Which equations are true for x = –2 and x = 2? Select two options

x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0

Answer:

Subtracting a number is the same as adding its opposite. So, subtracting a positive number is like adding a negative; you move to the left on the number line. Subtracting a negative number is like adding a positive; you move to the right on the number line.

Step-by-step explanation:

Given: A pizza box's volume has been reduced by 25% by flattening the curved side of the box. The dimensions of the box are given.

Required: To determine the angle, the area of the sector of the top surface of the old box design, the area of the top surface of the newly designed box, and the volume, V, of the newly designed box. Also, determine the height of the box, h.

Explanation: The given box is-

If we draw a perpendicular as shown in the figure, the angle is bisected, and the side 24 cm is also bisected as the triangle on the top is an isosceles triangle. This can be easily proved by showing that the smaller triangles on the top face are congruent.

Next, we can use the trigonometric ratio sine to determine the angle as follows-

Thus,

Next, the top of the new box is now a triangle with a base of 24 cm and a height-

Hence, the area is-

Now, the old box is a sector with a central angle of 38.94 degrees and a radius of 36 cm. Hence the area of the old box is-

Substituting the values as-

Lastly, the volume of the new box is 25% less than the old box. Hence the volume of the new box is-

We can determine the height as follows-

Hence,

Final Answer: A)

B) i) The area of the top of the old box=440.18 sq centimeters.

ii) The area of the top of the new box=407.30 sq centimeters.

C) i) The volume of the new box is 819 cubic centimeters.

ii) h=2.01 cm

The square has a 48 centimeter perimeter.

To find the perimeter of the square, we need to calculate its side length. The area of a rectangle is given by its length multiplied by its width, so we can use the given measurements of the rectangle to calculate its area: 25 cm x 16 cm = 400 cm². The area of a square is given by the square of its side length, so we can use the area of the rectangle to calculate the side length of the square: √400 cm² = 20 cm.

Thus, the perimeter of the square is equal to 4 times its side length, or 4 x 20 cm = 80 cm.

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Answer:

Step-by-step explanation:

The following are linear equations for the distance that John has biked (J) and the distance that Gymn has biked (G). These two equations represent the situation being described using the values provided.

J = 22x + 10

G = 28x + 0

In these equations the variable x represents the number of hours each of the bicyclists have biked.

The area of the surface is given by: Area = ∫(0 to π/2) ∫(0 to 2) (9 + r^2 cos^2 θ - r^2 sin^2 θ) r dr dθ

To find the area of the surface defined by the vector field F(x, y) = 9 + x^2 - y^2 over the region R, we can use the surface integral. The surface integral calculates the flux of the vector field across the surface.

The surface integral is given by the formula:

∬S F(x, y) · dS

where S represents the surface, F(x, y) is the vector field, and dS represents the differential surface area.

In this case, the region R is defined as x^2 + y^2 ≤ 4, x ≥ 0, and -2 ≤ y ≤ 2. This corresponds to the circular region in the first quadrant with a radius of 2 and height from -2 to 2.

To calculate the surface integral, we need to parameterize the surface S. We can use polar coordinates to parameterize the surface as follows:

x = r cos θ

y = r sin θ

where r ranges from 0 to 2 and θ ranges from 0 to π/2.

Next, we need to calculate the cross product of the partial derivatives of the parameterization:

∂r/∂x × ∂r/∂y = (cos θ, sin θ, 0) × (-sin θ, cos θ, 0) = (0, 0, 1)

The magnitude of this cross product is 1.

Now, we can calculate the surface integral:

∬S F(x, y) · dS = ∬S (9 + x^2 - y^2) · dS

Since the magnitude of the cross product is 1, the surface integral simplifies to:

∬S (9 + x^2 - y^2) · dS = ∬S (9 + x^2 - y^2) dA

where dA represents the differential area in polar coordinates.

To integrate over the circular region, we can use the following limits:

r: 0 to 2

θ: 0 to π/2

Evaluating this double integral will give the area of the surface defined by the vector field F(x, y) = 9 + x^2 - y^2 over the region R.

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There are 7 students who are studying both programming languages in the given class of 55 freshman.

This can be determined using a Venn diagram.

A Venn diagram is a graphical representation of sets or classes. The diagram shows sets, their elements, and the union, intersection, and complement of these sets.

A set is a collection of distinct objects, considered as an object in its own right. The elements of a set are frequently things of a similar nature, and sets are characterized by a distinctive property.

The size of a set is represented by the number of elements it contains. Let's use the following symbols to represent sets:

A={Elements in set A}

B={Elements in set B}

The intersection of sets A and B is the set of elements that are in both sets A and B. This can be expressed in the following way

n(A∪B) = n(A) + n(B) - n(A⋂B) where n(A⋂B) is known as intersection

The number of students studying both programming languages can be calculated by taking the intersection of the two sets.

We can use this formula to calculate the number of students studying both programming languages

:|A∩B|=|A|+|B|-|A∪B|

Where |A| denotes the number of elements in set  A studying C programming

|B| denotes the number of elements in set B studying Java

|A∪B| denotes the number of elements in the union of sets A and B (total students)

Now we can substitute the given values into the formula as follows

|A∩B|=38+24−55=7

Therefore, there are 7 students studying both programming languages.

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The curve y = 8e^x has maximum curvature at the point (0, 8).there is no point where the second derivative equals zero,

To determine the point of maximum curvature on the curve y = 8e^x, we need to find the second derivative of the function and identify the point where it equals zero. The second derivative represents the rate of change of the slope, or the curvature, of the curve.

First, we find the first derivative of y = 8e^x with respect to x:

dy/dx = 8e^x

Then, we differentiate again to find the second derivative:

d²y/dx² = d(8e^x)/dx = 8e^x

Setting the second derivative equal to zero:

8e^x = 0

Exponential functions, such as e^x, are never equal to zero for any value of x. Therefore, there is no point where the second derivative equals zero, indicating that the curve y = 8e^x does not have any inflection points or points of maximum curvature.

However, we can determine the point where the curvature is the greatest by considering the graph of y = 8e^x. Since the exponential function e^x is always positive, the curve y = 8e^x is always concave up. This means that the curvature is positive throughout the curve, but there is no specific point of maximum curvature.    

In conclusion, the curve y = 8e^x does not have a point of maximum curvature but is always positively curved.  

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Answer: 4\(\sqrt{3\\}\)

Step-by-step explanation:

It is because to get rid of radical of 48, because you factor 48 and it comes out to be 12 and 4, factor of 4 is 2 x 2. Factor of 12 is 6 x 2. Simplify the 6 to

3 x 2. You find the pair and the ones that have a pare become one and go outside of the radical sign on the left. 2 has 2 pairs so it is only 2 x 2 = 4. So 4 goes outside of the radical sign. Then the number that is alone with no pair is 3 so you put the number 3 inside the radical sign.

4\(\sqrt{3}\) is your answer.

Hope this helps, sorry if not...

Answer:

Step-by-step explanation:

1) g(f(x)) = 16\(x^{2}\) -116x + 223 and 2) area of the room is 11,388 feet.

2. Area of the room (rectangle)

Area of rectangle

Given:

length = 156 feet

width or breadth = 73 feet

To find = area of the room (rectangle in shape)

Formula for area of rectangle

Area of rectangle = l x b

                               = 156 feet x 73 feet

                               = 11,388 feet.

Therefore, Area of the room is 11,388 feet.

1. g(f(x))

Given:

f(x) = -4x+13

g(x)=\(x^{2}\) + 3x + 15

To find : g(f(x)).

g(f(x)) = g(-4x + 13)

Substitute the f(x) value in g(x)

         = \((-4x + 13)^{2}\) + 3 (-4\(x\) + 13) + 15  

                                                             \((a+ b)^{2}\) = \(a^2 + b^2 + 2ab\)

          = 16\(x^{2}\) + 169 - 104x -12x + 39 + 15

g(f(x)) = 16\(x^{2}\) -116x + 223

Therefore, g(f(x)) = 16\(x^{2}\) -116x + 223

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The height of the pile is increasing at a rate of approximately 0.056 feet per minute when the pile is 12 feet high.

We are given that sand is falling off at a rate of 14 cubic feet per minute, and the diameter of the base of the cone is approximately three times the altitude. Let h be the height of the pile at a given time t, then we can write the volume of the cone as V = (1/3)πr^2h, where r is the radius of the base of the cone. Since the diameter is three times the altitude, we have r = 3h/2.

Taking the derivative of the volume with respect to time, we get dV/dt = (1/3)π(9h^2/4)(dh/dt). Plugging in the given values, we get:

14 = (1/3)π(9h^2/4)(dh/dt)

Simplifying, we get:

dh/dt = 56/(3πh^2)

When the height of the pile is 12 feet, the rate of change of the height of the pile is:

dh/dt = 56/(3π(12)^2) ≈ 0.056 ft/min.

Therefore, the height of the pile is changing at a rate of approximately 0.056 ft/min when the pile is 12 feet high.

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A. The initial concentration of the drug in the organ is 0.06 mg/cm³.
B. the concentration of the drug in the organ after 19 seconds is approximately 0.1043 mg/cm³.

(a) The initial concentration of the drug in the organ can be found by evaluating x(t) at time t=0.

x(0) = 0.06 + 0.14(1 − e^(-0.02*0))
x(0) = 0.06 + 0.14(1 − 1)
x(0) = 0.06 + 0.14(0)
x(0) = 0.06

The initial concentration of the drug in the organ is 0.06 mg/cm³.

(b) To find the concentration of the drug in the organ after 19 seconds, plug t=19 into the given equation:

x(19) = 0.06 + 0.14(1 − e^(-0.02*19))
x(19) = 0.06 + 0.14(1 − e^(-0.38))
x(19) ≈ 0.06 + 0.14(1 − 0.6835)
x(19) ≈ 0.06 + 0.14(0.3165)
x(19) ≈ 0.10431

After rounding to four decimal places, the concentration of the drug in the organ after 19 seconds is approximately 0.1043 mg/cm³.

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Answer:

t=1/2u

Step-by-step explanation:

Since t=tens digit and u=units digit, as given in the equation that means that t+u=9. Since the tens digit is one-half the units digit that means: \(t=\frac{1}{2}u\) since it's one half the units digit.

The number of possible permutations of the three letters C, D, and E is d.6

A permutation is an arrangement of objects in a specific order. In this case, we are looking at the number of possible arrangements of the three letters C, D, and E. To find the number of permutations, we can use the formula:

n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1

where "n" is the number of distinct objects to be permuted.

So for our problem, we have three distinct objects (C, D, and E). Therefore, we can plug in n=3 to get:

3! = 3 x 2 x 1 = 6

This means there are 6 possible ways to arrange the letters C, D, and E in different orders. We can list all of these permutations as follows:

CDE

CED

DCE

DEC

ECD

EDC

So the answer to the question is 6, as given in option (d).

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Answer:

Hi there!!

Your answer is:

B. 7^8

Step-by-step explanation:

When you divide two numbers that have exponents, you subtract the value of the exponents!

7^12 - 7^ 4

equals (12-4) which is 8!

The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:

To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.

To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes

(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)

= 6x^2 - 15x + 8x - 20

= 6x^2 - 7x - 20.

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Answer: 14 blocks

Step-by-step explanation: Go up on the y-axis by 14 and you'll get (10,-8).

Answer:

14 blocks :D :( :D

Step-by-step explanation:

Answer:

190

Step-by-step explanation:

192 is closer to 190 than it is to 200, so the answer is 190.

Hope that helps!

Answer:

190

Step-by-step explanation:

192 looking a the ones number (2) if the last number is 5 or higher round up if not go down. therefore 190

The value of |x - y| which is not possible is 8.

Here we have to find the value of | x - y| which is not possible.

Given data:

The sides of a triangle are 4,6 and x and the other sides of a triangle are 4, 6, and y.

We know the fact that the sum of the lengths of two sides of a triangle is always greater than the third side.

Let us take the minimum and maximum values of the third side as x and y.

Minimum value is ≥ 6 - 4 that is ≥ 2

Maximum value is ≤ 6 + 4 that is ≤ 10

So, | x - y | ≤ | 10 - 2| that is ≤ 8.

The smallest positive number that is not the possible value of | x - y| is 8.

Therefore the value of | x-y| which is not possible is 8.

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The statement that is NOT correct about hypothesis testing is: "We cannot eliminate both type l error and type II error at the same time."

In hypothesis testing, we aim to make a decision about a population parameter based on sample data. Type I error refers to rejecting a true null hypothesis, while Type II error refers to failing to reject a false null hypothesis. While it is not possible to completely eliminate both types of errors simultaneously, we can minimize the chances of committing either of them by choosing an appropriate significance level and conducting a power analysis.

Therefore, the statement that we cannot eliminate both Type I and Type II errors at the same time is incorrect.

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Answer:

9a^3b^3.

Step-by-step explanation:

The GCF of 9 and 27 is 9.

For a^4 and a^3 it is a^3.

For b^4 and b^3 it is b^3.

Answer is therefore:

9a^3b^3.

Answer:

9a^3 b^3

Step-by-step explanation:

hope this helps you have a nice day :)

i use to use this but its whatever works for you the second picture for prime factors

Answer:

1246cm

Step-by-step explanation:

26*10=260

29*34=986

986+260=1246

Answer:

There are no possible real values for x.

Step-by-step explanation:

The equation states:

4-x²>10

-x²>10-4 (Move 4 to the other side)

-x²>6 (Multiplying by -1 changes the sign)

x²<-6

In the case that we aren't working with imaginary numbers, no number squared would give -6, or anything below -6.

Hope this helps, and let me know if imaginary numbers are necessary for this question ♡

Answer:

Factors for 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Factors for 53: 1 and 53.

Answer:

(6m² + 12m + 2) / (6m + 1)

Step-by-step explanation:

multiply both sides by m.

we get m² - 1 = 6m

move the -1 to the other side, so it becomes +1

m² =  6m + 1

so m² + 1/m² = (6m + 1) + 1/(6m + 1)

get a common denominator by squaring (6m + 1)

(6m + 1)².

we now have (6m + 1)² / (6m + 1)  + 1/(6m + 1).

we now add the numerators.

(6m + 1)² + 1 = (6m² + 6m + 6m + 1) + 1 = 6m² + 12m + 2.

numerator over denominator = (6m² + 12m + 2) / (6m + 1)

Answer:

m = 8

Step-by-step explanation:

I looked at the line 8 and looked at m and noticed they're literally the same length. so m = 8.

The 95% confidence interval estimate for the difference between the percentages of men and women who prefer beef over chicken is given as follows:

0.2 ± 0.0748.

The difference of proportions is given as follows:

0.75 - 0.55 = 0.2.

The standard error for each sample is given as follows:

Hence the standard error for the distribution of differences is given as follows:

\(s = \sqrt{0.0274^2 + 0.0266^2}\)

s = 0.0382.

The critical value for a 95% confidence interval of proportions is given as follows:

1.96.

Hence the margin of error is:

M = 0.0382 x 1.96

M = 0.0748.

Hence the interval is:

0.2 ± 0.0748.

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\(\\ \sf\longmapsto sin44=\dfrac{x}{48}\)

\(\\ \sf\longmapsto 0.69=\dfrac{x}{48}\)

\(\\ \sf\longmapsto x=48(0.69)\)

\(\\ \sf\longmapsto x=33.12\)

_________

\( \: \)

Sin (44°) = x/48

0.69 = x/48

x = 48 × 0.69

x ≈ 33.12