Answer:
b) the coefficient of x of jamie's polynomial is 5 .
c) The two polynomials are :
x³ + 4x² + 5x + 4
x³ - 2x² + 5x + 4
Step-by-step explanation:
consider these two Monic polynomials of degree 3:
P : x³ + ax² + bx² + c
Q : x³ + a₁x² + bx² + c
P × Q = x⁶+ (a+a₁)x⁵ + (aa₁+2b)x⁴ + (ab+a₁b+2c)x³ + (ac+a₁c+b²)x² +2bcx + c²
Now we compare the coefficients of P × Q and x⁶ + 2x⁵ +2x⁴ + 18x³ + 33x² + 40x + 16
b)
c² = 16 ⇒ c = 4 (c is positive)
2bc = 40 ⇒ 8b = 40 ⇒ b = 5 then the coefficient of x of jamie's polynomial is 5 .
c)
In order to find a and a₁ we need to solve this system:
a+a₁ = 2 a+a₁ = 2
⇔
aa₁+2b = 2 aa₁ = -8
Solve the system and you’ll get :
a = 4 and a₁ = -2 or a = -2 and a₁ = 4
Let’s choose a = 4 and a₁ = -2 then
the two polynomials are respectively:
P : x³ + ax² + bx² + c = x³ + 4x² + 5x + 4
Q : x³ + a₁x² + bx² + c = x³ - 2x² + 5x + 4
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Question 2(Multiple Choice Worth 5 points)
(06.08A LC)
Look at the triangle ABC.
Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 1, and C at ordered pair 4, 1.
What is the length of the side AB of the triangle?
2
Square root of 20
6
Square root of 38
Answer:
√20 units
Step-by-step explanation:
[tex]Solution,\\\\\hookrightarrow Here,\\\\\hookrightarrow Coordinate\:of\::\\\\\hookrightarrow A(4,5),B(2,1),C(4,1)\\\\Now,\\\\Let,\\\\(x_1,y_1)=(4,5)\\\\(x_2,y_2)=(2,1)\\\\Using\:distance\:formula\\\\Distance\:of\:AB=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}} \\\\Distance\:of\:AB=\sqrt{(2-4)^{2}+(1-5)^{2}} \\\\Distance\:of\:AB=\sqrt{(2-4)^{2}+(1-5)^{2}} \\\\Distance\:of\:AB=\sqrt{(-2)^{2}+(-4)^{2}} \\\\Distance\:of\:AB=\sqrt{4+16} \\\\Distance\:of\:AB=\sqrt{20}\: units[/tex]
Can somebody give me the answer to this?
Step-by-step explanation:
y = x - 4
Let's look at this a different way.
Y will be 4 less than x, so if x was 5, y would be 1
(x, y)
0, -4
1, -3
2, -2
3, -1
4, 0
5, 1
(If more points are needed, just continue where I left off.)
What is the greatest number of lines of symmetry that can be drawn on the figure
shown below?
А о
B 1
C 2
D 4
The greatest number of lines of symmetry that can be drawn on the figure will be C. 2.
What is a line of symmetry?The line of symmetry is defined as the axis or imaginary line that passes the center of the shape or object and divides it into identical halves.
Here, the greatest number of lines of symmetry that can be drawn on the figure will be 2. This means that if one was to fold the shape along the line, both halves would match exactly.
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Ella ate half of her gummy bears before
adding thirteen more to the bowl. If she now
has 25 gummy bears, how many did she start
with?
Give an equation.
Oliver draws a straight angle, and then two rays to divide the angle into 3 equal parts. What is the measure of each smaller angle?
The measure of each smaller each angle is 30 degrees.
We have given that,
Oliver draws a straight angle, and then two rays to divide the angle into 3 equal parts.
What is the measure of the straight angle?The measure of the straight angle is 90 degrees.
Therefore we get a straight angle is 90 degrees.
we have to divide the straight angle into 3 equal parts.
that is, 90/3=30
Therefore each angle is 30 degrees.
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Each day, a salesperson earns $25 plus 5% of their total sales for the day. The salesperson's goal is to earn more than $50 on Thursday.
given that 9x=28-5x.find the value of x
[tex]~~~~9x=28-5x\\\\\implies 9x +5x = 28\\\\\implies 14x = 28\\\\\implies x = \dfrac{28}{14}\\\\\implies x = 2[/tex]
Step-by-step explanation:
Given Equation,
[tex]\\ \longrightarrow \qquad \sf 9x=28-5x \\ \\ [/tex]
Now, Adding 5x to both sides we get :
[tex]\\ \longrightarrow \qquad \sf 9x + 5x=28-5x + 5x \\ \\ [/tex]
[tex] \longrightarrow \qquad \sf 14x=28 \\ \\ [/tex]
Dividing 14 from both sides we have :
[tex]\\ \longrightarrow \qquad \sf \frac{14x}{ 14 } = \frac{28}{14} \\ \\ [/tex]
[tex] \longrightarrow \qquad \sf x=2 \\ \\ [/tex]
Therefore,
The value of x is 2Tyler made a scale drawing of his apartment. The scale is 1 millimeter: 2 meters. The living room is 6 meters long in real life. How long is the living room on the drawing in millimeters?
Answer:
Step-by-step explanation:
6/2 = 3
3:6 =
1:2
Which of these is NOT likely to be found on your credit report? A) current address B) previous employer C) church membership D) Social Security number
i need help asap !!!!!!
Answer:(6, -4)
Step-by-step explanation: That’s where they meet at point B
Answer:
Answer:(6,-4)
Step-by-step explanation:
they meet at point B
can anyone pls help?
Answer:
Yes!!
Step-by-step explanation:
It is because -4 is smaller than 3. All negative numbers are smaller than positive ones. :)
Have an amazing day!!
Please rate and mark brainliest!!
Samantha is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 9 pairs of shoes. How many different outfits does Samantha have to choose from?
Using the Fundamental Counting Theorem, it is found that Samantha has 36 different outfits to choose from.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the pants, there are 2 options, hence [tex]n_1 = 2[/tex].For the t-shirts, there are 2 outcomes, hence [tex]n_2 = 2[/tex].For the shoes, there are 9 outcomes, hence [tex]n_3 = 9[/tex].Thus, the total number of outfits is given by:
N = 2 x 2 x 9 = 36.
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If you had a spinner with four possible outcomes and a six sided cube numbered 1-6. What is the sample space for the experiment?
Answer:
24
Step-by-step explanation:
The spinner has 4 equally possible outcomes. The die has 6 equally possible outcomes.
Multiply the possible outcomes.
4*6=24
The area of a gymnasium is 956 yd2. The width of the gymnasium is 4 yd longer than its length. Find the length and width of the gymnasium (round to the nearest yard). Include a labeled diagram in your work for full credit?
Answer:
L = 29
w = 33
Step-by-step explanation:
Area = w × L
= (L + 4) × L
⇔ 956 = L² + 4L
⇔ 956 = (L + 2)² − 4
⇔ 956 + 4 = (L + 2)²
⇔ 960 = (L + 2)²
[tex]\Leftrightarrow L+2=\sqrt{960}[/tex]
[tex]\Leftrightarrow L+2=30.983866769659[/tex]
[tex]\Longrightarrow L+2 \approx 31[/tex]
[tex]\Longrightarrow L \approx 29[/tex]
[tex]\Longrightarrow w=L+4 \approx 29+4\approx33[/tex]
What is the yield on a corporate bond with a $1000 face value purchased at a discount price of $925, if it pays 6% fixed interest for the duration of the bond?
For a $1000 face value purchased at a discount price of $925, if it pays 6% fixed interest for the duration of the bond is the yield on a corporate bond mathematically given as
Yield = 6.5%
What is the yield on a corporate bond?Generally, the equation for the interest paid is mathematically given as
Interest paid = value of bond x Interest rate
Interest paid = 1000 * 6%
Interest paid = 60
Therefore
Yield = Interest paid / Price paid
Yield = (60 / 925)x 100
Yield = 6.5%
In conclusion, the yield on a corporate bond is
Yield = 6.5%
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Grayson was given a large box of 42 chocolates for his birthday. If he eats exactly 2 chocolates each day, how many chocolates would Grayson have remaining 15 days after his birthday?
Answer:
12
Step-by-step explanation:
Let's write this in ratio form.
Days : Chocolates
1 : 2
15 : 30
So, he would eat 30 chocolates in 15 days. To find the remaining ones, we will subtract from the total of the chocolates given.
Chocolates = 42 - 30
= 12
solve for g:2(g-h)=b+4
Answer:
[tex]g = \frac{b}{2} + 2 + h[/tex]
Step-by-step explanation:
[tex]2(g - h) = b + 4 \\g - h = \frac{b}{2} + \frac{4}{2}\\g = \frac{b}{2} + 2 + h[/tex]
Which polynomial is in standard form?
In how many distinguishable ways can the letters of the word ILLINOIS
be ordered?
Answer:
3360 ways
Step-by-step explanation:
ABCDEFGH-- there are 8! ways to organize these letters
since the I is repeated 3 times and the L is repeated 2 times we have to divide by (3!*2!)
[tex]\frac{8!}{2!3!}[/tex]=3360
3360
Answer:
7
Step-by-step explanation:
Since the two L’s must be consecutive, we consider them to be a single letter LL. Then the word ILLINOIS has n = 7 letters: 3 I’s, 1 LL, 1 N, 1 O and 1 S. Hence the numbers of ways to permute letters of the word ILLINOIS if the two L’s must be consecutive is: 7!
Ms. Lance is planning a birthday party. She decided that she
would spend no more than $I20 to buy a cake and balloons.
If the price of the cake is $45 and each balloon costs $15.
how many balloons can she buy?
Need the inequality and equality answer, and final answer
Answer:
The answer is 3
Step-by-step explanation:
You have to subtract 120-45 and that gets you to 75 Then divide 75 by 15 and that gives you 3. So the answer is 3
Answer:
15n + 45 ≤ 120
n ≤ 5
She can buy up to 5 balloons.
Step-by-step explanation:
Fixed amount: $45
Amount per balloon: $15
Let n = number of balloons
Total expense: maximum of $120, which means less than or wequal to $120
15n + 45 ≤ 120
15n ≤ 75
n ≤ 5
She can buy up to 5 balloons.
use long division to determine the decimal equivalent of 7 over 9
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Answer:
C. 0.8
Step-by-step explanation:
Write 7 as 7.00:
[tex]\begin{array}{ c c c c }& 0. & 7 & 7\\\cline{2-4} 9\:)&7.&0&0 \\-& 0 & \downarrow & \downarrow\\\cline{2-4} & 7 & 0 & \downarrow \\- & 6 & 3 & \downarrow\\\cline{2-4} & & 7 & 0\\& - & 6 & 3\\\cline{2-4} & & & 7\\\end{array}[/tex]
Therefore:
[tex]\sf \dfrac79=0.\.{7}=0.77777..=0.8\:(nearest\:tenth)[/tex]
A park maintenance person stands 16m from a circular monument. Assume that her lines of sight from tangents to the monument and make an angle of 47 what is the measure of the arc of the monument that her lines of sight intersect?
A) 23. 5
B) 94
C) 266
D) 133
Answer:
D 133 degrees
Step-by-step explanation:
The measure of an angle external to a circle = the difference of the two arcs intercepted divided by 2
47 = [ (360 - x) - x ] / 2
94 = 360 - 2x
x = 133 degrees of the arc
please answer/fix these questions
Christina also plans on leaving her $10,000 invested for 20 years. Write an equation representing her investment’s value, y, after x years. What is the value of Christina’s investment after 20 years?
The required equation is y = 10000(1.0.25)^2x. The value of Christina’s investment after 20 years is $30,773.14
Compound interest
The interest accrued on a sum of money is known as interest. The formula for calculating the compound interest is expressed as:
y = y0(1+r/n)^nx
where
x is the time taken
r is the rate in decimal
n is the compounding time
Given the following
x = 20 years
n 2(semi annually)
r = 5.7% = 0.057
Substitute
y = 10000(1+0.057/2)^2(20)
y = 10,000(1 + 0.0285)^40
y = 10000(1.0285)^40
y = 30,773.14
Hence the value of Christina’s investment after 20 years is $30,773.14
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A triangle has side lengths measuring 2x 2 ft, x 3 ft, and n ft. which expression represents the possible values of n, in feet? express your answer in simplest terms. x – 1 < n < 3x 5 n = 3x 5 n = x – 1 3x 5 < n < x – 1
The expression x – 1 < n < 3x + 5 represents the possible values of n, in feet whose side lengths are (2x+2) ft, (x+3) ft, and n ft.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have a triangle whose side lengths measures are (2x+2) ft, (x+3) ft, and n ft.
If we take the first two sides are (2x+2) ft, (x+3) ft, and third is n ft.
By the triangle property, that sum of the two sides is always greater than the third side.
2x+2+x+3 > n
3x+5 > n .....(1)
Now take first two sides as n ft, (x+3) ft, and third side (2x+2) ft
n+x+3 > 2x+2
n > x-1 .....(2)
From the inequality (1) and (2), we get:
x – 1 < n < 3x + 5
Thus, the expression x – 1 < n < 3x + 5 represents the possible values of n, in feet whose side lengths are (2x+2) ft, (x+3) ft, and n ft.
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Given: ABCD is a parallelogram.
Prove: ∠A ≅ ∠C and ∠B ≅ ∠D
Parallelogram A B C D is shown.
By the definition of a ▱, AD∥BC and AB∥DC.
Using, AD as a transversal, ∠A and ∠
are same-side interior angles, so they are
. Using side
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.
Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
answers: d, supplementary, bc, d
Answer:
E2020
Step-by-step explanation:
Answer:
d, supplementary, bc, addition
Step-by-step explanation:
whats 40 + 40 + 40 X 2
Answer:
160
Step-by-step explanation:
40 + 40 + 40 X 2=160
This is the answer
I need so much help with these two and quick if anybody can helpe out thanks.
Answer:I need so much help with these two and quick if anybody can helpe out thanks.
Step-by-step explanation:
I need so much help with these two and quick if anybody can helpe out thanks.
to decide which tin of coffee is better value for money, calculate the price per gram of a 250g tin of coffee for R29.49 and a 750g tin of coffee for R69.99
Answer:
250g tin
Step-by-step explanation:
250g tin is 8.48g per R
750g tin is 10.77g per R
Which expression is equivalent to 15 + 3x?
A. 3(5+x)
B. 5(3+x)
C. 3(5+3x)
D. 5(3+3x)
Answer:
3(5+x)
Step-by-step explanation:
3(5 + x)
Answer:
See below ~
Step-by-step explanation:
Taking common factors
Factorize both the terms.
15 = 3 * 53x = 3 * xThe common factor is 3.
Now, group them together and solve.
15 + 3x3(5 + x)Option A