The vertex form of the equation of a parabola is y=6(x-2)2-8. What is the standard form of the equation?

Answer:

10 different groups of three CDs are possible

Step-by-step explanation:

Total CDs are five and 3 has to be chosen where order doesn't matter.

In these kind of scenarios, combinations are used for calculating different ways in which the CDs can be given.

So,

Number of ways in which groups of CDs are possible = ⁵C₃

[tex]= \frac{n!}{r!(n-r)!} \\= \frac{5!}{3!(5-3)!}\\=\frac{5!}{3!2!}\\=\frac{5*4*3!}{3!2!}\\=\frac{5*4}{2}\\=\frac{20}{2}\\=10[/tex]

Therefore, 10 different groups of three CDs are possible ..

Answer:

65

Step-by-step explanation:

25+2x8+3x8

Answer:

25 + 8(2 + 3)

Step-by-step explanation:

[tex]\huge{\boxed{n=-4}}[/tex]

[tex]\begin{array}{cc}\begin{flushright}\text{Divide both sides of the equation by 3.}\end{flushright}&\begin{flushleft}-4n-9=7\end{flushleft}\\\begin{flushright}\text{Add 9 on both sides.}\end{flushright}&\begin{flushleft}-4n=16\end{flushleft}\\\begin{flushright}\text{Divide both sides by -4.}\end{flushrigh}&n=-4\end{array}[/tex]

Answer:

[tex]\Huge \boxed{n=-4}[/tex]

Step-by-step explanation:

First thing you do is divide by 3 from both sides of equation.

[tex]\displaystyle \frac{3(-4n-9)}{3}=\frac{21}{3}[/tex]

Simplify.

[tex]\displaystyle -4n-9=7[/tex]

Then add by 9 from both sides of equation.

[tex]\displaystyle -4n-9+9=7+9[/tex]

Simplify.

[tex]\displaystyle 7+9=16[/tex]

[tex]\displaystyle -4n=16[/tex]

Divide by -4 from both sides of equation.

[tex]\displaystyle \frac{-4n}{-4}=\frac{16}{-4}[/tex]

Simplify, to find the answer.

[tex]\displaystyle 16\div-4=-4[/tex]

[tex]\huge\boxed{\textnormal{N=-4}}[/tex], which is our answer.

Answer:

g(x) = 7x^2

Step-by-step explanation:

Given a function f(x), the function kf(x) is stretched by a factor of k. In this case, if we stretch the function f(x) = x^2 by a factor of seven, the new function is going to be the base function multiplied by 7, as follows:

g(x) = 7x^2

Answer:

"No, because using the y-axis tests only whether x = 0 is mapped to multiple values."

Shayla's use of the vertical line test is incorrect because she is only considering the number of y-intercepts, which is not conclusive in determining if a graph is a function. The correct method is to see if any vertical line intersects the graph at more than one point.

Shayla is not applying the vertical line test correctly. The correct use of the test involves drawing vertical lines through various points on the graph and checking to see if any vertical line intersects the graph at more than one point. A graph represents a function if, and only if, every vertical line intersects the graph at most once. The number of y-intercepts, or where the graph intersects the y-axis, is not a reliable indicator of whether a graph is a function. For example, a straight line with a slope and a y-intercept, such as in the form y = mx + b, will always be a function, regardless of the number of y-intercepts it has.

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=\cfrac{3}{5}(x-2) \implies y+4=\cfrac{3}{5}x-\cfrac{6}{5} \\\\\\ y=\cfrac{3}{5}x-\cfrac{6}{5}-4\implies \implies y=\cfrac{3}{5}x-\cfrac{26}{5}[/tex]

Answer:

Point-slope form: [tex]y+4=\frac{3}{5}(x-2)[/tex]

Slope-intercept form: [tex]y=\frac{3}{5}x-\frac{26}{5}[/tex]

Standard form: [tex]3x-5y=26[/tex]

Step-by-step explanation:

The easiest form to use here if you know it is point-slope form.  I say this because you are given a point and the slope of the equation.

The point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

Plug in your information.

Again you are given [tex](x_1,y_1)=(2,-4)[/tex] and [tex]m=\frac{3}{5}[/tex].

[tex]y-y1=m(x-x_1)[/tex] with the line before this one gives us:

[tex]y-(-4)=\frac{3}{5}(x-2)[/tex]

[tex]y+4=\frac{3}{5}(x-2)[/tex] This is point-slope form.

We can rearrange it for different form.

Another form is the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept.

So to put [tex]y+4=\frac{3}{5}(x-2)[/tex] into y=mx+b we will need to distribute and isolate y.

I will first distribute. 3/5(x-2)=3/4 x -6/5.

So now we have [tex]y+4=\frac{3}{5}x-\frac{6}{5}[/tex]

Subtract 4 on both sides:

[tex]y=\frac{3}{5}x-\frac{6}{5}-4[tex]

Combined the like terms:

[tex]y=\frac{3}{5}x-\frac{26}{5}[/tex] This is slope-intercept form.

We can also do standard form which is ax+by=c. Usually people want a,b, and c to be integers.

So first thing I will do is get rid of the fractions by multiplying both sides by 5.

This gives me

[tex]5y=5\cdot \frac{3}{5}x-5 \cdot 26/5[/tex]

[tex]5y=3x-26[/tex]

Now subtract 3x on both sides

[tex]-3x+5y=-26[/tex]

You could also multiply both sides by -1 giving you:

[tex]3x-5y=26[/tex]

You are told the middle part is a square, so all 4 sides are equal.

The height is shown as 4 feet, so the width of the square is also 4 feet.

This means the height of the 2 triangles is 7 - 4 = 3 feet, so each triangle is 1.5 feet high ( 3 feet / 2 = 1.5).

The area of the square is 4 x 4 = 16 square feet.

The area of 1 triangle is 1/2 x base x height = 1/2 x 4 x 1.5 = 3 square feet.

The total area = 16 + 3 + 3 = 22 square feet.

Answer:

C. 18

Step-by-step explanation:

Both triangle are same (compared with angles), but are different size.

This is based on simple ratio.

AB/AC = DE/DF

27/15 = x/10 //Multiply both sides by 10

270/15 = x

x = 18

Therefore DE is 18.

Hence, the length of DE is 18.

Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects.

It can be observed that the given 2 triangles are similar.

we know, for similar triangles, the ratio of corresponding sides is equal.

Hence,

          [tex]\frac{15}{10} = \frac{27}{x}[/tex]

          [tex]x = 18[/tex]

Therefore, the value of x is 18.

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Answer:

135°

Step-by-step explanation:

In a parallelogram the opposite angles are congruent, so

∠BCD = ∠BAD = 135°

Answer:

9/4  or 2 1/4.

Step-by-step explanation:

3/4 / 1/3

=3/4 * 3/1

= 9/4

Answer:

3/4 ÷ 1/3 equals

(3/4 x 3/1) = 9/4

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{(2a+1)^2}{50a}}[/tex]

Step-by-step explanation:

[tex]10a-5=5(2a-1)\\\\4a^2-1=2^2a^2-1^2=(2a)^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2a-1)(2a+1)\\\\\dfrac{2a+1}{10a-5}\div\dfrac{10a}{4a^2-1}=\dfrac{2a+1}{5(2a-1)}\div\dfrac{10a}{(2a-1)(2a+1)}\\\\=\dfrac{2a+1}{5(2a-1)}\cdot\dfrac{(2a-1)(2a+1)}{10a}\qquad\text{cancel}\ (2a-1)\\\\=\dfrac{2a+1}{5}\cdot\dfrac{2a+1}{10a}=\dfrac{(2a+1)^2}{50a}[/tex]

Answer: The answer is D

Step-by-step explanation: got it right 2023 edge

Step-by-step explanation:

After the raise, his pay is:

62000 + 0.05×62000

62000 (1 + 0.05)

65100

His pay after one year is $65,100.

To calculate Carlos's new salary after a 5% raise on his initial $62,000 salary, you multiply $62,000 by 0.05 to find the raise amount of $3,100, and then add it to the initial salary, resulting in a new salary of $65,100.

The question involves calculating the new salary of Carlos after a 5% raise following his initial year of employment. Carlos's starting salary is $62,000 per year. After one year, he receives a 5% raise. To calculate Carlos's new salary, follow this step:

Now, let's do the math:

Therefore, after a 5% raise, Carlos's new annual pay will be $65,100.

The Answer is 2.

2x10=20+10x10=100 100+20=120

12x10=120

recall your d = rt, distance = rate * time.

so the tour boat left at a speed of 10 mph, say the fishing boat left "h" hours later, traveling faster at 12 mph in the same direction.

By the time the fishing boat caught up with the tour boat, the distances travelled by both must be the same, say "d" miles, thus the idea of catching up, the distance of the fishing boat is the same as the distance of the tour boat.

Since the fishing boat caught up with the tour boat after going for 10 hours, and had left "h" hours later, then when that happened, the tour boat has already been travelling for 10 + h hours.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{Tour boat}&d&10&10+h\\ \textit{Fishing boat}&d&12&10 \end{array}~\hfill \begin{cases} d=(10)(10+h)\\ d=(12)(10) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{doing substitution on the 2nd equation}~\hfill }{(10)(10+h)=(12)(10)\implies \cfrac{~~\begin{matrix} (10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(10+h)}{~~\begin{matrix} 10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=12} \\\\\\ 10+h=12\implies h=2[/tex]

Answer:

$39

Step-by-step explanation:

Let original price be x, so we need to subtract 16 2/3 % from that to get 32.50

So we can write:

[tex]100x-16\frac{2}{3}x=3250\\83\frac{1}{3}x=3250\\x=39[/tex]

So basically, the original price was $39.

Answer:

A) 41 laps

Step-by-step explanation:

Round 17 4/7 to the nearest whole number:

18

Round 23 5/14 to the nearest whole number:

23

18 + 23 = 41

Final answer:

By rounding the fractional laps to the nearest whole numbers (18 for Monday and 23 for Wednesday), and adding them together, we estimate that Kira swam a total of 41 laps. Option A is the closest answer.

Explanation:

To estimate the total number of laps Kira swam on Monday and Wednesday, we should round the numbers to the nearest whole number and then add them together. Kira swam 17 4/7 laps on Monday, which we can round to 18 laps for estimation purposes. On Wednesday, she swam 23 5/14 laps, which rounds to 23 laps. Adding the estimated numbers together, we get:

Monday: 18 (estimated from 17 4/7)

Wednesday: 23 (estimated from 23 5/14)

Therefore, the estimated total number of laps is 18 + 23 = 41 laps.

The closest answer to our estimation is Option A: 41 laps.

Answer:

(- ∞, - 4 ] ∪ [7, + ∞ )

Step-by-step explanation:

Determine the zeros by equating to zero, that is

x² - 3x - 28 = 0 ← in standard form

(x - 7)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4

The zeros divide the domain into 3 intervals

(- ∞ , - 4 ], [ - 4, 7 ], [ 7, + ∞)

Choose a test point in each interval and compare value with required solution

x = - 5 : (- 5)² - 3(- 5) - 28 = 25 + 15 - 28 = 12 > 0

x = 0 : 0 - 0 - 28 = - 28 < 0

x = 10 : 10² - 3(10) - 28 = 100 - 30 - 28 = 42 > 0

Solutions are the first and third interval, that is

x ∈ (- ∞, - 4 ] ∪ [ - 7, + ∞)

Answer:

it's C on edge

Step-by-step explanation:

got it right:)

The side of the square whose perimeter is 20 feet is given by the equation A = 5 feet

The perimeter of a square is given by four times the length of its each side

The equation for the perimeter of the square with the side 'a' is given by

Perimeter of Square = 4a

Given data ,

Let the perimeter of the square be represented as P

Now , the value of P is

P = 20 feet   be equation (1)

Now , for a square

Perimeter of Square = 4A , where A is the measure of side

Substituting the values in the equation , we get

20 = 4A

Divide by 4 on both sides of the equation , we get

A = 20/4

A = 5 feet

Therefore , the value of A is 5 feet

Hence , the side of the square is 5 feet

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Answer:

6 seconds

Step-by-step explanation:

First: equalize the equation to zero

f(t) = -5t² + 20t + 60

-5t² + 20t + 60 = 0

Second: find its roots

-5(t² - 4t - 12) = 0

-5 (t - 6)(t + 2) = 0

[tex]t - 6 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t + 2 = 0 \\ t = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t = - 2[/tex]

Time can't be negative so the answer is: it takes 6 seconds to hit the ground

Answer:

A. $2,506.50

Step-by-step explanation:

First you must acknowledge that you are dealing with a line therefore you must write linear equation or linear function in this case.

Linear function has a form of,

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

Then calculate the slope m using the coordinates of two points. Let say A(x1, y1) and B(x2, y2),

[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Now pick a point either A or B and insert coordinates of either one of them in the linear equation also insert the slope you just calculated, I will pick point A.

[tex]y_1=mx_1+n[/tex]

From here you solve the equation for n,

[tex]

y_1=mx_1+n\Longrightarrow n=y_1-mx_1

[/tex]

So you have slope m and variable n therefore you can write down the equation of the line,

[tex]f(x)=m_{slope}x+n_{variable}[/tex]

Hope this helps.

r3t40

Answer:

x = 3.5

Step-by-step explanation:

To solve this you need to solve for x.

This is a two step equation so you need to first subtract 5 from itself and whatever you do to one side of the equation you have to do to the other side as well.

So 5 - 5 = 0

12 - 5 = 7

Then the equation becomes 2x = 12

Now it is a one step equation, so find the inverse operation of multiplication, which is division .

So 2 divided by 2 is 1 which also equals x by itself

7 divided by 2 equals 3.5

So x = 3.5

Answer:

[tex]\huge\boxed{x=\frac{7}{2}, x=3.5}[/tex]

Step-by-step explanation:

Subtract by 5 from both sides of equation.

[tex]\displaystyle 2x+5-5=12-5[/tex]

Simplify.

[tex]\displaystyle 12-5=7[/tex]

[tex]\displaystyle2x=7[/tex]

Divide by 2 from both sides of equation.

[tex]\displaystyle \frac{2x}{2}=\frac{7}{2}[/tex]

Simplify, to find the answer.

[tex]\displaystye x=\frac{7}{2}, x=3.5[/tex]

x=7/2 and x=3.5 is the correct answer.

Answer:

See below.

Step-by-step explanation:

a. That would be a cylinder.

b.The height of the cylinder will be n * thickness of one circle where  n is the number of circles.  The volume of the cylinder is π r^2 h where h is the height of the stack.

c.  That would be a cone

d. The height of the cone will be n * thickness of one circle where n is the number of similar circles.

Volume of the cone = 1/3 * π r^2  h    where h is the height of the stack of circles.

49/b - 5 = 2

First add 5 to both sides:

49/b = 7

Multiply both sides by b:

49 = 7b

Divide both sides by 7:

b = 49/7

b = 7

Answer:

A

Step-by-step explanation:

The polynomial (x+4)(x-1)(x-2)(x-4) has zeros at x=-4,1,2,4.

The related polynomial equation is (x+4)(x-1)(x-2)(x-4)=0.

In order for this equation to be true at least one of the factors must by 0 that is the only way a product can be zero (if one of it's factors is).

So you wind up needing to solve these 4 equations:

x+4=0            x-1=0          x-2=0             x-4=0

x=-4                 x=1              x=2                   x=4

First equation, I subtracted 4 on both sides.

Second equation, I added 1 on both sides.

Third equation, I added 2 on both sides.

Fourth equation, I added 4 on both sides.

-4,1,2,4 are all integers

Integers are real numbers.

So A.

The polynomial (X+4)(x-1)(x-2)(x-4) corresponds to option A: The related polynomial equation has a total of four roots; all four roots are real, with no root having a multiplicity. Hence the correct answer is A.

To match the polynomial (X+4)(x-1)(x-2)(x-4) to the correct description, we can look at its factors to determine the roots. Each factor of the form (x - c) represents a real root at x = c. For this polynomial, the factors indicate there are four roots: -4, 1, 2, and 4. These roots all come from different factors, so there is no repeated root, implying no multiplicity among them. Hence, the correct description must state that there are four real roots and none of them is repeated.

Since options B, C, E, and F suggest either roots with multiplicity, a mixture of real and complex roots, or fewer than four roots, they are not correct. Therefore, this leaves us with option A as the correct match: The related polynomial equation has a total of four roots; all four roots are real. None of the roots are repeated, there are no complex roots, and all roots can be identified directly from the given factors of the polynomial.

Answer:

a(x)=2x^2+9x+4

Step-by-step explanation:

We have been given the length and width, as well as the formula to find the area:

Length: 2x + 1

Width: x + 4

A = l * w

A = (2x + 1)(x + 4)

2x^2 + 8x + x + 4

We can add like terms now:

2x^2 + 9x + 4

Our area is 2x^2 + 9x + 4

Our answer would be a(x)=2x^2+9x+4

Answer:

The correct answer is third option

a(x) =  2x² + 9x + 4

Step-by-step explanation:

It is given that,the length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.

To find the area of the rectangle

Area of rectangle = Length * Breadth

a(x) = l(x) * w(x)

 = (2x + 1)(x + 4)

 = 2x² + 8x + x + 4

 = 2x² + 9x + 4

The correct answer is third option

a(x) =  2x² + 9x + 4

Answer:

[tex]y=\frac{3}{2} x+\frac{20}{3}[/tex]

Step-by-step explanation:

First, to find the original line, employ the slope formula.

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{6-8}{4-1} \\\\\frac{-2}{3}[/tex]

The slope of your original line is [tex]-\frac{2}{3}[/tex].

Next, plug in your slope and the third point to the point-slope formula.

[tex]y-y1=m(x-x1)\\\\y-8=-\frac{2}{3} (x+2)\\\\y-8=-\frac{2}{3} x-\frac{4}{3}\\\\y=-\frac{2}{3} x+\frac{20}{3}[/tex]

To find the line which is perpendicular to the line, take the opposite reciprocal of the slope.

To find the opposite, flip the sign. [tex]-\frac{2}{3}[/tex] is negative, so it will become [tex]\frac{2}{3}[/tex], which is positive.

To find the reciprocal, flip the fraction. [tex]\frac{2}{3}[/tex] would become [tex]\frac{3}{2}[/tex].

Your slope for the perpendicular line is [tex]\frac{3}{2}[/tex], so your line is:

[tex]y=\frac{3}{2} x+\frac{20}{3}[/tex]

Answer:

[tex] a = \frac{100}{3}[/tex]

Step-by-step explanation:

We have the following equation:

[tex]\frac{1}{2} a + \frac{2}{3} b = 50[/tex]

If [tex]b=50[/tex], then:

[tex]\frac{1}{2} a + \frac{2}{3}[/tex]×50 [tex] = 50[/tex]

Solving for 'a':

[tex]\frac{1}{2} a = \frac{50}{3}[/tex]

[tex]\frac{1}{2} a = \frac{50}{3}[/tex]

[tex] a = 2\frac{50}{3}[/tex]

[tex] a = \frac{100}{3}[/tex]

Answer a=60 (3rd option)

Step-by-step explanation:

Answer:

-2k + 6

Step-by-step explanation:

-2k - (-5) + 1 //-1 times -5 = 5 ( - - gives +)

-2k + 5 + 1 //Combine like terms

-2k + 6

Remember you can't add or sub -2k with 6 since -2 is multiplying with k (which is constant and you don't know it's value)

//Hope this helps

Answer:

-2k+6

Step-by-step explanation:

Answer:

x<-1

Step-by-step explanation:

-5x-15>10+20x

Add 5x to each side

-5x+5x-15>10+20x+5x

-15> 10+25x

Subtract 10 from each side

-15-10 > 25x

-25 >25x

Divide each side by 25

-25/25 >25x/25

-1>x

x<-1

Answer:

true

explanation:

because vertical angles are congruent.