In an inverse variation,y = 4when x = 2.Write an inverse variatione quation thats hows there relationship between x and y . Write the equation using a decimal or an integer.
When y = 4 and x = 2, the inverse variation equation is y = 8/x
What is inverse variation?Inverse variation is variation in which the relationship between two variables is an inverse one. That is, while one variable increases, the other decreases.
How to write an inverse variation equation that shows there relationship between x and y.Given that in an inverse variation, y = 4 when x = 2. Since y and x have an inverse relationship, we have that
y ∝ 1/x, this implies that
⇒ y = k/x where k = constant of proportionality
Now, given that in an inverse variation, y = 4 when x = 2. Substituting the values of y and x into the equation, we have that
y = k/x
4 = k/2
k = 4 × 2
k = 8
So, susbstituting k = 8 into the equation for y, we have
y = k/x
y = 8/x
So, the inverse variation equation is y = 8/x
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In 11 years, John's age will be 5 less than 5 times his current age. How old is he?
If xrepresents John's current age, which of the following equations could be used to solve this problem?
Answer:
x=4
Step-by-step explanation:
ABC=40 and Bd is angle bisector of ABC what is Y= ?
The measure of angle ABD is 20 degrees and this can be determined by using the properties of the angle bisector.
Given :
ABC = 40 and BD is the angle bisector of angle ABC.
The following steps can be used in order to determine the angle ABD:
Step 1 - According to the given data, BD is the angle bisector of angle ABC.
Step 2 - An angle bisector bisects the angle into two equal parts.
Step 3 - So, the measure of angle ABD is calculated as:
So, the measure of angle ABD is 20 degrees.
Ruth's new lunch box is only 5 centimeters in height, so it fits in her backpack along with all her books. The lunch box has 3 sections for different types of food. The length and width of the lunch box are 22 centimeters and 14 centimeters. What is the volume of Ruth's new lunch box?
The volume of Ruth's new lunch box is 1,540 cm³.
What is the volume?The volume is a measure of an object occupied in a three-dimensional space.
Volume is a three-dimensional quantity that measures the capacity of a shape or the amount of three-dimensional space a closed figure can occupy.
The formula for computing a volume is height x length x width.
Data and Calculations:Height = 5 cm
Length = 22 cm
Width = 14 cm
Volume = 1,540 cm³ (5 x 22 x 14)
Thus, the volume of Ruth's new lunch box, showing the three-dimensional space within, is 1,540 cm³.
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What is 2m to the 4th power times 5m to the second power
Answer:
hope this helps if this is what you meant
10m6
Step-by-step explanation:
=2*m4*5*m2
=10*m6
=10m6
Can someone please help me really quick
The amount of the shed that Jack would have built when Kyle finishes the shed is 8/25.
How much shed would Jack have built?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 8/25. 8 is the numerator and 25 is the denominator.
When Kyle finishes building the shed, he would have finished building a fraction of 1/1 of the shed. S
So, the amount of shed, that Kyle still needs to build to complete the shed is 1 ÷ 5/8
= 1 x 8/5 = 8/5
The amount of shed that Jack will have built when Kyle finishes the shed is:
8/5 x 1/5 = 8/25
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Which number sentence represents 8 times as many as 9
Answer:
72
Step-by-step explanation:
this number sentence will be represented as,
72 is 8 times as many as 9
Help me with my problem please I NEED HELP!!!!!!!
The second
The correct answer is N ∈ line MN
The third
The correct answer is P ∉ line MN
The fourth
The correct answer is B ∉ line MN
How to interpret the symbolsThe symbols are interpreted as follows
∈ is interpreted as "is a member of"∉ is interpreted as "is not a member of"Given data
line MN
How to describe the location with respect to line MNThe first
It is already given that is M ∈ line MN
point M can be located in line MN
The second
The correct answer is N ∈ line MN
point N can be located in line MN
The third
The correct answer is P ∉ line MN
point P cannot be located in line MN it is off the line
The fourth
The correct answer is B ∉ line MN
point B cannot be located in line MN it is off the line
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Jack is in a marathon. He rides his bike 64 miles in 4 hours. How many miles does Jack ride his bike per hour?
Answer: 16mph
Step-by-step explanation:
64 miles divided by the 4 hours comes out to 16 per hour
Answer: 16 miles per hour
a chessplayer won 32 of the games he played if the ratio of wins to lossses was 8:3 how many games did he play total
Answer:
Step-by-step explanation:
i don't know if this is right but here is how i would do it.
Wins: Losses = 8:3 = 32: 12 = 32 wins + 12 losses = 44 games played.
A floor 5m by 20m is covered by square tiles
The number of tiles is mathematically given as
x=2500Tiles
This is further explained below.
How many tiles are needed??Generally, the equation for the Area of the floor is mathematically given as
A= 20*5
A = 100m^2
Where
20*20=400cm
Therefore no tiles needed is
x=100*10000/400
x=2500Tiles
In conclusion, the number of tiles is
x=2500Tiles
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CQ
\A floor 5m by 20m is covered by square tiles of side 20cm. How many tiles are needed?
you conduct a survey of your small town about having a townwide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results. write an absolute value equation for the least and greatest percentages that could be opposed. use x for the variable.
In the given statement is:
You conduct a survey of your small town about having a town wide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results.
Using the absolute value function, we have that:
A. The least percentage is of 39% and the greatest is of 49%.
B. Since the greatest percentage is below 50%, the statement conflicts with the survey data.
What is the absolute value function?
The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
For this problem, the difference between the percentage of opposed and 44% can be of at most 5%, hence the absolute value equation is:
|x - 44| = 5.
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How do you solve this −6x−16<2x
Answer:
x >-2
Step-by-step explanation:
subtract 2x from both sides
-6x - 16 - 2x < 0
subtract 2x from 6x
-8x - 16 < 0
add 16 to both sides
-8x < 16
divide by -8
x> -2
what is the inverse of (x) = [tex]\sqrt{x+9}[/tex] x[tex]\geq[/tex] -9
f−1(x)=(x−9)2, x≥9
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals left parenthesis x minus 9 right parenthesis squared, , , x is greater than or equal to 9
f−1(x)=−(x−9)2, x≤9
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative left parenthesis x minus 9 right parenthesis squared, , , x is less than or equal to 9
f−1(x)=x2−9, x≥0
f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x squared minus 9, , , x is greater than or equal to 0
f−1(x)=x2−9, x≤0
The inverse of [tex]f[/tex], denoted [tex]f^{-1}[/tex], is such that
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given [tex]f(x)=\sqrt{x+9}[/tex], we have
[tex]f\left(f^{-1}(x)\right) = \sqrt{f^{-1}(x) + 9} = x[/tex]
Solve for [tex]x[/tex].
[tex]\sqrt{f^{-1}(x) + 9} = x[/tex]
[tex]\left(\sqrt{f^{-1}(x) + 9}\right)^2 = x^2[/tex]
[tex]f^{-1}(x) + 9 = x^2[/tex]
[tex]f^{-1}(x) = x^2 - 9[/tex]
Note that [tex]f(x)\ge0[/tex], so we must also have [tex]f\left(f^{-1}(x)\right) = x \ge 0[/tex]. This makes the third choice the correct one.
Find the area of the polygon with th
Ay
7.
A(-2,3)
-4
C(-2,-3)
4
2
-2
4-
2'
4 X
B(3, -3)
The area of the triangle is 15 square units after using the distance formula.
What is a distance formula?
It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
It is given that:
The triangle is shown on the coordinate plane.
Using the distance formula:
The height of the triangle:
[tex]\rm AC=\sqrt{(-2+2)^2+(-3-3)^2}[/tex]
AC = 6 units
Again using the distance formula:
[tex]\rm BC =\sqrt{(3-(-2))^2+(-3-(-3))^2}[/tex]
BC = 5 units
The area of the triangle = (1/2)6x5
The area of the triangle = 15 square units
Thus, the area of the triangle is 15 square units after using the distance formula.
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Cara used 4 1/6 sheets of construction paper to make 1/6 of her poster borad project. At that rate, how many sheets will she use for the whole project?
Based on the number of sheets of construction paper that Cara uses to make 1/6 of her project, the number of sheets for the whole project would be 25 sheets
How to find the number of sheets needed?Cara will use 4¹/₆ sheets of construction paper for 1/6 of her poster board project so to find the sheets needed for the whole project, use direct proportion.
4¹/₆ sheets of construction paper : 1/6 of project
x sheets of construction paper : 1
1/6 × x = 4¹/₆
1/6x = 4¹/₆
x = 4¹/₆ ÷ 1/6
x = 25/6 x 6/1
x = 25 sheets
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What is the x value of the solution to the system shown?
2y = 2x + 12
2-y=4
Answer:
[tex]x = -8[/tex]
Step-by-step explanation:
[tex]\begin{cases}2y = 2x + 12\\2-y = 4\end{cases}[/tex]
It would be easier to start with the second equation.
[tex]2 - y = 4 \text{ // Add y and subtract 4}\\\to 2 - y - 4 = 4 - y - 4\\\to -2 = y[/tex]
From here, we can substitute [tex]y = -2[/tex] into the first equation, to solve for [tex]x[/tex].
[tex]2(-2) = 2x + 12\\\to -4 = 2x + 12 \text{ // Subtract 12 on both sides}\\\to -4 - 12 = 2x + 12 - 12\\\to -16 = 2x \text{ // Divide by 2}\\\to -\frac{16}2 = \frac{2x}2\\\to -8 = x[/tex]
Ill need asap please
D. 37.8204
A negative absolute value is always positive.
Answer:
d) 37.8204
Step-by-step explanation:
Given that,
→ |-18.531| + |-19.2894|
Let's solve the problem,
→ |-18.531| + |-19.2894|
→ 18.531 + 19.2894
→ 37.8204
Thus, option (d) is correct.
Fill in the tables and create a recursive and explicit equation for all three questions.
Answer:okay
Step-by-step explanation:hm
19 1/5 - 11 1/11?????????
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{19\frac{1}{5}}\implies \cfrac{19\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{96}{5}} ~\hfill \stackrel{mixed}{11\frac{1}{11}}\implies \cfrac{11\cdot 11+1}{11}\implies \stackrel{improper}{\cfrac{122}{11}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{96}{5}~~ - ~~\cfrac{122}{11}\implies \stackrel{\textit{using the LCD of 55}}{\cfrac{(11)96~~ - ~~(5)122}{55}}\implies \cfrac{1056~~ - ~~610}{55} \\\\\\ \cfrac{446}{55}\implies {\LARGE \begin{array}{llll} 8\frac{6}{55} \end{array}}[/tex]
P = IV
●
Here is what you know about the baseball field parking lot situation.
There are 9 lamp posts connected to this circuit.
Each lamp post has a 400 watt lamp installed.
The circuit is 120-volt and 20-amp.
Here is what you don't know, but can figure out:
How many watts does 9
lampposts require?
How many lamposts could this
circuit handle? HELP
Answer:
1M
Step-by-step explanation:
HOPE ITS HELP!! PLEASE STAY ALIVE!! :D
solve for r -17= 2/3r
Answer:r=51
Step-by-step explanation:
Answer:
r = 51
Step-by-step explanation:
r - 17 = [tex]\frac{2}{3}[/tex] r ( multiply through by 3 to clear the fraction )
3r - 51 = 2r ( subtract 2r from both sides )
r - 51 = 0 ( add 51 to both sides )
r = 51
Find the total amount given the original price and tax rate. Round to the nearest cent if necessary
$31.69, 6%
The total amount including the tax rate is found as $34.
What is defined as the percentage?A percentage is a fraction of a whole articulated as just a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the fraction of the total by the total and multiply by 100.For the stated conditions in the question.
The original amount = $31.69.
The tax rate is 6%.
The total mount will be the sum of original amount and tax price.
First calculated the tax price;
6% of 31.69 = 6×31.69/100
6% of 31.69 = 1.9014
Tax price = $1.9014.
Total price = original amount + tax price
Total price = $31.69 + 1.9014
Total price = 33.5914
Total price = $34 (Round to the nearest cent.)
Thus, the total amount is estimated as $34.
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Mike drove a nail 2.5 in. long through a board 0.75 in. thick into a post. How far did the nail go into the post?
Answer:
1.75 inches deep into the post
Step-by-step explanation:
First, you do 2.5 - 0.75 which is 1.75 in
The answer is 1.75 in
Hope this helps!
how do i right it please help
The contrapositive statement is:
If x ≠ 2, then x^2 ≠ 4
And it is false.
How to write the contrapositive statement?
First, we have two propositions:
p = "x^2 = 4"
q = "x = 2"
The contrapositive statement is:
¬q → ¬p
The negation of the propositions are:
¬q = "x ≠ 2"
¬p = "x^2 ≠ 4"
Then the contrapositive statement with the given propositions is:
If x ≠ 2, then x^2 ≠ 4
Now, is this statement true?
No, because we can have:
x = -2 (which is different than 2, so the hypothesis is true)
and x^2 = (-2)^2 = 4
Then the conclusion is false, so the statement is false.
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a group of 10 people have gotten together to play basketball. they will begin by dividing themselves into two teams of 5 players each. one team will wear red uniforms and the other will wear blue uniforms. in how many ways can this be done?
Answer:
9!
Step-by-step explanation:
Because a person who switch with 9 people, then another person switch with 8 people (because the first person was already counted), then another person who switch with 7 people (becsuse the first and the second person was already counted)... and you will get 9!. 9! is 9 factorial which is 9×8×7×6×5×4×3×2×1. :)
What are the slope of the two lines?
Kinsley went rock climbing at Red River Gorge. At noon, she was at an elevation of 76 feet. Then, she climbed 28 feet higher to reach the peak.
What was Kinsley's elevation at the peak?
Answer:
Step-by-step explanation:
28 + 76=
104
Her elevation is 104 at the peak.
A cell phone company charges its customers $40 each month for owning a cell phone plan and $0.25 for
each minute the customer talks on the phone. These costs are modeled by the following equation:
C=25m +40, where Crepresents the total cost of the bill and m represents the number of minutes the
customer talked on the phone that month. Given this equation, how many minutes would the customer
have to talk on the phone for their monthly bill to be $84.25? (Hint: plug in 84.25 for the total cost, C, and
solve for the unknown, m).
Answer:
The customer would have 177 minutes to talk on the phone for their monthly bill to be 84.25
Step-by-step explanation:
Point of correction it's not C=25m +40 but it is
C=0.25m +40
Where,
C = $84.25➟ 84.25 = 0.25m + 40
Let's solve your equation step-by-step.
84.25=0.25m+40
Step 1: Flip the equation.
0.25m+40=84.25
Step 2: Subtract 40 from both sides.
0.25m+40−40=84.25−40
0.25m=44.25
Step 3: Divide both sides by 0.25.
0.25m/0.25 = 44.25/0.25
m=177
∴ The customer would have 177 minutes to talk on the phone for their monthly bill to be 84.25
please just solve this, I'm confused.
The quotient of each of the expressions are:
a. 1⅖ / -1/5 = -7
b. -0.4 ÷ 0.25 = 1.6
c. 7/8 ÷ -3/4 = -7/6
d. 0.7 ÷ -1 1/6 = -0.6
How to Find the Quotient?Quotient is the result you get after dividing one quantity by another. For example, the quotient of a and b is a/b.
Find the given quotient as shown below:
a. 1⅖ / -1/5
Convert mixed fraction to improper fraction
7/5 / -1/5
Change the division sign to multiplication and turn the fraction upside down
7/5 × (-5/1)
= -(7 × 5)/(5 × 1)
= -(7 × 1)/(1 × 1)
= -7/1
= -7
b. -0.4 ÷ 0.25
-0.4/0.25
= 1.6
c. 7/8 ÷ -3/4
Change the division sign to multiplication and turn the fraction upside down
7/8 × -4/3
= -(7/8 × 4/3)
= -(7 × 4)/(8 × 3)
= -(7 × 1)/(2 × 3)
= -7/6
d. 0.7 ÷ -1 1/6
0.7 ÷ -7/6
Change the division sign to multiplication and turn the fraction upside down
0.7 × -6/7
0.1 × -6/1
= 0.1 × -6
= -0.6
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