I’m struggling on this, and I need help??

Answer:

-61

by both methods

Step-by-step explanation:

Let's first see what the terms direct substitution and synthetic substitution mean.

Direct Substitution

In direct substitution, to find the value of a polynomial f(x) at any point x = k. we simply substitute the value of k into the polynomial function and solve for f(k)

Synthetic Substitution

In synthetic substitution we make use of the Remainder Theorem..
The Remainder Theorem states that when we divide a polynomial [tex]f(x)[/tex] by [tex]x-c[/tex], the remainder [tex]R[/tex] equals [tex]f(c)[/tex]

Solving using direct substitution

The given polynomial is

[tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex]
and we are asked to evaluate this function at [tex]x = - 2[/tex]

Using Direct Substitution,
[tex]f(-2) = =3\left(-2\right)^5-\left(-2\right)^3+6\left(-2\right)^2-\left(-2\right)+1\\\\=3\left(-32\right)-\left(-8\right)+6\left(-2\right)^2-\left(-2\right)+1\\\\=- -96 + 8 + 6(4) + 2 + 1\\=-96 + 8 + 24 + 2 + 1\\\\= -61\\\\[/tex]

Using direct substitution we get [tex]\bold{f(-2)= -61}[/tex]

Using Synthetic Substitution
Since the remainder when [tex]f(x)[/tex] is divided by [tex]x - c[/tex] is [tex]f(c)[/tex] , we will divide the polynomial [tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex] by [tex]x -(-2) = x + 2[/tex] and find out the remainder which will give f(-2)

This is the technique used in synthetic division
Step 1. Write only the coefficients of [tex]x[/tex]  in the dividend inside an upside-down division symbol. Write -2 as the divisor on the left of this row

[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 2
Carry down the leading coefficient as is to below the division symbol

[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\;\;\;\;3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 3
Multiply the above carry-down value by -2 and carry that result to the next column:
[tex]3\left(-2\right)=-6[/tex]

[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 4

Add down the column

[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 5

Multiply the above carry-down value by -2 and carry that result to the next column:
(-6)(-2) = 12

2 | 3     0      -1        6     -1       1
  |        -6      12  
  -------------------------------------------------
     3    -6      

Step 6
Add down the column
-1 + 12 = 11

2 | 3     0      -1        6     -1       1
  |        -6      12    
  -------------------------------------------------
     3    -6      11

Repeat this process for the other two coefficients

The final result is

2 | 3     0      -1        6     -1       1

  |        -6      12    -22   32   -62
  -------------------------------------------------
     3    -6     11       -16   31   -61

The last carry-down value s the remainder and the value of f(-2) = - 61

Answer:
Study a Times Tables map each day if you can soon you will get the hang of it

The numerical expression for the verbal expression is 18 ÷ (2+7).

Given,

Verbal expression = Eighteen divide by the sum of two and seven

we know that ,

We can write any  verbal expression  to numerical expression by using playing with numbers.

Playing with numbers:

Playing with numbers involves activities like arranging the numbers, understanding , finding out whether a given number is a factor of another number or a multiple of another number, and understanding the properties of factors and multiples

Now, According to question

Eighteen divided by the sum of two and seven

18÷(2+7)

Therefore,

The numerical expression is 18÷(2+7).

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The secant line connects two points on a graph's curve:

Point P: (15, 1257)

(a) The secant lines' slopes PQ.

The points are as follows:

The slope (m) is calculated using:

Therefore, the secant line connects two points on a graph's curve:

The slope (m) is calculated as follows:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So far, we have:

The slope of the secant line for Q = (5,3410) is:

[tex]\begin{aligned}m_1 &=\frac{1275-3410}{15-5} \\m_1 &=\frac{-2135}{10} \\m_1 &=-213.5\end{aligned}[/tex]

The slope of the secant line for Q = (10, 2210) is:

[tex]\begin{aligned}&m_2=\frac{1275-2210}{15-10} \\&m_2=\frac{-935}{5} \\&m_2=-187\end{aligned}[/tex]

The slope of the secant line for Q = (20, 550) is:

[tex]\begin{aligned}&m_3=\frac{1275-550}{15-20} \\&m_3=\frac{725}{-5} \\&m_3=-145\end{aligned}[/tex]

The slope of the secant line for Q = (25, 145) is:

[tex]\begin{aligned}&m_4=\frac{1275-140}{15-25} \\&m_4=\frac{1135}{-10} \\&m_4=-113.5\end{aligned}[/tex]

The slope of the secant line for Q = (30, 0) is:

[tex]\begin{aligned}&m_5=\frac{1275-0}{15-30} \\&m_5=\frac{1275}{-15} \\&m_5=-85\end{aligned}[/tex]

(b) The average slope of the tangent.

The secant lines that are closest to tangent P are:

This is because point P (15, 1275) is located between the two previous points.

The slopes of secant lines at Q = {( 10, 2210), (20, 550)} are:

[tex]\begin{aligned}&m_2=-187 \\&m_3=-145\end{aligned}[/tex]

The average slope (m) is as follows:

[tex]\begin{aligned}&m=\frac{m_2+m_3}{2} \\&m=\frac{-187-145}{2} \\&m=\frac{-332}{2} \\&m=-166\end{aligned}[/tex]

Hence, the average slope is -166.

Therefore, the secant line connects two points on a graph's curve:

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The complete question is given below:
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).

Answer:

12x-94

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

Hope this helps!

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A function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 is g(x) = 5 - |x|

The question asks to find a function g, that is, g(x)

The graph of g(x) is a reflection in the x axis of the graph of  f(x) = |x| - 5

Reflection of a function in the x-axis gives us

y = g(x) = - f(x)

=> g(x) = - ( |x| - 5 )

=> g(x) = - |x| + 5

=> g(x) = 5 - |x|

Therefore, using the concept of reflection of a function in x axis of the graph of the given function, we get a function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 as g(x) = 5 - |x|

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Answer:

D. 140. ....,.....

Step-by-step explanation:

160-20=140

Answer: y = 5x/4 - 13

Step-by-step explanation:

y=mx+b

7=5/4 *16+b

7=5*16/4 +b

7=80/4+b

7=20+b

b=-13

y = 5x/4 - 13

The number of mezzanine tickets sold = 540

Total number of tickets sold = 910

Total number of tickets sold is the sum of the number of regular seats and the number of the mezzanine seats sold.

Let 'x' be the number of regular seats and 'y' be the number of mezzanine seats.

Then x + y = 910     ----------(1)

Cost of a regular seat = $ 18.50

So cost of x regular seats = 18.50x dollars

Cost of a mezzanine seat = $ 16.25

So cost of y mezzanine seats = 16.25y

Total amount of money she got by selling tickets = $ 15620

Therefore, 18.5x + 16.25y = 15620 ----------------(2)

Solve equations (1) and (2) for x and y.

Multiplying (1) with 18.5 throughout,

18.5x + 18.5y = 16835 ---------------(3)

Subtracting (2) from above equation (3), we get,

(18.5 - 16.25)y = 16835 - 15620

⇒ 2.25y = 1215

⇒ y = 1215/2.25

⇒ y = 540

Hence 540 mezzanine tickets were sold.

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The baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.

It should be noted that from the information given, the Shah family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.

Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated thus:

= Pancake recipe ÷ Teaspoon

= 2 ÷ 1/3

= 2 × 3

= 6

Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.

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Using translation concepts, the transformations that are used to map △RST onto △VWX are:

Rotation, then a translation.

The two triangles are given at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

Looking at the image, we have that:

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the combinations that work are "A" and "B" as they both equal to 80

Answer:

Your answer would be 3.075.

Step-by-step explanation:

15 - 6.8 = 8.2

8.2 - 5 1/8 = 3.075

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

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Answer:

These are dividend, divisor, quotient and remainder.

Step-by-step explanation:

Determine the first digit or set of digits your divisor will go into at least once.

Determine the maximum number of times your divisor will go into the said digit or digits.

Place the answer over the corresponding digit. For multiple digits, place it over the last digit.

Multiply the answer from above by your dividend.

Place the result under your dividend starting from the left most digit.

Subtract the result from your dividend. Only subtract the digits that line up. For instance, if you have a five digit dividend, but the result is only two digits, only subtract using the first two digits of your dividend.

Bring down the next digit of your dividend beside the result.

Repeat the process using the new set of digits. Each time, bring down the next digit of your dividend.

Answer: B

Step-by-step explanation:

4 times 3 times 3 times 3 times 3=108

Answer:

A. 39

Step-by-step explanation:

Given:

Length of a pyramid (lpy ) = 4 cm

Width of a pyramid (wpy ) = 3 cm

Height of a pyramid (hpy ) = 3 cm

It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.

So, Length of a prism (lpr) =3 cm, width of a prism (wpr) = 3cm and height of a prism (hpr) = 3 cm

Volume of Prism (Vpr) = lpr × wpr × hpr

⇒ Vpr = 3 cm × 3 cm × 3 cm

⇒ Vpr = 27 cm³ ....(eq 1)

Volume of Rectangular Pyramid Vpy

= (lpy × wpy × hpy ) / 3

⇒ Vpy = (4 × 3 × 3) ÷ 3

⇒ Vpy = 12 cm³ ....(eq 2)

From 1 and 2, Volume of composite space,

Volume of composite space = Volume of prism + Volume of Pyramid

⇒ V = 27 cm³ + 12 cm³ = 39 cm³

⇒ V = 39cm³

Answer:

The other diagonal of the kite is 56 meters

Step-by-step explanation:

To find the length of the other diagonal you find to know the formula for finding the area of a kite which is A = (p×q)/2. It is given that the area is 252m² and one diagonal is 9m.

The length of the line segment NO is 12 units

The ratios of the line segments are given as:

LM : MN : NO = 5 : 1 : 2

The length of LO is given as:

LO = 48

The above means that

NO = (NO Ratio)/(Total Ratio) * LO

So, we have

NO = 2/(5 + 1 + 2) * 48

Evaluate the product

NO = 12

Hence, the length of NO is 12 units

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Answer:

9!

Step-by-step explanation:

Answer: 9

Step-by-step explanation:So you look at whatever can be multiplied to get 27 or 36. When you do that 9 is your biggest number

true!!!

school 1 spent 13 hours in the weight room whereas school 2 spent 11 hours in the weight room

Step-by-step explanation:

the domain is the interval or set of all valid x (input) values.

the range is the interval or set of all valid y (function result) values.

so, we see here, x goes from -2 to +2.

and y stays between -5 and -1.

the hole point at (-2, -1) means the point itself is not included. the full point (2, -1) means the point itself is included.

the domain is

-2 < x <= +2

"-2 < x" because (-2, -1) is not included.

"x <= +2" because (2, -1) is included.

the range is

-5 <= y <= -1

"y <= -1" because for the included point (2, -1) y can reach -1, even though (-2, -1) is excluded.

Answer:

18.

Step-by-step explanation:

2 = 2

9 = 3*3

So, the LCD = 2*3*3     (no duplicates in the 2 lists).

= 18.

Answer: $100

Step-by-step explanation:

3,000 divided by 30 is 100

Answer: 100

Step-by-step explanation: divide 3,000 by 30

Answer:

1 1/6

Step-by-step explanation:

1 2/3 - 1/2 =

1 2/3 = 1 4/6

1/2 = 3/6

1 4/6 - 3/6 =

1 1/6

Using the concept of ratio the number of cups of chips Charlie needs can be found out.

A ratio in mathematics shows how many times one number is contained in another. The ratio symbol is represented by a colon (:).A ratio is still valid if all of the quantities are multiplied by the same number. By dividing each quantity by the sum of all the numbers' common factors, ratios can be lowered (much like fractions are). The simplest version of a fraction is one in which the ratio's numbers are the smallest feasible integers.

Amount of dip required by the recipe be 'a' =[tex]1\frac{1}{4}[/tex] cups=[tex]\frac{5}{4}[/tex]cups

Amount of chips required by the recipe be 'b'= [tex]\frac{1}{5}[/tex]cups

Amount of chips to be used be 'c'= 1 cup

Number of cups of chips Charlie needs

=[tex]\frac{c*a}{b}[/tex]

=[tex]\frac{1*\frac{5}{4} }{\frac{1}{5} }[/tex]

=[tex]\frac{5*5}{4}[/tex]

=[tex]\frac{25}{4}[/tex] cups

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Answer:

It's learn proper English. I'll rewrite your statement. I need help, I do not understand how to solve this. Thank you!