Area of a circe = Pi x radius^2
solve for the following system by using Elimination4x-2y=86x+6y=30
System
[tex]\begin{gathered} 4x-2y=8 \\ 6x+6y=30 \end{gathered}[/tex][tex]\begin{gathered} 3(4x-2y)=8 \\ 6x+6y=30 \\ \\ 12x-6y=24 \\ + \\ 6x+6y=30 \\ \\ 12x+6x-6y+6y=24+30 \\ 18x=54 \\ x=3 \end{gathered}[/tex]Now, for y
[tex]\begin{gathered} 4x-2y=8 \\ -2y=8-4x \\ 2y=4x-8 \\ y=\frac{4x-8}{2} \\ y=\frac{4\cdot3-8}{2} \\ y=\frac{12-8}{2} \\ y=\frac{4}{2} \\ y=2 \end{gathered}[/tex]Write an equation of variation to represent the situation and solve for the indicated information A bottle of 150 vitamins costs $5.25. If the cost varies directly with the number ofvitamins in the bottle, what should a bottle with 250 vitamins cost?Wei received $55.35 in interest on the $1230 in her credit union account. If the interestvaries directly with the amount deposited, how much would Wei receive for the sameamount of time if she had $2000 in the account?
A bottle of 150 vitamins costs $5.25.
The cost varies directly with the number of vitamins in the bottle.
What should a bottle with 250 vitamins cost?
Let C denotes cost and V denotes the number of vitamins.
The direct variation equation is
[tex]C=kV[/tex]Let us first find the value of k (constant of proportionality)
[tex]k=\frac{C}{V}=\frac{5.25}{150}=0.035[/tex]Now the cost of 250 vitamins may be found as
[tex]\begin{gathered} C=kV \\ C=0.035\times250 \\ C=\$8.75 \end{gathered}[/tex]Therefore, the cost of 250 vitamins is $8.75.
What is the area of the shaded region?____ square miles.
Finding the area of the shaded part means finding the area of the yellow triangle,
The exercise provide us the base and the height of the triangle, so we must replace these values in the next equation
[tex]A_{triangle}=\frac{b\cdot h}{2}[/tex]Where, b is the base and h is the height
[tex]A=\frac{5\text{ mi}\cdot4\text{ mi}}{2}=\frac{20\text{ mi}}{2}=10\text{ mi}[/tex]So, the area of the shaded region is 10 mi.
identify the place occupied by the digit 9. 1,664,963
Let us define place value
Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that we understand that whilst a digit can be the same, its value depends on where it is in the number.
Given the number 1,664,963, the place values of each of the numbers are
1= 1 Million
the first 6 from the left= 6 hundred thousands
the second 6 from the left = 6 ten thousands
4= 4 thousands
9= 9 hundreds
the last 6 from the left = 6 tens, and
3= 3 units
Hence, the place occupied by 9 in the number 1,666,963 is 9 hundreds
The data set shown below represents the time in minutes spent using a computer at Kinko's copy center by 25 people on a randomly selected day construct a stem and leaf plot for the data and analyze the results 16, 25, 18, 39, 25, 17, 29, 14, 37 22, 18, 12, 23, 32, 35, 24, 26 20, 19, 25, 26, 38, 38, 33, 29
areTo produce a stem and leaf plot, we should follow these steps:
Step 1- Rearrange the numbers in ascending or descending order: This will make the plotting of the stem and leaf plot a lot easier.
Step 2- Next, we select the stems from each number in the data. the stem is the first digit in the number in consideration. For example, the stem of 16 is 1 because it is the first digit. We do this selection of stems for all the numbers in the dataset.
Step 3- Next, we select the leaves. The leaves are the digits that come after the stem in a number. For example, in the number 16, while 1 is the stem, 6 is the leaf of the number.
Step 4- We arrange the stems and leaves in a table and this represents the stem and leaf plot.
With this information, we can proceed to solve the question
Solution
Step 1:
Rearranging the numbers, we have:
12, 14, 16, 17, 18, 18, 19, 20, 22, 23, 24, 25, 25, 25, 26, 26, 29, 29, 32, 33, 35, 37, 38, 38, 39
Step 2:
The stems of this data are just the first digit of each number.
12, 14, 16, 17, 18, 18, 19 all have a stem of 1
20, 22, 23, 24, 25, 25, 25, 26, 26, 29, 29 all have a stem of 2
32, 33, 35, 37, 38, 38, 39 all have a stem of 3.
Thus, the stems of this data are: 1, 2, and 3.
Step 3:
The leaves of the data are the second digits of the numbers. Thus, we have that
The leaves of these numbers 12, 14, 16, 17, 18, 18, 19 are: 2, 4, 6, 7, 8, 8, 9.
The leaves of these numbers 20, 22, 23, 24, 25, 25, 25, 26, 26, 29, 29 are: 0, 2, 3, 4, 5, 5, 6, 6, 9, 9
The leaves of these numbers 32, 33, 35, 37, 38, 38, 39 are: 2, 3, 5, 7, 8, 8, 9.
Step 4:
Thus, we can proceed to generate the leaf plot as follows:
How many bushels will there been in the figure hold? (1 cu ft≈ 1.24 bushels)
Answer:
151.93 bushels
Explanation:
First, let's find the volume of the truncated cone using the following equation
[tex]V=\frac{1}{3}\pi h(r^2+rR+R^2)[/tex]Where h is the height of the cone, r is the smallest radio and R is the largest radio. So, replacing h = 4 ft, r = 1.5 ft and R = 4.5 ft, we get:
[tex]\begin{gathered} V=\frac{1}{3}(3.14)(4)((1.5)^2+(1.5)(4.5)+(4.5)^2) \\ V=\frac{1}{3}(3.14)(4)(29.25) \\ V=122.52ft^3 \end{gathered}[/tex]Because the radius is half the diameter, so r = 3ft/2 = 1.5 ft and R = 9ft/2 = 4.5 ft.
Now, we know the volume in cubic feet. To find the volume in bushels, we will use the conversion factor 1 ft³ = 1.24 bushels.
[tex]122.52ft^3\times\frac{1.24\text{ bushels}}{1ft^3}=151.93\text{ bushels}[/tex]Therefore, the answer is 151.93 bushels
Maria made $161 for 7 hours of work.
At the same rate, how many hours would she have to work to make $115?
Answer: 5 hours
Step-by-step explanation: 161$/7h= 23 per hour, therefore, 115$/23 per hour= 5 hours.
Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form
The ratio of a 30-60-90 triangle is the following:
This means that the side that is opposite to the 60 degrees angle is "a" times the square root of 3, where "a" is the side adjacent to the 60 degrees angle. Therefore, applying this to the given triangle we get:
[tex]m=n\sqrt[]{3}[/tex]Also, the hypotenuse is "2a", therefore, we have:
[tex]84=2(n)[/tex]From there we can solve for "n" by dividing both sides by 2:
[tex]n=\frac{84}{2}=42[/tex]Now we can use this value to determine the value of "m":
[tex]m=42\sqrt[]{3}[/tex]To find a weekly average temperature, you add up all of the temperatures
and then divide by the number of days. Using the table of temperatures
below from Anchorage, Alaska, determine the average temperature for the
week given.
MONDAY
-31.4
TUESDAY
-35.2
WEDNESDAY
-33.8
THURSDAY
-34.9
FRIDAY
-32.7
The most appropriate choice for average will be given by-
Weekly average temperature of Anchorage = -33.6
What is average?
In a data set, there are many numbers. There has to be a number which will represent all the numbers in a data set. That representative is called average.
Average is calculated by dividing the sum of all observations by the number of observation.
Temperature on monday at Anchorage = -31.4
Temperature on monday at Anchorage = -35.2
Temperature on monday at Anchorage = -33.8
Temperature on monday at Anchorage = -34.9
Temperature on monday at Anchorage = -32.7
Weekly average temperature =
[tex]\frac{(-31.4) + (-35.2) + (-33.8) + (-34.9) + (-32.7)}{5}\\\\-\frac{168}{5}\\\\-33.6[/tex]
Weekly average temperature of Anchorage = -33.6
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Which are the foci of the hyperbola represented by… Thanks!
The equation is given to be:
[tex]x^2-3y^2+12=0[/tex]We can write the equation in the standard form of the equation of a hyperbola to be:
[tex]\frac{\left(y-0\right)^2}{2^2}-\frac{\left(x-0\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]Therefore, we have the following parameters:
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:a=2,\:b=2\sqrt{3}[/tex]Recall the hyperbola foci definition:
[tex]\begin{gathered} \mathrm{For\:an\:up-down\:facing\:hyperbola,\:the\:Foci\:\left(focus\:points\right)\:are\:defined\:as}\:\left(h,\:k+c\right),\:\left(h,\:k-c\right),\: \\ \mathrm{where\:}c=\sqrt{a^2+b^2}\mathrm{\:is\:the\:distance\:from\:the\:center}\:\left(h,\:k\right)\:\mathrm{to\:a\:focus} \end{gathered}[/tex]Therefore, the value of c will be:
[tex]\begin{gathered} c=\sqrt{2^2+(2\sqrt{3})^2} \\ c=4 \end{gathered}[/tex]Therefore, the foci will be:
[tex]\begin{gathered} \left(h,\:k+c\right),\:\left(h,\:k-c\right)=\left(0,\:0+4\right),\:\left(0,\:0-4\right) \\ Foci=\left(0,\:4\right),\:\left(0,\:-4\right) \end{gathered}[/tex]The correct option is the FIRST OPTION.
Which of the following phrases translates to m - 7?
A. the difference between seven and a number
B. a number subtracted from seven
C. seven minus a number
D. a number decreased by seven
m is an unknown number that is being decreased by 7.
OPTION A IS WRONG BECAUSE MATHEMATICALLY IT IS WRITTEN AS
[tex]7 - m[/tex]
B IS WRONG BECAUSE IT MEANS
[tex]7 - m[/tex]
C IS WRONG BECAUSE IT MEANS
[tex]7 - m[/tex]
BUT D IS THE ANSWER BECAUSE IT MEANS
[tex]m - 7[/tex]
SINCE m IS TREATED AS AN UNKNOWN NUMBER.
GOODLUCK!!!!
Write a mathematical model that estimates the average cost of tuition and fees, T, at public 4 years college for the school year ending x years after 2000
The mathematical model that estimates the average cost of tuition and fees, T, at public 4 years college for the school year ending x years after 2000 is T = 3349 + 379x.
We can use the data in Figure from 2000 and 2016 to estimate the
yearly increase in tuition and fees.
Yearly increase in tuition and fees is approximately = change in tuition and fees from 2000 to 2016 / change in time from 2000 to 2016
⇒ ≈ 9410 - 3349 / 2016 - 2000
⇒ 6061/16
= 378.8125
= 379
Each year the average cost of tuition and fees for public four-year
colleges is increasing by approximately $379.
Now we can use variables to obtain a mathematical model that estimates the average cost of tuition and fees, T, for the school year ending x years after 2000.
⇒ The average cost of tuition and fees is:
⇒ T = 3349 + 379x
The mathematical model T = 3349 + 379x estimates the average cost
of tuition and fees, T, at public four-year colleges for the school year
ending x years after 2000.
Hence we get the mathematical model as T = 3349 + 379x
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Find the slope of the line that passes through (97, 21) and (54, -17).
Given data:
The first point given is (97, 21).
The second point given is (54, -17).
The slope of the line passing through the given points is,
m=(-17-21)/(54-97)
=-38/-43
=38/43
Thus, the slope of the line passing through the given points is 38/43.
Use the Pythagorean theorem to determine the unknown length of the right triangle Determine the length of side c in each of the triangles that followers Do not include any units in your answer
Recall the Pythagorean Theorem:
For a right triangle with legs of lengths A and B and hypotenuse C, the following relation is satisfied:
[tex]A^2+B^2=C^2[/tex]If two variables are known (it could be the hypotenuse and one leg, or both legs), then the third can be calculated. If the hypotenuse is not known, it can be calculated as:
[tex]C=\sqrt[]{A^2+B^2}[/tex]If one of the legs is not known, then we can substract the other length squared, and then take the square root:
[tex]\begin{gathered} A^2=C^2-B^2 \\ \Rightarrow A=\sqrt[]{C^2-B^2} \end{gathered}[/tex]For problems involving the Pythagorean Theorem, use these equations by replacing the corresponding numerical values of A, B or C. Remember that C does not always stand for the hypotenuse, it always depend on the diagram. For example, if the legs of the right triangle were labelled as X and Y, and the hypotenuse was A, then:
[tex]X^2+Y^2=A^2[/tex]Be careful with that.
In the diagram, AC = 12 V3. Find BC and AB. Write your answers in simplest form.B60930O BC = 72. AB = 36O BC = 36. AB = 72O BC = 24, AB = 12O BC = 12. AB = 24
constructing the triangle
From the figure,
We will be applying trig. ratios
[tex]\text{SOH CAH TOA}[/tex]Finding BC with respect to angle 30
[tex]\begin{gathered} \text{Tan 30 = }\frac{opp}{adj} \\ \text{Tan 30 = }\frac{BC}{12\sqrt[]{3}} \\ \text{cross multiply} \\ BC\text{ = Tan 30 }\times12\sqrt[]{3} \\ BC\text{ = }\frac{\sqrt[]{3}}{3}\text{ }\times\text{ 12}\sqrt[]{3} \\ BC\text{ = }\sqrt[]{3\text{ }}\text{ }\times\text{ 4}\sqrt[]{3} \\ BC\text{ = 4 }\times3 \\ BC\text{ = 12} \end{gathered}[/tex]Finding AB with respect to angle 30
[tex]\begin{gathered} \cos \text{ 30 = }\frac{adj}{hyp} \\ \cos \text{ 30 = }\frac{12\sqrt[]{3}}{AB} \\ \text{cross multiply} \\ \cos \text{ 30 }\times\text{ AB = 12}\sqrt[]{3} \\ \text{divide both sides by cos30} \\ AB\text{ = }\frac{12\sqrt[]{3}}{\cos \text{ 30}} \\ AB\text{ = }\frac{12\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ AB\text{ = 12}\sqrt[]{3}\text{ }\times\text{ }\frac{2}{\sqrt[]{3}} \\ AB\text{ = 12 }\times2 \\ AB\text{ = 24} \end{gathered}[/tex]Therefore,
BC = 12 and AB = 24
Tiana said that her cable bill of $25 is less than $3 more than 5 times what Lottie pays for cable. Write an inequality that shows Tiana's comparison.
If c is the bill that Lottie pays for cable, the given situation can be represented by the following inequality:
25 < 3 + 5c
in the previous inequality, you have that 25 is less (<) than 3 more (3 + ) than 5 times (5x) what Lottie pays for cable.
The previous inequality can be also written as follow:
3 + 5c > 25
Evaluate.
(15+12)2+310⋅5
Enter your answer as a mixed number in simplest form.
Answer:
337.5
Step-by-step explanation:
first you solve what is in the bracket and add the 2 to give you 27 then add the 310.5
If x and y are in direct proportion and y is 2 when x is 4, what is y when x is 12.
If x and y are in direct proportion and y is 2 when x is 4 and y is 6 when x is 12.
By definition of proportionality,
If y is directly proportional to x,
y α x
i,e y = k(x)
K is the constant of proportionality
when x = 4, y =2
2 = k(4) --> k = 1/2
Now y = k.x
y = 1/2 (12)
y = 6
What is the Constant of Proportionality?
The proportional constant is a ratio that connects two given values in a so-called proportional relationship. Other names for the constant of proportionality are constant ratio, constant rate, unit rate, constant of variation, or even rate of change.
To find the constant of proportionality, first identify the variables x and y. To find out the relationship between weight and number of sticks, x is the weight and y is the number of butter sticks. Use the equation k = y÷ x to find the constant of proportionality.
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I need to know the following steps to find the range and domain.
In a radical function as given the domain is any x-value for which the radical (value under the radical sing) is not negative:
[tex]\begin{gathered} x^2+1\ge0 \\ x^2\ge-1 \\ \end{gathered}[/tex]As any value of x makes x squared be possitive or 0, the domain is:
[tex]\begin{gathered} x\in\R \\ Interval\text{ notation:} \\ (-\infty,\infty) \end{gathered}[/tex]Any value of x makes x squared greater than or equal to zero the range is:
[tex]\begin{gathered} x^2\ge0 \\ \\ \text{Range stars in x=0:} \\ f(0)=\sqrt[]{0+1} \\ f(0)=\sqrt[]{1} \\ f(0)=1 \\ \\ Range\colon \\ y\ge1 \\ \\ \text{Interval notation;} \\ \lbrack1,\infty) \end{gathered}[/tex]Solve x/2 -3 =71. 52.403.104.20
We have the expression:
[tex]\frac{x}{2}-3=7[/tex]We solve as follows:
[tex]\Rightarrow\frac{x}{2}=10\Rightarrow x=20[/tex]From this, we have that the solution is option 4, x = 20.
Edwin deposited money into a savings account that pays a simple annual interestrate of 1.2%. He earned $27 in interest after 3 years. How much did he deposit?Round answer to the hundredths place. If answer does not have a hundredths placethen include zeros so it does.
Solution
Given
r = 1.2% = 0.012
A = $27
t = 3 years
Since Amount(A) = Principal(P) + (Principal(P) × Rate(r) × Time(t))
[tex]\begin{gathered} A=P+PRT \\ \\ \Rightarrow A=P(1+RT) \end{gathered}[/tex]=> 27 = P(1 + r × t)
[tex]\begin{gathered} \Rightarrow27=P(1+r\times t) \\ \\ \Rightarrow P=\frac{27}{1+(r\times t)} \\ \\ \Rightarrow P=\frac{27}{1+(0.012\times3)}\approx\$26.06 \end{gathered}[/tex]Hence, the principal is $26.06
Angel, Brandon, and Carla work in the same office.
•Angels age is 4 years more than twice than Carla’s age
•Brandon is 5 years younger than Carla
If N represents Carla’s age, write and expression for Angels age and Brandon’s age. The sun of Angels,Brandon’s, and Carla’s age is 123
What is the answer to 2 tokens + 2 tokens
Answer: 4 tokens
Step-by-step explanation: 2+2=4
Answer:
4
Step-by-step explanation:
We can figure this out by counting. Using our fingers, we start with two, then when we add two more we have four fingers, or in this case tokens.
Identify the arc length of BD in terms of pi and rounded to the nearest hundredth.
The radius of the circle, r = 8 in
m
That is the angle, θ = 92°
The length of arc BD is given by the formula:
[tex]\begin{gathered} \text{Arc BD = }\frac{\theta}{360}\times2\pi r \\ \text{Arc BD = }\frac{92}{360}\times2(8)\pi \\ \text{Arc BD = }4.09\pi\text{ in} \end{gathered}[/tex]If π = 3.142
Arc BD = 4.09 (3.142)
Arc BD = 12.85 in
593 divided 60 with remainder
Use each of the numbers from 1 to 9 exactly once to create three mixed numbers with the greatest possible product. Then use each of the numbers exactly once to create three mixed numbers with the least possible product. Find each product. Explain your reasoning. The fraction portion of each mixed number should be proper.
Answer:
here
Step-by-step explanation:
hitler demanded to be appointed as chancellor. German President Paul von Hindenburg initially resisted this demand. However, he gave in and appointed Hitler as Chancellor of Germany on January 30, 1933. Hindenburg appointed Hitler to this position as the result of a political deal.
if n (A)=4, n (B) =9, and n(A ∩ B) =2; what is n( A U B)?
Given:
[tex]\begin{gathered} n(A)=4 \\ n(B)_{}=9 \\ n\mleft(A\cap B\mright)=2 \end{gathered}[/tex]To find:
[tex]n(A\cup B)[/tex]Using the formula,
[tex]\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ =4+9-2_{} \\ =11 \end{gathered}[/tex]Hence the answer is 11.
Find the I- and y-intercepts of the following equation: 2x + 3y = -24 Choose one · 1 point Oy, intercept: (0,8) intercept: (12,0) Oy- intercept: 0,-8) I - intercept: (-6,0) Oy- intercept : (0,8) I - intercept: (-12,0) Oy- intercept : (0,8) intercept: (-6,0)
The x-intercept and y-intercept are (-12,0) and (0,-8) for the equations is 2x+3y=-24.
Given that,
The equation of 2x+3y=-24
We must determine the equation's x-intercept and y-intercept.
In the cartesian coordinate system, the horizontal X-axis and the vertical 'Y-axis' are two perpendicular axes that make up the coordinate plane. The line's intercepts—where it crosses the two axes are referred to as.
We have to find x-intercept.
To find x-intercept take the y value as zero.
2x+3y=-24
2x+3(0)=-24
2x=-24
x=-24/2
x=-12
Now, To find y-intercept take x value as zero.
2x+3y=-24
2(0)+3y=-24
3y=-24
y=-24/3
y=-8
Therefore, The x-intercept and y-intercept are (-12,0) and (0,-8) for the equations is 2x+3y=-24.
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1. An Uber driver charges a $3 boarding rate in addition to $2 for every mile. What is the equation of the
line that represents this driver's rate? How much is the rate for 5 miles? For 7 miles? What is the x axis?
What is the y axis? What is the y-intercept?
2. An office has an envelope stuffing machines. The machine can stuff a batch of envelopes in 5 hours.
How long would it take the machines to stuff 10 batches of envelopes? 14 batches of envelopes? What
is the x axis? What is the y axis?
3. Sarah has a job working for Boeing constructing plane wings. She earns a Salary of $67,500.00 a year,
with an overtime flat rate of $20.00 an hour. How much money did she make before taxes if she worked
88 hours of overtime last year? What is the x axis? What is the y axis? What is the y-intercept?
For 5 miles ride uber driver charges $13and for 7 miles ride uber driver charges $17.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
The y-intercept is the point where the graph intersects the y-axis.
2- For 10 batches of envelopes machine take 50 hours and for 14 batches of envelopes machine take 70 hours.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
3-Sarah makes $1760 money if she worked 88 hours of overtime last year.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
Solution 1 -
What is linear equation?
A linear equation is an algebraic equation where each term has an exponent of 1, it always results in a straight line.
uber driver charges a $3 and for every mile charge $2
let assume driver complete x miles ride and charge y $.
so, 3 + 2x = $y
For 5 miles, put the value of x = 5
3 + 2(5) = y$
y=$13
For 7 miles, put the value of x = 7
3 + 2(7) =$ y
y=$17
Therefore, for 5 miles ride uber driver charges $13and for 7 miles ride uber driver charges $17
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
The y-intercept is the point where the graph intersects the y-axis.
solution 2-
given information a batch of envelopes machine stuff in 5 hours.
so, for 10 batches of envelopes machine take 10 x 5 = 50 hours.
given information a batch of envelopes machine stuff in 5 hours.
so, for 14 batches of envelopes machine take 14 x 5 = 70 hours.
Therefore, for 10 batches of envelopes machine take 50 hours and for 14 batches of envelopes machine take 70 hours.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
Solution 3 -
given - Sarah earns a salary of $67,500 a year.
Boeing company pay her for per hour overtime =$20.00
if Sarah worked 88 hours, then company will pay her = 88 ($20.00)
= $1760
Therefore, Sarah makes $1760 money if she worked 88 hours of overtime last year.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
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A sign above a basket of DVD reads "3 for $17." Kellen decides to buy 6 DVDs and use a coupon for 25% off. If sales tax is 6%, what will he pay in total?
The pay in total will be:
since 3 cost $17then 6 will cost 2(17)=$34
then we apply the coupon for 25% off, obtainning 34-0.25(34)=$25.5
now we add the taxes, 25.5+0.06(25.5)=$27.03
Then the final price will be 27.03 dollars