General Idea:
When we are working with word problems, we need to follow the below steps:
Step 1: Assign variable for the unknown that we need to find.
Step 2: Write a meaningful mathematical equation using the sentence given
Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.
Applying the concept:
Step 1: Let 'x' be the length of longest side of the fence.
Step 2: We need to set up an equation based on the information given.
[tex] Perimeter\; of\; rectangle=\; 2(\; Longest \; side\; +\; Shortest \; side\; ) [/tex]
Substituting 20 for the perimeter of rectangle, x for Longest side and [tex] \frac{7}{2} [/tex] for the shortest side in the above formula, we get the below equation.
[tex] 2(x+\frac{7}{2} )=20 [/tex]
Step 3: Solving the equation.
[tex] 2(x+\frac{7}{2} )=20\\ Distribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\\ \\ 2x+2 \cdot \frac{7}{2} =20\\ Simplify \; in \; the\; left\; side \; of \;the \;equation\\ \\ 2x+7=20\\ Subtract \; 7 \;on\; both \;sides \; of\; the \; equation\\ \\ 2x+7-7=20-7\\ Combine\; like \; terms\\ \\ 2x=13\\ Divide \; by \; 2\;on \; both\; sides\\ \\ \frac{2x}{2} =\frac{13}{2} \\ Simplify \; fraction\;on \; both \; sides\\ \\ x=6.5 [/tex]
Conclusion:
The length of longest side of the fence is 6.5 feet.
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box. °
police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d = s^2 / 30.25 where is the speed in miles per hour d is the length of the vehicle's skid marks. What was the approximate speed of a vehicle that left a skid mark measuring 160 feet?
1.about 36 miles per hour
2."" 60 ""
3."" 13 ""
4"" 54 ""
The answer would be ≈60mph, hence the answer is B.
PLEASE HELP! WILL MARK BRAINLIEST!
If the domain is {0, 2, -6}, what is the range of y = -2x + 3?
The range of the function is {-1, 3, 15}.
What is the range of the function?The set of a function's potential output values is known as its range.
Given that, the domain of the function is {0,2,-6}.
The range is the set of the output of the functions for the given domain values.
The value of y for x = 0 is:
y = -2(0) + 3
y = 3
Similarly, the values of y for x = 2 and x = -6 are:
y = -2(2) + 3
y = -1, and
y = -2(-6) + 3
y = 15
Hence, the range of the function is {-1, 3, 15}.
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. (02.02 HC) Dominic earns $18 an hour plus $25 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the week. Part A: Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 35 hours. (3 points) Part C: Dominic earned $730 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points) (10 points)
Please help and show all work thank you!
When dividing which number goes first in the calculator?
Are the two triangles are congruent ?
The area of a rectangular wall of a barn is 96 square feet. its length is 4 feet longer than twice its width. find the length and width of the wall of the barn?
Final answer:
To find the dimensions of the barn's wall, we set up the equation w x (2w + 4) = 96 and solved for w to find the width is 8 feet. Then, we used the width to find the length, which is 20 feet.
Explanation:
To solve the problem of finding the dimensions of the rectangular wall of the barn, we need to set up and solve an algebraic equation. Let's call the width of the wall w feet. According to the problem, the length is 4 feet longer than twice the width, so we can express the length as 2w + 4 feet.
The area of the rectangle is given by multiplying the length by the width. We know the area is 96 square feet, so our equation to solve is w × (2w + 4) = 96.
Expanding this equation gives us 2w^2 + 4w - 96 = 0. This is a quadratic equation that we can solve by factoring, completing the square, or using the quadratic formula.
Factoring the quadratic equation, we look for factors of -96 that add up to 4. These factors are 12 and -8. So, we can write our equation as (2w + 12)(w - 8) = 0.
Setting each factor equal to zero gives us two possible solutions for w: w = -6 or w = 8. Since width cannot be negative, we discard w = -6 and keep w = 8 feet. The length is then 2(8) + 4 = 16 + 4 = 20 feet.
Therefore, the width of the barn's wall is 8 feet, and the length is 20 feet.
Solve x + y + z = 12
2x – y – z = -6
x + 3y + 5z = 44
(4, 3, 5)
no solutions
(2, 4, -6)
(2, 4, 6)
Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly distributed between 1.0 and 2.1 minutes. (a) determine the mean of x. (round your answer to 2 decimal places.)
Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3
Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
The ratio of zoya's age to nelya's age is 1:4. twenty years from now, nelya will be twice as old as zoya will be then. find their present ages.
Answer:
Zoya is 10 years old. Nelya is 40 years old.
A grocer wants to make a 10 pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pounds and peanuts cost $2.20 per pound how many pounds of each nuts must he mix?
8.04 A
Graph each pair of parametric equations.
(2 points each)
x = 3 sin3t
y = 3 cos3t
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 7 sin t + sin 7t
y = 7 cos t + cos 7t
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 2t
y = t + 5, -2 ≤ t ≤ 3
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 2t – 1
y = t2 + 5, -4 ≤ t ≤ 4
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
Does the function model exponential growth or decay? g(t)=1.7 * 0.8^t
Answer:
decay
just answered this question.
Step-by-step explanation:
Answer:
decaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecay
Step-by-step explanation:
What is the sum of the polynomials (m+n+3)(m+n+4)
Answer:
2m+2n+7
Step-by-step explanation:
Given: Two polynomial
[tex]P_1=m+n+3[/tex]
[tex]P_2=m+n+4[/tex]
We need to find the sum of polynomial.
[tex]Sum=P_1+P_2[/tex]
[tex]\Rightarrow (m+n+3)+(m+n+4)[/tex]
write like term together
[tex]\Rightarrow m+m+n+n+3+4[/tex]
Combine the like term
[tex]\Rightarrow 2m+2n+7[/tex]
Hence, The sum of two polynomial is 2m+2n+7
Quadrilateral JPRAQuadrilateral JPRA is similar to quadrilateral KDEWquadrilateral KDEW . PR=27 mmPR=27 mm , DE=15 mmDE=15 mm , and WE=25 mmWE=25 mm .
What is AR?
Segment AB has endpoints A(–4, 6) and B(1, 4). After a dilation, centered at the origin, the image of A is (–6, 9). Without measuring the distance, explain how you could find the image of B
Answer:
To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).
Step-by-step explanation:
Sakura speaks 150150150 words per minute on average in hungarian, and 190190190 words per minute on average in polish. she once gave cooking instructions in hungarian, followed by cleaning instructions in polish. sakura spent 555 minutes total giving both instructions, and spoke 270270270 more words in polish than in hungarian. how long did sakura speak in hungarian, and how long did she speak in polish?
Answer:
3 minutes polish 2 minutes hungarian
Step-by-step explanation:
I just did it on Kahn Academy, and this was correct.
Mr. Berger assigned the following system of equations to be solved for homework. 2x-3y = -12
4x+ y= -10
Which is the x-coordinate of the correct solution?
Answer:
A: x= -3
Step-by-step explanation:
The x- coordinate is of solution is -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
2x-3y = -12...........(1)
4x+ y= -10..............(2)
Now, multiply Equation (1) by 2 we get
4x - 6y = -24
4x + y = -10
________
-7y = -14
y= 2
and, 4x+ y= -10
4x + 2 = -10
4x = -12
x= -12/4
x= -3.
Hence, the x- coordinate is -3.
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Consider the quadratic equation. x^2=4x-5. How many solutions does the equation have? a.) one real solution b.) two real solutions c.)no real solutions d.)cannot be determined
How do you do x ^4-4? What is the x values?
On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?
Answer:
Q(2, −1), S(−6, 5)
Step-by-step explanation:
The original ordered pairs were (2, 1) and (−6, −5). When you reflect across the x-axis the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
so since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hope this helped fellow FLVS student!!
The coordinates are Q(2, −1) and S(−6, 5)
What is reflection of points?A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.
Given that, On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis.
We know that, when you reflect across the x-axis, the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
So, since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hence, The coordinates are Q(2, −1) and S(−6, 5)
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PLEASEEEEE HELP WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Triangle HJK is transformed to similar triangle H’J’K’:
What is the scale factor of dilation?
1/2
1/3
1/4
1/5
Answer:
The scale factor of the dilation is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
Let
z------> the scale factor
so
[tex]z=\frac{K'J'}{KJ}=\frac{K'H'}{KH}=\frac{J'H'}{JH}[/tex]
substitute the values
[tex]z=\frac{K'J'}{KJ}[/tex] -----> [tex]z=\frac{1}{4}[/tex]
The scale factor is less than 1
therefore
The dilation is a reduction
Workers have 1600 m of fencing to enclose a rectangular area where a music festival will be held. The table represents a quadratic function that shows how the area of the rectangle formed by the fence depends on the length of the rectangle.
Length (m) Area (m²)
0 0
100 70,000
200 120,000
300 150,000
400 160,000
500 150,000
600 120,000
700 70,000
800 0
Select from the drop-down menu to correctly complete the sentence.
The x-coordinate of the vertex represents
the length that result in the largest possible area
the smallest possible area of the rectangle
the greatest possible length of any rectangle formed
the greatest possible area of a rectangle
This should get you a hundred on the 4.11 quiz. :)
The correct option is the x-coordinate of the vertex representing the length.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
As it is given that the perimeter of the rectangular fencing is 1600 m.
Now, since the shape of the fence is rectangular, therefore, the x-coordinate of the vertex represents the length that results in the largest possible area, while the y-coordinate is the width of the rectangular fencing.
Hence, the correct option is the x-coordinate of the vertex representing the length.
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The height and radius of a right cylinder are each 8 cm. what is its volume
What number is 22 spaces to the right of negative 7?
Final answer:
By adding 22 to -7, we find that the number 22 spaces to the right of -7 on the number line is 15.
Explanation:
The question asks for the number that is 22 spaces to the right of negative 7 on a number line. To find this, you can simply add 22 to negative 7. Here's the calculation: -7 + 22 = 15. Therefore, the number that is 22 spaces to the right of negative 7 is 15. To determine the number that is 22 spaces to the right of -7 on the number line, we need to add 22 to -7. Moving 22 spaces to the right indicates an increase in value by 22. Therefore, when we add 22 to -7, we get the final answer of 15. This calculation reflects the concept that moving to the right on the number line corresponds to increasing the numerical value, while moving to the left corresponds to decreasing it. In this case, starting from -7 and moving 22 spaces to the right results in a value of 15. Hence, 15 is the number that is 22 spaces to the right of -7.
A packet contains 24 pens.
Henry and Alice share them in the ratio 3 : 5
How many does Alice receive?