Solve
x2+ 4x = 4 for x by completing the square.

Answer:

B.

Step-by-step explanation:

So we have the function:

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

As we can see, the degree of this function is 3. This is a cubic function. In other words, this is nonlinear. Let's go through each of the choices:

Already, we can eliminate C and D since the function is nonlinear as it's a cubic function. So, we only need to check A and B.

A: If we change the -2 to 2 like so:

[tex]y=-2x^3\\y=2x^3[/tex]

The function remains a cubic. The only thing we've changed is how the graph is oriented. With -2, the graph goes from top to bottom. With 2, the graph goes from bottom to top. Nevertheless, it's still a cubic function. What we need to change is the exponent and not the coefficient. A is not correct.

B: If we change the 3 to 1 like so:

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

This is now a linear equation. The degree is 1 and as you can probably picture, it's a downwards sloping line. The correct answer is B.

Answer:

Step-by-step explanation:

1 km= 1000 m

1 dam= 10 m

8 km= 8000m

700 dam = 7000m

so Plane A

plane A is higher by 700m!

hope it helped!

Plane A  flying with greater altitude

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.

Given:

plane A= 8 km

plane  B= 700 dam

Now,

1 km= 1000 m

1 dam= 10 m

So,

8 km= 8000m

700 dam = 7000m

Hence, Plane A is flying higher.

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Answer:

17

Step-by-step explanation:

let the side of square be x then length and breadth of rectangle will be x+1 and x-3

perimeter of rectangle=2(l+b)

64=2(x+1+x-3)

32=2x-2

x=17

Answer:

B

Step-by-step explanation:

So we have the expression:

[tex]\sqrt{-10}[/tex]

And we want to rewrite it in terms of i. Recall that i is:

[tex]i=\sqrt{-1}[/tex]

Therefore, we can simplify the expression as:

[tex]\sqrt{-10}=\sqrt{-1\cdot10}=\sqrt{-1}\cdot\sqrt{10}=i\sqrt{10}[/tex]

Therefore, the statement given is not correct.

And the correct answer is B.

Answer:

2.56p

Step-by-step explanation

Because the variable is the same for every input, and are all addition, you can just all them all together. You must remember p = 1p

Hope this helps!

-The Business Man

Answer:

2.26p

Step-by-step explanation:

0.7p + p + 0.56 p (The coefficient is 1)

0.7p + 1p + 0.56p (Collect the like terms)

(0.7 + 1 + 0.56)p

Calculate the sum

And this brings you to your answer: 2.26p

Answer:

x = 3, -10

Step-by-step explanation:

Step 1: Write out quadratic

f(x) = x² + 7x - 30

Step 2: Set quadratic equal to 0

0 = x² + 7x - 30

Step 3: Factor quadratic

0 = (x - 3)(x + 10)

Step 4: Find roots

x - 3 = 0

x = 3

x + 10 = 0

x = -10

Answer:B

Step-by-step explanation:

None of the others work

Given:

[tex]\bold{A. \ (16 - 12)2} \\\\\bold{B.\ - | -4 |} \\\\\bold{C. \ (96 \div 8) - 23} \\\\\bold{D.\ 24 - 42}[/tex]

Find:

Which expressions have a value of 4

Solving the given expression:

A)

[tex]\bold{\to (16 - 12)2 = (4)2=4\times 2=8} \\\\[/tex]

B)

[tex]\bold{\to - | -4 |} \\\\\bold{\therefore} \\\\ \to\bold{|4|=4 \ \ and \ \ |-4|=4}\\\\\bold{\because}\\\\\bold{\to - | -4 |=-(4)=-4} \\\\[/tex]

C)

[tex]\bold{\to (96 \div 8) - 23=( \frac{96}{8})-23= 12-23=-11}[/tex]

D)

[tex]\bold{\to 24 - 42=-18}[/tex]

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Answer:

Step-by-step explanation:

Speed is the change in distance of a body with respect to time.

Speed = Distance/Time

If the library made a copy of leslie's 3 page essay in just 1/10 of a minute, this means that she made 3 pages in (1/10 * 60)secs i.e 6secs

To get the speed, we need to calculate the amount of page of essay that are produced in a minute (60secs).

If 3 page essay = 6secs

x page essay = 60 secs

cross multiply

3*60 = 6x

180 = 6x

x = 180/6

x = 30

This shows that 30 page essays are produced in just a minute. Hence the speed of the copy machine is 30page essay/min.

Answer:

30

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

From the question:

2 Cos x = 1

x =?

Thus, we can obtain the value of x as follow:

2 Cos x = 1

Divide both side by 2

Cos x = 1/2

Cos x = 0.5

Take the inverse of Cos.

x = Cos¯¹ (0.5)

x = 60

Therefore, the value of x is 60

**** Check ****

2 Cos x = 1

x = 60

2 Cos 60 = 1

2 × 0.5 = 1

1 = 1

Answer:

what idea and experience do you get after being lockdown for long three or four months due to corona virus. write your experience in the form of article that is published in school magazine on the topic lack of physical activity.

Step-by-step explanation:

Answer:

Parallel lines are two lines that are facing the same direction and never intersect.

Step-by-step explanation:

for example, the number II

those are two ones are straight lines pointing the same direction, and no matter how long they go on they will never touch.

Appreciates means increases.

Appreciation formula:

Future value = starting value x (1 + interest rate) ^ time.

Future value = 32,500(1+0.049)^11

Value in 11 years = $55,006.46

Answer:

Hello your question lacks the required option below is the diagram of the complete question with the options

answer : The absolute minima is 0 at x = (0,π ) the absolute maxima is 3 at x = [tex]\frac{\pi }{2}[/tex]  ( B )

Step-by-step explanation:

Attached below is the detailed solution of the problem

The absolute minima is 0 at x = (0,π ) the absolute maxima is 3 at x = [tex]\frac{\pi }{2}[/tex]  ( B )

Answer:

1.the corresponding angles are propositional

2.the corresponding sides are proportional

The properties of similar triangles  is the corresponding angles are congruent and the corresponding sides are proportional.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio or proportional.

The properties of similar triangles include the following;

1. The corresponding angles are congruent

2. The corresponding sides are proportional

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Answer:

(-2.5, -10)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Step 1: Plug in

x = (-2 + -3)/2

y = (-8 + -12)/2

Step 2: Evaluate

x = -5/2

y = -20/2 = -10

Step 3: Format into coordinates

(-5/2, -10)

Step 4: Convert to decimal

(-2.5, -10)

Answer:

Length = 10 cm

Width = 10-2 = 8 cm

Step-by-step explanation:

Area formula (L)(W)

80 = 10(x-2)

80 = 10x - 20

Add 20 to both side

100 = 10x

x= 10

Length = 10 cm

Width = 10-2 = 8 cm

Answer:

Below

Step-by-step explanation:

You can use it if you added a hight.

When you a hight you are creating a right triangle. If not you cannot use directly

Answer:

Yes

Step-by-step explanation:

If you mean just sine in general, then yes, it can be used with other triangles.

If you mean  [tex]sin=\frac{opposite}{hypotenuse}[/tex] , then there has to be a right triangle. But in other cases, sine is used to find missing sides as well as angles in triangles that are not right-angled.

Answer:

901 grams

Hope it helps

Answer:

a) [tex]\mathbf{\mu_ \hat p = 0.6}[/tex]

b) [tex]\mathbf{\sigma_p =0.01732}[/tex]

Step-by-step explanation:

Given that:

population mean [tex]\mu[/tex] = 30,000

sample size n = 800

population proportion p = 0.6

a)

The mean of the the sampling distribution is equal to the population proportion.

[tex]\mu_ \hat p = p[/tex]

[tex]\mathbf{\mu_ \hat p = 0.6}[/tex]

b)

The standard deviation of the sampling distribution can be estimated by using the formula:

[tex]\sigma_p = \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]\sigma_p = \sqrt{\dfrac{0.6(1-0.6)}{800}}[/tex]

[tex]\sigma_p = \sqrt{\dfrac{0.6(0.4)}{800}}[/tex]

[tex]\sigma_p = \sqrt{\dfrac{0.24}{800}}[/tex]

[tex]\sigma_p = \sqrt{3 \times 10^{-4}}[/tex]

[tex]\mathbf{\sigma_p =0.01732}[/tex]

The mean of a distribution is the average of the distribution.

The given parameters are:

[tex]\mathbf{n = 800}[/tex]

[tex]\mathbf{p = 0.6}[/tex]

(a) The mean

This is calculated as:

[tex]\mathbf{\bar x = np}[/tex]

So, we have:

[tex]\mathbf{\bar x = 800 \times 0.6}[/tex]

[tex]\mathbf{\bar x = 480}[/tex]

Hence, the mean is 480

(b) The standard deviation

This is calculated as:

[tex]\mathbf{\sigma = \sqrt{np(1 - p)}}[/tex]

So, we have:

[tex]\mathbf{\sigma = \sqrt{480 \times (1 - 0.6)}}[/tex]

[tex]\mathbf{\sigma = \sqrt{480 \times 0.4}}[/tex]

[tex]\mathbf{\sigma = \sqrt{192}}[/tex]

Take square roots

[tex]\mathbf{\sigma = 13.86}[/tex]

Hence, the standard deviation is 13.86

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Answer:

n=-5

Step-by-step explanation:

Let "n" represent the unknown number.

So, the equation asks for 4n and two more, or +2, that is all equal to -18.

So, your equation will be:

[tex]4n+2=-18[/tex]

First, subtract 2 from both sides:

[tex]4n+2-2=-18-2\\4n=-20[/tex]

Then, divide both sides by 4:

[tex]\frac{4n}{4}=\frac{-20}{4}\\n=-5[/tex]

Therefore, n=-5.

Answer:

See Explanation

Step-by-step explanation:

The question has mission options; However, the question is still solvable.

Given

[tex]A = \{a,b,c\}[/tex]

[tex]B = \{3,4,5,6\}[/tex]

Required

Determine possible ordered pairs of A to B

A function is of the form (x,y)

Let A be the range of the function and B, the domain

Let (x,y) be a function of A to B, where x represents any of the values in A sets and y represents any of the values in B

A ordered pair can only be regarded as a function if and only if it has unique y-values

Hence, a possible ordered pair is:

[tex](A,B) = \{(a,3),(b,4),(c,5)\}[/tex]

Another possible ordered pair is

[tex](A,B) = \{(a,4),(b,5),(c,6)\}[/tex]

Note that there as as many as possible ordered pair as long as the y-values are unique

There are many possible ordered pair as long as the y-values are unique.

           Given that, A = {a, b, c} and B = {3, 4, 5, 6}

           Order pair may be,

               [tex](a,3),(b,4),(c,5)[/tex]

    May be,   [tex](a,6),(b,5),(c,4)[/tex]

There are many possible ordered pair as long as the y-values are unique.

Learn more:

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Answer:

1/10

Step-by-step explanation:

6,7,8,9,10,11,12,13,14,15

ten TOTAL possible numbers= denominator

chance of picking the ONE possible number in mind= numerator

1/10

The probability is 1/10.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Given:

A magician asks an audience member to pick any number from 6 to 15

Possible outcome = {6,7,8,9,10,11,12,13,14,15}

So, chance of picking the number the magician has in mind = numerator

hence, the theoretical probability is = 1/10.

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Answer:

A.    [tex]\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}[/tex]

B.    [tex]\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }[/tex]

Step-by-step explanation:

Given that:

An investment of  Amount = $8000

earns  at an annual rate of interest = 7% = 0.07 compounded continuously

The objective is to :

A)  Find the instantaneous rate of change of the amount in the account after 2 year(s).

we all know that:

[tex]A = Pe^{rt}[/tex]

where;

[tex]A = (8000) \ e ^{0.7t}[/tex]

The instantaneous rate of change = [tex]\dfrac{dA}{dt}[/tex]

[tex]\dfrac{dA}{dt} = \dfrac{d}{dt}(8000 \ e ^{0.07t} )[/tex]

[tex]= 8000 \dfrac{d}{dt}e^{0.07 \ t}[/tex]

[tex]\dfrac{dA}{dt}= 8000 (0.07)e^{0.07 \ t}[/tex]

[tex]\dfrac{dA}{dt}= 560 e^{0.07 \ t}[/tex]

At t = 2 years; the instantaneous rate of change is:

[tex]\dfrac{dA}{dt}|_{t=2}= 560 e^{0.07 \times 2}[/tex]

[tex]\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}[/tex]

(B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $12,000.

Here the amount = 12000

[tex]12000 = (8000)e^{0.07 \ t}[/tex]

[tex]\dfrac{12000 }{8000}= e^{0.07 \ t}[/tex]

[tex]1.5= e^{0.07 \ t}[/tex]

㏑(1.5) = 0.07 t

0.405465 = 0.07 t

t = 0.405465 /0.07

t = 5.79

[tex]\dfrac{dA}{dt}= 560 e^{0.07 \ t}[/tex]

At t = 5.79

[tex]\dfrac{dA}{dt}|_{t = 5.79}= 560 e^{0.07 \times 5.79}[/tex]

[tex]\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }[/tex]

Answer:

Sum: 10.5 Arithmetic mean (Simple Average):1.5 Median: 1.6 Range: 0.7 Variance: 0.09 Standard Deviation: 0.09 =0.29

The answer is 0.29

hope this helped

Answer: Ivan has created 6 sculptures.

Step-by-step explanation:

If Ivan creates 1 sculpture for every 5 paintings and he makes 30 paintings.

30 divided by 5 =6

30 being the total

5 being how much for one

6, the answer, being for the total amount of sculptures.

Answer:

About 27.5 minutes

Step-by-step explanation:

When looking at the graph, you can see that the red line intersects about 27.5 minutes with $55.

Barry consumed almost 27.28 minutes.

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                                {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)      {Two point - slope form}

x/a + y/b = 1                                        {intercept form}

x cos(β) + y sin(β) = L                          {Normal form}

We have a graph shows Barry's monthly phone bill and the number of minutes used.

The points that lie on the graph are -

(0, 25) and (60, 90)

Slope of the line will be -

m = (90 - 25)/(60 - 0)

m = 65/60 = 1.1

[c] = 25

The equation of the line would be -

y = 1.1x + 25

For y = 55, we get -

55 = 1.1x + 25

1.1x = 30

x = 30/1.1

x = 27.28

Therefore, Barry consumed almost 27.28 minutes.

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Answer:

we have 8 quarts of 40% antifreeze,

according to the britain equivalent, 1 quart = 1.13L

so, we have 8 * 1.13L  = 9.04 L

out of the 9.04 L, 40% is antifreeze

amount of antifreeze = 0.4 * 9.04 = 3.616 L

moles of antifreeze present = 3.616/22.4 = 0.16 moles

moles of antifreeze in 60% solution = 0.6 * v/22.4 = 0.027 * v          

(where v is the volume of final solution)

molarity of initial solution = 0.16/9.04 = 0.018 M

molarity of final solution = 0.027*v/v = 0.027 M

m1*v1  = m2*v2

0.018 * 9.04 = 0.027 * v

v = 0.018 * 9.04/0.027

v = 6.026 L

amount if antifreeze in the final solution = 6.026 * 0.027 =  

0.163 Moles of antifreeze

amount in L = 0.163 * 22.4 = 3.65 L

amount in quarts  = 3.65/1.13 = 3.23 quarts

Answer: 5:7 and 10:14 are equivalents to 20:28

Step-by-step explanation:

We have the ration 20:28, and we want to find equivalent ratios to this:

One way to do this is by dividing both numbers by the same number.

For example, both 20 and 28 are even numbers, then we can divide them by 2.

20/2 = 10

28/2 = 14.

Then we have that 10:14 is equivalent to 20:28.

And we can do it again, this time only with words:

10:14 means that for each 10 glow sticks, we have 14 stickers.

The taking half of each, we have that for each 10 = 5 + 5 glow sticks, we have 14 = 7 + 7 stickers.

Then the ratio 5:7 is also equivalent to 10:14 and to 20:28

Answer:

- reflecting over x -axis

Step-by-step explanation:

Given equation

[tex]$ h(x) = 12x^8 +49 $[/tex]

Now, [tex]$ h(-x) = 12(-x)^8 +49 $[/tex]

                   = [tex]$ - 12x^8 +49 $[/tex]

Therefore, h(x) ≠ h(-x) ≠ -h(-x)

So, the function is neither odd nor even.

Therefore, reflecting the equation over x - axis would result a function that in neither even nor odd.

Answer:

Reflecting over x axis

Answer:

[tex]\Huge \boxed{15}[/tex]

Step-by-step explanation:

[tex]((2+3) \times 3) \div 5(2+3)[/tex]

Solving the brackets.

[tex](5 \times 3) \div 5(5)[/tex]

[tex]15 \div 5(5)[/tex]

Dividing and simplifying.

[tex]3(5)[/tex]

[tex]15[/tex]

Answer:

15

Step-by-step explanation:

   (2 + 3) * 3

= --------------- x (2 + 3)

       5

   5 * 3

= -------- x  5

       5

= 15

Answer:

7000

Step-by-step explanation:

1000x7

Answer:

7000

Step-b7y-step explanation: