If the polynomials p(x) = ax³+4x²+3x-4 and q(x) = x² - 4x + a, leave the same remainder when divided by (x-3), find value of a.




Steps pls​

The age of the grandfather in years according to the task content is; 84.

It follows that the age of the grandfather and granddaughter are; x and y respectively.

Hence, the two equations which follow are;

x = 12y

x + y= 91

Hence, the age of the grandfather, x can be evaluated as follows;

x = 12(91-x)

13x = 1092

x = 1092/13

x = 84 years.

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For f(x) we have:

And for g(x):

The domain of a function is the set of inputs that we can use on the function, and the range is the set of outputs.

a) f(x) = -2x

This is just a linear equation, as you can see, for no value of x we have a problem, then the domain is the set of all real numbers.

Similar for the range, it covers the set of all real numbers, then:

b) g(x) = 0.5*x² + 5

This is a quadratic function, so the domain is the set of all real numbers again.

Now the range will have a minimum, which is at the vertex of the parabola.

For the parabola the vertex is at x = 0:

g(0) = 0.5*0² + 5 = 5

Then the range is the set of all real numbers equal to or larger than 5.

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Answer:

a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm

b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)

= 4√10 cm

c) Simplifying √72: √36 x √2 = 6√2

   Simplifying √18: √9 x √2 = 3√2

   Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm

Using limits, it is found that the correct statement defining the sequence is:

The sequence converges to 1.

The numerator starts at 3 and increases by 1, while the denominator starts at 4 and increases by 1, hence the rule is:

[tex]\sum_{n = 0}^{\infty} \frac{3 + n}{4 + n}[/tex]

To verify if it converges, we find the limit as n goes to infinity, hence:

[tex]\lim_{n \rightarrow \infty} \frac{3 + n}{4 + n} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]

Hence the sequence converges to 1.

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Answer:

B i took quiz

Step-by-step explanation:

Answer:

#3

Step-by-step explanation:

The y-intercept (the point where the line intersects with the y-axis) is -2, and the slope is 2/3 (two units up every three units to the right).

Answer:

C.

Step-by-step explanation:

First, look for the graph that shows a line with a y-intercept of -2. There is only one graph that shows a line with a y-intercept of -2. The graph will be the third graph. Please see attachment for the equation in a graphing calculator.

Hope this helps!

Answer:

1. 4x²-6x-4

2. 8x³+4x²-8x-4

3. x⁵-x⁴+3x³+x²+12

Step-by-step explanation:

1. (4x+2)(x-2)

apply foil method (a+b)(c+d)=ac+ad+bc+bd

(4x+2)(x-2)=4x.x + 4x(-2) + 2x + 2(-2)

2. (4x²-4) (2x+1)

apply the same method as question no.1

(4x²-4) (2x+1)=4x².2x + 4x².1 + -4.2x-4.1

3. (x²+3) (x³-x²+4)

Distributive parentheses

(x²+3) (x³-x²+4)= x².x³ + x²(-x²) + x².4+ 3x³+3(-x²) +3.4

The correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

From the given steps, we can see that when a scatter plot is constructed,  the independent variable is the input variable and should be represented by the x-axis.

Hence, the correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

The complete question is;

Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.

The independent variable is the input variable and should be represented by the y-axis.

The dependent variable is the input variable and should be represented by the x-axis.

The dependent variable is the input variable and should be represented by the y-axis.

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Answer: A; The independent variable is the input variable and should be represented by the x-axis.

Step-by-step explanation:

I just know

The number of possible combinations would be 56.

Permutation is the changing of the order in which things have been arranged or the arranging of things in a certain order.

Analysis:

Total number of fiction books available = 8

number of fiction books Ruthie wants = 1

Number of combination for Ruthie = 8C1 = 8 ways

Total number of non fiction books available = 7

number of non fiction books needed by Ruthie = 1

possible combination = 7C1 = 7 ways

Total number of magazines available = 3 ways.

Total possible combinations for all the Reading materials = 8 x 7 x 1 = 56 ways.

number of magazines Ruthie wants = 3C3 = 1 way

In conclusion, the number of possible combinations of The reading materials is 56.

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Answer:

PRQ = 65 degrees

Step-by-step explanation:

Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).

SPR + QPR = 180

135 + QPR = 180

QPR = 45

TQP + RQP = 180

110 + RQP = 180

RQP = 70

Since interior angles of a triangle add up to 180 ...

QPR + RQP + PRQ = 180

45 + 70 + PRQ = 180

PRQ = 65

Answer:

Reuben will have to pay $19,183.77 when he starts to pay the loan off after 3 years.

Step-by-step explanation:

There are 3 important parts to this equation:

1) 16,902

2) 4.5%

3) 3 years

First, let's find the interest rate in decimal form. This is easy enough to do.

take the interest rate (4.5%) and divide by 100. You can do this in your head by moving the decimal point but I will just write it out for the example:

4.5/100 = 0.045

Now that we have that number. we want to get the dollar amount for the interest. this is done by taking the loan amount and multiplying it by the decimal form of the percentage:

16,902 * 0.045 = 760.59

Since the interest rate is NOT compounding the rest is simple.

760.59 * 3 = 2,281.77

2,281.77 + 16902 = 19,183.77

Hope this helps.

Hello,

John : n

Brad : n + 12

n + n + 12 = 84

2n + 12 = 84

2n = 84 - 12

2n = 72

n = 72/2

n = 36

John $36 and Brad $36 + $12 = $48

Answer:

jhon =36 brad=48

Step-by-step explanation:

B=J+12

J+B=84

12+J+J=84

2J=72

J=36

B=J+12=36+12=48

we conclude that the correct option or the translated function is the last one.

f(x) = (x - 8)² - 1

The parent quadratic function is:

y = g(x) =  x²

If we translate this function 8 units to the left, then we will have the new function:

f(x) = g(x - 8)

And if now we translate this function one unit downwards, we will get:

f(x) = g(x - 8) - 1

Now we can replace g(x) by the parent quadratic function we willl get:

f(x) = (x - 8)² - 1

From this, we conclude that the correct option is the last one.

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The additional number of people is [4, 13]

Brittany and four of her friends are five people.

So, we have:

n = 5

The conditions are given as

Let the additional number of people be x

So, we have the following inequalities

x + 5 ≥ 9 and x + 5 ≤ 18

Subtract 5 from both sides

x ≥ 4 and x ≤ 13

Express as interval notation

[4, 13]

Hence, the additional number of people is [4, 13]

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Answer:

42000*1.04^(n-1)

Step-by-step explanation:

4% is equal to 0.04, a raise is 1+0.04=1.04

1.04 is now the number we are multiplying by to get a new yearly salary for Harmony.

42000*1.04^(n-1) since n is how many years after she has the job you have to raise it to the power and subtract one.

Using it's concept, the domain of the function shown in the graph is:

B. [tex]-6 \leq x \leq 6[/tex].

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.

From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:

B. [tex]-6 \leq x \leq 6[/tex].

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We can conclude that the true statement from the given expressions are DE || AC and 2DE = AC

Triangles are similar if the measure of the similar sides are all equal to a constant.

From the given diagram, you can see that the measure of BA is congruent to BC. This shows that the line DE is parallel to AC that is DE || AC.

Also twice the measure of the sides DE will be equivalent to AC that is 2DE = AC.

Hence we can conclude that the true statement from the given expressions are DE || AC and 2DE = AC

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Answer:

9.2195445 (9.22 rounded)

Step-by-step explanation:

#1: Use the distance formula to determine the distance between the two points:

Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

#2: Substitute the actual values of the points into the distance formula:

[tex]\sqrt{((-4)-3)^{2}+(5-(-1))^{2}}[/tex]

#3: Simplify:

- Subtract 3 from -4: [tex]\sqrt{(-7)^{2}+(5-(-1))^{2}}[/tex]

- Raise -7 to the power of 2: [tex]\sqrt{49+(5-(-1))^{2}}[/tex]

- Multiply -1 by -1: [tex]\sqrt{49+(5+1)^{2}}[/tex]

- Add 5 and 1: [tex]\sqrt{49+6^{2}}[/tex]

- Raise 6 to the power of 2: [tex]\sqrt{49+36}[/tex]

- Add 49 and 36: [tex]\sqrt{85}[/tex] (Decimal form: 9.2195445 (9.22 rounded))

The distance between the two points (3,1) and (4,-5) is 9.22.

Answer:

30.7

Step-by-step explanation:

It's 30.7 because 707/23

Answer:

16261 u3

Step-by-step explanation:

V = (base area)(height)=(707)(23)= 16261 u3

Hope this helps

Answer: 7 Switches will be made.

Step-by-step explanation:

[tex]\frac{90}{12.5}=[/tex] number of switches

[tex]7.2=[/tex] number of switches

The functions that have the properties are (d) I and II only

The function property is given as:

[tex]a(x) = a^{-1}(x)[/tex]

The above implies that the inverse function and the original function are equal.

From the list of options, we have:

(a) y = x

Make x the subject

x = y --- the same as the  original function

(b) y = 1/x

Make x the subject

x = 1/y --- the same as the  original function

Hence, the functions that have the properties are (d) I and II only

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The area of the triangle is 557. 7cm²

In order to determine the area of a triangle, we have to know the size of the base and the size of the height

The formula for finding the area of a triangle is given as = half the base multiplied by the height

In mathematical form, it is written as;

Area = 1/ 2 × base × height

From the figure given, we have their lengths to be'

base = 57. 2 m

height = 19. 5 m

Let's substitute the values

Area = 1/ 2 × 57. 2 × 19. 5

Area = 1/ 2 × 1115. 4

Find the ratio

Area = 557. 7 m²

The area of the triangle is 557. 7cm²

Hence, the area of the triangle is 557. 7cm²

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Using proportions, the lengths of the unknown sides are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the triangles are similar, hence the lengths of it's sides follow the proportion given next:

[tex]\frac{2x}{4} = \frac{5}{x - 3}[/tex]

Applying cross multiplication:

2x(x - 3) = 20

2x² - 6x - 20 = 0

x² - 3x - 10 = 0

(x - 5)(x + 2) = 0.

Then the positive solution is:

x - 5 = 0 -> x = 5.

And the lenghts are:

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For easy estimation, option A = nearest hundred,B = nearest ten, C = nearest hundred and D= nearest thousand.

3529 and 3689

3529 to the nearest hundred = 3500 and,

3689 to the nearest hundred = 3700

∴ Required sum = (3500+3700) = 7200

33 and 99

33 to the nearest ten = 30 and,

99 to the nearest ten = 90

∴ Required sum = (30+90) = 120

120777 × 523

777 to the nearest hundred = 800 and,

523 to the nearest hundred = 500

∴ Required sum = (800+500) = 1300

1300495420 and 123512

495420 to the nearest thousand = 495000 and,

123512 to the nearest thousand = 124000

∴ Required sum = (495000 + 124000 ) = 619000

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Answer:

17 and 18

Step-by-step explanation:

Writing every 2 digit number gives us :

10-99 including 10 and 99

For the first one we are looking for numbers where the number 3 appears only once so 33 would be invalid.

13,23,30,31,32,34,35,36,37,38,39,43,53,63,73,83,93

There are 17 2-digit numbers that have 3 exactly once

For the second one we are looking for number where the number 3 appears a minimum of once so 33 would be valid :

13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93

There are 18 2-digit numbers that have 3 at least once

Hope this helped and have a good day

Answer:

2x/19

Quotient = division

Product = multiplication

Difference = subtraction

Sum = addition

Answer: $92.30

Step-by-step explanation:

Finding the area of one of the triangles formed by the diagonal,[tex]s=\frac{9+12+19}{2}=20\\\\A=\sqrt{(20)(20-9)(20-12)(20-19)}=4\sqrt{110}[/tex]

Therefore, the area of the entire parallelogram is [tex]8\sqrt{110}[/tex].

Therefore, the cost is [tex](8\sqrt{110})(1.1) \approx 92.30[/tex]

Answer:

$92.30   i got it right.

Step-by-step explanation:

edg 2023 its right.