The quotient is 2x² + 10x − 5, and the remainder is 0.
What is synthetic division?
Synthetic division is a method in algebra for manually performing Euclidean division of polynomials that requires less writing and fewer calculations than long division. It is typically taught for division by linear monic polynomials, but the method can be applied to any polynomial.
The given polynomial is (2x³ + 4x² - 35x + 15) and we have to divide this polynomial by (x - 3).
By using synthetic division
2x³ + 4x² - 35x + 15
Take the constant term of the divisor with the opposite sign and write it to the left
3 | [tex]x^3[/tex] [tex]x^2[/tex] [tex]x^1[/tex] [tex]x^0[/tex]
| 2 4 -35 15
----|----------------------------
Write down the first coefficient as it is
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
3 | 2 4 -35 15
| 3.2 = 6
----|----------------------------
2 10
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
3 | 2 4 -35 15
| 6 30
-----|----------------------------
2 10 -5
Again, we get
3 | 2 4 -35 15
| 6 30 -15
-----|----------------------------
2 10 -5 0
We have completed the table and have obtained the following resulting coefficients: 2,10,−5,0.
Thus, the quotient is 2x² + 10x − 5, and the remainder is 0.
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The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
Answer:
hi do you mind making the question a bit clear? where is the table?
Step-by-step explanation:
For every point on the graph of F(x), there is a point on the graph of F1(x)
with exactly the same coordinates.
A. True
B. False
I need help with 9 10 and 11
A mountain climber found that the relationship between his altitude and the surrounding air temperature is linear. The function
represents this relationship, where is the altitude in meters and is the temperature in degrees Fahrenheit. According to this function, by how much is the temperature decreasing for every meter that the mountain climber’s altitude increases?
The temperature decrease for every meter that the mountain climber's altitude increases is given by:
-100 ºF.
What is the temperature decrease?The function that models this situation is a linear function, which has the format defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function, representing by how much y changes when x is increased by one.b is the y-intercept of the function, representing the numeric value of y when x = 0.In the context of this problem, the function is defined as follows:
f(a) = -100a + 75.
Hence the slope of the function is of:
-100.
Representing the temperature decrease for each meter of altitude increase of the climber.
Missing InformationThe function is defined as:
f(a) = -100a + 75.
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Student are going on a field trip to a play. The play i elling kid ticket and adult ticket. They old a total of 60 ticket. One kid ticket ell for $3 while the adult ticket i $5. They made a profit of $220 that day. How many kid ticket were old?
Number of kids ticket is 40
What do you mean by system of linear equation?
A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.
Total number of tickets = 60
Cost of 1 kid ticket = $3
Cost of 1 adult ticket = $5
Total profit = $220
Let number of kid tickets = x
number of adult tickets = y
According to question:
x + y = 60 ......(1)
3x + 5y = 220 ........(2)
Substitute the value of x from eq(1) to eq(2)
3(60 - y) + 5y = 220
180 - 3y + 5y = 220
180 + 2y = 220
2y = 220 - 180
2y = 40
y = 40/2
y = 20
Substitute this value of y in eq(1)
x + 20 = 60
x = 60 - 20
x = 40
Therefore, number of kids ticket is 40
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Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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The graphs of functions f(x) and g(x) = f(x) + k are shown: Graph of line f of x going through ordered pairs 0, 1 and 2, 6. Graph of line g of x going through ordered pairs 0, negative 1 and 2, 4. What is the value of k? a k = 2 b k = −2 c k = 1 d k = −1
Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:
y = f(0) = 1.
Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:
y = g(0) = -1.
From the information provided above, we have the following function:
g(x) = f(x) + k
g(0) = f(0) + k
Making k the subject of formula, we have:
k = g(0) - f(0)
k = -1 - 1
k = -2.
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7(x-1)=3x+2 in a improper fraction
Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good
Step-by-step explanation:
7(x-1)=3x+2
Distribute through the parentheses
7x-7=3x+2
Move the variable to the left-hand side and change its sign
7x-7-3x=2
or Move the constant to the right-hand side and change its sign
7x-7-3x=2
Collect like terms
4x=2+7
And then Add the numbers
4x=9
Divide both sides of the equation by 4
x=9/4
Mixed number is 2 1/4
I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If
x machines are made, then the unit cost is given by the function C(x)=1.2²-600x+82,738. What is the minimum unit cost?
Do not round your answer.
The minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738
What is meant by unit cost?A company's unit cost is the cost of producing, storing, and selling one unit of a specific product. Unit costs encompass all fixed and variable production costs. A cost unit is a quantity measuring unit for a product or service.
A unit cost is the overall cost incurred by a business to manufacture, store, and sell one unit of a specific product or service. Unit costs are the same as cost of goods sold (COGS). This accounting metric incorporates all fixed and variable expenses related with the manufacture of a good or service.
Given,
C(x)=1.2x²-600x+82,738
Minimum value [tex]C_{min}[/tex]=c-(b²/4a)
Where a=1.2, b=-600, c=82738
[tex]C(x)_{min}[/tex]=82738-((-600)²/4(1.2))
=82738-(360000/4.8)
=7738
Therefore, the minimum unit cost is 7738.
Hence, the minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Examine the table, which represents the number of guests visiting a museum during a period of time.
If the relationship between hours and guests is proportional, what is the value of h?
Enter your answer as a number, like this: 42
Answer:
7
Step-by-step explanation:
649-531=118
We know that there are 118 more guests per hour.
Divide 826 by 118 to get 7.
Answer: 7
Step-by-step explanation:
The first line of the table is 2 and 236 if you divide 236 by 2 you get 118
Then after that you times it by any number after 5.5 until you get 826.
In 8 day, a ample of vanadium-48 decay to 1/√2 of it original amount. Determine the half-life of vanadium-48
The half-life of vanadium-48 is 16 days.
What is half life?
The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.
According to law of radio active decay, IN=N
N-- amount of sample present
N1--- initial amount of sample
Decay 0 constant
Half life = 16 days
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David's iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time
x
of these songs. What are the mean and the standard deviation of the sampling distribution of
x?
Explain.
The mean and the standard deviation of the sampling distribution of x are given as follows:
Mean: 225 seconds.Standard deviation: 19 seconds.How to obtain the mean and the standard deviation of the sampling distribution of x?The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:
The mean is the same as the population mean.The standard deviation is the division of the population standard deviation by the square root of the sample size.The parameters for this problem are given as follows:
Population mean of 225 seconds.Population standard deviation of 60 seconds.Sample size of 10 seconds.Hence the standard deviation for the sampling distribution of x is given as follows:
s = 60/sqrt(10) = 19 seconds.
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What is the y-intercept, b, of the additive relationship represented by this table?
Enter your answer as an integer in the box.
b = ?
Answer:
3
Step-by-step explanation:
Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
The area of a triangle is always one half the base b times the height h.
If the base is represented by the expression 4x + 2 and the height is represented by 3x, which expression gives the area of the triangle?
9x
9x2
12x2 + 6x
6x2+ 3x
The correct option is [tex]6x^2+3x[/tex] which is the area of triangle. It can be obtained by the formula of area of triangle and algebriac multiplication.
What is the are formula of area of a triangle?
Area of any shape is the measure of the 2 dimentional space occupied by that shape. Its SI unit is [tex]m^2[/tex]. Area of the triangle is given by the following formula:
[tex]A=\frac{1}{2}bh[/tex]
Here, A is the area, b is the base, and h is the height.
Substitute 4x+2 for b and 3x for h in the above equation.
[tex]A=\frac{1}{2}(4x+2)(3x)[/tex]
Now, multiply using algebriac multiplication as follows:
Initially, use distributive property as follows:
[tex]A=\frac{1}{2}[(4x)(3x)+(2)(3x)][/tex]
Now, multipliy and again open brackets as follows
[tex]A=\frac{1}{2}(12x^2+6x)\\=6x^2+3x[/tex]
This gives the area of the triangle is [tex]6x^2+3x[/tex]. Hence, the correct option is the last option.
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Answer:
d
Step-by-step explanation:
a penny is thrown from the top of a 52.6-meter building and hits the ground 3.31 seconds after it was thrown. the penny reached its maximum height above the ground 0.85 seconds after it was thrown. define a quadratic function, h , that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.
The quadratic function which models the motion of the penny is
h(t) = -4.9t² -0.327761 t + 52.6
and the maximum height reached is 57.43
h(t) = - 0.5gt² + vt + h
g = 9.8 m/s²
h = 52.6 m
v = ?
For v,
h(t) = -0.5gt² + vt + 52.6
h(t) = - 4.9t² + vt + 52.6
Time when penny hits the ground ; t = 3.31
h(3.31) = 0
0 = -4.9(3.31)² + v(3.31) + 52.6
0 = -53.68489 + 3.31v +52.6
3.31v = -1.08489
v = -1.08489/3.31
v = -0.327761 m/s
Therefore,
h(t) = -4.9t² -0.327761 t + 52.6
2.) Maximum height of the penny above the ground
t = 0.85 seconds
h(0.85) = -4.9(0.85^2)-0.327761 (0.85) + 52.6
Maximum height reached = 57.43 meters
Therefore, the maximum height reached is 57.43 meters.
An object changing its position with regard to time is referred to as motion. Motion is mathematically characterised in terms of displacement, distance, velocity, acceleration, and speed as well as the observer's frame of reference and the measurement of the change in the body's position with respect to that frame over time. Kinematics is the area of physics that studies how motion is affected by forces, whereas dynamics is the area that studies how motion is affected by forces.
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Solve for x:
7x(x+1. 8)=0
Need help ASAP.
Answer is not x=-1. 8 or x=0
Answer:
Step-by-step explanation:
x = -9/5 = -1.800 or
x = 0
Michael swam 2,000 yards on each of eighteen days.
The scatterplot above shows his swim time for and
corresponding heart rate after each swim. The line of
best fit for the data is also shown. For the swim that
took 34 minutes, Michael's actual heart rate was
about how many beats per minutes less than the rate
predicted by the line of best fit?
A) 1
B) 2
C) 3
D) 4
Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B
What is a scatterplot?A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.
On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.
From the graph the actual heart rate=150
but calculated heart rate from best fit line=148
Difference between actual and calculated=150−148=2
Option B is correct.
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The bill for two book came to $28. 48. One book cot $7. 44. What wa the cot of the other one
Answer:
Step-by-step explanation:
Ok:
If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price
2. 28.45-7.44=$21.01
3. Answer: The cost of the other one is $21.01
If the lowest price in the past year occurred 35 days ago, find the approximate average change per day since then. a. $2.08 b. $2.64 c. $0.90 d. $2.99
The approximate change per day since the lowest price occurred 35 days ago, is a. $2.08.
How to find the approximate average change?The approximate average change can be found by the formula :
= ( Current price of stock - Lowest price ) / Number of days since lowest price
Current price of Dagofi Radar stock = $ 130. 58 closing price
Lowest price = $ 57. 71
The approximate average change is:
= ( 130. 58 - 57. 71) / 35
= 72. 87 / 35
= $ 2.08
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Missing part of question:
Consider today's stock listing for Dagofi Radar, shown below.
52 wk High
52 wk Low
Symbol
Div.
Close
Net Change
162.22
57.71
DFR
9.75
130.58
-2.64
Which of the following are essential elements of hypothesis testing?
-It uses probability theory to determine if a hypothesis is a reasonable statement.
-It makes use of sample data.
The following are crucial factors in hypothesis testing:
It employs probability theory to evaluate if a hypothesis is a valid claim.It employs sample data.Explain the term hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.
The type of data being used and purpose of the study will determine the methodology the analyst uses. A basic hypothesis can anticipate a causal relationship between variables, i.e., that one has an impact on the other. This is known as hypothesis testing, and it uses sample data to determine the plausibility of a hypothesis.It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an investigation are reliable.Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
If you vertically stretch the exponential function f(x) = 2x by a factor of 4, what is the equation of the new function?
The equation of the new function is g(x) = 4(2ˣ)
How to determine the equation of the new function?The exponential equation is given as
f(x) = 2ˣ
Then, we have the transformation to be:
Vertically stretch by a scale factor of 4
The scale factor can be represented as k
So, we have
k = 4
The rule of vertical stretch by a scale factor of k is represented a
g(x) = kf(x)
So, we have
g(x) = 4 * 2ˣ
This gives
g(x) = 4(2ˣ)
Hence, the equation is g(x) = 4(2ˣ)
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➤ Solve the inequalities.
T -3 is less than or equal to 2
-3 is less than 2
< is the symbol
Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
please help im suffering right now
Answer:
C
Step-by-step explanation:
If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.
May I please have brainliest for this? Thank you very much!
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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