6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
Given,
The expression : 6x³ + 2x² + 3x - 4
We have to divide the given expression by x² + 3x - 4.
Let's take 6x³ + 2x² + 3x - 4 as p(x) and x² + 3x - 4 as g(x).
If p(x) is divisible by the factors of g(x), then p(x) is divisible by g(x).
So, let's factorize x² + 3x - 4
x² + 3x - 4 = (x - 1) (x + 4)
Now,
p(x) = 6x³ + 2x² + 3x - 4
By using remainder theorem,
If p(1) = 0 and p(4) = 0, then p(x) is divisible by g(x).
So,
p(1) = 6 × 1³ + 2 x 1² + 3 x 1 -4
p(1) = 6 + 2 + 3 - 4
p(1) = 11 - 4
p(1) = 7
Next,
p(4) = 6 x 4³ + 2 x 4² + 3 x 4 - 4
p(4) = 6 x 64 + 2 x 16 + 12 - 4
p(4) = 384 + 32 + 12 - 4
p(4) = 424
Here, p(1) and p(4) is not 0.
So, p(x) is not divisible by g(x).
That is, 6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
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You are buying a house and will borrow $330,000 on a 25-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.15 percent. Alternatively, she tells you that you can “buy down” the interest rate to 3.8 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
The number of points the borrower needs to buy down interest rate to 3.8% is 0.350 points
What is the desired annual percentage rate for the borrower?
The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%
difference in interest rate=4.15%-3.8%
difference in interest rate=0.35%
We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point
number of points required to buy down interest=1 point*0.35%
number of points required to buy down interest=0.350
In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%
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PLEASE ANSWER ALL OF THEM:))) AND LABEL ANSWERS!!
Answer:
Step-by-step explanation:
13-b
put ixes in equations and see which is correct that b is correct.
14- c
in this question put known points in equations.
A passenger train's distance traveled is monitored over time. The results are displayed in this table.
Time (h)
2
3
4
5
Distance traveled (mi)
60
120
180
240
300
What is the constant of proportionality of this proportional relationship?
Enter your answer in the box.
Answer:
Step-by-step explanation:
60
4 friends buy 16 pizzas. Each pizza is cut into
12 pieces. Each person eats the same number
of pieces.
How many pieces does each person eat?
On a map of the Thunderbird Country Club golf course, 1.5 inches equals 15 yards. How
long is the 15th hole if the map shows 17.5 inches?
175 yards long is the 15th hole if the map shows 17.5 inches.
hole = c yards
1.5 / 15 = 17.5 / c
1.5 c = 15 * 17.5
1.5 c = 262.5
c = 175 yards
A length unit equal to 36 inches, or 3 feet (see foot), in the United States Customary System, or 0.9144 metre in the International System of Units. A cloth yard is 37 inches long, and it was also the standard length for arrows.
The yard is an English unit of length that equals 3 feet or 36 inches in both the British imperial and US customary measurement systems. Since 1959, it has been standardized as 0.9144 meter by international agreement. One mile is equivalent to 1,760 yards. The survey yard in the United States is slightly longer.
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what is an equivalent fraction for 6/10
Answer:
3/5, 9/15 - some equivalent fractions for 6/10
write in a number in which the value of the 8 is ten times greater than the value of the 8 in 8304?
Thee number in which case has the value of the 8 ten times greater than than the value of the 8 in 8304 as required in the task content is; 83450.
Which number has the value of the 8 is ten times greater than the value of the 8 in 8304?It follows from the task content that the number which satisfies the condition that, the value of its 8 is ten times greater than the value of the 8 in 8304 is to be determined.
It follows from place value that the 8 in 8304 has a value of; 8 × 1000 = 8000.
Hence, an example of a number that is ten times greater is; 10 × 80,000.
Ultimately, an example of the required number as in the task content is; 83450 where it's 8 digit is ten times greater than that in 8304.
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-Solve the system. y - 10=3x
(2y=6x+20
infinite solutions
no solution
(10,40)
(2,13)
Step-by-step explanation:
[tex]y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20[/tex]
you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.
Prove that math is an art and not science.
Your friend tells you he is going to start investing and would like to earn a 10% return. He says stocks make him nervous, so he will only be investing 10% in stocks and the remaining 90% will be invested in bonds. What would you say to him?
If you invest a 100% in stocks however, you stand to make an average of 9.2% but a chance of a worst return of -40.40%.
In the given statement is:
Your friend tells you he is going to start investing and would like to earn a 10% return. He says stocks make him nervous, so he will only be investing 10% in stocks and the remaining 90% will be invested in bonds.
Based on the graph given on bond and stock returns, the average return if one invested 100% in bonds or in stocks is 5.0% and 9.2% respectively.
What happens if you invest 100% in either stocks or bonds?
The graph shows that when you invest a 100% in bonds, the average return you stand to make it 5.0% while the worst return is -2.1%.
If you invest a 100% in stocks however, you stand to make an average of 9.2% but a chance of a worst return of -40.40%.
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What two numbers are a distance of 7 away from 2 on the number line?
Answer: 9 and -5
Step-by-step explanation: 2+7=9 and 2-7=-5
Please help me! I have a fe of this for me to finish my homework! Please
(LOTS OF POINTS ANSWE FAST) multiply (5 4/7) (-2 2/5)
Answer:
-13 13/35
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation: Just took it
Evalute f(x) = x² + 1 for f(10)
Answer:
101
Step-by-step explanation:
Because if f(x) = [tex]x^{2}[/tex] + 1 and f(x) is f(10), this means that x = 10. If x = 10, then you can plug that into the equation, getting you [tex]10^{2}[/tex] + 1. [tex]10^{2}[/tex] is 100, plus 1 is 101.
Hope this helps!
-10/17 divided by (-15/17)
Answer:
0.66
Step-by-step explanation:
A spherical tank has a capacity of 750 gallons. Using the fact that one gallon is about 0.1337 , find the radius of the tank to the nearest hundredth of a foot.
The radius of the spherical tank of capacity 750 gallons to the nearest hundredth is 2.88 ft.
How much s a gallon?
In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L[1] (231 cubic inches); and the US dry gallon ("usdrygal"), which is defined as 18 US bushel (exactly 4.40488377086 L).
Given data: 1 gallon ≈ 0.1337 ft³
Then, 750 gallons = 0.1337 x 750 ≈ 100.275 ft³
We know, Volume of sphere, [tex]V=\frac{4}{3}\pi r^{3}[/tex]
then, r = [tex]\sqrt[3]{\frac{3}{4\pi }V }[/tex]
= [tex]\sqrt[3]{\frac{3}{4\pi } 100.275}[/tex]
= [tex]2.88 ft.[/tex]
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I need help! Can someone help me with these problems please!
Regarding the average rate of change of the function, it is found that:
a) 245 habitants per year between 1998 and 2001.
b) The average rate of change was of -328.5 habitants per year between 2002 and 2004.
c) The rate of population increase was greater between 1998 and 2001.
d) The rate of population decrease was greater between 2002 and 2004.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, we have that:
In 1998 the population was of 856.In 2001 the population was of 1591.Hence the rate is:
(1591 - 856)/3 = 245.
The average rate of change was of 245 habitants per year between 1998 and 2001.
For item b, we have that:
In 2002 the population was of 1483.In 2004 the population was of 826.Hence the rate is:
(826 - 1483)/2 = -328.5.
The average rate of change was of -328.5 habitants per year between 2002 and 2004.
Hence:
c) The rate of population increase was greater between 1998 and 2001.
d) The rate of population decrease was greater between 2002 and 2004.
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A triangle has a perimeter of 13. If it has
sides of x/2,( x – 5), and (x - 2) lengths,
then:
a) find the value of x
b)find the length of the longest side
find the value of x.
find length of the longest side.
Step-by-step explanation:
perimeter=s+s+s
p=x/2+x-5+x-2
13=x/2+x-5+x-2
26=x+x+x-10-4
26=3x-14
26+14=3x
3x/3=40/3
x=13.3cm
b.
x/2=6.65
x-5=8.3
x-2=11.3
longest side=11.3cm
What are the coordinates for the image of the figure E(0,4), F(2,2), G(0,0), D(-4,3) if it has been dilated with a scale factor of 1/4
Answers:
E ' = (0, 1)
F ' = (0.5, 0.5)
G ' = (0, 0)
D ' = (-1, 0.75)
Notes: 0.5 = 1/2 and 0.75 = 3/4
================================================
Explanation:
Assuming the origin is the center of dilation, then we multiply each coordinate by the scale factor of 1/4 = 0.25
For instance, the point E(0,4) moves to E ' (0, 1) since
x coordinate: 0*0.25 = 0y coordinate: 4*0.25 = 1Do the same for the other points.
Let L be the line that passes through the points with coordinates (1,1) and (-1,3).
(a) Determine the equation (in the form y = mx + b) of the line L.
(b) Determine the equation of the line K that passes through the (0, -1) and is perpen-
dicular to the line L.
(c) Find the coordinates of the point at which the lines and K intersect.
(a). The equation of the line L in the form of y = mx + b is y + 2x = 0.
(b). The equation of the line K that passes through the point (0, -1) and is perpendicular to the line L is y = 2x - 1.
(c). The intersection of the lines and K is located at a location with the coordinates (0,-1).
Define equation of line.The equation of a line has the usual form axe + by + c = 0. Here, x and y are the variables, a and b are the coefficients, and c is the constant term. You may also find and see the equation of a line in the slope-intercept form, point-slope form, two-point form, intercept form, and normal form.
The formula of slope is given by m = (y₂-y₁)/(x₂-x₁).
Here, m is the slope of the line.
(x₁, y₁) and (x₂, y₂) are the two points of the line.
Now put the value of x₁, y₁, x₂, y₂ in
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
m = [tex]\frac{3-1}{-1-1}[/tex]
m = 2/-1
m = -2
The slope of the line perpendicular is:
mₐ = - 1/m
mₐ = -1/-2
mₐ = 2
(a) The equation (in the form y = mx + b) of the line L.
(y-y₁) = m(x-x₁)
(y-1) = -2(x-1)
y-1 = -2x-1
y = -2x
y + 2x = 0
(b) The equation of the line K that passes through the (0, -1) and is perpendicular to the line L.
x = 0 and y = -1
y = mx + b
y = 2x + b
-1 = 2×0 + b
-1 = b
b = -1
Substituting the above in y = mx + b to get:
y = mx + b
y =2x + (-1)
y = 2x - 1
(c) The coordinates of the point at which the lines and K intersect.
y = 2x - 1
y+2x+1=0
(2x-1)+2x+1=0
4x =0
x = 0, y = -1
The intersection of the lines and K is located at a location with the coordinates (0,-1).
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Which expression is equivalent to 8(12+30)?
A) 8 + 12 x 8 + 30
B) 8 x 12 + 8 x 30
C) 8 x 12 x 8 x 30
D) 8 x 12 + 30
Answer:
b) 8 × 12 + 8 × 30
Step-by-step explanation:
Now we have to,
→ Find the equivalent expression.
The property we use,
→ Distributive property.
The expression is,
→ 8(12 + 30)
Let's simplify the expression,
→ 8(12 + 30)
→ 8(12) + 8(30)
→ (8 × 12) + (8 × 30)
→ 96 + 240
→ 336
Hence, the option (b) is correct.
Suppose a deep sea diver dives from the surface to 206 feet below the surface. He then dives down 18 more feet. Use integers to represent this situation. Then find the diver's present depth. (Simplify)
Answer:
Step-by-step explanation:
Expand and simplify 4(2x - 1) + 3(2x + 5)
Answer:
14x+11
Step-by-step explanation:
An urn contains twenty chips, numbered 1 through
20. Two are drawn simultaneously. What is the probabil-
ity that the numbers on the two chips will differ by more
than 2?
The probability that the numbers on the two chips will differ by more than 2 will be ( 1 / 2 ).
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that an urn contains twenty chips, numbered 1 through 20. Two are drawn simultaneously.
Number of favorable outcomes = ( 4 - 2 ) , ( 3 - 1 ) , ( 6 - 4 ) , ( 10 - 8 ), ( 11 - 9 ), ( 7 - 5 ), ( 14 - 12), ( 15- 13 ) , ( 18 - 16 ), ( 19 - 17 ) = 10
Number of samples = 20
Probability = Number of favorable outcomes / Number of sample
Probability = 10 / 20
Probability = 1 / 2
Therefore, the probability that the numbers on the two chips will differ by more than 2 will be ( 1 / 2 ).
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cual es el resultado de y=−2x+5
Answer:3
Step-by-ste
la respuesta es 3 porque si sumas -2x a 5 pues -2 es. un numero negativo y 5 es positivo restas 5-2 y obtienes 3
The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation’s central office during the year. A random sample of 25 clerical workers reveals the following: Absenteeism: days, days. 12 clerical workers were absent more than 10 days. Construct a 95% confidence interval estimate for the mean number of absences for clerical workers during the year. Interpret. (Assume that the population is normally distributed)
The 95% confidence interval estimate for the mean number of absences for clerical workers during the year is (8.132, 11.268).
What is confidence interval?It should be noted that the mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given a = 0.05, Z(0.025) = 1.96 (from standard normal table).
The 95% confidence interval will be:
xbar +/- Z*s/vn
= 9.7 +/- 1.96*4/✓(25)
= (8.132, 11.268)
Therefore, the 95% confidence interval is (8.132, 11.268).
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Can someone help wit this problem I’m confused on it
Answer:
1/9
Step-by-step explanation:
When the quantities are proportional, you are able to find the constant of proportionality by y/x. If you take each one of the y's listed and divide it by x, you will get 1/9.
For example 1 2/9 ÷11
1 2/9 is the same at 9/9 + 2/9 or 11/9
[tex]\frac{11}{9}[/tex] ÷ 11 is the same as [tex]\frac{11}{9}[/tex] ÷ [tex]\frac{11}{1}[/tex] To divide with fractions, you multiply by the reciprocal.
[tex]\frac{11}{9}[/tex] x [tex]\frac{1}{11}[/tex] The 11 can cancel out and we are left with [tex]\frac{1}{9}[/tex]
Answer: r = [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
y = rx
finding r (substitute y and x):
5 = r x 45
5/45 = r
r = [tex]\frac{5}{45} = simplify = \frac{1}{9}[/tex]
checking:
rx = y
[tex]\frac{1}{9}[/tex] x 11 = 1 [tex]\frac{2}{9}[/tex]
[tex]\frac{11}{9}[/tex] = 1 [tex]\frac{2}{9}[/tex]
convert mixed fraction into improper fraction
[tex]\frac{11}{9}[/tex] = [tex]\frac{11}{9}[/tex]
correct
A tower has a revolving restaurant 785 feet above the ground. The restaurant makes a
complete revolution every 90 minutes. While a visitor was at the tower, the restaurant
rotated through 82°. How long was the visitor at the tower?
The visitor was at the tower for ______
minutes.
Answer:
1 revolution is 360 degrees
1 hour = 60 minutes
360/60 = 6
so it rotates 6 degrees every minute
135/6 = 22.5 minutes
What is 5 1/3 PERCENT as a fraction in simplest form?
In simplest form, I believe it would be 4/75.
Anumeha is mowing lawns for a summer job. For every mowing job, she charges an initial fee of $10 plus a constant fee for each hour of work. Her fee for a 5-hour job, for instance, is $35
Let y represent Anumeha's fee (in dollars) for a single job that took x hours for her to complete.
The equation that can represent the fee for x hours is y = 10 + 5x.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
We have,
Initial fee = $10
Let the constant fee for each hour of work = M
Fee for 5 hours of work = $35
Every mowing job for 5 hours = Initial fee + constant fee for 5 hours
$35 = $10 + M x 5
35 = 10 + 5M
25 = 5M
M = 5
So,
If y represents Anumeha's fee (in dollars) for a single job that took x hours for her to complete.
We can write an equation as:
y = 10 + 5x
Thus the equation that can represent the fee for x hours is y = 10 + 5x.
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