(7−4n)⋅6 Apply the distributive property to create an equivalent expression.

Answer: [tex]y=-3(x+1)^2+4[/tex]

Step-by-step explanation:

The vertex form of the equation of  a parabola is:

 [tex]f(x) = a(x - h)^2 + k[/tex]

Where (h, k) is the vertex of the parabola.

To write [tex]y=-3x^2 - 6x +1[/tex] in vertex form, you need to complete the square:

1. Move the 1 to the other side of the equation:

[tex]y-1=-3x^2 - 6x[/tex]

2. Since the leading coefficient must be 1, you need to factor out -3:

[tex]y-1=-3(x^2 + 2x)[/tex]

3. Divide the coefficient of the x-term inside the parentheses by 2 and square it:

  [tex](\frac{2}{2})^2=1[/tex]

4. Now add 1 inside the parethenses and -3(1) to the other side of the equation (because you factored out -3):

[tex]y-1-3(1)=-3(x^2 + 2x+1)[/tex]

[tex]y-4=-3(x^2 + 2x+1)[/tex]

5. Convert the right side of the equation to a squared expression:

 [tex]y-4=-3(x+1)^2[/tex]

6. And finally, you must solve for "y":

[tex]y=-3(x+1)^2+4[/tex]

Answer:

[tex]x<-2\\\\y\leq-x-2[/tex]

Step-by-step explanation:

From the given graph , the shaded region is bounded by two lines ( one is dotted and another is solid line).

Dotted line :  It is parallel to y-axis and intersecting the x -axis at .

so the equation of the line is x=-2.

But it is represented in dotted form it means the inequality sign used here is strictly less than.

i.e. the equation for dotted line = [tex]x<-2[/tex]

Solid line : It is passing through (-2,0) and (-1,-1).

Equation of line passing through (a,b) and (c,d) :-

[tex](y-a)=\dfrac{d-b}{c-a}(x-b)[/tex]

Then equation of sold line:

[tex](y-0)=\dfrac{-1-0}{-1-(-2)}(x-(-2))\\\\\Rightarrow\ y=\dfrac{-1}{-1+2}(x+2)\\\\\Rightarrow\ y=\dfrac{-1}{1}(x+2)\\\\\Rightarrow\ y=-x-2[/tex]

Hence, the inequality represents solid line(≤)= [tex]y\leq-x-2[/tex]

Hence, the system of linear inequalities is graphed will be :-

[tex]x<-2\\\\y\leq-x-2[/tex]

Answer:

Rule:

a_n = 9^(n - 1)

8th term:

a_8 = 9^(8 - 1) = 9^7 = 4,782,969

Step-by-step explanation:

a_1 = 1 = 9^0

a_2 = 1 * 9 = 9^1

a_3 = 1 * 9 * 9 = 9^2

a_4 = 1 * 9 * 9 * 9 = 9^3

Notice that the exponent on the 9 is always 1 less than the number of the term.

Rule:

a_n = 9^(n - 1)

8th term:

a_8 = 9^(8 - 1) = 9^7 = 4,782,969

Answer:

[tex]\large\boxed{x=\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{x}=\dfrac{6:2}{2:2}\\\\\dfrac{2}{x}=\dfrac{3}{1}\qquad\text{cross multiply}\\\\3x=2\qquad\text{divide both sides by 3}\\\\x=\dfrac{2}{3}[/tex]

ANSWER

The equivalent form is 8.

EXPLANATION

The given expression is

[tex] ({16}^{ \frac{3}{2} } )^{ \frac{1}{2} } [/tex]

This is the same as:

[tex] {16}^{ \frac{3}{2} \times \frac{1}{2} } [/tex]

[tex]{16}^{ \frac{3}{4}} [/tex]

[tex]{16}^{ \frac{3}{4}} = { {2}^{4 \times } }^{ \frac{3}{4}} [/tex]

We cancel out the common factors in the exponents to get,

[tex]{2}^{3} = 8[/tex]

The correct answer is B.

Answer:

no

Step-by-step explanation:

to know if a number is divisible by 4, you need to look only at the last two digits and see if that is divisible, 15 is not divisible by 4 and therefore the whole number isnt.

if you tried to divided 262,015 by 4 you would get 65503.75, a decimial so not divisible

Answer:

No, 262,015 will not divide evenly into 4.

Step-by-step explanation:

262,015 ÷ 4 = 65503.75.

Therefore, it will not divide evenly into 4.

Another way to do this is to check if the last two digits are divisible by 4.

The last two digits are 15. 15 is not divisible by 4. Therefore, the entire number will not be divisible by 4.

Answer:

9

Step-by-step explanation:

9x5 is 45

Answer:

c) (3-7x^2)(x-3)

Step-by-step explanation:

-7x^3+21x^2+3x-9

Factor out a -7x^2 from the first two terms and a 3 from the last two terms

-7x^2 (x -3) +3(x-3)

Now factor out (x-3)

(x-3) (-7x^2+3)

Rearranging)

(x-3) (3-7x^2)

Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x - 2y = - 6 into this form

Subtract 3x from both sides

- 2y = - 3x - 6 ( divide all terms by - 2 )

y = [tex]\frac{3}{2}[/tex] x + 3 ← in slope- intercept form

with slope m = [tex]\frac{3}{2}[/tex]

• Parallel lines have equal slopes, hence

y = [tex]\frac{3}{2}[/tex] x + c ← partial equation of parallel line

To find c substitute (4, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = [tex]\frac{3}{2}[/tex] x - 4 ← equation of parallel line

Answer:

13/102

Step-by-step explanation:

There are 52 cards in a standard deck (not including the jokers).

So let's start with the first thing... the red part. Half the deck is red which means 52/2=26 cards are red.

So the probability of the red being drawn is 26/52 (I'm going to keep it an un-reduced form for now)

So now since it says we don't replace (we don't put the card back into the deck), there is only 51 cards to choose from now.  There are 4 suits so there are 13 of each kind of suit. So to draw a spade, the probability would be 13/51.

So the end: The probability of drawing a red then a spade without replacing is the multiplication of these probabilities I found:

So the answer is 26/52  * 13/51=13/102

Answer:

B) 9.2

Step-by-step explanation:

To find an average, you have to combine all of your numbers and then divide by how many there are.

So first, combine the values.

9.7 + 8.6 + 9.3 = 27.6

Now, divide by how many numbers you had, which is 3.

27.6 ÷ 3 = 9.2

Firstly , combine the all values

[tex]9.7 + 8.6 + 9.3 = 27.6[/tex]

Now , divided by 3

[tex] 27.6 \div 3 \\ \\ \frac{27.6}{3} \\ \\ 9.2 [/tex]

The correct answer is 9.2 - option (b) (✔)

The answer is 33R1.

Hope this helps :)

Answer:

33 with a remainder of 1

Step-by-step explanation:

Answer:

I think B is right because,

5x-3y=-6

or,5x_3y+6=o

now,we representing quadratic formula

The equation that represents a quadratic function is y = 2x² - 12x + 9

Which of the equations represents a quadratic function?

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

The equations

By definition

A quadratic function is represented as any of the following forms

y = ax² + bx + c

y = a(x - h)² + k

Using the above as a guide, we have the following:

The equation that is a quadratic function is y = 2x² - 12x + 9

Others are not quadratic functions

1. Carl's constant rate of speed is the slope of the straight line graph.

This straight line passes through: (0,0), (5,1), (10,2) etc

We can use the slope formula with any two points to find the slope of this line.

The slope formula is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Let [tex](x_1,y_1)=(0,0)[/tex] and [tex](x_2,y_2)=(5,1)[/tex]

Then [tex]m=\frac{1-0}{5-0}[/tex], [tex]\implies m=\frac{1}{5}[/tex].

Carl's speed is [tex]\frac{1}{5}[/tex] miles per minute.

But we must leave our answer in miles per hour

Hence Carl's speed is [tex]\frac{1}{5}\times 60=12[/tex]  miles per hour

After 2 hours, Carl will travel [tex]12\times 2=24[/tex] miles.

2. The given line has equation [tex]-4x+y=10[/tex]

We write this in slope-intercept form by solving for y.

[tex]\implies y=4x+10[/tex]

This is in the form [tex]y=mx+c[/tex], where [tex]m=4[/tex] is the slope.

When x=3,  [tex]y=4(3)+10[/tex]

[tex]\implies y=12+10=22[/tex]

When x=3, y=22

3. The given straight line graph that models the situation passes through:

(0,0) and (20,30).

The slope of this line is [tex]\frac{Rise}{Run}=\frac{300}{20}=15[/tex]

Therefore the rate is $ 15 per ticket.

If the theater sells 150 tickets, the earnings will be: [tex]150\times 15=2,250[/tex] dollars.

Undefined terms such as points and lines are central to defining geometric concepts such as line segments and angles. They also play a crucial role in the Cartesian coordinate system, where points are defined in relation to lines (axes).

In Mathematics, particularly in Geometry, the undefined terms points and lines are used to define several other concepts. One such concept defined by these undefined terms is the 'Line Segment'. A Line Segment is simply part of a line that is bounded by two distinct endpoints, and contains every point on the line between its endpoints. Both points and lines have a defining role in constructing this definition. A line segment is an example of 'one-dimensional' structure, as it only extends in one direction, unlike a plane or volume that extend in two or three dimensions, respectively.

Another major concept that is defined using points and lines is the 'Angle'. An angle is formed when two lines meet at a point. The point is called the vertex of the angle, and the lines are the sides of the angle.

In the Cartesian coordinate system, the interaction of points and lines is at the core of defining and plotting positions. For example, a point in this system is represented by two coordinates (x, y) - where x represents its position along the x-axis (a horizontal line) and y represents its position along the y-axis (a vertical line).

https://brainly.com/question/31408211

#SPJ12

Answer:

5x³ + 2x - 1

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 5x³ - 2 + 2x + 1 ← collect like terms

= 5x³ + 2x - 1

Answer:

-1

Step-by-step explanation:

A-(b+c)

Let a=2 b=-5 c=8

2 - (-5+8)

2 - (3)

2-3

-1

Answer:179.95in

That is the awnser so how it helped

Step-by-step explanation:

Answer:

15.00 inches

Step-by-step explanation:

Recall the formula for the surface area of a sphere and a radius of r

A = 4πr²

In our case, we are given that A = 2826 ft² = 406944 in²

so,

406944 = 4πr²

r² = 406944 / (4π)      (use π=3.142)

r² = 406944 / (4π)  = 32383.57

r = √32383.57 = 179.95 in

Answer:

A Quadratic Equation can have upto 2 roots maximum. So,if one of the roots is a Real number, there are following two possibilities:

1) The other root is also a real number, but a different number

2) Its a repeated root, so the other root is the same number.

The other root cannot be a complex number as its not possible for one root to be real and other to be complex. Either no root will be complex or both will be complex roots.

Following are 3 possibilities for the roots of a quadratic equation:

Answer:

Step-by-step explanation:

Any line through a vertex and the center of the opposite side is a line of symmetry. One of them is vertical in the figure shown. Two of them are diagonal. The three lines are 360°/3 = 120° apart, so the figure has 3-fold rotational symmetry.

Answer:

Step-by-step explanation:

For clarity regarding what the denominator is, please use parentheses.

I believe you meant:

f(x)= 2/(x-1) +4​

This function f is a variation of the parent function y = 1/x.  The 2 stretches the graph vertically; the change from x to x - 1 translates the entire graph 1 unit to the right; and the +4 translates the entire graph up by 4 units.

I suspect you had 4 answer choices.  But you've only shared 2.  The second of the ones you've shared is the correct answer here.

Answer:

Should be D on ed.

Step-by-step explanation:

Answer:

3/4*x - 3/4*8=12

3/4x -6=12

3/4x=12+6

3/4x=18

x=24

Step-by-step explanation:

multiply 3/4 into the content inside the brackets

have -3/4*8 cross the equal sign changing its sign from - to +

divide both sides by 3/4

[tex]\textbf{$\left[\begin{array}{cc}x & y\\-3 & 12\\-6 & 24\\-9 & 36\end{array}\right]$}[/tex]

Two variables have a proportional relationship if the ratios are equivalent. In other words, in this type of cases two quantities vary directly with each other, so we can write this in a mathematical language as follows:

[tex]y=kx[/tex]

Here [tex]k[/tex] is the slope of the linear equation defined above. So, verifying that k is constant we have:

[tex]k=\frac{24-12}{-6-(-3))}=\frac{36-24}{-9-(-6)}=\frac{36-12}{-9-(-3)}=-4 \\ \\ \therefore \boxed{k=-4}[/tex]

One way to prove this is by writing the equation that represents the table. From the two-point intercept form of the equation of a line we have:

[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1}) \\ \\ P(x_{1},y_{1})=P(-3,12) \\ \\ P(x_{2},y_{2})=P(-6,24) \\ \\ Subtituting \ x_{1}, x_{2}, y_{1}, y_{2}: \\ \\ y-12=\frac{24-12}{-6-(-3)}(x-(-3)) \\ \\ y-12=-4(x+3) \\ \\ Solving: \\ \\ y-12=-4x-12 \\ \\ Adding \ 12 \ to \ both \ sides: \\ \\ y-12+12=-4x-12+12 \\ \\ \boxed{y=-4x}[/tex]

So, this implies that the ordered pairs of the last option represent a proportional relationship

Answer:

Step-by-step explanation:

In this case, an proportional realtionship refer to the existence of a contant ratio of change between variables, that is, each y-value can be found by multiplying each x-value with this constant ratio of change.

So, notice that in the first table, is we multiply by four, you can get the first two pairs, but the last one doesn't fall into the ratio. That's not the answer.

Similarly, the second table doesn't have a constant ratio of change, because the last pair has different ratio.

However, the last table shows a constant ratio of change, because each x-value can be multiplied by -4, to get each y-value, that is

-3 x -4 = 12

-6 x -4 = 24

-9 x -4 = 36

Therefore, the right answer is the last table.

Answer:

12.5 times larger is the storage capacity of Meredith's new hard drive

Step-by-step explanation:

Meredith's new computer storage capacity = 1.5 x 10^12

Meredith's old computer storage capacity = 1.2 X 10^11

times the storage capacity of Meredith's new hard drive is larger = Meredith's new computer storage capacity/Meredith's old computer storage capacity

= 1.5X10^12/1.2X10^11

= 12.5

So, 12.5 times larger is the storage capacity of Meredith's new hard drive

Answer:

Step-by-step explanation:

Givens

To find how many times larger is the new hard drive thatn the old one, we just need to divide

[tex]\frac{1.5 \times 10^{12}bytes }{1.2 \times 10^{11} bytes }=1.25 \times 10 = 12.5[/tex]

Therefore, the new hard driave can store 12.5 times more than the old hard drive.

The length of the rope swing for the considered case is found being of 5 meters approximately.

If we've got:

Then, we get:

[tex]T \approx 2\pi \sqrt{\dfrac{L}{g}}[/tex]

This is the period of oscillation, the time taken for a complete cycle in a simple gravity pendulum.

Using the above formula, as for this case, we're specified that:

Then, the length of the rope is obtained as:

[tex]T \approx 2\pi \sqrt{\dfrac{L}{g}} \: \rm \:sec\\\\L = \dfrac{T^2g}{4\pi^2} \: \rm meters\\\\\L \approx \dfrac{(4.5)^2\times 2\times (9.8)}{4\pi^2} \approx 5 \: \rm meters[/tex]

Thus, the length of the rope swing for the considered case is found being of 5 meters approximately

Learn more about length and period oscillation of a pendulum here:

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Answer:

E)82

Step-by-step explanation:

The formula is

A^2 + B^2= C^2

the two sides that make up the right angle is always A and B

Answer:

E

Step-by-step explanation:

Since the triangle is right use Pythagoras' theorem to solve for BC

The square on the hypotenuse (BC) is equal to the sum of the squares on the other 2 sides, that is

BC² = 80² + 18² = 6400 + 324 = 6724 ( take the square root of both sides )

BC = [tex]\sqrt{6724}[/tex] = 82 → E

Answer:

0.63

Step-by-step explanation:

The fraction is 5/8. It is equivalent to ...

5/8 = (5·125)/(8·125) = 625/1000 = 0.625

This exact decimal equivalent rounds to 0.63.

_____

It can be useful to memorize the decimal equivalents of common fractions, including multiples of 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10.

Answer:

n = 50

Step-by-step explanation:

The equation to solve is  [tex]9+\frac{n}{5}=19[/tex]

We can take 9 to the other side and cross multiply and solve using rules of algebra (shown below):

[tex]9+\frac{n}{5}=19\\\frac{n}{5}=19-9\\\frac{n}{5}=10\\n=5*10\\n=50[/tex]

So, n = 50

In order to find the answer to this question you must first rearrange the terms and then solve.

[tex]9+\frac{n}{5} =19[/tex]

[tex]\frac{n}{5} =19-9[/tex]

[tex]19-9=10[/tex]

[tex]\frac{n}{5} =10[/tex]

[tex]5\times10=50[/tex]

[tex]n=50[/tex]

Which means your answer is "n=50."

Hope this helps.

Answer:

column chart

Step-by-step explanation:

hope this helps :)

It's probably a photo graph                    

Answer:

75.00

Step-by-step explanation:

1500*0.05

because 5% is her interest you convert 5% into a decimal = 0.05

then you multiply 1500 by 0.05 and you get 75.00