Solve the system of equations.
y=8x-11
y=x+17

Answer:

-67 I belive

Step-by-step explanation:

Answer:

normally I'd make a joke and say 76 but the answer would be -67 lol

Step-by-step explanation:

Answer:

62

Because u do 180-90-28=62

The population growth rate can be calculated using the equation x = x₀ (1+r)ⁿ. The population after 8 years will be 66 frogs.

The population growth is the increase in population after the specified number of years. Lets look into the data which is given.

The initial population is 6 tree frogs.

Population growth percent = 35%    

Rate of growth, r = 35/100 = .35

The population growth is calculated using the equation,  x = x₀ (1+r)ⁿ

     x₀ is  initial population

     r is the rate

    n is the number of years.

x = 6 (1+r)⁸ = 66.19

So the population of frog after 8 years will be 66.

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a) The inverse of the matrix is:

⎣⎡​−6 3​1 0​⎦⎤​

b) The solution to the system of equations is x1 = -24, x2 = -24, x3 = -24.

c) Matrix A is:

⎣⎡​3/4 -1/4​-7/4 1/2​⎦⎤​

d) Matrix A is:

⎣⎡​-4/20 15/20​-12/20 2/20​⎦⎤

a) To find the inverse of the matrix:

⎣⎡​−113​011​10−1​⎦⎤​

We can use the formula for the inverse of a 3x3 matrix. Let's call the given matrix A:

A = ⎣⎡​−113​011​10−1​⎦⎤​

The formula for the inverse of a 3x3 matrix A is:

A^(-1) = (1/det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate of A.

To calculate the inverse, we need to find the determinant and adjugate of A.

The determinant of A, denoted as det(A), can be calculated as follows:

det(A) = (-1) * ((-1) * (0 * (-1) - 1 * 1) - 1 * (0 * 1 - 1 * (-1)))

det(A) = (-1) * ((-1) * (-1) - 1 * (0 - (-1)))

det(A) = (-1) * ((-1) - 1 * (0 + 1))

det(A) = (-1) * ((-1) - 1)

det(A) = (-1) * (-2)

det(A) = 2

Now, let's find the adjugate of A. The adjugate of A, denoted as adj(A), is obtained by taking the transpose of the matrix of cofactors of A.

The matrix of cofactors of A is obtained by taking the determinant of each minor of A, where each minor is obtained by removing one row and one column from A.

The matrix of cofactors of A is:

C = ⎣⎡​0−1​1−1​⎦⎤​

Taking the transpose of C gives us the adjugate of A:

adj(A) = ⎣⎡​01​−11​⎦⎤​

Finally, we can calculate the inverse of A using the formula:

A^(-1) = (1/det(A)) * adj(A)

A^(-1) = (1/2) * ⎣⎡​01​−11​⎦⎤​

A^(-1) = ⎣⎡​12​−12​⎦⎤​

Therefore, the inverse of the given matrix is:

⎣⎡​12​−12​⎦⎤​

b) To solve the system of equations using matrix inversion:

The given system of equations can be written in matrix form as:

AX = B

where A is the coefficient matrix, X is the column vector of variables (x1, x2, x3), and B is the column vector on the right-hand side (4, -6, 3).

A = ⎣⎡​−1 1 0​1 0 1​3 1 −1​⎦⎤​

X = ⎣⎡​x1​x2​x3​⎦⎤​

B = ⎣⎡​4​−6​3​⎦⎤​

To solve for X, we can use the formula:

X = A^(-1) * B

Substituting the values:

X = ⎣⎡​12​−12​⎦⎤​ * ⎣⎡​4​−6​3​⎦⎤​

X = ⎣⎡​(-12) * 4 + (-12) * (-6) + 12 * 3​(12) * 4 + (-12) * (-6) + 12 * 3​⎦⎤​

X = ⎣⎡​-24​-24​⎦⎤​

Therefore, the solution to the given system of equations is x1 = -24, x2 = -24, x3 = -24.

To find matrix A, we are given that (4A)^(-1) = ⎣⎡​2 1​7 3​⎦⎤​.

Let's solve for A:

(4A)^(-1) = ⎣⎡​2 1​7 3​⎦⎤​

Multiplying both sides by 4:

4A = ⎣⎡​2 1​7 3​⎦⎤​^(-1)

4A = ⎣⎡​2 1​7 3​⎦⎤​^(-1)

4A = ⎣⎡​3 -1​-7 2​⎦⎤​

Dividing both sides by 4:

A = (1/4) * ⎣⎡​3 -1​-7 2​⎦⎤​

A = ⎣⎡​3/4 -1/4​-7/4 1/2​⎦⎤​

Therefore, matrix A is:

⎣⎡​3/4 -1/4​-7/4 1/2​⎦⎤​

To find matrix A, we are given that A * ⎣⎡​4 -3​-2 2​⎦⎤​ = ⎣⎡​1 3​−4 2​⎦⎤​.

Let's solve for A:

A * ⎣⎡​4 -3​-2 2​⎦⎤​ = ⎣⎡​1 3​−4 2​⎦⎤​

Multiplying both sides by the inverse of the matrix ⎣⎡​4 -3​-2 2​⎦⎤​:

A = ⎣⎡​1 3​−4 2​⎦⎤​ * ⎣⎡​4 -3​-2 2​⎦⎤​^(-1)

A = ⎣⎡​1 3​−4 2​⎦⎤​ * (1/20) * ⎣⎡​2 3​-2 4​⎦⎤​

A = (1/20) * ⎣⎡​12 + 3(-2) 13 + 34​−42 + 2(-2) −43 + 24​⎦⎤​

A = (1/20) * ⎣⎡​-4 15​-12 2​⎦⎤​

Therefore, matrix A is:

⎣⎡​-4/20 15/20​-12/20 2/20​⎦⎤​

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An approximation that is closest to the volume, in cubic centimeters, of the cone is: B. 340.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, we have the following;

Distance = √[(10 + 2)² + (-4 - 1)²]

Distance = √[(12)² + (-5)²]

Distance = √[144 + 25]

Distance = √169

Distance = 13 units.

Volume of cone, V = 1/3 × πr² × h

Volume of cone, V = 1/3 × 3.142 × 5² × 13

Volume of cone, V = 340.38 ≈ 340 cm³

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Yes, its a rectangle because it has one right angle. A rectangle is a shape having all sides 90° and pair of two opposite same sides.

Different arrangements of candidates are possible is 210.

Given:

There are 7 students on a team. if they must elect a president, a vice president, and a treasurer.

Number of arrangements = \(7_p_{3}\)

= 7!/(7-3)!

= 7!/4!

= 7*6*5*4! / 4!

= 7*6*5*1

= 42*5*1

= 42*5

= 210

Therefore Different arrangements of candidates are possible is 210.

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The amount accumulated after investing a principal P for t years at an interest rate compounded annually is  $46,057.58.

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.

\(A = p(1 + \frac{r}{n} )^{nt}\)

where

p = 15,500

r = 9.5%

t = 12

n = 1

\(A = 15500(1 + \frac{0.095}{1} )^{1(12)}\)

A = 15,500.00(1 + 0.095)¹²

A = $46,057.58

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$46,057.58, answer for acellus

Answer:

22, 24, and 26

Step-by-step explanation:

hope this helps!

The smallest possible whole-number length for the third side of the triangle is 3 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Triangle Inequality theorem simply states that the sum of two sides of a triangle must be greater than the third side.

Therefore, if the sides of a triangle are a, b and c. The following rules applies.

Hence, let the unknown sides be x. The triangle has two sides of length 11 and 9.

Therefore,

11 + 9 > x

11 + x > 9

9 + x > 11

Therefore, the smallest number to form the length of the third side is 3 units.

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To transform a score of 18 to standard scores, we use the formula for z-score:

z = (X - μ) / σ

where X is the score, μ is the mean, and σ is the standard deviation.

Using the given mean and standard deviation of the test (μ = 22, σ = 5), we can calculate the z-score for a score of 18:

z = (18 - 22) / 5 = -0.8

Now, let's transform this z-score to standard scores with different means and standard deviations:

a) For X = 100 and S = 15:

X' = μ + z * σ

X' = 100 + (-0.8) * 15

X' = 100 - 12

X' = 88

So, with a mean of 100 and a standard deviation of 15, the standardized score for a score of 18 is 88.

b) For X = 50 and S = 10:

X' = μ + z * σ

X' = 50 + (-0.8) * 10

X' = 50 - 8

X' = 42

With a mean of 50 and a standard deviation of 10, the standardized score for a score of 18 is 42.

c) For X = 10 and S = 2:

X' = μ + z * σ

X' = 10 + (-0.8) * 2

X' = 10 - 1.6

X' = 8.4

With a mean of 10 and a standard deviation of 2, the standardized score for a score of 18 is 8.4.

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The distance across the river is approximately 597 feet.

The Law of Cosines is a formula that connects a non-right triangle's sides and angles. When the lengths of two sides and the angle between them, or the lengths of all three sides, are known, it is used to determine the length of a side or measure of an angle.

For the given figure:

Using trigonometry, we can find the length of PR as follows:

tan(43) = QR/PS

PS = QR/tan(43)

tan(68) = QR/RU

RU = QR/tan(68)

Since PS + RU = PR,

PR = QR/tan(43) + QR/tan(68)

Since triangle PQR is a right triangle, we can use the Pythagorean theorem:

QR² = PS² + RU²

Substituting the expressions for PS and RU gives:

QR² = (QR/tan(43))² + (QR/tan(68))²

QR ≈ 325.4 feet

Now we can substitute this value into the expression for PR to get:

PR ≈ 596.7 feet (rounded to the nearest foot)

Therefore, the distance across the river is approximately 597 feet.

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The complete question is:

Answer:

no image or coordinates so people can't answer it

Step-by-step explanation:

Answer:

e= (4 1/2) divided by 2/5

=45/4= 11 1/4

Answer:

37/5

Step-by-step explanation:

7 2/5 = 37/5

5x7=35

35+2=37

Multiply the whole number and denominator then, add the numerator and put the sum of that back ontop of the denominator

Example:

W N/D   DxW=X  X+N= Y  

W N/D = Y/D

Answer:

\(\overline{DF}\) could be a midsegment of ∠ABC.

Step-by-step explanation:

A midsegment of a triangle must be two things:

1. Parallel to the 3rd side, in this case, \(\overline{AD}\).

2. Half the length of the 3rd side, in this case, \(\overline{AD}\).

Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to  \(\overline{AD}\) and it is \(\overline{DF}\).

Hope this helped!

Answer:7

Step-by-step explanation:

Answer:

20 m/s

Step-by-step explanation:

72000 m/hr

72000 m/3600 s

20 m/s

Answer:

20 m/s

Step-by-step explanation:

=> 72 km/hr

In changing the speed from km/hr to m/s, we multiply by \(\frac{10}{36}\)

So,

=> 72 × \(\frac{10}{36}\)

=> 2 × 10

=> 20 m/s

Answer:

Step-by-step explanation By verified ✔️

So The answer for this question is 6cm

The p-value based on a standard normal distribution for z = -1.86 and Ha: p < 0.5 is 0.031.

To find the p-value based on a standard normal distribution for a given test statistic and alternative hypothesis.

We need to calculate the probability of obtaining a test statistic as extreme as the observed value or more extreme under the null hypothesis.

In this case, the test statistic is z = -1.86 and the alternative hypothesis is Ha: p < 0.5.

Since the alternative hypothesis is one-sided (p < 0.5), we are interested in the probability of obtaining a test statistic smaller than -1.86.

To find the p-value, we can use a standard normal distribution table or a calculator to determine the cumulative probability to the left of -1.86.

Looking up the z-score -1.86 in a standard normal distribution table or using a calculator, we find that the cumulative probability to the left of -1.86 is approximately 0.031.

Therefore, P-value: 0.031

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The standard form of a linear equation is Ax+By=C, where A, B. and C are integer.

The  standard form of a linear equation can be seen in the question above, which is been written as  Ax+By=C.  however the equation can be changed  i.e the one that is been written in slope-intercept form (y=mx+b) .

This can be charged to the to standard form,  however the x and y on the same side must be found.

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a) 10 additional days are required for both to cost the same.

b) The cost is 70$.

At Johan's Rental:

Rent= (50+2x)$

At Martinez Rent:

Rent= (30+4x)$

For both the cost same

By using Elimination method,

50+2x = 30+4x

50-30 = 4x-2x

20 = 2x

x = 10

10 additional days are required for both to cost the same.

Cost = 50+2x

= 50+2*10

=50+20

=70.

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a. The equation that represents the given data is y = 700x + 2,000.

b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.

We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.

We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.

(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)

(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)

(y - 30,000) = [(14,000)/(20)]*(x - 40)

(y - 30,000) = (700)*(x - 40)

y = 700x - 28,000 + 30,000

y = 700x + 2,000

Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.

y = 700*80 + 2,000

y = 56,000 + 2,000

y = 58,000

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The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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Answer:

k = - \(\frac{16}{15}\)

Step-by-step explanation:

Since x = - 2 is a zero , then p(- 2) = 0 , that is

2(- 2)² - 3(- 2)(5k + 4) = 0

2(4) + 6(5k + 4) = 0 ← distribute parenthesis

8 + 30k + 24 = 0

30k + 32 = 0 ( subtract 32 from both sides )

30k = - 32 ( divide both sides by 30 )

k = \(\frac{-32}{30}\) = - \(\frac{16}{15}\)

Given Polynomial P(x) = 2x^2-3x(5k+4)

Zero = -2

We know that

If -2 is zero of the Polynomial then it satisfies the given Polynomial

⇛P(-2) = 0

⇛ 2(-2)^2-3(-2)(5k+4)=0

⇛ 2(4)+6(5k+4) = 0

⇛ 8+30k+24 = 0

⇛ 30k+32 = 0

⇛ 30 k = -32

⇛ k = -32/30

⇛ k = -16/15

Answer:- The value of k = -16/15.

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9514 1404 393

Answer:

  C  3

Step-by-step explanation:

The first function is given in slope-intercept form:

  y = mx + b

When we compare this to the given equation, we see the y-intercept is 4.

__

The table represents a function with a slope of ...

  m = (y2 -y1)/(x2 -x1) = (32 -17)/(5 -2) = 15/3 = 5

Then the y-intercept can be found from ...

  b = y1 -m(x1)

  b = 17 -5(2) = 7

The table is a function with a y-intercept of 7.

__

The difference between the y-intercepts of the two functions is ...

  7 - 4 = 3 . . . difference of y-intercepts