what dose 2+7x=5x+14 equal

Answer:

  p(x) = -x⁵ -4x⁴ +9x³ +40x² +4x -48

Step-by-step explanation:

You want a polynomial of 5th degree with x-intercept (3, 0), point (-2, 0) a local maximum, and a limit as x→-∞ of p(x)→∞.

The requirements placed on the polynomial mean that the graph will cross the x-axis at x=3 and will touch the x-axis from below at x=-2. The touch from below means the zero at x=-2 must have even multiplicity. That multiplicity can only be 2 in order for the other requirements to be met.

Since the polynomial is positive for large negative x-values, the leading coefficient must be negative, and there must be a zero that is less than -2.

So far, we have four (4) zeros accounted for, but we need 5. The 5th zero must be greater than -2.

For the polynomial shown in the graph, we have elected to have zeros at x=-4 and x=1. Each zero at x=q means (x-q) is a factor. The multiplicity of the zero is the exponent of the factor.

This makes the factored form be ...

  p(x) = -(x +4)(x +2)²(x -1)(x -3)

The expanded form is ...

  p(x) = -x⁵ -4x⁴ +9x³ +40x² +4x -48

(a) To find the limit as x approaches infinity of (1 + 2x)^(1/(2x)), we can use the limit properties and the concept of exponential functions. The limit is e^2.
(b) To evaluate the integral of f(x) = e^(3x) * cos(2x) dx, we can use integration techniques such as integration by parts. The integral evaluates to (1/13)e^(3x) * (3cos(2x) + 2sin(2x)) + C.

(a) To find the limit limx→∞ (1 + 2x)^(1/(2x)), we can rewrite it as e^(limx→∞ (1/(2x) * ln(1 + 2x))). As x approaches infinity, 1/(2x) approaches 0, and ln(1 + 2x) approaches ln(2x). Therefore, the limit simplifies to e^(limx→∞ (ln(2x))). Using the limit properties, we have limx→∞ (ln(2x)) = ln(limx→∞ (2x)) = ln(∞) = ∞. Hence, the limit is e^∞, which equals infinity. Therefore, the limit limx→∞ (1 + 2x)^(1/(2x)) does not exist.
(b) To evaluate the integral ∫(e^(3x) * cos(2x)) dx, we can use integration by parts. Let u = e^(3x) and dv = cos(2x) dx. Differentiating u with respect to x gives du = 3e^(3x) dx, and integrating dv gives v = (1/2)sin(2x). Applying the integration by parts formula, ∫u dv = uv - ∫v du, we have ∫(e^(3x) * cos(2x)) dx = (1/2)e^(3x) * sin(2x) - (1/2)∫(3e^(3x) * sin(2x)) dx. Simplifying further, the integral evaluates to (1/2)e^(3x) * sin(2x) - (3/2)∫(e^(3x) * sin(2x)) dx. To compute the remaining integral, we can apply integration by parts again or use other integration techniques. The final result is (1/13)e^(3x) * (3cos(2x) + 2sin(2x)) + C, where C is the constant of integration.

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Answer:true

Step-by-step explanation:

The top line segment (12) is twice as long as the original, smaller (6), segment

Given:

The two points are (-5,8) and (-3,1).

To find:

The distance between the given two points in simplest radical form.

Solution:

Distance formula: The distance between two points is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Using distance formula, the distance between (-5,8) and (-3,1) is

\(d=\sqrt{(-3-(-5))^2+(1-8)^2}\)

\(d=\sqrt{(-3+5)^2+(-7)^2}\)

\(d=\sqrt{(2)^2+(-7)^2}\)

\(d=\sqrt{4+49}\)

\(d=\sqrt{53}\)

Therefore, the distance between two points (-5,8) and (-3,1) is \(\sqrt{53}\) units.

Answer:

169

Step-by-step explanation:

14 + 162 - 7 = 169

hoped this helped:)

Answer:

21

hope it's helpful ❤❤❤❤❤

THANK YOU.

Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

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The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because  A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.

To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:

A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.

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The surface area of the sphere based on the information will be 2304π.

It should be noted that the radius of the circle will be 1/2 the length of the line. Therefore, the radius in the shape will be:

= 1/2 × 48

= 24 units.

Therefore, the area of the sphere will be:

= 4πr²

= 4 × π × 24²

= 2304π

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The cone company that offers a better deal is the sugar cone factory because the volume of ice-cream it can contain is bigger than the Coney Island factory ice-cream cones.

To determine the volume of the cones, the formula that should be used would be given below as follows. That is;

Volume of cone = 1/3πr²h

For sugar cone factory:

Radius = 3cm

Height = 10cm

The volume of their ice-cream cone = 1/3× 3.14× 3×3×10

= 94.2cm³

For Coney Island;

Radius = diameter/2 = 5/2 = 2.5cm

Height = 14

The volume = 1/3×3.14×2.5×2.5×14

= 274.75/3= 91.6cm³

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The function S maps subsets of X to bit strings of length 3. For each element in X, if it belongs to the subset Y, the corresponding bit in the string is set to 0; otherwise, it is set to 1. The value of S(X) will provide the bit string representation of all elements in X.

Given the set X={a, b, c}, the function S maps subsets of X to bit strings of length 3. Let's determine the value of S(X).

For element a, since a∈X, the corresponding bit s1 is set to 0.

For element b, since b∈X, the corresponding bit s2 is set to 0.

For element c, since c∈X, the corresponding bit s3 is set to 0.

Therefore, the value of S(X) is 0, 0, 0; representing that all elements a, b, and c are present in the set X.

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Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

\(M = ( \frac{x_1 + x_2}{2} , \: \frac{y_1 + y_2}{2} )\\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-1,-3) and (-5,12)

The midpoint is

\(M = ( \frac{ - 1 - 5}{2} \: , \: \frac{ - 3 + 12}{2} ) \\ = ( - \frac{6}{2} \: , \: \frac{9}{2} )\)

We have the final answer as

\(( - 3 \: , \: \frac{9}{2} ) \\ \)

Hope this helps you

Step-by-step explanation:

Hey there!

The given coordinates are; (-1,-3) and (-5,12).

Now;

Use formula for midpoint.

\(m(x,y) = ( \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} )\)

Put all values.

\((x,y) = ( \frac{ - 1 - 5}{2} ,\frac{ - 3 + 12}{2} )\)

Simplify it to get answer.

\((x,y) = ( \frac{ - 6}{2} , \frac{9}{2}) \)

\((x,y) = ( - 3, \frac{9}{2} )\)

Therefore the midpoint is; (-3,9/2).

Hope it helps..

Answer:

x = 2

y = -3

Step-by-step explanation:

y = x-5

y = -x-1

2x -4 = 0

2x = 4

x =2

y = 2-5

y = -3

Answer: 0

Step-by-step explanation:

0 = x

4=y

0=8-(2)(4)

0+(3)(4)=12

By applying the binomial distribution formula, it can be concluded that the probability that more than 6 will say yes is 0.423 (option B).

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!) where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

n = 22

p = 28% = 0.28

q = 1 - 0.28 = 0.72

The probability that r adults will say yes is given by the binomial distribution:

P(X=r) = C(n,r) * \(p^{r}\) * \(q^{n-r}\)

= C(22,r) * \(0.28^{r}\) * \(0.72^{22-r}\)

P(X≤6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

Now we calculate for each probability:

P(X=0) = C(22,0) * 0.28⁰ * 0.98²² = 0.000726633

P(X=1) = C(22,1) * 0.28¹ * 0.98²¹ = 0.00621676

P(X=2) = C(22,2) * 0.28² * 0.98²⁰ = 0.025385

P(X=3) = C(22,3) * 0.28³ * 0.98¹⁹ = 0.0658131

P(X=4) = C(22,4) * 0.28⁴ * 0.98¹⁸ = 0.121571

P(X=5) = C(22,5) * 0.28⁵ * 0.98¹⁷ = 0.1702

P(X=6) = C(22,6) * 0.28⁶ * 0.98¹⁶ = 0.187535

If we sum up the results, we get P(X≤6) = 0.577447493

P(X>6) = 1 - P(X≤6)

           = 1 - 0.577447493

           = 0.422552507

           ≈ 0.423

Thus the probability that more than 6 will say yes is 0.423.

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Answer:

0, 2/5, 1/6,-3/4,-7/10

Step-by-step explanation:

this is just what i think i didint understand the no spaces or no commas or negatives thing but here you go i hope its right

Answer:

Yes, the amount of sugar you need proportional to the amount of lemonade mix you use.

Step-by-step explanation:

You are making lemonade. The amount of sugar you need depends on the amount of lemonade mix you use. Cups of sugar

1/3

1

3

Packets of lemonade mix

1

3

9

Is the amount of sugar you need proportional to the amount of lemonade mix you use?

Cups of sugar ∝ Number of packets

C ∝ N

C = k/N

k = C/N

a) For

1/3 cups of sugar and 1 packet of Lemonade mix

1/3 ∝ 1

1/3 = 1k

k = 1/3/1

k = 1/3

b) For

1 cups of sugar and 3 packets of Lemonade mix

1 ∝ 3

1 = 3k

k = 1/3

k = 1/3

c) For

3 cups of sugar and 9 packets of Lemonade mix

3 ∝ 9

3= 9k

k = 3/9

k = 1/3

Therefore, Yes, the amount of sugar you need proportional to the amount of lemonade mix you use. This is because the value is k is the same

Answer:

yes

Step-by-step explanation:

not sure how the format is for the question but i think its

for the second column: y=2+2, y=6+2, y=7+2

for third column: 4, 8, 9

for the fourth column: (2,4), (6,8), (7,9)

for the according to the table:

(6,8), when his brother is 6 he is 8

for the graph: graph out the points (2,4), (6,8), (7,9)

another solution can be when he is 5 his brother is 3

(these should be right)

Answer:

8) Table

2...

6...

7...

According to table 6, the point (6,8) means when his brother is 8 Trisjohn is 6

For the graph plot points at (2,4) (6,8) and (7,9) and connect with a straight line

When Kimarius is 5 his brother is 3

Have a lovely day :)

Answer:

1. P = 125 + 50w

2. I can't make a graph on your image, (since there are no increments) but the image attached is an image of a graph on desmos.

3. The y intercept represents the original 125 pounds of aluminum cans he starts with, and the slope represents the aluminum cans he collects.

Step-by-step explanation:

We already know that the solution is (9, -3/5), let's show that

Let's plug our solution into the equation

The second equation is true!

The number of solutions to the equation (cos x)(b sin x - a) = 0 on the interval 0 ≤ x < 2π is c) 2.

To determine the number of solutions to the equation (cos x)(b sin x - a) = 0 on the interval 0 ≤ x < 2π, we need to analyze the behavior of each term separately.

The equation can be true if either (cos x) = 0 or (b sin x - a) = 0, or both.

For (cos x) = 0:

The cosine function is equal to 0 at two points within the interval 0 ≤ x < 2π, which are π/2 and 3π/2. Therefore, (cos x) = 0 has two solutions.

For (b sin x - a) = 0:

To solve this equation, we isolate the sin x term:

b sin x = a

Since a and b are integers, the values of sin x must be rational numbers to satisfy the equation.

Considering the unit circle and the properties of the sine function, the values of sin x are rational at four points within the interval 0 ≤ x < 2π: 0, π, 2π, and π/2.

Now, let's consider the two cases:

a) If sin x = 0:

This occurs at x = 0 and x = π.

b) If sin x ≠ 0:

This occurs at x = π/2 and x = 3π/2.

In both cases, if we substitute these values into (b sin x - a), we get:

b sin(0) - a = -a ≠ 0

b sin(π) - a = -a ≠ 0

b sin(π/2) - a = b - a ≠ 0

b sin(3π/2) - a = -b - a ≠ 0

So, (b sin x - a) = 0 does not have any solutions within the interval 0 ≤ x < 2π.

Therefore, the number of solutions to the equation (cos x)(b sin x - a) = 0 on the interval 0 ≤ x < 2π is equal to the number of solutions of (cos x) = 0, which is 2.

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Answer:

QR

Step-by-step explanation:

The question is just trying to see if you can read the order of the lines.

PQ is the first 2 letters of PQR so XY has to be the first 2 letters of XYZ

Answer

YZ is the second and third letters of xyz.

QR are the 2nd and 3rd letters of PQR

There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.

In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).

Therefore, the calculation is as follows:

total number of ways = nCr

                    = 5C4

                    = 5! / 4!(5-4)!

                    = 5! / 4!1!

                    = 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1

                    = 5 x 4 x 3 x 2

                    = 120

Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

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Answer: it is 3/2x x + 0

Step-by-step explanation:

you do rise over run which is 3 up and 2 over in this case. and the 0 is the y intercept but its at the center also known as the origin so its 0

Answer:

Step-by-step explanation:

Tracy ran 3 laps around the track.

Laps can refer to the circular tracks used for running or racing. For example, a running track is often called a "track and field oval" or a "400-meter oval" because it is a loop that is 400 meters long. Each loop around the track is called a "lap."

Laps can also refer to a unit of measurement for swimming. In swimming, a "lap" is typically defined as two lengths of a pool. For example, if a pool is 25 meters long, one lap would be swimming from one end to the other and back again.

In some contexts, "laps" can also refer to a measurement of time. For example, if someone says they ran 10 laps around a track, they might mean they ran 10 loops around the track, or they might mean they ran for a certain amount of time (e.g., 10 minutes) without specifying how many laps that involved.

given by the question.

To find out how many laps Tracy ran, we can divide the total distance she covered (1 1/2 miles) by the distance of each lap (1/2 mile).

1 1/2 miles is the same as 3/2 miles.

So, to find the number of laps, we can divide 3/2 miles by 1/2 mile:

(3/2) ÷ (1/2) = 3

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Answer:

Interest is $14,400

Step-by-step explanation:

I = Prt

I = (80,000)(0.09)(2)

I = 14,400

The degree measure of angle A is 90 degrees if the measure of angle A is three times as big as the measure of angle C and the measure of angle B is 30 degrees bigger than the measure of angle C.

Let x be the measure of angle C in degrees.

According to the problem statement, angle A is three times as big as angle C, measuring 3x degrees.

Angle B is 30 degrees bigger than angle C, so its measure is x + 30 degrees.

The sum of the measures of the angles in a triangle is always 180 degrees so that we can write:

A + B + C = 180

Substituting the expressions we found for the angles in terms of x, we get:

3x + (x + 30) + x = 180

Simplifying and solving for x, we get:

5x + 30 = 180

5x = 150

x = 30

Therefore, angle C has a measure of 30 degrees, angle B has an estimate of 30 + 30 = 60 degrees, and angle A has a measure of 3(30) = 90 degrees.

So the degree measure of angle A is 90 degrees.

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The complete table of the algae area is:

Day   1     2   3   4   5   6

Area  1/2  1   2   4   8   16

The initial area is given as;

A(1) = 1/2 square meters

When it doubles every day, we have:

A(n) = 2 * A(n - 1) where A(1) = 2

So, we have the following values

A(2) = 1/2 * 2 = 1

A(3) = 1 * 2 = 2

A(4) = 2 * 2 = 4

A(5) = 4 * 2 = 8

A(6) = 8 * 2 = 16

Hence, the complete table is:

Day   1     2   3   4   5   6

Area  1/2  1   2   4   8   16

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Answer: ;otherwise, your eyes will become very irritated from the chlorine.

Step-by-step explanation: I took the test

Answer:

the answer above is right i jus took the test

Step-by-step explanation: