Functions f(4) determine what f(x)=40

Answer:

Expression: (65+25)÷10(12-17)

simplification:
45

Answer:

The average rate of change is −10.

Step-by-step explanation:

The average rate of change of f(x) on the interval [a,b] is f(b) − f(a) / b−a.

We have, a=3, b=5, f(x) = -1x^2 − 2x + 2.

Thus, f(b) − f(a) = −(5)^2 −2(5) + 2 − [−(3)^2 −2(3) + 2]

= -25 - 10 + 2 - ( -9 - 6 + 2 )

= -33 - 13

= - 20

Then, b−a = 5 - 3 = 2

f(b) − f(a) / b−a = - 20 / 2 = −10

Answer: the average rate of change is −10.

Answer:

The third option C: -5∛2x is a like radical to the expression 6∛2x.

In mathematics, the symbol √ is used to represent or show that a number is a radical. Radical expression is defined as any expression containing a radical (√) symbol.

The expression 6∛2x can be expanded into two factors which bare 6 and ∛2x

Also for the third option C, the expression -5∛2x can be expanded into two factors which are -5 and ∛2x

By observation, we will notice the two expressions 6∛2x and -5∛2x have same factor ∛2x which make them like radical expressions.

In conclusion, the expression -5∛2x is a like radical expression to 6∛2x.

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The statement that "the midpoint of a line is found by subtracting two coordinates and dividing the answers by two" is false

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula midpoint involves addition two coordinates instead of subtraction, and dividing by two.

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Answer:

Step-by-step explanation:

452.39 is the area

The ratio of the amount Peter spent to that of John is 2:3, so:

(a) If Peter spent 500 dollars, then John spent 75p dollars

(b) If John spent 600 dollars, then they spend altogether 1000 dollars.

(c) If both boys spent 2000 dollars altogether, then John spent 1200 dollars and Peter spent 800 dollars.

(d) If John spent 100 dollars more than Peter, then they both spent 500 dollars as Peter will spend 200 dollars while John spends 300 dollars.

Let us represent the amount of money spent for Peter and John with P and J respectively.

Using the ratio 2:3 for the amount Peter spent to that of John;

If Peter spent 500 dollars, then;

2/3 = $500/J {cross multiply}

J = (3 × $500)/2

J = $1500/2

J = $750

If John spent 600 dollars, then;

2/3 = P/$600 {cross multiply}

P = (2 × $600)/3

P = $1200/3

P = $ 400

Peter and John spent altogether = $1000

If both boys spent 2000 dollars altogether, then;

their total ratio = 5

unit amount = $2000/5

unit amount = $400

Peter spent = 2 × $400 = $800

John spent = 3 × $400 = $1200

If John spent 100 dollars more than Peter, then;

2/3 = P/(P + $100) {cross multiply}

3P = 2(P + $100)

3P = 2P + $200 {collect like terms}

3P - 2P = $200

P = $200.

Peter spent = $200

John spent = $300.

In conclusion, using the ratio 2:3 for the amount of money spent by Peter and John respectively, we have the answers: $750, $1000, $800 for Peter and $1200 for John, and $200 for Peter and $300 for John for the questions lettered (a), (b), (c), and (d) respectively.

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The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.

Therefore, 2 quarts will be:

= 2 × 4.

= 8 cups

Therefore, the price per cup will be:

= $5.36 / 8

= $0.67

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On solving the provided question we can say that - the value of the equation x = y^2 -5 from the graph will be 59.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here, the equation from the graphs is

[tex]x = y^2 -5[/tex]

and y = 8

x = 59

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The coordinates for graph are (4, -3)(-8, 6)(8, -6)(-4, 3)(0, 0).

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

Given, equation

2/3y = -1/2x

according to option

when x = 0

y = 0

(0, 0)

when x = 4

2/3y = -1/2(4)

y = -3

(4, -3) and similarly (-4, 3)

when x = 8

2/3y = -1/2(8)

2/3y = -4

y = -6

(8, -6) similarly (-8, 6)

Hence the coordinates for equation are  (4, -3)(-8, 6)(8, -6)(-4, 3)(0, 0).

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Answer:

Step-by-step explanation:

ur mom

Answer: Width is 70 yd and length is 120 yd

The required value of the given antiderivative function is G(4) = -7+∫₂⁴f(t)dt which is the correct answer that would be an option (E).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The antiderivative of a function is a function that when differentiated gives the original function.

Since G(x) is an antiderivative for f(x), G'(x) = f(x).

If G(2) = -7, then we know that G(4) = G(2) + ∫₂⁴ f(t)dt.

So, G(4) = -7+∫₂⁴f(t)dt

Therefore, the answer is (E) -7+∫₂⁴f(t)dt.

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The height of triangle A ABC is 4 units.

What is the triangle's height, h?

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Answer:

1 - False

2 - False

3 - True [for prism which can separate white light into 7, i.e, ordinary prism]

4 - False [for the type of prism stated above]

5 - True

Step-by-step explanation:

If you can, get a picture of a normal prism and look at it. There are MANY different types of prisms. The answers I have given above are only applicable to the prism we refer to normally, i.e., the pyramid-like shaped one.

The function that best shows the relationship between n and f(n) is;

f(n) = 24(0.5)ⁿ⁻¹

The function table that shows the amount of chlorine is given as;

n    1        2      3     5

f(n)  24     12      6    3

Where;

f(n) is the amount of chlorine in ounces, that was left in the pool after n weeks:

We can see that the value of f(n) is decreasing as n increases from the table.

Due to the fact that f(n) does not have common difference. Let us attempt tp see if it has a common ratio;

12/24 = 0.5

6/12 = 0.5

3/6 = 0.5

Using the formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

Where;

a represents the first term = 24

r represents the common ratio = 0.5

Thus, the equation of the function is;

f(n) = 24(0.5)ⁿ⁻¹

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Pablo's salary is modeled with the linear equation:

S = $60*N + $1900

Its graph is on the image at the end.

Here we know that Pablo is a software salesman, he wins a fixed salary of $1900, plus $60 for each copy of History is Fun that he sells.

So, if he sells N of these books, then his monthly salary is:

S = $60*N + $1900

So we have a linear equation, and now we want to graph it, to do so, we need to find two points on the line, and then connect them, to find the two points, we need to evaluate the linear equation.

If N = 0, then we get:

S = $60*0 + $1900

S = $1900

So we have the point (0, $1900)

Evaluating in N = 1 we get:

S = $60*1 + $1900

S = $1960

So we have the point (1, $1960)

Now we can graph these two points and connect them with a line, the graph of the salary equation is below.

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Answer:

[tex]8\sqrt{5x}[/tex]

Step-by-step explanation:

I'm assuming the "x" is also under the square root, making the equation:

[tex]9\sqrt{5x} - \sqrt{5x}[/tex]

This may look difficult to simplify at first, but this is really a matter of subtracting coefficients. It may help to explicitly write the coefficient of the square root, which is one.

[tex]9\sqrt{5x} - 1\sqrt{5x}[/tex]

This can be thought of as having 9 of something, and taking away 1 of that thing, this logically means you have 8 left. In this case, that "thing" is the: [tex]\sqrt{5x}[/tex], so we have 8 of this, or in other words: [tex]8\sqrt{5x}[/tex] which is our answer! Note: It also may help to think of the equation as: [tex]9x-x[/tex] which you may be more used to, making it easier to remember just to subtract coefficients, except in this case, [tex]x=\sqrt{5x}[/tex]

Another way to think of this problem, which will lead to the same step of subtracting one from nine, is factoring. Starting with the equation:

[tex]9\sqrt{5x} - 1\sqrt{5x}[/tex]

We can factor out the [tex]\sqrt{5x}[/tex] which leads to the equation:

[tex]\sqrt{5x}(9-1)[/tex]

now just simplify that 9-1, and you get:

[tex]8\sqrt{5x}[/tex]

Answer:

$5.00

Step-by-step explanation:

2.00/40% = x/100%

Using the butterfly method becomes:

200/40x

then solve for x:

200/40 = 40x/40

5 = x

6x²+11x+4

6x² + 8x + 3x + 4

2x(3x+4) + 1( 3x + 4 )

Answer:

[tex](3x + 4)(2x + 1)[/tex]

Step-by-step explanation:

We can factor the expression

[tex]6x^2+11x+4[/tex]

using the grouping method.

First, multiply the coefficient on the x² term by the constant term.

6 × 4 = 24

Then, list out the factor pairs of the product.

24  

1, 24

2, 12

3, 8

4, 6

If one of the pair's numbers add to the coefficient of the x term in the polynomial, then we can substitute in that pair of numbers for the x's in the expression.

In this case, the 3 and 8 pair add to 11, the x term's coefficient.

[tex]6x^2+11x+4[/tex]

[tex]6x^2 + 3x + 8x + 4[/tex]

Next, we can factor a term out of the first and last two terms of the polynomial.

[tex](6x^2 + 3x) + (8x + 4)[/tex]

[tex]3x(2x + 1) + 4(2x + 1)[/tex]

Finally, we can apply the distributive property to the expression to rewrite it in factored form.

[tex](3x + 4)(2x + 1)[/tex]

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

y = –1 2 x + 3 and y = 1 2 x - 1, the systems of linear equations.

from the graph , we have,

the solution set to this system of equations is,

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

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Answer: D

Step-by-step explanation:

1. If a value of 120.5° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, D. The mean increases by 3.1°.

2. If a shoe size of 6 is added to the ordered data, 5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, B. The IQR remains a 2.

3. If a value of 101° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, B. The mean increases by 1.6°.

4. If a shoe size of 9 is added to the ordered data, 5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, the median that was 6.75, now D. The median increases to 7.

5. If a value of 60° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, C. The median decreases to 77°.

6. If a value of 80.2° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, C. The range stays at 48°.

7. If a value of 58° is added to the data, (57, 58, 61, 66, 71, 77, 80.8, 82, 91, 95, 100, 102, 105), the measure that chances the most is the D. IQR with the new value as 32°.

The mean refers to the average value while the median is the middle value in the dataset.  The range shows the difference between the highest value in the dataset and the lowest value.

The Interquartile Range (IQR) is the median value or 50% percentile, the difference between the 75th and 25th percentiles of the data set.

To compute the interquartile range, determine the median of the data's lower and upper half and subtract quartile 1 from quartile 3.

1. Average high temperatures for a city:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Total = 965°

Average = 80.4° (965° ÷ 12)

New average with 120.5° added:

New total = 1,085.5° (965° + 120.5°)

Average = 83.5° (1,085.5° ÷ 13)

The difference in mean = 3.1° (83.5° - 80.4°)

2. Shoe Sizes:

5  5.5  6  6.5   6.5   7  7.5  8  8  8.5

Median = 6.75 (6.5 + 7)/2

Interquartile = 8 - 6 = 2

Add shoe size 6 to the data:

5  5.5  6    6   6.5   6.5   7  7.5  8  8  8.5

Median = 6.5

IQR = 8 - 6 = 2

3. Average Temperature:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Total = 965°

Mean = 80.4° (965° ÷ 12)

If a value of 101° is added to the data, the new mean becomes:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 101

Total = 1,066

Mean = 82° (1,066 ÷ 13)

The difference in the mean = 1.6° (82° - 80.4°)

4. Raw Data:

 5.5   6   7     8.5   6.5

 6.5   8   7.5  8      5

Arranged:

5  5.5  6  6.5   6.5   7  7.5  8  8  8.5

Median of data = 6.75 (6.5 + 7) ÷ 2

When 9 is added to the data:

5  5.5  6  6.5  6.5  7  7.5  8  8  8.5  9

Median = 7

5. 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Ordered Data:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Median = 79.5 (77 + 82)/2

Add 60°, the new ordered data:

57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Median = 77

6. Range:

Highest value = 105

Lowest value = 57

Difference = 48

Range = 48 (105 - 57)

Add 80.2°, the range stays at 48° (105 - 57)

7. Average high temperatures:

Raw Data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Ordered Data:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Total = 965

Mean = 80.4 (965 ÷ 12)

Median = 79.5 (77 + 82)/2

IQR = 39 (100 - 61)

Range = 48 (105 - 57)

A new temperature of 58° is added,

57, 58, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Total = 1,023

Mean = 78.7 (1,023 ÷ 13)

Median = 77

IQR = 32 (93 - 61)

Range = 48 (105 - 57)

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The number of days that the skier would have to go skiing for the season pass to be less expensive than the daily passes would be 5 days.

The season ski pass would cost $ 350 while a pass a day would cost $ 79. The skier would then rent skis with either of the passes for the same price of $ 20 per day, which means that this factor is irrelevant in calculating the number of days till the season pass is less expensive.

The number of days till the season pass is less expensive is therefore:

= Cost of season pass / Cost of daily ski pass

= 350 / 79

= 4. 43

= 5 days

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The final answer of the corrected expression is  (-22, -26).

What is the solution to the linear equation?

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

We have given:

 y = x - 4

-2x + y = 18

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

-2x + (x - 4) = 18

-x - 4 = 18

x = 22

y = 22 - 4

y = 18

Solution: (22, 18)

The error is in lines 3, 4, and 5.

It should have,

 y = x - 4

-2x + y = 18

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

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22

x = -22

y = -22 - 4

y = -26

Solution: (-22, -26)

Hence, the final answer of the corrected expression is  (-22, -26).

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(A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

What is the explicit formula?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

A. The data provided is modeling a geometric sequence.

This is because the common ratio between consecutive terms is a constant value, specifically in this case is the ratio between consecutive terms is multiplied by 2.

B. To find the time Aurora will complete station 5 using a recursive formula,

we can use the formula T(n) = T(n-1) * r,

where T(n) is the time at the nth station, T(n-1) is the time at the (n-1)th station, and r is the common ratio.

In this case T(5) = T(4) * 2

and T(4) = 24 (from the data provided)

Therefore, T(5) = 24 * 2 = 48 minutes

C. To find the time Aurora will complete the 9th station using an explicit formula,

we can use the formula T(n) = T(1) * r^(n-1)

In this case, T(9) = T(1) * 2^(9-1)

and T(1) = 3 (from the data provided)

Therefore, T(9) = 3 * 2^8 = 3 * 256 = 768 minutes

The explicit formula assumes that the first term of the sequence is T(1) and the common ratio of the consecutive term is r.

Hence, (A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

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On solving the provided question, we can say that - the value of the quadratic equation will is 3X1 + 18 X 2 = 39.

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

the quadratic equation we have is -

[tex]3x^2 + 16y[/tex]

and x= 1

and y = 2

so,  3X1 + 18 X 2 = 39

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Answer:

a,b

Step-by-step explanation:

The equation for age of dog and cat is d = c - 3.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Given Elijah's dog is 3 years younger than his cat,

and  Let d represent his dog's age and c represent his cat's age,

when cat age is c,

dog age will be 3 less than c, which is c - 3

the equation is d = c - 3

Hence the equation is d = c - 3.

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Answer: 25.99205

Step-by-step explanation: The way I have solved it is by multiplying the answer and the only know number to be multiplied. Then I got 25.99205 and double checked it by dividing it by 7.21 and got 3.605.

Answer: 12.8

Step-by-step explanation:

Just do 0.32 x 40.