if (2x^3 + ax^2+bx-2) when divided by (2x-3) and (x+3) leaves remainder 7 and -20 respectively, find the values of a and b
Answers
your answer
thank you
9514 1404 393
Answer:
a = 3b = -3Step-by-step explanation:
The remainder from division by (2x-3) is the same as the value of the function when that divisor is zero—at x = 3/2.
((2(3/2) +a)(3/2) +b)(3/2) -2 = 7
((3 +a)(3/2) +b)(3/2) = 9 . . . . add 2
9/2 +3/2a + b = 6 . . . . . . . . multiply by 2/3
3/2a +b = 3/2 . . . . . . . . . . . subtract 9/2
3a +2b = 3 . . . . . . . . . . . . . multiply by 2 [eq1]
The remainder from division by (x+3) is the same as the value of the function for x = -3.
((2(-3) +a)(-3) +b)(-3) -2 = -20
(-6 +a)(-3) +b = 6 . . . . . . add 2 and divide by -3
18 -3a +b = 6 . . . . . . . . . eliminate parentheses
3a -b = 12 . . . . . . . . . . . subtract 18, multiply by -1 [eq2]
Subtracting the [eq2] from [eq1], we have ...
(3a +2b) -(3a -b) = (3) - (12)
3b = -9 . . . . . simplify
b = -3 . . . . . . divide by 3
From [eq2], ...
3a -(-3) = 12 . . . . substitute for b
3a = 9 . . . . . . . . subtract 3
a = 3 . . . . . . . . . divide by 3
The values of 'a' and 'b' are 3 and -3, respectively.
Related Questions
how many 1/2 cups are needed to fill the gap in this prism
A. 2
B. 4
C. 6
D. 8
have a great day!♡
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Answer:
I don't know what prism. once you see this put it in the description of this
Step-by-step explanation:
6152÷100 simplified +into mixed number?
Answers
Answer:
61.52
Step-by-step explanation:
Whenever dividing by 100 move the decimal point 2 times to the left since there are 2 zeros and you're dividing.
Answer:
61 13/25.
Step-by-step explanation:
6152/100
= 61.52
= 61 52/100
= 61 13/25.
35% of what number is 35
Answers
Answer:
Answer: 100
Step-by-step explanation:
kelly has a bag containing white and yellow marbles
Answers
... and then?
You didn't eve give a question
Answer:
cool
Step-by-step explanation:
i dont know what the question is
if the corresponding sides of 2 quadrilaterals are propotional, then the 2 quadrilaterals must be similar
Answers
Answer:
False
Step-by-step explanation:
A square and a parallelogram could have proportional sides but the angles would not be the same
A package of colored paper contains 20 pieces of yellow paper. This represents 25% of the total pieces of colored paper in the package. How many total pieces of colored paper are in the package?
Answers
Answer: 80
Step-by-step explanation:
80x 0.25=20
What is the volume of this triangular prism?
A. 576 ft3
B. 288 ft3
C. 34 ft3
D. 29 ft3
Answers
Answer:
576
Step-by-step explanation:
4x16=64
64x9=576
The temperature in degrees Fahrenheit was recorded every two hours starting at midnight on the first day of summer. The data is show in the table.
Which type of graph would best display the change in the temperatures throughout the day?
bar graph
line graph
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Answers
Hope this helps :D
(please answer quick its pretty easy)
Divide.
−36÷(−4)
Answers
Answer 9
Hope this helps!!
Answer: 9
Steps:
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}[/tex]
[tex]=\frac{36}{4}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{36}{4}[/tex]
=9
Hope This Helps!
pls help, 'll mark the brainliest. SOS
Answers
Answer:
Which one do you need the answer for
Step-by-step explanation:
Pls help these are due TODAY!!!!
Answers
Answer:
10
Step-by-step explanation:
the two triangles formed from c are similar which means the sides are proportional
the proportion of one length of a side of a triangle to a similar side of the other triangle is the same as another side to its corresponding side of the other triangle. god im bad explaining stuff
anyway 2 is to 8 what 2.5 is to length BC. 2/8 = 2.5/x
-crossmultiplyyy
2*x = 2.5*8
2x = 20
2x/2 = 20/2
x = 10
The MEAN is _______________ a value in the data set
A) sometimes
B) always
C) never
Answers
Answer:
B
Step-by-step explanation:
help please with math
Answers
Answer:
If they want irregular fractions its
1= 14/4 . 2= 11/2 3= 14/8
4= 21/4 . 5= 27/6 . 6= 125/13
7= 61/9 . 8= 69/9 . 9= 84/8
If they just want the few simplified then
1= 3 1/2
3= 1 3/4
5= 4 1/2
8= 7 2/3
9= 10 1/2
Step-by-step explanation:
If the angles 2xº and 4yº
are
complementary, find the value of x + 2y.
Answers
Answer:
Solution given:
the angles 2xº and 4yºare complementary
so
2x+4y=90°
dividing both side by 2we get
x+2y=45°
the value of x + 2y is 45°.
rew wants to build a square sandbox with an area of 324 square feet. What is the total length of wood Drew needs to make the sides of the sandbox?
Answers
Answer: 44
Step-by-step explanation:
Bertha Devys had the oil changed in her company car. She had a $3.00-off coupon from the Grease Monkey oil change service. The regular
price of an oil change is $29.99. What is the final price?
Answers
Answer:
your answer is $26.99
Step-by-step explanation:
seven hamburgers and four sodas cost $27.35. Four hamburgers and five sodas cost $18.75
I need to find the equation of each sentence.
WILL MARK BRAINLIEST (or however you spell it)
Answers
Answer:
equations:
7x + 4y = 27.35
4x + 5y = 18.75
Step-by-step explanation:
x = burgers
y = sodas
---------------------------------
7x + 4y = 27.35
4x + 5y = 18.75
(x2–5x+6)(x-1) dx
Sol
x-2
Answers
Step-by-step explanation:
[tex]y =( {x}^{2} - 5x + 6)(x - 1) \\ y =( {x}^{3} - 5 {x}^{2} + 6x - {x}^{2} + 5x - 6) \\ \frac{dy}{dx} = 3 {x}^{2} - 12x + 11[/tex]
HELP ME PLEASE HURRYYY
Answers
Find the volume of this regular solid. 5 yd 4 yd 8 yd
Answers
Answer:
160 yd
Step-by-step explanation:
Volume = L * W * H
V= 5 * 4 * 8
V= 160 yd
The length of a table is 2 meters 50 centimeters. What is the length of the table in millimeters?
Answers
Answer:
A
Step-by-step explanation:
2 meters=2000millimeters
50 centimeters=500 millimeters
7. Gloria took out a loan for $8000. If she was given the loan with a 4.5%
interest rate compounded monthly for 5 years. How much interest did she
have to pay over the 5 years? Round to the nearest whole number?
Answers
4+6=3
4.5=3
77.35.52.=5
How many free throws could you make out of 20
Answers
Awnser :
Ten
Explanation :
In a relaxed practice setting with no pressure, the average player should be able to make at least ten in a row. But free throws typically come in pressure situations, so managing the pressure is as important as practicing form.
B
Diagram NOT
accurately drawn
2
489
D
E
A, Band D are points on a circle, centre O.
CDE is a tangent to the circle.
Angle ADO = 48°
Work out the size of angle ABD.
(4 marks)
please help asap ill give brainliest
Answers
Answer:
∠ ABD = 42°
Step-by-step explanation:
∠ ODC = 90° ( angle between tangent and radius )
∠ ADC = 90° - 48° = 42°
The angle between a tangent and a chord is equal to the angle in the alternate segment, that is
∠ ABD = ∠ ADC = 42°
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
[tex]y=-\frac{1}{4} x-6[/tex]
Step-by-step explanation:
The slope-intercept form is [tex]y=mx+c[/tex], where m is the slope of the line and c is where the line crosses the [tex]y[/tex]-axis.
To calculate [tex]m[/tex] we can use the formula [tex]m = \frac{dy}{dx}[/tex] where [tex]dy[/tex] is the difference in [tex]y[/tex] between two points and [tex]dx[/tex] is the difference between [tex]x[/tex].
Information we can get from the graph given: [tex]c=-6[/tex]. Since [tex]c[/tex] is the point at which the line crosses the [tex]y[/tex]-axis.
To find [tex]m[/tex] let's get two points from the graph.
Point 1: [tex](4,-7)[/tex]
Point 2: [tex](8,-8)[/tex]
Now use the equation [tex]m = \frac{dy}{dx}[/tex].
[tex]m = \frac{-7 - (-8)}{4-8} = -\frac{1}{4}[/tex].
Now we have [tex]m[/tex] and [tex]c[/tex], let's put them back into the general equation.
[tex]y=-\frac{1}{4} x-6[/tex]
Which expressions are equivalent to Negative 9 (two-thirds x + 1)
Answers
Answer:2-3x+1(-9)
Step-by-step explanation:
-9(2-3x+1) can also be written as 2-3x+1(-9)
Which fraction is equivalent to —(7/8)?
Answers
The answer should be -14/16
Harper is getting a new rug in her bedroom. Her bedroom is in the shape of a rectangle with a length of 9 feet and a width of 14 feet. If the rug cost $1.75 per square foot, how much will it cost to purchase the rug?
Answers
Answer:
D) 220.50
Step-by-step explanation:
9x14 = (9x9)+(9x5) =126 126 x 1.75 (.75x126) + 126 = 220.50
AKA: 9x14 = 126 126 x 1.75 = 220.50
What equation is being modeled below? *please help* fast*
Answers
Answer:
y = -3x + 21
Step-by-step explanation:
Answer:
4+6-3=7 I think
Step-by-step explanation:
1 7/10 - 1 1/2
it has to be a fraction and no links
Answers
17/10 - 3/2
Now we have improper fractions; fractions that have a numerator larger than the denominator
Next we will find the common denominator using LCM but what I personally do is I multiply both sides by the opposite fraction’s denominator, like this:
17 x 2 _ 3 x 10 —-> 34 - 30
10 x 2 2 x 10 20 - 20
Now we have 34/20 - 30/20 and with the help of collecting the common denominator, all we have to do now is subtract 30 from 34, and our answer will be 4/20
**when we have the same number as our denominator we only add or subtract the numerator, depending on what question your teacher asks you to answer
*** sum = addition/adding
difference = subtraction/subtracting/taking away
At first when you subtract you will get 4/20 however answers should always be in reduce /simplified do answer is
1/5