Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 9x^4 − 35x^2 − 4(x − 2)
[tex]9x^4-35x^2-4[/tex]
Lets divide this polynomial by x - 2
9x^4 0x³ -35x² 0x -4 | x - 2
-9x^4 +18x³ | 9x³
18x³ -35x² 0x -4 | x - 2
-18x³ 36x² | 9x³ + 18x²
x² 0x -4 | x - 2
-x² +2x |9x³ + 18x² + x
2x -4 |x - 2
-2x + 4 |9x³ + 18x² + x +2
0
Since there is no rest for the division, x - 2 is a factor of the given polynomial:
[tex]9x^4-35x^2-4=(x-2)\cdot(9x^3+18x^2+x+2)[/tex]At the end of a party, 3/4 cup of smoked fish dip is left. Jim divides 4/5 of the leftover smoked fish dip equally between 2 friends. How much dip does each friend get?
Each friend gets 3/10 or 0.3 dips if, at the end of a party, 3/4 cup of smoked fish dip is left.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let each freind get x part.
The 3/4 part dipped:
The value of x can be found as follows:
x = (3/4)(4/5) ÷ 2
x = 3/(5×2)
x = 3/10
x = 0.3
Thus, each friend gets 3/10 or 0.3 dips if, at the end of a party, 3/4 cup of smoked fish dip is left.
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please look at screenshots
Answer:
c
Step-by-step explanation:
it not linear relationship
A college student realized that he was spending too much money on music. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towardsmusic. How much can he spend in December, taking into consideration that in the other 4 months he spent $20, $70, S30, and $85, respectively? Round your answerto two decimal places. If necessary
The mean is given by the sum of all the months divided by the number of months.
Then:
Let's set x for the spending money for December.
There are 5 months.
Hence:
[tex]\operatorname{mean}=\frac{20+70+30+85+x}{5}[/tex]We need to have a mean equal to $50. Set mean = 50.
[tex]50=\frac{20+70+30+85+x}{5}[/tex]Solve for x:
[tex]\begin{gathered} 50=\frac{20+70+30+85+x}{5} \\ 50=\frac{205+x}{5} \\ 5\cdot50=205+x \\ 250=205+x \\ \text{Therefore:} \\ x=250-205 \\ x=45 \end{gathered}[/tex]Hence, If the student wants to complete his goal, he will need to spend $45 in December.
10s = 12 help!!!! pls
Answer:
12-10=2 which means an extra 2seconds was added therefore it's impossible for 10seconds to be equal to 12
The Whistling Straits Corporation needs to raise $40 million to finance its expansion intonew markets. The company will sell new shares of equity via a general cash offering toraise the needed funds. If the offer price is $35 per share and the company'sunderwriters charge a 11 percent spread, how many shares need to be sold?
Solution
Explanation:
Total Finance Needed = $40,000,000
Offer price per share = $35 per share
Charges of underwriter = 11%
Total Number of shares needed to be sold = ( $40,000,000 / $35 ) x 111%
Total Number of shares needed to be sold = 1,142,857 x 111%
Total Number of shares needed to be sold = 1,267,571 shares
The Whistling Straits Corporation needs 1,267,571 shares to raise $40 million
i know the answer i just don’t know the steps.
Answer:
x = 4Step-by-step explanation:
1/2x - 2 = 0
1/2x = 2
x = 2 * 2/1
x = 4
----------------------------
check1/2(4) - 2 = 0
2 - 2 = 0
0 = 0
the answer is good
y + 3 = 2/5(x + 5) , put that into standard form
Given:
[tex]y+3=\frac{2}{5}(x+5)[/tex]The standard form of the linear equation is,
[tex]Ax+By=C[/tex]Simplify the given equation,
[tex]\begin{gathered} y+3=\frac{2}{5}(x+5) \\ 5(y+3)=2(x+5) \\ 5y+15=2x+10 \\ 2x-5y=15-10 \\ 2x-5y=5 \end{gathered}[/tex]Answer: Standard form is 2x - 5y = 5
What is the value of 7 + z ÷ 2, when z = 10?
Answer:
12
Step-by-step explanation:
7 + z ÷ 2 ,z=10(bodmas , division is the first)
7 + 10 ÷2
7 + 5
12
Answer:
12
Step-by-step explanation:
Substitute 10 for z
7+10 ÷ 2
divide first
7+5=
12
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different gift-wrapping options are available at this store?
14*12*8=1344
1344 options
HELP! How do I solve this!!?
x ki power 3 is the answer
Step-by-step explanation:
use x is equal to root over x
Evaluate the expression when m = -4. M^2+6m+9
The answer is 1
operations of rational algebraic expression 1/4+2/4
Answer:
3/4
Step-by-step explanation:
10 Caleb divides powers of 10 using exponents . He says that 0.6 divided by increases the value of the 6. Do you agree with Caleb ? 10 ^ 2 Explain your thinking
I disagree with Caleb because the value decreased after the quotients are carried out
How to determine the true statement?From the question, the statement is given as
He says that 0.6 divided by 10² increases the value of the 6.
The mathematical expression of the above statement is represented as
0.6 divided by 10²
So, we have
0.6/10²
When the above quotient is evaluated, we have
0.6/10² = 0.006
The above result is different from Caleb's reasoning
This is so because 0.6 divided by 10² decreases the value of the 0.006, instead of increasing the value to 6, as stated by Caleb
Hence, Caleb's reasoning is incorrect
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Complete question
Caleb divides powers of 10 using exponents. He says that 0.6 divided by 10² increases the value of the 6.
Do you agree with Caleb? Explain your thinking
XZ¯¯¯¯¯¯¯¯ has a point Y between points X and Z. XY=17, YZ=4x+9, and XZ=11x−9.
Applying the segment addition postulate, the value of x = 5.
What is the Segment Addition Postulate?According to the segment addition postulate, if three lines, X, Y, and Z are collinear points, that is they lie on a straight line such that Y is between points X and Z, then the sum of the lengths of segments XY and YZ would be equal to the length of segment XZ.
Therefore:
XY + YZ = XZ [segment addition postulate]
Given:
XY = 17
YZ = 4x + 9
XZ = 11x − 9.
Substitute
17 + 4x + 9 = 11x - 9
26 + 4x = 11x - 9
26 + 9 = 11x - 4x
35 = 7x
35/7 = x
x = 5
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Percents are the result of expressing numbers as a part of
Answer:
percentage of fractions
Washing his dad's car alone, Matt takes 6 hours. If his dad helps him, then it takes 2 hours. How long does it take Matt's dad to wash the car by himself?
If it takes 6 hours for Matt to wash the car, then he washes at a rate of 1/6 cars per hour:
[tex]\begin{gathered} \frac{1}{x}=6 \\ x=\frac{1}{6} \end{gathered}[/tex]Let y be the time in which Matt's dad washes the car and state an equation that describes the situation in which Matt and his dad wash the car together:
[tex]\begin{gathered} \frac{1}{6}+\frac{1}{y}=2 \\ \frac{1}{y}=2-\frac{1}{6} \\ \frac{1}{y}=\frac{11}{6} \\ y=\frac{6}{11} \end{gathered}[/tex]It means that he washes the car in 6/11 hours (approximately 0.54hours).
Can anyone answer this question fast?
the rest of the question say find the length of the whole secant of the bottom
According to the Intersecting Secants Theorem,
[tex]\begin{gathered} x\times6=(12+8)\times8 \\ 6x=20\times8 \\ x=\frac{80}{3} \\ x=26.\bar{66} \\ x\approx26.67 \end{gathered}[/tex]Thus, the first option is the correct choice.
f(x)=x^2-8, g(x)=17-x
(f/g)(-4)=?
The quotient between the two functions evaluated in -4 is equal to 8/21.
How to find the quotient?
Here we have the two functions:
f(x) = x^2 - 8
g(x) = 17 - x
And we want to find:
(f/g)(-4)
That can be rewritten as:
f(-4)/g(-4)
By evaluating the two functions we get:
f(-4) = (-4)^2 - 8 = 16- 8 = 8
g(-4) = 17 - (-4) = 17 + 4 = 21
replacing that in the quotient we get
f(-4)/g(-4) = 8/21
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What is the reflection image of p (0,0) after two reflections,first across x=4 and Than across y= -3
After two reflections, P(0, 0)'s reflection image is P (8,-6).
What do we mean by reflection of image?A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when it is equidistant from every corresponding point in the other figure.The given point is(0,0)
A point will reflect across x = 4 ,then(x,y) → (-x+8,Y)(0,0)→(-0+8,0)(0,0)→(8,0)A point will reflect across x = -3 ,then(X,Y)→(X,-Y-6)(8,0)→(8,-0-6)(8,0)→(8,-6)Therefore, P' is the reflection image of P(0, 0) following two reflections (8,-6).
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Philip purchased s pairs of shoes for the school year. He also purchased jeans and T-shirts.
The number of pairs of jeans is 3 more than the number of pairs of shoes and the number of
T-shirts is twice as many as the number of pairs of jeans. How many shoes did he purchase if he purchased a total of 17 items?
Answer:
3 pairs of shoes
Step-by-step explanation:
You can represent the amount of each item with these:
2(jeans) = t-shirts
shoes + 3 = jeans
shoes + t-shirts + jeans = 17
By plugging in 3 for s, you get:
(3) + 3 = 6
(6) × 2 = 6
3 + 6 + 6 = 17
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Does the equation y-250x=500 represent the same relationship between the distance from the start of the trail and the elevation? Explain your reasoning pls
The equation of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Isolate y from the given equation to write it in slope-intercept form:
[tex]\begin{gathered} y-250x=500 \\ \Rightarrow y=250x+500 \end{gathered}[/tex]The given equation corresponds to a line with slope 250 and y-intercept 500.
From the image, we can see that the y-intercept is indeed 500, since it is the value of y when x=0.
Notice also that for each increase of 1 unit of the variable x, the variable y increases 250 units. Then, the slope of the graph is 250, the same as the slope of the equation.
We can also check if the equation represents the same line as the graph by evaluating th
Write the correct expression for the following statement:
A difference of x and six
What was done to the linear parent function, f(x) = x, to get the functiong(x) = ?A. Horizontally compressed by a factor of 6B. Vertically stretched by a factor of 6C. Vertically compressed by a factor of 6D. Shifted unit up
Given
Two functions
[tex]\begin{gathered} f(x)=x \\ g(x)=\frac{1}{6}x \end{gathered}[/tex]Procedure
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
I only need help with the gauss elimination and back substitution, and cramers rule. I know hwo to do everything else.
To solve the equation by Gauss elimination method first convert the equation in matrix form.
The cramers rule is as follows;
HELPP ASPP PLS HELP Combine "like terms" in this expression:
6x - 8x - 4y - x + 5y - 2y
A. -6x - y
B. -3x + y
C. -3x -2y
D. -3x - y
Answer:-3x-y
Step-by-step explanation:
6-8-1=-3
-4+5-2=-1
-3x-y
which expression is equivalent to (4^2)^-2?
Answer:
[tex](4^2)^{-2}=\frac{1}{x^4}[/tex]Explanation: We need to simplify the given expression to get an equvilant expression: The given is as follows.
[tex](4^2)^{-2}[/tex]Simplification:
Using the following exponent property:
[tex](x^a)^{-b}=x^{a\times(-b)}^{}=x^{-ab}^{}=\frac{1}{x^{ab}}[/tex]The equvilant expression we get is:
[tex](4^2)^{-2}=x^{2\times-2}=x^{-4}=\frac{1}{x^4}[/tex]Write a quadratic function in standard form, with a leading coefficient of 1, given x-intercepts 7 and 10. Use "y" as the dependent variable
and "x" as the independent variable.
Standard form of quadratic function with leading coefficient 1,
x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
As given in the question,
Given :
y is the dependent variable of the required quadratic function.
x is the independent variable of the required quadratic function.
Leading coefficient of quadratic function is 1
X-intercept of the required function is 7 and 10
Standard form of required quadratic function is equal to
y = k (x-a)(x -b)
Here k=1 , a=7 , b=10
y = 1 (x -7)(x - 10)
⇒ y = x² -7x -10x +70
⇒ y= x² -17x +70
Therefore, standard form of quadratic function with leading coefficient 1, x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
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I believe the answer to be 0.15 but I just want to make sureSuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.89? Please do not round your answer
First, we need to find the z-score for the measure x=3.89. This is given by
[tex]z=\frac{x-\mu}{\sigma}=\frac{3.89-2.57}{0.44}[/tex]which gives
[tex]z=3[/tex]Now, from the empirical rule :
we can see that
[tex]P(x>3.89)=P(z>3)\approx0.15\text{ \%}[/tex]Then, the answer is 0.15%