Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.

-4 + 4x + x2 = 0
A) (x + 2)2 = 4
B) (x + 2)2 = -4
C) (x + 2)2 = 8
D) (x + 2)2 = -8

Answer:

C

Step-by-step explanation:

We can see that there is a closed dot and the function is going left and it is a cubic function.

Additionally, the only one with a [tex]x^3+n\leq 2[/tex] inequality is C.

Answer:

520

Step-by-step explanation:

Is means equals and of means multiply

78 = 15% * W

Change to decimal form

78 = .15 *W

Divide by .15 on each side

78/.15 = .15W/.15

520 = W

Answer:

520

Step-by-step explanation:

78/0.15 = 520

Answer:

Option 1

Step-by-step explanation:

In order to find the value of the function at x=6, we have to replace x by 6 in the given function.

[tex]f(x)=\frac{3}{2}x -\frac{1}{2}[/tex]

Replacing(Substituting) x = 6 in above equation we get:

[tex]f(6)=\frac{3}{2} (6) -\frac{1}{2}\\\\f(6)=9-\frac{1}{2}\\\\ f(6)=\frac{18}{2}-\frac{1}{2}\\\\ f(6)=\frac{17}{2}\\\\ f(6)=8\frac{1}{2}[/tex]

Thus, 1st option gives the correct answer.

Answer:

The correct answer is option 1

8 1/2

Step-by-step explanation:

It is given that,

f(x) = 3x/2 - 1/2

We have to find f(x) when x = 6

To find the value of f(6)

we have, f(x) = 3x/2 - 1/2

when x = 6

f(x) = f(6)

f(6) = (3 * 6)/2 - 1/2

 = 18/2 - 1/2

 = (18 - 1)/2 = 17/2

 = 8 1/2

Therefore the correct answer is first option

[tex]\bf 4\pi \qquad \approx \qquad 12.57 \\\\[-0.35em] ~\dotfill\\\\ \sqrt{79}+\sqrt{63}\qquad \approx \qquad 8.89 + 7.94\implies 16.83 \\\\[-0.35em] ~\dotfill\\\\ \sqrt{143}\qquad \approx \qquad 11.96 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{11.96}{\sqrt{143}}\qquad \stackrel{12.57}{4\pi }\qquad \stackrel{16.83}{\sqrt{79}+\sqrt{63}}~\hfill[/tex]

[tex]4\pi = 1.27323954474\\\sqrt{143} = 11.9582607431\\\sqrt{79} + \sqrt{63} = 16.8254483505[/tex]

Answer:

[tex]125.3 \times 3 = 375.9[/tex]

[tex]125.3 \times \frac{3}{4} = 93.975[/tex]

[tex]375.9 + 93.975 = 469.875[/tex]

Answer:

11/3 . . . or . . . 3 2/3

Step-by-step explanation:

Adding the three equations will give 2x+2y+2z:

(x +y) +(y +z) +(z +x) = 6 +7 +9

2x +2y +2z = 22

Dividing by 2 gives the sum of three variables:

x +y +z = 11

The average of x, y, and z is their sum divided by 3:

(x +y +z)/3 = 11/3

Answer:

[tex]\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}[/tex]

Step-by-step explanation:

f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4

Step 1. Calculate the difference between the functions

(a) Write the two functions, one above the other, in decreasing order of exponents.

ƒ(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³           - 7x + 4

(b) Create a subtraction problem using the two functions

        ƒ(x) =    9x³ + 2x² - 5x + 4

      -g(x) =  -(5x³           - 7x + 4)

ƒ(x) -g(x)=

(c). Subtract terms with the same exponent of x

        ƒ(x)   =    9x³ + 2x² - 5x + 4

      -g(x)  =   -(5x³          -  7x + 4)

ƒ(x) -g(x) =      4x³ + 2x² + 2x

Step 2. Factor the expression

y = 4x³ + 2x² + 2x

Factor 2x from each term

y = 2x(2x² + x + 1)

[tex]\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}[/tex]

Answer:

Step-by-step explanation:

x / 2.25 seconds = 28 times / 12 seconds

multiply by sides by 2.25 seconds

x / 2.25 seconds * 2.25 seconds = 28 times / 12 seconds * 2.25 second

x = 2.3333333  times/ second * 2.25 seconds

x = 5.8333

Answer:

315 times

Step-by-step explanation:

We know that the friend can clap his hands 28 times in 12 seconds. First, we need to know how many times can he clap his hands in 1 second:

To do it we have to divide the times he can clap his hands by the time in seconds:

28/12 = 2.333333

He can clap his hands 2.333333 times in 1 second:

Now we want to know how many times will he clap his hands in 2.25 minutes

We have to change 2.25 minutes into seconds:

1 (minute) = 60 (seconds in 1 minute)

2.25 (minutes) * 60 (seconds in 1 minute) = 135 seconds

After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:

2.3333333 times * 135 seconds = 315

315 times in 2.25 minutes

Answer:

Next term doubles

Hope this helps :)

Have a great day !

5INGH

Brainliest please

Step-by-step explanation:

Answer:

8.4 in. per seconds

Step-by-step explanation:

14yd=42ft.

42ft=504in per min

504/60=1 min / 60

8.4=1 sec.

Answer:

8.4 inches/second

Step-by-step explanation:

1 yd = 3 ft

1 ft = 12 inches

1 minute = 60 seconds

These are the conversion factors we need to convert 14 yds /minutes to inches per second

14 yds        3 ft

--------  * -------------

minutes    yd

The yds cancel and we are left with

42 ft

--------

minutes

42 ft        12 inches

-------- * ------------------

minutes   1 ft

The feet cancel

504 inches

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

minutes

504 inches          1 minute

------------------- *--------------

minutes                60 seconds

The minutes cancel

504 inches

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

60 seconds

Simplifying the numbers

8.4 inches

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

second

Answer:

piccctures?

Step-by-step explanation:

Answer:

help me first

Step-by-step explanation:

Answer:

200.96

Step-by-step explanation:

First, divide 50.24 by the pi (3.14)

50.24 / 3.14 = 16

Second, divide 16 by two (so that the radius is found).

16 / 2 = 8

Now that we have the radius length, solve for the area.

area of circle = πr^2

Area of circle = (3.14) (8^2)

Area of circle = 3.14 x 64

Area of circle = 200.96

the answer is B because you will add and subtract each element with it's corresponding one

The result of this operation is option B. This is obtained by using matrix addition and subtraction.

Adding and subtracting the terms of the matrix since these are matrices with same order. Hence we get,

[tex](\left[\begin{array}{ccc}13&10&7\\6&8&1\\2&5&0\end{array}\right] -\left[\begin{array}{ccc}3&-2&6\\14&-6&11\\8&-12&9\end{array}\right] ) +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]

= [tex]\left[\begin{array}{ccc}10&12&1\\-8&14&-10\\-6&17&-9\end{array}\right] +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]

=[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex]

Thus the required matrix is option B.

Learn more about matrix addition and subtraction here:

brainly.com/question/34923885

#SPJ2

Answer:

The area of the composite figure is 1360 ft.

Step-by-step explanation:

First, you should split up the composite figure into separate shapes.

So to find area of the triangle all the way on the left, you multiply base x height then divide by 2.

30 x 34 = 1020 ÷ 2 = 520.

Then, moving on to next shape, we can break up the trapezoid into a rectangle and a triangle.

To find area of the rectangle you multiply length x width.

16 x 30 = 480.

Finally, we have the last triangle right above the rectangle. Keep in mind that the rectangle does not have a length of 40!

You have to subtract 40 - 16 which equals 24.

30 x 24 = 720 ÷ 2 = 360.

Now that we have all 3 numbers, we simply add them all together and you will get an answer of 1360 ft.

Remember to label your answer!

Answer:

1080 ft^2

Step-by-step explanation:

We are given a composite figure that consists of a triangle and a trapezoid.

We know that the area of these two shapes is given by the following formulas so we will put in the given values to get:

Area of triangle = [tex]\frac{1}{2} \times b \times h[/tex] = [tex]\frac{1}{2} \times 16 \times 30[/tex] = 240 ft^2

Area of trapezoid = [tex]\frac{a+b}{2} h[/tex] = [tex]\frac{16+40}{2} 30[/tex] = 840 ft^2

Area of composite figure = [tex]240+840[/tex] = 1080 ft^2

Answer:

C.  522 m^2.

Step-by-step explanation:

The area of the 3 rectangles in the net

= 10 * (9 + 16.6 + 14)

= 10 * 39.6

= 396. m^2.

The area of the 2 triangles

=  2 * 1/2 * 14 * 9

= 126 m^2.

Total surface area =  522 m^2.

Answer:

27.9 mm2

27.9 mm2 = 2.79 × 10^ -5 m2

We know that functions are mathematical entities that assign unique outputs to given inputs. In other words, a function can't have repeated values in the input repeated x-value.

For example consider the relation {(1,4), (1,5), (2,6), (3,7), (4,8), (5,9)}.

We see that above relation has repeated x-value "1" which is assigned to two different output values 4 and 5. So by definition of function, above relation can't be a function.

Option: A is the correct answer.

The quadratic equation that fits these data is:

            A.   [tex]y=2.09x^2+0.33x+3.06[/tex]

We are given a table of values as:

    x          y

    -4        35

    -3        20

    -2         12

    -1           6

    0           2

     1           6

     2          10

     3          24

     4          38

From the given data values we see that the points follow a parabolic path this means that the line of best fit will has a quadratic equation.

Also, the line that best represents these data points as is done by the regression calculator is:

                A.   [tex]y=2.09x^2+0.33x+3.06[/tex]

Answer:

132 calories in a bowl that holds 2 servings

Step-by-step explanation:

In order to find what 1 serving equals, you have to divide 858 by 13 and you get 66, but since the bowl holds 2 servings you have to multiply 66 by 2 and you get 132

Answer:

78

Step-by-step explanation:

Subtract 2 serving out of 13 and the then divide 858 by the number.

Answer:

16.629

Step-by-step explanation:

Start by setting up the numbers like the first picture. The borrow. To borrow we have to go the whole way over to the 7 since you can't borrow from 0. So the 7 becomes a 6 and the 0 becomes  10. Then the 10 becomes a 9 and the 0 becomes a 10. Then the 10 becomes a 9 and the 3 becomes a 13. Then subtract. Just bring the decimal point down.

Answer:

5. He rented 7 new releases videos

6. 4 3-bedrooms units.

7. length: 37, width: 18

8. 81 dimes, 47 quarters

Step-by-step explanation:

5. Videos

X: New releases

Y: Regular titles

EQ1: x + y = 18 (he rented 18 videos)

EQ2: 3x + 2y = 43 (he paid $43 for the 18 videos)

By EQ1, we can isolate y-value as y = 18 - x

We place this y-value into EQ2:

3x + 2(18 - x) = 43 and we solve:

3x + 36 - 2x = 43

3x - 2x = 43 - 36

x = 7

He rented 7 new releases videos

6. bedroom units

X: 2-bedrooms units

Y: 3-bedrooms units

EQ1: x + y = 7 (they have 7 units)

EQ2: 450x + 650y = 3950 (their monthly renting revenues)

By EQ1, we can isolate x as x = 7 - y (since we're looking for 3-bedrooms units), and place that value in EQ2:

450 (7 - y) + 650y = 3950

3150 - 450y + 650y = 3950

200y = 800

y = 4

So, they have 4 3-bedrooms units.

7. Rectangle

X:  length

Y: width

EQ1: x + y = 55 (since perimeter is 110 and includes 2x + 2y)

EQ2: x = 2y + 1 (length is twice the with, plus 1)

Since we are asked to find both values, it doesn't matter by which we begin.  By EQ1, we can do x = 55 -y, and place that value in EQ2, to get:

55 - y = 2y + 1

54 = 3y

y = 18

Place y = 18 in EQ1 to find x:

x + 18 = 55

x = 37

8. Dimes and quarters

X:  dimes

Y:  quarters

EQ1:  x = y + 34 (34 more dimes than quarters)

EQ2: 10x + 25y = 1985 (total value of the collection)

Let's place the value of x from EQ1 in EQ2:

10 (y + 34) + 25y = 1985

10y + 340 + 25y = 1985

35y = 1645

y = 47

From EQ1, we then have

x = 47 + 34 = 81

So, we have 81 dimes ($8.10) and 47 quarters ($11.75), for a total of $19.85.

Hello,

Starting with problem one:

Subtract 66 from both sides.

z2−9z−66=66−66

z2−9z−66=0

Use quadratic formula with a=1, b=-9, c=-66.

z = 9/2+1/2√345

Problem two:

Subtract 17 from both sides.

y^2+16y−17=17−17

y^2+16y−17=0

Factor left side of equation.

(y−1)(y+17)=0

Set factors equal to 0.

y−1=0 or y+17=0

y=1 or y=−17

ANSWER: y=1 or y=−17

Problem 3:

2h^2−5h−(−1)=−1−(−1)

2h^2−5h+1=0

Use quadratic formula with a=2, b=-5, c=1.

ANSWER: h=5/4+1/4√17

Have an amazing day.

Answer:

The measure of angle k is (1/2)(140°) = 70°.

Answer:

36

Step-by-step explanation:

half dollar equals 50 cents.

72/2=35

Answer:

36

Step-by-step explanation:

divide it by two since it says that each are half a dollar meaning 50 cents each.

Answer:

Choice B is correct

Step-by-step explanation:

The normal distribution has extensive applications in statistics. The distribution is characterized by a symmetric bell-shaped density curve. Most of the observations or data points fall in the middle of the distribution while both the right and left tails are equally longer.

The histogram that can be approximated by a normal distribution must meet the above conditions.

The histogram in alternative A is skewed to the right since most of the values fall in the lower end of the distribution. A skewed distribution is not symmetric.

The histogram in choice C is approximately uniformly distributed since most of the observed values have an approximately equal frequency. Each of the values is approximately equally likely. The uniform distribution is not symmetric.

The histogram in D follows no know pattern and nevertheless it lacks the symmetric property.

The histogram in B is approximately symmetric in distribution since most of the observed data values fall in the middle of the distribution while the left and right tails are nearly equal. This histogram can thus be approximated by a normal distribution.

Answer:

option B 5

option D -6

Step-by-step explanation:

Given in the question an inequality

x² > 16

Step 1

Take square root on both sides of inequality

√x² > ±√16

x < -√16 or x > √16

x < -4 or x > 4

Step 2

-4 > x > 4

x = 5 x > 4    accepted

x = -6 x < -4   accepted

Step 3

x = 4 rejected

x = -1 rejected

Answer:

A)$1667 in 7.5%, $833 in 6%

Step-by-step explanation:

Let amount of money invested 6% account = x

Let amount of money invested 7.5% account = y

Then we get equations:

x+y=2500

or x=2500-y ...(i)

6% of x+7.5% of y=7% of (2500)

or 0.06x+0.075y=0.07(2500)

or 60x+75y=175000...(ii)

plug (i) into (ii)

60x+75y=175000

60(2500-y)+75y=175000

150000-60y+75y=175000

-60y+75y=175000-150000

15y=25000

y=$1666.66666667

or y=1667

plug into (i)

x=2500-y=2500-1667=833

Hence final answer is A)$1667 in 7.5%, $833 in 6%

hence y is 7 ,x is 1/7

hope it helps you

For this case we must find the inverse of the following function:

[tex]f (x) = 8 \sqrt {x}[/tex]

For this, we follow the steps below:

We change f (x) to y:

[tex]y = 8 \sqrt {x}[/tex]

We exchange the variables:

[tex]x = 8 \sqrt {y}[/tex]

We solve for y:

[tex]8 \sqrt {y} = x[/tex]

We divide between 8 on both sides of the equation:

[tex]\sqrt {y} = \frac {x} {8}[/tex]

We raise both sides of the equation to the square to remove the root:

[tex]y = (\frac {x} {8}) ^ 2\\y = \frac {x ^ 2} {64}[/tex]

So, the inverse is:[tex]f ^ {- 1} (x) = \frac {x ^ 2} {64}[/tex]

ANswer:

Option C

Answer:

Option B. [tex]9x^{3}-2x^{2}-4x-2[/tex]

Step-by-step explanation:

we have

[tex]7x^{3}-2x^{2} +5[/tex]

[tex]2x^{3}-4x-7[/tex]

Adds the polynomial

Group terms that contain the same variable

[tex](7x^{3}+2x^{3})-2x^{2}-4x+(5-7)[/tex]

Combine like terms

[tex]9x^{3}-2x^{2}-4x-2[/tex]

Janice's error was

[tex]-2x^{2} +5-4x-7=6x^{2}-12[/tex]

so

[tex]-2x^{2}-4x=6x^{2}[/tex]

instead

[tex]-2x^{2}-4x=-2x^{2}-4x[/tex]

and

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

instead

[tex]5-7=-2[/tex]  

Answer:

B

Step-by-step explanation:

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