the perimeter of the rectangle belowis 112 units. Find the value of y
Answers
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]
Related Questions
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after 7 minutes?
Answers
Tank B originally had 80 liters of water.
Water is being drained off the tank at a rate of 2.5 liters per minute.
After 7 minutes have passed, the tank has lost 7*2.5 = 17.5 liters of water.
This means the tank still has 80 - 17.5 = 62.5 liters of water.
After 7 minutes 62.5 liters of water remain in the tank
find the value of. abe, bec, and the minor arc ec
Answers
Answer
Angle ABE = 64°
Angle BEC = 48°
Minor arc EC = 134°
Explanation
The key to solving this is to take a look at this image below
According to the tangent-chord theorem, we know that
Tangent Chord angle ABE = (Intercepted arc BE)/2
Angle ABE = (128°/2)
Angle ABE = 64°
Tangent chord angle CED = (Intercepted arc EC)/2
68° = (Minor arc EC/2)
Multiply both sides by 2
136° = Minor arc EC
To find the Angle BEC, we need to first obtain the arc BC
The total angle around a circle is 360°
Arc BE + Arc BC + Arc EC = 360°
128° + Arc BC + 136° = 360°
Arc BC = 360° - 128° - 136°
Arc BC = 96°
Then to find the Angle BEC, the image attached below guides us
So, we can easily say that
Angle BEC = ½ (Arc BC)
Angle BEC = ½ (96°)
Angle BEC = 48°
Hope this Helps!!!
Find the derivativef(x) = 1 / (x - 2)
Answers
ANSWER
[tex]\frac{df}{dx}=-\frac{1}{(x-2)^2}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]f(x)=\frac{1}{x-2}[/tex]First, we have to rewrite the function as follows:
[tex]f(x)=(x-2)^{-1}[/tex]Next, make the following substitution:
[tex]a=x-2[/tex]The function now becomes:
[tex]f(x)=a^{-1}[/tex]Apply the chain rule of differentiation:
[tex]\frac{df}{dx}=\frac{df}{da}\cdot\frac{da}{dx}[/tex]Therefore, we have that:
[tex]\frac{df}{da}=-1\cdot a^{-1-1}=-a^{-2}[/tex]and:
[tex]\frac{da}{dx}=1[/tex]Therefore, the differentiation of the function is:
[tex]\begin{gathered} \frac{df}{dx}=-a^{-2}\cdot1 \\ \Rightarrow\frac{df}{dx}=-(x-2)^{-2}\cdot1 \\ \frac{df}{dx}=-\frac{1}{(x-2)^2} \end{gathered}[/tex](blank)+(7x+24)=180
7x + (blank)+ = 180
7x =
x =
Answers
Answer:
first blank: 72°
2nd blank: 96
next line: 84
last: 12
Step-by-step explanation:
The two marked angles are called same-side interior angles or consecutive angles.
They add up to 180°
Thats how you know how to set up the equation.
72° + 7x + 24 = 180
Add the plain numbers (the 72 and 24)
7x + 96 = 180
subtract 96 from both sides.
7x = 84
Divide both sides by 7.
x = 12
Question HelpMultiple Representations A vehicle ses 7 gallons of gasoline to travel 147 miles. The vehicle uses gasoline at a steady rate. Use pencil and paper to draw a picture that models the situation Write a table of equivalent ratiosThen use the table to find the number of gallons of gasoline the vehicle uses to travel 63 milesComplete the tableGallons Miles1231411421
Answers
We know a vehicle uses 7 gallons of gasoline to travel 147 miles.
This gives us a ratio: 147/7 = 21
The vehicle travels 21 miles per gallon of gasoline
The situation can be modeled as a line with a constant slope of 21 miles/gallon
If we use the horizontal axis for the number of gallons and the vertical axis for the miles traveled, we can draw an approximate graph
Let's give the gallons (g) some values to fill up the table:
For g=1, miles = 21
For g=2, miles = 42
For g=3, miles = 63
For g=7, miles = 147
For g=14, miles = 294
For g=21, miles = 441
The graph is shown below
Hey could someone help me out with this thank you
Answers
Karen will run more than 28
Solve the system of equations.y= x2 - 3x + 6y = 2x + 6
Answers
We have the following:
[tex]\begin{gathered} y=x^2-3x+6 \\ y=2x+6 \end{gathered}[/tex]We subtract the equations:
[tex]\begin{gathered} y-y=x^2-3x+6-2x-6 \\ 0=x^2-5x \\ 0=x(x-5) \\ x=0;x=5 \end{gathered}[/tex]for y:
[tex]\begin{gathered} y=2\cdot0+6 \\ y=6 \\ y=2\cdot5+6 \\ y=16 \end{gathered}[/tex]therefore, the answer is:
(0,6) and (5,16), the option D.
how do I use a right triangle to write the following expression as an algebraic expression?
Answers
So, we want to express the following:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]As an algebraic expression.
If:
[tex]\begin{gathered} \sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}})=\theta \\ \text{Then,} \\ \sin (\theta)=\frac{x}{\sqrt[]{x^2+81}} \end{gathered}[/tex]We could draw the following triangle:
Remember that the secant function relations the hypotenuse of the triangle and the adjacent side of the triangle. So first, we should find the adjacent side using the pythagorean theorem:
[tex]\begin{gathered} a^2=(\sqrt[]{x^2+81})^2-x^2 \\ a^2=x^2+81-x^2 \\ a^2=81\to a=9 \end{gathered}[/tex]Therefore, the adjacent side is 81. And, the value of:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]Is:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))=\frac{\sqrt[]{x^2+81}}{9}[/tex]in health class, the students were asked what grain they prefered in their breakfast cereal. The results are shown in the table. what's the probability that a randomly chosen student in the health class listed oats as their favorite grain?A. 20%B. 25%C. 35%D. 14%
Answers
To find the probability of a randomly choosen student listing oats as its favorite grain, divide the number of students that chose oats by the total number of students and multiply the fraction by 100%.
To find the total number of students, add the numbers under each cereal:
[tex]12+14+8+6=40[/tex]The number of students who chose oats, is 14. Then, the requested probability, is:
[tex]\frac{14}{40}\times100=35\text{ \%}[/tex]Your psychology class has 45 students. You want to ask an SRS of four students from your class whether they prefer taking online or face-to-face courses. You label the students 01, 02, . . . , 45. You enter the table of random digits at this line:
78314 96529 67532 98144 28944 26687 49634 88274 20361
Your SRS contains the students labeled
A. 14, 32, 42, 44.
B. 31, 29, 44, 28.
C. 31, 29, 29, 44.
D. 31, 49, 29, 44.
E. 78, 31, 49, 65.
Answers
Answer:
Step-by-step explanation:
The answer is c! :)
Answer:
The answer is B. 31, 29, 44, 28.
Step-by-step explanation:
f(x) = x + 4 and g(x) = x - 1Step 3 of 4: Find (f 3)(x). Simplify your answer.Answer(f)(x) =
Answers
For this problem, we are given two functions, we need to determine the composite between these two expressions.
The two functions are:
[tex]\begin{gathered} f(x)=x+4\\ \\ g(x)=x-1 \end{gathered}[/tex]This composite is the product of the two functions, therefore we have:
[tex]\begin{gathered} (f\cdot g)(x)=(x+4)\cdot(x-1)\\ \\ (f\cdot g)(x)=x^2-x+4x-4\\ \\ (f\cdot g)(x)=x^2+3x-4 \end{gathered}[/tex]The answer is x²+3x-4.
How to solve 11 3/7 × 7/10 =
Answers
Given:
The objective is to solve the given equation.
The given equation can be solved by,
[tex]\begin{gathered} =11(\frac{3}{7})\cdot\frac{7}{10} \\ =\frac{11\cdot3}{10} \\ =\frac{33}{10} \\ =3.3 \end{gathered}[/tex]Hence, the value of the equation is 3.3
Consider functions h and k. Every x value has a relationship in k of x. What is the value of (h o k)(1)? A. 28 B. 4 C. 1 D. 0
Answers
Recall that:
[tex](f\circ g)(x)=f(g(x)).[/tex]Therefore:
[tex](h\circ k)(1)=h(k(1)).[/tex]From the given diagram we get that:
[tex]k(1)=3.[/tex]Then:
[tex]h(k(1))=h(3).[/tex]Now, from the given table we get that:
[tex]h(3)=28.[/tex]Therefore:
[tex](h\circ k)(1)=28.[/tex]Answer: Option A
IF log x = 1/₂, find log (10x²)
Answers
Answer:
2
Step-by-step explanation:
log ab = log a + log b
Similarly,
log 10x² = log 10 + log x²
log a^b = b log a
Similarly,
log 10x² = 2 log x
= 2 * 1/2
= 2/2
= 1
Note :-
The value of log 10 = 1
Hence,
log 10x²
= log 10 + log x²
= 1 + 1
= 2
2.3x + 8 = - 1.7x - 8 solve for x
Answers
The value of x after solving (2.3x + 8) = (-1.7x-8) is -4.
According to the question,
We have the following expression:
(2.3x + 8) = (-1.7x-8)
Now, moving -1.7x from the right hand side to the left hand side will result in the change of its sign from minus to plus:
2.3x+1.7x +8 = -8
4x+8 = -8
Now, moving 8 from the left hand side to the right hand side will also result in the change of the sign from plus to minus:
4x = -8-8
4x = -16
x = -16/4 (4 was in multiplication on the left hand side. So, it is in division on the right hand side.)
x = -4
Hence, the value of x is -4.
To know more about solving here
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Ben, Claire and Devon are training for a triathalon. Today, they are practicing their swimming by swimming one mile. Ben swam 0.77 of the mile before stopping. Claire swam 3/5 of the mile and Devon swam 82% of the mile before stopping. Who swam the farthest distance? Who swam the shortest distance?
Answers
Given:
Ben, Claire, and Devon are swimming one mile.
Ben swam 0.77 of the mile before stopping.
So, the distance Ben swam = 0.77 x 1 = 0.77 mile
Claire swam 3/5 of the mile.
So, the distance Claire swam = 3/5 x 1 = 3/5 = 0.6 miles
Devon swam 82% of the mile before stopping.
So, the distance Devon swam = 82% of 1 mile = 0.82 x 1 = 0.82 miles
Arrange the distances in order from the largest to the least:
0.82, 0.77, 0.6
So, the answer will be:
The farthest distance is for Devon = 0.82 miles
The shortest distance is for Claire = 0.6 miles
See photo for problem
Answers
Answer:
possible outcome= {H,T}
number of possible outcome=2
obtaining a tail(T)=1
n(T)=1
P(T)=n(T)/number of possible outcome
=1/2
A rectangle with an area of 20 square units is dilated by the scale factor of 3.5. find the area of the new rectangle
Answers
We are given the area of a rectangle. The area of a rectangle is the product of the length and the height. Therefore, we have:
[tex]A=lh[/tex]If we scale the rectangle by a factor of 3.5 this means that we multiply the length and the height by 3.5, like this:
[tex]A^{\prime}=(3.5l)(3.5h)[/tex]Solving the product:
[tex]A^{\prime}=12.25lh[/tex]Since "lh" is the original area we have:
[tex]A^{\prime}=12.25A[/tex]Now, we substitute the value of the original area:
[tex]A^{\prime}=12.25(20)[/tex]Solving the operations:
[tex]A^{\prime}=245[/tex]Therefore, the new area is 245 square units.
a gate that is 5 ft tall casts a shadow 9 ft long the house behind the gate cast a shadow of 54 ft how about how many feet tall is the house
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
gate:
hg = 5 ft
shadow = 9ft
house
hh = ?
shadow = 54 ft
Step 02:
We must apply the theorem of thales.
[tex]\frac{hg}{hh}=\frac{shadow\text{ gate}}{\text{shadow house}}[/tex][tex]\frac{5ft}{hh}=\frac{9ft}{54\text{ ft}}[/tex]hh * 9 ft = 5 ft * 54 ft
hh = (5 ft * 54 ft ) / 9 ft
hh = 270 ft ² / 9 ft = 30 ft
The answer is:
The house is 30ft tall.
The system of equations may be solved by hand calculation or by using the crossing-graphs method.Solve the following system using the crossing-graphs method.2x - y = 04x + 2y = 48(x, y) = (_____,_____)
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The first thing you can do is graph each of the equations. To do this, you can write the equations following the form
[tex]y=mx+b[/tex]Where m is the slope of the line and b the intersection point with the y axis. Then
[tex]\begin{gathered} 2x-y=0 \\ 2x=y \\ y=2x \\ \text{ And the other equation} \\ 4x+2y=48\text{ } \\ \text{To simplify the equation, you can divide by 2 both sides of the equation} \\ 2x+y=24 \\ y=-2x+24 \end{gathered}[/tex]Graphing you have
The solution of the system of equations will be the point at which both lines intersect. Therefore, the solution is (6,2).
The area of a rectangle is 28m^2, and the length of the rectangle is 5 meters less than three times the width. Find the dimensions of the rectangle. L:W:
Answers
The area of a rectangle is given by the formula
[tex]A=L*W[/tex]where
A=28 m2
L=3W-5
substitute given values in the formula
[tex]\begin{gathered} 28=(3w-5)W \\ 28=3w^2-5w \\ 3w^2-5w-28=0 \end{gathered}[/tex]Solve the quadratic equation
Using the formula
we have
a=3
b=-5
c=-28
substitute
[tex]w=\frac{-(-5)\pm\sqrt{-5^2-4(3)(-28)}}{2(3)}[/tex][tex]w=\frac{5\pm19}{6}[/tex]The solutions for w are
w=4 and w=-2.33 ( is not a solution because is a negative number)
so
The width w=4 m
Find out the value of L
L=3w-5=3(4)-5=7 m
therefore
L=7 mW=4 mSimplify the following expression.(12x-2.1)-(19x+6.9)
Answers
The given algebraic expression is
[tex](12x-2.1)-(19x+6.9)[/tex]To simplify this expression, we need to solve those parentheses in the first place, multiplying the sign in front of each of them.
[tex]12x-2.1-19x-6.9[/tex]Now, we reduce like terms. Remember that like terms are those who have the same variable, and those who don't have variables at all.
[tex]12x-19x-2.1-6.9=-7x-9[/tex]Therefore, the simplest form of the given expression is[tex]-7x-9[/tex]Derrick's football team needs to raise at least $1,000 for new uniforms they have collected 480 so far which inequality represents the amount of money,m, the team still needs to raise A. m>$480 B. m<$480 C.m<$520 D.m>$520
Answers
The inequality representing the amount of money, m. Derrick's football team needs to raise is D. m>$520
What is inequality?In mathematics, Inequality is part of equations solved with the use of the some special type of equality signs. The signs used inequality calculations are
greater thanless thangreater than or equal toless than or equal toGiven that:
Derrick's football team needs to raise at least $1,000
The team collected 480
To solve the given problem we have the inequality in the form
at least $1,000 ≡ greater than or equal to 1000
m > $1000
having collected $480 so far. The amount collected is subtracted from the $1000
m > $1000 - $480
m > $520
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Which is a perfect square?583644
Answers
Solution:
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
Hence,
[tex]36=6^2=6\times6[/tex]Therefore, the perfect square is 36.
REI pays $330.30 for a 6-person tent and the markup is 35% of cost. Find the markup.
Answers
First convert 35% into decimal
35% → 0.35
To find 35% of $330.30, multiply it to its decimal
$330.30 ˣ 0.35 = $115.605
Rounding off to the nearest cent.
The markup of the tent is $115.61
On its website a tv station displays temperature data for each hour during the past 24 hours. The data are displayed as using two different functions on a line graph. One function shows the current temperature and the other function shows the historical average. Which quantities are represented by the y-values on the line graph
Answers
, Given the question, we are asked to find which of the quantities are represented by the y-values on the line graph .
Explanation
In the question, we are told that the tv station displays temperature data using two different functions on a line graph. One of the functions shows the current temperature and the other function shows the historical average.
A function, by definition, can only have one output value(y) for any input value. In this case the input values are the time the temperature which we result in the output value of the historical average and temperature.
Therefore,
Answer
Option D
ABC is dilated by a factor of 5 produce A'B'C.What is A'C, the length of AC after the dilation? What is the measure of angle A?
Answers
We have that the scale factor is 5, then, the dilation is an enlargement.
Then, the new lengths are:
[tex]\begin{gathered} A^{\prime}C^{\prime}=5AC=5\cdot5=25 \\ A^{\prime}B^{\prime}=5AB=5\cdot4=20 \\ B^{\prime}C^{\prime}=5BC=5\cdot3=15 \end{gathered}[/tex]therefore, A'C' =25.
Finally, the dilations don't affect the angles, therefore, angle A remains with the measure of 37°
helpppppppppppppppppppp
Answers
Answer: [tex]f^{-1}[/tex] = {(17, 16), (8, 3), (3, 8), (4, 4)}
Step-by-step explanation:
To list the inverse function, we will simply switch the x- and y-values in each coordinate pair. Coordinate points are written as (x, y).
f = {(16, 17), (3, 8), (8, 3), (4, 4)}
[tex]f^{-1}[/tex]= {(17, 16), (8, 3), (3, 8), (4, 4)}
Mikayla and Courtney both leave the internet cafe at the same time, but in opposite directions. If Courtneytravels 7 mph faster than Mikayla and after 6 hours they are 162 miles apart, how fast is each traveling?
Answers
Courtney travels at 17mph and Mikayla at 10mph
1) In this question, we need to set equations for that.
Courtney Mikayla
v +7 v speed
2) Note that we have to use this relation:
[tex]Speed\, {\times time=distance}[/tex]So, we can write out the following:
[tex]\begin{gathered} v6+(v+7)6=162 \\ v6+6v+42=162 \\ 12v+42-42=162-42 \\ 12v=120 \\ v=10 \end{gathered}[/tex]So we can now plug into Mikayla's speed and Courtney
Mikayla travels at 17mph and Courtney at 10mph
Renta scored 409 points in a video game. This was 223 more points than Sadia score (s). Which equation does not represent this situation? And why?
A) 223 = 409 - s
B) s = 409 - 223
C) s = 409 + 223
D) 223 + s = 409
Answers
Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409