Write a linear function f with f (5)=7 and f(-2)=0

The sum symbol is represented as

Sum is determined by putting the values all together and results is called "total" or sum. The plus symbol (+) is used as sum symbol in case of small numbers of digits for addition. For example: sum of 5 and 6 is represented as 41 + 15 = 56 .

The symbol Σ (sigma) is used to denote a sum of multiple terms. This symbol is generally used by an index that varies to represent all terms that must be considered in the sum. For example, the sum of first whole numbers can be represented in the following 1 + 2 + 3 + 4 + .......+ n = \( \sum_{i = 1}^{n} {i}\)

where, ∑ is the symbol that is denoted as "sigma".

Summation is used in case of sum of arithmetic sequence, geometric sequence and other sequences.

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Answer:

C.10 units

Step-by-step explanation:

To find the distance between two points in the coordinate plane, i use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

In this case, we have two points: (5, 2) and (-3, -4). We can plug these coordinates into the distance formula:

distance = sqrt[(-3 - 5)^2 + (-4 - 2)^2]

distance = sqrt[(-8)^2 + (-6)^2]

distance = sqrt[64 + 36]

distance = sqrt[100]

distance = 10

Therefore, the distance between (5, 2) and (-3, -4) on the coordinate plane is 10 units.

Check the picture below.

Make sure your calculator is in Degree mode.

Answer: The form of payment that Courtney can lose and not get back would be cash.

Step-by-step explanation:

The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.

Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated  verification process.

Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!

-From Certified 5th Grade Honors Student

Answer:

31-2=X+6

29=X+6

29-6=X

23=X

Answer:

10 and 7 are the numbers

Step-by-step explanation:

Let the number be x and y, ATQ, x+y=17 and x-y=3, solving it we will get x=10 and y=7

The sum of two numbers is 17 and their difference is 3.

Let's define the two numbers as x and y.

Sum of two numbers is 17

x + y = 17

Their difference is 3

x - y = 3

-----------------------------------------

Solve for x

x + y = 17

x = 17 - y

now that we have x, substitued x into x - y = 3

x - y = 3

17 - y - y = 3

17 - 2y = 3

-2y = -14

y = 7

we have y, 7, now let's substitue that into one of the equations to find x

x - y = 3

x - 7 = 3

x -7 + 7 = 3 +7

x = 10

the numbers are 10 and 7

Answer:

$1258.74

Step-by-step explanation:

Answer:

24 thereabouts

Step-by-step explanation:

Well every two months there are two new rabbits so I multiplied two and twelve. This got me twenty-four. I hope this helps! :) I don't know if this is right or not I attempted this in my head.

Answer:

The answer is D

Step-by-step explanation:

Took the test

Work Shown:

area = 0.5*base*height

area = 0.5*11*13.4

area = 73.7 square cm

The other values 15 and 14 are not used. Your teacher probably put them in as a distraction.

Answer: Number of kids who attended the party = 12 / 0.60

Step-by-step explanation:

60% = 12

x 0.60 = 12

Number of kids attending =  x = 12 / 0.60

Answer:

12 is 60

Step-by-step explanation:

Answer: 12 is 60 percent of 20. (60% of 20 = 12) Percentages are fractions with 100 as the denominator.

Answer:

3.6hours

Step-by-step explanation:

kevin-6hrs

so he gets 1/6 called in 1 minute

Anne-9 hrs

so she gets 1/9 called in 1 minute

together

1/6+1/9=5/18 called in one minute

so what about all which are 18/18

you get 3.6 hrs I guess

Answer:

How many gallons can Ivan's tank hold? 24

The domain of the function exists for when x ≤ 2 while the range exists for the value of y >0

For f⁻¹(x), the domain and the range exists on all real values

Given the expression

f(x)=√−2x+4

Get the inverse of the function f⁻¹(x)

ley u = f(x)

y = √−2x+4

Replace x as y

x = √−2y+4

Make y the subject of the formula

x² = -2y + 4

-2y = x²-4

y = (x²-4)/-2

Hence f⁻¹(x)=  (x²-4)/-2

For f(x), the domain of the function exists for when x ≤ 2 while the range exists for the value of y >0

For f⁻¹(x), the domain and the range exists on all real values

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Answer:

Step-by-step explanation:

The Sum:

The difference:

Subtract the sum from the difference:

Answer:

See below.

Step-by-step explanation:

First Let's us find the sum.

\(\sf\longmapsto \: 3x²y - 5a + 4b + (-9x²y - 7b + 4a)\)

\(\sf\longmapsto3x²y - 9x²y - 5a + 4a + 4b - 7b \)

\(\sf\longmapsto \: -6x²y - a - 3b\)

Now, let's us find the difference (minus)

\(\sf\longmapsto \: 3x²y - 5a + 4b - (-9x²y - 7b + 4a)\)

\(\sf\longmapsto3x²y + 9x²y - 5a - 4a + 4b + 7b\)

\(\sf\longmapsto \: 12x²y - 9a + 11b\)

Now minus the sum from the difference.

\(\sf\longmapsto \: 12x²y - 9a + 11b - (-6x²y - a - 3b)\)

\(\sf\longmapsto \: 12x²y + 6x²y - 9a + a +11b + 3b\)

\(\sf\longmapsto \: 18x²y - 8a + 14b\)

Therefore,\(\sf\longmapsto \: 18x²y - 8a + 14b\) is the answer.

Answer:

C

Step-by-step explanation:

You should always measure your following distance in seconds. The correct answer for measuring following distance is A.  

It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.

The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.

Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.

The correct answer for measuring following distance is A.  

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Complete question is:

You should always measure your following distance in __________

A. seconds. B. car lengths. C. feet.

The value of c-b based on the given integral is given as 0

We recognize the limit as the definition of the integral.

The integral represents the area under the curve of the function \(f(x) = x^3\)from 1 to 6.

Using the limit definition, we can rewrite the integral as:

\(\int^6_1x^3dx= \lim_{n\to\infty}\sum^n_{i=1}f\left(1+\frac{bi}{n}\right)\frac{c}{n}\)

Comparing this with the general form for Riemann sums:

\(\int^b_ax^3dx= \lim_{n\to\infty}\sum^n_{i=1}f\left(a+\frac{(b-a)i}{n}\right)\frac{b-a}{n}\)

We can identify \(a = 1,b = 6\)

Then, we have \(1 + \frac{bi}{n} = 1 + \frac{5i}{n}\) and \(\frac{c}{n} = \frac{5}{n}\)

Hence, \(b = 5\)and \(c = 5\)

Thus, \(c - b = 5 - 5 = 0\)

The limit of an integral refers to a value an integral approaches as the interval of integration approaches a certain point, often used in improper integrals.

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Answer:

x=84

y=59

Step-by-step explanation:

if the triangles are similar than the angles don't change so and y is equal to 59.

to find the missing side we do 40/30 x 63 and we get that x=84

Answer:

ab and cd intersect at E because they are vertically opposite angles they always intersect at a point

Answer:

150

Step-by-step explanation:

The restaurant should expect to serve 180 customers in week 10.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. Therefore, the number of customers served in week 10 will be 180.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. This means that after 10 weeks, the number of customers served will be the same as it was in week 1. Since week 1 had 180 customers served, week 10 will also have 180 customers served.

As you can see, the number of customers served in week 10 is the same as the number of customers served in week 1. Therefore, the restaurant should expect to serve 180 customers in week 10.

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The amount of commission expense that will appear on the flexible budget if 2900 units were sold is; $11600

The activity variance is favourable.

According to the question;

To solve this;

We must be aware that the commission expense is directly proportional to the number of units sold.

In essence;

By cross product;

Ultimately, the activity variance is favourable bas less commission expense is recorded for less sale.

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To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.

In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.

If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.

On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.

Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.

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(11) The measure of angle IGJ is  46⁰.

(12) The measure of arc JH is determined as 138⁰.

The measure of the arc or central angle indicated is calculated as follows;

(11) The measure of angle IGJ is calculated as follows;

m∠LGK =  arc angle LK (interior angle of intersecting secants)

m∠LGK = 48⁰

m∠HGI = m∠LGK = 48⁰ (vertical opposite angles are equal)

m∠IGJ + m∠HGI + m∠JGK = 180⁰  (sum of angles in a straight line)

m∠IGJ + 48⁰ + 86⁰ = 180

m∠IGJ = 180 - 134

m∠IGJ = 46⁰

(12) The measure of arc JH is calculated as follows;

arc JH = arc JI + arc IH

arc JI = arc FG

arc FG = 180 - 137⁰ (sum of angle in a straight line)

arc FG = 43⁰

arc FG = arc JI (vertical opposite angles are equal)

arc JH = arc JI + arc IH

arc JH = 43⁰ + 95⁰

arc JH = 138⁰

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Step-by-step explanation:

Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649

Angle = arctan(-4/-12) = 198 degrees

The Magnitude: 12.649 and Direction: 18° (option c).

To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:

Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)

Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)

where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.

Let's calculate:

Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)

Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°

Since we need to round the direction to the nearest degree, the direction is approximately 18°.

So, the correct answer is:

Magnitude: 12.649 (rounded to the thousandths place)

Direction: 18° (rounded to the nearest degree)

The correct option is: 12.649; 18°

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Gabrielle does not perform a translation after dilating circle V.

To show that circle V and circle W are similar, Gabrielle performs two transformations on circle V. First, she dilates circle V about its center with a scale factor of (3/4). Then, she translates the dilated circle.

The translation that Gabrielle performs can be represented by the equation:

(x, y) → (x + a, y + b)

where (x, y) represents the coordinates of a point on circle V, and (x + a, y + b) represents the coordinates of the corresponding point on the translated circle.

Since the dilation scale factor is (3/4), the translation amounts to shifting the dilated circle horizontally and vertically. The values of a and b can be calculated as follows:

a = (1 - 3/4) * center of circle V's x-coordinate

b = (1 - 3/4) * center of circle V's y-coordinate

In this case, since the dilation is centered around the center of circle V, the center of circle V remains the same after the dilation. Therefore, a and b are both zero.

Thus, the translation that Gabrielle performs simplifies to:

(x, y) → (x + 0, y + 0)

which means there is no translation in this case. The dilated circle V remains in the same position as circle V.

In summary, Gabrielle does not perform a translation after dilating circle V.

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