Which statement is true regarding the graphed functions? ((help please :,)​

Which Statement Is True Regarding The Graphed Functions? ((help Please :,)

Answers

Answer 1
The answer is F(-2)=G(-2) . Even tho they aren’t actual coordinates on the graph they are the points where the two lines intersect

Related Questions

Find In(2.1) rounded to the nearest tenth. If necessary, include a leading 0 with any decimals less than 1. For example, 0.5 instead of .5. Provide your answer below

Answers

Therefore, the answer to the question is 0.7.

Explanation: In(2.1) is the natural logarithm of 2.1, which is approximately equal to 0.741. Rounding this number to the nearest tenth gives 0.7. When rounding decimals less than 1, it is important to include a leading 0 to avoid confusion.
To find In(2.1) rounded to the nearest tenth, we first need to know that In(2.1) is the natural logarithm of 2.1. This means that In(2.1) is the exponent to which the constant e (approximately 2.718) must be raised in order to get 2.1. Using a calculator, we can find that In(2.1) is approximately 0.741. Rounding this number to the nearest tenth gives us 0.7. It is important to include a leading 0 when rounding decimals less than 1 to avoid confusion.

Therefore, the answer to the question is 0.7 .

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A river runs through a certain city and divides the city into two parts, west and east. The population proportion of residents in the west who are in favor of building a new bridge across the river is known to be pW=0.30. The population proportion of residents in the east who are in favor of building a new bridge across the river is known to be pE=0.20. Two random samples of city residents of size 50, one sample from the west and one sample from the east, were taken to investigate opinions on the bridge, where pˆW=0.38 and pˆE=0.25 represent the sample proportions. For samples of size 50 from each population, which of the following is the best interpretation of the mean of the sampling distribution of the difference in the sample proportions (west minus east) of residents from the west and east who are in favor of building the bridge?

Answers

The mean of the sampling distribution of the difference in the sample proportions is an estimate of the difference in the population proportions, and the standard deviation of the sampling distribution measures the variability of this estimate.

The mean of the sampling distribution of the difference in the sample proportions (west minus east) of residents from the west and east who are in favor of building the bridge is 0.08. This means that on average, the sample from the west had a proportion that was 8% higher than the sample from the east in terms of favoring the new bridge.

The difference in sample proportions between the west and east can be interpreted as an estimate of the difference in the population proportions of residents who are in favor of building the bridge. Since the sample sizes are both 50 and greater than 30, we can use the central limit theorem to approximate the sampling distribution of the difference in sample proportions as a normal distribution.

The mean of this normal distribution is equal to the difference in population proportions, which is pW - pE = 0.30 - 0.20 = 0.10. The standard deviation of the sampling distribution can be estimated using the formula sqrt[(pW(1-pW))/nW + (pE(1-pE))/nE], where nW and nE are the sample sizes from the west and east, respectively.

Given the values provided, the estimated standard deviation is approximately 0.089.

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I need helppp please​

I need helppp please

Answers

Answer:

How pooor are you it'svery hard

I need help with finding 12x+3y=-3 on a graph.

Answers

Let's graph the equation

\(12x+3y=-3\)

Notice that this equation corresponds to a line.

1. First, let's clear y, so we can get the equation of the line in the slope-intercept form:

\(\begin{gathered} 12x+3y=-3 \\ \rightarrow3y=-12x-3 \\ \rightarrow y=-4x-1 \end{gathered}\)

This way, he equation of the line in the slope-intercept form is

\(y=-4x-1\)

2. Now, we have to expose two points contained in the line. To do so, we give x any value we want and we calculate the corresponding y value.

Let's do this with x = 0 and x = 1

\(\begin{gathered} y=-4x-1 \\ \\ x=0\Rightarrow y=-4(0)-1\rightarrow y=-1 \\ \text{This way, the point} \\ (0,-1) \\ \text{Belongs to the line} \\ \\ x=1\Rightarrow y=-4(1)-1\rightarrow y=-5 \\ \text{This way, the point } \\ (1,-5) \\ \text{belongs to the line} \end{gathered}\)

3. Put those points in the cartesian plane:

4. Draw a straight line that passes through both points. This will be the graph of the line

I need help with finding 12x+3y=-3 on a graph.
I need help with finding 12x+3y=-3 on a graph.

Question 2(Multiple Choice Worth 4 points)
(01.04 LC)
Given the linear functions f(x) = x -2 and g(x)=-3x + 4, determine (f- g)(x).
(f-g)(x) = -3x - 8
(f-g)(x)=-3x²-8
(f-g)(x) = -3x² + 10x - 8
(f-g)(x) = -3x² - 2x - 8

Answers

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

What is linear function?

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

According to given information:

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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H= Substitute the given values into the given formula and solve for the unknown variable. If necessary round to one decimal place

H= Substitute the given values into the given formula and solve for the unknown variable. If necessary

Answers

We need to evaluate the following expression:

\(S=4LW+2WH\)

Where S is equal to 108, L is equal to 7 and W is equal to 3. We have:

\(\begin{gathered} 108=4\cdot7\cdot3+2\cdot3\cdot H \\ 108=84+6\cdot H \\ 84+6\cdot H=108 \\ 6\cdot H=108-84 \\ 6\cdot H=24 \\ H=\frac{24}{6}=4 \end{gathered}\)

if y1 = 116 and y7 = 255, then the simple index number for period 7 (denoted i7) is:

Answers

The index number indicates that the value in period 7 has increased by about 119.83% compared to the value in period 1.

How to determine the simple index number for period 7

Based on the information provided, we will calculate the simple index number for period 7 (i7) using the given values for y1 and y7.

The simple index number formula is:

i7 = (y7 / y1) × 100

Where y1 represents the value in period 1 (116) and y7 represents the value in period 7 (255).

Plugging in these values, we get: i7 = (255 / 116) × 100 i7 ≈ 219.83

Thus, the simple index number for period 7 (i7) is approximately 219.83.

This index number is a measure that compares the value of y7 to the value of y1, with y1 being the base period.

In this case, the index number indicates that the value in period 7 has increased by about 119.83% compared to the value in period 1.

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which term describes the percent of voters casting ballots?

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The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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186 div by 20 because i am lost

Answers

Answer:

9.3

Step-by-step explanation:

186/20 = 18.6/2 = 9.3

\(Hello\) \(There!\)

The answer is...

\(\frac{93}{10}.\)

Hopefully, this helps you!!

\(AnimeVines\)

(Hurry giving brainliest) Which idea does Arnold need to correct? In specular reflection, reflected rays move in the same direction. In scattering, light strikes particles in the atmosphere. In diffuse reflection, reflected rays move in different directions. In scattering, long wavelengths are scattered the most.

Answers

Answer:

D. In scattering, long wavelengths are scattered the most.

Step-by-step explanation:

Scattering of light is the effect observed when there is an interaction between light energy and some particles. This occurs often in the earth's atmosphere which consists of different sizes of particles that interacts with the sunlight.

In scattering, light of shorter wavelengths are scattered by small sized particles compared to those with longer wavelengths. Example is the scattering of the sunlight by the atmospheric particles where colors with short wavelengths are scattered the most.

Arnold need to correct the statement; In scattering, long wavelengths are scattered the most. To read; In scattering, short wavelengths are scattered the most.

Answer:

D on edgen

Step-by-step explanation:

how far is the point (5,2) from the x axis

how far is the point (5,2) from the x axis

Answers

Answer:

B     5 units

Step-by-step explanation:

Answer:

5 left (b)

Step-by-step explanation:

the x-axis the bottom axis and it starts at 0 and -5 is 5 from 0

Your friend took an introductory statistics class last year and learned all about density curves. she tells you that two requirements of a density curve are:______.

Answers

The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.

Given that,
Two requirements of a density curve are to be determined.

What is a density curve?

A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.

Here,

The two requirements of a density curve should be,

a. The area under the density curve should be equal to 1.

 

b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.

Thus, the required requirement of the density curve is mentioned above.

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.A ball that is dropped from a window hits the ground in 7 seconds. How high is the window? (Give your answer in feet; note that the acceleration due to gravity is 32 ft/s² . Height = _______

Answers

Answer:

(1/2)(32 ft/sec^2)((7 sec)^2)

= (16 ft/sec^2)(49 sec^2)

= 784 feet

Height = 112 feet.

To find the height of the window, we can use the following kinematic equation for motion with constant acceleration:

y = yo + voyt + ½at²

Here, y is the final height of the ball above the ground, yo is the initial height of the ball (which is the height of the window in this case), voy is the initial velocity of the ball (which is 0 because the ball is dropped from rest), t is the time taken for the ball to hit the ground (which is 7 seconds), and a is the acceleration due to gravity (which is 32 ft/s²).

Substituting the values, we have:y = yo + 0 + ½(32)(7)

Simplifying the expression, we get:y = yo + 112

Thus, the height of the window (in feet) is given by:y = 112 feet

Answer: Height = 112 feet

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Which number is rational?
OA. 0.83587643...
B. ♬
OC. 0.333...
ODT

The answer is C 0.333

Which number is rational?OA. 0.83587643...B. OC. 0.333...ODTThe answer is C 0.333

Answers

The number that is rational in the given options is C. 0.333...

What are rational numbers?

A rational number is a given number which can be expressed as a fraction, or which has a series of recurring digits on expressing it in decimal. Such that it can be rounded off to a required number of decimal places or significant figure of the recurring digits.

In the given question, comparing the values of the given options, it can be observed that only 0.333... is the rational number. Therefore, the required number that is rational is option C. 0.333...

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Answer:

C. 0.333 is the answer.

Step-by-step explanation:

(ii) n is a negative integer.
Write down all the values of n which satisfy 2n + 13 > 6

Answers

Answer:

\(0 >n>-\frac{7}{2}\)

Step-by-step explanation:

\(2n+13-13>6-13\)

\(2n>-7\)

\(\frac{2n}{2}>\frac{-7}{2}\)

\(n>-\frac{7}{2}\)

n is negative, so it must be less than zero, \(0 >n>-\frac{7}{2}\)

I need the answer ASAP !!! Pls

I need the answer ASAP !!! Pls

Answers

Given:

The diagram of two right triangles.

To find:

The value of d and a.

Solution:

In a right angle triangle,

\(\tan \theta=\dfrac{Perpendicular}{Base}\)

\(\sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)

(a) In first triangle,

\(\tan 60^\circ=\dfrac{d}{4}\)

\(\sqrt{3}=\dfrac{d}{4}\)

\(4\sqrt{3}=d\)

Therefore, \(d=4\sqrt{3}\).

(b) In second triangle,

\(\sin 45^\circ=\dfrac{a}{2}\)

\(\dfrac{1}{\sqrt{2}}=\dfrac{a}{2}\)

\(\dfrac{2}{\sqrt{2}}=a\)

\(\sqrt{2}=a\)

Therefore, \(a=\sqrt{2}\).

10 Points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

10 Points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

x=9

Step-by-step explanation:

9 to the power of 6 is 531441

9 to the power of 3 is 729

531441 divided by 729 is 729

a third root of 729 is 9 because 9 times 9 times 9 is 729

so x is 9

please mark me as brainliest!!<3

Answer:

Step-by-step explanation:

I think it's X9?

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

Answers

If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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PLEASE ANSWER QUICK NEED TO FINISH TO GRAUATE
Part I: Using triangle BCD, find the distance between Rex and the dolphin, and between Rex and Paulo. Assume the distance between Paulo and the dolphin is exactly 100 feet. Round your answers to one decimal place. Show your work. (4 points, 2 points each distance)

HINT: The hypotenuse of a 30-60-90 triangle is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg.

Distance between Rex and the dolphin:










Distance between Rex and Paulo:

Answers

Answer:

160

Step-by-step explanation:

The distance between Rex and the dolphin is 112 feet.

What is a triangle?A triangle is a 3-sided polygon every now and then (but not very normally) referred to as the trigon. every triangle has three sides and 3 angles, some of which may be equal.Sum to all the three interior angles of a triangle is 180°There are different kinds of triangles.Right angle triangleisosceles triangleequilateral triangle

calculation:-

The distance between  Paulo and the dolphin is = 100 feet distance between

Let the  Rex and Paulo is 50 feet ( according to the question)

∴The Distance between Rex and the dolphin \(\sqrt{(100)^{2} +\sqrt{50}^{2} }\)

                                                                         ⇒\(\sqrt{10000+2500}\)

                                                                         ⇒\(\sqrt{12500}\)

                                                                         ⇒111.8

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if the cost of gasoline in Calgary is S151 CDN dollars/L and the cost of gasoline in Dallas, Texas is $4.19 US dollars/US gallon, which place has the better deal for gasoline? (1 CDN dollar $0.77 US Dollar; 1 US gallon 3.81) Use Proportional Reasoning to convert the cost of gasoline in Canada to SUSD/gallon

Answers

Given that the cost of gasoline in Calgary is S151 CDN dollars/L and the cost of gasoline in Dallas, Texas is $4.19 US dollars/US gallon.

Let's first convert the exchange rates into US dollars:

1 CDN dollar $0.77 US Dollar1 US dollar $1.30 CDN Dollar Now,

let's convert the cost of gasoline in Calgary from S/L to USD/L:

\(S151 \text{ CDN dollars/L} \times 0.77 \text{ US Dollar/1 CDN dollar} = \boxed{$116.27 \text{ US dollars/L}}\)

\(\$116.27\text{ US dollars/L}\) Now,

let's convert the cost of gasoline in Dallas from US dollars/gallon to USD/L:$4.19 US dollars/US gallon x 1 US gallon/3.81

= $1.10 US dollars/L

Now we can compare the prices:

$116.27 USD/L (Calgary) vs $1.10 USD/L (Dallas)Since the cost of gasoline in Dallas is significantly cheaper than in Calgary, Dallas is the better deal for gasoline.

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Number of defective items in a production line per day follows a Poisson process, therefore the time between two consecutive defective items is exponentially distributed with a mean of ul #) Suppose, you have just started your 8 hours shift what is the probability that there will be no defective item during your 8 hours shift? b) What is the probability that you observe one defective item in less than 3 hours?

Answers

Hence, the probability that there will be no defective item during an 8-hour shift is e^(-8/ul) and the probability that you observe one defective item in less than 3 hours is 1 - e^(-3/ul).

a) Probability that there will be no defective item during an 8-hour shift can be calculated using the Poisson distribution formula, where the mean is given as λ:$$P(X=0) = \frac{\lambda^0 e^{-\lambda}}{0!}$$

Here, the mean is given as ul # which represents the number of defective items per unit of time.

Since the unit of time is not given, we can assume it as hours.

Therefore, the mean can be given as λ = 8/ul.

The formula can be substituted to find the probability:$$P(X=0) = \frac{\left(\frac{8}{ul}\right)^0 e^{-\frac{8}{ul}}}{0!}$$$$P(X=0) = e^{-\frac{8}{ul}}$$b) Probability that you observe one defective item in less than 3 hours can be calculated using the cumulative distribution function of exponential distribution, which is given as:$$F(x) = P(X \le x) = 1 - e^{-\frac{x}{\mu}}$$

Here, x is the time we need to find the probability for. Since the mean time between consecutive defective items is given as ul, the parameter μ of exponential distribution is also given as ul.

To find the probability that one defective item occurs in less than 3 hours, we need to find P(X < 3), which can be calculated as:$$P(X < 3) = F(3) = 1 - e^{-\frac{3}{ul}}$$

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Answer:

Step-by-step explanation:

Given: Number of defective items in a production line per day follows a Poisson process, therefore the time between two consecutive defective items is exponentially distributed with a mean of ul.

a) The probability that there will be no defective item during the 8-hour shift is 0.3679.

b) The probability of observing one defective item in less than 3 hours is 0.021.

a) To find the probability that there will be no defective item during the 8-hour shift, we use the Poisson distribution with parameter λ = ul.

Hence, P(no defective item in 8 hours) = P(X=0),  where X ~ Poisson(λ).

P(X=0) = e^-λ λ^0 / 0!

= e^-λ

= e^-ul

= e^-(0.4*2.5)

= e^-1

= 0.3679

Therefore, the probability that there will be no defective item during the 8-hour shift is 0.3679.

b) The time between two consecutive defective items follows an exponential distribution with a mean of ul = 2.5.

Therefore, the parameter

λ = 1/ul

λ = 0.4.

The probability of observing one defective item in less than 3 hours is P(X=1), where X is the number of defective items in 3 hours.

Since the defective items follow a Poisson distribution, X ~ Poisson(λt), where λ = 0.4 and t = 3/8 (since 3 hours is 3/8 of the 8-hour shift).

P(X=1) = e^-λt (λt)^1 / 1!

= e^(-0.4*3/8) (0.4*3/8)^1 / 1!

= e^-0.15 * 0.15

= 0.021

Therefore, the probability of observing one defective item in less than 3 hours is 0.021.

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You are shopping for single-use cameras to hand out at a party. The daylight cameras cost $2.75 and the flash cameras cost$4.25. You must buy exactly 20 cameras and you want to spend between $65 and$75, inclusive. Write and solve a compound inequality for this situation. Then list all the solutions that involve whole numbers of cameras.

Answers

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Determine the slope of the line that passes through the points (-2, 5) (1, -7)

Answers

Answer:

-4

Step-by-step explanation:

Given points

(-2, 5) (1, -7)

Use slope formula to find the slope

m = (y2 - y1)/(x2 - x1)m = (-7 -5)/(1 + 2) = -12/3 = -4

Slope is -4

Answer:

slope is -4

Step-by-step explanation:

Find slope which is also referred to as m:

m = (y₂ - y₁) / (X₂ - X₁)

   = (-7 - 5) / (1 - (-2)

   = -12 / 3

m = -4

Not asked in question but if you want to find equation for the line:

Find b using any one of the two provided coordinates. Let's use (-2, 5).

y = mx + b

5 = -4(-2) + b

5 = 8 + b

b = -3

Use m and b to make equation.

y = mx + b

y = -4x - 3

What are the factors and zeros of the function f(x)=−2x2+7x+15?

Answers

Solving the quadratic function, it is found that the factors/zeros of the function are given by x = -1.5 and x = 5.

What are the factors/zeros of a function?

They are given by the solutions of the function, that is, the values of x for which f(x) = 0.

In this problem, the function is given by:

f(x) = -2x² + 7x + 15.

Then:

-2x² + 7x + 15 = 0.

Which is a quadratic function with coefficients a = -2, b = 7, c = 15, hence:

\(\Delta = 7^2 - 4(-2)(15) = 169\)

\(x_1 = \frac{-7 + \sqrt{169}}{2(-2)} = -1.5\)

\(x_2 = \frac{-7 - \sqrt{169}}{2(-2)} = 5\)

The factors/zeros of the function are given by x = -1.5 and x = 5.

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How to graph y=x^2+6x+7 on a quadratic graph​

How to graph y=x^2+6x+7 on a quadratic graph

Answers

The graph of the function y = x²+ 6x + 7 is given in the attachment.

To graph the quadratic function y = x²+ 6x + 7:

Find the vertex using the formula -b/(2a), where a is the coefficient of x²and b is the coefficient of x.

The vertex will be at (-3, -2).

Plot the vertex (-3, -2) on the graph.

Choose additional x-values and calculate the corresponding y-values by substituting them into the equation.

Plot these points on the graph.

Connect the plotted points smoothly to form a U-shaped curve, which represents the parabola.

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How to graph y=x^2+6x+7 on a quadratic graph

Write 6-12 as an addition expression.

Answers

Answer:

-12 + 6

Step-by-step explanation:

Answer:

-12+6

Step-by-step explanation:

The two terms are

-12

and

+6

Put them together in the reverse order and you have -12+6

Find five rational numbers between -1/2 and 4/7

Answers

The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

According to the statement

we have to find that the rational numbers.

So, For this purpose, we know that the

Rational number, a number that can be represented as the quotient p/q of two integers such that q ≠ 0.

From the given information:

The given numbers are between -1/2 and 4/7

Then to find the numbers then

Rational numbers = (-1/2 +4/7) /2

Rational numbers = (-1 +2/7)

Rational numbers = -5/7.

And then the number becomes -6/7, 2/7,3/7.

Now, The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

So, The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

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Which is greater between 38 and 6.343443444

Answers

Answer:

38 is greater

Step-by-step explanation:

6.343443444 is a decimal between 6 and 7 :3

38 is greater.

6.34… is a decimal and 38 is a whole number. which means the whole number, 38, is greater

A time traveler can take 3 books with him, and he has 57 books to choose from. How many different ways can the books be selected?

Answers

The time traveler can choose 3 books with him, but he can only take 57.

So in this case the order doesn't matter, therefore, we are going to use a combination:

Use the combination formula:

\(C\text{ =}\frac{n!}{r!(n-r)!}\)

When n is the total of books and r the sample.

n = 57 and n =3

Replace these values on the formula:

\(C=\frac{57!}{3!(57-3)!}=\frac{57!}{3!54!}=29260\)

Hence, there are 29260 ways that the books can be selected.

last year at a certain high school, 10 students sought the nomination for president of the student body. in how many ways could the voters (student body) rank their first 5 choices? a) 5 b) 50 c) 30,240 d) 3,628,800 e) 252 f) none of the above.

Answers

The number of ways voters could rank their first 5 choices out of 10 is 30240.

Given,

Number of students sought the nomination for president of the student body = 10 students

We have to find the number of ways voters could rank their first 5 choices.

Permutation;

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

Here we have to use permutation formula;-

ⁿPr = n! /  (n - r)!

Here,

n is the number of students = 10

r is the choices = 5

Then,

ⁿPr = n! /  (n - r)!

¹⁰P₅ = 10! / (10 - 5)!

¹⁰P₅ = 10! / 5!

¹⁰P₅ = 10 x 9 x 8 x 7 x 6

¹⁰P₅ = 30240

That is,

The number of ways voters could rank their first 5 choices out of 10 is 30240.

Learn more about permutation here;

https://brainly.com/question/1216161

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