Answer:
Length = 39 inches , breadth = 13 inches
Step-by-step explanation:
Given:
The perimeter of a rectangular atrium is 104 inches.
The length of the atrium is three times the width.
Question asked:
The length and the breadth of rectangular atrium = ?
Solution:
Let breadth of rectangular atrium = [tex]x[/tex]
Then, the length of rectangular atrium = [tex]3x[/tex] (given)
Perimeter of rectangle = [tex]2\times(length + breadth)[/tex]
[tex]104 = 2\times( 3x + x )[/tex]
[tex]104 = 2\times 4x[/tex]
[tex]104 = 8x[/tex]
Dividing both side by 8
[tex]13 = x[/tex]
breadth of rectangular atrium = [tex]x[/tex] = 13 inches
length of rectangular atrium = [tex]3x[/tex] = [tex]3 \times13 = 39[/tex] inches
Thus, length and the breadth of rectangular atrium are 39 and 13 inches.
ABCD is a parallelogram. Segment AC = 4x + 10. Find the value of x and y.
Answer:
The values of x and y in the diagonals of the parallelogram are x=0 and y=5
Step-by-step explanation:
Given that ABCD is a parallelogram
And segment AC=4x+10
From the figure we have the diagonals AC=3x+y and BD=2x+y
By the property of parallelogram the diagonals are congruent
∴ we can equate the diagonals AC=BD
That is 3x+y=2x+y
3x+y-(2x+y)=2x+y-(2x+y)
3x+y-2x-y=2x+y-2x-y
x+0=0 ( by adding the like terms )
∴ x=0
Given that segment AC=4x+10
Substitute x=0 we have AC=4(0)+10
=0+10
=10
∴ AC=10
Now (3x+y)+(2x+y)=10
5x+2y=10
Substitute x=0, 5(0)+2y=10
2y=10
[tex]y=\frac{10}{2}[/tex]
∴ y=5
∴ the values of x and y are x=0 and y=5
Find the geometric mean of
6 and 24.
Answer:
15
Step-by-step explanation:
6+24=30
30÷2=15
the formula for calculating the mean is the total of the numbers ÷ the number of numbers
estimate the sum 7.234 + 3.9 + 6.56
7.234 + 3.9 + 6.56
7.234 + 10.46
17.694 (actual)
17.69 (rounded to the hundredths place)
17.7 (rounded to the tenths place)
18 (rounded to the ones place)
Hope this helps! ;)
Ty sells signs in a monthly craft fair,and he can make 7 signs every 2 hours. Harrison can sign 15 signs every 4 hours. Who has the greater rate?
Answer:
If Ty can make 7 signs in 2 hours that means in 4 hours he could double that output to make 14 signs. Harrison, on the other hand, makes 15 signs every 4 hours. Therefore, by default - Harrison makes 1 more sign every 4 hours than Ty. Harrison has the greater rate. You have to figure out how many signs Ty can make in 4 hours, by multiplying 2 x 7 = 14. Hope that helps.
Step-by-step explanation:
HELP ME FOR A BRAINLIST AND 20 POINTS
Answer:
Area = [tex]\frac{5}{12}[/tex] x²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = [tex]\frac{5}{6}[/tex] x and h = x, thus
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{5}{6}[/tex] x × x = [tex]\frac{5}{12}[/tex] x²
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Sanchez applied 6 fluid Ounces of an herbicide per acre on 300 acres of com. How many gallons
did he apply
Click here to enter text.
Answer:
Sanchez applied 1,800 fluid ounces of herbicide to his 300 acres of corn.
Step-by-step explanation:
Let's identify what we already know:
1) Sanchez has 300 acres of corn
2) For every 1 acre, Sanchez applies 6 fluid ounces of an herbicide.
So, we need to figure out how many fluid ounces Sanchez used for the entire six acres. We can create a formula for this:
300 acres x 6 fluid ounces = x
x equals total number of fluid ounces. We multiple the number of acres by the fluid ounces, to get 1,800 fluid ounces for the entire 300 acres of corn.
Final answer:
Sanchez applied a total of 14.0625 gallons of herbicide on 300 acres of corn, after converting the total amount of herbicide from fluid ounces to gallons using the equivalence of 1 gallon equal to 128 fluid ounces.
Explanation:
Sanchez applied 6 fluid ounces of herbicide per acre on 300 acres of corn. To determine how many gallons he applied, we'll use the unit equivalence that 1 gallon = 128 fluid ounces. First, we'll calculate the total amount of herbicide in fluid ounces by multiplying the rate of application by the number of acres:
6 fluid ounces/acre imes 300 acres = 1800 fluid ounces total.
Next, we'll convert fluid ounces to gallons:
1800 fluid ounces imes (1 gallon / 128 fluid ounces) = 14.0625 gallons.
Therefore, Sanchez applied 14.0625 gallons of herbicide on the 300 acres of corn.
The cost c, in dollars, of a taxi ride is related to the
distance d, in miles, of the ride. The cost for taxi A is
given by the equation c = 3.5d + 2, and the cost for
taxi B is given by c= 3d + 5. For what distance is
the cost of each taxi ride the same? How much would
this trip cost?
Answer:
(3 , 2.5)
the trip would cost $12.5
12.5 = 3.5 (3)+2
12.5 = 3 (2.5)+5
Step-by-step explanation:
The distance at which the cost of each taxi is the same is 6 miles.
The trip would cost $23.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
Taxi A:
c = 3.5d + 2
Taxi B:
c = 3d + 5
Where c is the cost of the taxi after d distance.
Now,
The cost of the taxi is the same.
3.5d + 2 = 3d + 5
3.5d - 3d = 5 - 2
0.5d = 3
d = 3/0.5
d = 30/5
d = 6
The cost of the taxi at d = 6.
c = 3.5d + 2 = 3.5 x 6 + 2 = 21 + 2 = 23
c = 3d + 5 = 3 x 6 + 5 = 18 + 5 = 23
Thus,
The cost of both taxis is the same after 5 miles.
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Suppose that y varies directly with x
and y = 10 when x = 20. What is y
when x = 15?
It’s a fraction
Answer:
15/2
Step-by-step explanation:
y varies directly as x can be written as:
y & x
y = Kx
K = y/x
But from the question, we were told that:
y = 10
X = 20
K = y/x
K = 10/20
K = 1/2
The formula for the expression is:
y = Kx
y = 1/2 x
Now let us solve for y, when:
x = 15
y = 1/2 x
y = 1/2 x 15
y = 15/2
Final answer:
To find the value of y when x = 15, we first determined the constant of proportionality (k) using the given y and x values, which was found to be 0.5. We then plugged x = 15 into the direct variation formula y = kx, resulting in y = 7.5.
Explanation:
If y varies directly with x and y = 10 when x = 20, then we can write this direct variation as y = kx, where k is the constant of proportionality. To find k, we substitute the known values of x and y and solve for k:
10 = k × 20
k = 10 / 20
k = 0.5
With k found, we can now determine what y is when x = 15:
y = k × x
y = 0.5 × 15
y = 7.5
–2(5n + 7) + 8n = 2(1 – 3n)
Answer:
n = 4
Step-by-step explanation:
Solve using the distributive property. This means you can multiply the number outside the brackets with each number inside the brackets. Then isolate "n" by moving all other numbers to the right side, leaving "n" alone on the left.
–2(5n + 7) + 8n = 2(1 – 3n) Distribute
(5n)(-2) + (7)(-2) + 8n = (1)(2) – (3n)(2) Multiply with each number in brackets
–10n + (–14) + 8n = 2 – 6n Remove brackets around –14
–10n – 14 + 8n = 2 – 6n Adding a negative is subtracting it's positive
–14 –2n = 2 – 6n
–14 + 14 –2n = 2 + 14 – 6n Add 14 to both sides
–2n = 16 – 6n
–2n + 6n = 16 – 6n + 6n Add 6n to both sides
4n = 16
4n/4 = 16/4 Divide both sides by 4
n = 4 Solved for "n"
Check answer by substituting "4" whenever there is "n" in the original equation. Then solve each side.
–2(5n + 7) + 8n = 2(1 – 3n)
–2(5(4) + 7) + 8(4) = 2(1 – 3(4)) Solve inside brackets
–2(20 + 7) + 32 = 2(1 – 12) Distribute
(20)(–2) + (7)(–2) + 32 = (1)(2) – (12) (2) Multiply where necessary
–40 + (–14) + 32 = 2 – 24 Simplify
–22 = –22 Same answer
LS = RS Left side equals right side
The answer we found is correct.
Melissa's family is on vacation. They spend $125 per day on food
and entertainment. They have budgeted only up to $750 for food
and entertainment. How many days of vacation can they afford?
How do you show your work if the answer is *6*???
Answer:6
Step-by-step explanation:
Dividing 750 by 125 you get 6
Kareem has 216 role playing games cards . his goal is to collect all 15 set of cards. There are 72 cards in a set . How many more cards does kareem need to reach his goal
Answer:
864 cards
Step-by-step explanation:
72 cards per set times 15 sets = 1080 cards - 216 cards he already has =864 cards
PLEASE ANSWER
The graphs shown are of two different functions.
A. Both Graph A and Graph B have multiple y-intercepts.
B. Both Graph A and Graph B have only one x-intercept.
C. Graph A is a linear function because it has a constant rate of change.
D. Graph B is not a linear function but also has a constant rate of change.
Answer:
C: Graph A is a linear function and Graph B is also a function but a low and high constant rate
20 points
Please help
Answer:
I = 0.5[tex]t^{4}[/tex] + 6.5t³ + 16t² + 10t
Step-by-step explanation:
Given
V = [tex]\frac{I}{R}[/tex] ( multiply both sides by R )
I = VR
= (0.5t³ + 6t² + 10t)(t + 1) ← distribute
= 0.5[tex]t^{4}[/tex] + 6t³ + 10t² + 0.5t³ + 6t² + 10t ← collect like terms
= 0.5[tex]t^{4}[/tex] + 6.5t³ + 16t² + 10t
Which statement describes the graph of f(x) = x² - 6x + 9?
a line with an x-intercept of (-3, 0)
a parabola with an x-intercept of (-3, 0)
a line with an x-intercept of (3, 0)
a parabola with an x-intercept of (3, 0)
Answer:
A parabola with an x-intercept of (3, 0)
Step-by-step explanation:
We can immediately rule out the first and third options, because the equation of a second degree function is a parabola.
Your equation is
ƒ(x) = x² - 6x + 9 = 0
We can factor this equation as
ƒ(x) = (x - 3)²
The parent parabola, y = x², has its x-intercept at (0,0).
Your function subtracts three from x, so the intercept is shifted three units to the right.
The graph of your function is a parabola with an x-intercept of (3, 0).
The figure below shows the graph of your function shifted three units by subtracting three from x.
Determine which type of transformation is illustrated in the figure.
A. composition
B. dilation
C. reflection
D. translation
An equation is shown : 5x + 3x = 5x + 15/2 what value of 3x makes the equation true?
Answer:
15/2
Step-by-step explanation:
Subtract 5x from both sides of the equation to find out.
5x +3x -5x = 5x +15/2 -5x . . . . . . subtract 5x
3x = 15/2 . . . . . . . . . . . . . . . . . . . . collect terms
The required value of 3x is 15/2.
The larger of two numbers is 15 more than the smaller number. Five times the larger number is 40 more than twelve times the smaller number. Find the num
Answer:
The numbers are 20 and 5.
Step-by-step explanation:
x = y + 15
5x = 12y + 40
5(y + 15) = 12y + 40
5y + 75 = 12y + 40
-7y = -35
y = 5
x = 5 + 15 = 20
The numbers are 20 and 5.
other dude correct
Step-by-step explanation:minecraft IGN Toothpaste123 and use code gki in the fortnite item shop. i play hypixel skyblock btw!
Mr. Slater invested $100,000 in a portfolio that is contains 60% stocks and 40% bonds. Over the course of a year, the value of the stocks
increased to 67%, and the value of the bonds decreased to 33%. The current value of his investment is $118,400. How much should Mr. Slater
move from stocks to bonds to rebalance his portfolio to 60% stocks and 40% bonds?
A.
$8,900
OB. $8,500
C.
$8.288
D.
$8,100
Answer:
c.8288
Step-by-step explanation:
Answer:
Mr. Slater invested $100,000 in a portfolio that is contains 60% stocks and 40% bonds. Over the course of a year, the value of the stocks increased to 67%, and the value of the bonds decreased to 33%. The current value of his investment is $118,400. How much should Mr. Slater move from stocks to bonds to rebalance his portfolio to 60% stocks and 40% bonds?
A.
$8,900
B.
$8,500
C.
$8,288
D.
$8,100
Step-by-step explanation:
#platofam
which expressions are equivalen to 2^5/6^5
[tex]\text{Hey there!}[/tex]
[tex]\bf{Which\ expressions\ are\ equivalent\ to\ \dfrac{2^5}{6^5}?}[/tex]
[tex]\bf{First:\ 2^5=2\times2\times2\times2\times2=4\times4\times2=16\times2\rightarrow32}[/tex]
[tex]\rightarrow\bf{2^5=32}[/tex]
[tex]\bf{Second: \ 6^5 = 6\times6\times6\times6\times6=36\times36\times2 = 1296\times6\rightarrow7,776}[/tex]
[tex]\rightarrow\bf{6^5=7,776}[/tex]
[tex]\bf{You\ can\ convert\ your\ new\ equation \ to (\text{ If this is helpful to you}):}\\\bf{\dfrac{32}{7,776}}[/tex]
[tex]\mathsf{\dfrac{32\div32}{7776\div32}}\\\\\mathsf{32\div32 = 1\leftarrow Your\ numerator}\\\\\mathsf{7,776\div32=243\leftarrow Your\ denominator}\\\\=\dfrac{1}{243}\\\\\boxed{\mathsf{Answer\#1: \dfrac{32}{7,776}}}\checkmark\\\\\boxed{\mathsf{Answer\#2:\dfrac{1}{243}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
2. Standard form: 8x + y = 9
Slope-intercept form:
Answer:
y = - 8x + 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
8x + y = 9 ( subtract 8x from both sides )
y = - 8x + 9 ← in slope- intercept form
The required slope intercept of the given equation of the line is given as y = -8x + 9.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given the equation of the line,
8x + y = 9,
Rearrange the equation in slope intercept form,
y = -8x + 9
Thus, the required slope intercept of the given equation of the line is given as y = -8x + 9.
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Round 6.677 to the nearest tenth,
Answer:
6.7
Step-by-step explanation:
the tenths place is one spot after the decimal
Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
How old is Daniel?
Answer:
2 years
Step-by-step explanation:
K = 4D. K = D + 6
4D = D + 6
-D. -D
3D = 6
3. 3
D = 2
Answer:
d=2
Step-by-step explanation:
We can use the given information to write down two equations that describe the ages of Kevin and Daniel.
Let Kevin's current age be k and Daniel's current age be d.
k=4d
k=d+6
Now we have two independent equations, and we can solve for our two unknowns.
Since we are looking for d, and both of our equations have k alone on one side, this is a convenient time to use elimination.
Subtracting the second equation from the first equation, we get:
0=4d-(d+6)
which combines the information about d from both of our original equations.
Solving for d, we get: 3d = 6.
d=2
Suppose f(x) = x+1. Find the graph of f(1/4x)
The graph of the equation [tex]f(\dfrac{1}{4}x)=\dfrac{1}{4}x+1[/tex] has a slope of 1/4 and y-intercept of 1.
What is the graph of a linear equation.
The graph of a linear equation is a straight line graph. It can be expressed as function of x i.e. f(x) = y = mx + b.
Given that: f(x) = x + 1, we are to graph the function of f(1/4x). We will have to replace (1/4x) into the original equation.
[tex]f(\dfrac{1}{4}x)=\dfrac{1}{4}x+1[/tex]
It implies that the graph of f(1/4x) has a slope of 1/4 and the y-intercept is 1. So it will be less steeper than the equation f(x) = x + 1.
when factoring, what is the first thing you need to do?
Answer:
1st step would be to check to see if you can factor anything out:
Greatest Common Factor. This means the greatest number that you can divide EVERY term by.
Evaluate \dfrac{e}{4}+2f-3
4
e
+2f−3start fraction, e, divided by, 4, end fraction, plus, 2, f, minus, 3 when e=12e=12e, equals, 12 and f=\dfrac12f=
2
1
f, equals, start fraction, 1, divided by, 2, end fraction.
Answer:
The value of given expression is 1.
Step-by-step explanation:
Consider the given expression is
[tex]\dfrac{e}{4}+2f-3[/tex]
When e=12 and [tex]f=\dfrac{1}{2}[/tex].
Substitute e=12 and [tex]f=\dfrac{1}{2}[/tex] in the given expression.
[tex]\dfrac{12}{4}+2(\dfrac{1}{2})-3[/tex]
On simplification we get
[tex]3+1-3[/tex]
[tex]1[/tex]
Therefore, the value of given expression is 1.
The evaluated result of the expression e/4 + 2f - 3, given specific values e = 12 and f = 5, is 13.
To evaluate the expression e/4 + 2f - 3, we need to follow a systematic procedure. First, we replace 'e' and 'f' with their respective values or expressions, if provided. Once these values are substituted, we perform the mathematical operations in the given order: division, multiplication, and subtraction.
Assuming we have specific values for 'e' and 'f', let's say e = 12 and f = 5. Substituting these values into the expression, we get:
e/4 + 2f - 3
= 12/4 + 2 * 5 - 3
Now, we simplify each part of the expression step by step:
12/4 = 3 (division)
2 * 5 = 10 (multiplication)
3 - 3 = 0 (subtraction)
Summing up the simplified components, we get:
3 + 10 - 0
Finally, performing the remaining additions and subtractions:
3 + 10 = 13
13 - 0 = 13
So, when e = 12 and f = 5, the evaluated result of the expression e/4 + 2f - 3 is 13.
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Complete Question:
Evaluate the equation: e/4 + 2f - 3 when e = 12 and f = 5
Jesse finished the first race in two minutes and seven seconds. Tim finished 12 seconds faster than Jesse. Juan finish eight seconds faster then Tim. How long did it take Juan to finish.
To find out how long it took Juan to finish, we add the time differences to Jesse's time. Tim finished 12 seconds faster than Jesse and Juan finished 8 seconds faster than Tim.
Explanation:To find out how long it took Juan to finish, we need to add the time differences to Jesse's time. First, we know that Tim finished 12 seconds faster than Jesse, so we can add 12 seconds to Jesse's time which becomes 2 minutes and 19 seconds. Next, we know that Juan finished 8 seconds faster than Tim, so we can add 8 seconds to Tim's time which becomes 2 minutes and 27 seconds. Therefore, it took Juan 2 minutes and 27 seconds to finish the race.
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A bag contains blue marbles and red marbles, 58 in total. The number of blue marbles is 4 more than 5 times the number of red marbles. How many blue marbles are there?
Answer:
49 blue marbles
Step-by-step explanation:
From the question we are given;
Total number of marbles = 58 Blue marbles are 4 more than 5 times the red marblesWe need to determine the number of blue marbles;
Assuming the number of red marbles is x
Then, blue marbles will be 5x + 4
Therefore;
x + 5x + 4 = 58
6x + 4 = 58
6x = 54
x = 9
5x + 4 = 5(9) + 4 = 49
Therefore, the red marbles are 9 while the blue marbles are 49
Hence there are 49 blue marbles
Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Explain.
Answer:
No
Step-by-step explanation:
A triangular prism has a uniform cross-section.A parallel cut of the solid will produce a cross section which is parallel to the triangular base.
A right prism contains uniform cross-sections, meaning the area of each cross-section is the same.
In this case, the position of the line indicating a cut will not produce polygons congruent to the base.
Can someone please answer this question please answer my question and answer it correctly and show work please
Answer:
Hours inequality (solution set): 0 ≤ x ≤ 7
Cost inequality: $2 ≤ y ≤ $100
Step-by-step explanation:
The babysitter charges $14 dollars per hour + bus fare
Price per hour = $14
Bus fare = $2
Mr. Tyler wants to spend no more than $100
Subtract the bus fare from the total amount, as that will not contribute to the babysitter's hours
$100 - $2 = $98
Divide by $14 per hour
$98 ÷ $14 = 7 hours
The maximum amount of time that Mr. Tyler could hire the babysitter for is 7 hours
This means that the hours cannot be greater than 7. It is given that x cannot be less than 0, because the babysitter cannot work negative hours.
0 ≤ x ≤ 7
This inequality shows that the Mr. Tyler will not have the babysitter work for less than 0 hours, or more than 7 hours. He will have to pay $2 minimum, or $100 max. Below is the inequality to represent this:
(y represents amount Mr. Tyler will pay)
$2 ≤ y ≤ $100
Hope this helps :)