Miss Nestor is randomly passing out books to her students for free reading time. In her book basket, she has 10 mysteries, 8 historical fiction novels, and 2 biographies. If there are 10 students in Miss Nestor's class for free reading time today, which of the following is the best prediction of the number of students who will receive historical fiction novels for free reading time?

The polynomial 1 - bx - x + b can be factored by rearranging the terms to (1 + b) - x(1 + b), allowing us to factor out 1 + b, resulting in the factored form (1 + b)(1 - x).

The polynomial in question, 1 \\u2212 bx \\u2212 x + b, can be factored by rearranging and grouping terms. Indeed, the suggestion to factor out at least one x from all terms that contain it can be helpful in some cases, for example, ax^2+bx+c. However, for the polynomial given, we need to rearrange the terms to (1 + b) \\u2212 x(1 + b). Notice that 1 + b can be factored out, resulting in (1 + b)(1 \\u2212 x).

Therefore, the factored form of 1 \\u2212 bx \\u2212 x + b is (1 + b)(1 \\u2212 x).

In general, when factoring polynomials, being attentive to common factors and rearranging terms to identify them can lead to a simpler expression. For a quadratic equation like ax^2+bx+c=0, factoring is a powerful tool, often applied after identifying an integrating factor or using the quadratic formula.

Answer:

15

Step-by-step explanation:

To isolate the variable, subtract 95 on both sides.

110=m + 95

m=15

Hope this helped! :)

Answer:

m=15

Step-by-step explanation:

110=m+95

Just subtract 95 from each side to isolate m and get your answer

110=m+95

-95     -95

15=m

Answer: x+b>c/x

Step-by-step explanation: hope it helps please give brainliest!

Answer:

what kind of math is that?

Answer:

6780

Step-by-step explanation:

(60/9) * 1017 = 6780

Answer:

(6,-7)

(2,1)

(-4,13)

Step-by-step explanation:

we have

[tex]2x+y=5[/tex] -----> equation A

[tex]3y=15-6x[/tex] ----> equation B

Multiply the equation A by 3 both sides

[tex]3(2x+y)=3(5)[/tex]

[tex]6x+3y=15[/tex]

isolate the variable 3y

[tex]3y=15-6x[/tex] -----> equation C

equation B and equation C are equal

That means -----> is the same line

so

The system has infinity solutions

Remember that

If a ordered pair is a solution of the line, then the ordered pair must satisfy the equation of the line

Verify each ordered pair

1) (6,-7)

substitute the value of x and the value of y in the linear equation

[tex]3(-7)=15-6(6)[/tex]

[tex]-21=-21[/tex] ---> is true

so

The ordered pair is a solution of the system of equations

2) (2,1)

substitute the value of x and the value of y in the linear equation

[tex]3(1)=15-6(2)[/tex]

[tex]3=3[/tex] ---> is true

so

The ordered pair is a solution of the system of equations

3) (-2,-9)

substitute the value of x and the value of y in the linear equation

[tex]3(-9)=15-6(-2)[/tex]

[tex]-27=27[/tex] ---> is not true

so

The ordered pair is not a solution of the system of equations

4) (-4,13)

substitute the value of x and the value of y in the linear equation

[tex]3(13)=15-6(-4)[/tex]

[tex]39=39[/tex] ---> is true

so

The ordered pair is a solution of the system of equations

Answer:

(6,-7)

(2,1)

(-4,13)

Step-by-step explanation:

got it right on edg2020 :)

The slope-intercept form is [tex]y=\frac{1}{2} x+5[/tex].

Solution:

Given data:

Slope of the line, m = [tex]\frac{1}{2}[/tex].

Point on the line = (–2, 4)

Here [tex]x_1=-2, y_1=4[/tex]

Let us find the slope-intercept form of the line using point-slope formula.

Point-slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]$y-4=\frac{1}{2} (x-(-2))[/tex]

[tex]$y-4=\frac{1}{2} (x+2)[/tex]

[tex]$y-4=\frac{1}{2} x+1[/tex]

Add 4 on both sides of the equation.

[tex]$y=\frac{1}{2} x+5[/tex]

Hence the slope-intercept form is [tex]y=\frac{1}{2} x+5[/tex].

Answer:

[tex]\frac{x-2}{2(x+2)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4x}{x+2}[/tex] × [tex]\frac{x-2}{8x}[/tex]

Cancel 4x and 8x on the numerator/ denominator, thus

[tex]\frac{1}{x+2}[/tex] × [tex]\frac{x-2}{2}[/tex]

= [tex]\frac{x-2}{2(x+2)}[/tex]

4    180

8    360

12   720

The formula is x*2 | y * 2

Hey there!

Let's set up a proportion to figure this out.

[tex]\frac{x}{y} =\frac{4}{180} =\frac{8}{360} =\frac{12}{y}[/tex]

As we can see, 180 is being added each time, on the bottom. If we continue with the pattern, we get that your final blank will be 540.

I hope this helps! Have a great day!

The largest radius for the swimming pool is 15.1 feet

Step-by-step explanation:

Step 1:

Circumference of the circular swimming pool built by Dan  = 95 feet

We need to determine the largest radius for the pool.

Step 2 :

Circle's circumference  is given by 2πr

Where r represents the radius

This shows that the radius is in direct proportion to the circumference. Hence the radius corresponding to the maximum circumference will be the largest possible radius

So we have 2πr = 95

=> r = [tex]\frac{95}{2\pi }[/tex]  

=> r =   [tex]\frac{95}{2}[/tex] × [tex]\frac{7}{22 }[/tex]  where [tex]\pi = \frac{22}{7}[/tex]

=> r = 15.1 feet (rounded off to tenth of a foot)

Step 3 :

The largest radius for the swimming pool is 15.1 feet

Final answer:

the largest radius possible for the pool, to ensure the circumference does not exceed 95 feet, is 15.1 feet.

Explanation:

Calculating the Largest Radius for a Swimming Pool

To find the largest possible radius for Dan's circular swimming pool with a circumference of no more than 95 feet, we will use the formula for the circumference of a circle, which is C = 2πr.

We need to solve for r (radius) when C ≤ 95 feet.

Setting up the equation:

Therefore, the largest radius possible for the pool, to ensure the circumference does not exceed 95 feet, is 15.1 feet.

Answer:

There were 36 space rocks in total.

Answer:

1 over 14

Step-by-step explanation:

reduce the expression, if possible. by canceling the common factors.

Answer:

[tex] {12}^{ - 11} [/tex]

Step-by-step explanation:

The expression to be simplified is

[tex] {12}^{ - 6} \times {12}^{ - 5} [/tex]

We can see that the expression involves the idea of indices.Thus,we need to consider one of the laws of indices when dealing with the expression.

One of the laws of indices states that,

[tex] {a}^{m} \times{a}^{n} = {a}^{m + n} [/tex]

This means that when multiplying indices and the bases are equal, you repeat one of the bases and add the exponents.

This implies that

[tex] {12}^{ - 6} \times {12}^{ - 5} = {12}^{ (- 6 - 5)} [/tex]

Simplifying the exponent we obtain

[tex] = {12}^{ - 11} [/tex]

Using the cost equation C = $25 + ($1.50 x M), we solve for the greatest number of miles Kelly can travel with an $80 budget, which is 36 miles after rounding down to the nearest whole number.

To determine the greatest number of miles Kelly can travel, we use the equation provided by the truck rental company. The total cost of renting a truck is composed of a one-time fee and a per-mile charge. To begin, we subtract the one-time fee from the total budget to find out how much money is left for the per-mile charges.

The equation representing the total cost (C) for the miles (M) driven is:

C = $25 + ($1.50 × M)

Kelly has $80 to spend, so we set the total cost equal to $80:

$80 = $25 + ($1.50 × M)

Now, we solve for M:

$55 = $1.50 × M

M = $55 / $1.50

M = 36.67

Since Kelly cannot travel a fraction of a mile, we round down to the nearest whole number. The greatest number of miles Kelly can travel is 36 miles.

In this problem, we know that Harry saved $100 each week for 8 weeks. In other words, he saved a total amount of money:

[tex]\text{Amount of money saved}=8\times 100=\$800[/tex]

We know that he earned $48 on his savings of $800, so for every $100 the interest (I) he earns is:

[tex]I=\frac{48}{8}=\$6[/tex]

So, in conclusion Harry did earn $6 in interest for every $100

Answer:

Step-by-step explanation:

65=5x (5x means 5 X as many bikes)

so 65=5x

x=13 bikes in stock (65 is divisible by 5)

Answer:

14 4/5 went by car.

Out of 15 friends traveling to Washington DC, 6 went by bus, 5 by metro, and 4 by car, making the fraction that went by car 4/15.

To find out how many friends traveled by each mode of transportation to Washington DC and what fraction went by car, we can follow these steps:

So, the fraction that went by car is 4/15.

Summary of transportation mode:

Answer:

[tex]minor\ arc\ BD=100^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

A circumscribed angle is the angle made by two intersecting tangent lines to a circle

so

In this problem

BC and CD are tangents to the circle

BC=CD ----> by the Two Tangent Theorem

That means

Triangle ABC and Triangle ADC are congruent

so

[tex]m\angle BAC=m\angle DAC[/tex]

Find the measure of angle BAC

In the right triangle ABC

[tex]m\angle BAC+m\angle BCA=90^o[/tex]

substitute given value

[tex]m\angle BAC+40^o=90^o[/tex]

[tex]m\angle BAC=90^o-40^o=50^o[/tex]

Find the measure of angle BAD

[tex]m\angle BAD=2m\angle BAC[/tex]

[tex]m\angle BAD=2(50^o)=100^o[/tex]

Find the measure of minor arc BD

we know that

[tex]minor\ arc\ BD=m\angle BAD[/tex] -----> by central angle

therefore

[tex]minor\ arc\ BD=100^o[/tex]

Final answer:

The measure of the minor arc BD is d. 80°, because it is twice the measure of the inscribed angle BCA, which is 40°.

Explanation:

When we are looking for the measure of a minor arc in a circle, and we know the measure of the inscribed angle that subtends that arc, we can find the measure of the arc by understanding that the inscribed angle is half the measure of the arc it cuts from the circle. Given that angle BCA measures 40°, and assuming BCD is an inscribed angle that subtends the arc BD, we can deduce that the minor arc BD is actually twice the measure of the inscribed angle BCA.

Therefore, to find the measure of minor arc BD, we double the measure of angle BCA:

Measure of minor arc BD = 2 × measure of angle BCA
Measure of minor arc BD = 2 × 40°
Measure of minor arc BD = 80° (d.)

Answer:

The multiplication property of equality states that if two values a and b are equal when you multiply each by the same value c, the products are equal.

Step-by-step explanation:

Multiplication property of equality:

So, if

[tex]a = b[/tex]

Then, we can write by multiplication property of equality

[tex]a=b\\\Rightarrow a\times c = b \times c\\\Rightarrow ac = bc[/tex]

Thus, the correct answer is

The multiplication property of equality states that if two values a and b are equal when you multiply each by the same value c, the products are equal.

Final answer:

The statement in question highlights the equality property of multiplication, which states that if two values are equal, their products with a same multiplier are also equal. This principle is fundamental in mathematics, particularly in algebra, where it underpins the manipulation and understanding of equations.

Explanation:

The statement "if two values a and b are equal when you multiply each by the same value c, the products are equal" refers to the basic principle of the equality property of multiplication in mathematics. This property underlines that if a = b, then a × c = b × c. This fundamental concept is crucial for understanding algebraic expressions and equations, where the manipulation of variables and constants is based on such properties.

For example, if we assert that 3 (number a) and 3 (number b) are equal and we choose to multiply both by 2 (number c), the resulting products, 6 and 6, are indeed equal. This example clearly illustrates how the equality of products remains consistent regardless of the multiplier, as long as the initial quantities are equal.

This principle is foundational in mathematics and serves as a cornerstone for solving equations, thereby reinforcing the understanding that equality is maintained through operations of multiplication by a constant.

Answer:   D) (x + 3)² + (y + 5)²  = 16

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²    

where (h, k) = center   and    r = radius

Given: (h, k) = (-3, -5)  r = 4

Equation: (x - (-3))² + (y - (-5))² = 4²

                 (x + 3)²  +  (y + 5)²  = 16

Answer:

d

Step-by-step explanation:

the coordinate of k would be (-6,10.5)

Answer:

Option D, 32

Step-by-step explanation:

Step 1:  Identify the equation

6y = 192

Step 2:  Solve for y by dividing both sides by 6

6y / 6 = 192 / 6

y = 32

Answer:  Option D, 32

Answer:

Step-by-step explanation:

8 2

16 4

24 6

32 8

40 10

???

Answer:

The answer is metastatic

Explanation:

metastasis is the spread of cancer cells from the place where they first formed to another part of the body. 

Answer:

D)

Step-by-step explanation:

i got it corect on the test

Answer:

i got the wrong answer when i picked d and the answer is group b

Step-by-step explanation:

Answer:

93°

Step-by-step explanation:

Vertical angles have the same measure

Answer:

93%

Step-by-step explanation:

Answer:

p = 3n + 2

Step-by-step explanation:

let n be the number of shapes and p the perimeter

We can construct the following table

n : 1    2    3

p : 5   8    11

The differences in p are constant

8 - 5 = 11 - 8 = 3

Thus p = 3n + ?

n = 1 → 3(1) + ? = 5 ⇒ 3 + ? = 5 ⇒ ? = 2

n = 2 → 3(2) + ? = 8 ⇒ 6 + ? = 8 ⇒ ? = 2

n = 3 → 3(3) + ? = 11 ⇒ 9 + ? = 11 ⇒ ? = 2

We require to add 2 to 3n

Thus

p = 3n + 2

The answer should be about 36,491,112‬

Sorry for harassing you I've had a less the good day, also sorry if it's wrong I haven't done this type of stuff in a while

Answer: 37%

Step-by-step explanation:

n( green ) = 15

n( yellow) = 18

n(Orange) = 16

Total = 49

P(yellow) = n(yellow) / Total number

P(yellow) = 18/49

P(yellow) = 0.367

converting to percentage

P(yellow) = 0.367 x 100 = 36.7

To the nearest percent

P(yellow) = 37%