Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6

The value of C (8,5) is 56.

A combination is made up of n different items that are taken one at a time without repeating itself.

The given expression is C(8,5).

The expression C (8,5) can be denoted as ₈C₅.

The formula for selecting x thins from n things is:
ₙCₓ = n!/( (n-x)! x!)

Therefore, the value of ₈C₅ is:

₈C₅ = 8!/( (8-5)! 5 !)

     = 8!/( 3! ×5!)

      = (8×7×6×5!)/( 3! ×5!)

      = (8×7×6)/(3!)

      = (8×7×6)/(6)

      = 8×7

      =56

Hence, the value of C (8,5) is 56.

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Answer:

D.) 11

Step-by-step explanation:

-9=-k^2-7k+k Plugging in k for x

-9=k^2-6k Combine like terms

0=k^2-6k+9 Add 9 to both sides

0=(k-3)(k-3) Factor

k=3

The equation is now

f(x)=x^2-7x+3

so

f(-1)=(-1)^2-7(-1)+3

f(-1)=1+7+3

f(-1)=11

The expression that represents the number of tiles on Wendy's kitchen floor is B. 8 × 8t.

An expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, Wendy lays rows of 8 tiles each to cover her kitchen floor.

Let t = the number of rows.

Therefore, the number of tiles on Wendy's kitchen floor will be:

= 8 × 8t.

Therefore, the correct option is B.

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The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°

A secant line is a straight-line which has two points of intersection with a circle.

From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°

The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.

Mathematically;

[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]

Where;

The outside angle formed by the secant ZW and ZV, m∠z = 41°

[tex]\widehat{VW}[/tex] = 112°

Which gives;

[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]

2 × 41° = 112° - [tex]\widehat{XY}[/tex]

82° = 112° - [tex]\widehat{XY}[/tex]

[tex]\widehat{XY}[/tex] = 112° - 82° = 30°

[tex]\widehat{XY}[/tex] = 30°

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the answer to that question is 34cm² of the circumference

The dividend is 35286 and the divisor is 7. The value of the division is $540.8571

When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.

On the other hand, the number that is being divided by which is in this case 7 is the dividend.

The division will be:

= $35286 ÷ 7

= $540.8571

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Answer:

Step-by-step explanation:

x=5

Answer:

amount owed = $7434.57

Step-by-step explanation:

To solve this problem, we have to use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],

where:

• A = final amount

• P = principal (initial) amount

• r = annual interest rate

• n = amount of times the interest is compounded per time period

• t = number of years the money is kept for

In this case, the principal amount, P = $5000 and the money is owed for two years, so t = 2. The annual interest rate, r = 0.20 (20% = [tex]\frac{20}{100}[/tex] = 0.2). The interest is compounded monthly, which means it is compounded 12 times per year. Therefore, n = 12.

Using the above information and formula, we can calculate the amount owed after 2 years:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

   [tex]= 5000(1 + \frac{0.2}{12})^{12 \times 2}[/tex]

   [tex]=[/tex] $7434.57

Therefore, the amount Edgar owes after 2 years is $7434.57.

The value of  x is 26.125°

The measures of each angle are as shown below:

∠P  = 115.625°

∠Q =21.125°

∠R=43.25°

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

In ∆PQR

∠P is 14 less than five times x = 5x-15

∠Q is five less than x=x-5

∠R is nine less than twice x=2x-9

Angle sum property of triangle : The sum of all angles of triangle is 180°

So,5x-15+x-5+2x-9=180

8x-29=180

8x=180+29

x=( 180+29 )/8

x=26.125

So,∠P  = 5x-15 =5(26.125)-15=115.625°

  ∠Q =x-5=26.125-5=21.125°

 ∠R=2x-9=2(26.125)-9=43.25°

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From the graph,

a. Friend runs at constant rate because of the straight line graph

b. the domain of the function representing your run 0 ≤ x ≤ 60

the domain of the function representing your friend's run 0 ≤ x ≤ 60

The graph of a straight line shows that the variables are constantly varying hence the graph that has a straight line which is your friend's graph is the graph at constant rate.

The domain is controlled by the x direction, it consist of all the values that the s coordinate ca get to

The graph shows that both you and your friend has similar x coordinate and will have same domain

The x coordinate from the beginning of the graph is at 0. At the end it is at at point 60

point 60 is not marked but reading the graph it can be deduced that the last line is point 60. hence the domain is 0 ≤ x ≤ 60

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Answer:

289560

Step-by-step explanation:

Answer: See coordinate graph below.

Step-by-step explanation: Again, the black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

D': (-6, 5)

Have a great day! :)

Answer:

  D(8, -11)

Step-by-step explanation:

You want the coordinates of end point D if C is (2, -3) and the midpoint of CD is M(5, -7).

The midpoint is the average of the endpoint coordinates:

  M = (C +D)/2

Solving for D, we find ...

  D = 2M -C

Then point D is ...

  D = 2(5, -7) -(2, -3) = (2·5-2, 2(-7)+3)

  D = (8, -11)

The probability that X will be greater than 25 is 0.42

Given,

The sample size, n = 39

The mean of the population, μ = 23

The standard deviation of the population, σ = 10

We have to find the probability for X > 25.

Here,

Z score = (X - μ) / σ

Z score = (X - 23) / 10

Now,

We have to find P(X > 25)

Then,

P(X > 25) = P(z >  (25 - 23) / 10)

P(X > 25) = P(z > 2/10)

That is,

P(X > 25) = P(z > 0.2)

Here,

0.5 - P(0 ≤ z ≤ 0.2)

= (0.5 - 0.0792)

= 0.42

Therefore,

The probability that X will be greater than 25 is 0.42

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The integer +3 describes the statement, 3 inches above average.

What is an average?

A single number chosen to represent a group of numbers is called an average, and it is typically calculated by dividing the total number of numbers in the group by the number of numbers in the group. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.

One point in the average refers to the amount of 1 inch.

If the average is above 3 inches, it means that the value of the average is above 3 inches. It further implies that the total value has gained 3 inches on that average.

Inches mainly describe the gains and losses in short-time investments. A positive sign (+) shows the above average, and a negative sign (-) represents the below average.

Therefore, the integer +3 describes the statement, 3 inches above average.

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The number of tongue depressors = 56

The number of Band-Aids = 128

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the number of tongue depressors.

Let y be the number of Band-Aids

Convert cents to dollars

1 cent = $0.01

So, 4 cents = 0.01*4 = $0.04

     8 cents = 0.01* = $0.08

The materials are worth $12.48 .

This means, 0.04x+0.08y=12.48......(1)

There are 184 individual packages in total.

This means,  x+y=184.......(2) => x=184-y.....(3)

Substitute (3) in (1),

0.04(184-y)+0.08y=12.48

7.36-0.04y+0.08y=12.48

=> y= 128

(3) => x=184-128=56

So, the number of tongue depressors = 56

     The number of Band-Aids = 128

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Answer:

he read 9 chapters

Step-by-step explanation:

4:30 pm to 6:00 pm is 1:30 hours, which is 90 minutes

90/10=9

Answer: 7

Step-by-step explanation:

Answer:

7 is the GCF of 21 and 28

Step-by-step explanation:

The GCF of 21 and 28 is 7. To calculate the greatest common factor (GCF) of 21 and 28, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 21 and 28, i.e., 7.

The value of x in the given triangle is x = -8  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of first angle is 51°

the measure of second angle is 83°

the measure of third angle is (x + 54)°

So , By Angle sum property ,

we get

first angle [tex]+[/tex] second angle [tex]+[/tex] third angle [tex]=[/tex] 180°

substituting the values of angles

we get

51° +  83° + (x + 54)° = 180°

134 + x + 54 = 180

188 + x = 180

x = 180 - 188

x = -8

Therefore , the value of x in the triangle is -8  .

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The perimeter of the shape is 38 total unit.

The perimeter of a shape is a measure of the distance round the boundary or edge of the shape.

The given shape comprises of squares of 1 length each, hence to calculate for the perimeter of the shape, we add up each boundary of 1 unit length which will amount to 39 in total.

Therefore by careful observation, the perimeter of the plane shape is calculated to give us 39 total perimeter length.

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Answer:

Step-by-step explanation:

The expression equivalent to [tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex] is m - 2.

Equivalent expressions are expressions that work the same even though they look different.

In other words, equivalent expressions are expressions that have the same value.

Therefore, the expression that is equivalent can be calculated as follows:

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex]

Hence, let's simplify the expression to find it's equivalent,

open the bracket

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m[/tex]

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m = -\frac{21}{2}+\frac{17}{2}+2m-m[/tex]

[tex]-\frac{21}{2}+\frac{17}{2}+2m-m=-\frac{4}{2} + m[/tex] = m - 2

Therefore,

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = m-2[/tex]

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Answer: no slope

Step-by-step explanation:
m= y2-y1/x2-x1

m= 6-(-6)/4-4

m=12/0

m= no slope

Answer:

y = 0.8x - 0.8

Step-by-step explanation:

Δy ÷ Δx = gradient (x)

4 - -4 = 8

6 - -4 = 10

8 ÷ 10 = 0.8

equation of line; y = mx + c

substitute one of the coordinates into the equation

(6, 4) y  = 4, x = 6

4 = 0.8(6) + c

4 = 4.8 + c

- 4.8 to get the y intercept on it's own

-0.8 = y intercept (c)

confirmation

substitute the new values to get the other y

(-4, -4) y = -4 <-- should be the answer, x = -4

y = mx + c

y = 0.8(-4) - 0.8

y = -3.2 - 0.8

y = -4 the gradient and the y intercept have been proven right

The rational zeros for F(x)=3x^4-4x^3+x^2+6x-2 are x= -1 and x= 1/3 while the linear factors are (x+1) and (3x-1)

Synthetic division has to do with dividing polynomials.

The process involves:

Step 1: Set up the synthetic division.

Step 2: The leading coefficient should be brought down to the bottom row.

Step 3: Multiply this by the value just written on the bottom row.

Step 4: Then, add the column created in step 3.

This can be illustrated thus:

Given: f(x) = 3x⁴-4x³+x²+6x-2

3x⁴-4x³+x²+6x-2 = 0

We will try x = -1 in f(x). In this case, replace x with -1. This will be:

= 3x⁴-4x³+x²+6x-2 = 0

Since f(-1)= 0 so (x+1) is a factor

Using synthetic division:

-1)....3....-4....1....6....-2

.........3.....-7...8....-2..|..0

Remainder = 0

Quotient = 3x³ -7x² + 8x -2

For 3x³ -7x² + 8x -2,  f(1/3) = 0 so (x- 1/3) is a factor

1/3)....3....-7....8....-2

..........3.....-6...6...|..0

Remainder = 0

Quotient = 3x²-6x+6

= 3(x²-2x+2)

Since there are no more rational zeros or linear factors for x²-2x+2. Therefore, the rational zeros are x= -1 and x= 1/3.

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Answer:

[tex]\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)[/tex]

[tex]\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=3x^3-2x^2-11x+10[/tex]

If (x + 2) is a factor then:

[tex]\implies f(x)=(x+2)(ax^2+bx+c)[/tex]

Expand:

[tex]\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c[/tex]

[tex]\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c[/tex]

[tex]\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c[/tex]

To find a, compare the coefficients of x³:

[tex]\implies a=3[/tex]

To find b, substitute the found value of a into the coefficient for x² and compare:

[tex]\implies 2a+b=-2[/tex]

[tex]\implies 2(3)+b=-2[/tex]

[tex]\implies b=-8[/tex]

To find c, compare the constants:

[tex]\implies 2c=10[/tex]

[tex]\implies c=5[/tex]

Therefore:

[tex]\implies f(x)=(x+2)(3x^2-8x+5)[/tex]

Now factor (3x²-8x+5):

[tex]\implies 3x^2-3x-5x+5[/tex]

[tex]\implies 3x(x-1)-5(x-1)[/tex]

[tex]\implies (3x-5)(x-1)[/tex]

Therefore the factored function is:

[tex]\implies f(x)=(x+2)(3x-5)(x-1)[/tex]

Zero Product Property

[tex]\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}[/tex]

To find the zeros, set each factor equal to zero and solve for x:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies 3x-5=0 \implies x=\dfrac{5}{3}[/tex]

[tex]\implies x-1=0 \implies x=1[/tex]

Therefore, the zeros of the function are:

[tex]x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]

The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).

what is the slope-intercept?

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

The slope-intercept form: y = mx + b

m - a slope

b - y-intercept

Here, we have

A slope m = 1/4.

Substitute: y = 1/4 x + b

We know that

the line passes through the point (8, 3) → x = 8, y = 3.

Put the values of x and y into the slope of the line:

1/4 · 8 + b = 3

2 + b = 3 |-2

b = 1

Hence, the y-intercept is (0, 1)

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