After dividing ( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 ), we get the quotient as 5 x² - 7 x + 4 and the remainder as 11 x - 21.
We are given an expression:
( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 )
We need to perform division of the algebraic expression:
5 x² - 7 x + 4
3 x² + x + 1 √15 x⁴ - 16 x³ + 10 x² + 8 x - 17
15 x⁴ + 5 x³ + 5 x²
______________________
- 21 x³ + 5 x² + 8 x - 17
- 21 x³ - 7 x² - 7 x
______________________
12 x² + 15 x - 17
12 x² + 4 x + 4
______________________
11 x - 21
______________________
Therefore, after dividing ( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 ), we get the quotient as 5 x² - 7 x + 4 and the remainder as 11 x - 21.
Learn more about division here:
https://brainly.com/question/25289437
#SPJ9
You have a block of metal with a volume of 56 cubic centimeters and a mass of 153 grams.
What is the density?
Answer:
C
Step-by-step explanation:
153/56= 207G
Four lines are plotted on the coordinate plane.
Line 1
-10
Line 1
Line 2
Line 3
-10
O Line 4
10
Which line shows a proportional relationship?
Line 2
Line 3
Line 4
Answer:
Line 3
Step-by-step explanation:
Proportional relationship:
• They are straight lines that have a constant slope
• The line must pass through the origin at (0,0)
• The y intercept is zero
The only line passing through the origin at the point (0,0), is Line 3
When adding 7 to -15 using a number line, which direction would you move on the number line from -15?
Answer: To the right
Step-by-step explanation:
The negatives on a number line are on the left side and the positives on the right.
Step-by-step explanation: educated guess
What is the probability that a hand of five cards chosen at random and without replacement from a standard 52 card deck will have a king of spades, exactly one other king, and exactly two queens?
The probability that a hand of five cards chosen at random and without replacement from a standard 52 card deck will have a king of spades, exactly one other king, and exactly two queens = 0.000332
A deck of cards consist of 52 cards in which each 13 cards are from 4 suits: Spades, Hearts, Diamonds and Clubs.
Each suit consist of cards Ace, King, Queen, Jack and other 9 cards.
So in 52 cards there is 4 kings and 4 queens each.
Five cards are selected at random and without replacement.
Five cards from a 52 deck cards can be chosen in 52C5 ways.
A spade king can be chosen in 1C1 way. [ Since there is only one spade king]
Exactly one other king can be chosen in 3C1 ways. [Since now only 3 kings are remaining after choosing 1 spade king]
Exactly 2 queens can be chosen in 4C2 ways.
Now 4 cards are selected out of 5. The remaining 1 card is chosen out in 48C1 ways.
So the probability that the five cards chosen will have a king of spades, exactly one other king, and exactly two queens
= (1C1 x 3C1 x 4C2 x 48C1) /52C5 = 18/54145 =0.000332
Learn more about probability in cards at https://brainly.com/question/28528072
#SPJ4
When you divide an even number by an even number, is the result always an even number
Answer: No, for example, 50/2=25, 25 isn't even
Step-by-step explanation:
Answer:
No, it's not
Step-by-step explanation:
when u divide an even number with even number,the ans maybe appear in even as well as odd number also
For e.g:
1. 36/12=3
2. 12/6=2
3. 30/6=5
4. 60/10=6
(5x+3)(5x-3) what is the answer if multiplied
Answer:
25x^2 -9
Step-by-step explanation:
(5x+3)(5x-3)
FOIL
first 5x*5x = 25x^2
outer 5x*-3 = -15x
inner 3*5x = 15x
last = 3*-3 = -9
Add them together 25x^2 -15x+15x -9
Combine terms 25x^2 -9
Answer:
[tex] \sf25 {x}^{2} - 9[/tex]
Step-by-step explanation:
We can use Foil method to find the answer for this expression.
(5x + 3) (5x - 3)
That is:
F --> First ---> (5x)(5x)
O --> Outside ---> (5x) (-3)
I --> Inside ---> (3)(5x)
L --> Last ---> (3) (-3)
And now we have to add those terms together while combining like terms.
[tex] \sf(5x)(5x) + (5x)( - 3) + (3)(5x) + (3)( - 3) \\ \sf25 {x}^{2} - 15x + 15x - 9 \\ \sf25 {x}^{2} - 9[/tex]
Yasmin invests money in an account paying a simple interest of 3% per year. If no money will be added or removed from the investment, what should she multiply her current balance by to find her total balance in a year in one step?
hi
so the amount will be increased by 1 + 3/100 = 1.03
so multiply current balance by 1.03 and she will know balance in a year
Use the following items to determine the total assets, total liabilities, net worth, total cash inflows, and total cash outflows.
Rent for the month $ 1,390 Monthly take-home salary $ 3,920
Cash in checking account $ 1,340 Savings account balance $ 2,770
Spending for food $ 1,110 Balance of educational loan $ 3,050
Current value of automobile $ 8,020 Telephone bill paid for month $ 85
Credit card balance $ 334 Loan payment $ 143
Auto insurance $ 321 Household possessions $ 3,510
Stereo equipment $ 3,320 Payment for electricity $ 189
Lunches/parking at work $ 204 Donations $ 116
Home computer $ 2,490 Value of stock investment $ 1,160
Clothing purchase $ 139 Restaurant spending $ 223
Total assets is $20,120; total liabilities is $3,384; net worth is $16,7366; total cash inflows is $3,804; and total cash outflows is $3,920.
How do we calculate the net worth?Total assets = Cash in checking account + Savings account balance + Current value of automobile + Household possessions + Stereo equipment + Home computer + Value of stock investment = $1,340 + $2,770 + $8,020 + $3,510 + $3,320 + $1,160 = $20,120
Total liabilities = Balance of educational loan + Credit card balance = $3,050 + $334 = $3,384
Net worth = Total assets - Total liabilities = $20,120 - $3,384 = $16,736
Cash outflows = Rent for the month + Spending for food + Telephone bill paid for month + Loan pyment + Auto insurance + Payment for electricity + Lunches/parking at work + Donations + Clothing purchase + Restaurant spending = $1,390 + $1,110 + $85 + $143 + $321 + $189 + $204 + $139 + $223 = $3,804
Cash inflows = Monthly take-home salary = $3,920
Learn more about net worth here: https://brainly.com/question/27231515.
#SPJ1
19
Select the correct answer.
A boat is anchored in the water. At low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its
anchor. At high tide, the boat is a horizontal distance of 35 feet away from its anchor.
low tide
high tide
20 ft
? ft
40 ft
35 ft
Approximately how high is the boat floating above the seafloor at high tide? Assume the anchor rope remains tight, without any slack.
OA 22.5 ft
OB. 27.8 ft
OC
15.6 ft
OD. 35.7 ft
Reset
Next
The height of the boat floating above the seafloor at high tide is 17.5 feet.
In this question, we have been given a boat which is anchored in the water.
At low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its anchor.
And at high tide, the boat is a horizontal distance of 35 feet away from its anchor.
We need to find the distance the boat floating above the seafloor at high tide.
Consider the following diagram.
Let the boat floating m feet above the seafloor when the boat is a horizontal distance of 35 feet away from its anchor.
Since both the triangle are similar triangles, the corresponding sides must be in proportion.
⇒ 20/40 = m/35
We need to find the value of m.
⇒ 20 × 35 = m × 40
⇒ m = 35 / 2
⇒ m = 17.5 feet
Therefore, the height of the boat floating above the seafloor at high tide is 17.5 feet.
Learn more on similar triangles here:
https://brainly.com/question/25882965
#SPJ1
What is the area of the semicircle? Use 3.14 for pi.
150.72 mm^2
138.16 mm^2
69.08 mm^2
189.97 mm^2
The area of the semicircle with the given diameter is 189.97 mm^2
How to determine the area of the semicircle?The given parameters are
Diameter, d = 22 mm
The area of the semicircle is calculated as
A = 1/2 * pi * (d/2)^2
So, we have
A = 1/2 * 3.14 * (22/2)^2
Evaluate the expression
A = 189.97 mm^2
Hence, the area of the semicircle with the given diameter is 189.97 mm^2
Read more about area at:
https://brainly.com/question/22972014
#SPJ1
Dilate the figure by the scale factor. Then enter the new coordinates. A(-3,1) C(0,-4) B(2,4) K=7 A'([?], []) B'(11) C'([],[])
The new coordinates are A'(-21, 7), B'(0, -28), C'(14, 28).
Dilating the given triangle by the scale factor means multiplying each coordinate by the given scale factor.
Given coordinates are A(-3, 1), B(2, 4), and C(0, -4).
The scale factor k = 7.
Let, the new coordinate obtained by dilating A with scale factor k be A'.
Then x-coordinate of A' = k × x-coordinate of A
⇒ x-coordinate of A' = 7 × (-3)
⇒ x-coordinate of A' = -21
And y-coordinate of A' = k × y-coordinate of A
⇒ y-coordinate of A' = 7 × 1
⇒ y-coordinate of A' = 7
So, A' → (-21, 7)
Let, the new coordinate obtained by dilating B with scale factor k be B'.
Then x-coordinate of B' = k × x-coordinate of B
⇒ x-coordinate of B' = 7 × 2
⇒ x-coordinate of B' = 14
And y-coordinate of B' = k × y-coordinate of B
⇒ y-coordinate of B' = 7 × 4
⇒ y-coordinate of B' = 28
So, B' → (14, 28)
Let, the new coordinate obtained by dilating C with scale factor k be C'.
Then x-coordinate of C' = k × x-coordinate of C
⇒ x-coordinate of C' = 7 × 0
⇒ x-coordinate of C' = 0
And y-coordinate of C' = k × y-coordinate of C
⇒ y-coordinate of C' = 7 × -4
⇒ y-coordinate of C' = -28
So, C' → (0, -28)
Refer to the image attached for the new triangle formed.
Therefore, the new coordinates are A'(-21, 7), B'(0, -28), C'(14, 28).
Learn more at:
https://brainly.com/question/24873454
#SPJ9
Pls help i will give brainly
Answer:
B. y = -1/4x + 2
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So slope is -1/4
Using m = -1/4, y =4, x = -8
y = mx + b
4 = -1/4(-8) + b
4 = 2 + b
b = 2
so y = -1/4x + 2
Find an equation of the line through (3,4) and parallel to y = 2x + 2: y =____. (Type your answer in slope-intercept form.)
Answer:
y = 2x - 2
Step-by-step explanation:
y = 2x + 2
4 = 2(3) + c
4 = 6 + c
c = -2
y = 2x - 2
The line is parallel so slope remains same but intercept changes.
Ryan works for a delivery service. The function f(n) is used to calculate his daily pay, in dollars, on a day when he makes n deliveries.
Write an absolute value inequality for the graph below.
Use x for your variable.
Answer:
The absolute value inequality will be |x| ≥ -2.
Step-by-step explanation:
Franchise agreements are popular with fast-food companies such as McDonald's, Wendy's, and Burger King.
a. True
b. False
Answer:
cdf
Step-by-step explanation:
VV Goku uiiuuyujn. b. nnm, 1
Step-by-step explanation:
make a scale drawing of swimming pool where 1 centimeter represents 5 meters
Draw the graph of y = x² – 4x + 3. Identify the intercepts (x and y), the vertex, and the axis of symmetry.
Answer:
y-intercept : 3
x-intercepts are 1 and 2
Vertex is at (2,-1)
Axis of symmetry is at x = 2
Step-by-step explanation:
See attached graph.
The equation y = x² – 4x + 3 represents a parabola
y-intercept at is at B(0,3); y-intercept is 3
x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3
The vertex is the lowest point on this parabola (2-1)
Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2
My number is less than 50. - it is a factor of 70. - it is a multiple of 5 and 7. what is minnu's number? a. 5 b. 35 c. 14 d. 70
Answer:
B) 35
Step-by-step explanation:
35 is less than 50 and it's a factor of 70, a multiple of 5 and 7 is 35 just by multiplying the numbers it will give you that answer.
Find values of m so that the function y xm is a solution of the given differential equation. x^2y''-7xy' 15y=0
If [tex]y=x^m[/tex] is a solution to the ODE
[tex]x^2 y'' - 7xy' + 15y = 0[/tex]
then substituting [tex]y[/tex] and its derivatives
[tex]y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}[/tex]
gives
[tex]m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0[/tex]
[tex]m(m-1)x^{m} - 7mx^{m} + 15x^m = 0[/tex]
[tex](m(m-1) - 7m + 15)x^{m} = 0[/tex]
We ignore the trivial case of [tex]y=x^m=0[/tex]. Solve for [tex]m[/tex].
[tex]m(m-1) - 7m + 15 = 0[/tex]
[tex]m^2 - 8m + 15 = 0[/tex]
[tex](m - 3) (m - 5) = 0[/tex]
[tex]\implies \boxed{m=3} \text{ or } \boxed{m=5}[/tex]
Your bank offers you a 36-month, 3 pr car loan for a $50000 new mercedes slk300 roadster. what will your monthly payment be?
The monthly payment will be $1454.06048
You can calculate the Car Loan EMI Amount with the help of the mathematical formula: EMI Amount = [P x R x (1+R)^N]/[(1+R)^N-1] , where P, R, and N are the variables. This also means that the EMI value will change, each time you change any of the three variables. Let’s discuss these three variables in detail.
‘P’ stands for the Principal Amount. It is the original loan amount given to you by the bank on which the interest will be calculated.
‘R’ stands for the Rate of Interest set by the bank.
N is the number of years given for the repayment of the loan. As you must pay the EMIs each month, the duration is calculated in the number of months.
Here , P=$50000,R=3/12/100=0.0025,N=36 Months.
EMI=[50000 x 0.0025 x (1+0.0025)^36]/[(1+0.0025)^36-1]
= $1454.06048
To know more about "Principal amount"
Refer this link:
https://brainly.com/question/25720319
#SPJ4
Last week, 3/4 of the students in Mr. Zanker's class went on a field trip. 5/8 of the
students in Mr. Haynes's class went. What is the average fraction of students
in the two classes who went on the field trip?
A. 2/3
B. 11/16
C. 15/32
D. 15/16
The average fraction of students in the two classes who went on the field trip is 11/16
What is the average fraction of students in the two classes who went on the field trip?The given parameters are:
Class 1 = 3/4
Class 2 = 5/8
The average is calculated as
Average = 1/2 * (Class 1 + Class 2)
So, we have
Average = 1/2 * (3/4 + 5/8)
Evaluate
Average = 11/16
Hence, the average fraction of students in the two classes who went on the field trip is 11/16
Read more about average at:
https://brainly.com/question/20118982
#SPJ1
Matt and Ryan are playing an exciting round of Rock Paper Scissors: The Collectible Card Game. Matt is convinced that Rock can beat anything, so his deck consists only of 8 Rock cards. Ryan's deck consists of 5 Paper cards and 3 Scissors cards. In the game, Matt randomly selects 3 cards from his deck and places them on the table. Ryan then randomly selects 3 cards and places one on each of Matt's cards. If Rock beats Scissors, Scissors beats Paper, and Paper beats Rock, then what's the probability that Ryan beats Matt in a landslide by choosing 3 Paper cards in a row?
Using the hypergeometric distribution, there is a 0.1786 = 17.86% probability that Ryan beats Matt in a landslide by choosing 3 Paper cards in a row.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, we have that Ryan will win if he takes 3 Paper cards from a set of 8(5 paper and 3 scissors), hence the parameters are given as follows:
N = 8, k = 5, n = 3, x = 3.
Hence the probability is given by:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,8,3,5) = \frac{C_{5,3}C_{3,0}}{C_{8,3}} = 0.1786[/tex]
0.1786 = 17.86% probability that Ryan beats Matt in a landslide by choosing 3 Paper cards in a row.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
#SPJ1
help please
15 points
1) d - c is calculated as; -4
2) Simplifying ³/₄ - ²/₅ gives; 7/20
What is the solution to basic arithmetic?
1) We are given;
c = 12 and d = 8. Thus;
d - c is calculated as;
8 - 12 = -4
2) We want to simplify ³/₄ - ²/₅
Factoring out 1/20 gives;
1/20(15 - 8) = 7/20
3) Number of pencils purchased = 888 pencils
Number of pencils in a box = 12
Thus;
Number of boxes purchased = 888/12 = 74 boxes
4) An integer is a whole number (not a fractional number) that can be positive, negative, or zero. The only one that is not an integer here is; 20/6
5) √64 = 8
6) (30 - 4 * 2)/(2 * 2²)
= (30 - 8)/8
= 22/8 = 11/4
7) 11 = x + 19
x = 11 - 19
x = -8
Read more about Basic Arithmetic at; https://brainly.com/question/20628271
#SPJ1
n+2.1 - 12
what is it
Adam, Craig and Gary play hockey. Adam has scored twice as many goals as Craig. Gary scores 7 more goals than Craig. Altogether they score 51 goals. How many more goals did Adam score than Gary?
1/19 7/4 -4/7 in order from least to greatest
Answer:
-4/7, 1/19, 7/4
Step-by-step explanation:
-4/7 is less then zero, and the only negative number so it is first
1/19 is the second lowest
7/4 is the highest because it is the only one that is greater then 1. (simplified, 7/4= 1 3/4)
Find the quotient.
77/−11=
64÷32=
48÷ −6=
−56÷ −8=
110/10=
Answer:
fsfdsesdfsesd 'jp
Step-by-step explanation:
efsdsfefsggsesds
A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not
replacing it, and then choosing a red marble?
O
16
O
12
O
11
Answer:
The answer will be
[tex] \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} [/tex]
Or 12%
pls help with this question ASAP
What equations do u insert in between these numbers to get the answer
a.5 8 3 9 =50
b.12 6 2 10=14
c.4 5 6 10=24
d.7 4 6 9 7= 16
e.4 9 6 2 =52
f.45 5 9 3 7=102
hduodoydiyd9ydiydoyeykdoyx95eeykyei6djj
Step-by-step explanation:
a) 5
Solve the following inequality. Graph the solution.
8a-30> 66
What is the solution? Select the correct choice below and fill in the answer box within your choice.
(Type an integer or a decimal.)
A. az
B. as
OC. a>
D. a<
The solution to the given Inequality is a > 12 and the graph is as attached.
What is the Solution to the Inequality?
We are given the Inequality as;
8a - 30 > 66
Now, use addition property of equality to add 30 to both sides to get;
8a - 30 + 30 > 66 + 30
8a > 96
Now, use division property of equality to divide both sides by 8 to get;
8a/8 > 96/8
a > 12
The graph of this is as attached.
Read more about Inequality Solution at; https://brainly.com/question/25275758
#SPJ1