Instructions: varies indirectly with . If =7 when =−4, find when =2. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12).
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y varies directly as x
This can be written mathematically as:
y = kx
If y = 7, x = -4
Solve for the constant k
7 = -4k
k = -7/4
The equation is:
y = -7/4 x
When x = 2
substitute x =2 anto the equatio n y = -7/4 x
[tex]\begin{gathered} y=-\frac{7}{4}\times2 \\ \\ y=-\frac{7}{2} \end{gathered}[/tex]Related Questions
What are lim f(x) and lim f(x) if they exist?
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SOLUTION:
Case: Limits
Method:
Right and left-sided limits.
The right sided limits is gotten from the right-hand side and gives an f(x) of 0 while the left sided limits gives an f(x) of 1.
Final answer: Option
[tex]\begin{gathered} \lim_{x\to0^-}f(x)=1 \\ \lim_{x\to0^+}f(x)=0 \end{gathered}[/tex]O GEOMETRY Perimeter involving rectangles and circles A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 88 m long and 67 m wide. What is the length of a training track running around the field? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.) 88 m 1 67 m 1 0 m X m² S m³ 1/5 ?
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Step 1
to know the full distance for the track running we need to add twilce the length of the rectangle to the perimeter of the circel, so
so
a) find the circumference of the circle , it is given by
[tex]\begin{gathered} C=\text{ }\pi d\text{ } \\ where\text{ d is the diameter} \end{gathered}[/tex]hence
[tex]\begin{gathered} let\text{ d=67 m} \\ so \\ C=\pi *67\text{ m=210.38 m} \end{gathered}[/tex]finally, add twice the length of the rectangle, so
[tex]\begin{gathered} traininin\text{ track = 210.38+\lparen2*88\rparen=210.38+176} \\ traininin\text{ track = 386.38} \end{gathered}[/tex]therefore, the answer is
[tex]386.38\text{ m}[/tex]I hope this helps you
Use an alternative method to express the following set: {y:y is a person in your math class and also more than 100 years old.}
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Let's use the letter M to label the math class. The fact that person y is in that class can be expressed by:
[tex]y\in M[/tex]We also have to show that is older than 100 so we have:
[tex]y>100[/tex]If we put all this information together we get:
[tex]\mleft\lbrace y\colon y\in M,y>100\mright\rbrace[/tex]And that's an alternative way to express the set.
Find the total amount in the compound interest account $10000 is compounded semiannually at a rate of 11% for 20 years. (Round to the nearest cent.)
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The compound interest formula is:
[tex]A=P(1+\frac{r}{m})^{mt}\begin{cases}A=amount \\ P=initialValue \\ r=interest \\ m=\#timesCompounedPerYear \\ t=years\end{cases}[/tex]Therefore:
[tex]A=(10000)(1+\frac{0.11}{1})^{20}=80623.12[/tex]-4x-2y = -6a. y = -2x + 3b. y = 2x-3C. y = 2x + 3d. y = -2x - 3
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Determine the domain and range of the function shown below. Assume the entire function is shown. Domain: Range:
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The function is made of the following ordered pairs:
(-1,-3) (1, -5) (2, 3) (3, 6) (5, 6) (7, -1)
The first coordinate of the ordered pairs is the input value and the second coordinate is the output value of the function.
The domain is the set of all the input values as shown below:
Domain: {-1, 1, 2, 3, 5, 7}
Range: {-3, -5, 3, 6, -1}
Sorting the values of the range.
Range: {-5, -3, -1, 3, 6}
7. Simplify28120.51 +423) + (222 +7.51).
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Answer: 581.5i + 140.64
Explanation:
574i + 118.44 + 22.2 +7.5i
grouping the terms yield
574i + 7.5i + 118.44 + 22.2
⇒
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The domain is the set of all possible inputs that would satify the function while the range is the set of possible output values
Looking at the given graph,
Domain = ( - infinity, 4)
Range = (- 5, 2)
Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).
Oa y-4-2
(x+3)
Oby+3=-2 (x-4)
OC y-3= -2(x-4)
y+3= =(x-4)
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The point-slope form that passes through (4, -3) and (2, 1) is y+3 is −2(x−4). A slope of a line is the change in y coordinate with respect to the change in x coordinate.
How to calculate Point-slope form ?The slope of the line and any points on the line determine the point-slope form of a line. When given a point on the line and the slope, the form's purpose is to describe the equation of the entire line.
The slope of a line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by m = y2−y1 / x2−x1
We have that x1=4, y1=−3, x2=2, y2=1.
Plug the given values into the formula for slope: m = (1)−(−3)/(2)−(4)
=4−2 =−2.
Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).
b=−3−(−2)⋅(4)=5.
Finally, the equation of the line can be written in the form y=mx+b.
y=−2x+5.
The slope of the line is m=−2.
The equation of the line in the slope-intercept form is y=−2x+5.
The equation of the line in the point-slope form is y+3=−2(x−4).
The equation of the line in the point-slope form is y−1=−2(x−2).
The general equation of the line is 2x+y−5=0.
To learn more about Point-slope form refer :
https://brainly.com/question/24907633
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9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If theycombine efforts to fill one order to sew 30 dresses, how long will they take to fill the order?Answer
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Given that Alberta Emery can sew 1 dress in 3 days. so the efficiency of Alverta Emery is given by,
[tex]=\frac{1}{3}\text{ work per day}[/tex]Similarly, given that Allison Taylor takes 2 days to sew 1 dress, so the efficiency of Allison Taylor is given by,
[tex]=\frac{1}{2}\text{ work per day}[/tex]When they combine their efforts, the amount of work done per day is given by,
[tex]\begin{gathered} =\frac{1}{3}+\frac{1}{2} \\ =\frac{2+3}{6} \\ =\frac{5}{6}\text{ work per day} \end{gathered}[/tex]So the number of days required to sew 30 dresses when both of them work together, is calculated as,
[tex]\begin{gathered} =\frac{30}{\frac{5}{6}} \\ =30\cdot\frac{6}{5} \\ =6\cdot6 \\ =36 \end{gathered}[/tex]Thus, they will take 36 days to sew 30 dresses.
The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 69?
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Given:
The box-and-whisker plot below represents some data set.
As shown:
The median = 65
The value of Q1 = 61
The value of Q3 = 69
The percentage of the data values that are greater than 69 will be the percentage of the data that are greater than Q3
So, the answer will be 25%
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds
worth of pie, and has 7 people to feed, including herself. How much does each
person get if Charlotte is finished making pies?
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more
people to feed, how much pie will each person get from Charlotte's 5.04
pounds?
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Step-by-step explanation:
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds worth of pie, and has 7 people to feed, including herself. How much does each person get if Charlotte is finished making pies?
5.04 / 7 = 0.72 pounds per person
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more people to feed, how much pie will each person get from Charlotte's 5.04 pounds?
7 + 2 = 9 people now
5.04 / 9 = 0.56 pounds per person
The half-life of a certain substance is 27 years. How long will it take for a sample of this substance to decay to 66% of its original amount? for the sample of the substance to decay to 66% of its original amount
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This is a type of radioactive decay problem. Given an initial amount of N0, the amount at t years is given by
[tex]N(t)=N_0e^{-\lambda t}[/tex]The information "27 years is the half-life of the substance" means that if we replace t by 27, we will get exactly half of the initial amount we had. That is
[tex]N_0e^{-\lambda\cdot27}=\frac{N_0}{2}[/tex]We can cancell out N0 on both sides, so we get
[tex]e^{-\lambda\cdot27}=\frac{1}{2}[/tex]using the properties of exponentials, we have the equivalent equation
[tex]\frac{1}{2}=\frac{1}{e^{\lambda\cdot27}}[/tex]which is also equivalent to
[tex]e^{\lambda\cdot27}=2[/tex]If we apply natural logarithm on both sides, we get
[tex]\ln (e^{\lambda\cdot27})=\lambda\cdot27=\ln (2)[/tex]Finally, we can divide both sides by 27, to get
[tex]\lambda=\frac{\ln (2)}{27}[/tex]So, the function that describes the amount of the subtances at time t is given as
[tex]N(t)=N_0e^{\frac{-\ln (2)\cdot t}{27}}[/tex]Now, we want to calculate the value of t, for which the amount we have at year t is exactly 66% of what we have at t=0. That is
[tex]\frac{N_0e^{-\frac{\ln (2)\cdot t}{27}}}{N_0}=0.66[/tex]We can cancell out N0 and, by equivalence by using the properties of exponents, we get
[tex]\frac{1}{e^{\frac{\ln(2)}{27}\cdot t}}=0.66[/tex]which is also equivalent to
[tex]\frac{1}{0.66}=e^{\frac{\ln (2)t}{27}}[/tex]if we apply the natural logarithm on both sides, we get
[tex]\ln (\frac{1}{0.66})=\ln (e^{\frac{\ln(2)\cdot t}{27}})=\ln (2)\cdot\frac{t}{27}[/tex]Finally, we want to solve for t. To do so, we can multiply by 27 and then divide by ln(2). So we get
[tex]t=\frac{27}{\ln(2)}\cdot\ln (\frac{1}{0.66})[/tex]with help of a calculator, we have that t is approximately 16.185. That is, about after 16 years, we will have 66% of the initial amount.
Simplify the expression 8h + (-7.3d) - 14 + 5d - 3.2h
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The expression is:
8h + (-7.3d) - 14 + 5d - 3.2h
collecting like terms, we have:
8h - 3.2h +(-7.3d) + 5d - 14
= 4.8h - 7.3d + 5d - 14
= 4.8h - 2.3d - 14
That is the expression simplified
8. (07.01 MC)If the sin 60º = 13, then which statement is true? =2cos 30º =V3, because the cosine and sine are complements523cos 120º =2because the cosine and sine are supplementscos 30º = 0, because the cosine and sine are complementscos 120º = 0, because the cosine and sine are supplements
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Note that if the angles are complementary with each other, the sine and cosine are the same.
From the problem, sin 60 = √3/2, the complement of 60 degrees is 30,
so cos 30 is the same as sin 60.
The best answer is Choice A
Simplify the following expression. 7m+7(4m+2)
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Given the expression:
7m + 7(4m + 2)
Use distributive property to expand the parenthesis:
= 7m + 7*4m + 7*2
= 7m + 28m + 14
Sum up like terms:
= 35m + 14
ANSWER:
35m + 14
what do factors 12 and 24 have in common
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Mcd (max common divisor) of 12, 24 = 12
(Because 24/12= 2 )
are
2,3,4,6,12
Vihaan got 38/48 on his geography test. Sahaj got 80% on his geography test. Jada got 0.8125 on her geography test. Quinn thinks that Vihaan got a higher mark on his test than Sahaj and Jada.Is Quinn right? Prove whether he is right or wrong by showing your work (5 marks)
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Vihaan got 38 in her geography test
Since the geography test has a total score of 48
Since Sahaj got 80% of it, then multiply 80/100 by 48 to find his score
[tex]\frac{80}{100}\times48=38.4[/tex]Sahaj got 38.4 on the geography test
Since Jada got 0.8125 on her geography test, then multiply 0.8125 by 48 to find her score
[tex]0.8125\times48=39[/tex]Jada got 39 on the geography test
The greatest one is Jada, then Sahaj, then Vihaan
Quinn thinks that Vihaan got the higher score
But Jada the one who got the higher score
Then Quinn is not right
Question 6: a study of several cities show a positive correlation between the percent of people biking to work and percent of people spending their vacation time at home.What statement is most likely true? A. Correlation implies causation; therefore vacationing at home make people want to ride their bike.B. Correlation implies causation; therefore, bike riding makes people want to vacation at home.C. Correlstion does not imply causation; therefore,the correlation is due to a third. variable: cost of milk.D. Correlation does not imply correlation, therefore is due to a third variable: cost of gas.
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If the study shows a positive correlation means that as people bike to work increase also the percentage of people spending their vacation time at home increases
since work happens before vacation one of the statemens that is most likely to be true will be B.
Can you please help me out with a question
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The volume of the figure = volume of first cone + volume of second cone + volume of a hemisphere
Formula
Volume of a cone = 1/3πr²h
The volume of hemisphere = 2/3πr³
Therefore
r = radius , h = height
where h1 = 20in , h2 = 18in and r = 15in
Volume of the first cone = 1/3πr²h1
= 1/3 x π x (15)² x 20
= 1500π in³
Volume of the second cone = 1/3πr²h2
= 1/3 x π x (15)² x 18
= 1350π in³
Volume of hemisphere = 2/3πr³
= 2/3 x π x (15)³
= 2250π in³
Therefore
The volume of the figure = 1500π in³ + 1350π in³ + 2250π in³
= 5100π in³
Hence the volume of the figure = 5100π in³
Convert 15% to a fraction. Write in lowest terms.Convert 26% to a fraction. Write in lowest terms.Read the "Fractions, Decimals & Percents" lesson. Then answer each of the following questions to practice converting between fractions, decimals and percents.
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Convert 15% to a fraction. Write in the lowest terms.
So,
[tex]15\%=\frac{15}{100}=\frac{5\times3}{5\times20}=\frac{3}{20}[/tex]So, the answer will be 15% = 3/20
=========================================================
Convert 26% to a fraction. Write in the lowest terms.
So,
[tex]\frac{26}{100}=\frac{2\times13}{2\times50}=\frac{13}{50}[/tex]So, the answer will be 26% = 13/50
A credit union client deposits $2,700 in an account earning 6% interest, compounded annually. What will the balance of the account be at the end of 31 years?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Balance ≈ $________ after 31 years.
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Answer:
Balance ≈ $7,722 after 31 years
Step-by-step explanation:
multiply your deposit by your interestMultiply by how longAdd your base deposit to the interestEx.
2, 700(0.06) =$162.
162(31)= $5,022.
5,022 + 2,700 = $7,722.
Mr. Cumme bought the amount of clay listed for his class.- 2.2 kilograms- 1.5 kilograms- 850 grams - 700 gramshow many grams of clay did Mr.Cumme buy?
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Hello there. To solve this question, we have to remember how to convert kilograms to grams.
Given an amount in kilograms, to determine its value in grams, we simply multiply it by 1000.
In this case, we know that Mr. Cume bought the amount of clay listed for his class:
- 2.2 kilograms
- 1.5 kilograms
- 850 grams
- 700 grams
To determine how many grams of clay he bought, we start converting the values from kilograms to grams
2.2 kilograms * 1000 = 2200 grams and
1.5 kilograms * 1000 = 1500 grams
Now, we add everything
2200 + 1500 + 850 + 700 = 5250 grams
This is the final answer to this question.
PLEASE HELP ME !!!!!!!!
Find and describe the error in the following problem
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Answer:
When multiplying the bottom equation, they did not multiply 4y by -2, but instead by 2.
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 50 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
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Answer:
See below
Step-by-step explanation:
Final amount of pure antifreeze = .75 (50)
amount of 70 % that is pure antifreeze = .70 x
amount of 95 % that is pure antifreeze = .95 (50-x)
ingredients in = ingredients out
.70x + .95 (50-x) = .75 (50)
x = 40 gal this is the amount of 70 %
then 95 % = 50 - 40 = 10 gal
fill in the blanks.30x8=3x_____x840x7=_____x10x7
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Answer:
30x8=3x_10_x8
40x7=_4_x10x7
First one: 10
Second one: 4
radical 9 cubed times radical -24 cubed=?
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we can easily calculate that -6 times -6 times- 6 =- 216 it is why we can do this equality
because we have an exponent 3 and a cubic root we can cancel both so the answer of
[tex]\sqrt[3]{9}\text{ }\cdot\sqrt[3]{-24}=\text{ -6}[/tex]A store makes a profit of $25 on each watch it sells. What solution setwill represent how many watches the store must sell to make a profitof at least $375?US
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Here, the variable is the number of watches.
The profit on each watch it sells is, $25.
The least profit to be made is, $375.
Let x be the number of watches, Then we have, the total profit as,
[tex]25x[/tex]This profit should be atleast 375, therefore, we have,
[tex]\begin{gathered} 25x\ge375 \\ \frac{25x}{25}\ge\frac{375}{25} \\ x\ge15 \end{gathered}[/tex]5. * 20 points Rotate 180° about the origin. 3 Y 4 5 3
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In order to rotate these point 180° about the origin, we just need to change the signal of all coordinates.
So we have that:
[tex]\begin{gathered} X(-1,3)\to X^{\prime}(1,-3) \\ W(-2,5)\to W^{\prime}(2,-5) \\ V(-5,5)\to V^{\prime}(5,-5) \\ T(-4,3)\to T^{\prime}(4,-3) \end{gathered}[/tex]Looking at the options, the correct one is c. (the third one).
uueJUU Telp Find the area of the polygon. The area of the polygon is (Type a whole number.) 4 cm 7 cm 7 cm -14 cm 14 cm יד 4 cm
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The area of the polygon = Sum of area of eight triangles + area of a square.
Area of the square
[tex]\begin{gathered} \\ \text{Length = 14cm} \\ \text{Area of the square = Length}^2 \\ \text{ = 14}^2 \\ =196cm^2 \end{gathered}[/tex]Area of one triangle
[tex]\begin{gathered} =\text{ }\frac{Base\text{ x Height}}{2} \\ \text{Base = 4cm} \\ \text{Height = 7cm} \\ =\text{ }\frac{4\text{ x 7}}{2} \\ =\text{ }\frac{28}{2} \\ =14cm^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the eight triangles = 8 x 14 } \\ \text{ = 112 cm}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the polygon = 196 + 112} \\ \text{ = 308 cm}^2 \end{gathered}[/tex]