The value obtained from the given function f(z) = 10z²-9z+3 are-
a = 10h.b = 71h.What defined as the quotient function?A quotient function is a function that consists of two functions isolated by a division sign.The domain of the quotient between two functions, f(x) and g(x), is A ∩ B ("A intersected with B" implies the set among all points that Both A and B have in common), excluding where g(x) = 0.In mathematics, a quotient is the result of dividing one number by another.For the given function;
f(z) = 10z²-9z+3.
The quotient is given as;
Quotient = f(4+h)-f(4)
Put the values (4 + h) and 4 at the place of z in the function.
f(4+h)-f(4) = 10(4 + h)² - 9(4 + h) + 3 -[10(4)² - 9(4) + 3)]
f(4+h)-f(4) = 10h² + 160 -9h + 80h + 3 - 160 + 36 - 3
Cancel the values;
f(4+h)-f(4) = 10h² + 80h - 9h
f(4+h)-f(4) = 10h² + 71h.
Thus, comparing the obtained equation by give form of (ah + b)
a = 10h and b = 71h.
Therefore, the obtained values for the given function f(z) is;
a = 10h and b = 71h.
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Choose the definition for the function.
A.
C.
√4x - if x < 0
3
2x + 2
if x ≥ 0
2x - 2
--4
if x ≤ 0
if x > 0
B.
D.
2x + 2
x + 4
x + 4
2x + 2
if x ≤ 0
if x > 0
if x ≤ 0
if x > 0
Answer:
B
Step-by-step explanation:
we need to look at the y-intercept (the y value when x=0).
we need equating with +2 and +4 at the end.
that eliminates A and C, leaving B and D as potential right answer.
but then we see that the y-intercept "+2" must be in an equation for x <= 0, because that line with +2 intercept only covers negative x.
so, B is correct.
If b2 is changed from 7 to 9 what value will appear in c3 if c3 contains the formula =b2*2
The value of C3, when B2 is changed from 7 to 9 is 18.
Given that, B2 is changed from 7 to 9.
What is the formula?The formula is a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign. When you know the value of one quantity, you can find the value of the other using the formula.
The given formula = B2 × 2
When B2 is 7, the value of C3 is 14
When B2 is changed from 7 to 9, the value of C3 is B2 × 2 = 9 × 2
=18
Therefore, the value of C3, when B2 is changed from 7 to 9 is 18.
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Mia Wong is receiving the total accounts receivable of Wong's department store. Credit customers paid $90,000 this month. This represents 60% of all receivables due. What is Mia's total accounts receiving?
Mia's total accounts receiving is $1,50,000.
What is the total accounts receiving?Accounts receivable refers to the sum of money due to a company for goods or services delivered or utilized but not yet paid for by customers (AR). The balance sheet classifies accounts receivable as a current assets. Any money that clients owe for purchases they purchased using credit is referred to as "AR" (account receivable).Given :
receivables dues paid by customers = $90,000
Let Mia's total accounts receiving be $ x.
According to the question,
⇒ 60% of x = 90,000
⇒ [tex]\frac{60}{100} x[/tex] = 90,000
⇒ x = (90,000×100) /60
= 1,50,000
Therefore, Mia's total accounts receiving is $1,50,000.
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Which explanation could be used to verify whether the functions are inverses?
Neither of the lines is parallel to the line y = x; therefore, the functions are inverses of each other.
Neither of the lines is parallel to the line y = x; therefore, the functions are not inverses of each other.
The point of intersection of the two functions is not on the line y = x; therefore, the functions are inverses of each other.
The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
The explanation that could be used to verify whether the functions are inverses is; The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
How to Interpret Function Inverses?
If we assume that (a, b) is a point that lies on both the graph y = f(x) and the graph y = f⁻¹(x), then from the second condition, it follows that the point (b, a) lies on the graph of f.
So, we’re looking for a function whose graph includes two points (a, b) and (b, a) and we want a ≠ b. An example is;
f(x) = -1/x³
So that the inverse function is f⁻¹(x) = 1/x^(1/3)
Thus, applying that concept to this question and we can conclude that the point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
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you are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 7/8 inch and an inside diameter of 3/4 inch. How much refrierant can 12 feet of the tubing hold?
The amount of refrierant the tubing can hold is 0.037 cubic feet..
How much refrierant can the tubing hold?A cylinder is a three-dimensional object that is made up of a prism with a circular base. In order to determine how much refrigerant that cylindrical coil can hold, the volume of the cylinder has to be determined.
First, the dimension of the inside diameter has to be changed to feet
1 inch = 1/12 feet
3/4 x 1/12 = 1/16 feet
Volume of a cylinder = πr²h
Where:
π = pi = 22/ 7r = radius = diameter / 2 = 1 /16 ÷ 2 = 1 /16 x 1/2 = 1/32h = heightVolume = 22/7 x (1/32)² x 12 = 0.037 cubic feet.
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Find the average of the numbers:
4 2/5,3/38, 2 3/4
Express your answer as a mixed number or a fraction in lowest terms.
The average of the numbers expressed as a mixed number is 2⁴⁶⁷/₁₁₄₀
What is the average of numbers?The average of a given set of numbers is given by X = ∑x/N where
x = individual values of the numbers and N = total number of values How to find the average of the given numbers?Since we are given the numbers
x₁ = 4²/₅,x₂ = ³/₃₈, and x₃ = 2³/₄. Since we have three numbers N = 3.So,the average is X = ∑x/N
= (x₁ + x₂ + x₃)/N
= (4²/₅ + ³/₃₈ + 2³/₄)/3
= (22/5 + 3/38 + 11/4)/3
Taking the L.C.M of the numbers in the bracket. So, the L.C.M of the nunbers in the bracket is 380. So, simplifying, we have
= (1672 + 30 + 1045)/380 ÷ 3
= 2747/(380 × 3)
= 2747/1140
= 2⁴⁶⁷/₁₁₄₀
So, the average of the numbers expressed as a mixed number is 2⁴⁶⁷/₁₁₄₀
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PLS HELP 30 POINTS
The graph represents a quadratic function. Write an equation of the function in standard form.
Answer: [tex]y=x^2 -4x-2[/tex]
Step-by-step explanation:
The equation in vertex form is [tex]y=a(x-2)^2 -6[/tex]. Substituting in the coordinates (5, 3),
[tex]3=a(5-2)^2 -6\\\\3=9a-6\\\\9=9a\\\\a=1[/tex]
So, the equation is [tex]y=(x-2)^2 -6[/tex]. This expands as follows:
[tex](x-2)^2 -6\\\\=x^2 -4x+4-6\\\\=x^2 -4x-2[/tex]
Answer:
f(x) = [tex]x^{2}[/tex] -4x -2
Step-by-step explanation:
What is the distance between –12 and –7 on a number line?
Twice the difference of a number and three is four. Find the number.
Answer: 5
Step-by-step explanation:
2(x-3)=4
2x-6=4
Add 6to each side
2x=10
Divide each side by 2
X=5
Does this help?
Question Find the equation of a line that contains the points (-7, 6) and (3, 8). Write the equation in slope-intercept form.
The equation of a line that contains the points (-7, 6) and (3, 8) is [tex]y=\frac{1}{5} x+\frac{37}{5}$$[/tex]
Find the line [tex]$y=m x+b$[/tex]passing through [tex]$(-7,6),(3,8)$[/tex]
Compute the slope [tex]$(-7,6),(3,8): \quad m=\frac{1}{5}$[/tex]
Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=\frac{37}{5}$[/tex]
Construct the line equation [tex]$\mathrm{y}=\mathrm{mx}+\mathrm{b}$[/tex]where [tex]\mathrm{m}=\frac{1}{5}$ and $\mathrm{b}=\frac{37}{5}$[/tex]
[tex]y=\frac{1}{5} x+\frac{37}{5}$$[/tex]
The Slope intercept form is a system for determining a straight line's equation. The equation of a straight line is the relationship that
The slope- intercept form of a straight line is used to find a line's equation. The pitch of the line and the intercept cut by the line with the y- axis are needed for the pitch- intercept formula. Consider a straight line with pitch' m' and y- intercept For a straight line with a pitch, 'm,' and' b' as the y- intercept, the pitch intercept form equation is y = mx b. Then are some cases of pitch intercept forms.
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Tracey paid $135 for an item that was originally priced at $260. What percent of the original price did Tracey pay?
Round your percentage answer to two decimal places.
Do NOT include a
%
symbol with your answer
Answer:
51.92
Step-by-step explanation:
135/260 = .51923076923 x 100 to get the percentage
51.923076923 and round
A rule for creating a pattern is given below. The rule begins with a number called the input and creates a number called the output. Rule: Multiply the input by 6 to get the output. Which input and output table works for the rule? Choose 1 answer:
2 is the input value, while 6 is the result.
We know the rule is Multiply the input by 6 to get the output.
= (2*5)-4
=10-4
=6.
A function rule is the equation-based relationship between dependent and independent variables. How to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, is explained by the function rule of a particular function. A function table includes a function rule as well as input and output values. If we plug in various values for the input, we obtain corresponding values of output according to the function rule. The relationship between the input values x and the output values y always follows a pattern that is specified by the function rule.
Hence, the input and output value of a table is 2 and 6.
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Line h passes through point (3,0) and is perpendicular to the graph of y=1/5x-19. Line g is parallel to line h and passes through point (-1.15). What is the equation in slope intercept form of line g?
Answer:
y = -5x + 10
Step-by-step explanation:
Answer:
-5x + 10
Step-by-step explanation:
If a line 2 is perpendicular to line 1 and line 1 has slope m, then line 2 must have slope = [tex]\sf -\dfrac{1}{m}[/tex] which is the negative of the reciprocal of m
Essentially the product of the two slopes = -1
The line
[tex]y = \dfrac{1}{5}x - 19[/tex]
has slope of [tex]\dfrac{1}{5}[/tex] so the slope of line h which is perpendicular to this line must have slope = negative of reciprocal of [tex]\dfrac{1}{5}[/tex]
Reciprocal of [tex]\dfrac{1}{5}[/tex] is 5
Negative of reciprocal is thus -5
Equation of h is of the form
y = -5x + b where b is the y intercept, the value of y at x = 0
Since line h passes through (3, 0) we plug in these values for x and y and solve for b
0 = -5(3) + b
0 = -15 + b
15 = b (Adding 15 on both sides)
b = 15
Equation of line h is y = -5x + 15
Line g is parallel to line h. Parallel lines have the same slope so the equation for line g is
y = -5x + b (since slope of g = slope of h = -5)
Since this line passes through x = -1, y = 15 we can solve for b as before by plugging these values into the equation
15 = -5(-1) + b
15 = 5 + b
10 = b (Subtracting 5 on both sides)
b = 10
So equation of line g = -5x + 10
Find the quotient and the remainder when x- + 5x + 2 is divided by x + 1
Answer: The quotient is when x+ 5x + 2 = 6
The reminder is when x+ 5x + 2 = -4
Step-by-step explanation:
Given data,
The quotient and the remainder when x + 5x + 2 is divided by x + 1
Let, f(x) = x + 5x + 2
g(x) = x+1
we can write,
g(x) = x+1 = 0
g(x) = x = -1
so, f(x) = x + 5x + 2
we can substitute x = -1 value
f(x) = x + 5x + 2
f(-1) = (-1) + 5(-1) + 2
f(-1) = (-1) - 5 + 2
f(-1) = (-1) - 3
f(-1) = -4
Therefore,
The quotient is when x+ 5x + 2 = 6
The reminder is when x+ 5x + 2 = -4
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A 6.5 foot tall man casts a shadow that is 4.7 feet long. If the shadow of a flag pole is 8 feet long, how tall
is the flag pole?
The flag pole is
feet tall.
Enter an integer or decimal number [more..]
Round to the nearest tenth of a foot if needed.
Answer:
11.1
Step-by-step explanation:
This is a question involving ratios and proportions
The ratio of man's height to his shadow length = 6.5/4.7
The ratio of flagpole height to its shadow must be in the same ratio
If h is the height of the flagpole then h/8 is the ration of height to shadow length
Therefore,
[tex]\dfrac{6.5}{4.7} = \dfrac{h}{8}\\\\\mathrm{Multiplying \;both\;sides\;by\;8\;}\\\\\dfrac{6.5 \times 8 }{4.7} = h \\\\Or,\\h = \dfrac{6.5 \times 8 }{4.7} \\\\Which\;simplifies\;to:\\\\h = 11.0638\\\\h = 11.1 \;rounded\;to\;the\;nearest\;tenth\;of\;a\;foot[/tex]
Harriet's Flowers is having a sale on petunias for $0.25 each with the purchase of any $12 item. The Premiere
Garden Shop is selling them for $0.15 each with the purchase of any $15 item. What number of petunias would
cost the same at either shop?
Premiere
Answer:
30 petunias
Step-by-step explanation:
p=petunias
0.25p +12 = 0.15p + 15
-0.15p -0.15 p Subtract 0.25 with 0.15
0.10p + 12 = 15
-12 -12 Subtract 15 with 12
0.10p = 3 Divide 0.10p with 3
p=30
Given a rectangle that is 46 cm longer than it is wide. Express the perimeter (in cm) of a rectangle in terms of its width w.
Answer:
2(46+w) + 2(w)
Step-by-step explanation:
Consider the event of a coin being flipped eight times. If that event is repeated 10000 different times. it is expected that the event would result in 8 heads about __times
If the event of a coin is being flipped eight times. If that event is repeated 10000 different times. it is expected that the event would result in 8 heads about 39.06times
ProbabilityThe probability of flipping heads onetime= 1/2
Hence,
Probability of flipping heads 8 times in a row is:
Probability= (1/2)^8
Probability=0.00390625
Now let determine the expected times
Number of times=0.00390625×10,000
Number of times=39.06 times
Therefore If the event of a coin is being flipped eight times. If that event is repeated 10000 different times. it is expected that the event would result in 8 heads about 39.06 times
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Write an expression in factored form for the polynomial of the least possible degree graphed below.
The expression in factored form for the polynomial of the least possible degree is f(x) = (3 / 16) · (x + 2) · (x + 1) · (x - 2) · (x - 4).
How to write a polynomial in factored form
A polynomial can be written as a product of a constant named lead coefficient and binomials of the form x - r, where r is the root of the polynomial. A root is a value of x such that the polynomial is equal to zero and the lead coefficient can be determined by using the y-intercept of the graph, then:
f(x) = a · (x + 2) · (x + 1) · (x - 2) · (x - 4)
Where a is the lead coefficient.
If we know that f(0) = 3, then the value of the lead coefficient is:
3 = a · (0 + 2) · (0 + 1) · (0 - 2) · (0 - 4)
3 = 16 · a
a = 3 / 16
The expression in factored form for the polynomial of the least possible degree is f(x) = (3 / 16) · (x + 2) · (x + 1) · (x - 2) · (x - 4).
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Midtown Antiques collects 2% sales tax on all sales. If total sales including tax are
$1591.62, find the portion that is the tax amount.
Answer:.05*1493.47 = $74.67 also
Step-by-step explanation:
A shirt you want to buy is $25.50 but is marked down 30%. What is the sale price? O A. $7.65 O O 8. $17.85 C. $33.15 O D. $21.24
Which property is illustrated by the equation below?
(7 + 6) + 4 = 7 + (6 + 4)
A. Distributive property
B. Identity property
C. Associative property
D. Commutative property
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - -
[tex]\textsf{The illustrated property is the associative property, which states that you}\\\textsf{can change the grouping of the numbers, but the result will be the same.}\\\textsf{In other words,}\\\textsf{(a+b)+c=a+(b+c)}[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]
Kylie and her sister started watching an action movie at 10:11 A.M. The movie was 2 hours
and 30 minutes long. After the movie, they played soccer in the backyard for 2 hours and 5
minutes. What time was it when Kylie and her sister finished playing soccer?
Answer:
2:46 p.m.
Step-by-step explanation:
Answer:
2:46 p.m.
Step-by-step explanation:
Start time: 10:11 a.m.
movie end time: 10:11 a.m. + 2hrs 30 min = 12:41 p.m.
soccer end time: 12:41 p.m. + 2hrs 5 min = 2:46 p.m.
There are about 1,045,000, people living in City A. There are 2.5 times that number of people living in City B. What is the approximate number for people living in City B?
The approximate number for people living in City B is 2612500 people
What is the approximate number for people living in City B?The given parameters are
City A = about 1,045,000, people
City B = 2.5 times that number of people living in City B
Substitute City A = about 1,045,000, people in City B = 2.5 times that number of people living in City B
So, we have
City B = 2.5 times 1,045,000, people
Rewrite as
City B = 2.5 * 1,045,000, people
Evaluate the product
So, we have
City B = 2612500 people
Hence, the approximate number for people living in City B is 2612500 people
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Answers these please
Answer:
2. 4f+s, 3. 3c+10, 4. b-3, 5. f < 2t, 6. 3p + b, 7. 5w + 2, 8. c + 2w + f < 100
ZRQT is a straight angle. What are mZRQS and
mZTQS?
mZRQS =
m/TQS=
RQS(9x+1)°
TQS(7x+3)°
The measure of the angle RQS is 100 degrees, and the measure of the angle TQS is 80 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
ZRQT is a straight angle
The sum of the angle RQS and angle TSQ will be 180 degrees
9x + 1 + 7x + 3 = 180
16x + 4 = 180
16x = 176
x = 176/16
x = 11
RQS(9x+1)° = 9x11 + 1 = 100
TQS(7x+3)° = 7x11 + 3 = 80
Thus, the measure of the angle RQS is 100 degrees, and the measure of the angle TQS is 80 degrees.
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I need help with this
Answer:
d is the answer to your question
Tinsley, Incorporated, wishes to maintain a growth rate of 14 percent per year and a debt-equity ratio of .5. The profit margin is 4.6
percent, and total asset turnover is constant at 1.16.
a. What is the dividend payout ratio?
Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer
as a percent rounded to 2 decimal places, e.g.. 32.16.
The dividend payout ratio is -53.43% when a growth rate of 14 percent per year and a debt-equity ratio of .5. The profit margin is 4.6
percent, and total asset turnover is constant at 1.16.
To calculate the ROE we would have to use the following formula:
ROE=Profit margin x Total asset turnover x Equity multiplier
ROE=0.046 x 1.16 x (1 +0.5)
ROE=0.08004
Therefore, dividend payout ratio would be calculated as follows:
0.14 = (0.08004 x dividend payout ratio) / [ 1 - (0.08004 x dividend payout ratio))
0.14 = 0.08004 x dividend payout ratio / (1 - 0.08004 dividend payout ratio)
0.14 - 0.0112056 dividend payout ratio = 0.08004 dividend payout ratio
0.14 = 0.0912456 dividend payout ratio
dividend payout ratio=1.53432
Therefore, dividend payout ratio=1-1.53432
dividend payout ratio=-53.43%
The dividend payout ratio is -53.43% when a growth rate of 14 percent per year and a debt-equity ratio of .5. The profit margin is 4.6
percent, and total asset turnover is constant at 1.16.
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The hypotenuse of a right triangle is 13 cm long. The longer leg is 7cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg:
Length of the longer leg:
Length of the hypotenuse:
The information about the triangle will be:
Length of the shorter leg: = 5cm
Length of the longer leg: = 12cm
Length of the hypotenuse: = 13cm
How to illustrate the information?It should be noted that the formula for illustrating the information is:
c² = a² + b²
where c = hypothenuse
The shorter leg = x
Longer leg = x + 7
Hypothenuse = 13
Therefore, c² = a² + b²
13² = x² + (x + 7)²
169 = x² + x² + 14x + 49
169 = 2x² + 14x + 49
169 - 2x² - 14x - 49 = 0
-2x² - 14x + 120 = 0
Multiply through by minus
2x² + 14x - 120 = 0
Divide through by 2
x² - 7x - 60
x² - 12x + 5x - 60
x(x - 12) + 5(x - 12)
Therefore, the smaller length is 5cm and the bigger Length is 12cm
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Translate the following into a math expression:
twenty less than the product of five and a number
A: (x+5) - 20
B: 20-5x
C: 5x-20
D: 5/x - 20
Answer:
[tex]5x - 20[/tex]
Step-by-step explanation:
Product means the result of the multiplication of two numbers. A part of our expression will include the product of five and a number. We don't know what number it is, therefore, we'll call it [tex]x[/tex]. The product of those two numbers can be algebraically expressed as [tex]5x[/tex] (we usually eliminate the multiplication sign between numbers and variables).
We are then asked to express the number that is 20 less than the product we found earlier. To find this expression, we should subtract 20 from the product, giving us [tex]5x - 20[/tex].