Which expressions are equivalent to (a^2-16(a+4)? Select the three equivalent expressions
A.) a^3-64
B.) (a-4)^3
C.) (a+4)^3
D.) (a+4)^2(a-4)
E.) (a-4)^2(a+4)
F.) [(a)^2-(4^2)](a+4)
G.) (a-4)(a+4)(a+4)

Answer:

(9, 3)

Step-by-step explanation:

I'd strongly suggest that you write these two equations one above the other:

x-2y=3

2x-3y=9

Let's eliminate x by addition / subtraction:  Multiply the first equation by -2 to obtain -2x in the first row over +2x in the second row:

-2x + 4y = -6

2x -  3y =  9

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

           y = 3

Now subst. 3 for y in the first equation:  x - 2y = 3 becomes:

x - 2(3) = 3, or

x = 6 + 3  =  9

The solution is (9, 3).

Again, scale factor is 12 / 4 = 3.

So Perimeter = 16 * 3 = 48.

The perimeter of the larger flag, which is a square with each side measuring 8 inches, is 32 inches. This is calculated by multiplying the side length by 4, as a square has four sides.

To find the perimeter of the larger flag, which resembles a larger square, you need to know the length of one of its sides. Since the problem states that the dimensions are twice that of a smaller square, first, determine the side length of the smaller square. If the side length of the larger square is 8 inches, obtained by scaling up the smaller square's side length by a factor of 2 (4 inches x 2 = 8 inches), you can find the perimeter by multiplying the side length of the larger square by 4 (since a square has four sides).

The calculation for the perimeter of the larger square is as follows: 8 inches x 4 = 32 inches. Therefore, the perimeter of the larger flag is 32 inches.

Answer:

c

Step-by-step explanation:

the top pair and the middle pair

The number of lines of symmetry that this regular polygon have is: D. 5.

In Mathematics and Geometry, the order of rotational symmetry of any geometrical shape can be defined as the number of times in which the geometrical shape can be rotated around a full (complete) circle and still look the same.

As a general rule in geometry, a geometrical shape with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."

Based on the above rule, we can reasonably infer and logically deduce that the order of rotational symmetry for this geometrical figure is equal to 5 because a pentagon has five sides.

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Answer:

The missing coefficient is -8

Step-by-step explanation:

Let

a------> the missing coefficient

we have

[tex]ay^{2}-[-5y-y(-7y-9)]-[-y(15y+4)]=0[/tex]

[tex]ay^{2}-[-5y+7y^{2}+9y]-[-15y^{2}-4y]=0\\ \\ ay^{2}+5y-7y^{2}-9y+15y^{2}+4y=0\\\\ay^{2}-7y^{2}+15y^{2}=0\\\\ay^{2}+8y^{2}=0\\ \\a=-8[/tex]

Answer:

C. Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines.

Step-by-step explanation:

The two equations are in slope intercept form which is y = mx + b where m is the slope and b is the y-intercept.

In the first equation (y = -2x + 3), -2 is the slope since it is the coefficient. "b" is 3 since it is the constant of the equation.

In the second equation (y = -4x -1), -4 is the slope is the coefficient, and the y-intercept is -1 since it is the constant.

To solve the equations graphically, graph them and find the point where they intersect.

The required explanation that is best for the solution of the given equation is given by option c. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a system of equations,
y = −2x + 3                 (1)
y = −4x − 1                   (2)

The slope of equation 1
m = -2 and y-intercept  = 3
The slope of equation 2
m = -4 and the y-intercept = -1
So, From option that matched the calculation is

Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines.

Thus, the required explanation that is best for the solution of the given equation is given by option c. Option C is correct.

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Step-by-step explanation:

First we have to find percent change by doing change/original

To find change: 45000-18000=27000

Now divide by original. 27000/18000=1.5

The change was 150 percent. Now we multiply 45000 by 150 percent to get the projected population for 2015.

45000*1.5=67500 people

Brainliest? :)

Projected population for 2015 using exponential growth model is 112,500, calculated with initial population of 18,000 and growth rate.

To determine the projected population for 2015 using an exponential growth model, we need to identify the growth rate and use it to extrapolate the population.

The exponential growth model can be represented as:

[tex]\[ P(t) = P_0 \times e^{rt} \][/tex]

Where:

- [tex]\( P(t) \)[/tex] is the population at time [tex]\( t \)[/tex]

- [tex]\( P_0 \)[/tex] is the initial population (in 2005)

- [tex]\( r \)[/tex] is the growth rate

- [tex]\( t \)[/tex] is the time in years since the initial population was measured

First, we need to find the growth rate [tex](\( r \))[/tex]. We can use the data provided from 2005 to 2010:

[tex]\[ P_0 = 18000 \][/tex]

[tex]\[ P(5) = 45000 \][/tex]

Using these values in the formula:

[tex]\[ 45000 = 18000 \times e^{5r} \][/tex]

Now, let's solve for [tex]\( r \)[/tex]:

[tex]\[ \frac{45000}{18000} = e^{5r} \][/tex]

[tex]\[ 2.5 = e^{5r} \][/tex]

Taking the natural logarithm of both sides:

[tex]\[ \ln(2.5) = 5r \][/tex]

Now, divide by 5:

[tex]\[ r = \frac{\ln(2.5)}{5} \][/tex]

Now, we have the growth rate [tex]\( r \)[/tex]. We can use this rate to project the population for 2015 [tex](\( t = 10 \) years)[/tex]:

[tex]\[ P(10) = 18000 \times e^{\frac{\ln(2.5)}{5} \times 10} \][/tex]

Now, calculate this:

[tex]\[ P(10) = 18000 \times e^{\ln(2.5) \times 2} \][/tex]

[tex]\[ P(10) = 18000 \times e^{\ln(2.5^2)} \][/tex]

[tex]\[ P(10) = 18000 \times e^{\ln(6.25)} \][/tex]

[tex]\[ P(10) = 18000 \times 6.25 \][/tex]

[tex]\[ P(10) = 112500 \][/tex]

So, the projected population for 2015 is 112,500.

Answer:

Option C From day 7 to day 8

Step-by-step explanation:

The given graph shows the total number of hours Katrina worked over the period of 10 days.

Now we will calculate the number of hours worked by Katrina for every given options in the question.

Option A - From day 1 to day 2

Katrina worked (6 - 3) = 3 hours

Option B - From day 4 to day 5

Katrina worked (12-12) = 0 hours between the period of 4 to 5 days

Option C - From day 7 to day 8

Katrina worked (18-12) = 6 hours

Option D - From day 9 to day 10

Katrina worked ( 18 - 18) = 0 hours so she took the rest.

According to this, options C represents the work done for maximum hours in one day interval.

Answer:

The function translated 4 units right and 9 units down

The third answer

Step-by-step explanation:

* To solve the problem you must know how to find the vertex

  of the quadratic function

- In the quadratic function f(x) = ax² + bx + c, the vertex will

 be (h , k)

- h = -b/2a and k = f(-b/2a)

* in our problem

∵ f(x) = x²

∴ a = 1 , b = 0 , c = 0

∵ h = -b/2a

∴ h = 0/2(1) = 0

∵ k = f(h)

∴ k = f(0) = (0)² = 0

* The vertex of f(x) is (0 , 0)

∵ g(x) = -8x + x² + 7 ⇒ arrange the terms

∴ g(x) = x² - 8x + 7

∵ a = 1 , b = -8 , c = 7

∴ h = -(-8)/2(1) = 8/2 = 4

∵ k = g(h)

∴ k = g(4) = (4²) - 8(4) + 7 = 16 - 32 + 7 = -9

∴ The vertex of g(x) = (4 , -9)

* the x-coordinate moves from 0 to 4

∴ The function translated 4 units to the right

* The y-coordinate moves from 0 to -9

∴ The function translated 9 units down

* The function translated 4 units right and 9 units down

Final answer:

The question seeks the translation moving the vertex of f(x) = x^2 to match the vertex of g(x) = -8x + x² + 7. To achieve this, the function f(x) needs to be translated right by 4 units and down by 9 units, resulting in the translation (x, y) -> (x+4, y-9).

Explanation:

The student's question is asking for the translation that would move the vertex of a quadratic function f(x) to match the vertex of another quadratic function g(x). We are given two functions: f(x) = x2 and g(x) = -8x +  x² + 7. To find the translation, we need to determine the vertices of both parabolas.

In the standard form of a quadratic function, y = a x²  + bx + c, the vertex can be found using the formula h = -b/2a for the x-coordinate of the vertex. For f(x), the vertex is at (0, 0) since there is no b or c value, and it's just  x² . For g(x), we can calculate the vertex by finding the x-coordinate: h = -(-8)/2(1) = 4. The y-coordinate can be found by substituting x = 4 into g(x) to get g(4) = -8(4) + 4² + 7 = -32 + 16 + 7 = -9. Therefore, the vertex of g(x) is at (4, -9).

To translate the vertex of f(x) to the vertex of g(x), we need to shift it right by 4 units and down by 9 units. The translation that does this is (x, y) -> (x+4, y-9).

Answer:For a system of equations, we'll use something fairly simple:

y = 2x (linear)

y = x^2 (quadratic)

Now to solve, we can set them equal to each other since they are both equal to y.

x^2 = 2x

Now to solve for the appropriate values of x, set equal to zero and factor.

x^2 = 2x ---> subtract 2x from both sides

x^2 - 2x = 0 ----> now factor out an x.

x(x - 2) = 0

Now to get the values of x, set each factored part equal to 0 on their own.

x = 0

x - 2 = 0

x = 2

A system of equations that includes a linear equation (y = 2x + 4) and a quadratic equation (y = x^2 - x - 6) can be solved algebraically by equating the two equations and solving the resultant quadratic equation. The solutions to this system are (5,14) and (-2,0). These solutions are the intersection points of the line and the parabolic curve on a coordinate plane.

To create a system of equations that includes both a linear and a quadratic equation we might choose for example:

Linear equation: y = 2x + 4

Quadratic equation: y = x^2 - x - 6

Part 1: The algebraic solution is found by setting the two equations equal to each other and solving for x:

2x + 4 = x^2 - x - 6

This simplifies to: 0 = x^2 - 3x - 10

Then, we factor to find: (x - 5)(x + 2) = 0

Setting each factor equal to zero gives us: x = 5 and x = -2

Substitute back into the linear equation to find y: y1= 2(5) + 4 = 14 and y2= 2(-2) +4 = 0

Hence, the solution to the system of equations are (5,14) and (-2,0).

The solutions would be graphically represented by the intersection points of the line and the parabola on the coordinate plane.

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8 times because you take 4 times 2 and get 8

Reasoning:

There are 2 outcomes if you flip only one coin (H or T).

There are 2^2 = 2*2 = 4 outcomes if you flip two coins (HH, HT, TH, TT).

There are 2^3 = 2*2*2 = 8 outcomes if you flip three coins.

There are 2^4 = 2*2*2*2 = 16 outcomes if you flip four coins.

Answer:

200

Step-by-step explanation:

1/6 because the die has 6 sides so if you were to roll it 1200 times you would do 1/6*1200=200 , hope this helps!

Answer:

45%

Step-by-step explanation:

It is 45% because is 1/4 of the circle

Answer:

37.5%

Step-by-step explanation:

The probability is 3/8, which is 37.5%.

Answer:

1/4 or 0.25

Step-by-step explanation:

*I'm assuming you're asking about the probability of this happening...

There are 4 different results you can get when flipping a coin twice...

First Flip: heads

Second Flip: tails

First Flip: heads

Second Flip: heads

First Flip: tails

Second Flip: heads

First Flip: tails

Second Flip: tails

only one of these is heads, then tails, so our probability is

1/4, or 0.25

Answer:

factor left the side of the equation

(2k_9)(k+2)=0

set factors equal to 0

2k_9=0 or k+2=0

the answer is K= 9/2 or K =-2

2k^2 - 5k - 18 = 0 can be solved by splitting the middle term to get k = -2 and k = -4.5.

An equation can be solved by many methods which include using the quadratic formula, splitting the middle term, etc. When an equation is solved, it means we are finding the value of the variable in the equation.

Given : 2k^2 - 5k - 18 = 0

2k^2 - 5k - 18 = 0

⇒ 2k^2 +4k - 9k - (9*2) = 0

⇒ 2k( k + 2 ) -9( k + 2 )  = 0

⇒ ( 2k - 9 )( k+2 ) = 0

⇒ k = 4.5, k = -2

Therefore, we have solved 2k^2 - 5k - 18 = 0 to get k = 4.5 and k = -2.

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Final answer:

To find the probability that the red die shows an even number or the green die shows an even number, we can use the concept of probability of a union of two events. The probability is 3/4.

Explanation:

To find the probability that the red die shows an even number or the green die shows an even number, we can use the concept of probability of a union of two events. Let's denote the event that the red die shows an even number as E and the event that the green die shows an even number as F.

Since each die has 6 equally likely outcomes, the probability of rolling an even number on the red die is P(E) = 3/6 = 1/2, and the probability of rolling an even number on the green die is P(F) = 3/6 = 1/2.

To find the probability of the union of two events (E or F), we add the probabilities of E and F and subtract the probability of their intersection (E and F) to avoid double-counting. In this case, the intersection is the event that both dice roll an even number, which has a probability of P(E and F) = (1/2) × (1/2) = 1/4.

Therefore, the probability that the red die shows an even number or the green die shows an even number is P(E or F) = P(E) + P(F) - P(E and F) = 1/2 + 1/2 - 1/4 = 3/4.

A card shuffling machine picks cards from a standard deck.

Answer:

Vertical Shrink by 1/2 and down 5

Answer:

The transformations are a rotation and a translation.

Answer:

the answer is 87.5%

Step-by-step explanation:

first, we have to turn 7/8 into a fraction with a denominator of 100. to do that, we can divide 100 by 8 to get 12.5. now, we multiply 7/8 x 12.5 which equals 87.5/100 which is equal to 87.5%

Answer: the answer would be 90%

Step-by-step explanation:

Hey there!

The first thing we should do is to make the fractions have a common denominator.

The least common multiple of 4 and 6 is 12, which we can find by taking the multiples of both and finding the smallest one they have in common.

What we should do it multiply both sides of the equation by 12, which eliminates both fractions.

We now have:

9x - 60 = 10

Hope this helps!

The results of the equation without fraction is 118x = 175

Given the equation

[tex]\frac{3}{5} x - 5 = \frac{5}{6}\\[/tex]

Step 1: Add 5 to both sides of the equation:

[tex]\frac{3}{5} x - 5 +5= \frac{5}{6} + 5\\\frac{3}{5} x= \frac{5}{6} + 5\\[/tex]

Multiply through by 30:

[tex]\frac{3}{5} x \times 30= (\frac{5}{6} \times 30 )+( 5 \times 30)\\(3x \times 6) = (5\times 5) + 150\\18x = 25 + 150\\18x = 175[/tex]

Hence the result of the equation without fraction is 118x = 175

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Answer:   0.93 radians & 2.21 radians

Step-by-step explanation:

[tex]-4sin^2\theta-3sin\theta+5=0\\\\\text{Since this is not factorable, use the quadratic formula to find the roots:}\\\\sin\theta=\dfrac{-(-3)\pm \sqrt{(-3)^2-4(-4)(5)}}{2(-4)}\\\\\\.\quad=\dfrac{3\pm \sqrt{9+80}}{-8}\\\\\\.\quad=\dfrac{3\pm\sqrt{89}}{-8}\\\\\\.\quad=\dfrac{3\pm9.43}{-8}\\\\\\.\quad=\dfrac{12.43}{-8}\quad and\quad \dfrac{-6.43}{-8}\\\\\\.\quad=-1.55\quad and\quad 0.80\\\\\\\theta=sin^{-1}(-1.55)\quad and\quad \theta=sin^{-1}(0.80)[/tex]

[tex]\theta=not\ valid\qquad and\quad \theta=0.927[/tex]

[tex]\theta = 0.927\ radians\text{\ in the 1st quadrant and}\\\pi-0.927=2.21\ radians\text{\ in the 2nd quadrant}[/tex]

Answer:

2.21

0.93

Step-by-step explanation:

Given that; [tex]-4\sin^2\theta-3\sin \theta+5=0[/tex]

This is a quadratic equation is [tex]\sin \theta[/tex], where [tex]a=-4,b=-3,c=5[/tex]

We want to solve for [tex]\theta[/tex] in radians, where 0≤θ<2π.

We apply the quadratic formula given by;

[tex]\sin \theta=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

We substitute the given values to obtain;

[tex]\sin \theta=\frac{--3\pm\sqrt{(-3)^2-4(-4)(5)}}{2(-4)}[/tex]

Simplify;

[tex]\sin \theta=\frac{3\pm\sqrt{9+80}}{-8}[/tex]

[tex]\sin \theta=\frac{3\pm\sqrt{89}}{-8}[/tex]

[tex]\sin \theta=0.804[/tex] or [tex]\sin \theta=-1.55[/tex]

When [tex]\sin \theta=0.804[/tex] , [tex]\theta=\sin^{-1}(0.804)[/tex]

[tex]\Rightarrow \theta=0.93[/tex] --In the first quadrant.

In the second quadrant;

[tex]\theta=\pi-0.93=2.21[/tex]

When [tex]\sin \theta=-1.55[/tex] , [tex]\theta[/tex] is not defined.

Answer:

y = 15x + 20

Step-by-step explanation:

He charges a flat rate of $20, so any total for hours worked will have an additional $20 added to it.  

The 15x represents his earnings per hour.  He makes 15 per every hour worked, x represents the number of hours worked

Answer:

1: f; 110

2: b; 70

3: e; 105

4: c; 75

5: a; 35

Step-by-step explanation:

Start with one that is easy to find, like 5, 4, or 3.

5. We know that 5 is on a 180 degree line with the angle of 145. Subtract 145 from 180 to find 5. This angle is 35.

4. We also know that 4 is a vertical angle to 75, which means 4 will also be 75.

3. Solve like you did for 5. 180 - 75 = 105.

2. First, find another angle inside the triangle shape. Look at the angle for 5 for this one. We know it is 35. That means the vertical angle inside is also 35. Subtract both interior angles to find 2. 180 - 75 - 35 = 70.

1. Finally, take the angle you got for 2, 70, and subtract it from the straight line, 180. 180 - 70 = 110.

Answer:

1: f; 110

2: b; 70

3: e; 105

4: c; 75

5: a; 35

Step-by-step explanation:

Answer:

show me the other picture and closer up

Step-by-step explanation:

Answer: 26.8 feet

Step-by-step explanation:

In the figure attached you can see two right triangles  triangle ABD and a triangle ACD.

You are located at point B and the other person at point C.

The approximate height of the lifeguard station is x.

Keep on mind that:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

Therefore:

For the triangle ABD:

[tex]tan(36\°)=\frac{x}{DC+11}[/tex]    [EQUATION 1]

For the triangle ACD:

[tex]tan(46\°)=\frac{x}{DC}[/tex]    [EQUATION 2]

Solve from DC from [EQUATION 2]:

[tex]DC=\frac{x}{tan(46\°)}[/tex]

Substitute into [EQUATION 1] and solve for x:

[tex]tan(36\°)=\frac{x}{(\frac{x}{tan(46\°)}+11)}\\tan(36\°)(\frac{x}{tan(46\°)}+11)=x\\11*tan(36\°)=x-\frac{xtan(36\°)}{tan(46\°)}\\7.991=0.298x[/tex]

[tex]x=26.81ft[/tex]≈26.8ft

Answer:

7x -14=35        add 14 on both sides

7x= 49        then, divide 7 on the whole equation

x=7

Step-by-step explanation:

Parking lot:

Angie=x

Sister=x+12

Amom=2•(sister) or 2(x+12)=2x+24

Betty=x-3

Bmom=4•(betty) or 4(x-3)=4x-12

--------

Part A: Amom=2x+24

Part B: Bmom=4x-12

PartC:

x=angie

Amom=Bmom+6

2x+24=4x-12+6

2x+24=4x-6

24-6=4x-2x

18=2x

9=x

Angie is 9 years old.

Answer:

24 cm²

Step-by-step explanation:

Using proportion to solve

let the area of the smaller triangle be x, then

[tex]\frac{5}{2}[/tex] = [tex]\frac{60}{x}[/tex] ( cross- multiply )

5x = 120 ( divide both sides by 5 )

x = 24

Area of smaller triangle = 24 cm²

Answer:

Step-by-step explanation:

[tex]Let\\A_1,\ A_2-areas\ of\ triangles\ (A_1>A_2)\\\\A_1=60\ cm^2\\\\A_1:A_2=5:2\\\\\text{Substitute:}\\\\\dfrac{60}{A_2}=\dfrac{5}{2}\qquad\text{cross multiply}\\\\5A_2=(60)(2)\\\\5A_2=120\qquad\text{divide both sides by 5}\\\\A_2=24\ cm^2[/tex]

Answer:

28 times

Step-by-step explanation:

18 x 28 = 504

Answer:

p²(5p - 2)

Step-by-step explanation:

p² is a factor common to both terms, and thus should be factored out:

p²(5p - 2)