The length of the rug is 4 ft.
The width of the rug is 2.5 ft.
Explanation:
The area of the rug is 10 ft.
The length of the rug be l.
Let us convert the inches to feet.
Thus, [tex]18 inches = 1.5 ft[/tex]
Thus, the length of the rug is [tex]l=1.5+w[/tex]
Let the width of the rug be w.
Substituting these values in the formula of area of the rectangle, we get,
[tex]A=length\times width[/tex]
[tex]10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0[/tex]
Solving the expression using the quadratic formula,
[tex]$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]
Substituting the values, we have,
[tex]$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\[/tex]
[tex]$w=\frac{-15 \pm \sqrt{4225}}{20}$[/tex]
[tex]$w=\frac{-15 \pm 65}{2 0}$[/tex]
Thus,
[tex]w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5[/tex] and [tex]w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4[/tex]
Since, the value of w cannot be negative, the value of w is 2.5ft
Thus, the width of the rug is 2.5ft
Substituting [tex]w=2.5[/tex] in [tex]l=1.5+w[/tex], we get,
[tex]l=1.5+2.5\\l=4[/tex]
Thus, the length of the rug is 4 ft.
It's A
length 4 and width 2.5
Joyce paid $98.00 for an item at the store that was 30 percent off the original price. What was the original price?
Answer:
$68.60
Step-by-step explanation:
If the original price is $98
30% = 0.03
0.30*98=29.40
Then, 98−29.40=$68.60
Is 5/8 greater than 6/16
Write two division expressions that have the same value as 61.12 divided by 3.2
the following are choice you can pick 2 from
611.2÷32
6112÷32
6.112÷32
6112÷320
6.112÷0.32
Two division expressions equivalent to 61.12 divided by 3.2 are 611.2 divided by 32 and 6.112 divided by 0.32. These are derived by scaling both numbers by the same power of 10, and such scaling does not change the value of the quotient.
Explanation:When looking for division expressions that have the same value as 61.12 divided by 3.2, we want to maintain the ratio between the dividend and the divisor.
By multiplying both the dividend and the divisor by the same power of ten, we can create equivalent expressions without changing the actual value of the division.
For the given problem, 61.12 ÷ 3.2, two equivalent division expressions from the choices provided are:
611.2 ÷ 326.112 ÷ 0.32Both of these are arrived at by multiplying the original dividend and divisor by 10 and 100 respectively. This operation does not change the value of the quotient but simply scales the numbers involved.
The expressions that have the same value as 61.12 divided by 3.2 are Option1. 611.2÷32 and Option 3. 6.112÷0.32
Given the choices, let's identify the equivalent expressions that will have the same value as [tex]\( 61.12 \div 3.2 \)[/tex]
The original division:
[tex]\[ 61.12 \div 3.2 = 19.1 \][/tex]
We need to find two expressions that also equal 19.1
Let's test the given options:
1. [tex]\( 611.2 \div 32 \)[/tex]
[tex]\[ 611.2 \div 32 = 19.1 \][/tex]
2. [tex]\( 6.112 \div 0.32 \)[/tex]
[tex]\[ 6.112 \div 0.32 = 19.1 \][/tex]
So, the two division expressions that have the same value as are:
[tex]\[ 611.2 \div 32 \quad \text{and} \quad 6.112 \div 0.32 \][/tex]
Thus, the answers are: [tex]\[ \boxed{611.2 \div 32 \quad \text{and} \quad 6.112 \div 0.32} \][/tex]
Full question
Write two division expressions that have the same value as 61.12 divided by 3.2
the following are choice you can pick 2 from
611.2÷326112÷326.112÷326112÷3206.112÷0.32A large bag of marbles contains equal amounts of each of 5 colors (red,
orange, yellow, green, and blue). Keisha selects 1 marble, looks at it, puts it
back, and then selects another. Find the probability of Keisha first picking a
yellow marble and then an orange marble.
O A. 0.5
O B. 0.008
O c. 0.04
OD. 0.2
Answer:
The answer would be 0.2
Step-by-step explanation:
Because there is five numbers and if you split 1 into five equal parts there is 0.2 which leads to the answer being 0.2
The required probability of Keisha first picking a yellow marble and then an orange marble is 0.04. Option c is correct.
A bag contains marbles and has an equal number of marbles in 5 colors.
The probability of Keisha first picking a yellow marble and then an orange marble is to be determined.
Probability is the ratio of a favorable number of events to the total number of events.
The total number of samples is = 5
Probability for yellow marble = 1/5 = 0.2
Probability for orange marble = 1/5 = 0.2
Probability for first picking yellow than orange = 0.2*0.2
= 0.04
Thus, the required probability of Keisha first picking a yellow marble and then an orange marble is 0.04.
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2x - 3y = 45 and x + y = 10 what is the x - value of the solution of the system
Answer:
x=15
Step-by-step explanation:
This is a simultaneous equation
2x-3y=45 ------------------------------ equation i
x+y=10 -------------------------------equation ii
from equation ii
x+y=10
make x the subject of the matter
we have,
x=10-y
in equation i
substitute x for 10-y
2x-3y=45----------------------i
since x=10-y
we have,
2(10-y) - 3y=45
20-2y=3y=45
collect like terms
-2y-3y=45-20
-5y=25
divide both sides by -5
we have y=-5
substitute y for-5 in equation i
x+y=10
x+-5=10
collect like terms
x=10+5
x=15
therefore
x=15
Answer:
x = 15
Step-by-step explanation:
Use the second equation to write an expression for y:
y = 10 -x
Then, substitute this into the first equation and solve for x.
2x -3(10 -x) = 45
5x -30 = 45 . . . . . eliminate parentheses
x -6 = 9 . . . . . . . . .divide by 5
x = 15 . . . . . . . . . . .add 6
in a fundraiser, Mrs. Smith pledges $1 for each mile walked . if Sam walks 20 miles how much will Mrs. Smith donate? what is yhe constant proportionality of the problen
Final answer:
Mrs. Smith will donate $20 for Sam walking 20 miles, illustrating a direct proportional relationship with a constant of proportionality of $1 per mile, which is a simple yet effective example of how constants of proportionality function in everyday scenarios.
Explanation:
In the fundraiser mentioned, Mrs. Smith pledges $1 for each mile walked. If Sam walks 20 miles, Mrs. Smith will donate $20. The constant of proportionality in this problem is $1 per mile.
You can see this relationship as a simple formula: total donation = $1 × number of miles walked. So, if we replace "number of miles walked" with 20, the formula would be total donation = $1 × 20 = $20. This illustrates how the initial pledge creates a directly proportional relationship between the money donated and the miles walked.
The constant of proportionality here is crucial because it tells us how much money will be donated per mile that Sam walks. It is a straightforward example of how constants of proportionality work in real-life scenarios, similar to being paid for each call made in a phone drive or being charged per hour of tutoring.
What is the mean of the data set?
66, 71, 75, 83, 88, 89, 90, 91
Express your answer to three decimal places.
Enter your answer in the box.
Answer:
81.625
Step-by-step explanation:
a mean is the average. an average is calculated by adding up all the numbers and then dividing the sum by the amount of numbers there are. these numbers added up = 653. 653 divided by 8 = 81.625. since it only goes up to three decimal places, no need to round.
Final answer:
The mean of the given data set is calculated by summing all the values and then dividing by the number of values. The calculated mean for this data set is 81.625.
Explanation:
To find the mean of the data set, we need to add all the data values together and then divide by the number of data values.
Add all the data values together: 66 + 71 + 75 + 83 + 88 + 89 + 90 + 91 = 653.Divide the sum by the number of data values: 653 ÷ 8 = 81.625.Thus, the mean of the data set is 81.625, which when expressed to three decimal places is 81.625.
Please answer my question please answer my please show work and answer it correctly please please show work answer number 17 and 19
17)
Find how many more pencils are needed:
250 - 108 = 142
Divide by the number of pencils in a box:
142 / 16 = 8.875 = 9 more boxes.
18) 5/4x - 3(8x-1/4)
Use the distributive property:
5/4x - 24x - 3/4
Rewrite 24x as 96/4x
Now you have:
5/4x - 96/4x-3/4
Combine like terms:
-91/4x - 3/4
19)
Car: 3 feet in 4 seconds
60 seconds / 4 = 15
3 feet x 15 = 45 feet per minute
Truck: 2 feet in 6 seconds
60 seconds / 6 = 10
2 feet x 10 = 20 feet per minute
45 - 20 = 25 feet
The car travels 25 feet per minute faster.
9. Find the length of the arc shown in brown. Leave your answer in terms of 2 (1 point)
4pi in.
8pi ft
16pi in.
48pi in.
The length of the arc is 4π.
Step-by-step explanation:
Given,
Diameter = 24 ftradius, r = diameter/2 r = 24/2 = 12 ftcentral angle, ∅ = 60°Arc length = ∅/360° (2πr)
⇒ 60°/360° (2π[tex]\times[/tex]12)
⇒ 24π/6
⇒ 4π
∴ The length of the arc is 4π.
What is the value of x in the equation 1,331x^3 -216=0
Answer:
x = 6/1.1
Step-by-step explanation:
hello :
1,331x^3 -216=0 means : x^3 = 216/1.331
x^3 = (6^3)/(1.1)^3 because : 216 = 6^3 and 1.331 = (1.1)^3
so : x^3 = (6/1.1)^3
x = 6/1.1
Jethro has to pay his annual taxes,he knows his tax rate is 27% of his taxable income . If he made $68,000 last year,which proportion should he use to determine how much he owes in taxes
Answer:
Step-by-step explanation:
Step-by-step explanation:
Let he owes x amount in taxes
He made amount last year = $68,000
His tax rate = 27%
So, he pays tax = 27% of the earning
So, A.T.Q.
27% times 68000 = x
{27}{100} times 68000 = x
27times 68000 = 100 times x
Someone please help me with this question I am stuck.
Answer: vertex
Step-by-step explanation:
Answer:
Vertex. The vertex is the point where two points meet, and the point 12 is where the lines meet.
Choose ALL that give an interval where the function is increasing.
A. (-infinity, -3)
B. (-3,-1)
C. (-1,2)
D. (2,4)
E. (4, infinity)
Answer:
(-∞,-3), (-1,2), and (4,∞)
Step-by-step explanation:
If f(x) is increasing on (a,b), then f(a)<f(b) on (a,b).
From the given graph, the graph is increasing on (-∞,-3), (-1,2), and (4,∞).
Think of it as the portion of the graph that slopes forward.
The correct options are A, C, an E
Answer:
(-∞,-3), (-1,2), and (4,∞)
A woman is throwing a party and has $200 to spend on snacks. She is purchasing packages of chips, c, for $1 each and Oreos, o, for $3 each. She needs to have 100 packages of snacks total. How many packages of chips and Oreos should she buy if she spends exactly $200?
Use your words to explain how you would solve the question and express your answer.
Don’t understand which expression represents the perimeter of the rectangle
Answer:
The perimeter of a rectangle is found by using this equation: P = 2 (L + W)
Step-by-step explanation:
I cannot see the picture that you posted, but that is the above equation. Take the length of the rectangle, and the width... plug that in for (L and W), and you have your formula! :)
Hope this helps!
The rectangle shown has a perimeter of 86 cm and the given area. Its length is 7 more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle
Length = 34 cm
Width= 9 cm
Step-by-step explanation:
Let the width of the rectangle to be.........w
Length is 7 more than three times the width..........3w+7
Perimeter = 86 cm
Perimeter of a rectangle = 2(l+w)
Perimeter of the rectangle = 2 (w + 3w +7)
= 2w +6w + 14
86= 8w +14
86-14 =8w
72=8w
72/8 =8/8w
9=w
Width= 9 cm
Length = 3*9 + 7= 27+7 = 34 cm
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Keywords: rectangle,perimeter,length, equation, dimensions
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List all the factors of each number.
81
Answer:
Step-by-step explanation:
1,3,9,27, and 81
a person is standing 15 feet away from a basketball hoop and randomly shoots a basketball four times.
What are the random variables in this situation? Select all that apply.
The random variables in this situation will be:
The distance the basketball lands from the hoop.The distance the basketball lands from the person.What is a random variable?It should be noted that a random variable simply means the numerical description of the outcome of a statistical experiment.
In this case, the distance that the basketball lands from the hoop and the distance the basketball lands from the person are the random variables.
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Answer:
The distance the basketball lands from the hoop.
The distance the basketball lands from the person.
6x + 4y = 6
3x = -15
x = ____ y = ____
Answers:
x = -5
y = 9
============================================
Work Shown:
Start by solving the second equation for x.
3x = -15
3x/3 = -15/3 .... divide both sides by 3
x = -5
Then plug this into the first equation and isolate y.
6x + 4y = 6
6(-5) + 4y = 6 .... every x replaced with -5
-30 + 4y = 6
-30+4y+30 = 6+30 .... add 30 to both sides
4y = 36
4y/4 = 36/4 .... divide both sides by 4
y = 9
What is the measure x? Enter your answer in the box .
X=
Answer: X= 83°
Step-by-step explanation: If we observe closely, the angle between 41° and X° is an angle opposite angle 56° (opposite angles are equal)
So what we have are three angles on a straight line, which are
41°, 56° and X.
Sum of angles on a straight line = 180°
Therefore,
41 + 56 + X = 180
97 + X = 180
Subtract 97 from both sides of the equation
X = 180 - 97
X = 83°
Acellus... can you help please
Based on the image we can see that angle B and angle E will be the same so we can write this into an equation.
x + 4 = 48°
Now, we can solve for x.
x + 4 - 4 = 48 - 4
x = 44 (answer)
Best of Luck!
Answer:
x=44
Step-by-step explanation:
I know because I had it!
x+4=48
x=48-4
x=44
Name the sides,angles and vertices of the triangle below
The given image is a triangle.
Property of triangle:
A triangle has three sides.
A triangle has three angles.
A triangle has three vertices.
To find the sides, angles and vertices of the triangle RST:
Sides of the triangle SRT:
RS, ST and RT
Angles of the triangle RST:
∠A, ∠B and ∠C
Vertices of the triangle RST:
A, B and C
These are sides, angles and vertices of the triangle.
What is 7 7/9 divided by 4/7
Answer:
4 44/49
Step-by-step explanation:
7 7/9 is 70/9
then u use 70/9 multiply by 7/4(I call it keep, change, flip method for division of fraction)
You keep the 1st fraction and because it is a mixed fraction, changing it to improper fraction is easier to solve it later on.
after that, you change the division sign to multiply sign(÷ to ×)
then you flip the 2nd fraction, which means 7/4 becomes 4/7
So overall it becomes 60/7 × 4/7 =240/49,4 44/49 as a mixed fraction.
Answer is 4 44/49
Machine a has a fixed daily cost of $40 and variable cost of one dollar per item produced. machine B has a fixed daily cost of $30 and a variable cost of $1.50 per item produced. A) what is the number of Items X for which the total daily cost C in dollars of each machine will be the same x items? B) what is the total daily cost per machine for this number of items?
To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up an equation and solve for x. The number of items x for which the total daily cost C of each machine will be the same is 20. For 20 items produced, the total daily cost per machine is $60.
Explanation:To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up the following equation:
40 + 1x = 30 + 1.5x
Simplifying, we get:
0.5x = 10
Dividing both sides by 0.5, we find:
x = 20
Therefore, the number of items x for which the total daily cost C of each machine will be the same is 20.
To find the total daily cost per machine for this number of items, we can substitute x = 20 into the equations for each machine:
Machine A: C = 40 + 1(20) = 60
Machine B: C = 30 + 1.5(20) = 60
So, for 20 items produced, the total daily cost per machine is $60.
Given (x, y) = (5, 15). Find tan 0.
Step-by-step explanation:
Given by question,
(x, y) = (5, 15)
Here, x = 5 and y = 15
To find, the value of [tex]\tan \theta[/tex] = ?
We know that,
[tex]\tan \theta[/tex] = Sope = [tex]\dfrac{y}{x}[/tex]
∴ [tex]\tan \theta[/tex] = [tex]\dfrac{15}{5}[/tex]
⇒ [tex]\tan \theta[/tex] = [tex]\dfrac{3}{1}[/tex]
⇒ [tex]\tan \theta[/tex] = 3
∴ The value of [tex]\tan \theta[/tex] = 3
Thus, the value of [tex]\tan \theta[/tex] is equal to 3.
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If you are driving 60 miles per hour, how many hours will it take you to drive from Lubbock to San Antonio? Round your answer to the nearest hour.
(use the chart below)
Abilene ....n/a......185..... 447...... 165.......... 261
Dallas .....185........n/a.... 633...... 351.......... 277
El Paso ...447..... 633.....n/a....... 344...........558
Lubbock ..165 ......351... 344........n/a...........394
San Ant....261..... 277.... 558....... 394...........n/a
1. 7
2. 8
3. 9
4. 10
Final answer:
To calculate the travel time from Lubbock to San Antonio at 60 miles per hour, divide the distance (394 miles) by the speed, resulting in about 7 hours when rounded to the nearest hour.
Explanation:
The question is about calculating the travel time from Lubbock to San Antonio when driving at a speed of 60 miles per hour. Based on the provided chart, the distance between Lubbock and San Antonio is 394 miles. To find the travel time, we use the formula time = distance ÷ speed. Therefore, the travel time is calculated as 394 miles ÷ 60 miles/hour = 6.5667 hours. Rounding this to the nearest hour gives us approximately 7 hours. So, it will take about 7 hours to drive from Lubbock to San Antonio at a speed of 60 miles per hour.
The length of the rectangle is x + 12. The width of the rectangle is x + 3. Please determine the area of the rectangle.
Answer:area = x^2 +15x +36
Step-by-step explanation:
Included angle between SW and WA
< A
< S
< W
Answer:
The answer is W
Step-by-step explanation:
The answer is W because it is included in both angles.
Answer:
< WStep-by-step explanation:
what is the answer to 7(2m + 6)+ 8m
Answer:22m+42
Step-by-step explanation:
7•2m =14m + 8m = 22m
7•6=42
Simplify the expression 4x+10+6x+2x
Answer:
12X+10
Step-by-step explanation:
It's easy. Just combine like terms. Like terms must have the same variable and to the same power in this case all the terms have a power of 1, but it doesnt show it because it doesn't really matter. So 4x,6x, and 2x all have the same variable so add them together. That gets you 10x. Since nothing else in the expression has the same variable with 10, you leave the 10 at the end resolving in 12x+10
Answer:
12x+10
Step-by-step explanation:
Collect the like terms to one side.