Given:
Dividend = [tex]2x^2+5x-3[/tex]
Divisor = [tex]x+3[/tex]
To find:
The remainder by using the synthetic division.
Solution:
We have,
Dividend = [tex]2x^2+5x-3[/tex]
The coefficients of dividend are 2, 5, -3. Write these elements in the top row of synthetic division.
Divisor = [tex]x+3[/tex]
The value of divisor is 0 at [tex]x=-3[/tex]. So, write -3 on the left side of division.
Write down the first coefficient of dividend in bottom row, then multiply it by -3 and write the result below the next coefficient of dividend then add the coefficient and write the result in bottom row, then repeat the steps up-to last coefficient.
-3 | 2 5 -3
| -6 3
------------------------------------------
2 -1 0
-----------------------------------------
Here, the first two elements of the bottom row represent the coefficient of quotient and last element represent the remainder.
Therefore, the remainder is 0.
Estimate the slope of the regression line manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime in thousands of holes drilled of bits at different speeds in surface feet per minute (sfm). Suppose you want to create a model that estimates the drill bit lifetime ( y) based on rotation speed ( x). Summary statistics for 20 observations collected are given below.
20 20 20 20
Σ xi = 2,000 ; Σ yi = 86.6 Σ xi^2= 216,000 Σ xiyi= 8,338
i= 1 i=1 i=1 i=1
Estimate the slope of the regression line.
a. -0.017
b.-0.037
c. -0.057
d.-0.077
Answer:
[tex]b_i = -0.020125[/tex]
Step-by-step explanation:
Given
[tex]\sum x_i= 2000[/tex]
[tex]\sum y_i= 86.6[/tex]
[tex]\sum x_i^2= 216000[/tex]
[tex]\sum x_iy_i = 8338[/tex]
[tex]n = 20[/tex]
Required
Determine the slope (b) of the regression line
This is calculated as:
[tex]b_i = \frac{\sum xy - \frac{\sum x\sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}{n}}[/tex]
Substitute values for each term, we have:
[tex]b_i = \frac{8338 - \frac{2000 * 86.6}{20}}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the numerator
[tex]b_i = \frac{8338 - 8660}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the denominator
[tex]b_i = \frac{8338 - 8660}{216000 - 200000}[/tex]
[tex]b_i = \frac{-322}{16000}[/tex]
[tex]b_i = -0.020125[/tex]
The function F(x) = log2 x is increasing.
True or false
Answer: i think true
Step-by-step explanation:
Two trains, Train A and Train B, weigh a total of 243 tons. Train A is heavier than Train B. The difference of their weights is 87 tons. What is the weight of each train?
Answer:
Train A weighs 156 tons, and Train B weighs 78 tons.
Step-by-step explanation:
Given that two trains, Train A and Train B, weigh a total of 243 tons, and Train A is heavier than Train B, with a difference of their weights of 87 tons, to determine what is the weight of each train, the following calculation has to be done:
(243 - 87) / 2 = B
156/2 = B
78 = B
243 - 87 = A
156 = A
Therefore, Train A weighs 156 tons, and Train B weighs 78 tons.
A baseball field is being designed. There is 60 ft between the pitcher and 3rd
baseman and 90 ft between the catcher and 3rd baseman. The half-way
distance from the catcher to the 3rd baseman is 45 ft. How far is the distance
between the pitcher and the catcher?
441 = 21
3600 = 60
5400 = 73.5
7650 = 87.5
1800 = 42.4
Answer:
30ft.
your welcome. ...................
solve y=x-2 and x+y=12 using substitution
Step-by-step explanation:
y=x-2....eqn1
x+y=12.....eqn2
now,
from eqn 1
y= x-2
again, putting value of y in eqn 2
x+y=12x+x-2=122x=12+2x=14/2x=7in eqn 1
y=x-2y=7-2y=5hope it helps..
4.
What is the equation of the circle with a radius of 5 and center at (2, 3)?
AO (x + 2)2 + (y + 3)2 = 25
BO (x - 2)2 + (y - 3)2 = 25
CO (x - 2)2 + (y - 3)2 = 5
D. (x + 2)2 + (y + 3)2 = 5
Answer:
the answer is A
Step-by-step explanation: since the radius is 5 and we have (2,3) then we are going into 2 and 3 the x and y represent 5 so the answer wouldn't be 5 then you would have done no work. so it is A. i suck at explaining things hope this helps!
Step-by-step explanation:
[tex]general \: equation \\ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0 \\ centre : ( - g, - f) = (2,3) \\ g = - 2 \: and \: f = - 3 \\ c = {g}^{2} + {f}^{2} - {r}^{2} \\ c = {( - 2)}^{2} + {( - 3)}^{2} - {(5)}^{2} \\ = - 12 \\ therefore \\ {x}^{2} + {y}^{2} - 2x - 3y - 12 = 0[/tex]
PLEASE HELP WITH THIS GEOMETRY ASSIGNMENT... IT WOULD MEAN A LOT BEING IT'S HALF MY GRADE... AND PLEASE EXPLAIN IT SO I CAN FINALLY UNDERSTAND OR IF YOU DONT WANT TO GIVE ME THE ANSWER JUST TELL ME HOW TO DO IT. THIS IS FORM IS FROM PLATO OR EDMENTRUM IF YOU WILL.L...
Question 2
The vertex form of the equation of a horizontal parabola is given by , x=1/4p(y-k)2+h where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use GeoGebra to create a horizontal parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below.
Part A
Mark the focus of the parabola you are going to create at F(-5, 2). Draw a vertical line that is 8 units to the right of the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part B
Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?
Part C
Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.
Part D
Which way will the parabola open? Explain.
Part E
How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Part F
What is the value of p for your parabola?
Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
Part J
To practice writing the equations of horizontal parabolas, write the equations of these two parabolas in vertex form:
focus at (4, 3), and directrix x = 2
focus at (2, -1), and directrix x = 8
equation is below...
y=[tex]y=\frac{1}{4p} (x-h)^{2} +k[/tex]
Answer:
OH MY GOD!!! GIRL IMMA TRY!
Step-by-step explanation:
It gave me out of time. Its understandable but search your answers up online and you'll find the answers! SORRY
Find the sum of the measures of the interior angles of the indicated covex
Very confused
Answer:
Step-by-step explanation:
Hope it helps u!!
In a lab experiment, 2000 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 23 hours. How many bacteria would there be after 26 hours, to the nearest whole number?
Answer:
4,261
Step-by-step explanation:
after 23 hours, the number of bacteria =
4,000.
so, after 26 hours = 4,000+ (3/23 ×4000)
= 4,000 + 261 = 4,261
Round to the nearest hundredth (2 decimal places) when necessary
Answer:
volume = 91 cm²
perimeter = 41.1 in
Step-by-step explanation:
volume = 1/2(b1+b2)(h) = 1/2(11 + 15)(7) = 91 cm²
7) Write an inequality that represents 7 more than three times a number, n, is less than 16.
Answer:
3n + 7 < 16
Step-by-step explanation:
7 more than 3 times a number, n, is less than 16 is represented by
3n + 7 < 16 where:
3n = three times a number, n,
+ 7 = 7 more than
and
< 16 = is less than 16.
Answer:
Step-by-step explanation:
help me pls (: l: ):
Fraction: 5/10
Demical: 0.5
Percent: 50%
Estimate the product. 3 1/3 x 4 1/8 =
Answer:
13 3/4 or 14 if rounded
Step-by-step explanation:
Answer:
Step-by-step explanation:
55/4
13 3/4
3. The cost of renting a car is $26.50 plus $10 per day. Sales tax is 6%. Select all expressions that represent the cost of renting a car for d days. 1.06(26.50 + 100) 28.09d 26.50 + 6d 28.09 + 10.6d 26.50 + 1.06d
Answer this question pls!!
Answer:
(6, 7)
Step-by-step explanation:
A rectangle means that opposite sides are parallel to each other and that opposite sides are equal in measurements.
If we look at the opposite side starting at (2, 1), we can count how long the other side should be. Counting the next point of the rectangle is (6, 1) which is a difference of 4. This means if we count from (2, 7) 4 spaces to the right, we will find our missing vertex.
(2 + 4, 7) = (6, 7)
Find the Find the marginal cost function, given the average cost function AC=100100Q+2arginal cost function, given the average cost function AC=100100Q+2
Answer:
Step-by-step explanation:
a) total fixed cost is 100(derived from total cost function). It is not depended on output.
b)AFC=TFC/Q.AFC=TFC/Q.
AFC(100)=100/100=1.AFC(100)=100/100=1.
AFC(300)= 100/300=1/3.AFC(300)=100/300=1/3
Solve for x
Please help!
Answer:
Hello! answer: x = 20
Step-by-step explanation:
Because 3 multiplied by x which equals 20 gets us 60 then we just add the 2 and get 62 these are vertical angles so they will have the same measure hope that helps!
a) Expand and simplify (x + 4)(x - 7)
Answer:
X x X=x²
X x -7=-7x
4 x X=4x
4 x -7=-28
-7x + 4x=-3x
x² + -3x -28
hope that helped :)
Step-by-step explanation:
Help plis I don’t understand ✋✋
Trapezoid Area =
[ ( Sum of the rules ) × ( height ) ] ÷ 2
_________________________________
Area = [ ( 2 + 3 ) × 3 ] ÷ 2
Area = [ 5 × 3 ] ÷ 2
Area = 15 ÷ 2
Area = 7.5 m^2
Can someone help me with this please ?
Answer:
I think it’s A.
Step-by-step explanation:
The Hutton's records for the past six months show that their expenditures totaled $2.768, $3,001, $2,663, $2,471, $2,893, and $2,803. What is their average monthly expenditure for the six months?
Answer
2766.5
Step-by-step explanation:
Well to solve for average all you have to do is add the values together then divide by the number of values you started with. So we add them together(2768+3001+2663+2471+2893+2803) and get 16599. Then, since there were 6 values we divide that by 6 and you get your answer.
HELP ME PLEASEEEEEEEEEE
Answer:
2, - 6 your welcome caubububyvyvybubufwrduvibuvc
PLEASE HELP!!!!!!! Will mark brainlest!!!
Answer:
Step-by-step explanation:
78-90 = 12
ASCD is a parallelogram. Determine whether each statement must be true. Select Yes
or No for each statement
B
Answer:
angel DAC=angle BAC because opposite angle of parallelogram is equal
WILL MARK BRAINLEST Select the correct answer.
The stem and leaf plot shows the number of coples of a newly released book ordered from several bookstores.
Answer:
the median is 139
Step-by-step explanation:
there are 19 numbers in the data set. Therefore, the 10th number would be the median.
In what direction does the function f(x)=−(14x−1)(4x+1) open? Explain.
Answer: Direction opens downward
Step-by-step explanation:
X-Intercept: (1/14,0),(-1/4,0)
Y-Intercept: (0,1)
Find the vertex using x= -b/2a
Plug it into the vertex form = y=a(x-h)^2 +k
H,K will identify the direction.
Please help!
1. What is the perimeter of the triangle below? Show your work.
Answer:
16.73 I THINK
Step-by-step explanation:
my guess is n1 is relating to the 4.9, and if it then you would do the Pythagorean theorem. because the degrees are there to let you know it's a right angle and you are able to use the theorem..... so -
4.9^2 + 4.9^2 =C^2
48.02 =C
√48 = 6.93 (rounded to nearest hundredth)
then you add them all together
4.9+4.9+6.93=16.73
3/2 of a number is less than this number?
true or false, justify your answers
Answer:
False because 1/2 would be half the number 2/2 or 1 would be the whole number so 3/2 would be a whole and half or 1 1/2
Answer:
false
if the number is X
3/2 of X= X 1/2
[tex]x \frac{1}{2} > x[/tex]
3 + 6x = 15?
pls help :D
Answer:
x = 2
Step-by-step explanation:
3 + 6x = 15
rearrange to 6x + 3 = 15
subtract 3 to both sides 3 - 3 and 15 - 3
simplify 6x = 12
x = 2
Find the area and perimeter
Answer:
Step-by-step explanation:
Add all 4 sides to get perimeter so the first one is 9+9+2+2=22cm
the area is length x width so the first one is 9 x 2 =18cm ^2