex]

Substituting, you get:

[tex]weight\ together=x+x+18[/tex]

Therefore, the expression that tells how much the two of them weigh together is the one provided in the second option:

[tex]x + x + 18[/tex]

Answer: Sample B: A random sample of 100 customers leaving a store

Step-by-step explanation: In mathematics and especially when gathering data, you will gather the most accurate results with a larger portion. The larger portion will ensure a more accurate reading.