Which choice is a solution to this system of equations? -x=y-4 y=4x+9

Answer:

D. 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

B :10/(x+1)  +5

Answer:

  x = √65

Step-by-step explanation:

You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.

The Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.

  x² = 4² +7² . . . . . . . . . Pythagorean relation

  x² = 16 +49 = 65 . . . evaluate the expression

  x = √65 . . . . . . . . . . take the square root

Given parameters:

   Coordinates of the points =  (3,4) and (19, 16)

Unknown:

The distance between the points = ?

The midpoint  = ?

Solution:

  The distance between two points can be mathematically solved using;

    D  = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }\)

 where  x₁  = 3, x₂  = 19  and y₁  = 4, y₂  = 16

Input the parameters and solve;

   D  = \(\sqrt{(19 - 3)^{2} + (16 - 4)^{2} }\)   = 20

Midpoint;

    The expression is given as;

     x\(_{m}\) , y\(_{m}\)  = \(\frac{x_{1} + x_{2} }{2}\)  , \(\frac{y_{1} + y_{2} }{2}\)

         input the parameters and solve;

                   = \(\frac{3 + 19}{2}\)  , \(\frac{4 + 16}{2}\)

                   = 11 , 10

The midpoint is (11, 10)

Answer:

The rate of change is of of the area when the radius is 4 centimeters \(48\pi\) square centimeters.

Step-by-step explanation:

Area of a circle:

The area of a circle of radius r is given by:

\(A = \pi r^2\)

Implicit derivative:

To solve this question, we have to derivate implictly the equation as a function of t. Thus:

\(\frac{dA}{dt} = 2\pi r \frac{dr}{dt}\)

The radius of a circle is increasing at a rate of 6 centimeters per minute.

This means that \(\frac{dr}{dt} = 6\)

Find the rate of change of the area when the radius is 4 centimeters.

This is \(\frac{dA}{dt}\) when \(r = 4\). Thus

\(\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 2\pi(4)(6) = 48\pi\)

The rate of change is of of the area when the radius is 4 centimeters \(48\pi\) square centimeters.

This equation represents a parabola. we can find the vertex of this parabola in order to know what's the value to make the maximum profit.

For a equation of the form:

The vertex V(h,k) is given by:

for:

so:

Answer:

Answer:

domain is just all of the x values while range is all of the y values

so domian is

1,2,3,5,7,8

there are 2  5's but you only put 1

never put two of the same number for range or domain

Step-by-step explanation:

Part A: We can complete the model representing Sage's minutes by putting n and 7 in the box.

Part B: We can complete the model representing Tom's minutes by putting n and 7 in the box

Part C: An algebraic expression to represent the number of minutes Sage has left is S = n - 7, where S equals the remaining talk minutes for Sage and n is the initial number of talk minutes.

Part D. An algebraic expression to represent the number of minutes Tom has left is T = n - 7, where T equals the remaining talk minutes for Tom and n is the initial number of talk minutes.

Part E: Sage and Tom have the same number of talk minutes left on their cell phone plans because they started with the same amount and consumed the same amount at the end of the month.

An algebraic expression is a mathematical expression that consists of variables and constants, along with algebraic operations and equality or inequality symbols.

The basic algebraic operations include addition, subtraction, division, and multiplication.

Thus, algebraic expressions can be used to mathematically model or represent the number of minutes that Sage and Tom have left.

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Answer:

only 1 is the factor as 11 is a prime number

Answer:

c

Step-by-step explanation:

Answer: Answer C x^2+(y-4)^2=16

Step-by-step explanation:

on edge 2023

Answer:

n = 21

Step-by-step explanation:

12 = n - 9

12 + 9 = n - 9 + 9

12 + 9 = n

21 = n

So, the value of n is 21

Answer:

n = 21

Step-by-step explanation:

Let's simplify this.

First, we reorder the terms.

12 = n - 9

n - 9 = 12

Add 9 to both sides.

n = 12 + 9

For now I am going to focus on the right side.

n = 21

Therefore, n = 21 is the answer.

Answer:

x≤43

Step-by-step explanation:

22+6x ≤ 280

subtract 22 from both sides

6x ≤ 258

divide both sides by 6

x ≤ 43

Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

Step-by-step explanation:

70 ÷ 3 = 23  1/3

Answer:

1 hour and 30 minutes

Step-by-step explanation:

I think this because it said his top speed was 20,000 and he flew 30,000 if you add another 20,000 to the 20,000 he flew in 30,000 you would get 40,000 which is 2 hours so 1 hour and 30 min. Hope it Helped!

Answer:

D

Step-by-step explanation:

Absolute value is the distance from a point 0. Absolute value is always a positibe number, so think of all of these as positive numbers

Answer:A. 8.5 ft

Step-by-step explanation:

edge2021

The width of the footpath is 8.5 feet.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

given equation is :x² + y² = (r)²

We have for the pool:

x²  +  y²  = 2500      or   x²  +  y²  = (50)²

So, for the outside edge of the footpath

x²  +  y²  = 3422.25  or x² + y²  = (58.5)²

So, we find the radius of each circumference

r₁  = 50 feet

r₂ = 58,5  feet

58,5  - 50  =  8,5 feet

Thus, width of the footpath is 8.5 feet.

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Answer:

Step-by-step explanation:

Let's start by using the formula for the perimeter of a rectangle:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width.

We are given that the perimeter is 70 cm, so we can substitute this in the formula:

70 = 2L + 2W

Dividing both sides by 2, we get:

35 = L + W

We are also given that the length is six times the width, so we can write:

L = 6W

Substituting this in the equation we just derived, we get:

35 = 6W + W

Simplifying, we get:

35 = 7W

Dividing both sides by 7, we get:

W = 5

So the width of the rectangle is 5 cm.

Using the equation L = 6W, we can find the length:

L = 6 x 5 = 30

So the length of the rectangle is 30 cm.

Therefore, the length of the rectangle is 30 cm and the width is 5 cm.

Answer:

19

Step-by-step explanation:

Don't swear to god jeez

Answer:

19

Step-by-step explanation:

Unless you're referring to the vine, then 9+10= 19.

If you are referring to the vine of 9+10, then its 21

Answer:

300+40+7

Step-by-step explanation:

The force in the rod when the temperature is 150 °F is 718.72 pounds-force.

Let suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force (\(F\)), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.

Given simmetry considerations, we derive an expression for the spring force (\(F\)), in pounds-force,  as a sum of mechanical and thermal effects by principle of superposition:

\(F = k\cdot (\Delta x + 0.5\cdot \Delta l)\)   (1)

Where:

The rod elongation is described by the following thermal dilatation formula:

\(\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})\)   (2)

Where:

If we know \(k = 1000\,\frac{lb}{in}\), \(\Delta x = 0.7\,in\), \(\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}\), \(L_{o} = 48\,in\), \(T_{o} = 30\,^{\circ}F\) and \(T_{f} = 150\,^{\circ}F\), then the force in the rod at final temperature is:

\(F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right]\)

\(F = 718.72\,lbf\)

The force in the rod when the temperature is 150 °F is 718.72 pounds-force. \(\blacksquare\)

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Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

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

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

Answer:

\(\displaystyle x = \frac{Uk}{v + w}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

\(\displaystyle U = \frac{x(v + w)}{k}\)

Step 2: Solve for x

The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

From the complete question, we understand that Mr. A wants to plays the game until he wins

This means that

He might win at the first game and he might win after n attempts

So, the values of X are

X = 0, 1, 2, 3, 4.......n

Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1

The probability of x is represented as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, the probability that X = n is:

P(n) = nCn * p^n * (1 - p)^(n - n)

Evaluate the exponent

P(n) = nCn * p^n * 1

Evaluate the combination expression

P(n) = 1 * p^n * 1

This gives

P(n) = p^n

Hence, the probability that X = n is p^n

The distribution satisfies PMF conditions because

The expected value E(x) is calculated using

E(x) = n * p

So, we have:

E(x) = np

Hence, the value of E(x) is np

The variance V(x) is calculated using

V(x) = √n * p * (1 - p)

So, we have:

V(x) = √np(1 - p)

Hence, the value of V(x) is √np(1 - p)

The memoryless property of X is that each probability of X is independent

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Step-by-step explanation:

perimeter of a rectangle = 2×length + 2×width = 28 ft

width = length - 2

length = width + 2

2×(width + 2) + 2×width = 28

2×width + 4 + 2×width = 28

4×width + 4 = 28

4×width = 24

width = 6 ft

and the length is width + 2 = 6+2 = 8 ft.

Answer:

Step-by-step explanation:

Hello!

The Psychomotor Development Index (PDI) has an average value of μ= 100

The Mental Development Index (MDI) has an average value of μ= 100

At an approximate age of 1 year of normal healthy infants.

Using the group data set heart = 1 for all calculations (see attachment for complete table), you can define two variables of interest and obtain the descriptive statistics:

X₁: PDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₁= 69

X[bar]₁= 97.61

S₁= 14.73

X₂: MDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₂= 69

X[bar]₂= 106.33

S₂= 14.67

a)

You have to test the hypothesis that the average PDI for kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

H₀: μ₁ = 100

H₁: μ₁ ≠ 100

α: 0.05

\(Z= \frac{X[bar]_1-Mu_1}{\frac{S_1}{\sqrt{n_1} } }\)≈N(0;1)

\(Z_{H_0}= \frac{97.61-100}{\frac{14.73}{\sqrt{69} } } = -1.347\)

p-value: 0.17798

Using this approach the decision rule is:

The p-value is greater than the level of significance, the decision is to not reject the null hypothesis. Then the average PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

b)

H₀: μ₂ = 100

H₁: μ₂ ≠ 100

α: 0.05

\(Z= \frac{X[bar]_2-Mu_2}{\frac{S_2}{\sqrt{n_2} } }\)≈N(0;1)

\(Z_{H_0}= \frac{106.33-100}{\frac{14.67}{\sqrt{69} } } = 3.584\)

p-value: 0.000338

Using this approach the decision rule is:

The p-value is less than the level of significance, the decision is to reject the null hypothesis. Then the average MDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is different from 100.

c)

\(Z_{1-\alpha /2}= Z_{0.975}= 1.96\)

95% CI for PDI

X[bar]₁ ± \(Z_{1-\alpha /2}\) * \(\frac{S_1}{\sqrt{n_1} }\)

97.61 ± 1.96 * \(\frac{14.73}{\sqrt{69} }\)

[94.134; 101.086]

95% CI for MDI

X[bar]₂ ± \(Z_{1-\alpha /2}\) * \(\frac{S_2}{\sqrt{n_2} }\)

106.33 ± 1.96 * \(\frac{14.67}{\sqrt{69} }\)

[102.869; 109.791]

The CI for the mean PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life contains 100, this is to be expected since the null hypothesis in the hypothesis test made at complementary confidence level, was not rejected.

I hope this helps!

Answer:

100% = 65 Gallons; 70% = 45.5 Gallons

Step-by-step explanation:

The important piece of information here is that 13 gallons of water makes the container 1/5 of the way full, aka 20%.  If the question is simply, how many gallons will it hold, then we multiply 13 by 5 to get 100% at 65 gallons.  To get the amount held at 7/10, or 70%, we simply multiply 65 with 7/10 to get 45.5 gallons.

Cheers.

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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