8x^{3}+26x^{2}+19x+38x
3
+26x
2
+19x+3 is divided by 4x+34x+3.
Answers
Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:
2x² + 5x + 1.
Synthetic division algorithmIn the synthetic division algorithm, the coefficients of a polynomial are each divided by a value.This divisor is the zero of the divided polynomial, which goes into the far left box.In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:
8, 26, 19 and 3.
The divisor is found as follows:
4x + 3 = 0
4x = -3
x = -3/4
x = -0.75.
The resulting coefficients of the quotient are given as follows:
8, 20, 4 and remainder of 0.
Hence the quotient is:
8x² + 20x + 4.
Which can be simplified as:
2x² + 5x + 1.
The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.
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Related Questions
If the cost of an 800 number is $29.95 per month plus 28 cents per minute, then the monthly cost varies directly as the number of minutes.TrueFalse
Answers
We have the monthly cost is fixed: $29.95.
The cost varies directly as the number of minutes since the total cost per month will be:
[tex]29.95+\frac{28}{100}x[/tex]If we make a call and spend 30 minutes. We need to add this cost to the payment:
[tex]undefined[/tex]Which of the binomials below is a factor of this expression?
25x^2-4y^2z^2
answer- 5x-2yz
Answers
The binomials 5x-2yz are a factor of this expression
25x^2-4y^2z^2
This is further explained below.
What are binomials?Generally, A binomial is a kind of polynomial that is used in algebra and is defined as the sum of two terms, each of which is a monomial.
After monomials, this is the sort of sparse polynomial that is the easiest to understand.
The word "binomial" refers to an algebraic expression that consists of just two different terms. This is a polynomial with two terms.
25 x^2-4 y^2 z^2
Rewrite 25 x^2 as (5 x)^2.
(5 x)^2-4 y^2 z^2
Rewrite 4 y^2 z^2 as (2 y z)^2.
(5 x)^2-(2 y z)^2
Since both terms are perfect squares, factor using the difference of squares formula, a^2-b^2=(a+b)(a-b) where a=5 x and b=2 y z.
(5 x+2 y z)(5 x-(2 y z))
Simplify.
(5 x+2 y z)(5 x-2 y z)
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13+14=3×f;f=9 helppp
Answers
Answer: 3x=13+14
3x=27
x=27/3
x=9
Step-by-step explanation: Maybe.
Use each of the three corresponding base and height pairs to find the area of the triangle. Why is the area the same for each calculation?
Answers
Answer:
The three correct corresponding pairs that gives the same area are;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]The areas are the same in each case because the product of each pair is the same.
Explanation:
Given the base and height pairs in the question.
Let us use the corresponding pairs that gives the same area.
Firstly, for the first pair;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times10\times7=35cm^2 \\ A=\frac{1}{2}\times10\times2.5=12.5cm^2 \end{gathered}[/tex]Secondly, the second pair is;
[tex]\begin{gathered} A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times5\times3.5=8.75cm^2 \\ A=\frac{1}{2}\times5\times2.5=6.25cm^2 \end{gathered}[/tex]Thirdly, the third pair;
[tex]\begin{gathered} A=\frac{1}{2}\times14\times3.5=24.5cm^2 \\ A=\frac{1}{2}\times14\times7=49cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]Therefore, the three correct corresponding pairs that gives the same area are;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]The areas are the same in each case because the product of each pair is the same.
Please Help Please ASAP
Answers
ASAP please Hurry
The number of issues of books from a library are given for the years 2001–2011. The numbers are in hundreds of thousands.
Answers
Answer:
See attached graph.
Step-by-step explanation:
Use DESMOS graphing software. Free.
describe the transformation of f represented by G then graph each function
Answers
Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Transformation 2: the function is shifted 2 units up
Explanation
[tex]f(x)=x^4[/tex]Step 1
the first transformation is the function multiplied by a constant ( 1/2)
If the function is multiplied by a value less than one, all the values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction
so
[tex]\begin{gathered} f(x)=x^4\Rightarrow\frac{1}{2}x^4 \\ \frac{1}{2}is\text{ smaller than 1, so} \end{gathered}[/tex]Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Step 2
the second transformation is add 5
[tex]f(x)=x^4\Rightarrow\frac{1}{2}x^4\Rightarrow g(x)=\frac{1}{2}x^4+5[/tex]If a positive number is added, the function shifts up the y-axis by the amount added.
so,
Transformation 2: the function is shifted 2 units up
I hope this helps you
On what day does frank first get charged an overdraft fee? a. wednesday b. thursday c. friday d. saturday
Answers
Frank first get charged an overdraft fee on Wednesday
Frank has $66.50 in his account as of Sunday.
He made a debit of $60.33 on Monday (66.50 - 60.33), leaving him with a balance of $6.17. He added $80.75 to the account on that same Monday (6.17 plus 80.75). He has $86.92 left over as of Monday.
Frank had a balance of $86.92 on Tuesday when he made a $54.45 debit (86.92 - 54.45). The remaining balance is $32.47.
Frank had a balance of $32.47 at the beginning of the day on Wednesday. He subsequently made withdraw of $49.20. debit(32.47 - 49.20). Frank has overdrawn and will be assessed an overdraft fee following the debit because his balance is -$16.73. Frank still has a negative balance even after making a deposit of $15.
Therefore, Frank was therefore assessed an overdraft fee on Wednesday.
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What is -2=-1+n/8? I’ve been stuck on it for a while
Answers
Answer: n= -8
Step-by-step explanation:
1. -2 = -1 + [tex]\frac{n}{8}[/tex]
2. -1 = [tex]\frac{n}{8}[/tex]
3. -8 = n
Provide an example and explain the steps to convert a fraction into a percent.
Answers
A fraction is one way of writing a division. ...
Convert 2⁄5 to a percentage. ...
Divide the numerator (2) by the denominator (5). ...
To convert 2⁄5 to a percentage, divide 2 by 5 and then multiply the result by 100.
The graph of a figure is shown below.
Which graph represents the reflection of this figure across the x-axis?
the first triangle in the photo
which is reflected on the x-axis
Answers
A graph which represents the reflection of this figure across the x-axis is: graph 5.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:
(x, y) → (x, -y) = (3, 1) → (3, -1).
(x, y) → (x, -y) = (4, 0) → (4, 0).
(x, y) → (x, -y) = (3, -1) → (3, 1).
(x, y) → (x, -y) = (4, -2) → (4, 2).
(x, y) → (x, -y) = (2, -4) → (2, 4).
(x, y) → (x, -y) = (0, -2) → (0, 2).
In conclusion, a reflection across the x-axis would transform the geometric figure to that shown in the graph attached in the image below.
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two cyclists, 42 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answers
The speed of the faster cyclist is 14\ miles/hr.
What is speed?
It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.
Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,
[tex]2s+s=42\\3s=42\\s=14[/tex]
Now, distance coverd by the first cyclist is [tex]2s=2\times 14\\=28 \ $miles[/tex].
Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.
[tex]Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr[/tex]
Hence, the speed of the faster cyclist is 14\ miles/hr.
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what is Vivian's new account balance?
Answers
Answer: 218.65 US$
Step-by-step explanation: $187.56+$49.73= $237.29
237.29 US$- $18.64
Answer:
$218.65
Step-by-step explanation:
She starts with a balance of $187.56. When she deposits money she is adding to the account.
$187.56 + $49.73 = $237.29
When she spends money money is being subtracted from her account.
$237.29 - $18.64 = $218.65
2. What is the equation of a line that passes through the points (-0.92, 2.49) and (-5.62, 9.76)? Write your answer in point-slope form.
Answers
Answer:
Step-by-step explanation:
-0.92 2.49
-5.62 9.76
Rise = 9.76 - 2,49 = 7.27
Run: -5.62 - (-0.92) = -4.7
Slope (Rise/Run) = (7.27.`-0.92) = -1.55
The line has the form:
y = 1.55x + b
We need to find a value of b that forces the line through both point, Use one of the points and solve for b. I'll use (-0.92, 2.49).
y = 1.55x + b
2.49 = 1.55(-0.92) + b
b = 2.49 - 1.426 = 1.064
The equation is y = 1.55x + 1.0
2 Four friends go to the ice cream shop to purchase frozen
yogurt. Each friend gets a part strawberry and part
vanilla.
• Lucas gets 0.25 strawberry.
Adrianna gets % strawberry.
Ricardo gets 0.8 strawberry.
Jasmine gets % strawberry.
•
•
Arrange the friends in order from least to greatest amount of
strawberry in their yogurt.
Least
Greatest
Answers
Answer:
12
Step-by-step explanation:
Look at the table below. Which of the following is the constant rate of change?
Answers
Given data:
The first value of x is a=-16.
The first value of y is b=20.
The second value of x is c=-12.
The second value of y is d=15.
The expression for the rate change is,
x=(d-b)/(c-a)
Substitute the given values in thhe above expression.
x=(15-20)/(-12+16)
=-5/4
Thus, he constant rate of change is -5/4.
The sum of 4 consecutive integers is 170. What is the largest number in the group?
Answers
The largest number when the sum of 4 consecutive integers is 170 will be 44.
According to the question,
We have the following information:
Sum of four consecutive integers = 170
Now, let's take the first integer to be x.
So, the next 3 integers will be (x+1), (x+2) and (x+3) respectively.
Now, the largest number will be (x+3).
Adding 4 consecutive integers:
x+ (x+1) + (x+2) + (x+3) = 170
4x+6 = 170
4x = 170-6 (Moving 6 from the left hand side to the right hand will result in the change of the sign from plus to minus.)
4x = 164
x = 164/4
x = 41
So, the next three consecutive integers will be 42, 43 and 44.
Hence, the largest of the four consecutive integers is 44.
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what is the size of the angle between south and south east
Answers
The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.
Find the slope of the line that passes through the following points: (-4,-2) and (-3,5)
Answers
label your variables by x and y.
subtract y2 from y1, then x2 from x1.
simplify your answer
The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are less than 250 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places
Answers
For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.
The average total number of shoppers on a grocery store in 1 day is 506; the standard deviation is 115.
The number of shoppers is normally distributed.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 506 and standard deviation of 115.
Then, we can say that,
Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P(X<200)
[tex]=P(Z < \frac{200-506}{115})[/tex]
=P(Z<-2.66)
Where, Z is the standard normal variate.
ρ = -0.266
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.0039
For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.
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A normal distribution has = 32 and = 5.
(a) Find the z score corresponding to
x = 27.
(b) Find the z score corresponding to
x = 43.
(c) Find the raw score corresponding to
z = −3.
(d) Find the raw score corresponding to
z = 1.1.
Answers
a) z score corresponding to x = 27 is -1
b) z score corresponding to x = 43 is 2.2
c) Raw score corresponding to z = -3 is 17.
d) Raw score corresponding to z = 1.1 is 37.5
Given,
Normal distribution with μ = 32 and σ = 5
a) z score corresponding to x = 27
z = (x - μ) / σ
Then,
z = (27 - 32) / 5 = -5/5 = -1
That is, z score corresponding to x = 27 is -1.
b) z score corresponding to x = 43
z = (x - μ) / σ
Then,
z = (43 - 32) / 5 = 11/5 = 2.2
That is, z score corresponding to x = 43 is 2.2
c) Raw score corresponding to z = -3
z = (x - μ) / σ
Then,
-3 = (x - 32) / 5
-3 × 5 = x - 32
-15 = x - 32
x = 32 - 15 = 17
That is, raw score corresponding to z = -3 is 17.
d) Raw score corresponding to z = 1.1
z = (x - μ) / σ
1.1 = (x - 32) / 5
1.1 × 5 = x - 32
x = 32 + 5.5 = 37.5
That is, raw score corresponding to z = 1.1 is 37.5
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Greg is at his house he gets in his car drives north 8. 9 miles and stops at a store then he turns around and drives south 7. 7 miles to his friends house how far is the friends house from Greg’s houses?
Answers
His friend's house is 1.2 miles away from his house.
How do you know his friend's house is 1.2 miles away from his house?Well, the solution to this math problem is very simple. We just need to remove a number away from another. In other words, we only need to do some subtraction.
Subtraction is one of four main arithmetic operations in which we use to take away a number or an amount from another number or amount. Remember that the commutative law doesn't apply to subtraction, so we really need to be careful to pick what number is subtracted by the other number.
The distance from Greg's house to the store is 8.9 miles away. That's the number that is going to be subtracted. His friend's house is 7.7 miles away from the store. This is the number that we're going to subtract from the previous number. Mathematically, we can express this as:
8.9 - 7.7 = 1.2
We're left with 1.2, which is the distance in miles from Greg's house to his friend's house.
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Use the figure to find the measures of the numbered angles. The problem number 2. I’m just trying to make sure I’m doing these correctly.
Answers
Angle 2 and angle of 34° are vertical angles, then they are congruent, that is,
[tex]m\angle2=34\degree[/tex]Angle 6 and angle of 34° are corresponding angles, then they are congruent, that is,
[tex]m\angle6=34\degree[/tex]Angle 4 and angle of 34° are alternate interior angles, then they are congruent, that is,
[tex]m\angle4=34\degree[/tex]Angle 7 and angle of 34° are same-side interior angles, then they are supplementary, that is,
[tex]\begin{gathered} m\angle7+34\degree=180\degree \\ m\angle7=180\degree-34\degree \\ m\angle7=146\degree \end{gathered}[/tex]Angles 4 and 3 are same-side interior angles, then they are supplementary, that is,
[tex]\begin{gathered} m\angle4+m\angle3=180\degree \\ 34\degree+m\angle3=180\degree \\ m\angle3=180\degree-34\degree \\ m\angle3=146\degree \end{gathered}[/tex]Angles 7 and 5 are vertical angles, then they are congruent, that is,
[tex]\begin{gathered} m\angle5=m\angle7 \\ m\angle5=146\degree \end{gathered}[/tex]Angles 1 and 3 are vertical angles, then they are congruent, that is,
[tex]\begin{gathered} m\angle1=m\angle3 \\ m\angle1=146\degree \end{gathered}[/tex]Whats the Point-Slope Equation for the line that goes through
(-3, 5) and (-7, 4)
Answers
Step by step
The point slope formula is y − y1 = m (x − x1 )
First we need to find “m” or slope
Slope formula is (y2 - y1) over (x2 - x1)
4-5 over -7 - -3
-1 over -4 or 1/4
Now for point slope formula using (-3, 5)
y - 5 = 1/4 (x + 3) (x - -3 is same as x + 3)
Distribute
y -5 = 1/4x + 3/4
add 5 to both sides to solve for y
y -5 +5 = 1/4x + 3/4 + 5
Combine
y = 1/4x + 5 3/4 is your answer
Photo plus charges $2 for each print plus a $6 processing fee. Picture time charges $3 for each print plus a $4 processing fee. for what number of prints is the price the same at both stores
Answers
According to the rules of significant figures 7.898 + 5.23 = 13.13. This is because the least precise value in the problem is 5.23, which is precise only to the hundredths digit, so the answer must also be rounded to the nearest hundredths.True or False
Answers
The given expression is
[tex]7.898+5.23=13.13[/tex]It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.
In other words, the answers can't be more precise than the least precise number in the sum.
Therefore, the given statement is true.
How many more votes did bill clinton get than george bush? about 44 million about 6 million about 25 million
Answers
Answer:
Step-by-step explanation:
B - 6 million
b. 6 Million
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A basket contains 12 black marbles and 8 blue marbles. What is the probability Josiah will
select a blue marble, replace it, and then a black marble? Express your answer as a percent.
Answers
Answer:
24%=====================
GivenBlack marbles = 12,Blue marbles = 8.SolutionTotal number of marbles:
12 + 8 = 20Probability of selecting a blue marble:
P(blue) = number of blue / total = 8/20 = 2/5Probability of selecting a black marble after replacing the blue:
P(black) = number of black / total = 12/20 = 3/5Probability of selecting blue and black marbles in same order with replacement:
P(blue, then black) = 2/5*3/5 = 6/25 = 24/100 = 24%A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals, then how many of them can be dogs in a ratio
Answers
Answer:We have 70 dogs
Step-by-step explanation:
dogs: cats: total5 2 7We want 98 animals98/7 =14We need to multiply each number by 14dogs: cats: total…
hope this helps
explain how you got the answer please
Answers
Answer:
I cannot include a picture, but the slope is -2/3, and the y-intercept is (0, 3).
Step-by-step explanation:
When given an equation like this, remember the formula y=mx+b that you should have learned. This formula is the slope-intercept formula that you can use. The m is the slope and the b is the intercept. In the equation, the x is what we are trying to find.
y=-2/3x+3
y=mx+b
m=-2/3
b= (0,3)
So, graph the slope as -2/3 and the y-intercept as (0,3).
Hope this helps!