Bobby built 12 forts
Answer:
12 forts
Step-by-step explanation:
6x2=12
According to the synthetic division below, which of the following statements are true?
Check all that apply.
A, D and E are correct
given ( x - 4 ) is a factor then x = 4 is a root
the remainder on division by (x - 4 ) = 0 as indicated by the 0 on the right side of the quotient
(x - 4 ) is a factor of 3x² - 13x + 4 → A
the number 4is a root of f(x) = 3x² - 13x + 4 → D ( explained above )
thus 3x² - 13x + 4 ÷ (x - 4 ) = 3x - 1 → E
the quotient line 3 - 1 0
3 and - 1 are the coefficients of the linear quotient and 0 is the remainder
The correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].
Further explanation:
In any synthetic division, the dividend polynomial [tex]F\left( x \right) = {a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} + \cdots {a_0}[/tex] and the divisor polynomial [tex]g\left( x \right) = x - b[/tex] can be written as,
[tex]\begin{aligned}b\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&{a}_n&{ a_{n-1}}&_\cdot_\cdot_\cdot{a_0}\\{ }&{}&{ }\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{ }}{c}_n}&_\cdot_\cdot_\cdot{ c_0}&{{\text{ }}0}\end{array} \hfill\\\end{aligned}[/tex]
Here, the monic polynomial is divided by the polynomial that provides the polynomial after division that is also a factor of the polynomial .
Given:
The synthetic division is given below.
[tex]\begin{aligned}4\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{ }}3}&{ - 1}&{{\text{ }}0}\end{array} \hfill\\\end{aligned}[/tex]
Step by step explanation:
We have to determine the answer among all the options.
Option A: [tex]\left( {x - 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].
It can be observed from the given synthetic division the polynomial is [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] that is divisible by the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the polynomial [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option A is correct option.
Option B: [tex]\left( {x + 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].
From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial
[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]
Therefore, [tex](x+4)[/tex] is a not factor of [tex]3{x^2} - 13x + 4[/tex].
Thus, the option B is not correct option.
Option C: The number [tex]-4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial
[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]
Now substitute 0 for [tex]g\left( x \right)[/tex] in the equation [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] to find the root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex] as,
[tex]\begin{aligned}0&= \left( {x - 4} \right) \hfill\\x&= 4 \hfill\\\end{aligned}[/tex]
It can be seen that the value of [tex]x[/tex] is 4 it means [tex]-4[/tex] is not a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option C is not correct option.
Option D: The number [tex]4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
It can be seen that the value of [tex]x[/tex] is 4 in option C it means [tex]4[/tex] is a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option D is correct option.
Option E: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x - 4} \right) = \left( {3x - 1} \right)[/tex]
The option E is also correct as [tex](x-4)[/tex] is the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Option F: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x + 4} \right) = \left( {3x - 1} \right)[/tex]
The option F is not correct as [tex]\left( {x + 4} \right)[/tex] is not the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Result:
Therefore, the correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].
Learn more:
Learn more about the function is graphed below https://brainly.com/question/9590016 Learn more about the symmetry for a function https://brainly.com/question/1286775 Learn more about midpoint of the segment https://brainly.com/question/3269852Answer details:
Grade: Medium school
Subject: Mathematics
Chapter: Synthetic division
Keywords: Synthetic division, polynomial, monic polynomial, function, factor, real number, root, divisible, addition, remainder, quotient, divisor, dividend.
Please help! question attached
The expression predicts profit. When the expression is zero, the profit is zero.
The expression uses unit price as the indpendent variable. Then the zeros correspond to values of unit price that make profit = 0.
Your selection is correct.
The U.S. public debt as of October 2010 was $9.06 × 1012. What was the average U.S. public debt per American if the population in 2010 was 3.08 × 108 people? Round the multiplier to the nearest hundredth.
Answer-
The average U.S. public debt per American is approximately $29,400
Solution-
Given in the question,
U.S public debt as of October 2010 = $9.06×10¹²
Population of U.S in 2010 = 3.08×10⁸
We have to calculate the average U.S. public debt per American,
[tex]\text{Average debt per American}=\frac{\text{Total debt}}{\text{Population}}\\\\=\frac{9.06\times 10^{12}}{3.08\times 10^8}\\\\=2.9415\times 10^{(12-8)}\\\\=2.9415\times 10^4 \approx 2.94\times 10^4=29,400[/tex]
Therefore, the average U.S. public debt per American is $29,400 (after rounding off)
Consider the expression . It has been simplified below with some values unknown.
-33/-10- (-45.3+ 35.2)= -33/-10+?
What is the smallest and largest unknown value from the equation? Must say the smallest value and largest value.
Given expression is
-33/-10- (-45.3+ 35.2)
Problem says that it is simplified.
After simplification it gives:
-33/-10+?
Now we need to find the unknown value that goes in place of ?.
Notice that it is expression having only constants so we will get a unique answer not the smallest or largest value.
Now let's find the value of unknown that goes in place of ?
-33/-10- (-45.3+ 35.2)= -33/-10+?
we see that -33/-10 is on both sides so we can remove that
- (-45.3+ 35.2)= ?
Now let's simplify the left side by distributing the negative sign
+45.3 - 35.2= ?
10.1 = ?
Hence the unknown value is 10.1 that goes in place of ?.
Answer:
answer is 3 on edge
Step-by-step explanation:
wwww
how do i wright linear functions
A linear function is the equation of a line. Here, you are given two points on the line, one of which is the y-intercept, and asked to write the equation. It can work reasonably well to use the 2-point form of the equation of a line.
For points (x1, y1) and (x2, y2), the equation of the line through them can be written as
... y = (y2 -y1)/(x2 -x1)·(x -x1) + y1
When it is possible to use x1 = 0, this is simplified somewhat, so we choose
... (x1, y1) = (0, -5) . . . . . . from f(0) = -5
... (x2, y2) = (5, -1) . . . . . .from f(5) = -1
Putting these values in the above formula, we get ...
... y = (-1 -(-5))/(5 - 0)·(x -0) -5
... y = 4/5x -5 . . . . . simplified
This can be put in the desired functional form using f(x) instead of y:
... f(x) = 4/5x -5
Here we're given two points on a line: (0,-5) and (5, -1). Going from the first point to the second, x increases by 5 and y increases by 4. Thus, the slope of the line is
m = 4/5 = 1. Use the point-slope formula to find the equation of this line:
y-(-5) = (4/5)(x). Thus, y = (4/5)x - 5 or f(x) = (4/5)x - 5
James works as a waiter. He served meals with bills of 23.59, 40.65, 30.50, and 15.68. If his total for tips was 17.67, what percent tip did he receive for serving these meals? Round the answer to the nearest percent
16%
the percent tips is calculated as
[tex]\frac{tips}{total bill}[/tex] × 100%
total bills = 23.59 + 40.65 + 30.50 + 15.68 = 110.42
percent tips = [tex]\frac{17.67}{110.42}[/tex] × 100% = 16%
rounded 3,428,583 rounded to the nearest 10,000
3,400,000 because the 2 is the in the 10,000
Order from least to greatest 0.044 0.445 0.004 0.040
A) 0.004 0.040 0.044 0.445
B) 0.040 0.004 0.044 0.445
C) 0.040 0.004 0.044 0.445
D) 0.445 0.044 0.040 0.004
A is th3e correct answer... ten hundreths thousandths
How do I solve this?
x = 6
given
[tex]\frac{x+2}{x-2}[/tex] = [tex]\frac{4}{8}[/tex]
cross- multiply to obtain
8(x + 2) = 4(x - 2) ( distribute parenthesis on both sides )
8x + 16 = 4x - 8 ( subtract 4x from both sides )
4x + 16 = - 8 ( subtract 16 from both sides )
4x = - 24 ( divide both sides by 4 )
x = [tex]\frac{-24}{4}[/tex] = - 6
Hello there!
Answer: ⇒ x=-6
_________________________________________________________
Step-by-step explanation:
Apply fraction cross multiply.
[tex](x+2)*8=(x-2)*4[/tex]
Expand.
[tex]8x+16=4x-8[/tex]
Subtract by 16 from both sides of equation.
[tex]8x+16-16=4x-8-16[/tex]
Simplify.
[tex]8x=4x-24[/tex]
Subtract by 4x from both sides of equation.
[tex]8x-4x=4x-24-4x[/tex]
Simplify.
[tex]4x=-24[/tex]
Divide by 4 from both sides of equation.
[tex]\frac{4x}{4}=\frac{-24}{4}[/tex]
Simplify it should be correct answer.
[tex]x=-6[/tex]
__________________________________________________________________
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a number cube is labeled 1 to 6. the cube will be tossed once. what is the probability that the cube will show a number less than 3?
Answer:
1/3 of the time.
Step-by-step explanation:
This is because since the dice is being tossed 1 time, that would mean that there is only a 2 in 6 chance to roll a number under 3
The probability that the cube will show a number less than 3 is 1/3 and this can be determined by using the given data.
Given :
A number cube is labeled 1 to 6. the cube will be tossed once.
The following steps can be used in order to determine the probability that the cube will show a number less than 3:
Step 1 - According to the given data, a number cube is labeled 1 to 6. the cube will be tossed once.
Step 2 - So, the number under three is 1 or 2.
Step 3 - Therefore, the probability that the cube will show a number less than 3 is:
[tex]\rm P=\dfrac{2}{6}[/tex]
[tex]\rm P=\dfrac{1}{3}[/tex]
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If data for the topics below were collected and displayed in a frequency table, which topic would most likely need to be shown in intervals? eye color heights of trees foot length of newborn babies favorite food
Answer:
The heights of trees
Step-by-step explanation:
Because trees vary a lot, I would say trees.
Eye color does not vary that much and this is true for new born babies.but trees on the other hand are a different story. They range from 0 to hundreds of feet so it would be a good idea to bind.
Answer:
The heights of trees
Step-by-step explanation:
I did the lesson and got 100% also the guy above explains it perfectly.
What is the remainder when the polynomial 8 x^2 +4x−3 is divided by 2x−1 ?
[tex]8x^2 +4x-3[/tex] is divided by 2x-1
We use long division
4x +4 ------------> Quotient
----------------------------
2x-1 8x^2 +4x−3
8x^2 - 4x (Subtract it from the top)
---------------------------
+ 8x -3
8x - 4 (Subtract it from the top)
----------------------------------
+1 ------------> Remainder
So , 1 is the remainder.
Solve for x: 3x − 24 = 81
57/3
105/3
57
105
To solve for x, we need to get all our constants on one side of the equal sign and all our variables on the other side of the equal sign.
3x - 24 = 81
3x -24 + 24 = 81 +24
3x = 81 + 24
3x = 105
3x/3 = 105 / 3
x = 105 / 3
Answer:
[tex]x=\frac{105}{3}[/tex]
Step-by-step explanation:
To solve for x, we need to get all our constants on one side of the equal sign and all our variables on the other side of the equal sign.
[tex]3x-24=81[/tex]
[tex]3x-24+24=81+24[/tex]
[tex]3x=81+24[/tex]
[tex]3x=105[/tex]
[tex]\frac{3x}{3}=\frac{105}{3}[/tex]
Therefore, the answer is: [tex]x=\frac{105}{3}[/tex]
PLZ HELP FOR BRAINLIEST!!!
The graph of a function is shown:
scatterplot of the following points: negative 3 and 2, negative 2 and negative 1, 2 and negative 1, and 3 and 3
Which of the following correctly identifies the set of outputs?
A) {–3, –2, 3}
B) {–1, 2, 3}
C) {(–3, 2), (–2, 1), (3, 3), (3, –1)}
D) {(2, –3), (1, –2), (3, 3), (–1, 3)}
Inputs are the first number output is the second. So youre outputs are 2, -1, -1, and 3. so i would say b
The set of outputs for the function represented by the scatterplot is {-1, 2, 3}, which matches Option B from the given choices.
You are looking to identify the set of outputs (also known as the range) of a given function based on a scatterplot. The output of a function is comprised of the second element in each ordered pair, which represents the y-value on the Cartesian plane. In this case, the scatterplot includes the points (-3, 2), (-2, -1), (2, -1), and (3, 3).
To find the correct set of outputs, we need to list the y-values from each point: 2, -1, -1, and 3. When listing a set, we do not repeat values, so the set of outputs for this function would be {2, -1, 3}. Therefore, the correct answer is Option B) {-1, 2, 3}.
What is the value of sinC ?
Answer:
[tex]sin \:C =\frac{8}{17}[/tex]
Step-by-step explanation:
In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
[tex]sin \:x =\frac{O}{H}[/tex]
From the formula above we know that the sine of an angle is the opposite side divided by the hypotenuse. The opposite side is AB and has a length of 8. The hypotenuse is AC with a length of 17. So we can write
[tex]sin \:C =\frac{8}{17}[/tex]
What is the value of x? Enter your answer in the box.
the value of x is 12
List of the partial product 0f 42 ×28
1,2,3,6,7,14,21,42
1.2,4,7,14,28
A number, n, is multiplied by -3/8. The product is -0.5 What is the value of n?
Answer:
n=4/3
Step-by-step explanation:
n*(-3/8)=-0.5
n=0.5/3/8
n=1/2 / 3/8
n=4/3
Check:
4/3*-3/8=-0.5
4/3*-3/8=-1/2
-1/2=-0/5
CORRECT!
a day care program has an average daily expense of $75 the standard deviation is $5 the owner takes a sample of 64 bills what is the probability the mean of his sample will be between $70 and $80? The answer choices are 68 1.0 34 + 30. Step 1 calculate a z-score for $70 step to give the probability for Step 1. Step 3 calculate the Z score for $80. Step for give the probability for step 3.
you can use the formula for sample means:
[tex][tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex][/tex]
where m stands for a value of the sample mean.
We are looking for the value, specifically for its two borderline values: 70 and 80
and their cumulative probabilities, p(z(80)) and p(z(70)). The difference p(z(80))-p(z(70))
will give the probability that m falls in the interval [70,80]
So let's get cracking at it:
[tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex]
[tex]z(80) = \frac{80-75}{5 / \sqrt{64}} = 8[/tex]
These are very large values of z. You may notice that any z-table online won't even bother covering range that high - the probabilities for these values are virtually 0 (in the neg case) 1 (in the pos case).
This means that numerically the probability of the sample mean of 64 samples falling within the range of 1 standard deviation is very close to 1
So the answer choice should be 1.0
Which expression best estimates
A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 15 feet per second. One day, the equipment elevator begins to descend. After 30 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 14 seconds? At that time, which elevator is deeper?
The equipment elevator descends to 176 feet below the surface while the miners' elevator descends to 210 feet below the surface after 14 seconds. Therefore, the miners' elevator is deeper.
Explanation:To solve this, we first need to determine the position relative to the surface of both elevators in the gold mine. As the equipment elevator begins to descend first and moves at a speed of 4 feet per second, it had already traveled 30 (seconds) * 4 (feet per second) = 120 feet downward before the miners' elevator begins to descend.
Then, an additional 14 seconds pass. In these 14 seconds, the equipment elevator will descend a further 14 * 4 = 56 feet. Therefore, the equipment elevator is 120 + 56 = 176 feet below the surface.
The miners' elevator descends at 15 feet per second, and it has been moving for 14 seconds. Therefore, it is 15 * 14 = 210 feet below the surface. At this point in time, the miners' elevator is deeper than the equipment elevator by 210 - 176 = 34 feet.
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The equipment elevator will be at a depth of 176 feet, while the miners' elevator will be deeper at a depth of 210 feet from the surface after the given time. The miners' elevator is deeper.
Explanation:The position of each elevator relative to the surface after another 14 seconds can be found by first determining the distance each has traveled. The equipment elevator descends at 4 feet per second, and it had already been descending for 30 seconds before the miners' elevator started. Therefore, by the time the miners' elevator begins to descend, the equipment elevator will have descended 4 feet/second * 30 seconds = 120 feet.
From that point, after another 14 seconds, the equipment elevator descends an additional 4 feet/second * 14 seconds = 56 feet. Thus, its total descent is 120 feet + 56 feet = 176 feet from the surface.
On the other hand, once the miners' elevator starts, it descends at a rate of 15 feet per second. After 14 seconds, the miners' elevator will have descended 15 feet/second * 14 seconds = 210 feet.
Comparing both distances, the elevator for the miners is at 210 feet while the equipment elevator is at 176 feet from the surface. So, the miners' elevator is deeper.
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What is the missing value in the data set that would make the mean equal 80? Show your work or explain how you got your answer.
{71, 91, 82, 90, 88, 61, 70, __ }
all the numbers have to equal 640
because mean is add the all up and devide by how many. Theres 8 numbers and times that by 80 to get 640
so add them all up
71
91
82
90
88
61
70
553
subtract 640 by 553
youre answer is 87
The missing value in the data set is 87.
Here,
The data set is,
{71, 91, 82, 90, 88, 61, 70, __ }
The mean of data set = 80
We have to find the missing value in data set.
What is Mean?
Mean is calculate as, Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.
Now,
The data set is,
{71, 91, 82, 90, 88, 61, 70, __ }
The mean of data set = 80
Hence,
Let the missing number in data set = x
Mean of data set = [tex]\frac{71+ 91+ 82+ 90+ 88+61+ 70+x}{8}[/tex]
[tex]80 = \frac{553+x}{8}\\\\640 = 553 + x\\\\x = 87[/tex]
Therefore, The missing value in the data set is 87.
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how do you find a parallel aandmd perpendicular line using a graph
The problem asks for the equations of the lines, so you use the information given in the graph to help you write the equations.
The given line has a "rise" of -4 for a "run" of 1, hence a slope of -4/1 = -4. This is the information you need from that line to write the equations of lines through the given point, (4, 3).
(a) The parallel line will have the same slope. You are asked for "an equation", so the simplest is to provide the necessary equation in point-slope form.
The equation of a line with slope m through point (h, k) is ...
... y - k = m(x - h)
For m = -4, (h, k) = (4, 3) your parallel line is ...
... y - 3 = -4(x -4)
(b) The perpendicular line will have a slope that is the negative reciprocal of that of the given line: -1/-4 = 1/4. Using the same point-slope form, your perpendicular line has equation ...
... y - 3 = (1/4)(x - 4)
PLEASE ANSWER!! SHOW ALL YOUR WORK!
The perimeter of an isosceles triangle is 7.5m, and the length of a leg is 2m. Find the length of the base.
Answer:
3.5 m
Step-by-step explanation:
The perimeter is the sum of the lengths of the three sides of the triangle, so is the sum of two legs and the base.
... 7.5 m = (2 m) + (2 m) + base
... 3.5 m = base . . . . . . subtract 4 m
base = 3.5m
Since the triangle is isosceles both legs are equal to 2m
base = 7.5 - 2 - 2 = 3.5m
express the area of a rectangle with length 7ab and width 2a as a monomial area = _____
The area is the product of the length and width.
... Area = (7ab)×(2a) = (7×2)×(a×a)×(b)
... Area = 14a²b
Suppose a pony Express rider was paid 192$ for 12 weeks of work if he was paid the same amount each week,how much was he paid for 3 weeks.
Answer:
$48
Step-by-step explanation:
1. 192/12 = 16
2. 16 * 3 = 48
3. Your answer is 48
192/12 = $16 * 3 = $48. $48 dollars was how much he was paid for 3 weeks.
The U.S. Maritime Administration estimated that the cost per ton of building an oil tanker could be represented by the model y=104,000/x+235 where y is the cost in dollars per ton and x is the tons (in thousands). What size of oil tanker (in thousands of tons) can be built for $350 per ton? a. 62 thousand tons b. 6 thousand tons c. 532 thousand tons d. 178 thousand tons
(c)
substitute x = 350 into the equation for y
y = [tex]\frac{104000}{350}[/tex] + 235 ≈ 532 000
Final answer:
To find the size of the oil tanker that can be built for $350 per ton, solve the equation 350 = 104,000/x + 235 for x, yielding approximately 904 thousand tons. None of the multiple-choice options match this result.
Explanation:
The student is asked to calculate the size of an oil tanker that can be built for $350 per ton using the given model for cost per ton, which is y = 104,000/x + 235, where y is the cost in dollars per ton, and x is the tons in thousands. To find x, set the equation equal to 350 and solve for x.
350 = 104,000/x + 235
Subtract 235 from both sides to get:
350 - 235 = 104,000/x
115 = 104,000/x
To solve for x, multiply both sides by x and then divide both sides by 115:
x = 104,000 / 115
x ≈ 904.35
Since x is in thousands of tons, the size of the oil tanker that can be built for $350 per ton is approximately 904 thousand tons. However, this answer does not match any of the options provided in the multiple choice (a. 62 thousand tons, b. 6 thousand tons, c. 532 thousand tons, d. 178 thousand tons), suggesting there might be an error in the question or the offered choices.
the equation y = 15x describes the amount of money Sandra earns, where x is the number of hours she works and y is the amount of money she earns. the table shows the amount of money Susan earns for different numbers of hours worked. (a) how much money does Sandra earn per hour? (b) who earns more per hour?
Answer:
(a) Sandra earns $15 per hour
(b) Sandra earns more per hour
Step-by-step explanation:
(a) y=15x tells Sandra's earnings for x hours. To find Sandra's earnings for 1 hour, let x=1.
... y = 15·1 = 15 . . . . Sandra earns $15 in 1 hour.
(b) To find Susan's earnings you can choose any number of hours and divide that into the corrsponding number of dollars. The math is really easy if you choose the last table entry:
... $80/(10 hours) = $8/hour
Sandra's earnings of $15 per hour are more than Susan's earnings of $8 per hour.
_____
Another way to compare the wages is to pick one of the hour numbers from the table and compute Sandra's equivalent earnings. Again, if we choose 10 hours, the math is easy
... y = 15·10 = 150
Sandra earns $150 for 10 hours' work, while Susan only earns $80 for the same time.
So based on the table, Susan's equation describing her earnings is:
y=8x (x being the hours, y amount earned)
(a) Sandra earns $8 per hour (the factor in front of x in the equation)
(b) Sandra's equation is y=15x which means for every unit of time she adds $15, so her hourly pay is $15. Therefore Sandra earns ($7) more per hour than Susan.
According to the table the investment has doubled in worth by the start of which year?
Answer:
The investment has doubled in worth by the start of 15th year.
Step-by-step explanation:
We are Provided a table which tells us that principal amount of $100 is invested on a interest rate of 5% for 15 years compounded annually and we are asked to find out by the start of which year our investment will be doubled.
We can see that after 14 years our amount is doubled but this can't be our answer as amount is doubled ($207.90) after 14 years not in the start of 14th year. We can see that by the start of 15 year our amount is doubled that is $207.90.
Therefore, by the start of 15th year our investment will be doubled.
The amount of money Jesse spent, $75, is subtracted from the amount he had at the start, m. This expression is equal to the amount he has left, $55. Therefore, the equation is m−75=55. How much money, m, did Jesse have before buying the shoes?
Answer:
$130
Step-by-step explanation:
You are given the one-step linear equation ...
... m - 75 = 55
You solve it by adding 75 to both sides.
... m -75 +75 = 55 +75
... m = 130 . . . . . . . . . . . . . simplify