Explain how to easily decide whether x - 6 is a factor of the polynomial P(x) = x ^ 7 - 5x ^ 5 + 2x ^ 4 - x ^ 2 + 9 without performing long division .
[tex]\text{According to the factor theorem,}\\\\x-a~ \text{is a factor of}~ f(x)~ \text{if}~ f(a) = 0, ~ \text{where}~ a \in\mathbb{R}\\\\\text{Given that,}\\ \\P(x) = x^7 -5x^5 +2x^4 -x^2 +9\\\\P(6) = 6^7 -5\cdot 6^7 +2 \cdot 6^4 -6^2 +9 = 243621 \neq 0\\\\\text{Since} ~ P(6)\neq 0~, ~ x -6 ~ \text{is not a factor of P(x).}[/tex]
(A+1)/a = y make a the subject of this equation
Use SOHCAHTOA to find the side measure. Show work. Round to one decimal place.
Using trigonometric ratios, the measure of side n to one decimal is 6.6 units.
How to solve for a side using trigonometric ratios?Using the trigonometric principle
SOHCAHTOA,
cos 20 = adjacent / hypotenuse
adjacent side = n
hypotenuse side = 7
Therefore,
cos 20° = n / 7
cross multiply
n = 7 cos 20°
n = 7 × 0.93969262078
n = 6.5778483455
n = 6.6 units
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Properties of Light Lab Report
Instructions: In the Properties of Light—Bending Light Lab you will explore how light rays interact as they pass from one material, or medium, to another. Record your observations in the lab report below. You will submit your completed report.
Name and Title:
Include your name, instructor's name, date, and name of lab.
Objective(s):
In your own words, what was the purpose of this lab?
Hypothesis:
In this section, please include the if/then statement you developed during your lab activity. This statement reflects your predicted outcome for the experiment.
If I project light rays through (choose one: air, water, glass), then they will refract, or bend, the most.
Procedure:
Please be sure to identify the test variable (independent variable) and the outcome variable (dependent variable) for this investigation. Remember, the test variable is what is changing in this investigation. The outcome variable is what you are measuring in this investigation.
Test variable (independent variable):
Outcome variable (dependent variable):
Select Intro to begin.
Once the simulation loads, you will drag the protractor onto the screen so that the 0 lines up with the dotted line in the center of the screen. Select the More Tools icon at the bottom of the lab interactive and be sure to select the Normal and Angles boxes. Do Not move the laser light.
You will test all three materials in the bottom, blue half of the screen: air, water, and glass. Remember, do not move the laser light.
Record your observations of how the light rays interact as they pass from air, on the top of the screen, through the three materials on the bottom of the screen
Data:
Record the data from each trial in the data chart below. Be sure to fill in the chart completely.
Material Interactions
List any observations you made as the light rays passed from the air on the top of the screen to the selected material on the bottom of the screen. Evidence
Using the protractor, measure the angle as the light passes from the top material to the bottom material on the screen. Also, note the index of refraction for each as indicated on the screen.
Trial One Air on top
Bottom angle:
Bottom index of refraction:
Air on bottom
Trial Two Air on top
Bottom angle:
Bottom index of refraction:
Water on bottom
Trial Three Air on top
Bottom angle:
Bottom index of refraction:
Glass on bottom
Conclusion:
Your conclusion will include a summary of the lab results and an interpretation of the results. Please write in complete sentences.
Did your data support your hypothesis? Use evidence to explain.
Which material refracted the light rays the most: air, water, or glass?
Which material refracted the light rays the least: air, water, or glass?
How does density affect refraction?
Diamonds are a very dense material. Predict what would happen to the light ray if you projected it from air through a diamond.
Explain where you observe reflection, refraction, and absorption of light in your everyday activities.
Answer:
Can You Give Me Some More Information
Step-by-step explanation:
Put these numbers in order from least to greatest 1/8, -0.333, -1/7
Answer:
-0.333, -1/7, 1/8
Step-by-step explanation:
1/8 is the greatest because it is a positive number while the other two numbers are negative.
-0.333 or -1/3 is smaller than -1/7.
Select the correct answer. Given the following formula, solve for y. w=x-y/2 -z
Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .
What is a simplification of an expression?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.
Given the following formula,
w=x-y/2 -z
We need to solve for y.
[tex]w = \dfrac{x-y}{2 -z}[/tex]
By cross multiplication
[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]
subtract x both side
2w - wz -x = x - y -x
y = x - 2w + wz
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k5500 is invested for a period of 4 years in a savings account. for the first year , the investment grows at a simple interest rate of 11% per annum and then at a rate of 12.5% per annum compound and quarterly for the rest of the period. Determine the value of the investment at the end of the 4 years
manyy is really short time samma basyo is really an amazing
The following scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.
Hint: A line of best fit follows the pattern of the data and is in the middle of the points.
Answer:
whats the question
Step-by-step explanation:
EASY POINTS
What is the slope-intercept equation of this line?
Answer:
B
Step-by-step explanation:
The y-intercept is 8
The slope is -2x
Therefore the slope-intercept is y = -2x + 8
Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
A card is drawn from a standard deck of cards without jokers
What is the probability that the card is either black or a heart
Answer:
Step-by-step explanation:
Remark
The two black suites are
Clubs
Spades
Each of them has 13 cards so the total number of black cards is 2*13 = 26
Add to that the hearts which also has 13 cards
The total number of possible good cards is 13 + 26 = 39
Answer
P(hearts or Black) = 39/52
P(hearts or Black) = 3/4
P(hearts or Black) = 0.75
A. Using the spinner above, what is the probability that a player will draw 3 cards?
B. What is the probability that a player will draw 1 card on the first spin and 2 cards on a second spin?
C. Harold wants the probability that a player draws 3 cards and moves 2 spaces to be 3/8. How can he change the spinners to result in this probability?
Answer:
A-1/3
B-1/8
C-?
Step-by-step explanation:
In a parallelogram PQRS, if angle P = (2x+25) degrees and angle Q = (3x-5) degrees, then write the measures of angle S and angle R.
Consecutive angles of a parallelogram are supplementary, so:
[tex]2x+25+3x-5=180\\5x+20=180\\5x=160\\x=32[/tex]
This means [tex]m\angle P=2(32)+25=89^{\circ}[/tex] and that [tex]m\angle Q=3(32)-5=91^{\circ}[/tex].
Since opposite angles of a parallelogram are congruent,
[tex]\boxed{m\angle S=91^{\circ}, m \angle R=89^{\circ}}[/tex]
HELP URGENT WILL GIVE
BRAINLIEST!!!
Elsa is putting money into a
savings account. She starts
with $550 in the savings
account, and each week she
adds $70.
Let S represent the total
amount of money in the
savings account (in dollars),
and let W represent the
number of weeks Elsa has
been adding money. Write
an equation relating S to W
Then use this equation to
find the total amount of
money in the savings
account after 11 weeks.
Equation:__
Total amount of money after
11 weeks:
$__
Answer:
S x W + 550 = answer
Step-by-step explanation:
eh u dont need to know, yw
Answer:
Step-by-step explanation:
S= total amount in savings acc.
W= # of weeks
You have 550 in your acc and your adding 70 every week?
S= 550+70w
Then for 11 weeks: Equation- S=550+70*11
70*11=770
S= 550+770 - S= 1320
Total after 11 weeks is 1320
14/2+5x4?? can anyone help me??
Answer: 27
Step-by-step explanation:
Use PEMDAS (Parenthesis,Exponents,Multiplication,Division,Addition,Subtraction)
to solve this problem. First multiply 5 times 4 to get 20. Then divide 14 by 2 to get 7. Lastly, add those two answers to get 27 as the final answer.
Use properties of operations to write two expressions that are equivalent
to 2n + (8 + 32).
The equivalent expressions of 2n + (8 + 32)are 2n + 40 and 2(n + 20)
How to determine the equivalent expressions?The expression is given as:
2n + (8 + 32)
The first equivalent expression
Evaluate the sum of the numbers in the bracket
2n + (8 + 32) = 2n + 40
This means that 2n + 40 and 2n + (8 + 32) are equivalent.
The second equivalent expression
In (a), we have:
2n + (8 + 32) = 2n + 40
Factor out 2 from the expression
2n + (8 + 32) = 2(n + 20)
This means that 2(n + 20) and 2n + (8 + 32) are equivalent.
Hence, the equivalent expressions are 2n + 40 and 2(n + 20)
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Determine if the triangle with the given sides is acute, obtuse, or right.
7, 12, 16
Noah borrowed $5000 from the credit union for 180 days. The interest rate is 11.4% per year. How much must Noah pay to the credit union after 180 days?
The amount that Noah pays to the credit union after 180 days will be $5143.85.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
We have
P = $5,000
r = 0.114 / 12 = 0.0095
n = 3
A = 5000(1 + 0.114)³
A = $5143.85
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Please Answer Fast
3.4 × 107 is the scientific notation for:
3.40000000
34 000 000
340 000 000
Answer:
34000000
Step-by-step explanation:
hope it helps you and give me a brainliest
The perimeter of a rectangle is 78 cm. If the length is 24 cm, how wide is the rectangle?
Write an equation you can use to answer this question. Use w as your variable in the equation.
Answer:
15(cm)
Step-by-step explanation:
48 + 2w = 78
2w = 30
w = 15(cm).
1. 5 M 20 CM of cloth is needed to stitch a shirt how much clothes will be needed to stitch 449 shirts
2. I have a pack of 100 rupees notes in series which start from number code 412 to 425 how much money do I possess
3. a tailor stitches 120 suits in one month. find out how many suits he stitches in an year
4. Radha can swim 348 m in 5 minutes what distance can she in 50 minutes
full explanation pls
#1
Length in cm
500+20=520cmShirts=449Total length
449(520)233480cm2334m 80cm#2
Total notes
425-412+1=14Total money
100(14)1400|
Total suits per month=120
per year
120(12)1440suits#4
Total 5mins
50/5=10total distance
348(103480mAre these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 1. Rational 2. Irrational please answer quickly I need to get this test done
Answer:
-7, rational
sqrt 10, irrational
sqrt 16 = 4, rational
52% = 0.52, rational
1.235, rational
[tex]\text{A rational number is a real number that is in the form of}~ \dfrac pq,\\\\\text{where p and q are integers and}~ q \neq 0\\\\\text{The real numbers that cannot be expressed as the ratio of two integers}~ \\\text{ are called Irrational numbers.}\\\\-7 = \dfrac{-7}1 \\\\\text{So}~ -7 ~ \textbf{is rational.}\\\\\\\sqrt{10} ~ \text{is irrational because 10 is not a perfect square.}\\\\\text{So}~ \sqrt{10}~ \textbf{is irrational.}\\\\\\[/tex]
[tex]\sqrt{16} = \sqrt{4^2} = \left(4^2 \right)^{\tfrac 12} = 4 = \dfrac 41\\\\\text{So,}~ \sqrt{16}~ \textbf{is rational.}\\\\\\52\% = \dfrac{52}{100}\\\\\text{So,}~ 52\%~ \textbf{is rational.}\\\\\\1.235 =\dfrac{1235}{1000}\\\\\text{So,}~1.235~ \textbf{is rational.}[/tex]
order the numbers from least to greatest
Answer:-3, -2, -1/10, -0.8, 0.8, 7
Step-by-step explanation:
Bob wants to take his wife, Jessica, to Europe in three years to commemorate their 40th wedding anniversary. He recently received a $23,000 inheritance from an uncle, which he plans to put towards the trip. The trip is expected to cost $32,200, according to Bill. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, F (From the tables provided, select the appropriate factor(s).)
What annual compounded interest rate must Bill earn to save enough money to pay for the trip? (Round to the nearest whole percentage your interest rate.)
Answer:
10%
Explanation:
Use future value formula
Future Value = Present Value ((1+r)^n)
26,600 = 20,000 ((1+r)^3
26,600/20,000 = (1+r)^3
1.33 = (1+r)^3
1.33^1/3 = 1+r
1.0997 = 1+r
1.0997 - 1 = r
r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)
(pls give brainliest)
6. Use the following matrices to answer the questions. (2 points each)
5 -8
2 -6
-8
-2 3
A
외
B =
[4
18] c- [5 5] -
C=
9 1
03
9
1
a. Is the operation E + C possible? Circle YES or NO
If yes, state the dimensions of the answer:
b. Is the operation B + C possible? Circle YES or NO
If yes, state the dimensions of the answer:
c. Is the operation E. D possible? Circle YES or NO
If yes, state the dimensions of the answer:
d. Is the operation D E possible? Circle YES or NO
If yes, state the dimensions of the answer:
e. Is the operation A D possible? Circle YES or NO
If yes, state the dimensions of the answer:
1
-1 10
E
11
7 -1 0
Answer:
its a such a hard questions i think you should ask to you're teacher ?
What is the sum of the 3rd and 5th square number??
Answer:
34
Step-by-step explanation:
3rd and 5th square numbers means 3² and
5² .
so we know 3² is another word of saying 3×3
3×3=9
5×5=25
9+25=34
help me solve this please help I will gave u brilliant answer
Answer: 1.) 3 2/3 2.) 2 9/10 3.) 9 11/15 4.) 7 11/12
B. Question 2,
My answer is reasonable, because if we round 1 7/10 to 2 and 1 1/5 to 1
2+1=3 and my answer is 2 9/10. This estimate makes sense because 2 9/10 can be rouned to 3, meaning it is reasonable.
Step-by-step explanation:
1 1/6 + 2 3/6= 3 4/6
Simplifyed=3 2/3
1 7/10 + 1 2/10 = 2 9/10
7 5/15 + 2 6/15= 9 11/15
4 8/12 + 3 3/12= 7 11/12
HELP WHAT DOES THIS EVEN MEAN
Answer:
59.5
Step-by-step explanation:
He is asking for angle A
cosA = adjacent/hypotenuse
= 33/65
we'll do shift cos(33/65) = 59.48 to bring A
Triangle DEF is a right triangle with point F at the origin. Segment DE has endpoints located at D(8, 0) and E(0, −2). What is the area of triangle DEF?
Answer: 8
Step-by-step explanation:
Using the formula [tex]A=\frac{1}{2}bh[/tex],
[tex]A=\frac{1}{2}(8)(2)=\boxed{8}[/tex]
What is the vertex of the quadratic function f(x) =(x-6)(x+2)
Answer:
(2, -16)
Step-by-step explanation: set both (x +2) and (x-6) = 0.
You get the two x-intercepts -2 and 6. Find the midpoint of the two intercepts by -2 + 6 / 2 which gives you x=2. Then plug 2 in for x and solve the original equation. ( 2 - 6)(2+2) = -16. Therefore the vertex is at (2,-16).
Answer:
Step-by-step explanation:
f(x) = x^2 - 4x - 12
x = -(-4)/2 = 4/2 = 2
(2)^2 - 4(2) - 12 = 4 - 8 - 12 = -4 - 12 = -16
vertex: (2, -16)