rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?

Answer:

A graph shows zeros to be ±3. Factoring those out leaves the quadratic

 (x-2)² +1

which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The function is :

f(x) = x⁴ - 4x² - 5

=============================================================

Plotting on a graph :

⇒ Once plotted on graph, check where the line of the function intersects the x-axis

⇒ Those will be the zeros of the function

===========================================================

Solution :

⇒ x = -2.236

⇒ x = 2.236

Answer:

Answer: -3/2

Step-by-step explanation:

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Answer:

The answer is in the picture.

Step-by-step explanation:

By hand, you can factor it. I did it on a website called Cymath.

Answer:

3x(y - 3)(y + 1)

Step-by-step explanation:

Factor 3x out of 3xy^2

Factor 3x out of -6xy

Factor 3x out of -9x

Factor 3x out of 3x(y^2)+3x(-2y)

Factor 3x out of 3x(y^2-2y) + 3x(-3)

Answer:

Add 3 to both sides

Property: Addition property of equality

Step-by-step explanation:

Action: Add 3 to both sides.

⇒ x - 3 =               12

(cancel out)+ 3     + 3

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

     x    =        15  

The property used:

→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.

Answer: 103/15

Step-by-step explanation:

We can simplify the right-hand side to be [tex]2 \left(\frac{1}{3}+6 \right)=2 \left(\frac{19}{3} \right)=\frac{38}{3}[/tex].

This means we need to solve:

[tex]\frac{1}{2}(5x-9)=\frac{38}{3}\\5x-9=\frac{76}{3}\\5x=\frac{103}{3}\\x=\boxed{\frac{103}{15}}[/tex]

Answer:

√121 = 11

Explanation:

11 × 11 = 121

Answer:

11

Step-by-step explanation:

The square root of 121 is 11.

= 11*11 = √(121)

= 121 = 11

done

The initial point of vector v if it has a magnitude of 10 and the terminal point (-3,3) is option B (-9,-5).

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

Given;

The magnitude of 10 and the terminal point (-3,3).

v = ai + bj

v = [tex]\sqrt{a^2 + b^2}[/tex]

10 =  [tex]\sqrt{a^2 + b^2}[/tex]

AB = (-3 - a)i + (3 - b)j

If we put (-9,-5)then

AB = (-3 - a)i + (3 - b)j

AB = (-3 + 9)i + (3 + 5)j

AB = 6i + 8j

Put the value in the vector magnitude

10 =  [tex]\sqrt{a^2 + b^2}[/tex]

   = [tex]\sqrt{6^2 + 8^2}\\\\\sqrt{36+ 64}\\\\\sqrt{100}[/tex]

10 = 10

Thus, The correct option is B (-9,-5).

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Answer:

see the attachment photo!

After 15 seconds rocket reaches to maximum height is 225 units.

Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.

Here, the given equation of height

            h(t) = -t² + 30t

             y = -t² + 30t

Now, on differentiating both side with respect to t, we get

        dy/dt = -2t + 30

put dy/dt = 0, we get

       0 = -2t + 30

        2t = 30

        t = 15

Now, at t = 15 sec. rocket reach at its maximum height.

maximum height at t = 15 sec is

     h(15) = -(15)² + 30(15)

     h(15) = -225 + 450

    h(15) = 225

Thus, after 15 seconds rocket reaches to maximum height is 225 units.

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The length of the intervals of the given frequency table is

500 ft.

The given list shows the lengths in feet of the 25 longest bridges in the United States.

we have to determine the median and mode of the bridge data.

The median is the middle number of the data set arranged in ascending order.

1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260.

The median is 1750.

Mode is the number that appears most often in the data set.

1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260

The mode is 1600.

Therefore the correct option is Median: 1750, Mode: 1600

So the length of the intervals of the given frequency table is

500 ft.

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The probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

Let A represent Female and B represents civil engineering.

The above representation means that the given parameters are:

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

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Some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a experiment. To avoid any ambiguity or surprise, a experiment must be properly defined.

A) Because human experimentation is immoral, animal research has been employed as a research approach.

However, using animals is unethical because they are subjected to unpleasant and hazardous procedures, as well as stress and injury. The use of non-animal methods to substitute animal methods as much as possible will provide both ethical and technical benefits. Researchers should make the use of non-animal methods for a top priority experiments.

B) Even though the purpose of an experiment is to ensure success in rabbits, this is incorrect in people because action is what will operate properly.

The absence of thyroid-stimulating hormone in rabbit serum is a mistaken notion. As a result, it is preferable to test the drug further, and it was a success. As a result, there will be no dysfunctionality for humans.

Thus, some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

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Answer:

none of the above

Step-by-step explanation:

4x + 7 = x + 2

4x - x + 7 = x - x + 2

3x + 7 = 2

3x + 7 - 7 = 2 - 7

3x = -5

3x / 3 = -5 / 3

x = -5 / 3 = -1.667

5x - 8 = x + 4

5x - x - 8 = x - x + 4

4x - 8 + 8 = 4 + 8

4x = 12

4x / 4 = 12 / 4

x = 3

3x + 2 = 5x + 2

3x - 5x + 2 = 5x - 5x + 2

-2x + 2 = 2

-2x + 2 - 2 = 2 - 2

-2x = 0

x = 0

Integers, As a whole number that can be written without a remainder,

x = 3

x = 0

(Mixed) Fraction

x = -5 / 3 = -1.667

The correct answer is 6 / 7 as it is closer to 1.

The fraction is defined as the division of the whole part into an equal number of parts.

The number near 1 will be calculated as:-

7/ 6 = 1.1666

6 / 7 = 0.8571

Difference of the first ratio from one.

1.1666 - 1  = 0.1666

Difference of the second ratio:-

1 - 0.8571 = 0.1429

So the difference of 6 / 7 is lower than the difference of the fraction 7 / 6 from one.

Therefore the correct answer is 6 / 7 as it is closer to 1.

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An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,

4.75 = x + (-0.25)

4.75 + 0.25 = x

x = 5

Hence, the original height of the water in the pool in feet is 5.

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Answer:

i think the answer is 25q - 5 / 4

The domain of the function is x > 0.

The correct option is (B)

Domain of a function is defined by the set of x-values of the graph of a function.

as, domain of a function is defined by the set of x-values of the graph of a function.

From the graph we can see that,

x-values are starts from x > 0 [Since x ≠ 0]

Also, moves towards infinity,

Hence, domain of the function be, (0, ∞) or x > 0

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Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A right triangle must have one of its 3 angles equal to 90°

the only triangle with an angle of 90° is Triangle C

Answer:

B:Triangle

Step-by-step explanation:

Answer:

Yes, x = 0 is a solution to the given equation

Step-by-step explanation:

Hi Student!

The goal of this question is to determine x = 0 is a solution of the expression that was provided.  The first step that we must take is input 0 into all of the x's that we have in the expression.  Then we just simplify both sides and determine if the end expression is true and if it is then x = 0 is a solution.

Plug in the values

Simplify both sides

Looking at the final expression, we can see that 1 is indeed equal to 1 and since the expression is true, we can say that x = 0 is a solution of the expression that was provided in the problem statement.

The advantages and disadvantages of the kind of technology we have access to in the early 21st century include:

Advantages:

The improvement of productivity.

Better and easier communication between people.

Disadvantages:

Can be bad for the environment.

Technology might be able to replace humans in jobs.

Technology is the result of accumulated knowledge and the application of skills, and processes used in industrial production and scientific research.

Technology is embedded in the operation of all machines for the intended purpose of an organization.

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Answer:

36

Step-by-step explanation:

possibility of slices of pie is 12/24, = 1/2

78 desserts, how much i expect is slices of pie

78*(1/2) = 36

We should expect about 39 of the next 78 desserts sold to be slices of pie.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Out of 24 desserts sold, 12 were slices of pie.

Therefore, the proportion of slices of pie sold is 12/24 = 1/2.

To estimate the number of slices of pie in the next 78 desserts sold, we can multiply the proportion of slices of the pie by the total number of desserts sold:

(1/2) x 78 = 39

Therefore,

We should expect about 39 of the next 78 desserts sold to be slices of pie.

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An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to factor out the GCF in the expression

[tex]\star~\star\mathrm{6x^3+3x}~\star~\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's divide.

But first. we should work out the GCF.

Both terms have 3x in common, so we divide both terms by 3x:

[tex]\mathrm{6x^3+3x}[/tex]

[tex]\mathrm{3x(2x^2+1)}[/tex]

To ensure that we've factored correctly, we can always use the distributive property, distribute 3x and see whether or not we end up with [tex]\mathtt{6x^3+3x}[/tex].

So the answer is

[tex]\mathrm{3x(2x^2+1)}[/tex]

Notice I put parentheses around 2x²+1. This indicates that 3x is multiplied times both 2x² and 1.

Hope it helps you out! :D

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Answer:

The answer is 7

Step-by-step explanation:

To find the volume you multiply the width, height, and the length.

Length= 7/3

width= 3/3

height= 9/3

When you multiply you then have to simplify which is 7/1 or 7.

Mark this correct to help me gain!!

[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

Step-by-step explanation:

Scale factor red to blue meaning 42 to 7

42÷7=6

Scale factor is 6

Perimeter of the blue quadrilateral = ?

If perimeter of red = 204

Then we use this following proportion

[tex]204 \div 42 = x \div 7[/tex]

[tex] \frac{204}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=7×204

42x=1428

x=34

Area of the blue quadrilateral = ?

If area of the red quadrilateral = 2880

Then we use the following proportion

[tex]2880 \div 42 = x \div 7[/tex]

[tex] \frac{2880}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=2880×7

42x=20160

x=480

Answer:

21. x = 18.1

22. x =28.7

Step-by-step explanation:

SOH = sin(theta) = opp/hyp

CAH = cos(theta) = adj/hyp

TOA = sin(theta) = opp/adj

21. You would be using tangent.

tan(theta) = Opp/Adj

tan(32°) = x/29

x = 29 * tan(32°)

x = 18.1

22. You would be using cosine

cos(theta) = Adj/Hyp

cos(43°) = 21/x

x * cos(43°) = 21

x = 21 / cos(43°)

x = 28.7

Use a Calculator to help you solve for those side lengths or degrees.

If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using

I am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.

Answer:

18 inches = 1.5 feet

8 inches = 2/3 foot

y = 1.5 + (2/3)x