What equation represents a line that passes through points (-1,2) and (3,1)
4x - y = -6
X + 4y = 7
X - 4y = -9
4x + y = 2

Answer:

here's your answer step by step explanation

Step-by-step explanation:

page 6 is missing comment me i will send you page 6

The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.

An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.

A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development.  Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.

Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.

From &22 = x²y 2

2

Given 2²+7+2=5

= <**,4),2=>

By Logange's multijet

(2643805 = 12'aresta

Mithaling by by and

and y

x²²* = P ←

: +(1,2,2) = $

= 125

279

The maximum value is 12r

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Answer: 9 diagonals

Step-by-step explanation:

Concluding, the end behavior is:

as x ⇒ ∞, f(x) ⇒ -∞

as x ⇒ -∞, f(x) ⇒ ∞

Here we have the function:

[tex]f(x) = -2*\sqrt[3]{x}[/tex]

When we evaluate the function in x that tends to positive infinity, the cubic root also tends to infinity, while because of the negative factor that multiplies it, we conclude that the end behavior is:

as x ⇒ ∞, f(x) ⇒ -∞

When x tends to negative infinity, the opposite happens:

as x ⇒ -∞, f(x) ⇒ ∞

Concluding, the end behavior is:

as x ⇒ ∞, f(x) ⇒ -∞

as x ⇒ -∞, f(x) ⇒ ∞

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Answer: 6

Step-by-step explanation: Since we substitute the b with 7, 10-7= 3. Since the 2 is next to the parentheses, we multiply 3 by 2, getting 6.

Hey there!

2(10 - b)

= 2(10 - 7)

= 2(10) + 2(-7)

= 20 - 14

= 6

OR

2(10 - b)

= 2(10 - 7)

= 2(3)

= 6

Therefore, your answer should be: 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

In this question we must determine both the surface area and the number of shingles to cover two roof configurations as well. In the first case, we calculate the surface area, which is the sum of the area of rectangles:

A = 2 · (8 ft) · (12 ft) + 2 · (6 ft) · (12 ft)

A = 336 ft²

And the number of shingles required to cover the root is:

n = (336 ft²) / (4 ft²)

n = 84

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

In the second, we only need to cover the very top surface. The area and the number of shingles are, respectively:

A = 2 · (5 ft) · (22 ft)

A = 220 ft²

n = (220 ft²) / (2 ft²)

n = 110

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

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Answer:Many

Step-by-step explanation:

As the unknown cancels itself out, it could be absolutely any number. So there are many solutions.

Answer + Step-by-step explanation:

(a)

Check the attached image.

(b)

Range of sample means : 7.5 - 5.75 = 1.25

(c)

The closer the range of the sample means is to 0 ,

the more confident they can be in their estimate . [tex]\huge \checkmark[/tex]

The farther the range of the sample means is from 0 ,

the more confident they can be in their estimate . 

The mean of the sample means will tend to be a better estimate

than a single sample mean . [tex]\huge \checkmark[/tex]

A single sample mean will tend to be a better estimate

than the mean of the sample means .

Answer:

j = 7.8.

Step-by-step explanation:

The slope of the line = difference in y-values / corresponding difference in x-values.

Slope = (7-3) / (j-5) = 10/7

so 10(j - 5) = 7*4

10j - 50 = 28

10j = 78

j = 7.8.

The equation of the line from give points is y = 2/3x - 5/3.

According to the statement

We have given that the two points which are (-2,-3) and (4,1)

And we have to find the equation of a line that passes through the given points.

So,For this purpose,

First, we need to determine the slope of the line. The slope can be found by using the formula:

[tex]m = \frac{(y_2) -(y_1)}{(x_2) -(x_1)}[/tex]

Where

m is the slope and

Substituting the values from the points in the problem gives:

m = 1 + 3 /4 + 2

m = 4/6

m = 2/3.

And then

Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:

[tex]y - (y_1) = m(x -x_1)[/tex]

Put the values in it then

y - (-3) = 2/3 (x-(-2))

y +3 = 2/3 (x +2)

3y + 9 = 2x + 4

3y - 2x = 4 -9

3y -2x = -5

3y = 2x - 5

y = 2/3x - 5/3.

So, The equation of the line from give points is y = 2/3x - 5/3.

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Answer:

x = 35.

Step-by-step explanation:

since they are odd, the second number isn't x + 1, it is x + 2.

x + x + 2 = 72

2x + 2 = 72

2x = 70

x = 35

Answer:

144π or 452.16 units³

Step-by-step explanation:

The formula for volume of a cylinder is [tex]\pi r^2 h[/tex]. We can use the given values for radius and height to find the volume of the cylinder.

[tex]V=\pi r^2 h\\V=\pi6^2(4)\\V=\pi36(4)\\V=144\pi \ OR\ 452.16[/tex]

The volume of the cylinder is 144π or 452.16 units³.

Answer:

d

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral sum to 180° , that is

∠ ABD + ∠ ACD = 180°

∠ ABD + 48° = 180° ( subtract 48° from both sides )

∠ ABD = 132°

Step-by-step explanation:

4x + 10 = -2 + 4

4x = -2 + 4 - 10

4x = -8

x = -2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{4x + 10 = -2+ 4}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{4x + 10 = 2}[/tex]

[tex]\huge\textbf{Subtract 10 to both sides:}[/tex]

[tex]\mathsf{4x + 10 - 10 = 2 - 10}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{4x = 2 - 10}[/tex]

[tex]\mathsf{4x = -8}[/tex]

[tex]\huge\textbf{Divide 4 to both sides:}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{-8}{4}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{-8}{4}}[/tex]

[tex]\mathsf{x = -2}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:   100 square cm

Step-by-step explanation:   the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.

Answer: 104

Step-by-step explanation:

area of trangle =33 because 6*11/2=33

area of rectangle 9*7=63

area of rectangle  2*2=4

33+63+4=100^2

The probability of p(2 aces) is greater than the probability of p(3 diamonds).

Probability is the chance of happening an event or incident. The probability of an event can be calculated by the ratio of the number of favorable events to the total number of events in that sample space.

A deck of cards always has 52 cards.

Out of those 52 cards, there are 4 different aces.

The deck of cards also contains 13 diamonds.

Therefore, the probability of p(2 aces) is the probability of getting at least 2 aces in that 5-card hand is = 2/4 = 1/2 = 13/26.

Now, the probability of p(3 diamonds) is the probability of getting at least 3 diamonds in that 5-card hand is= 3/13 = 6/26.

If we compare these two probabilities, it is clear that the probability of p(2 aces) is greater than the probability of p(3 diamonds).

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The algebraic expression of the statement is 4x + 6

The statement is given as:

The sum of four times a number and six

Rewrite as:

The sum of 4 times a number and 6

Let the number be x

So, we have

The sum of 4 times x and 6

Evaluate the product

The sum of 4x and 6

Evaluate the sum

4x + 6

Hence, the algebraic expression of the statement is 4x + 6

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Answer:

the answer is 1,2,4,5 and 7.

Answer: The answer is A,B,D,E,G

Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.

Answer:

a₁ = 5

a₂ = 8

a₃ = 13

a₄ = 20

Step-by-step explanation:

Given sequence formula

aₙ = n² + 4

Requirement of the question

Find the 4 terms in the sequence

Substitute 4 values into the sequence formula

a₁ = (1)² + 4 = 1 + 4 = [tex]\Large\boxed{5}[/tex]

a₂ = (2)² + 4 = 4 + 4 = [tex]\Large\boxed{8}[/tex]

a₃ = (3)² + 4 = 9 + 4 = [tex]\Large\boxed{13}[/tex]

a₄ = (4)² + 4 = 16 + 4 = [tex]\Large\boxed{20}[/tex]

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The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:

To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:

The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k

Where (h, k) is the vertex of the parabola, a is constant.

For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.

We will find a using f(-7) = 8:

The quadratic function for the sailboat is given by:

The equation for a circle with a radius of 5 and center (1, 2) is:

Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:

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The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

The expression of the equation will be:

x² - 8x = x(x - 8)

x² - 10x = x(x - 10)

x² - 5x = x(x - 5)

x² - 3x = x(x - 3)

It should be noted that an equation simply means the expression of the variables that are given.

In this case, the following can be represented:

x² - 8x = x(x - 8)

x² - 10x = x(x - 10)

x² - 5x = x(x - 5)

x² - 3x = x(x - 3)

This is illustrated above.

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If the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.

Given a function of x f(x)=1/(6x+6).

We are told to find out the value of the variable x for which the function does not lie.

Function is like a relationship between two or more variables expressed in equal to form. The values entered in a function is known as domain and the values which we get after entering of values are known as range.

f(x)=1/(6x+6)

It is in form of fraction. Fraction is a combination of numbers in which the above number is numerator and below number is denominator.

In this (6x+6) cannot be equal to 0 because if (6x+6) equal to 0 then the value of function becomes infinity.

So,

6x+6=0

6x=-6

x=-1

Hence if the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.

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The probability that the service time will be more than three minutes is 0.3012.

Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,

The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.

At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,

[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]

E(x)=1/θ

θ=1/2.5

θ=0.4

The probability that the service time will be longer than three minutes:

[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]

Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.

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Answer: -9

Step-by-step explanation:  You might think that the smallest two numbers are 11 and 1 but there are negative numbers. 1 - (-9) is equal to 10. 1 x (-9) is -9.

The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

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Answer: A

Step-by-step explanation:

Let f(y)=x.

[tex]x=\frac{y+2}{7}\\\\7x=y+2\\\\y=7x-2\\\\f^{-1}(x)=7x-2[/tex]

The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

The given coordinates on the graph are;

(-3, 0), (0, 3), (2, 4), and (5, 5)

The coordinates of the starting point of the graph = (-3, 0)

Shape of the graph = Extends from point (-3, 0), upwards and to the right

Therefore;

As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.

However, given that the graph is for a square root function, the correct option is option C;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

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Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

The most general antiderivative of the given function g(t) is (8t + t³/3 + t²/2 + c).

The antiderivative of a function is the inverse function of a derivative.

This inverse function of the derivative is called integration.

Here the given function is: g(t) = 8 + t² + t

Therefore, the antiderivative of the given function is

∫g(t) dt

= ∫(8 + t² + t) dt

= ∫8 dt + ∫t² dt + ∫t dt

= [8t⁽⁰⁺¹⁾/(0+1) + t⁽²⁺¹⁾/(2+1) + t⁽¹⁺¹⁾/(1+1) + c]

= (8t + t³/3 + t²/2 + c)

Here 'c' is the constant.

Again, differentiating the result, we get:

d/dt(8t + t³/3 + t²/2 + c)

= [8 ˣ 1 ˣ t⁽¹⁻¹⁾ + 3 ˣ t⁽³⁻¹⁾/3 + 2 ˣ t⁽²⁻¹⁾/2 + 0]

= 8 + t² + t

= g(t)

The antiderivative of the given function g(t)is (8t + t³/3 + t²/2 + c).

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Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

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