Under his cell phone plan, Magan pays a flat cost of $45 per month and $4 per gigabyte. He wants to keep his bill at $53.80 per month. Write and solve an equation which can be used to determine xx, the number of gigabytes of data Magan can use while staying within his budget.

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y-intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y-intercept is of function -

f(x) = 2x + 4

and the least y-intercept is of the function shown in graph [4] or function [4].

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Answer:

Carlos puts $3 into his bank account and it grows by 50% each year

f(x)=4^x+1

(The Table)

(The Graph)

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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The value of (n o p) (Δ) is X.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

(n o p) (Δ):

= n ( p(Δ) )

From the function map we have,

p(x) = (Δ, Y)

This means,

For x = Δ we get p(Δ) = Y.

So,
= n ( Y )

From the function map we have,

n(x) = (Y, X)

This means,

For x = Y we get n(Y) = X

So,

= X

Thus,

Using the function map,

(n o p) (Δ) is X.

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Answer:

9

Step-by-step explanation:

because half of the 8 pastries served were blueberry. so you would divide 18 by 2

The simplified value of the expression is -7/3 - 2√10/3.

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given (√2 + √5)/(√2 - √5)

simplifying the expression by rationalization

multiply and divide by (√2 + √5)

= (√2 + √5)/(√2 - √5) x (√2 + √5)/(√2 + √5)

= (√2 + √5)²/((√2)² - (√5)²)

using property (a + b)² = a² + b² + 2ab

= (2 + 5 + 2√10)/(2 - 5)

= -(7 + 2√10)/3 = -7/3 - 2√10/3

Hence the simplified form is -7/3 - 2√10/3.

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The height of the tree after 6 years can be expressed as "3 feet + 6f feet."

The correct answer is A. 3f + 6 feet.

To determine the current height of the tree in terms of "f,"

let's analyze the given information.

We know that the tree was initially 3 feet tall when it was planted 6 years ago.

Since the tree grows every year, we can assume that its growth rate is consistent.

Let's denote the current height of the tree as "h" (in feet).

After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").

Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."

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Answer:

45°

Step-by-step explanation:

m∠5 is 45°, and m∠7 is a vertical angle, so it has the same value.

Answer:

the number --4

Step-by-step explanation:

-7--4=-3

-3--4=1

1--4=5

5--4=9

Answer:

\(\frac{-1}{4} x^{2}\)

\(\frac{-1}{4} g(x)\)

Step-by-step explanation:

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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Answer:

It would be -\(\frac{1}{2}\)

Step-by-step explanation:

Use the slope formula to find the slope  m.

Answer:

4 units right, 2 units up

Step-by-step explanation:

For \(g(x)=(x-4)^2+2\), the graph of \(f(x)=x^2\) would need to move 4 units to the right and 2 units up. Hence, the vertex would be \((4,2)\) if we compare the function g(x) with the form \(y=a(x-h)^2+k\).

Answer:

378 students

Step-by-step explanation:

There are 900 students in total.

58% said their favorite color was purple.

To find the percentage of blue, we find subtract 100% by the percentage of purple.

100% - 58% = 42%

42% said their favorite color was blue.

Now we find 42% of the 900 students

0.42 x 900 or 42% of 900 = 378

378 students favorite color was blue.

At x = 0 and x = 7, the function g(x) is undefined.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression of the function is,

⇒ g (x) = 6 / x (x - 7)

Now, We know that;

The function f(x) = a(x) /b (x) is not defined at b (x) ≠ 0

Here, The expression of the function is,

⇒ g (x) = 6 / x (x - 7)

So, Function g (x) is not defined when,

x (x - 7) = 0

⇒ x = 0

or, x - 7 = 0

⇒ x = 7

Thus, At x = 0 and x = 7, the function g(x) is undefined.

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Hey there!

\( \displaystyle{ \red{ \boxed{ \green{ \bold{m = - 1}}}}}\)

\( \\ \)

To find the slope of a line using two points \( \displaystyle{(x_1 , y_1)} \) and \( \displaystyle{(x_2 , y_2)} \) , we can use the slope formula.

This formula corresponds to the quotient of the change in y \( \: \) over \( \: \) the change in x :

\( \displaystyle{m = \frac{ \blue{y_2} - \orange{y_1}}{ \green{x_2} - \red{x_1} }}\)

\( \\ \)

\( \hookrightarrow \) We are given the points (-2 , 3) and (-5 , 6) where:

\( \\ \)

\(\displaystyle{ \hookrightarrow m = \frac{\blue{6} - \orange{3}}{\green{-5} - \red{(-2)}}} \\ \\ \displaystyle{\implies m=\frac{3}{-3}} \\ \\ \displaystyle{\purple{\implies} \boxed{\bold{m=-1}}}\)

Therefore, the slope of the line is -1.

\( \\ \)

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Answer:

\( y = \frac{ 2}{ 3} x - 2\)

Step-by-step explanation:

\(2x - 3y = 6 \\ - 3y = - 2x + 6 \\ \\ y = \frac{ - 2}{ - 3} x + \frac{6}{ - 3} \\ \\ \huge \purple{ \boxed{ y = \frac{ 2}{ 3} x - 2}} \\ this \: is \: in \: the \: slope - intercept \: form.\)

Answer:

y = 2/ 3 x − 2

Step-by-step explanation:

slope intercept is y=mx+b

Answer:

x = 8

x = 7

Step-by-step explanation:

Solving    x2-15x+56 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =   -15

                     C   =   56

Accordingly,  B2  -  4AC   =

                    225 - 224 =

                    1

Applying the quadratic formula :

              15 ± √ 1

  x  =    —————

                   2

So now we are looking at:

          x  =  ( 15 ± 1) / 2

Two real solutions:

x =(15+√1)/2= 8.000

or:

x =(15-√1)/2= 7.000

The completely factorized form of the expression q² - 4 is (q + 2)(q - 2).

Given the expression in the question:

q² - 4

To factorize the expression q² - 4 completely, we can use the formula for the difference of squares.

The difference of squares formula states that :

a² - b² can be factored as (a + b)(a - b).

Given that:

q² - 4

Replace 4 with 2²
q² - 2²

From this expression, let a = x and b = 2

a² - b² =  (a + b)(a - b)

q² - 2² = (q + 2)(q - 2)

Therefore, the factored form is (q + 2)(q - 2).

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mp=n+x the P on the right side cancels out now you want to shift the n to the left side by subtracting it from both sides x=mp-n so that leaves us with the solution. m=n+x/p first you want to move the P over to the left side by x P so that leaves us with the answer. ...

mp=n+X  X=mp-n, where m=n+x/p multiplies p on both sides.

How can you change the formula so that x is the subject?

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x = mp - n ( x as the subject of m= n+ x/p)

How to make x the subject of m = n +x/p ?

\(m =\frac{n+x}{p} \\\\mp = n+ x\\\\mp - n = x\\\\x= mp -n\)

What is making x the subject?

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Answer:

Step-by-step explanation:

Full charge can be expressed as equation:

The limit for charge is $13, then we got inequality:

Option B: 10 is correct as the only number satisfying the inequality

Answer:

B:10

Step-by-step explanation: bcs it is

Answer:

THE ANS IS 0<-23

Step-by-step explanation:

4(X+3)< 7x-3x-11

4x+12< 4x-11

4x will be cancelled,

So we get,

4x-4x< -11-12

0 < -23

Thank YOU AND PLZ MARK AS BRAINLY AND GIVE RATING ALSO

Answer:

(x, y) = (4,-7)

Explanation:

To solve the system we need to graph the line that each equation represents, then the solution will be the point where the lines cross.

So, to graph the line for the first equation 2x + y = 1, we need to identify two points in the line.

Then, if x = 0, y is equal to:

2x + y = 1

2(0) + y = 1

y = 1

And if x = 1, y is equal to:

2(1) + y = 1

2 + y = 1

2 + y - 2 = 1 - 2

y = -1

So, for the first equation, we have the points (0, 1) and (1, -1)

In the same way, for the second equation x - 2y = 18, we get:

If x = 0, y is equal to:

0 - 2y = 18

-2y = 18

y = 18/(-2)

y = -9

If x = 2, y is equal to:

2 - 2y = 18

2 - 2y - 2 = 18 - 2

-2y = 16

y = 16/(-2)

y = -8

So, for the second equation, we have the points (0, -9) and (2, -8)

Therefore, the graph of both lines is:

So, the solution of the system is the point (x, y) = (4, -7)

Hey there!

\( \rightarrow \sf{ r = \sqrt{3 \frac{v}{\pi \ h} }} \: \rm{or} \: \sf{v = \frac{1}{3} \pi \: {r}^{2} \times h}\)

\( \rightarrow \sf{923.16 = \frac{1}{3} (3.14) {r}^{2} \times h}\)

\( \rightarrow \sf{\: 1.046667 {hr}^{2} =923.16}\)

\( \rightarrow \sf{ \frac{1.046667 {hr}^{2} }{1.046667} = \frac{923.16}{1.046667} }\)

\( \rightarrow \: \sf{ {r}^{2} = \frac{923.16}{1.046667h}}\)

\( \rightarrow \: \sf{ r = \sqrt{ \frac{923.16}{1.046667h}}}\)

The measure of angle B is approximately equal to 56.31 degrees, rounded to two decimal places.

An angle measure is a numerical value that represents the amount of rotation between two intersecting lines, line segments or rays. It is typically measured in degrees, although other units of measurement such as radians and grads may also be used. The size of an angle can range from 0 degrees (corresponding to no rotation or a straight line) to 360 degrees (corresponding to a full rotation). In geometry, angles are used to describe the relationships between lines and shapes, and are an important concept in fields such as trigonometry and calculus.

To find the measure of angle B given cot B = 0.57736, we can use the inverse tangent function.

The tangent of an angle is the ratio of the opposite side to the adjacent side,

So cot B = adjacent side / opposite side.

By taking the inverse tangent of both sides and substituting cot B for adjacent side / opposite side, we arrive at the equation

B = arctan(cot B).

Evaluating arctan(cot B) using a calculator gives us the measure of angle B as,

B = arctan(cot B) = 56.31° (rounded to two decimal places)

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The complete question is: "Given cot B = 0.57736, determine the measure of angle B".

Answer:

Step-by-step explanation:

To write an equation for a circle, we need to find the center and the radius.  We need to find the distance between the two endpoints to find the radius.  To do that, use the distance formula:

d = √(2 - 5)² + (1 + 3)²

√(-3)² + (4)²

√9 + 16 = √25 = 5

If the diameter is 5, the radius is 2.5

Now we need to find the center/midpoint.  Use the midpoint formula:

(5 + 2)/2, (-3 + 1)/2

7/2, -2/2

(3.5, -1)

Now that we have the center and the radius, we can make our equation.  Remember that the equation of a circle is: (x - x of center)² + (y - y of center) = radius²

(x - 3.5)² + (y + 1)² = 6.25

Hope this helps

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

so ya 4 kg 600 1 kg

= 600÷4 = 150 rs