Write the quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4.

STEP 1: a1 = 6.

STEP 2:  r = 0.75

STEP 3: The common ratio is less than one.

STEP 4: The sum of the  Sum of the Infinite Geometric series is Sn = 24

Since we have the expression for the sum of the infinite geometric series

\(\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \]\)

STEP 1:

The first term of the infinite geometric series is 6. Thus, a1 = 6.

STEP 2:

The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75

STEP 3:

The common ratio is less than one.

Because Sn = a/(1 - r)  is the formula we use when the common ratio is less than 1.

STEP 4:

Sn = a/(1 - r)

Sn = 6/(1 - 0.75) = 24

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Answer:

a

Step-by-step explanation:

the data is represented in the dot plot

Answer:

answer is 77.67

Step-by-step explanation:

explain by the x axis is 68 to y axis is 84 so the median is 77.67

In 288 ways a breakfast can be ordered.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The cafeteria offers 4 types of eggs, 2 types of toast, and 3 types of meat for breakfast.

Now,

The number of ways a breakfast can be ordered.

= 4! x 2! x 3!

= (4 x 3 x 2) x 2 x (3 x 2)

= 24 x 2 x 6

= 24 x 12

= 288

Thus,

288 ways.

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Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

Answer:

yes Bro it is correct ar u writing an exam

Answer:

7/8 x 14= 12.25 or 49/4 or 12 1/4

(3/8 x 6) + 2 1/5= 4.45

(hope this helps I probably wasn't fully understanding)

9514 1404 393

Answer:

  2

Step-by-step explanation:

Fill in the argument value and look up the function value on the graph.

  \((f\circ f)(-2) = f(f(-2)) = f(2) = \boxed{2}\)

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Answer: y = 5x - 4

Step-by-step explanation: The equation of a linear function can be found by using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (i.e., the point at which the line crosses the y-axis).

To find the equation of the linear function represented by the table, we can use the values from the table to calculate the slope. The slope is calculated as the change in y over the change in x, or (y2 - y1)/(x2 - x1). Using the values from the table, we can calculate the slope as (6 - 1)/(2 - 1) = 5/1 = 5.

Next, we can use the slope and one of the points from the table to find the y-intercept. If we use the point (1,1), we can substitute the values into the slope-intercept form to get 1 = 5*1 + b, so b = -4.

Therefore, the equation of the linear function represented by the table is y = 5x - 4.

Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

Answer:

The real and imaginary parts of the result are \(\frac{1441}{1601}\) and \(\frac{4}{1601}\), respectively.

Step-by-step explanation:

Let be \(f(z) = \frac{z}{z+1}\), the following expression is expanded by algebraic means:

\(f(z) = \frac{z\cdot (z-1)}{(z+1)\cdot (z-1)}\)

\(f(z) = \frac{z^{2}-z}{z^{2}-1}\)

\(f(z) = \frac{z^{2}}{z^{2}-1}-\frac{z}{z^{2}-1}\)

If \(z = 4 - i5\), then:

\(z^{2} = (4-i5)\cdot (4-i5)\)

\(z^{2} = 16-i20-i20-(-1)\cdot (25)\)

\(z^{2} = 41 - i40\)

Then, the variable is substituted in the equation and simplified:

\(f(z) = \frac{41-i40}{41-i39} -\frac{4-i5}{41-i39}\)

\(f(z) = \frac{37-i35}{41-i39}\)

\(f(z) = \frac{(37-i35)\cdot (41+i39)}{(41-i39)\cdot (41+i39)}\)

\(f(z) = \frac{1517-i1435+i1443+1365}{3202}\)

\(f(z) = \frac{2882+i8}{3202}\)

\(f(z) = \frac{1441}{1601} + i\frac{4}{1601}\)

The real and imaginary parts of the result are \(\frac{1441}{1601}\) and \(\frac{4}{1601}\), respectively.

Answer:

a

Step-by-step explanation:

the other ones are incorrect

Answer:

1. -5a

Step-by-step explanation:

The definition of combining like terms is adding their coefficients, for example: 2x + 3x = (2+3)x = 5x.

So for this one, -21a+16a = (-21+16)a = -5a.

Answer:

C

Step-by-step explanation:

You can determine this by the third and fourth quartiles.

Answer:

C

Step-by-step explanation:

1,4,4,9,10,10,14

We know the smallest number is 1 and the largest number is 14, so they are left and right whiskers

1,4,4, 9, 10,10,14

The middle number is the 4th number, which is 9 so it is the middle number of the box

Taking the numbers on the left

1,4,4

The middle number is 4  so it is the left hand side of the box

Taking the numbers on the right

10,10,14

10 is the middle number so it is the right hand side of the box

Since the coop is in square shape The fencing is in the shape of a square

So equation is 4x=20, x=5

From the table , the insurance cost for the second year based on the prescription given is : $1329

Using the prescription table, the six cylinder compact , second year car with a mileage of 14000 falls in the mid table category with the 13000 mileage label .

The operating cost in insurance for the second year is therefore $1329.

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Answer:

£2.10 should be right but it is rounded up

Sis : you : bro

10 : 9 : ?

? ? : 27 : 29

We can get the 9 at the top to 27, by multiplying the whole row by 3 to get:

30 : 27 :?

? : 27 : 29

Your age matches (in the ratios or relation to your sis & bro) now 27 yrs in both ratio. Creating a single ratio, whereby multiplying the top row by 3 to get you to 27 & bottom row by 1 to get you to 27. Knowing when you're 27 in both cases, you know how old your sis & bro is

So, replace the ? with the number above or below it, creating a single ratio, where you are in common with both, by being 27 in both cases.

The ratio of sis : you : bro is now -

The ratio of sis : you : bro is now - 30: 27 : 29

To find what your age is we need to increase the ratio in the same amount to find your maximum age under 70.

So, if we were to double your age to 54, by multiplying your previous age of 27 by 2. We've got to do the same for your sis & bro too, they're aging with you.

We get :

We get :60 : 54 : 58

(30 x 2) : (27 x2) : (29 x2)

Keep increasing the ratio, to the point you're not above 70 years. Now, I'll multiply all ages by 3.

30: 27 : 29

(30 x 3) : ( 27 x 3) : (29 x 3)

We get:

We get:90 : 81 : 87

Right now, you're above the age of 70.

Thus, your maximum age must be 54, where you're under 70 years, but over 40 years.

Answer : 54 years

Hope this helps!

Answer: 52

Step-by-step explanation:

    To find the range of a data set, we subtract the smallest value from the largest value.

54 - 2 = 52

Answer:

The answer is 0.4

Step-by-step explanation:

2/5 is equal to 0.4

Answer:

0.4

Step-by-step explanation:

start with 2/5.

multipy the 5 by 20 to get 100, and the 2 by 20 to get 40.

so, now your fraction should look like this:

40/100

then, shift the decimal in 40 over 2 spots to get 0.40, or 0.4

hope this helps :)

Answer:

25 units (cant see what it says on the side :/ ) per hour

Step-by-step explanation:

hope this helps <3

Answer:

The bottom one: The value is the difference of 42 and the sum of 20 and 3.

Step-by-step explanation:

The answer is what you get when you subtract 23 from 42. Using "the difference" means subtraction is involved and you expression is 42 - (minus) (20+3).

Answer

number 4

Step-by-step explanation:

The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

y=3/2, decimal form, y=1.5, mixed number y=1 1/2

Step-by-step explanation:

120-10\left(4y+8\right)=5\left(8y-16\right)\=120-40y-80

-40y+40

The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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