Answer:
[tex]A = 2[/tex]
[tex]B = -1[/tex]
[tex]C = -9[/tex]
Step-by-step explanation:
Given
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
Required
Find A, B and C
Rearrange the expression
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C[/tex]
To do this, we simply compare the expressions on both sides of the equation.
So, we have:
[tex]Ax\² = 2x\²[/tex] --- (1)
[tex]8Ax + Bx = 15x[/tex] --- (2)
[tex]16A + 4B + C = 19[/tex] --- (3)
Divide both sides by x² in (1)
[tex]Ax\² = 2x\²[/tex]
[tex]A = 2[/tex]
Divide both sides by x in (2)
[tex]8Ax + Bx = 15x[/tex]
[tex]8A + B = 15[/tex]
Substitute 2 for A.
[tex]8*2 + B = 15[/tex]
[tex]16+ B = 15[/tex]
Make B the subject
[tex]B = 15 - 16[/tex]
[tex]B = -1[/tex]
Substitute 2 for A and -1 for B in (3)
[tex]16A + 4B + C = 19[/tex]
[tex]16*2 + 4*-1 + C = 19[/tex]
[tex]32 - 4 + C = 19[/tex]
[tex]28 + C = 19[/tex]
Make C the subject
[tex]C = 19 - 28[/tex]
[tex]C = -9[/tex]
Answer:
it D
Step-by-step explanation:
I just used elimination like a small brain
like so
when a = 1, b = 0, c = 3, d = -3
x^3 + 8x – 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D
Solve the system of linear equations below, using substitution method.
8x+9y=368x+9y=36
3x+4y=163x+4y=16
Answer:
[tex]x = 0[/tex]
[tex]y=4[/tex]
Step-by-step explanation:
Given
[tex]8x + 9y = 36[/tex]
[tex]3x + 4y = 16[/tex]
Required
Solve using substitution method
Make x the subject in [tex]3x + 4y = 16[/tex]
[tex]3x = 16 - 4y[/tex]
Divide through by 3
[tex]x = \frac{1}{3}(16 - 4y)[/tex]
Substitute [tex]\frac{1}{3}(16 - 4y)[/tex] for x in [tex]8x + 9y = 36[/tex]
[tex]8*\frac{1}{3}(16 - 4y) + 9y = 36[/tex]
[tex]\frac{8}{3}(16 - 4y) + 9y = 36[/tex]
Open bracket
[tex]\frac{8}{3}*16 - \frac{8}{3}*4y + 9y = 36[/tex]
[tex]\frac{8*16}{3} - \frac{8*4y}{3} + 9y = 36[/tex]
Multiply through by 3
[tex]3 * \frac{8*16}{3} - 3 *\frac{8*4y}{3} +3* 9y = 36*3[/tex]
[tex]8*16 - 8*4y +3* 9y = 36*3[/tex]
[tex]128- 32y +27y = 108[/tex]
[tex]128-5y = 108[/tex]
Collect Like Terms
[tex]-5y = 108-128[/tex]
[tex]-5y = -20[/tex]
Make y the subject
[tex]y = \frac{-20}{-5}[/tex]
[tex]y=4[/tex]
Substitute 4 for y in [tex]x = \frac{1}{3}(16 - 4y)[/tex]
[tex]x = \frac{1}{3}(16 - 4*4)[/tex]
[tex]x = \frac{1}{3}(16 - 16)[/tex]
[tex]x = \frac{1}{3}(0)[/tex]
[tex]x = 0[/tex]
Find the third term of a proportional if the first, second and fourth terms are 24, 36, 126
Answer:
The third term of a proportional will be: 84
Step-by-step explanation:
We know that if a, b, c and d are in proportion, then:
[tex]\:\:a\:\times \:d\:=\:b\:\times \:c[/tex]
In our case, we are given the first, second, and fourth terms are [tex]24, 36, 126[/tex]
[tex]a = 24[/tex]
[tex]b = 36[/tex]
[tex]d = 126[/tex]
and we have to determine the third term 'c'.
as we know that if a, b, c, and d are in proportion, then:
[tex]\:\:a\:\times \:d\:=\:b\:\times \:c[/tex]
Thus,
substituting a = 24, b = 36, d = 126 to determine
[tex]24\:\times \:126\:=\:36\:\times \:c[/tex]
[tex]c=\frac{24\:\times \:\:126}{36}[/tex]
[tex]c=\frac{3024}{36}[/tex]
[tex]c = 84[/tex]
Thus, the third term of a proportional will be: 84
The ratio of a model car's dimensions to the actual car's dimensions is 1/52. The model has a length of 3 in.
What is the length of the actual car? Enter your answer in feet.
The actual car is ___feet long.
Answer:
13 feet
Step-by-step explanation:
3 inches times 52 equals 156.
156 divided by 12 equals 13.
The length of the actual car if The ratio of the model car's dimensions to the actual car's dimensions is 1/52, The model has a length of 3 inches, is 13 feet.
What is the scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.
The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).
Given:
The ratio of a model car's dimensions to the actual car's dimensions is 1/52, The model has a length of 3 inches,
Calculate the actual length of the car as shown below,
Models car length / The actual length of the car = 1 / 52
3 / The actual length of the car = 1 / 52
The actual length of the car = 3 × 52
The actual length of the car = 156 inches
The actual length of the car = 156 × 0.0833 feet (1 inch = 0.0833)
The actual length of the car = 13 feet
Thus, the actual car is 13 feet long.
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Find the a10 for the sequence a n =(3)(2)^ n
HELP EASY IF YOU KNOW SPANISH
Answer:
14 is "Yo tengo"
15 is Qué tienes en tu mochila?
a. How many 1/3s are in 2 2/3?
Answer:
1 2/3 = (1•3+2)/3 = 5/3. Therefore, 5/3 ÷ 1/3. = 5.
Step-by-step explanation:
So the answer is 5.
a light bulb consumes 6300 watt hours in 3 days and 12 hours. how many watt hours does it consume per day
Answer:
1800 watt hours
Step-by-step explanation:
6300 watt hours in 3 days and 12 hours
3 x 24 = 72 3 days worthof hours
72 + 12 = 84 total hours
6300/84 = 75 watt hours per hour
75 x 24 = 1800 watt hours per day
7515.904 rounded to nearest tenth
Answer:
7515.9
Step-by-step explanation:
Tenth is basically like 1 decimal point.
0-4 round dowm 5-9 round up
Which of the following are accurate factors of 4x2 + 5.0 – 21 when multiplied together? Select the two correct answers.
(2 points)
(40 - 7)
0 (x + 2)
(52 -3)
0 (+3)
Answer:
First and last
Step-by-step explanation:
(4x - 7) (x + 3)
FOIL
4x^2 + 5x - 21
3x^2yz^3-9x^3y^2z^2+12x^2y^3z^2
3×2=692047 82837=284749×2484r133.e9274
what is the equation of the function that is graphed as line a?
Answer:
B
Step-by-step explanation:
We see that the line intersects the y-axis at -1. As a result, we need to choose an equation with -1, either B or C. We see that the different is the slope. For choice B, the slope is [tex]\frac{1}{3}[/tex], meaning that every unit up equates to 3 blocks to the right. Counting along the line, we see that this is correct.
I need the answers ASAP
Answer:
Image attached
Step-by-step explanation:
Just wandering, no hate, you can post answers on brainly but can't read an analog clock.
BTW I've got one in my house
Sylvia set a goal of saving at least $200 in a savings account.
She currently has $60 in the account. If she invests $5 of her weekly allowance per
week, how many weeks will it take her to reach her goal?
Write the inequality to the problem.
Answer:
60+5x>200
Step-by-step explanation:
This is the answer
A quadratic function is given by the table. Anna and Marco are trying to locate the roots of the given function. Are their solutions accurate? Explain in detail and find the exact value of the roots. Approximate the roots to the nearest tenth. Math task
Answer:
what’s 2/3 x 7?
Step-by-step explanation:
how many inches would represent 315 miles
Answer: 19,958,400
Step-by-step explanation: Multiply the length value by 63360.
315 x 63,360 = 19,958,400
Find the set AUB.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A={1, 2, 4, 6}
B = {3, 6, 5)
Step-by-step explanation:
solution,
given,
U={1,2,3,4,5,6,7,8,9,10}
A={1,2,4,6}
B={3,6,5}
now,
AUB={1,2,4,6}U{3,6,5}
={1,2,3,4,5,6,}
this is the answer and thanks for giving the opportunity to help you....... follow me...have a nice day ahead..
To ride a horse at the state fair costs two dollars per minute. Paula buys a 16 minute ride. Next time he plans to write 25% longer. How much will he pay
Answer:
$40
because it is lol ya know smart
Find the area of the rhombus
Answer:
area of rhombus=d1×d2=1/2(5+5)×(10+10)=1/2 10×20=100m²
The area of the rhombus is 100 m².
We have,
The area of a rhombus.
Area = (diagonal A* diagonal B) / 2 _____(1)
Now,
From the figure,
Diagonal A = (5 + 5) = 10 m
Diagonal B = (10 + 10) = 20 m
Substitute the values in (1).
Area of the rhombus.
= 1/2 x (10 x 20)
Simplify the expression.
= 1/2 x 200
= 100 m²
Thus,
The area of the rhombus is 100 m².
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A. It takes 86 pounds of seed to completely plant a 9-acre field. How many pounds of seed are needed per acre?
B. At Garcia's Bike Rentals, it costs $27 to rent a bike for 6 hours.
How many hours of bike use does a customer get per dollar?
Answer:
A. about 9.6 pounds of seeds
B. $4.5 per hour
Step-by-step explanation:
Phyllis invested 32000 dollars, a portion earing a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After
one year the total interest earned on these investments was 1820 dollars. How much money did she invest at each rate?
9514 1404 393
Answer:
$10,000 at 5%$22,000 at 6%Step-by-step explanation:
Let x represent the amount invested at 6%. Then 32000-x is the amount invested at 5%, and the total interest earned is ...
0.06x +0.05(32000 -x) = 1820
0.01x +1600 = 1820 . . . . simplify
0.01x = 220 . . . . . . . . . . subtract 1600
x = 22,000 . . . . . . . . . . . multiply by 100
32000 -x = 10,000
Phyllis invested $22,000 at 6% and $10,000 at 5%.
729
800
9
150
8
515
125
512
612
Select all the cube numbers.
A curve has equation y=2/x square root what is dy/dx
Answer:
dee y by dee x
Step-by-step explanation: hope this helps! have a supercalifragilisticexpialidocious day! ◑﹏◐
Answer: (The answer is in the image below. Had to write it instead of type it.)
Step-by-step explanation: Differentiate each term with respect to x, then solve for y'.
I hope this helps you out!
Plot the points from the Fahrenheit chart in question 4 onto the graph below. Use the plotted
points to sketch out the graph of F(t).
(0, 26.24)(12, 104) (24, 26.24)
Answer:
should be easy just plot the points
Step-by-step explanation:
we don't have the chart, though.
Answer:
Answer is attached :)
Step-by-step explanation:
Calculate the area of the circle below.
Is the radius or diameter given? diameter
The area of the cirle is :
32 in
Answer:
The area of the circle is 100.48; the diameter is shown.
Step-by-step explanation:
The formula for finding the area of a circle is 3.14 (or pi) multiplied by the diameter. 3.14*32= 100.48
The radius is half of the diameter, or half of the circle. However, this drawing shows the whole distance of the circle, so the diameter is shown.
The first three terms of a geometric sequence are as follows.
-7, 14, -28
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
-7, 14, -28, CI
-7,14,-28,56,-112
an = a1(r)^n-1
a4 = -7(-2)^4-1
a4 = -7(-2)³
a4 = -7(-8)
a4 = 56
an = a1(r)^n-1
a5 = -7(-2)^5-1
a5 = -7(-2)⁴
a5 = -7(16)
a5 = -112
#CarryOnLearningThe radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second.
(a) Find the speed of the bicycle in feet per second and miles per hour.
ft/sec
mph
(b) Use your result from part (a) to write a function for the distance d (in miles) a cyclist travels in terms of the number n of revolutions of the pedal sprocket.
d =
(c) Write a function for the distance d (in miles) a cyclist travels in terms of time t (in seconds). Compare this function with the function from part (b).
d =
Please help ASAP, marking brainliest if correct!
Answer:
option 4
Step-by-step explanation:
the total interior angle of a triangle adds up to 180º. you're given it's a right triangle (90º) and the angle B, 21º. Add those up and you get 111º. 180º-111º=69º, angle C.
John owns 5 health food stores in the Columbia area, and they are realizing a good profit. John decides to invest a portion of the profits in an annuity
offered by Penn Life Insurance. Penn Life will guarantee John 8 percent interest compounded quarterly for the first 5 years, as long as he deposits
$10,000.00 every quarter of the term of the guaranteed rate. Assuming John fulfills the obligations of the investment, what will be the value of the
investment at the end of the 5-year term?
O $245,446.58
$261,832.74
O $242,970.00
O $255,446.40
Answer:
b. $242,970.00
Step-by-step explanation:
The value of the investment compounded quarterly at the end of 5 years is $242,970.00.
What is compounded quarterly?
Compounded quarterly is the "interest amount which is earned quarterly on an account or investment".
According to the question,
John rate of interest = 8%
Period (n) = 5years
Principal = $10,000
Amount of compounded quarterly = P(1+[tex]\frac{r/4}{100}[/tex])⁴ⁿ.
= 10000(1+[tex]\frac{8/4}{100}[/tex])⁴⁽⁵⁾
= 10000(1+[tex]\frac{2}{100}[/tex])²⁰
=10000([tex]\frac{102}{100}[/tex])²⁰
=10000(1.02)²⁰
=10000(1.4859)
=14,859.474.
As long as John deposits $10,000.00 every quarter of the term of the guaranteed rate is $228110.526.
In order to find the value of the investment at the end of the 5-year term
$14,859.474.+$228110.526
= $ 242,970.00
Hence, the value of the investment compounded quarterly at the end of 5 years is $242,970.00.
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Make the right answers plz
Answer:
thx for the free points
sorry that people are giving the wrong answers. thats happening to me too
What is the median for the following set of numbers? 10, 13, 15, 12, 9, 12, 16
Answer:
12
Step-by-step explanation:
Arranging in ascending order -> 9, 10, 12, 12, 13, 15, 16
n = 7
Median = value of ((n + 1) / 2) th term
= value of (7+1) / 2 th term
= value of 4 th term
= 12
Hope it helps :)