Simultaneous Equations
y=x-2
y=3x+5

Answer:

(gof)(x) = 14x + 1

Step-by-step explanation:

We can think of (gof)(x) as g(f(x)).  Writing it in this form shows that we must start with the inner function and work our way to the outer function.

Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.

f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1

Now, this output becomes the input for g(x):

g(2x-1) = 7(2x - 1) + 8

14x -7 + 8

(gof)(x) = 14x + 1

Part 1: a. A. The sample size needs to be greater than or equal to 30.

Part 2: The probability is approximately 0.0013.

Part 3: There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.

The number of individuals or items in a population that are selected for study.

A. The sample size needs to be greater than or equal to 30.

This is due to the Central Limit Theorem, which states that the sample size of a normal distribution must be 30 or more to produce reliable results.

If a sample size is less than 30, the results may be skewed and not accurately represent the true population mean and standard deviation.

B. The probability is approximately 0.0013.

This probability can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.

The z-score for a sample mean of 15 minutes =-3.3,

which translates to a probability of 0.0013 using the z-score table.

C. There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.

This can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.

The z-score for a 10% chance= -1.28,

which translates to a mean oil-change time of 14.9 minutes.

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The exponential equation represents a growth, and the rate of increase is 9%.

The general exponential equation is written as:

y = A*(1 + r)^x

Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).

Here we have:

y = 38*(1.09)^x

We can rewrite this as:

y = 38*(1 + 0.09)^x

So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:

100%*0.09 = 9%

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Answer:forgot the explanation

Step-by-step explanation: give me a equation to solve

Slope is zero and the y-intercept is (0,-5)

What is slope ?

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.

In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.

The formula for calculating slope is:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing the equation Y = -5 to y = mx + b, we can see that:

The slope, m, is 0, since there is no x-term in the equation.

The y-intercept, b, is -5, since that is the constant value in the equation.

Therefore, the correct answer is:

B. Slope is zero and the y-intercept is (0,-5)


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Final Answer: The critical number is x = DNE. The absolute maximum is x = 0.2, and y = -125.The absolute minimum does not exist on the interval.

we need to find the values of x where the derivative of y equals zero or does not exist. So, we first find the derivative of y: y' = 10x^{(-3)}

The derivative is defined for all x in the interval [0.2, 2], so there are no points where the derivative does not exist.

To find where y' = 0, we set the derivative equal to zero and solve for x: [tex]10x^{(-3)} = 0[/tex] x = DNE There are no critical numbers since the derivative does not equal zero at any point in the interval.

Next, we check the endpoints of the interval: [tex]y(0.2) = -5/ (0.2^2) =[/tex] [tex]-125y(2) = -5/(2^2) = -1.25[/tex] Since y is a decreasing function on the interval,

the absolute maximum occurs at the left endpoint x=0.2: Absolute maximum: [tex]y(-0.2) = -125[/tex]

Since y is an unbounded function as x approaches zero, there is no absolute minimum on the interval [0.2, 2].

Final Answer: The critical number is x = DNE.The absolute maximum is x = 0.2, and y = -125.The absolute minimum does not exist on the interval.

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Answer:

D

Step-by-step explanation:

The curve will be wider but the vertex would be in the same position.

If a<1, our function will be wider

If a>1, the function will be more narrow

The correct answer is D

Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

Answer:  mBED = 2(42°) = 84°

Step-by-step explanation:
  We are asked to find the measure of the central angle ∠BED in the circle given that the measure of the minor arc BD is 42°.

We can use the formula that states that the measure of a central angle is equal to twice the measure of its intercepted arc. That is,

m∠BED = 2*mBD

We can substitute the value of mBD, which is 42°, into our equation.

m∠BED = 2*42°

m∠BED = 84°

Therefore, the measure of the central angle ∠BED is 84°.

Answer:1 and 2

Step-by-step explanation:

so, they asked 50 students and then that was later broke down to smaller groups.

10,15,25

so, for every 10 students will be one. 1 vote= 10 students.

also, the dinosaur had the greatest number of votes so that explains answer 2.

Answer:

Dragonflies

Step-by-step explanation:

They can fly on top of the water, but also, they have the fastest turns per second for their wings.

the account balance after 12 years of continuous compounding at 7% annual interest, assuming no additional deposits or withdrawals are made, would be $32,447.44.

The formula for continuous compounding is:

A = P[tex]e^(rt)[/tex]

where:

A = the final amount

P = the principal amount (initial investment)

e = the mathematical constant approximately equal to 2.71828

r = the annual interest rate

t = the time in years

Plugging in the given values, we get:

A = 14000[tex]e^(0.0712)[/tex]

A = 14000*[tex]e^0.84[/tex]

A = 14000*2.31796

A = $32,447.44

Compound interest is a type of interest that is calculated not only on the initial principal amount, but also on the accumulated interest from previous periods. In other words, interest is added to the principal amount, and then interest is calculated on the new total amount.

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The value of y and z are 11 and 11.

We can see from the diagram that the two triangles are of equal lengths.

To determine the value of the variables, we have to note that;

In triangle QRS, the adjacent sides is y + 20

In triangle VX, the adjacent side is y = 31

Now, equate the values

y + 20 = 31

collect like terms

y = 31 -20

y = 11

Also, the hypotenuse sides are equivalent, then

y + 3z + 28 = 6y + z - 5

collect the like terms

y - 6y + 3z - z = -5 - 28

add or subtract the values

-5y + 2z = -33

Substitute the values

2z = -33 + 55

2z = 22

z = 11

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We need to add a volume of 39.69 fluid ounces of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.

Mensuration is the branch of mathematics concerned with the measurement of geometric figures and parameters such as length, volume, shape, surface area, and lateral area. 

According to information in the question:

The mixture is 40 parts gasoline and 1 part oil, there are 40 + 1 = 41 parts in total.

Let, the amount of oil in the mixture "x".

We know that there are 2 and 1/2 gallons of the mixture, which is the same as 2.5 * 128 = 320 fluid ounces.

So, the equation which can be formed is

x/41 * 320 = the amount of oil in the mixture (in fluid ounces)

Solving for "x":

x/41 * 320 = x/41 * 50 + 320 - (x/41 * 50)

Multiplying both sides by 41:

x * 320 = 50x + 41(320 - 50x)

Simplifying:

320x = 41(320)

x = 41 * 10 = 410 (fluid ounces of oil in the mixture)

Thus, amount of gasoline in the mixture is

40 parts gasoline / 41 parts total * 320 fluid ounces = 311.22 fluid ounces of gasoline.

Let the gasoline we need be "y", so a equation can be formed as follows

(311.22 + y)/(41 + y) * 320 = 410

Solving for y:

(311.22 + y)/(41 + y) = 410/320

Multiplying both sides by (41 + y) * 320:

311.22 + y = 410/320 * (41 + y) * 320

Simplifying:

311.22 + y = 205.625 * (41 + y)

311.22 + y = 8434.375 + 205.625y

Solving for y:

204.625y = 8123.155

y = 39.69 (fluid ounces of gasoline to add)

Therefore, we need to add 39.69 fluid ounces volume of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.

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Answer:

To calculate the surface area of an object, we need to know its shape. Please provide more information on the object's shape or context of the problem to calculate its surface area.

[tex]\sqrt{144} =12\\12*12=144[/tex]

Answer:

2/3

Step-by-step explanation:

A six sided number cube :

Sample space = 1,2,3,4,5,6

Non composite numbers on a six sided number cube = 1,2,3,5

Probability of an event = required outcome / Total possible outcomes

Required outcome = number of non composite number = 4

Total possible outcomes = sample space = 6

P(not composite)= 4/6 = 2/3

Answer:

Step-by-step explanation:

Yes, that's correct!

3/5 can be simplified to 12/20 by multiplying the numerator and denominator by 4:

3/5 x 4/4 = 12/20

And 1/20 is already in its simplest form, so it is equal to 1/20.

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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The answer to the puzzle is (3)O (7)N which makes word ON, (4)T (10)H (1)E which makes word THE, (6)B (8)E (2)A (9)C (5)H which makes the word BEACH

What is a quadrilateral?

A quadrilateral is a 4 sided polygon. On the basis of its properties quadrilaterals are classified as Trapezium,Kite, Parallelogram, Rectangle, Rhombus and square.

Complete the sentence:

1.Parallelogram-(E)

2.Quadrilateral-(A)

3.Supplementary-(O)

4.Bisect-(T)

5.Congruent-(H)

Using the diagram:

6.Given that KG=17 units, KJ=14 units.

As we know from the figure, GH is congruent to KJ and HJ is congruent to side KG.

Therefore, GH=KJ=14units- (B)

7.∠GKJ=86° and ∠GHJ=(x+6)°

We know that ∠GKJ is congruent to ∠GHJ

Therefore, x+6 = 86

                      x=86-6

                      x=80-(N)

8.Given KH=20 & KF= KH÷2  {diagonal pf parallelogram bisect}

                                  =20 ÷ 2

                                  =10 units-(E)

9.Given ∠HJK=82° & We know ∠HJK+∠GKJ=180°  {consecutive angles}

                                                               ∠GKJ=180-∠HJK

                                                                         =180-82

                                                                         =98°-(C)

10.Give that, ∠HJK=82° & we know  ∠HGK=∠HJK {opposite angles of parallelogram}

                                                            ∠HGK=82°-(H)

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Answer:

 To find the total number of shirts that would make the total cost for each company the same, we can set the two equations equal to each other and solve for the number of shirts:

Red Nose: t = 3.50r + 79

Green Machine: t = 5r + 40

3.50r + 79 = 5r + 40

Subtracting 3.50r from both sides, we get:

79 = 1.50r + 40

Subtracting 40 from both sides, we get:

39 = 1.50r

Dividing both sides by 1.50, we get:

r = 26

So the total cost for each company would be the same if 26 shirts are ordered.

To find the total cost for each company when 26 shirts are ordered, we can substitute 26 for r in each equation:

Red Nose: t = 3.50(26) + 79 = $192

Green Machine: t = 5(26) + 40 = $170

Therefore, if 26 shirts are ordered, the total cost would be $192 for Red Nose and $170 for Green Machine.

The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.

So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:

(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons

Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be  approximately 6.58 gallons.

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The complete question is :

What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?

The statements that are true regarding the diagram given are:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

We have in the diagram that in the diagram given, the statements that are all true are:

m∠3 + m∠4 = 180° (angles on a straight line)

m∠4 = m∠1 + m∠2 (external angle theorem)

m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).

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Answer:

7/8 - 2/3 = 5/8 pint of water left in the bottle.

Answer: 46

Step-by-step explanation: i took quiz i swear the answer is

Answer:

1 solution

Step-by-step explanation:

Y = 4

Y = 4x - 1

Substitute value of Y here,

4 = 4x - 1

4 + 1 = 4x

5 = 4x

5/4 = x

1.25 = x

•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.

______

hope this helps!

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

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Answer: 15 of those teachers are men

Step-by-step explanation: 2 out of 3, is of course written as 2/3

if 2/3 are women, this means 2/3 of 45 is 30, meaning 30 of the teachers are women, so if 30/45 are women, the remaining 15 are men