Answers
Answer:
7z^2/y -8z^4y -(9/2)z^2y^4
Step-by-step explanation:
The quotient of division of a polynomial by a monomial is the sum of quotients of each of the terms divided by the monomial. "Simplify" in this context generally means that no common factors remain factored out.
Rules of exponentsThe rules of exponents apply:
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
DivisionThe problem is effectively three (3) division/simplification problems.
[tex]\dfrac{-14z^4y^2+16z^6y^4+9z^4y^7}{-2z^2y^3}=\dfrac{-14z^4y^2}{-2z^2y^3}+\dfrac{16z^6y^4}{-2z^2y^3}+\dfrac{9z^4y^7}{-2z^2y^3}\\\\=7z^{4-2}y^{2-3}-8z^{6-2}y^{4-3}-\dfrac{9}{2}z^{4-2}y^{7-3}=\boxed{\dfrac{7z^2}{y}-8z^4y-\dfrac{9}{2}z^2y^4}[/tex]
__
Additional comment
We have elected to retain the original order of variables (z then y) and the original order of terms. Ordinarily, standard form would have the variables in alphabetical order (y then z) and the terms in order by decreasing degree. This order of terms also makes the leading coefficient positive. (The minus sign for a negative leading coefficient sometimes gets lost.)
Related Questions
The tile edging for a bathroom is in the shape of a triangle. The area of a triangle with base b and height h is A=1/2 bh. Find the area of the tile if the base measures 3.5 cm and the height measures 8 cm.
Answers
Final answer:
Area of tile is 14 cm².
Step-by-step explanation:
Area of triangle is:
[tex]\frac{1}{2} base.height[/tex]
Putting [tex]b=3.5[/tex] and [tex]h=8[/tex] in [tex]\frac{1}{2} base.height[/tex]
[tex]\frac{1}{2}bxh=\frac{1}{2}3.5x8[/tex]
[tex]=3.5x4[/tex]
[tex]=14[/tex]
In your own words, explain why every natural number is also a rational number but not every rational number is a natural number.
Answers
Answer:
Every natural number is also a rational number but not every rational number is a natural number because the set of natural numbers is a subset of the set of rational numbers.
Explanation:
Since all natural numbers, n can be written as n/1. Thus all natural numbers are rational. Since 3/4 is a rational number but not natural thus all rational numbers are not natural.
Hint:
Natural numbers : All positive numbers except zero.
Rational numbers: All numbers in the form of p/q, where q ≠ 0 (p,q are integers)
What is the factored form of 8x² + 12x?
O 4(4x² + 8x).
O 4x(2x + 3)
O8x(x + 4)
O 8x(x² + 4)
Answers
Answer:
Step-by-step explanation:
Solution
The factored form is going to be the HCF (highest common factor)
The fest way to do this is to turn this into primes.
8x^2 + 12x
8x^2 = 2*2*2*x*x
12x = 2 * 2 * x
Now bold the HCF.
8x^2 = 2*2*2*x*x
12x = 2 * 2 * x
The HCF = 2*2*x
Divide that into the original question to determine the second factor.
8x^2 / 4x = 2x
12x / 4x = 3 Notice how the x-s cancel
Answer
4x (2x + 3)
Solve for x. Round to the nearest tenth, if necessary.
X
H
Answers
In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.
Trigonometric Functions: SOH-CAH-TOA
Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.
tan(23) = x / 2
x = tan(23) * 2
x = 0.8489
x = 0.8
Hope this helps!
Step-by-step explanation:
ATTACHED IS THE SOLUTION!The bisection method is being used to calculate the zero of the following function between x = 0 and x = 1.
Answers
The bisection method will converge to the solution after three iterations.
How to illustrate the information?It should be noted that after one iteration, x1 will be:
= (1 + 9)/2
= 10/2
= 5
Since f(x¹) > 0, x² will then replace x1. Now x0 = 1 and x1 = 5.
After the second iteration, x2 will be:
= (1 + 5)/2
= 3
Also, this is greater than 0. The third iteration will be:
m= (1 + 3)/2
= 2.
Now, f(2) = 2⁴ -2³ - 2² - 4
= 0
Therefore, the method converges exactly to the root in 3 iterations.
Complete question:
The bisection method is applied to compute the zero to a function f(x) = x⁴ - x³ - x² - 4 in the interval (1, 9). The method converges y a solution after .............. iterations.
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Find the error in the calculations below:
Line (1): -3(2x + 5) <21
Line (2): -6x
15 < 21
Line (3): -6x < 36
Line (4): x <- 6
Line (5):
-
O The error occurred from line (1) to line (2).
O The error occurred from line (4) to line (5).
O The error occurred from line (3) to line (4).
O The error occurred from line (2) to line (3).
Answers
Answer: Line 3 to line 4
Step-by-step explanation:
When dividing by a negative, you need to flip the inequality sign.
Question Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function? Select all correct answers. Select all that apply: {(-3, 10), (-2, 13), (3, 13), (8, 12)} {(-2, 13), (-5, 9), (-5,-5), (-3,-1)} □ {(4,-4), (4,2), (-3, 4), (-2,-5)} □ {(-4,11), (5, 10), (-3, 3), (-1, 10)} □ {(1,7), (1,-5), (0, 13), (2, 1)}
Answers
The ordered pairs that represent functions are:
{(-3, 10), (-2, 13), (3, 13), (8, 12)} {(-4,11), (5, 10), (-3, 3), (-1, 10)}How to determine the ordered pairs?For a set of ordered pairs to represent a function, the following must be true:
The x value must point to only one y value
In {(-3, 10), (-2, 13), (3, 13), (8, 12)} and {(-4,11), (5, 10), (-3, 3), (-1, 10)}, the x value point to only one y value
Hence, {(-3, 10), (-2, 13), (3, 13), (8, 12)} and {(-4,11), (5, 10), (-3, 3), (-1, 10)} are functions
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The weights in ounces of a sample of running shoes for men and women are shown. Test the claim that the means are different. Use the P-value method with α = 0.05.
Men
9.6 12.6 11.2 15.0 11.6 13.3 12.5 12.6 12.7 13.6
Women
10.2 9.2 9.5 9.9 8.8 10.4 10.5 10.6 10.4 9.9
8.9 9.8 9.9 10.1 12.0
Group of answer choices
Since the P-value is greater than α = 0.05, do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the weights of running shoes.
Since the P-value is less than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes.
Since the P-value is less than α = 0.05, do not reject the null hypothesis. There is not enough evidence to support the claim that there is a difference in the weights of running shoes.
Since the P-value is greater than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes.
Answers
The conclusion will be; Since the P-value is less than α = 0.05, reject the null hypothesis. There is enough evidence to support the claim that there is a difference in the weights of running shoes. Option B.
What is the conclusion?Parameters
Group 1
n1=10
x=18.47
[tex]s^2_1[/tex]=2.12
Group 1
n2=15
x2=10.01
[tex]s^2_2[/tex]=0.62
Generally, the equation for the hypothesis is mathematically given as
[tex]H_0=\mu_1 =\mu=2 \\\\H_a= \mu_1 \neq \mu=2[/tex]
Therefore
[tex]t=\frac{12.47-10.01}{\sqrt{\frac{2.12}{10}+\frac{0.61}{15}}}[/tex]
t=4.8966
In conclusion, The pvalue from table is
p-value (4.8966, [tex]\alpha[/tex] =0.06)
[tex]p-value < \alpha=0.05[/tex]
since [tex]p-value < \alpha=0.05[/tex] we reject the null hypothesis and state that there is no difference b/w the two means.
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Which figure shows a line of reflectional symmetry for the letter T?
A letter T is folded at the horizontal line.
A letter T is folded diagonally.
A letter T is folded vertically through the middle.
A letter T is folded diagonally through its center.
Mark this and return
Answers
The figure that will depict a line of reflectional symmetry of letter T is: Option C: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry is defined as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, it means that two mirror images will be created.
Therefore, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
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e.Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not?
Answers
Answer:
Step-by-step explanation:
the objects which have less density than water will float
and the objects which have more density than the density of liquid will sink in liquid or will not float.
Find the sum of the first 5,000 odd numbers
Answers
Step-by-step explanation:
this is an arithmetic sequence :
a1 = 1
an = an-1 + 2 = a1 + (n-1)×2
the sum of n terms of an arithmetic sequence is
S = n×(a1 + an)/2
n = 5000
an = a1 + 4999×2 = 9999
S = 5000×(1 + 9999)/2 = 5000×5000 = 25,000,000
0,2,14,36,68,?
Find the next number in the sequence
Answers
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
Geometric sequenceGeometric sequence are sequence that increase in an exponential manner.
Given the recursive sequence 0, 2, 14, 36, 68
From the sequence
0 + 2 = 2
2 + 12 = 14
14 + 22 = 36
36 + 32 = 68
68 + 42 = 110
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
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a company promises to release model every month. each model's battery life will be 6% longer than the previous model's. if the current model's battery is 671.0 minutes, in how many months will the latest model's battery life reach 1,008.9 minutes?
Answers
The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months
How to solve geometric progression?
Each month, there is an increase by a factor of 0.06 of the previous months model.
From geometric sequence formula of aₙ = ar^(n - 1),
where;
a is first term
r is common ratio
aₙ is nth term
we have;
1,008.9 = 671 * 1.06^(n - 1)
1008.9/671 = 1.06^(n - 1)
In 1.504 = (n - 1) In 1.06
0.408 = (n - 1) * 0.058
n - 1 = 0.408/0.058
n = 7.03 + 1
n ≈ 8 months
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4. Identify a transformation of the function f(x) = x by observing the equation of the function g(x)
= x - 90.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
Answers
Answer: The base graph has been shifted down 90 units.
Step-by-step explanation:
See attached image.
A line that includes the points (-8, f) and (-6, 4) has a slope of 6. What is the value of f?
f =?
Answers
Answer:
-8
Step-by-step explanation:
Slope = (y1-y2) / ( x1-x2)
= ( f-4) / (-8 - -6) = 6
(f-4) / -2 = 6
f-4 = -12
f = - 8
Answer:
f = -8
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given:
points: (-8, f), (-6, 4)slope : 6Inserting into slope formula:
[tex]\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6[/tex]
[tex]\sf \rightarrow \dfrac{4-f}{2 } = 6[/tex]
[tex]\sf \rightarrow 4-f = 12[/tex]
[tex]\sf \rightarrow -f = 12-4[/tex]
[tex]\sf \rightarrow -f =8[/tex]
[tex]\sf \rightarrow f =-8[/tex]
Identify a horizontal or vertical stretch or compression of the function f(x) = x by observing the equation of the function g(x) = 5x.
Answers
The vertical stretch of f(x) to g(x) is a factor of 5
How to determine the dilation?The functions are given as:
f(x) = x
g(x) = 5x
Substitute f(x) = x in g(x) = 5x
g(x) = 5f(x)
In th above equation, the factor is 5.
5 is greater than 1 (this means vertical stretch)
Hence, the vertical stretch of f(x) to g(x) is a factor of 5
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Dominick borrowed $6,000 from a credit union at 9% simple interest for 30 months. What is the total amount of interest Dominick will pay throughout the life of the loan?
Answers
The total amount of interest Dominick will pay throughout the life of the loan is $1350
What is Simple Interest ?Simple Interest is the interest applied only on the Principal amount invested or borrowed .
It is calculated by the formula
I = ( P * R * T ) /100
P is the Principal
R is the Rate of Interest
T is the Time Period
Here
P = $ 6000
R= 9 %
T = 30 months = 30/12 year = 2.5 years
I = ( 6000 * 9 * 2.5 ) / 100
Interest = $1350
Therefore , the total amount of interest Dominick will pay throughout the life of the loan is $1350
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-3x+4y=2 & -6x+6y=-3 solve by elimination
Answers
Answer:(4,7/2)
Step-by-step explanation:
Find an equation of the line. Write the equation using function notation.
Through (8,8); perpendicular to 5y = x - 10
Answers
Answer:
f(x) = -5x +48
Step-by-step explanation:
A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.
Swapped coefficientsIn this instance, we find it convenient to leave the coefficient of y as positive.
5y = x -10 . . . . . . original equation
y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated
New constantAt the given point, the equation becomes ...
8 = -5(8) +c
48 = c . . . . . . . add 40
Equation of the perpendicular lineThe equation of the line is then ...
y = -5x +48
f(x) = -5x +48 . . . . . . in functional notation
QUESTION 1 -
If f(x)=3x²-5x+4, then f(-2)=
a.) - 18
b.) 26
c.) 2
d.) 6
Question 2 -
For an ordered pair (x, y) in a relation, the y element represents the _____
a.) input
b.) range
c.) domain
d.) function
Need help urgently! Will give brainliest.
Answers
Given: f(x) = 3x² -5x + 4
To find f(-2), simply substitute x = -2 in function f(x).
f(-2) = 3(-2)² -5(-2) + 4
f(-2) = 12 + 10 + 4
f(-2) = 26
Answer: 26
#2For an ordered pair (x, y) in a relation, the y element represents the range.
Answer: range
Given functions f and g, find f-g.
f(x) = 3x -8, g(x) = 8x - 3
OA. 5x+5
OB. 11x-11
O C. -5x -5
D.-5x-11
Answers
Answer:
[tex]-5x-5[/tex]
Step-by-step explanation:
original functions:
[tex]f(x)=3x-8\\g(x)=8x-3[/tex]
Subtract the polynomials:
[tex]f(x)-g(x) = (3x-8) - (8x-3)[/tex]
Distribute the negative sign:
[tex]3x-8-8x+3[/tex]
Combine like terms:
[tex](3x-8x)+(-8+3)[/tex]
Add like terms:
[tex]-5x-5[/tex]
A square room is 14m long. Find the area of its floor
Answers
Answer: 196m squared
Step-by-step explanation: A square has equal sides, so if one side were to be equal to 14m, the other would too. 14 x 14 = 196.
find the lowest common multiple ( L.C.M. ) of the (a² - 4), (a³ - 8), ( a + 2 ) ²
Answers
Answer: according to my work i got
LCM - Lowest Common Factor
HCF - Highest common factor
Step-by-step explanation:
please mark brainlest!!
yw! =^.^=
Simplify √3. √21
√24
√63
O 3√7
09√7
Answers
Answer:
•3✓7
✓3.✓21
=✓3×✓3✓7
=3✓7
Answer:
3rd answer is correct
Step-by-step explanation:
√3 × √21
√3 × √(7 × 3)
√( 3 × 3 × 7 )
√ ( 3 × 3 ) × √7
3√7
The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
A.
B.
C.
D.
Answers
The slope is m=6 and length of line is 3.5√37.
What is slope?The slope of a line is a measure of its steepness.
Given:
endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5
slope= 8-2/3-2= 6
Now, using distance formula,
d= √(3-2)² + (8-2)²
d= √1+ 36
d= √37
As, Line AB is dilated by a scale factor of 3.5.
So, new d= √37*3.5
new d= 3.5√37
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(07.01 MC)
The picture shows a triangular island:
Island
Z
O x sin 50°
O
Which expression shows the value of z? (1 point)
cos 50°
O x cos 50°
O
sin 50°
y
50
Answers
Answer:
Option (2)
Step-by-step explanation:
cos 50° = y/z
z = y/cos 50°
What is the determinant of K =
[6 8
0 3]
Answers
Choose what the expressions below best represent within the context of the word problem.
The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?
x represents
the ones
digit
2x represents
the tens
digit
Answers
The number which represent tens digit of a number is twice the ones digit is;
x represents the ones digit2x represents the tens digitWord problemComplete question:
The tens digit of a number is twice the ones digit. The sum of the digits in the number is
12. What is the number?
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If the sum of all other interior angles is 620∘, what is the angle measure of x. do not include x= or the degree sign in your answer.
Answers
The measure of angle x from the diagram is 100 degrees
Sum of interior angle of an hexagonThe formula for calculating the sum of interior angle of a polygon is given as:
s = (n-2)180
Since hexagon has 6 interior angles, the sum of the interior will be 720 degrees. Hence
x + 620 = 720
x = 720 - 620
x= 100
Hence the measure of angle x from the diagram is 100 degrees
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When you start your career, you decide to set aside $250 every month to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 9.0% compounded monthly. Assuming this to be true, how much money will your account be worth after 20 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
Answers
After 20 years of depositing and investing there will be 168474.01 dollars in your account.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
The formula for calculating how much money will your account be worth after 20 years of depositing and investing is:
P = $250, r = 9% = 0.09, t = 20 years, n = 12 and PMD = $250(per month deposit)
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]
[tex]\rm A = 250(1+\dfrac{0.09}{12})^{12\times20}+\dfrac{250((1+\dfrac{0.09}{12})^{12\times12}-1)}{\dfrac{0.09}{12}}[/tex]
A = 1502.287 + 166971.717
A = $168474.01
Thus, after 20 years of depositing and investing there will be 168474.01 dollars in your account.
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