For what values of x would the rectangle have a perimeter of at least 242?
a.9 or less
b.12 or less
c.12 or greater
d.25 or less
Paige measured 4/9 cup of onions, 3/4 cup of celery, and 2/7 cup of carrots. How many cups of vegetables did Paige measure out for her vegetable soup?
Answer:
Step-by-step explanation:
1) Make all the fractions have the same denominator.
- To do that you need to find the LCM (least common denominator) of 4, 9, and 7.
(look at image 1)
-Then apply the number you multiply the original denominator by to the original numerator
(look at image 2)
-Add the fractions together
(look at image 3)
Use complete sentences to describe why Set A = { X | X is an even whole number between 0 and 2} = ∅
Consider the Set A = {X | X is an even whole number between 0 and 2 } = [tex]\Phi[/tex].
Since, whole numbers are the set of numbers starting from zero upto infinity.
Even numbers are the numbers which are exactly divisible by '2'.
So, we have to find the even whole number between 0 and 2.
Since, only '1' is a whole number between 0 and 2 which is not an even number as '1' is not divisible by '2'.
Therefore, there is no even whole number between 0 and 2.
So, this set is empty.
Therefore, A = { X | X is an even whole number between 0 and 2} = [tex]\Phi[/tex]
Point a and point b are placed on a number line point a is located -20 and point b is 5 less then point a .which statement about paint b is true
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=7 -2x+6=9
Answer:
The y-coordinate of the solution is approximately 7.2.
Explanation:
To solve the system of equations:
1. [tex]\( 5x + 2y = 7 \)[/tex]
2. [tex]\( -2x + 6 = 9 \)[/tex]
We'll start by solving the second equation for [tex]\( x \):[/tex]
[tex]\[ -2x + 6 = 9 \][/tex]
Subtract 6 from both sides:
[tex]\[ -2x = 9 - 6 \][/tex]
[tex]\[ -2x = 3 \][/tex]
Divide both sides by -2:
[tex]\[ x = -\frac{3}{2} \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it into the first equation to find [tex]\( y \):[/tex]
[tex]\[ 5x + 2y = 7 \][/tex]
[tex]\[ 5(-\frac{3}{2}) + 2y = 7 \][/tex]
[tex]\[ -\frac{15}{2} + 2y = 7 \][/tex]
Add [tex]\( \frac{15}{2} \)[/tex] to both sides:
[tex]\[ 2y = 7 + \frac{15}{2} \][/tex]
[tex]\[ 2y = \frac{14}{2} + \frac{15}{2} \][/tex]
[tex]\[ 2y = \frac{29}{2} \][/tex]
Divide both sides by 2:
[tex]\[ y = \frac{29}{4} \][/tex]
Now, let's convert the fraction into a decimal rounded to the nearest tenth:
[tex]\[ y \approx 7.2 \][/tex]
Find the following measure for this figure.
Volume =
A. 275π cubic units
B. 91 2/3π cubic units
C. 36 2/3π cubic units
I need help with estimating and 920,026-535,722
The given difference of two numbers which we have to estimate is
920,026-535,722
Actual Difference=384,304
→Estimation Using Ones
920,030-535,720=384,310
→Estimation Using Tens
920,000-535,700=384,300
Estimation using Tens is Closer to Actual Difference.
So, Answer=384,300
The area of a rug is 36 square feet. the length of the rug is 5 feet longer than the width. what is the width of the rug?
twenty five is the quotient of a number y and 3.5
what is 25+120-10x=10x-35=
60/5(7-5)=2
I got 24, but some other people got 6.
60/5(7-5) - P
60/5(2) - M/D (left to right)
12(2) - M/D (left to right)
=24
Complete the solution of the equation. Find the value of y when x equals 15.
3x ‒ 8y = 5
y= ?
I hope that helps!
Consider the graph and equation, y = 3x, that represent Alonso’s walking speed. What relationship is represented by this equation and graph? What would the points (3, 9) and (5, 15) represent? Explain.
Answer with explanation:
The equation, y=3 x,
y=Distance traveled
x =Total time
[tex]\frac{\text{Distance traveled}}{\text{Time}}=\frac{y}{x}=3\\\\ \frac{dy}{dx}={\text{Rate of change}}={\text{Velocity}}=3 {\text{unit of time}][/tex]
Also, in terms of straight line
Slope =3= uniform Velocity
Point (3,9) and (5,15) represents Distance traveled in 3 (unit of time) =9 unit ,and 15 unit=Distance traveled in 5 (Unit of time).
→Alonso is moving with uniform speed=3 (unit of time), as velocity remains constant in the entire process.
The graph of line y = 3x, y represents distance and x represents the time and the point (3,9) repersents the distance covered by Alonso's is 9 unit in 3 unit of time and the point (5,15) repersents the distance covered by Alonso's is 15 unit in 5 unit of time.
Given :
y = 3x , represents Alonso's walking speed.
If y = 3x represents Alonso's walking speed than y represents distance and x represent time. The graph of y = 3x is attached below.
The point (3,9) on the line (y = 3x) represent that at 3 unit of time the distance covered by Alonso's is 9 unit.
The ponit (5,15) on the line (y = 3x) represent that at 5 unit of time the distance covered by Alonso's is 15 unit.
Therefore, in the graph of line y = 3x, y represents distance and x represents the time and the point (3,9) repersents the distance covered by Alonso's is 9 unit in 3 unit of time and the point (5,15) repersents the distance covered by Alonso's is 15 unit in 5 unit of time.
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The ratio of red to blue m7m's in a jar is 5:7. if there are 108 m&m's in the jar, how many are red
determine which equations below when combined with the equation 3x - 4y equals two or form a system with no solutions. choose all that apply.
1. 2y=1.5x-2
2. 2y=1.5-1
3. 3x+4y=2
4. -4y+3x=-2
The correct answers are:
1. 2y=1.5x-2 ; and 4. -4y+3x=-2.
Explanation:
Using the first equation, we have the system
[tex]\left \{ {{3x-4y=2} \atop {2y=1.5x-2}} \right.[/tex]
The second equation can be written in standard form just as the first one. To do this, we will subtract 1.5x from each side:
2y = 1.5x-2
2y-1.5x = 1.5x-2-1.5x
-1.5x+2y = -2
This makes our system
[tex]\left \{ {{3x-4y=2} \atop {-1.5x+2y=-2}} \right.[/tex]
To solve this, we will make the coefficients of x the same; we do this by multiplying the bottom equation by 2:
2(-1.5x+2y=-2)
-3x+4y=-4
This gives us the system
[tex]\left \{ {{3x-4y=2} \atop {-3x+4y=-4}} \right.[/tex]
We solve this by adding the two equations:
[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-4)}} \right. \\\\\\0+0 = -4\\0=-4[/tex]
There is no solution to this.
For the second system, we will follow the same process, subtract 1.5x from each side of the second equation:
2y=1.5x-1
2y-1.5x = 1.5x-1-1.5x
-1.5x+2y = -1
To make the coefficients of x the same, multiply the second equation by 2:
2(-1.5x+2y=-1)
-3x+4y=-2
We will add the two equations to solve:
[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-2)}} \right. \\0+0=0\\0=0[/tex]
This means that the equations are of the same line and there are infinite solutions.
For the third system, the coefficients are already the same. We will cancel by subtracting the bottom equation from the top:
[tex]\left \{ {{3x-4y=2} \atop {-(3x+4y=2)}} \right. \\\\-4y-4y=2-2\\-8y=0\\\frac{-8y}{-8}=\frac{0}{-8}\\y=0[/tex]
Since we have a value for y, this has a solution.
For the last system, we will rearrange the second equation with the x term in front:
3x-4y=-2
Now we will subtract this from the first equation:
[tex]\left \{ {{3x-4y=2} \atop {-(3x-4y=-2)}} \right. \\-4y--4y=2--2\\0=4[/tex]
This has no solution.
Solve the equation for the indicated variable :
A cab charges $1.45 for the flat fee and $0.55 for each mile. Write and solve an inequality to determine how many miles Ariel can travel if she has $35 to spend.
$1.45 + $0.55x ≥ $35;Answer:
The correct option is: $1.45 + $0.55x ≤ $35 ; x ≤ 61 miles
Step-by-step explanation:
Suppose, the number of miles Ariel can travel [tex]=x[/tex]
The cab charges $1.45 for the flat fee and $0.55 for each mile. So, the total charges for [tex]x[/tex] miles [tex]=\$1.45+\$0.55x[/tex]
Given that, she has $35 to spend. That means, the total charges must be less than or equal to $35.
So, the inequality will be: [tex]\$1.45+\$0.55x\leq \$35[/tex]
Solving the above inequality....
[tex]1.45+0.55x\leq 35\\ \\ 0.55x\leq 35-1.45\\ \\ 0.55x\leq 33.55\\ \\ x\leq \frac{33.55}{0.55}\\ \\ x\leq 61[/tex]
So, the number of miles Ariel can travel is 61 miles.
456 students participated in Switch Day. The students raised money for charity so that the principal would approve of the day. If the total amount money raised was 912, and each student brought in the same amount of money, how much did each student raise?
Make the following conversion.
0.075 m = _____ cm
0.075 m is 7.5 centimeters.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
Given that, convert 0.075 m into cm
We know that, 1 meter = 100 centimeters
0.075 meter = [(100) × 0.075] centimeter
0.075 meter = (100 × 0.075) centimeter
= (100 × 75/1000) centimeter
= (7500/1000) centimeter
= (75/10) centimeter
= 7.5 centimeter.
Hence, 0.075 m is 7.5 centimeters.
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Mrs. Decker walks for 30 minutes each day as often as possible. What is an equation that relates the number of days d that Mrs. Decker walks and the number of minutes m that she spends walking?
Write the equation of the line that passes through (2, 4) and has a slope of –1 in point-slope form.
The other person is correct i just did the test
The Porters’ food, clothing, and medical expenses are not fixed expenses. Explain what type of expense they are, and why.
Food, clothing, and medical are variable expenses because they occur regularly but can change from month to month.
The Porters’ food, clothing, and medical expenses are variable expenses.
A fixed expenses are the expenses that are constant and doesn't change while the variable expenses are those that are not fixed since they change.In this case, Porters’ food, clothing, and medical expenses are variable expenses since they can change every month.Read related link on:
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If h and k are constants and x^2+kx+7 is equivalent to (x+1)(x+h), what is the value of k?
To find the value of k when x^2+kx+7 is equivalent to (x+1)(x+h), we expand (x+1)(x+h), compare coefficients, and deduce that k is 8.
Explanation:If h and k are constants and x^2+kx+7 is equivalent to (x+1)(x+h), we are looking for the value of k. To find k, we expand the right-hand side and then compare coefficients.
Expanding (x+1)(x+h) gives us x^2+hx+x+h, which simplifies to x^2+(h+1)x+h.
Comparing this to x^2+kx+7, we can see that k must be equal to h+1.
Since there is no h term in x^2+kx+7, we infer that h must be equal to 7. Consequently, k=h+1 which leads us to k=7+1.
Therefore, the value of k is 8.
9/5 times a number plus 6 is 51 ?
Given a segment with endpoints A and B, what figure can you contrust using the steps below?
Step 1: Put the compass point on A and draw a long arc. Be sure the opening is greater than 1/2 AB.
Step 2: With the compass on the same setting, put the compass point on B and draw another long arc. Label the points where the two arcs meet as X and Y.
Step 3: Draw XY. (it has a line on top) Label the point of intersection of AB (it has a line on top too) and XY (has a line on top) as M, the midpoint of AB. (line on top)
a. a perpendicular bisector
b. a congruent segment
c. an angle bisector
d. a congruent angle
1. The perimeter of a rectangular garden is 690 ft. The short sides are each 55 ft. long. What's the length the other 2 sides? Which equation models the situation?
a) 55+2x=690
b) 55+x=690
c) 2(55)+2x=690
d) 55(x-2)=690
2. Two boys took turns driving home. Will averaged 52 miles per hour. Jim averaged 44 miles per hour and drove 2 hours longer than Will. X is the Will time drove, with D being the length of the trip in miles. The trip was 352 miles. If Jim's equation was 44(X+2)=D-52X. Which equation models the situation?
a) 143
b) 209
c) 238
d) 191
paul deposited 1,200$ into an account that earns 1.5% in annual simple interest. If paul does not make any deposites or withdrawls how much money will paul have in his account in 2 years?
Item 15 The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone. The formula for the surface area S of a right cone is S=πr2+πrl,S=πr2+πrl, where r is the radius of the base and l is the slant height. Find the height of the cone.
Final answer:
The height of the cone is equal to the slant height plus 1.
Explanation:
To find the height of the cone, we can use the formula for the surface area of a cone: S = πr^2 + πrl, where r is the radius of the base and l is the slant height. Since the problem states that the surface area is equal to the volume, we can set S equal to V and solve for h, the height of the cone.
Here's the step-by-step calculation:
S = V
πr² + πrl = V
πr² + πrl = πr²h
πr² + πrl - πr²h = 0
Combine like terms: πr²(1 - h) + πrl = 0
Divide both sides by πr to solve for h: 1 - h + l = 0
Subtract l from both sides: 1 - h = -l
Subtract 1 from both sides: -h = -l - 1
Multiply both sides by -1 to solve for h: h = l + 1
So, the height of the cone is h = l + 1.
How are polynomials like other number systems such as whole numbers and integers?
three times a number plus 16
The phrase 'three times a number plus 16' translates to '3x + 16' in mathematical terms, where 'x' represents any number.
Explanation:The phrase 'three times a number plus 16' can be converted into an algebraic expression. In mathematical terms, 'a number' is usually represented by the letter 'x'. 'Three times a number' can be written as '3x'. 'Plus' is represented by the '+', so 'three times a number plus 16' is written as '3x + 16'.
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