The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8
What is the remainder theorem?The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point
The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;
f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8
The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8
Learn more on the remainder theorem here: https://brainly.com/question/17256898
#SPJ1
6=a/4+2. This is a two step equation
Answer:
Step-by-step explanation:
6 = a / 4 + 2
=> 6 - 2 = a / 4 + 2 - 2
=> 4 = a / 4
=> a = 16
Answer:
a = 16
Step-by-step explanation:
[tex]6=a/4+2[/tex]
[tex]6(-2)=a/4+2(-2)[/tex]
[tex]4=a/4[/tex]
[tex]4(4)=(a/4)(4)[/tex]
[tex]16=a[/tex]
[tex]a=16[/tex]
The P(tossing a head) is 50%. Ann tossed a coin 100 times. It landed on heads 40 times. Did the
experimental match the theoretical probability?
The experimental probability did not match the theoretical probability.
How to find the experimental probability ?The experimental probability is the chance that is determined from the real results of an experiment or event. It is based on practical observations or information, rather than a mathematical expression.
The theoretical probability is the chance that is worked out using a mathematical equation founded on the assumptions and situations of the event or experiment.
The experimental probability of landing on heads :
= 40 / 100
= 40 %
The theoretical probability is 50 % which means the experimental and theoretical did not match.
Find out more on theoretical probability at https://brainly.com/question/1503266
#SPJ1
I'LL MARK BRAINLIST FOR BEST ANSWER
(10 POINTS)
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
k^2 − 28k + ____
NO LINKS!! URGENT HELP PLEASE!!!
8. Scott invested $1,600 into a retirement account that earns 2.4% interest compounded monthly. What will the balance of the account be after 30 years?
9. Kaylee used her graduation to set up a savings account that earns 3.4% interest compounded weekly. If the original amount deposited was $500, how much interest will she have earned after 10 years?
Answer:
8) $3,284.73
9) $202.40
Step-by-step explanation:
To solve both these problems, we can use the formula for compound interest:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Question 8Given values:
P = $1,600r = 2.4% = 0.024n = 12 (monthly)t = 30 yearsSubstitute the given values into the formula and solve for A:
[tex]A=1600\left(1+\dfrac{0.024}{12}\right)^{12 \cdot 30}[/tex]
[tex]A=1600\left(1+0.002\right)^{360}[/tex]
[tex]A=1600\left(1.002\right)^{360}[/tex]
[tex]A=3284.730430...[/tex]
[tex]A=3284.73[/tex]
Therefore, the balance of Scott's account after 30 years will be $3,284.73.
[tex]\hrulefill[/tex]
Question 9Given values:
P = $500r = 3.4% = 0.034n = 52 (weekly)t = 10 yearsSubstitute the given values into the formula and solve for A:
[tex]A=500\left(1+\dfrac{0.034}{52}\right)^{52 \cdot 10}[/tex]
[tex]A=500\left(1.000653846...\right)^{520}[/tex]
[tex]A=702.3957509...[/tex]
[tex]A=702.40[/tex]
Therefore, the balance of the account after 10 years will be $702.40, which includes both the principal and the interest.
To find the amount of interest earned, subtract the principal:
Interest earned = $702.40 - $500 = $202.40
Therefore, Kaylee will have earned $202.40 in interest after 10 years.
Please Help! 13 points!
a) The first mistake that Fatima made was in the first step.
b) She incorrectly changed the place value of 0.02 in the subtraction operation.
c) Based on the correct subtraction operation and place value in step one, Fatima has 0.395 kilograms of rose petals left.
What is a place value?The place value shows the position of a digit in a number.
The right place values are essential for correct mathematical operations.
The quantity of rose petals that Fatima bought initially = 0.454 kilograms
The quantity of rose petals used for making rose water = 0.02 kilograms
The remaining quantity of rose petals = 0.434 (0.454 - 0.02)
The additional quantity of rose petals Fatima bought = 0.056
The quantity of rose petals used for making the second rose water = 0.095
The quantity of rose petals left = 0.395 (0.434 + 0.056 - 0.095)
Learn more about place values at https://brainly.com/question/1654524.
#SPJ1
Find the value of x.
48°
126°
Answer:
78°
Step-by-step explanation:
angle on a straight line : 180° - 126° = 54°
Therefore, 48° + 54° = 102°
total angle in a triangle = 180°
So, 180° - 102° = 78°
Please Help me I have RSM tomorrow and I have to finish my homework. Thanks.
How many yards are equivalent to two miles
Answer:
2 miles = 3,520 yards
Step-by-step explanation:
You multiply the length value by 1,760.
3520 yards is equivalent to 2 miles.
Hope this helped! Have a nice day. :)What is 71% of 1,000
Answer:
710
Step-by-step explanation:
You realize that, despite what you expected, the soda actually tastes different depending on which flavor you choose first, second, etc. With this in mind, how many different sodas can you make if repetition is not allowed? Show your work and leave your answer in exponential or factorial form.
The number of different sodas that can be made is given by "n!" or factorial form.
If the soda tastes different depending on the order in which the flavors are chosen, we can calculate the number of different sodas that can be made without repetition using the concept of permutations.
Let's assume we have "n" different flavors of soda available. To calculate the number of different sodas we can make, we need to find the number of permutations of "n" flavors taken "r" at a time, where "r" is the number of flavors we want to choose for each soda.
The formula to calculate permutations is given by:
P(n, r) = n! / (n - r)!
Here, "n!" represents the factorial of "n," which is the product of all positive integers less than or equal to "n."
In this case, if repetition is not allowed, each soda can have only one flavor. Therefore, we have "r = 1" for each soda.
Applying the formula, we have:
P(n, 1) = n! / (n - 1)!
= n! / (n - 1)
= n
Hence, the number of different sodas that can be made without repetition is "n."
Therefore, the number of different sodas that can be made is given by "n!" or factorial form.
for such more question on different sodas
https://brainly.com/question/13614040
#SPJ11
What is the square root of 25*25*64*221?
8/5÷6=
i need help on this
Answer:
2 forms
Step-by-step explanation:
hope this helps <3
[tex] \sf \longrightarrow \: \frac{8}{5} \div 6 \\ [/tex]
[tex] \sf \longrightarrow \: \frac{5}{8} \times 6 \\ [/tex]
[tex] \sf \longrightarrow \: \frac{5 \times 6}{8} \\ [/tex]
[tex] \sf \longrightarrow \: \frac{30}{8} \\ [/tex]
[tex] \sf \longrightarrow \: \frac{8}{30} \\ [/tex]
[tex] \sf \longrightarrow \: 0.26 \\ [/tex]
_____________________________
Tyler is 8 years old his sister Olivia is 4 years less than twice his age write a numerical expression for Olivia’s age
Answer: yes
Step-by-step explanation:
Identify the center, radius, domain and range of the circle eith equation. Make sure to scroll down through all thr answer choices
(x+2)^2+(y-5)^2 = 9
Answer: Centre: (-2,5)
Radius = 3
so
Diameter = 6
Domain: (-5,1)
Range: (2,8)
Answer:
center (-2,5)
radius =3
domain = -5< x <1
range 2 <y<8
Step-by-step explanation:
siiuu
the diagram shows a regular pentagon a) work out the interior angle , b) work out the size of one angle
pls help
Measure of one exterior angle = 30 degree
Measure of one interior angle = 150 degree
In the given regular pentagon
Number of terms = 12
We know that,
Sum of all exterior angles = 360 degree
To find one exterior angle,
Divide the complete angle by number of terms
Therefore,
One exterior angle = 360/12 = 30 degree
Since,
Sum of all interior angles = 180 degree
And To find one interior angle,
subtract the interior angle by one exterior angle
Therefore,
One exterior angle = 180 - 30 = 150 degree
To learn more about pentagon visit:
https://brainly.com/question/27874618
#SPJ1
The common ratio of a geometric sequence is 1.5 and the sum of the first seven terms is 64.34375. Find the value of the first term.
The first term of the geometric progression has the value a1 = 2.
Let r = 1.5 be the common ratio of the GP given the data.
Now, the first seven terms added together equal 64.34375.
where Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
On simplifying , we get
64.34375 = a ( 1.5⁷ - 1 ) / ( 1.5 - 1 )
On simplifying , we get
64.34375 = 2a ( 1.5⁷ - 1 )
2a = 64.34375 / 16.0859375
2a = 4
Divide by 2 on both sides:
a = 2
Consequently, a = 2 is the first term of the GP.
Click here for additional information about geometric progression.
https://brainly.com/question/1522572
#SPJ1
What is the range of the function y=−7x−5?
Step-by-step explanation:
"Range'' is the values of 'y' that a graph can have....there are no limits on this one
(-∞,+∞)
BRAINLIEST
Write the equation for the translation of the graph of ( brackets = absolute value ) y=[2x+7] one unit to the left.
Answer:
y = |2x +9|
Step-by-step explanation:
You want the equation that will translate the graph of y = |2x +7| one unit to the left.
Horizontal translationTo translate the graph of f(x) by h units to the right, you want to replace x with x-h:
f(x-h) . . . . translates f(x) by h units to the right
ApplicationHere, we want a translation by 1 unit to the left, which is -1 unit to the right. This means we want to replace x in the function by (x -(-1)) = (x +1). Doing that gives ...
y = |2(x +1) +7)| = |2x +2 +7|
y = |2x +9|
The attachment shows the graphs.
#95141404393
a customer bought one science book and for math books the customer spend At most a $126 the science book costs $30 write an inequality that represents the cost of one math book show how you determine your answer
# (-20
01
160 Minutes boseng
and (4,0)
1. Use the equation to answer the question.
x² + 12x - 85
A
(x + 6)² = 11
B (x + 6)² = 9
C (x + 6)² = 7
D (x + 6)² = 15
D. They
Billy is completing the square to rewrite the equation. Which
equation could be his result?
A8 2002 2x2
bow 212
Edavad id doow to 202
12
AREI.4
After completing the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we find that the possible result is [tex]\((x + 6)^2 = 49\)[/tex].
To complete the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we follow these steps:
1. Take half of the coefficient of the [tex]x[/tex] term, which is [tex]\(12/2 = 6\)[/tex].
2. Square this result, [tex]\(6^2 = 36\)[/tex].
3. Add this value, 36, to both sides of the equation to maintain balance:
[tex]\[x^2 + 12x + 36 - 85 = 36 - 85.\][/tex]
4. Simplify both sides of the equation by combining like terms:
[tex]\[(x + 6)^2 - 49 = 0.\][/tex]
5. Rearrange the equation to isolate the perfect square term:
[tex]\[(x + 6)^2 = 49.\][/tex]
From this process, we can conclude that the equation [tex]\((x + 6)^2 = 49\)[/tex] could be the result of completing the square for the given equation [tex]\(x^2 + 12x - 85\)[/tex]. This equation represents a perfect square trinomial with a perfect square term, and it allows us to solve for the value of [tex]x[/tex] by taking the square root of both sides.
It's important to note that completing the square allows us to rewrite quadratic equations in a form that reveals key properties and facilitates solving for unknowns.
For more such questions on square for the equation: https://brainly.com/question/13981588
#SPJ11
Diana walks around a circular swimming pool of diameter 14 feet. What is the distance she has walked?
Step-by-step explanation:
She walks the entire CIRCUMFERENCE of the circle
circumference = pi X diameter
= pi X 14 ft = 43.98 ft = ~ 44 ft (rounded)
In the following rectangle, AC = 2x + 7 and BD = 5x - 14. Solve for x.
A
D
2=
B
C
Answer:
7
Step-by-step explanation:
yw ;)
Two systems of linear equations in two variables, x and y, are given.
System P:
(3x-10y=8
7x+2y=6
The two systems have the same solution..
What are the values of b and c?
b=
System T:
bx - 10 y + 10 y = 38
cx + 10 y = 30
=
C =
Answer:
Step-by-step explanation:
The graph represents the closing price per share of stock for a company each day for 28 days. What variable is represented on the horizontal axis? In the first week, was the stock price generally increasing or decreasing? During which period did the closing price of the stock decrease for at least 3 days in a row?
In the graph, the closing price per share of stock for a company is represented each day for 28 days. After analyzing the graph, the variable which is represented on the horizontal axis is days and the stock price generally increasing in the first week. The closing price of the stock decrease for at least 3 days in a row during day 7 to day 10.
The graph represents the closing price per share of stock for a company each day for 28 days. That's the number of days in the first week. So days is the variable represented in the horizontal axis.
In the first seven days, the graph is basically going up, and then it gets slower and then it's going up. So it's increasing the entire time. Not at the same rate, but it's increasing.
From day 7 to day 10, the closing price of the stock was decreasing three days in a row.
Know more about graph analysis,
https://brainly.com/question/28737035
#SPJ1
The owner of the course asks you to provide a scale drawing of the green section he requested that you use the length of the legs of the right triangle found in the previous step use the connect line tool to draw your green section in the grid.
The area of gs : 48.67
Length of one leg : 3.21
Length of other leg : 10.5
Length of other leg 12
Based on the information given, it should be noted that the length of other leg 12.
How to calculate the lengthsBased on the information, the owner of the course asks you to provide a scale drawing of the green section he requested that you use the length of the legs of the right triangle.
Based on the information, 1/2ab = 54
1/2 × 4/3b² = 54
b² = 81
b = ✓81
b = 9
a will be
= 4/3 × 9
= 12 feet.
Learn more about triangles on
brainly.com/question/17335144
#SPJ1
What is the break-even point? A graph has units on the x-axis, and cost (dollars) on the y-axis. 2 lines intersect at (11, 44). a. 11 units c. 3 units b. 44 units d. 6 units
The break-even point would be when the cost is equal to 44 dollars.
Option B is the correct answer.
We have,
The break-even point represents the point at which the cost equals the revenue or the point where there is no profit or loss.
Now,
In this case, if the graph represents the cost (dollars) on the y-axis and units on the x-axis, the break-even point occurs when the cost is equal to the revenue or total sales.
Given that two lines intersect at (11, 44),
The break-even point would be when the cost is equal to 44 dollars.
Thus,
The break-even point would be when the cost is equal to 44 dollars.
Learn mroe about break-even points here:
https://brainly.com/question/20038925
#SPJ1
What is the surface area of the cylinder with height 8 cm and radius 4 cm? Round your answer to the nearest thousandth.
Answer:
301.59289cm²
Step-by-step explanation:
plessee help me i dont know the answerr
volume: 2,160cm
please let me know if this was what you needed or if it was something else.
Can someone please help me? I need this fast and it’s really important that I get it right. Graph the function shown in the image.
Answer: attached in image, look at both
Step-by-step explanation:
12. In the figure, AB is a diameter, and ABL CD The figure is not drawn to scale.
If m AC-54°, what is m BD
(1 point)
0 36°
O 108
O 126°
O 144°
20 points
In the figure, AB is a diameter, and AB⊥CD, If m AC = 54°, BD is 36°. Option A
How do we calculate the line BD given the that AB is a diameter, and AB⊥CD?In a circle, a diameter divides it into two equal parts and forms a straight line that measures 180°.
Given that AB is a diameter = 180°.
AB is perpendicular to CD, therefore m∠AC + m∠BD = 90°.
Substituting m∠AC =54°, we get m∠BD + 54° = 90°.
Solving for m∠BD, we get 90° - 54° = 36°.
There BD is 36°.
Find more exercises on finding lines within a circle;
https://brainly.com/question/13080923
#SPJ1