to
5.2.2 Guided Instruction: Solutions to the
Products and Quotients of Polynomials on a
Graph
Graphs can be used to determine the products and
quotients of polynomials similarly to using graphs when
adding and subtracting polynomials.
The functions a(x) and b(x), and their product, a(x) b(x),
represented by c(x), are shown on the coordinate plane.
35A
(10, 34)
-10
-30
-25-(-0,24)
MATH
20
(0.805, 105)
10
(1.5, 6)
0
(0-3)
b(x10
-15
(8,13)
C(x)
(6.5, 10)
5
(0-8)
(10, 17)
(8.695-10)
3. Find the value of c(10).
2. What is the product of a(10) · b(10)?
10, 2
15
(8,0)
-20
1. Describe how to use the graph to determine the value
of a (10) b(10).
20
25

Albert has made mistake in double number line in step 3 and 4.

The best time to utilize a double number line diagram is when the quantities have various units. The existence of several, maybe indefinitely numerous pairs of numbers in the same ratio, including those with rational number elements, can be illustrated using double number line diagrams. Unit rates (R) appear in the pair, just like in tables (R, 1).

Numerous equivalent ratios can be discovered using a double number line diagram. For instance, "Mix 5 cups of cranberry juice with 2 cups of soda water," is how a recipe for fizzy juice is written. Cranberry juice and soda water are combined in a 5:2 ratio. Equivalent ratios are produced by multiplying each constituents by the same number.

Albert has made mistake in step 3 and step 4,

Firstly he has written wrong units for the respective number line,

If ratio of 2 parts of blue and 5 parts of red is used(2:5)

The equivalent ratio will be 10:25

We get the desired output by multiplying (2:5) by 5.

The Correct units will be 5 instead of 20

And the number corresponding to 25 will be 10.

The correct double number line is drawn below.

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The amount of interest a single deposit earns for the period of one year is equal to your initial investment multiplied by this yield.

Compound interest may be computed using the formula FV = P*(1+R/N)(N*T), where FV is the loan or investment’s future value, P is the original principle amount, R is the yearly interest rate, N is the number of times interest is compounded each year, and T is the period in years.

The amount of interest earned on a single deposit over a year is equal to your initial investment multiplied by this return. As an example: After a year, $1,000 invested at a 5.00% annual effective return yields $50.00 in interest. $1,000.00 x 5.00% = $50.00.

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We have P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.
Lincoln and West Pine high schools offer both hockey and golf.

P(A ∩ B) is the probability that a randomly chosen high school has both a hockey team and a golf team. The probability that a school picked at random offers both hockey and golf is 2/5 (Lincoln and West Pine are the only schools that offer both out of 5 total schools.)

East Valley, Lincoln, West Pine, Adams and North River high schools offer hockey or golf or both.

P(A ∪ B) is the probability that a randomly chosen high school has either a hockey team or a golf team or both. The probability that a school picked at random offers either hockey or golf or both is 5/5 (All 5 high schools in the district offer at least one of the sports.)

Therefore, the correct answers of the problem statement are P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.

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With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.

Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)

Given that mass of Becky is 50 Kg

gravity of earth is 9.8 m/s²

height of stairs is 3.0 m

time taken to run up in stairs is 2.5 s

Power = work done/ time taken

P = (50*9.8*3.0)/2.5

P = 1470/2.5

P = 588 watt

Becky is able to run up a 3.0 m high flight of stairs in 2.5 s

She is able to run up a 4.5 m high flight of stairs in t =  (2.5 * 4.5)/3

t = 11.25/3

t = 3.75 s

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Answer:

F.(8-√-11)(8+√-11)

8²-11²i²

8²-121×-1

64+121

=185

G.

(3+i)(2+i)

6+3i+2i+i²

6-1+5i

5+5i

H.

(4+6i)+(-7-7i)

5+6i-7-7i

-2-i

i.

i^24

(i^2)^12

=1

J.

(-3+10i)-(-5+4i)

-3+10i+5-4i

2+6i.

The simplified form of the expressions are 185, G. 5 + 5i, H. -2 - i, I. 1, j. 2 + 6i.

Usually, simplification involves proceeding with the pending operations in the expression.

Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

F. (8-√-11)(8+√-11)

[tex]8^2 - 11^2 i^2\\8^2 - 121 \times -1\\64+121\\=185[/tex]

G.

(3+i)(2+i)

[tex]6+3i+2i+i^2\\6-1+5i\\5+5i[/tex]

H.

[tex](4+6i)+(-7-7i)\\5+6i-7-7i\\-2-i[/tex]

i.

[tex]i^24(i^2)^12=1[/tex]

J.

[tex](-3+10i)-(-5+4i)\\-3+10i+5-4i\\2+6i.[/tex]

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The values of k are 3 and −1.

Note: The equation taken here is 4x^2 −2(k+1)x+(k+1)=0

Given: Equation 4X^2−2(k+1)x+(k+1)=0 has real and equal roots i.e., its discriminant is zero.

⇒b2−4ac=0

[An expression that can be produced from the square of a binomial equation is a perfect square trinomial. A perfect square trinomial is a formula that has the elements ax^2 + bx + c and satisfies the condition b^2 = 4ac. The roots of the quadratic equation ax2 + bx + c = 0 are real and equivalent if the discriminant is equal to zero (b2 - 4ac = 0), a, b, and c are real values, and a0.]

For given equation, a=4,  b=2(k+1),c=(k+1)

(2(k+1))^2 −4.4(k+1)=0

⇒(2k+2)^2−16(k+1)=0

⇒4k2+8k+4−16k−16=0

⇒4k2−8k−12=0

⇒4(k2−2k−3)=0

⇒k2−2k−3=0

⇒k2−3k+k−3=0

⇒k(k−3)+1(k−3)=0

⇒(k−3)(k+1)=0

⇒k−3=0   and   k+1=0

⇒k=3   and  k=−1

So, the values of k are 3 and −1.

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Step-by-step explanation:

this is a multiplication dot, right ?

so,

(f.g)(x)

or

(f×g)(x)

any arithmetic operation (like +, -, ×, ÷) between 2 functions is done by applying that operation to the functional expressions.

(f×g)(x) = (x² - 12x + 35)(x - 5) =

= x³ - 5x² - 12x² + 60x + 35x -175 =

= x³ - 17x² + 95x - 175

Step-by-step explanation:

(f.g)(x) = f(x) . g(x)

= (x² - 12x + 35)(x - 5)

=x(x²-12x+35) - 5(x²-12x+35)

= x³-12x²+35x-5x²+60x-175

(f.g)(x)=x³-17x²+95x-175

Answer:

Its 125.6

Step-by-step explanation:

20 times Pi is 62.8 and then you multiply this by 2.

Equation for the sentence's inequality are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

given

let X =  the number of bracelets

let Y =  the number of necklaces

The inequality equation = 7.62x + 15.67y >= 450

Equation for the sentence's inequality She needs to generate at least $450 in revenue because bracelets are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.

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Answer: He will have 8 1/3 nuts

Step-by-step explanation:

Amount of peanuts=4 2/3 cups

Amount of cashews=3 2/3 cups

Combing the nuts will give  Total amount of nuts ( peanuts and cashews)

=4 2/3  +3 2/3

=7  4/3

7 + 1 1/3

8 1/3 nuts

Answer:

[tex]f = m \times a = 3 \times 6 = 18 \: n[/tex]

??

¯\_(ツ)_/¯

4+3

7

the answer is 7.

Answer:

[tex] \huge \boxed{\displaystyle 7}[/tex]

Step-by-step explanation:

we would like to simplify the following expression:

[tex] \displaystyle (2 + 2) + (4 - 1)[/tex]

in order to do we can consider the order of PEMDAS which is the abbreviation of Parentheses, Exponent, Multiplication,or Division, Addition or substraction

since Parentheses come first we'll simplify parentheses:

[tex] \displaystyle 4 + 3[/tex]

simplify addition:

[tex] \displaystyle 7[/tex]

and we are done!

Answer:

Yes

Step-by-step explanation:

[tex] - ( - 3)[/tex]

[tex] - 1 \div - 3[/tex]

[tex]3[/tex]

Answer:

it is C.

Step-by-step explanation:

it is C.

The transformation is 6 units left and 2 units down and reflection about x = -2 thus option (C) is correct.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As the given XYZ.

Take coordinate of  Y(4,3)

Now, take it back 6 units and 2 units down as,

R(4 - 6,3 - 2) = R(-2,1)

Now, reflect the entire image about x = -2 gives the same image as OQR.

Hence "The transformation is 6 units left and 2 units down and reflection about x = -2"

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The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.

The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.

The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.

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The answer is 382.5! Also I rounded to the nearest tenth. I hope this helps, have a beautiful day!

The value of the composite function [f(g(f(f(f(g(27))))))], when f(x) = log₃(x) and g(x) = 3ˣ is 1

From the question, we have the following parameters that can be used in our computation:

Let f(x) = log base 3 of x and g(x) = 3^x.

Express the equations properly

So, we have the following representations

f(x) = log₃(x) and g(x) = 3ˣ

Calculating the composite function [f(g(f(f(f(g(27))))))], we have

[f(g(f(f(f(g(27))))))] = [f(g(f(f(f(3²⁷))))))]

Next, we have:

[f(g(f(f(f(g(27))))))] = [f(g(f(f(log₃(3²⁷))))))]

This gives

[f(g(f(f(f(g(27))))))] = [f(g(f(f(27))))))]

For f(27), we have

[f(g(f(f(f(g(27))))))] = [f(g(f(3)))))]

For f(3), we have

[f(g(f(f(f(g(27))))))] = [f(g(1))))]

Calculating g(1), we have

[f(g(f(f(f(g(27))))))] = f(3)

Lastly, we have

[f(g(f(f(f(g(27))))))] = log₃(3)

Evaluate

[f(g(f(f(f(g(27))))))] = 1

Hence, the solution is 1

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Scientists are developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time.

These variables include:

In summary, the variables are ranked in order of their likely impact on temperature predictions, with carbon dioxide emissions from the human activity being the most significant variable, followed by carbon dioxide emissions from activities in nature, global sea level, global rates of photosynthesis, and acidity of ocean water.

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The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.

The linear equation

2x - 3y = -15

can be written in the form

y = mx + b,

where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us

y = (2/3)x - 5.

This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us

y = -5.

Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.

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Answer:

x = 28

Step-by-step explanation:

Answer:

  the median will go up 2.5 points from 76 to 78.5

Step-by-step explanation:

You want to know the effect on the median of adding 85 to the list of scores: 76, 96, 81, 69, 41.

The median is the middle value when the list is sorted into order. The ordered list is ...

  41, 69, 76, 81, 96

The median is 76.

When 85 is added to the list, the sorted list becomes ...

  41, 69, 76, 81, 85, 96

There are two middle scores, so the median is their average:

  (76+81)/2 = 78.5

The median increases 2.5 points from 76 to 78.5 when the score is added.

It is Justified that P and Q are different point.

The coordinate plane where a location of a point is represented in the form of X and Y coordinate pair, is termed as cartesian plane. In this plane two reference axes are used which are perpendicular to each other.

In the question, two-point P (3, 2) and Q (2, 3) are given. As per the cartesian coordinate system a location of a point is represented by a pair of numerical terms. The first numerical terms denote the X coordinate of the point, and the next terms refers the Y coordinate of that point.

Therefore, P and Q are two different points on the cartesian plane. The point p (3, 2) where 3 is the X coordinate and the distance from Y axis is 3 and 2 is the Y coordinate and distance from X axis is 2.

Similarly for the point Q (2, 3), 2 denotes the X coordinate of the point Q and 3 is the Y coordinate.

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Answer:

no of face 8

no of vertices 16

no of edges 24

Answer:

7/25= 14/50 3/10= 15/50 common denominator: 50 so, 7/25 < 3/10

Answer: 3

Step-by-step explanation:

Answer:

What is the value of A?

–4

–3

3     <<< CORRECT

4

Step-by-step explanation:

Edge 2022

Answer:

x = -2 to x = 1

Step-by-step explanation:

A function is constant when the y value does not change (i.e. the graph is a horizontal line). This is true between x = -2 and x = 1.

Answer:The Funcation is Constact from x=-5 to x=8

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

its going to be the same as the other corner then on the top you have to times by 2 cause it double the size of the bottom