-4(x - 2) - 3x = 2(5x - 7) + 6

After distributing and combining like terms, this problem should read:

7 - 8x = -10 + 8x

-15x = 10x - 8

8x - 6 = 7x - 3

-11x + 8 = 10x - 8

-7x + 8 = 10x - 8

Answer:

Step-by-step explanation:

By the way, please use the symbol " ^ " to indicate exponentiation:

f(x) = x^2

Shifted 1 unit to the right, we get g(x) = (x - 1)^2

Vertically stretched by a factor of 5, we get h(x) = 5(x - 1)^2

Reflected over the x-axis:  j(x) = -5(x - 1)^2

Answer:

The correct option is A.

Step-by-step explanation:

The quadratic parent function is

[tex]f(x)=x^2[/tex]

The translation is defined as

[tex]g(x)=k(x+a)^2+b[/tex]                .... (1)

Where, k is vertical stretch, a is horizontal shift and b is vertical shift.

If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5

Substitute a=-1 and k=5 in equation (1).

[tex]g(x)=-5(x+(-1))^2+(0)[/tex]

[tex]g(x)=-5(x-1)^2[/tex]

Therefore the correct option is A.

Answer:

5a.  approximately 6 grams remain after 2 seconds

5b.  The graph shown cannot be a solution. The solution has negative slope everywhere.

5c.  y = 50/(t+5)

5d.  The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)

Step-by-step explanation:

5a. The tangent line has the equation ...

  y = f'(0)t +f(0)

Here, that is

  y = -0.02·10²·t +10 = 10 -2t

Then at t=2, the value is ...

  y = 10 -2·2 = 6 . . . . grams remaining

__

5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.

__

5c. The equation is separable so can be solved by integrating ...

  ∫y^-2·dy = -0.02∫dt

  -y^-1 = -0.02t +c . . . . for some arbitrary constant c

Multiplying by -50 gives ...

  50/y = t + c . . . . for some constant c

We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...

  50/10 = 0 +c = 5

Then, solving for y, we get ...

  y = 50/(t+5)

__

5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.

Answer:

h = 48

Step-by-step explanation:

So they played 48 home games. They won 3/4, so they won 36 and lost 12.  

They played 48 away games. They won 2/3, so they won 32 and lost 16.  

All tolled, they won 36 + 32 = 68 games and lost 12 + 16 = 28 games.

To calculate the percentage of home playoff games played by the Algenauts, we use a system of equations with the known win rates and number of games played. Solving, we find that approximately 71.43% of their playoff games were at home.

The student is asking about the percentage of home playoff games played by the Algenauts. The Algenauts won 3 division playoff games and then beat their rivals, the Geometers, with a score of 4-2. Given their win rates of 80% for home games and 60% for away games, we can calculate the percentage of games played at home using a system of equations.

Let H be the number of home games and A be the number of away games. Since the Algenauts played a total of 3 + 4 = 7 games, and won 3 + 4 = 7 games, we have the following equations:

H + A = 7 (total games)

0.80H + 0.60A = 7 (total games won)

Solving the system of equations, we get H = 5 and A = 2, meaning 5 out of the 7 games were played at home. Therefore, the percentage of home games is (5/7) * 100, which equals approximately 71.43%.

Answer:

Step-by-step explanation:

Delia's score X 5 = 65

d X 5 = 65

5d=65

The sentence 'The product of Delia's score and 5 is 65' translates into the equation '5d = 65', where 'd' represents Delia's score.

The given sentence, 'The product of Delia's score and 5 is 65', can be translated into an equation as follows:

So, the translated equation is: 5d = 65. Here, 'd' represents Delia's score.

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Answer:

Let's imagine that x is the number of 3 pound weights that the gym instructer has.

Since we know that there are 10 more 5 pound weights, which tells us that the number of 5 pound weight is x + 10, and the total amount is 60 hand weights, we have:

x + x + 10 = 60

2x            = 60 - 10

2x            = 50

x              = 50/2 = 25

So there are 25 3 pound weights at the gym.

From the number we have just found, we also know that the number of the 5 pound weights should be:

60 - 25 = 35 (hand weights)

Answer:

-4a^2 -7a^2 - 2ab +3ab +9b^2 -5b^2

11a^2 + ab +4b^2

Step-by-step explanation:

Answer:

-11a^2+ab+4ab^2

Step-by-step explanation:

Answer:

  1675 cm

Step-by-step explanation:

distance = speed · time

total distance = speed1 · time1 + speed2 · time2

 = (40 cm/s)(25 s) + (15 cm/s)(45 s) = 1000 cm + 675 cm = 1675 cm

Roberto's toy car travels 1000 cm at high speed (40 cm/sec for 25 sec) and 675 cm at low speed (15 cm/sec for 45 sec), totaling 1675 cm.

To calculate the total distance traveled by Roberto’s toy car, we need to consider the two separate speeds at which the car travels and the time it spends at each speed.

First, we calculate the distance at high speed using the formula distance = speed × time. At high speed, the car travels at 40 cm/sec for 25 seconds, so we multiply these two values to get the distance:

Distance at high speed = 40 cm/sec × 25 sec = 1000 cm

Next, we calculate the distance at low speed, where the car travels at 15 cm/sec for 45 seconds:

Distance at low speed = 15 cm/sec × 45 sec = 675 cm

Finally, we add these two distances together to find the total distance traveled by the toy car:

Total distance = Distance at high speed + Distance at low speed = 1000 cm + 675 cm = 1675 cm

Therefore, Roberto’s toy car would have traveled 1675 centimeters in total.

Answer: 9/20

Step-by-step explanation:

Easy!!!

Answer:

90 feet

Step-by-step explanation:

If we put t  = 6 into both the formulas, we will get the height of each.

Zinger 1:

Height = [tex]-16t^2 + 150t[/tex]

Putting t = 6,

[tex]-16(6)^2 + 150(6)=324[/tex]

Zinger 2:

Height = [tex]-16t^2 + 165t[/tex]

Putting t = 6,

[tex]-16(6)^2 + 165(6)=414[/tex]

The difference in height is 414 - 324 = 90 feet

I think it’s C. three types of shapes

because more than one repeating shape with no spaces or overlapping between shapes

A semi-regular tessellation may have three types of shapes. They do not have gaps between shapes, no overlapping shapes.

A. Gaps between shapes - false

B. Overlapping shapes - false

C. Three types of shapes - true

D. Only one type of shape - false

Thus, a semi-regular tessellation may have three types of shapes.

Learn more about semi-regular tessellations here:

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Answer:

The correct answer is B. (1,0).

Answer: B. (1,0)

Step-by-step explanation:

1. We will use the matrix method to solve this problem.

3 -5 3

3 -4 3

2. Apply to Row2 : Row2 - Row1.

3 -5 3

0 1 0

3. Simplify rows.

3 -5 3

0 1 0

Note: The matrix is now in row echelon form.

The steps below are for back substitution.

4. Apply to Row1 : Row1 + 5 Row2.

3 0 3

0 1 0

5. Simplify rows.

1 0 1

0 1 0

Note: The matrix is now in reduced row echelon form.

6. Therefore,

x=1

y=0

or (1,0).

range: 85.

media: 12.

mean: about 52.4

Answer: Option C.

Step-by-step explanation:

For a parent function [tex]f(x)=x^2[/tex], you have these transformations:

If [tex]f(x)=c(x^2)[/tex] and [tex]0 <c <1[/tex]  then the graph is compressed vertically by a factor "c".

If [tex]f(x)=c(x^2)[/tex] and [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor "c"

If [tex]f(x)=(cx)^2[/tex] and [tex]0 <c <1[/tex] then the graph is stretched horizontally by a factor "c"

If [tex]f(x)=(cx)^2[/tex] and [tex]|c| > 1[/tex] then the graph is compressed horizontally by a factor "c"

In this problem we have the function [tex]f(x)=x^2[/tex] and we know that this is  horizontally compressed to g(x), then the transformation is:

[tex]f(x)=(cx)^2[/tex] and the factor must be [tex]|c| > 1[/tex]

You can observe that the option that shows this form is the option C. Therefore, the equation of g(x) is:

[tex]g(x) = (5x)^2[/tex]

Where [tex]|5| > 1[/tex]

A horizontal compression of the function f(x) = x² is represented by the function g(x) = (5x)², where x is multiplied by a constant greater than 1, causing the function to be 'squeezed' together along the x-axis.

The question is asking for a horizontal compression of the function f(x) = x². A horizontal compression occurs when we multiply the x by a constant greater than 1 inside the function parentheses. This affects the rate at which the function grows horizontally.

A good way to visualize this is by thinking of the x-axis being 'squeezed' together. Given the choices, the function that represents a horizontal compression of f(x) = x² is C: g(x) = (5x)². In this case, we are multiplying x by a constant (5), thus compressing the function horizontally compared to the original function.

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A is the correct answer

Answer:

The correct option is A.

Step-by-step explanation:

An organization consists of 8,684 employees. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. It means

[tex]n=884[/tex]

[tex]p=\frac{36}{100}=0.36[/tex]

The value of z-score for 95% confidence level is 1.96.

The formula for margin of error is

[tex]ME=z\times \sqrt{\frac{p(1-p)}{n}}[/tex]

Where, z is z-score at given confidence level, p is sample proportion and n is number of samples.

[tex]ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}[/tex]

[tex]ME=\pm 0.0316425[/tex]

[tex]ME\approx \pm 0.032[/tex]

The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.

Corresponding sides of the two triangles occur in a ratio with one another. In particular, you have the relationship

[tex]\dfrac6{6+x}=\dfrac{10}{15}=\dfrac y{y+4}[/tex]

We only need the first two parts to solve for [tex]x[/tex]:

[tex]\dfrac6{6+x}=\dfrac{10}{15}\implies6\cdot15=10(6+x)\implies90=60+10x\implies30=10x[/tex]

[tex]\implies\boxed{x=3}[/tex]

Answer:

154.8-155.6

Step-by-step explanation:

155.2-.4=154.8 or maybe its more in that case the most it could be is 155.2+.4=155.6

Answer:

t = 24 yards

Step-by-step explanation:

Since the trapezoids are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{t}{c}[/tex] = [tex]\frac{u}{d}[/tex]

Substitute in given values

[tex]\frac{t}{0.4}[/tex] = [tex]\frac{15}{0.25}[/tex] ( cross- multiply )

0.25t = 6 ( divide both sides by 0.25 )

t = 24

Answer:

(x,y) = (-2, 0)

and

(x,y) = (2.5, 2.25)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equations.

Please see the attached image below, to find more information about the graph

s

The equations are:

y1 + 4 = x^2

y1 =  x^2 - 4

y2 - x = 2

y2 = x +2

The intersection of the two graphs correspond to

(x,y) = (-2, 0)

and

(x,y) = (2.5, 2.25)

Answer:

4. No solution

Step-by-step explanation:

To solve a system of equations, find the (x,y) solution that satisfies both equations. One method that can be used is substitution. It is done by substituting one function into the other function and simplify.

Substitute y = 4x - 6 into 8x - 2y = 14.

8x - 2(4x - 6) = 14

8x - 8x + 12 = 14

12 = 14 FALSE

Since the variable was eliminated and a false statement was found, there is no solution to this system.

Solve 3 and 5 similarly. If the variable is eliminated again, but a true statement is fund then the solution is infinite. If the variable is not eliminated then substitute it back into one equation to find the other.

Final answer:

Using the substitution method, we find that Problem 4 has no solution (D), Problem 3 also has no solution (A), and Problem 5 has an infinite number of solutions (C).

Explanation:

To solve the given systems of equations using the substitution method, we substitute the expression for y from the first equation into the second equation and solve for x. Once x is found, we plug it back into the first equation to find y.

Problem 4:

Starting with the equations:

y = 4x – 6

8x – 2y = 14

We substitute the first equation into the second equation:

8x – 2(4x – 6) = 14

Solving for x:

8x – 8x + 12 = 14

x = 1/2 (not a solution, as the x terms cancel out)

Since the equation simplifies to 12 = 14, which is not true, we conclude that:

Option D. There is no solution.

Problem 3:

The system appears similar:

y = 3x – 7

6x – 2y = 12

Substitution gives:

6x – 2(3x – 7) = 12

And solving for x:

6x – 6x + 14 = 12

Which simplifies to 14 = 12, another impossibility.

So the answer is:

Option A. There is no solution.

Problem 5:

From our system:

y + 2x = 7

14 – 4x = 2y

We express y from the first equation:

y = 7 – 2x

Substitute it into the second one, and solve for x:

14 – 4x = 2(7 – 2x)

14 – 4x = 14 – 4x

This equation is true for all x; hence, y can be found for any corresponding x and the system has infinite solutions:

Option C. There are an infinite number of solutions.

The answer is A. a=(-1) b=(7)

Answer: A

Step-by-step explanation: simple mafs

HelllllofffffffHellloxsbshsvwiwhjwhauwvvehwhwhwuwawgwveiebwyw8wbwiwbwiabak

Answer:

Step-by-step explanation:

The probability of picking a red candy from a full bag is 0.20.

But we also have experimental information represented by those 20 digits, each of which tells us how many red candies are in each package.

In the 2nd package there is 1 red candy.  In the fourth there is 1 red candy (since 2 represents a red candy, just like 1 represents a red candy).

Next, in the 6th and 8th packages there is 1 red candy each.  Finally, in the 19th package there is 1 red candy.    Now add up these results:  the number of red candies is 1 + 1 + 1 + 1 + 1, or 5.  This seems to indicate that there will be 5 red candies in the entire 20 packages.  

Caution:  What I have shared here is MY personal interpretation of what we are being asked.  

Answer:

-0.9007 it would be D. if I'm right

Step-by-step explanation:

X Values

∑ = 34

Mean = 6.8

∑(X - Mx)2 = SSx = 140.8

Y Values

∑ = 54

Mean = 10.8

∑(Y - My)2 = SSy = 164.8

X and Y Combined

N = 5

∑(X - Mx)(Y - My) = -137.2

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -137.2 / √((140.8)(164.8)) = -0.9007

Meta Numerics (cross-check)

r = -0.9007

Answer: Your answer is D. -0.901 !

Answer:

A)  

He will score over 100,000 points 4 times.  

B)  

He will score over 100,000 points 6 times.  

C)  

He will score over 100,000 points 8 times.  

D)  

He will score over 100,000 points 12 times.

Step-by-step explanation:

Answer is B

Answer:

B) He will score over 100,000 points 6 times.

Step-by-step explanation:

I got it correct on USATP.

Hope this helps!

From: Aug1e

Answer:

Step-by-step explanation:

I will assume that you meant F(x)= 12x + 12.  If you meant a fraction, write 1/2.

Then F(3) = 12(3) + 12 = 48

F(-12) = 12(-12) + 12 = -132.  

F(1/3) = 12(1/3) + 12 = 4 + 12 = 16

Please verify what you meant.  Then I will answer the remaining questions.

[tex]\(F(3) = 48\), \(F(-12) = -132\), \(F\left(\frac{1}{3}\right) = 16\), \(F\left(\frac{3}{4}\right) = 21\), \(F(x) = 12x + 12\).[/tex]

To find the values of the function [tex]\(F(x) = 12x + 12\)[/tex] for the given inputs:

1. F(3): Substitute x = 3 into the function: F(3) = 12(3) + 12 = 36 + 12 = 48.

2. F(-12): Substitute x = -12 into the function: F(-12) = 12(-12) + 12 = -144 + 12 = -132.

3. [tex]\(F\left(\frac{1}{3}\right)\)[/tex]: Substitute [tex]\(x = \frac{1}{3}\)[/tex] into the function: [tex]\(F\left(\frac{1}{3}\right) = 12\left(\frac{1}{3}\right) + 12 = 4 + 12 = 16\).[/tex]

4. [tex]\(F\left(\frac{3}{4}\right)\)[/tex]: Substitute [tex]\(x = \frac{3}{4}\)[/tex] into the function: [tex]\(F\left(\frac{3}{4}\right) = 12\left(\frac{3}{4}\right) + 12 = 9 + 12 = 21\).[/tex]

5. F(k): Substitute x = k into the function: F(k) = 12k + 12.

6. [tex]\(F\left(\frac{a}{2}\right)\)[/tex]: Substitute [tex]\(x = \frac{a}{2}\)[/tex] into the function: [tex]\(F\left(\frac{a}{2}\right) = 12\left(\frac{a}{2}\right) + 12 = 6a + 12\).[/tex]

7. F(x-1): Substitute x = x-1 into the function: F(x-1) = 12(x-1) + 12 = 12x - 12 + 12 = 12x.

8. F(x+h): Substitute x = x+h into the function: F(x+h) = 12(x+h) + 12 = 12x + 12h + 12.

These are the values of the function for the given inputs.

Answer:

Step-by-step explanation:

Given are two graphs.  f(x) will have x axis as asymptote while x=2 is asymptote for g(x).

Hence both graphs have exactly one asymptote

First graph passes through (0,2)

f(x) is exponential while g(x) is log.

Both graphs are shifted because f(x) is vertically shifted by 1, while g(x) is horizontally shifted by 3 units to left

Answer: 20 feet.

Step-by-step explanation:

Observe the right triangle attached.

You need to find the value of "x".

Then, you can use the Pythagorean Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.

 In this case, you can identify that:

[tex]a=25ft\\b=15ft\\c=x[/tex]

Substitute these values into  [tex]a^2=b^2+c^2[/tex]:

 [tex](25ft)^2=(15ft)^2+x^2[/tex]

Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:

[tex]x^2=(25ft)^2-(15ft)^2[/tex]

[tex]x=\sqrt{(25ft)^2-(15ft)^2}[/tex]

[tex]x=20ft[/tex]

ANSWER

20ft

EXPLANATION

The ladder, the wall and the ground formed a right triangle.

Let how far up the wall does the top of the ladder reached be x units.

The 25ft ladder is the hypotenuse.

The shorter legs are, 15ft and x ft

Then from Pythagoras Theorem,

[tex] {x}^{2} + {15}^{2} = {25}^{2} [/tex]

[tex] {x}^{2} + 225 = 625[/tex]

[tex] {x}^{2}= 625 - 225[/tex]

[tex]{x}^{2}= 400[/tex]

[tex]x = \sqrt{400} [/tex]

[tex]x = 20ft[/tex]

Therefore the ladder is 20 ft up the wall.

Answer:

Hence correct choice is C. [tex]Volume=400[/tex] [tex]units^3[/tex]

Step-by-step explanation:

Given that length of the square base of the pyramid a = 10 units

Given that height of the pyramid is h = 12 units

Now question says to find the volume of the given cone.

So plug these values into formula of volume of the square pyramid.

[tex]Volume=\frac{1}{3} a^2h[/tex]

[tex]Volume=\frac{1}{3} (10)^2(12)[/tex]

[tex]Volume=\frac{1}{3} (100)(12)[/tex]

[tex]Volume=\frac{1}{3} (1200)[/tex]

[tex]Volume=400[/tex]

Hence correct choice is C.

Answer:

The correct answer is option C.  400 units³

Step-by-step explanation:

Formula:-

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

From  the figure we can see a square pyramid

To find the volume of pyramid

here a = 10 units and h = 12 units

Volume = (a²h)/3 = (10² * 12)/3

 = 400 units³

Answer:

x = 3

Step-by-step explanation:

It should NOT be "fight of the origin", rather "right of the origin".

Now let's move on to solve the question...

The x-intercept is found by setting the function equal to 0. Thus:

0 = x^3 - 9x

Let's solve this using algebra:

[tex]0=x^3-9x\\0=x(x^2-9)\\0=x(x-3)(x+3)[/tex]

Hence, x = -3 and x = 3

The coordinate that is to the right of the origin is the positive one, so x = 3 is the x-intercept we are looking for.