Mathematics High School

Please answer this :(

Answers

Answer 1

Answer:

a = 4, b = 5

Step-by-step explanation:

we need to complete the square to get it in that form.

x^2 - 8x + 21

= x^2 - 8x + 16 + 5

= (x-4)^2 + 5

a = 4, b = 5

Related Questions

!!PLEASE HELP ASAP!!
The function g(x) is the height of a football x seconds after it is thrown in the air. The
football reaches its maximum height of 28 feet in 6 seconds, and hits the ground at
12 seconds.
What is the practical domain for the function f(x)?
Type your answer in interval notation.

Answers

Answer:

[0,12]

Step-by-step explanation:

The unit of the domain is seconds

x is greater than or equal to zero because time can't be negative

Time stops at 12 seconds since the ball hits the ground.

Brackets are used to include both 0 and 12 as values

The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l.

l = S – r2
l = S + r2
l = l equals StartFraction S Over pi minus r squared. – r2
l = l equals StartFraction S Over pi plus r squared. + r2

Answers

Answer:

The answer is:

[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]

Step-by-step explanation:

In order to determine the solution for I, we have to know about the equations.

In any equation there are variables. If we want to determine the value of one of them, we have to free that variable in any side of the equation.

Regarding the surface of a cone, i have attached an image that shows the real formula of the surface of a cone, We can see that in this case:

[tex]l=rI[/tex]

So, we have the next formula and we want to l:

[tex]S=\pi l+\pi r^2[/tex]

[tex]S-\pi r^2=\pi l[/tex]

[tex]\dfrac{S-\pi r^2}{\pi }=l[/tex]

Finally the solution for I is:

[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]

The volume of a triangle

Answers

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{9\times 7}{63}\\ h=6 \end{cases}\implies V=\cfrac{(63)(6)}{3}\implies V=126~cm^3[/tex]

now, for the slanted cone, we can use Cavalieri's Principle for an slanted cylinder, thus we can say that the slanted cone will have the same volume of a non-slanted cone, now, since this one has a diameter of 6, that means is has a radius of 3.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3} \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3}\implies V=21\pi \implies V\approx 66~cm^3[/tex]

Answer:

Step-by-step explanation:

[9,7] is the difference between 2 vectors with components [3,4] and [-6, b] what is b

Answers

The value of b is -6

We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).

So in this case, we have

[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]

Simplifying the right-hand side gives us

[-9, b - 4]

So we can set the components of the left-hand side equal to the corresponding components of the right-hand side

b1 - 3 = -9

b2 - 4 = b - 4

Solving for b in the first equation gives us

b1 = -9 + 3 = -6

Substituting this into the second equation and simplifying gives us

-6 - 4 = b - 4

-10 = b - 4

b = -10 + 4 = -6

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HELPPP URGENT!! Will give brainiest if it’s right !

If each of the numbers in the following data set were multiplied by 22, what would be the new median of the data set?
14, 20, 18, 58, 71, 36, 28

A. 792

B. 484

C. 616

D. 440

Answers

The new median of the data set is 616

Multiply all the numbers by 22

308, 396, 440, 792, 1276, 1562

looking at this number they both are in the middle. So you add both numbers and divide by two.

440 + 792 = 1232

1232 / 2 = 616

Determine if each of the following points would fall inside the parallelogram.

Answers

The points or coordinates that will fall inside the parallelogram are 0,4 and 4,7.

How to know which points will fall inside or outside the parallelogram?Start by creating a graph that shows the limits of the parallelogram as the one attached below.Once you have created the parallelogram check if each of the coordinates given would fit inside or outside the parallelogram.Categorize each pair of coordinates according to this principle.

Based on the above, the coordinates that would fit inside the parallelogram are:

0,44,7

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A triangle has angles that measure 70°, 55°, and u. What is u?

Answers

Answer: 55 degrees

Step-by-step explanation: 180-70-55=u

This answer is because the sum of all the angles is 180 degrees.

Answer:

u = 55°

Step-by-step explanation:

The sum of the internal angles of a triangle = 180°

Then:

70 + 55 + u = 180

125 + u = 180

u = 180 - 125

u = 55°

you want to estimate the average time college students spend studying per week. you know that the population standard deviation for studying time per week for college students is 3.5 hours. you want a 99% confidence interval with a margin of error of 30 minutes (0.50 hours). how many students do you need in your study?

Answers

You need a sample size of approximately 82 students to estimate the average time college students spend studying per week with a 99% confidence interval and a margin of error of 30 minutes (0.50 hours).

To determine the sample size, we will use the formula given below;

Where, n = sample size

Zα/2 = the z-score associated with the level of confidence

α = level of significance

σ = population standard deviation

d = margin of error of the estimation.

Substituting the given values, we have; n = [(Zα/2 * σ)/d]^2

We are given the population standard deviation, σ = 3.5 hours.

We are also given the margin of error, d = 0.5 hours.

We need to find the value of Zα/2 at 99% confidence level.

Since the sample size is large enough, we can use the z-distribution to find the z-value.

The area under the standard normal distribution curve for a 99% confidence level is as shown below;

Using the z-tables, the value of Zα/2 for a 99% confidence level is 2.576.

Substituting the values into the formula; n = [(Zα/2 * σ)/d]^2n = [(2.576 * 3.5)/0.5]^2= (9.006)^2= 81.12

Since we need a whole number for the sample size, we round up the value to get 82.

However, since the standard deviation of the population is known, we can use the z-distribution to construct a confidence interval for the population mean. This will give us an accurate interval estimate of the population mean.

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The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.

Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.

Answers

Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.

Fuel burn rate = Fuel capacity ÷ Range

Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km

We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.

Range in miles = Range in km ÷ 0.621371

Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles

Fuel burn rate = Fuel capacity ÷ Range in miles

Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile

Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:

Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)

F(t) = 63,500 - 2.69t

where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.

Step-by-step explanation:

Y=3/2x+4

which point lines on the line defined by the following equation?

Answers

The point (2, 7) lies on the line defined by the equation Y=3/2x+4

The given equation is [tex]Y = 3/2x + 4[/tex]

To find the point that lines on the line defined by this equation, we need to solve for x. Start by subtracting 4 from both sides of the equation:

[tex]Y - 4 = 3/2x[/tex]

Next, multiplying both sides by 2:

[tex]2Y - 8 = 3x[/tex]

Finally, divide both sides by 3:

[tex]x = (2Y - 8) /3[/tex]

Now, given a value, we can calculate the corresponding x value. For example, if Y = 7, then:

[tex]x = (2 * 7 - 8) / 3x = (14 - 8) / 3x = 6 / 3x = 2[/tex]

Therefore, the point (2, 7) lies on the line defined by this equation.

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Complete question :

What is the value of x for the point (x,7) that lies on the line defined by the equation Y = 3/2x + 4?

A. 1

B. 2

C. 3

D. 4

a vat with 500 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 5 galymin and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour?

Answers

The percentage of alcohol after an hour will be approximately 4.9%.

What is percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let p(t) be the percentage of alcohol at time t.

Where t is in minutes.

Amount of alcohol in vat = Volume of vat x p/100

Rate of change of alcohol in vat = Volume of vat x dp/dt time 1/100

Rate of change of alcohol in vat = 500 x dp/dt x 1/100

Rate of change of alcohol in vat = 5 x dp/dt

Net rate of change of alcohol = (Rate of inflow of alcohol) - (Rate of Outflow of alcohol)

Rate of Inflow of alcohol = 0.06 - 5 = -4.94 gal/min

Rate of outflow of alcohol = p(t)/100 x 5 = 0.05p(t) gal/min

Therefore, the rate of change of alcohol is 0.03 - 0.05 p(t) gal/min

Finally we can write

5 x dp/dt = 0.3 - 0.05 p

Divide both sides by 5

dp/dt = 0.06 - 0.01p

Integrate both sides

[tex]\int {dp} / 0.06 -0.01p = \int dt[/tex]

-100ln (0.06 - 0.01p) = t + C

At t=0, p=4, therefore

-100ln (0.06 - 0.04) = 0 + C

391.2 = C

Substitute the value of C, to get

-100ln (0.06 - 0.01p) = t + 391.2

Substitute t = 60 and solve for p

-100ln (0.06 - 0.01p) = 60 + 391.2

-100ln (0.06 - 0.01p) = 451.2

ln (0.06 - 0.01p) = -4.512

[tex]p = \frac{0.06 - e^{-4.512} }{0.01}[/tex] ≈ 4.9%

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What is the area of this trangle?

Answers

Answer:

Step-by-step explanation:

1/2*base*height

Select the action you would use to solve x - 3 = 12. Then select the property that justifies this action select all that apply A. Action: add 3 to both sides B. Action: Multiple both sides by 3

Answers

Answer: A. Action: add 3 to both sides

Step-by-step explanation:

The property that justifies this action is the addition property of equality, which states that if you add the same number to both sides of an equation, the equation remains true.

Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency

B 247

I 272

N 238

G 241

O 252

For which letter is the experimental probability closest to the theoretical probability? Explain please.

Answers

Answer: O: 252

Step-by-step explanation:

Theoretically, all of the letters would've been drawn 250 times as that is the theoretical possibility. The closest number to the theoretical number in this experiment would be 252 which belongs to O

Simplify the expression-4(-3x - 8) - 34

Answers

Answer:

12x-2

Step-by-step explanation:

-4(-3x-8)-34

12x+32-34

12x-2

if x>3, which of the following is equivalent to 1/(1/x+2)+(1/x+3)

Answers

Answer:Option B is correct.

Step-by-step explanation: Given:

x+2

x+3

1 =

(x+3)(x+2)

x+3+x+2

1 =

+5x+6

2x+5

+5x+6

The expression 1/(1/x+2) + (1/x+3) is equivalent to (x² + 4x + 44)/x(x + 11) when x > 3.

We have,

To simplify the expression 1/(1/x+2) + (1/x+3), we can apply the concept of finding a common denominator and combining fractions.

Let's start by finding the common denominator for the two fractions.

The denominators are (1/x + 2) and (1/x + 3).

To find the common denominator, we multiply the denominators together:

Common denominator = (1/x + 2) x (1/x + 3)

Expanding the expression:

Common denominator = (1/x * 1/x) + (1/x * 3) + (2 * 1/x) + (2 * 3)

Simplifying further:

Common denominator = 1/x^2 + 3/x + 2/x + 6

Combining the fractions with the common denominator:

1/(1/x+2) + (1/x+3) = (1/x) / (1/x^2 + 3/x + 2/x + 6) + (1/x+3)

To simplify the expression further, we can multiply the first fraction by x/x to clear the fraction in the numerator:

(1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3) = (x/x) * (1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3)

Simplifying:

= 1 / (x/x * 1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + 3/x + 2/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + (3 + 2)/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + 5/x + 6) + (1/x+3)

= 1 / (1/x²) / (1/x² + 5/x + 6) + (x/x) * (1/x+3)

Simplifying further:

= 1 / 1 / (1 + 5/x + 6x/x²) + (x/x² + 3x/x)

= 1 / (1 + 5/x + 6x/x²) + (x + 3x)/x²

= 1 / (1 + 5/x + 6/x) + (4x)/x²

= 1 / (1 + (5 + 6)/x) + (4x)/x²

= 1 / (1 + 11/x) + (4x)/x²

= 1 / (x + 11)/x + (4x)/x²

= x / (x + 11) + (4x)/x²

= (x² + 4(x + 11))/x(x + 11)

= (x² + 4x + 44)/x(x + 11)

Therefore,

The expression 1/(1/x+2) + (1/x+3) is equivalent to (x² + 4x + 44)/x(x + 11) when x > 3.

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Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.

(−3,−7) and (−7,−1)

Answers

The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.

What precisely is a triangle?

A triangle is a clοsed, dοuble-symmetrical shape cοmpοsed οf three line segments knοwn as sides that intersect at three places knοwn as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factiοns equal), isοsceles, οr scalene based οn their sides.

Next, we can find the length of the hypotenuse by using the distance formula, which is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, in this case, we have:

d = √((-7 - (-3))² + (-1 - (-7))²)

= √((-4)² + (-6)²)

= √(16 + 36)

= √52

= 2√13

Therefore, the distance between the two points in simplest radical form is 2√13.

The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.

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Penny has at least $4.50 plus 2/5 of the amount of money that Susie has. Write an expression for the amount Penny has (p) in terms of how much Susie has (s). If Susie has $11.50, use your expression to calculate how much Penny has.

Answers

We can begin by defining Penny's total wealth as a mix of a set sum and a portion of Susie's wealth to develop an expression of how much money she has. We are informed that Penny has at least $4.50 and an additional 2/5 of Susie's wealth. Hence, we can write:

p = $4.50 + (2/5)s

where p is Penny's wealth, s is Susie's wealth, and s is represented by the letters.

If Susie has $11.50, we may enter s = $11.50 into the formula for p to see how much Penny has:

p = $4.50 + (2/5)($11.50)

p = $4.50 + $4.60

p = $9.10

As a result, Penny has $9.10 and Susie has $11.50.

In conclusion, the equation for Penny's wealth in terms of Susie's wealth is p = $4.50 + (2/5)s. When we enter s = $11.50 into the formula, we obtain p = $9.10, which is how much money Penny has while Susie has $11.50.

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I need help finding area

Answers

The area of the parallelogram is approximately 193.73 square meters.

How to find the area?

To find the area of a parallelogram, we need to multiply the length of one side of the parallelogram by the perpendicular distance between that side and the opposite side.

In this case, we know that one side of the parallelogram is 11.8 m and the other side is 18.5 m. Let's call these sides "a" and "b" respectively.

To find the perpendicular distance between these two sides, we need to draw a perpendicular line from one of the endpoints of side "a" to side "b". Let's call this perpendicular distance "h".

We can use the formula for the area of a parallelogram:

Area = base x height

where the base is side "a" and the height is "h".

To find "h", we can use the Pythagorean theorem:

h² = b² - (a/2)²

where "a/2" is half of side "a".

Plugging in the values we know, we get:

h² = 18.5² - (11.8/2)²

h² = 302.25 - 34.81

h² = 267.44

h ≈ 16.36

Now that we know the height of the parallelogram, we can calculate its area:

Area = 11.8 x 16.36

Area ≈ 193.73 m²

Therefore, the area of the parallelogram is approximately 193.73 square meters.

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3
What is the measure of arc JR?
J
?
mJR
R
37°
K
L
degrees

Answers

The measure of angle subtended by the arc JR is determined as 74 ⁰.

What is the measure of arc JR?

The measure of arc JR is calculated by applying the following principle of circle geometry for a cyclic quadrilateral as shown below.

The measure of the angle tangent to the circle opposite the arc JR is given as 37 ⁰.

The measure of angle subtended by the arc JR is calculated as

m∠ JR = 2 x 37 ⁰ ( angle at the tangent is half of the angle subtended by the arc.

m∠ JR =74 ⁰

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Is the following equation true or false?

(14.6 ÷ 2) x 3 – 1.9 = 3 x (8 – 4)

True or false

Answers

Answer:

False

Step-by-step explanation:

14.6/2 = 7.3

7.3 x 3 = 21.9

21.9 - 1.9 = 20

Other side:

8 - 4 = 4

4 x 3 = 12

20 does not equal 12

therefore false :)

use partial fractions to find the indefinite integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 10x2 7x − 2 x3 x2 dx

Answers

The indefinite integral is:

-10 ln|x| + 3 ln|x - 2| + 7 ln|x + 1| + C

First, we factor the denominator of the integrand using partial fractions:

x^3 - x^2 - 2x = (x - 2)(x + 1)x

We then express the integrand as:

10x^2 - 7x + 2 = A/(x - 2) + B/x + C/(x + 1)

Multiplying both sides by the denominator and solving for A, B, and C, we get:

A = -4, B = 10, C = 1

Thus, we can rewrite the integrand as:

-4/(x - 2) + 10/x + 1/(x + 1)

Integrating each term separately and combining the results, we obtain the final expression for the indefinite integral.

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NO RANDOM ANSWERS
A bee colony produced 8 pounds of honey, but bears ate 0.32 pounds of it. How much honey remains?

Answers

7.68 pounds of honey remains after the bears ate 0.32 pounds.

What is a initial amount mean?

When referring to any Capital Appreciation Bond, Original Amount refers to the Bond's Accrued Value as of the date of issuance.

To find how much honey remains, we need to subtract the amount eaten by the bears from the initial amount produced:

Remaining honey = Initial honey - Honey eaten by bears

Remaining honey = 8 pounds - 0.32 pounds

Remaining honey = 7.68 pounds

Therefore, 7.68 pounds of honey remains after the bears ate 0.32 pounds.

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tripling the sample size will reduce the standard error of the sample proportion by one-third. group of answer choices true false

Answers

After tripling the sample size will reduce the standard error of the sample proportion by one-third we have:

a. Trueb. truec. falsed. falsee. false

The sample size in statistics is a measurement of the total number of samples utilised in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It is sometimes referred to as sample statistics.

One of the mathematical techniques used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It may be characterised as a projection of that standard deviation.

a. true

population = 25% = 0.25

sample = n= 12

n x p

= 12 x o. 25 = 3 and 3 is less than 10

12(1 - p)

= 12 x 0.75

= 9 and is less than 10

b. True

the sample distribution of the population is normal when

sample size x population > or equal to 10

40 x 0.75

= 30 and 30 is greater than 10

c. false

50 x 0.25 = 12.5

50 x 0.20 = 10

[tex]z = 10 - \frac{12.5}{\sqrt{12.5} }[/tex]

= -2.5/3.54

= -0.70

H0: Young American family who delayed

H1: young American family who did not delay

p(z = -0.70)

0.2420>0.005

therefore we accept the null hypothesis.

d. false

150 x 0.20 = 30

150 x 0.75 = 37.5

[tex]z = 30 - \frac{37.5}{\sqrt{37.5} }[/tex]

= -7.5/6.12

= -1.22

p(z = -1.22) = 0.1112 > 0.05

therefore we do not reject the null hypothesis.

e. false

[tex]se1 = \sqrt{(p(1-p)/n}\\se2 = \sqrt{(p(1-p)/3n}\\se2 = 1/\sqrt{(3)se2}[/tex]

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Complete question:

About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.

A parabola is defined as the set of points the same distance from (6,2) and line y=4. Select all points that are on this parabola

Answers

In conclusion there are no points among the given options that are on the parabola.

why it is?

The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:

(x - h)²2 = 4p(y - k)

where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).

Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:

(x - 6)²2 = 4(y - 3)

Now we can check which of the given points satisfy this equation:

A. (4, 6)

(4 - 6)²2 = 4(6 - 3)

4 = 12 - 12