The perimeter of the rectangle below is 90 units. find the length of side vy . write your answer without variables.
Answers
we know that
perimeter of a rectangle=2*[base+height]
base=3y+1
height=2y+3
perimeter=90 units
so
90=2*[(3y+1)+(2y+3)]-----> 90=2*[5y+4]----> 10y+8=90----> y=8.2 units
base=3y+1-----> base=3*8.2+1-----> 25.6 units
height=2y+3----> height= 2*8.2+3---> 19.4 units
the answer is
the length of side vy is (2y+3)-----> 19.4 units
the length of side VY is equal to the height, which is 19.4 units. The formula for the perimeter of a rectangle is given as `2 * (base + height)`.
It's correctly stated that the base of the rectangle is `3y + 1`, and the height is `2y + 3`. The perimeter is given as `90 units`.
To find the dimensions, we set up an equation using the formula for the perimeter:
90 = 2 * [(3y + 1) + (2y + 3)]
This equation represents that the perimeter is equal to twice the sum of the base and height.
The equation is then simplified:
90 = 2 * [5y + 4]
By dividing both sides by 2, it becomes:
5y + 4 = 45
Solving for y:
5y = 45 - 4
5y = 41
y = 41 / 5
y = 8.2 units
So, the value of y is correctly determined as 8.2 units.
With the value of y known, the base and height expressions are evaluated:
Base: `3y + 1 = 3 * 8.2 + 1 = 24.6 + 1 = 25.6 units`
Height: `2y + 3 = 2 * 8.2 + 3 = 16.4 + 3 = 19.4 units`
The dimensions of the rectangle are correctly calculated as follows:
Base: 25.6 units
Height: 19.4 units
It's also mentioned that the length of side VY is equal to the height, which is 19.4 units.
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Related Questions
A 12' by 20' rectangular garden is to have a walkway of uniform width added around its entire perimeter. if the area of the walkway is 68 square feet, find the width of the walkway.
Answers
In the school election, votes were cast for sam, mary, and bill in the ratio of 4:3:2. if a total of 2178 votes were cast, how many votes did mary receive?
Answers
Sam's votes=242×4=968
Mary's=242×3=726
Bill's=242×2=484
The diameter of a circle has endpoints (-3, 2) and (3, -2) which is closest to the length of the diameter of the circle?
Answers
D=√((x2-x1)²+(y2-y1)²) = √(3-(-3))²+(-2-2)²) = √(6² + 4²)=√(36+16)=√52
D=2√13≈7.21
Answer: Diameter = 7.21 units
Which graph represents g(x)=(x−3)2−5 ?
Answers
and it is looking upward because it is positive coefficient in front of (x-3)²
Correct answer is A.
The graph of g(x) = (x-3)^2 - 5 is a parabola that opens upwards. The vertex is located at (3, -5) and the function values are negative when x is less than 3.
Explanation:The graph of the equation g(x) = (x-3)^2 - 5 is a parabola. The vertex of the parabola is located at the point (3, -5), and the parabola opens upwards because the coefficient of the quadratic term is positive. When x is less than 3, the function values are negative, and when x is greater than 3, the function values are positive.
Joylin receives a 50 gift card for the local movie theater for her birthday. She uses the card to purchase tickets and snacks for her family.if joylin spends $6more on tickets than she does on snacks, how much does joylin spend on tickets.
Answers
amount spent on tickets be x+6
So, x+(x+6) = 50
2x = 44
x = 22 (44/2)
so, (x+6) = 22+6 = 28
Final answer is $28
Answer:
c
Step-by-step explanation:
edge 2020
A right triangle has legs that measure 7cm and 3cm. What is the length of the Hypotenuse?
Answers
49 + 9 = c²
58 = c²
c = √58
Answer:
square root of 58
Step-by-step explanation:
If its wrong e2020 says its right
A skier leaves an 8-foot-tall ramp with an initial vertical velocity of 28 feet per second. the function h = −16t^2 28t 8 represents the height h (in feet) of the skier after t seconds. the skier has a perfect landing. how many points does the skier earn? 1 point per foot in the air, 5 points per second in the air, and a perfect landing is 25 points.
Answers
We can find the height in the air by using -b/2a:
-28/2(-16) = -28/-32 = 0.875
This will give the skier 0.875 points.
To find the amount of time in the air, we solve the related equation:
0=-16t²+28t+8
We will first factor out the GCF, -4:
0=-4(4t²-7t-2)
Now we will factor the trinomial in parentheses using grouping. We want factors of 4(-2)=-8 that sum to -7; -8(1) = -8 and -8+1=-7. This is how we will "split up" bx:
0=-4(4t²-8t+1t-2)
Now we will group the first two and last two terms:
0=-4[(4t²-8t)+(1t-2)]
We will factor out the GCF of each group:
0=-4[4t(t-2)+1(t-2)]
This gives us the factored form:
0=-4(4t+1)(t-2)
Using the zero product property, we know that either t-2=0 or 4t+1=0:
t-2=0
t-2+2=0+2
t=2
4t+1=0
4t+1-1=0-1
4t=-1
4t/4 = -1/4
t=-1/4
Negative time makes no sense, so t=2. This gives the skier 5(2) = 10 points.
Counting the perfect landing, we have 25+10+0.875 = 35.875 points.
The skier earns approximately 27 points.
Explanation:To find the total points earned by the skier, we need to calculate the time it takes for the skier to reach the ground. In this case, the height function h = -16t^2 + 28t + 8 represents the height of the skier after t seconds. To find the time it takes for the skier to reach the ground, we need to find the value of t when h = 0.
Setting h = 0, we get:
-16t^2 + 28t + 8 = 0
Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = 28, and c = 8:
t = (-28 ± sqrt(28^2 - 4(-16)(8))) / (2(-16))
Simplifying the equation, we get:
t = (-28 ± sqrt(672)) / -32
t = (-28 ± 26) / -32
Since the skier has a perfect landing, we can disregard the negative value and take the positive value of t:
t = (-28 + 26) / -32
t = -2 / -32
t = 1/16
This means the skier takes 1/16 seconds to reach the ground. To calculate the total points earned, we need to find the total time the skier is in the air. Since the skier starts with an initial vertical velocity of 28 ft/s, we can use this velocity to find the time it takes to reach the ground:
t = h / v
t = 8 / 28
t = 2/7 seconds
Therefore, the skier is in the air for 2/7 seconds. To find the total points earned:
Points = (h * 1) + (t * 5) + 25
Points = (8 * 1) + ((2/7) * 5) + 25
Points = 8 + (10/7) + 25
Points = 189/7
So, the skier earns approximately 27 points.
Anyone know the answer?
Answers
4. Angle 2 = Angle 1
In a right triangle, the measure of one acute angle is 13°. What is the measure of the other acute angle?
32°
77°
90°
167°
Answers
-JJ
The sum of the angles in a triangle is always 180 degrees. In a right triangle, one angle is 90 degrees, and given that one acute angle is 13 degrees, the measure of the other acute angle is 180 - 90 - 13, which equals 77 degrees.
In the context of Euclidean geometry, we have a well-established theorem which stipulates that the sum of the angles in any triangle equals 180 degrees. Since we are dealing with a right triangle, we know that one of its angles measures 90 degrees. The question states that one acute angle measures 13 degrees. To find the measurement of the other acute angle, we subtract the known angles from 180 degrees.
180 degrees (sum of all angles in a triangle) - 90 degrees (right angle) - 13 degrees (given acute angle) = 77 degrees.
Therefore, the measure of the other acute angle is 77 degrees.
A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?
Answers
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft
aina, Kareem, and David have a total of $92 in their wallets. Kareem has $7 less than Raina. David has 3 times what Kareem has. How much do they have in their wallets?
Answers
-----
Step 1:
Solve this by using a system of equations. Start by changing what you're given from words into equations. Put variables in for the peoples' names. Let's say Raina = R, Kareem = K, and David = D. You will have 3 equations:
1) Raina, Kareem, and David have a total of $92 in their wallets.
R + K + D (sum of all three) = 92 (total)
2) Kareem has $7 less than Raina
K = R - 7 (seven less than Raina)
3) David has 3 times what Kareem has.
D = 3K (three times Kareem)
-----
Step 2:
You can solve for the values of R, K, and D using substitution. Let's put the first equation, R + K + D = 92, all in terms of one variable, so we can solve for that variable. Since both equations 2 and 3 have K in relation to one of the other variables, I will be putting equation 1 in terms of K! Do this by substitution some equation of K in for variables R and D in the first equation.
From equation 2, we know that K = R - 7. Add 7 to both sides, making R = K + 7.
From equation 3, we know that D = 3K. This is already in perfect form to substitute.
Now substitute both R = K + 7 and D = 3K into the first equation. Simplify and solve for K:
R + K + D = 92
(K + 7) + K + (3K) = 92
5K + 7 = 92
5K = 85
K = 17
Kareem has $17 in his wallet.
-----
Step 3:
Now that you know K = 17, plug that into equation 3, D = 3K, and solve for how much David has:
D = 3K
D = 3(17)
D = 51
David has $51 in his wallet.
-----
Step 4:
Finally, plug K = 17 into equation 2, K = R - 7, to find how much Raina has:
K = R - 7
17 = R - 7
R = 24
Raina has $24 in her wallet.
Kareem has $17, Raina has $24 ($17 + $7) and David has $51 (3 x $17).
Explanation:Let's represent the amount of money that Kareem has in his wallet as 'K'. Since Kareem has $7 less than Raina, we can represent Raina's amount of money as 'K + 7'. David has 3 times what Kareem has, so we can represent David's amount of money as '3K'.
According to the problem, the sum of all three amounts is $92. So we can set up the equation: K + (K + 7) + 3K = 92.
Combining like terms, we get 5K + 7 = 92. Subtracting 7 from both sides, we have 5K = 85. Dividing both sides by 5, we find that K = 17. Therefore, Kareem has $17, Raina has $24 ($17 + $7) and David has $51 (3 x $17).
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Trey's mom planted an 18 feet by 20 feet garden in his back yard. this new garden reduced the area of trey's backyard by 24%. which answer choice best represents the total area of the back yard
Answers
The garden area is given by:
[tex] A = (18) * (20)
A = 360
[/tex]
We are looking for the backyard area now.
For this, we make the following rule of three:
360 ---------------------> 24%
x -------------------------> 100%
From here, we must clear the value of x.
We have then:
[tex] x = (100/24) * (360)
x = 1500 ft ^ 2
[/tex]
Answer:
The total area of the back yard is:
[tex] x = 1500 ft ^ 2 [/tex]
PLS HELP ME ASAP WITH C!! (SKETCH A LINE THAT REPRESENTS THE DIFF SHAPES)
- ALSO INDICATE WHICH LINE IS WHAT FUNCTION
THANK YOU!!
(Random answers gets moderated!)
Answers
a) The horizontal width is narrow near the bottom, so the fill rate will be relatively fast until the depth where the width changes. Then the fill rate will slow to perhaps 1/3 of what it was.
b) The horizontal width is a linearly decreasing function of depth, so the fill rate will be increasing on a hyperbolic curve--increasingly fast as the depth increases.
c) This is the reverse of case (a). The fill rate is initially slow, then jumps dramatically when the depth reaches the point where the horizontal width suddenly narrows.
It is not clear whether you are supposed to graph fill rate as a function of depth or as a function of time. The desriptions are for fill rate. If you want to graph versus time, these descriptions apply to the slope of the curve, not its level.
Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen at random, what is the probability that it will be a vowel?
The number of favorable outcomes is .
The number of possible outcomes is .
So P(vowel) = , or about percent.
Answers
Number of possible outcomes = 26
P(vowel) = 5/26
Answer: 5/26
The probability of pulling a vowel out of the hat is [tex]\frac{5}{26}[/tex]
The number of favorable outcomes is [tex]5[/tex]
The number of possible outcomes is [tex]26[/tex]
The number of possible outcomes is the size of the sample space.
Since the sample space
[tex]S=\{\text{all the letters of the alphabet in the hat}\}[/tex]
then, the number of possible outcomes is
[tex]|S|=26[/tex]
The number of favorable outcomes is possible number of vowels that can be gotten from the hat. Since the set of vowels
[tex]V=\{a,e,i,o,u\}[/tex]
then, the number of favorable outcomes is
[tex]|V|=5[/tex]
The probability of pulling a vowel out of the hat
[tex]P(V)=\frac{\text{number of favorable outcomes}}{number of possible outcomes}=\frac{5}{26}[/tex]
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A lady bought plates and bowls, 24 items in all. The price of each bowl was 60 cents; the price of each plate was 75 cents. The cost of the whole purchase was $15. How many plates did the lady buy?
Answers
.60 .75 1.35
8.4(14) 7.5(10) 15.9
7.8(13) 8.25(11) 16.05
9.6(16) 6(8) 15.6
9(15) 6.75(9) 15.75
13.8(23) .75 14.55
13.2(22) 1.5(2) 14.7
12.6(21) 2.25(3) 14.85
12(20) 3(4) 15
answer: 4
What is the sun made of (by mass)?
a. 50 percent hydrogen, 25 percent helium, 25 percent other elements
b. 70 percent hydrogen, 28 percent helium, 2 percent other elements
c. 90 percent dark matter, 10 percent ordinary matter
d. 100 percent hydrogen and helium?
Answers
Find the value of each variable. If your answer is not an integer, express it in simplest radical form. Please explain how you got the answer! I can't figure it out.
Answers
sine (60) = y / 14
Clearing y we have:
y = 14 * sine (60)
Rewriting:
y = 14 * (root (3) / 2)
y = 7 * root (3)
For x we have:
cosine (60) = x / 14
Clearing x we have:
x = 14 * cosine (60)
x = 14 * (1/2)
x = 7
Answer:
the value of each variable is:
y = 7 * root (3)
x = 7
In the given right triangle, x and y are 7 and 7√3 respectively.
What is the sine of an angle?Sine of an angle = [tex]\frac{OPPOSITE SIDE}{HYPOTENUSE}[/tex]
From the diagram, we can see that y is the opposite side to angle B while x is the adjacent side while 14 is the hypotenuse.
Sin α = opposite side/ hypotenuse
Sin 60° = y/14(given)
y = 14sin60
y=7√3
Cos α = adjecent side / hypotenuse
Cos60° = x/14(given)
x = 14cos60
x= 7
So, for the given right triangle x and y are 7 and 7√3 respectively.
Therefore, In the given right triangle, x and y are 7 and 7√3 respectively.
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The function g(x)=(x-2^2. The function f(x)=g(x) +3
The function f(x) is shifted horizontally how many places to where ?
The function f(x) is shifted vertically how many places where ?
Answers
y = x ^ 2
Applying the following function transformation we have:
Horizontal translations:
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
We have then:
g (x) = (x-2) ^ 2
Then, we have the following function transformation:
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
We have then that the original function is:
g (x) = (x-2) ^ 2
Applying the transformation we have
f (x) = g (x) +3
f (x) = (x-2) ^ 2 + 3
Answer:
the function f(x) moves horizontally 2 units rigth.
The function f (x) is shifted vertically 3 units up.
Answer:
The function f(x) moves horizontally 2 units right.
The function f (x) is shifted vertically 3 units up.
Step-by-step explanation:
A restaurant offers 88 appetizers and 99 main courses. in how many ways can a person order a two-course meal
Answers
Answer: 8712
Isabel divided 32 by 8 and got 4. She says that if she divides 32 by 4,the quotient will be greater than 4. Is she correct? Explain.
Answers
8>4 so it make sense.
Find the geometric mean of 125 and 5.
Answers
A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?
Answers
Using the given dimensions, we can write:
Volume of right rectangular prism = 3 x 12 x 5 = 180 cubic inches
Volume of oblique rectangular prism = Base Area x Height
Base Area = 4 x 9 = 36 square inches
So, Volume of oblique rectangular prism = 36 x 5 = 180 cubic inches
Thus, we can conclude that the two volumes are the same.
From a carton containing 50kg of sugar 24 half-kilogram packets were taken . How many kilograms of sugar remained?
Answers
Sugar remained = 50 - 12 = 38 kg
Answer: 38 kg
Finish the pattern, 1, 2, 6, 22, __, __?
Answers
So,
1, 2, 6, 22, 86, 342 is your answer
Find the solution of this system of equations. Separate the x- and y- values with a comma. x+4y=1 and x-y=1
Answers
Equation 2: x-y=1
solve equation 2 for x: x=1-y
substitute 1-y into equation 1: (1-y) +4y=1
solve for y: 1-y+4y=1
1+3y=1
3y=0
y=0
Substitute y=0 into equation 2: x-(0)=1
x=1
Solution: (1,0)
You are considering two investment opportunities. For investment A there is a 25% chance that you lose $20,000, a 50% chance that you break even, and a 25% chance that you make $80,000. For investment B there is a 30% chance that you lose $50,000, a 50% chance that you break even, and a 20% chance that you make $180,000. Based on the expected value of each, which investment should you make?
Answers
Solution:
For investment A - the expected value of the investment is
($20,000) * 25% = ($5,000)
$80,000 * 25% = $20,000
$15,000
For investment B - the expected value of the investment is
($50,000) * 30% = ($15,000)
$180,000 * 20% = $36,000
$21,000
So you can gain more by $6,000 if you choose investment B.
Answer:
For investment A - $15,000
For investment B - $21,000
So you can gain more by $6,000 if you choose investment B.
Step-by-step explanation:
Jon has 8 blue marbles and 4 red marble sin a bag. he took 1 marble from the bag na fthen a second marble without replacing the first one. assuming a red marble was selected first, what is the probability that jon selected a red marble both times
Answers
4/12, and he gets a red one.
If he doesn't replace the first one, the next one would be 3/11. The probability that Jon selected a red marble both times is 1/11.
(I kind of forgot this lesson, but here's my guess.
The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. if in the last game he made 77 assists, how many standard deviations is that from the mean? 1.36 standard deviations below the mean 2.71 standard deviations above the mean 1.36 standard deviations above the mean 2.71 standard deviations below the mean
Answers
standard deviation=7
thus
77 is (77-58)=18 away from 58
This will be:
19/7=2.71
standard deviations from the mean.
Answer: 2.71 standard deviations above the mean
Answer:
(B)
Step-by-step explanation:
It is given that The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7.
Also, in the last game he made 77 assists, therefore
[tex]77-58=19[/tex] assists away from the mean.
Thus, To get the number of standard deviation that 77 is from the mean, we get the z-score which is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Substituting the given values, we get
[tex]z=\frac{77-58}{7}[/tex]
[tex]z=\frac{19}{7}[/tex]
[tex]z=2.71[/tex]
Thus, there are 2.71 standard deviations above the mean.
Hence, option B is correct.
If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2?
Answers
a triangle’s original dimensions are 24 cm by 40 cm
scale factor=2.2
then
a triangle’s enlargement dimensions=[scale factor]*original dimensions
a triangle’s enlargement dimensions=[2.2]*24------> 52.8 cm
a triangle’s enlargement dimensions=[2.2]*40------> 80 cm
the answer is
a triangle’s enlargement dimensions will be 52.8 cm by 80 cm
Answer:
52.8cm
&
88com
Step-by-step explanation:
A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?
Answers
90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;
Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.