divide 26x^4 - 13x^3 - 74x^2 - 46x - 24 by 2x^2 - 3x -5 and verify the result by division algorithm
Answer:
Step-by-step explanation:
Using long division:
13x^2 + 13x + 15 <------------Quotient
_________________________
2x^2 - 3x - 5 ) 26x^4 - 13x^3 - 74x^2 - 46x - 24
26x^4 - 39x^3 - 65x^2
26x^3 - 9x^2 - 46x
26x^3 - 39x^2 - 65x
30x^2 + 19x - 24
30x^2 - 45x - 75
64x + 51 <---- Remainder. Division algorithm:
a = bq + r
Here a = the original expression , b = the divisor (2x^2 - 3x - 5), q is the quotient and r = the remainder,
26x^4 - 13x^3 - 74x^2 - 46x - 24 = (2x^2 - 3x - 5)(13x^2 + 13x + 15) + 64x + 51
= 2x^2(13x^2 + 13x + 15) - 3x(13x^2 + 13x + 15) - 5(13x^2 + 13x + 15) + 64x + 51
= 26x^4 + 26x^3 + 30x^2 - 39x^3 - 39x^2 - 45x - 65x^2 - 65x - 75+64x+51
= 25x^4 - 13x^3 - 74x^2 - 46x - 24 which is the same as the above.
3a+8+2ax≥3ax-4a what is a
Answer:
A=3 I'm 95% sure but if you're not sure then use PEMDAS
P-parentheses
E-exponets
M-multiply
D-divide
A-add
S-subtract
A 35-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 21 feet from the base of the building. How far above the ground is the point where the ladder touches the building?
Answer:
Step-by-step explanation:
Help me please and show work and this is geometry
Answer:
-433
Step-by-step explanation:
Step 1: Define
-5(4 + 9s) - 7(4q - 6)
s = 7
q = 5
Step 2: Simplify expression
Distribute: -20 - 45s - 28q + 42
Combine like terms: -45s - 28q + 22
Step 3: Substitute
-45(7) - 28(5) + 22
Step 4: Evaluate
-315 - 140 + 22
-445 + 22
-433
olve. 4 + x 7 = 2 A) -14 B) 10 C) 12 D) 42
Answer:
-14 I believe
Step-by-step explanation:
Answer:
Its A.
Step-by-step explanation:
A line passing through the points (6,-2) and (-2,4). Complete the work shown
Answer:
2.5
Step-by-step explanation:
How many cups of flour are needed to make 3 dozens of dinner rolls
Answer: 1/15
Step-by-step explanation: A. If 1/3 cup makes 5 rolls, you need to know how many cups make one. (1/3)/5 = 1/15 Take the number of cups for one roll and multiply it by 3. 1/15 x 3 Final Answer = 3/15
B. Take the number of cups you have divided by 1/3 (since you know how many roles this makes) (5 2/3) / (1/3) Final Answer = 17
C. Well, we already solved for this one in A, didn't we? Final Answer = 1/15
Estimate the answers after rounding to the indicated place value.
56.1: 6.6 (ones)
A 9
B10
C8
D7
E6
100 x 0.64
Please help sorry I keep asking questions I’m doing a test and it’s kinda hard
100 x 0.64 = 64.
All you have to do is multiply the numbers as if there wasn’t a decimal.
Then you add a decimal after 2 numbers.
.64 has a decimal after 2 numbers so your answer would have a decimal after 2 numbers also.
So when you get 6400 you out a decimal after 00.
That gives you 64
What is the value expression for |-8|
Answer:
8
Step-by-step explanation:
At a carnival 7 out of 10 pepole order hotdogs if there is 90 pepole at the carnival how many of them did not order a hotdog
Answer:
20 people did not order hotdogs
Step-by-step explanation:
if there is 90 people and 7 must represent 70 / 90
If BC = 5x − 15, CD = 4x, and BD = 8x + 4, what is BD? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you please type it in a step by step.
Answer:
156
Step-by-step explanation:
CD+BC=BD
[tex](5x - 15) + 4x = 9x - 15 = 8x + 4 \\ x = 19 \\ bd = 8x + 4 = (8 \times 19) + 4 = 156[/tex]
Suppose we want a 99% confidence interval for the average amount spent on books by freshmen in their first year at college. The amount spent has a normal distribution with standard deviation $34. (a) How large should the sample be to guarantee the margin of error will be no more than $3?(b) If we wanted a smaller margin of error, we would need a sample. (Enter: ''LARGER'', ''SMALLER'' or ''SAME SIZE'', without the quotes.)
Answer:
a) 855
b) We would need a Larger sample.
Step-by-step explanation:
(a) How large should the sample be to guarantee the margin of error will be no more than $3?
The formula for Margin of Error = z × Standard deviation/√sample size
z = z score of 99% confidence interval = 2.58
Standard deviation = $34
Sample size = n = unknown
Margin of Error = $3
√n = z × Standard deviation/Margin of Error
Square both sides
n = (z × standard deviation/Margin of Error)²
n =( 2.58 ×34/ 3)²
n = (29.24)²
n = 854.9776
Approximately, the size of the sample be to guarantee the margin of error will be no more than $3 is 855
(b) If we wanted a smaller margin of error, we would need a sample. (Enter: ''LARGER'', ''SMALLER'' or ''SAME SIZE'', without the quotes.)
We would need a Larger sample.
This is because, the larger the sample, the smaller the margin of Emerror and the smaller the sample, the larger the margin of error. Therefore, for the question b, we would be needing a larger sample.
A 130 gallon tank initially contains 10 lbs salt dissolved in 60 gallons of water. Brine containing 1 lb salt per gallon begins to flow into the tank at the rate of 3 gal/min and the well-mixed solution is drawn off at the rate of 1 gal/min. How much salt is in the tank when it is about to overflow
Answer:
80 lb of salt
Step-by-step explanation:
Let us assume the water flows into the rank for x minutes.
There is an initial of 60 gallons of water in the tank and water flows in at 3 gal/min. In x minute, the amount of water in the tank = 60 + 3x
Water flows out at 1 gal/min, therefore in x minute the amount of water in the tank = 60 + 3x - x = 60 + 2x
The tank begins to overflow when it is full (has reached 130 gallons). Therefore:
130 = 60 + 2x
2x = 130 - 60
2x = 70
x = 35 minutes.
In 35 minutes the tank would start to overflow.
1 lb salt per gallon flows into the tank at 3 gal/min, in 35 min the amount of salt that entered the tank = 3 gal/min × 35 min × 1 lb/gal = 105 lb
1 lb salt per gallon flows out of the tank at 1 gal/min, in 35 min the amount of salt that flow out of the tank = 1 gal/min × 35 min × 1 lb/gal = 35 lb
Initially there is 10 lb of salt dissloved into 60 gallons of water.
Therefore the amount of salt is in the tank when it is about to overflow = 10 + 105 - 35 = 80 lb of salt.
Is 0 a real, imaginary, or complex number?
Answer: 0 is a imaginary number
Step-by-step explanation:
Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15
Answer:
45,42,126
multiply by 3
The next three terms in the sequence are : 45, 42 and 126
Given the sequence 2, 6, 3, 9, 6, 18, 15
Rule :
Multiply the first term by 3 to obtain the second term Subtract 3 from the 2nd term to obtain the third term The third term is multiplied by 3 to obtain the fourth term Subtract 3 from the fourth term to obtain the fifth term. And the process continues....Starting with the first term ; 2 ;
2nd term = 2 × 3 = 6
3rd term = 6 - 3 = 3
4th term = 3 × 3 = 9
5th term = 9 - 3 = 6
6th term = 6× 3 = 18
7th term = 18 - 3 = 15
8th term = 15 × 3 = 45
9th term = 45 - 3 = 42
10th term = 42 × 3 = 126
Hence, the next three terms of the sequence are : 45, 42 and 126
Learn more : https://brainly.com/question/18109692
Which of the following correctly uses absolute value to show the distance between -50 and 12? A: |-50 - 12| = |-62| = -62 units B: |-50 + 12| = |-38| = 38 units C: |-50 + 12| = |-38| = -38 units D: |-50 - 12| = |-62| = 62 units
A plane flew to its destination 300 miles away. With a tail wind, the flight took 5/6 of an hour. The return
trip, with a head wind, took 1 hour. Find the speed of the wind and the speed of the plane.
Thank youu
Answer:A plane flew to its destination 300 miles away. With a tail wind, the flight took 5/6 of an hour. The return trip, with a head wind, took 1 hour....
Step-by-step explanation:
Write the name of the
period that has the
digits 913.
What kind of number is 92 and why? if you know the others that'd be great!!
Answer:
hello!
Step-by-step explanation:
The number 92 is a rational number if 92 can be expressed as a ratio, as in RATIOnal. A quotient is the result you get when you divide one number by another number. For 92 to be a rational number, the quotient of two integers must equal 92.
what kind of number is -18 and explain why it is
Answer:
Step-by-step explanation:
-18 is a integer because it has negative sign
☽------------❀-------------☾
Hi there!
~
-18 is an integer number because of the " - " sign. I hope the picture will explain why -18 is an integer number!
❀Hope this helped you!❀
☽------------❀-------------☾
3. [W] Consider the following data from NASA about the density of the sun. • When you are 10% of the way out from the center of the sun (use x = 0.1), the density is approximately 82.9619 g/cm3 . • When you are 20% of the way out of the sun, the density is approximately 38.7504 g/cm3 . • When you are 70% of the way out of the sun, the density is approximately 1.7819 g/cm3 . • When you are 80% of the way out of the sun, the density is approximately 1.9824 g/cm3 . • When you are 90% of the way out of the sun, the density is approximately 0.7859 g/cm3 . We want to use this data to find a quartic (4th degree) interpolating polynomial for the density of the sun throughout. y = Ax4 + Bx3 + Cx2 + Dx + E (a) Set up this problem as a system of linear equations. (b) Find the quartic polynomial that goes through these data points. (c) Use this polynomial to approximate the density 50% of the way out of the sun.
Answer:
a)
A(0.1)^4 + B(0.1)^3 + C(0.1)^2 + D(0.1) + E = 82.9619 ----------1
A(0.2)^4 + B(0.2)^3 + C(0.2)^2 + D(0.2) + E = 38.7504 -------2
A(0.7)^4 + B(0.7)^3 + C(0.7)^2 + D(0.7) + E = 1.7819 ----------3
A(0.8)^4 + B(0.8)^3 + C(0.8)^2 + D(0.8) + E = 1.9824 ----------4
A(0.9)^4 + B(0.9)^3 + C(0.9)^2 + D(0.9) + E = 0.7859 ----------5
b) y = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155
c) 0.1875
Step-by-step explanation:
a)
Let y = Ax^4 + Bx^3 + Cx^2 + Dx + E
Setting up the problem as a system of linear equations
when x=(10%)=0.1, y = 82.9619
therefore
A(0.1)^4 + B(0.1)^3 + C(0.1)^2 + D(0.1) + E = 82.9619 ----------1
when x=(20%)=0.2, y = 38.7504
A(0.2)^4 + B(0.2)^3 + C(0.2)^2 + D(0.2) + E = 38.7504 -------2
when x=(70%)=0.7, y = 1.7819
A(0.7)^4 + B(0.7)^3 + C(0.7)^2 + D(0.7) + E = 1.7819 ----------3
when x=(80%)=0.8, y = 1.9824
A(0.8)^4 + B(0.8)^3 + C(0.8)^2 + D(0.8) + E = 1.9824 ----------4
when x=(90%)=0.9, y = 0.7859
A(0.9)^4 + B(0.9)^3 + C(0.9)^2 + D(0.9) + E = 0.7859 ----------5
b)
Find the quartic polynomial that goes through these data points
Now to find the values ( A,B,C,D,E)
[MATRIX]
║A║ ║ (0.1)^4 (0.1)^3 (0.1)^2 (0.1) 1 ║^-1 ║ 82.9619 ║
║B║ ║ (0.2)^4 (0.2)^3 (0.2)^2 (0.2) 1 ║ ║ 38.7504 ║
║C║ = ║ (0.7)^4 (0.7)^3 (0.7)^2 (0.7) 1 ║ ║ 1.7819 ║
║D║ ║ (0.8)^4 (0.8)^3 (0.8)^2 (0.8) 1 ║ ║ 1.9824 ║
║E║ ║ (0.9)^4 (0.9)^3 (0.9)^2 (0.9) 1 ║ ║ 0.7859 ║
║A║ ║ 29.7619 -47.619 166.667 -238.095 89.2857 ║ ║ 82.9619║
║B║ ║ -77.381 119.048 -333.333 452.381 -160.714 ║ ║ 38.7504║
║C║ = ║ 71.131 -102.381 208.333 -269.048 91.9643 ║ ║ 1.7819 ║
║D║ ║ -26.369 33.0952 -41.6667 52.619 -17.6786 ║ ║ 1.9824 ║
║E║ ║ 3.00 -2.4 -2.4 -3.00 -1.00 ║ ║ 0.7859 ║
║A║ ║ 519 ║
║B║ ║ -1630║
║C║ = ║ 1844 ║ , y = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155
║D║ ║ -889 ║
║E║ ║ 155 ║
c)
approximate the density 50% of the way out of the sun
so at 50% (0.5) x=0.5
we substitute
y = 519(0.5)^4 - 1630(0.5)^3 + 1844(0.5)^2 - 889(0.5) + 155
= 0.1875
what is the formular for 1+4+16+64+256
Answer:
341
Step-by-step explanation:
1+4=5
5+16=21
21+64=85
85+256=341
Service Costs are part of maintaining your car. It's that time again. You will need an oil change costing $45, four new tires costing $89.95 each, and 2 new windshield wipers costing $7.95 each. What is the total cost of your service cost?
Answer:
420.7
Step-by-step explanation:
Write Three and eight thousandths in standard form? What is it
Thousandths is the 3rd decimal place
The answer is 3.008
Andy is hanging wallpaper
Answer:
Mandy is painting the wall
1
Tamara spun the arrow on a spinner 50 times. The number of times the arrow landed on each colored section of the spinner is shown in the table.
Section
Red
Blue
Orange
Yellow
Number of Times
Arrow Landed on
23
8
10
9
Based on the results in the table, what fraction of the area of the spinner is most likely represented by the Red section?
А.
SO
O B. 3
Ос. 4
O D. 1 / 4
Answer:
Area covered by red target = 23/50
Step-by-step explanation:
Given:
Total number of shot = 50
Section Number of shots
Red 23
Blue 8
Orange 10
Yellow 9
Find:
Area covered by red target
Computation:
Area covered by red target = 23/50
Area covered by red target = 1/2 of total area
Answer:
The fraction of the area of the Red section is [tex]\dfrac{23}{50}[/tex]
Step-by-step explanation:
Given that,
The number of times the arrow landed on each colored section of the spinner is shown in the table.
Tamara spun the arrow on a spinner 50 times.
Section = Red, Blue, Orange, Yellow
Number of times arrow landed = 23, 8, 10, 9
We need to calculate the fraction of the area of the Red section
Using formula of fraction of area
[tex]fraction\ of\ area=\dfrac{Red\ section}{total\ section}[/tex]
Put the value into the formula
[tex]fraction\ of\ area=\dfrac{23}{50}[/tex]
Hence, The fraction of the area of the Red section is [tex]\dfrac{23}{50}[/tex]
1/2x^2+3x+7 find axis of symetry
Answer:
x=-3
Step-by-step explanation:
Help ASAP
Find the Distance between (5,2) and (-3,-4)
Answer:
[tex]d = 10[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in your 2 coordinates into the formula to find distance d:
[tex]d=\sqrt{(-3-5)^2+(-4-2)^2}[/tex]
[tex]d=\sqrt{(-8)^2+(-6)^2}[/tex]
[tex]d=\sqrt{64+36}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]d = 10[/tex]
I need help on this question 109^41/109^94
Answer:
[tex]\frac{1}{109^{53}}[/tex]
Step-by-step explanation:
[tex]\frac{109^{41}}{109^{94}}=109^{41-94}=109^{-53}=\frac{1}{109^{53}}[/tex]