The length of the rectangular garden is 28 feet.
Statement represents the mathematical solution to the given word problem.
The statement clearly explains the stated circumstance.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
The area of the rectangular garden = 448 square feet.
Also, the length of the garden is 4 feet less than the twice of the width.
Let the width of garden is x feet
Then length of garden = 2x - 4
The area of rectangular garden = 448
x (2x - 4) = 448
x (x - 2) = 224
x = 16
The width of the garden is 16 feet.
The length of the garden = 2x - 4 = 2(16) - 4 = 32 - 4 = 28 feet
The required length of the garden is 28 feet.
The mathematical model to the given word problem is statement.
Statement clarify the given condition clearly.
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Need to find x and y
Answer:
x = 55 degrees, y = 55 degrees
Step-by-step explanation:
1.) Since y and the given angle are Same Side Interior angles, that means that they are supplementary. This means that y + 125 = 180.
2.) By solving this equation, we get y = 55 degrees.
3.) Now, since y and x are corresponding, that means that they equal each other. Therefore, x = 55 degrees.
Quadrilateral KLMN is similar to quadrilateral OPRS. Find PR. Round your
answer to the nearest tenth if necessary. Figures are not drawn to scale.
11
K
N
M
6
R
X
PP
S
51
The ratio of two corresponding sides of two similar polygons will be the same thus PR = x = 27.82.
What is the similarity?Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
As per the given KLMN similar to OPRS.
The ratio of two corresponding sides of two similar polygons will be the same.
PR/51 = 6/11
PR = x = 27.82
Hence "As two comparable polygons' corresponding sides will have the same ratio, PR = x = 27.82.".
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A marble is launched from a ledge at a height of 2.8 m with a velocity of 3.27 m/s. How far from the ledge will the marble land
All objects fall at the same rate in a vacuum as long as the only force acting on them is gravity.
How height is the ledge from the ground?King employs a first person narrator and opens with the protagonist, a retired pro tennis star named Stan Norris, in the clutches of a wealthy, A horizontal projection forming a narrow shelf on a wall. A ledge is created when the working length can no longer be negotiated and the original pathway of the canal has been lost.The magnitude of the velocity of the ball is 26.3 m/s for the parabolic motion just before it hits the ground and this greater than the 17.1 m/s for the velocity of the ball that falls straight downward.Hence, the height of the ledge from the ground is 1.25m.
3.27m/s
Given parameters:
Initial velocity = 3.27m/s
Height of fall = 2.8m
Unknown:
Final velocity = ?
To solve this problem, we have to look at our given parameters and compare to the appropriate motion equation.
we have been given; u (initial velocity) and height of fall (h)
Since this body falls under acceleration due to gravity, g = 9.8m/s²
Now, we use;
V² = U² + 2gh\
where V is the final velocity
Input the parameters and solve;
V² = 3.27m/s + (2 x 9.8 x 2.8)
V = 65.4m/s
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The volume of water in a rectangular, in-ground, swimming pool is given by V(x ) =x3 + 11x2 + 24x where V (x) is the volume in cubic feet when the water is x ft high
What is the dimension of the base of the pool? (a) x + 3 and x + 8 (b) x + 4 and x + 7 (c) x + 4 and x + 8(d) x + 3 and x + 7 What is the volume of the pool when x = 3 ft?
(a) 298 ft3 (b) 148 ft3 (c) 268 ft3 (d) 198 ft3
If the volume is 100 ft3 of water, what is the height x ? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
If the maximum capacity of the pool is 520 ft3 what is the maximum depth? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
1) The dimension of the base of the pool is; (x + 3) and (x + 8)
2) The volume of the pool when x = 3 ft is; 198 ft³
3) If the volume is 100 ft³ of water, the height x is; 2 ft
4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft
How to find the volume of a cuboid?We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x
where;
V(x) is the volume in cubic feet when the water is x ft high
1) V(x ) =x³ + 11x³ + 24x
V(x) is the volume in cubic feet when the water is x ft high
Factorizing the polynomial into its' factors gives;
V(x) = x(x² + 11x + 24)
V(x) = x(x + 8)(x + 3)
The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)
2) We want to find the volume of the pool when x = 3 ft. Thus;
V(3) = 3(3 + 8)(3 + 3)
V(3) = 3 (11)(6)
V(3) = 198 ft³
3) If the volume is 100 ft³ of water, the height x is calculated as;
x(x + 8)(x + 3) = 100
Solving for x gives us;
x = 2 ft
4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;
x(x + 8)(x + 3) = 520
Solving for x gives us;
x = 5 ft
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The graphs below have the same shape. What is the equation of the blue graph?
The blue graph is a vertical shift of 2 units downwards from the red graph.
What is vertical shift?One simple transformation is to move the entire graph of a function up, down, right, or left. Because this transformation involves adding a positive or negative constant to the function, the simplest shift is a vertical shift, which moves the graph up or down.Here,
We are given the parent function f(x) as follows:
f(x) = x²
and it is depicted by a red graph.
Looking at the graph, we can clearly see that the graph of G(x) (represented by a blue graph) is a 2 unit downward translation of the graph of f(x).
As a result, the transformation function g(x) is as follows:
G(x) = f(x) - 2
which is also written as:
G(x) = x² - 2
As a result, the equation for G(x) is : G(x) = x² - 2.
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solve for x please I'm having a hard time on this one
Answer:
divide 2x by 2, that gives you x, then divide 104 by 2 and that gives you the answer to x
EXTRA POINTS!!
Law of Sines. Find the value of y. Round to the nearest tenth: 42,85, and 31
What does y equal? Please help asap!!
The side length of the triangle (y) will be 45.88 units.
The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The angle of a triangle is 42° and its opposite side is 31. And the angle of a triangle is 85° and its opposite side is y. Then by the sine law, the equation is written as,
y / sin82° = 31 / sin42°
Simplify the equation, then the value of the variable 'y' is calculated as,
y / sin82° = 31 / sin42°
y = 31 x sin82° / sin42°
y = 31 x 1.4799
y = 45.88 units
The side length of the triangle (y) will be 45.88 units.
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the larger of two numbrers is twice the smaller number if 2 is subtracted from the larger number the result is 7 more than the smaller number find the numbers
Answer:
Step-by-step explanation:
smaller number = x
larger number = 2x
12 is subtracted from the larger number= 2x - 12
7 more than the smaller number = x+7
2x - 12 = x+7
2x -x = 7 +12
x = 19
smaller number = x = 19
larger number = 2x= 2(19)=38
2. Estimate: then find sum
1.52
+1.21.
Answer:
Estimate: 3
Sum: 2.73
Step-by-step explanation:
To find the estimate, we can round our numbers to the nearest tenth (1.52 would become 1.5, and 1.21 would become 1.2). When we add these two numbers together, we get 2.7, which can be rounded up to 3.
To find the sum, we simply add 1.52 + 1.21, which equals 2.73.
The sides of a triangle measure 2x+52x+5, x-4x−4, and 3\left(2x+1\right)3(2x+1). What is the perimeter of the triangle?
The expression for the perimeter is given as 9x + 4.
What is a triangle?A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.
The sides of the given triangle are 2x + 5, x - 4 and 3(2x + 1) respectively.
Since, the perimeter is given as the sum of all the sides of a polygon.
In case of triangle, there are three sides which implies its perimeter will be the sum of all of its three sides given as,
Perimeter = 2x + 5 + x - 4 + 3(2x + 1)
⇒ 2x + x + 6x + 5 - 4 + 3
⇒ 9x + 4
Hence, the perimeter of the triangle is given as 9x + 4 units.
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You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0. 11. This means that
a. If each player gets an ace in only 2 of the first 50 deals, then each player should get an ace in more than 11% of the next 50 deals.
b. In a very large number of bridge deals, the percent of deals on which each player has 1 ace will be very close to 11%.
c. In 1 million bridge deals, the number of deals on which each player has 1 ace will be exactly 110,000.
d. In every 100 bridge deals, each player has 1 ace exactly 11 times.
c. In a very large number of bridge deals, the average number of aces in a hand will be very close to 0. 11
As per the given probability, this means that option (b) In a very large number of bridge deals, the percent of deals on which each player has 1 ace will be very close to 11%.
Probability:
In statistics, it denotes the possibility of the outcome of any random event.
Given,
Here we have given that You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0. 11.
Now, we need to find the meaning of the given probability.
Here We know that, Having one ace 10 or 12 times is likewise quite likely to happen.
And It is feasible to get 109,000 deals with just one ace.
Finally, For very large samples, the probability is always close to the corresponding percent.
Based on these details option (b) is correct.
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Got this on my math test today:
x^(-1/3)=32x^(-2)
The value of x for the given equation is 8.
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
For negative numbers, the logarithm are complex numbers.
The given equation is as below,
x^(-1/3) = 32x^(-2)
It can be solved as follows,
x^(-1/3) = 32x^(-2)
Take logarithm on both sides to obtain,
log (x^(-1/3)) = log (32x^(-2))
=> -1/3 log(x) = log(32) - 2log(x)
=> 2log(x) - 1/3 log(x) = log(32)
=> 5/3log(x) = log(32)
=> log (x^(5/3)) = log(32)
Remove log from both sides to get,
x^(5/3) = 32
=> x = 32^(3/5)
=> x = 8
Hence, the solution of the given equation is x = 8.
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D.J. is planning an end of the school year party for her friends. She has $55 to
spend on soda and pizza.
Soda (2-liter)
Large Pizza
$1.25, including tax
$7.50, including tax
She knows she has to buy five 2-Liter bottles of soda.
Choose the inequality and calculate how many pizzas she can buy.
A 5(1.25) +7.50p ≥ 55; 7 pizzas
B 5(7.50) +1.25p> 55; 6 pizzas
C 5(7.50) +1.25p ≤ 55; 7 pizzas
D 5(1.25)+7.50p ≤ 55; 6 pizzas
Answer:
D
Step-by-step explanation:
He has max $55, so the total cost must be minor or equal to this value
6.25 + 7.50p ≤ 55
7.50p ≤ 55 - 6.25
7.50p ≤ 48.75
p ≤ 48.75 / 7.50
p ≤ 6.5
p = 6
Maths qs
Dot diagram and mean mass
Answer:
mean 33.214
Step-by-step explanation:
465/14= 33.214
Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings.
Write an equation for this problem.
The equation for this problem will be 12x = 48.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Sergio has p works of art in his craft assortment. He and other nearby canvas gatherers consented to give a sum of 48 compositions to the neighborhood historical center. Every one of the 12 authorities will give a similar number of artistic creations.
Let 'x' be the number of donations by each. The equation for this problem is given as,
12x = p
12x = 48
The equation for this problem will be 12x = 48.
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5. in the system of linear equations above, k is a constant. if the system has no solution, what is the value of k?
The system of linear equations above, k is a constant. if the system has no solution is [tex]\frac{7}{6}[/tex]
[tex]\begin{aligned}& (k-1) x+\frac{1}{3} y=4 \\& k(x+2 y)=7\end{aligned}[/tex]
What is equations?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7
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Which set of coordinates
The coordinates of parallelogram in geometry ABCD are A( 0,2 ) ( 2,2 ) ( 1,1 ) ( -1, 1)
What is geometry?The area of mathematics known as geometry is concerned with the dimensions, sizes, angles, and shapes of various objects that we encounter every day.
Solution:
All the angles of a parallelogram are not equal. Only the opposite angles of a parallelogram are equal and the consecutive (adjacent) angles of a parallelogram are always supplementary.
Hence using this property coordinates of parallelogram in geometry ABCD are A( 0,2 ) ( 2,2 ) ( 1,1 ) ( -1, 1)
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NOT MANY POINTS BUT I NEED HELP ON MY FINAL
A linear pair's total angles are always equal to 180°. Hence ∠ HJL is 94°
What is a Linear Pair of Angles?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.Those two neighboring angles whose sum is 180° are referred to as a linear pair of angles. They are represented by a ray that serves as a common arm between the angles and is drawn on a straight line.The name "linear" comes from the standard illustration of a linear function in one dimension: a line drawn through the origingiven
∠HJL and ∠LJK are linear pair
∠ HJL = ?
∠HJL + ∠JLK =180
x + x -8 = 180
2x -8 =180
x = 188/ 2 = 94°
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The table how the amount of time, in minute, it take to walk a given ditance, in mile, along each path. Complete the table to how the average walking rate, in mile per hour, for each path
The data posted at the conclusion of the answer provides the finished table with the average walking rates.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured
According to our question-
The velocity in this problem is the average walking speed, hence the distances in the table are calculated by dividing the time in the same row by the velocity.
The velocity is reported as follows for the first row:
2.5 miles per hour is equal to v = 0.5/(12/60) = 0.5/0.2.
The minutes are split by 60 because the time is in hours.
The velocity is stated as follows for the second row:
1.5 x 4/3 divided by 45/60 equals 2 miles per hour, or v.
The velocity is given as follows for the third row:
v = 0.75 x 4 x (15/60) = 4 miles per hour.
Hence, 4 miles per hour.
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Question 20 of 25
If JKLM is a trapezoid, which statements must be true? Check all that apply.
A. Jis supplementary to K.
B. Jis congruent to K.
C. JK is parallel to LM.
D. JK a LM
E. KL is parallel to JM.
F. JM a KL
There are two parallel sides and two non-parallel sides to a trapezoid. These are the actual claims:
(A) J is supplementary to K
(E) KL is parallel to JM
What is a trapezoid?In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid.
It is referred to as a trapezium in British and other varieties of English.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.
So, a trapezoid's adjacent point angles sum up to 180 degrees.
This implies:
J+K = supplementary angles
L+M = supplementary angles
The highlights mentioned above indicate that J and K are supplemental angles. Thus, (a) is accurate.
A trapezoid also has two parallel sides.
Lines KL and JM must be parallel to one another because they are horizontal.
The highlighted portion above indicates that lines KL and JM are parallel. So, (e) is correct.
Therefore, there are two parallel sides and two non-parallel sides to a trapezoid. These are the actual claims:
(A) J is supplementary to K
(E) KL is parallel to JM
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True or False? You can find the mean, median, and mode of a data set from a box and whisker plot
Answer: false
Step-by-step explanation:
Find the x- and y-intercepts of the graph of x + 4y = 20. State each answer as an I refer or an improper fraction in simplest form.
x-intercept: 20
y-intercept: 5
To find the x- and y-intercepts of the graph of the equation x + 4y = 20, we need to solve the equation for x and y, respectively.
First, to find the x-intercept, we need to set y equal to 0 and solve for x. This gives us the following equation:
x + 4(0) = 20
x = 20
Therefore, the x-intercept is (20, 0).
Next, to find the y-intercept, we need to set x equal to 0 and solve for y. This gives us the following equation:
0 + 4y = 20
4y = 20
y = 5
Therefore, the y-intercept is (0, 5).
I need help with number nine please
On #9:
Slope-intercept form is y = mx + b
Based on the graph, the slope is -4/3 and the y-intercept is (0,0).
The answer is y = –4/3 x.
You could add "+0" at the end to have y = –4/3 x +0, but since adding 0 doesn't change it, it's usually left off.
Answer:
y = -4/3x + 0 or just y = -4/3
Step-by-step explanation:
you just find the slope by doing rise over run, and find the y-intercept by looking at what number the line hits on the y-axis.
Chloe made an apple pie. After measuring the pie tin, Chloe calculated it has a circumference of 56.52 centimetres. What is the pie tin's diameter?
Answer:
Step-by-step explanation:
154 times 3, and then you try simplifying that by 2. Then it'll give you 140.32
Answer:
Step-by-step explanation:
140.4 or rounded 140
five couples have reserved seats in a row for a concert. in how many different ways can they be seated?
five couples have reserved seats in a row for a concert, 3840 different ways can they be seated. So, using the concept of combination formula we get -
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
The formula becomes: [tex]^nC_r[/tex]
Where n = total number of objects in the set.
r = number of choosing objects from the set
Given that,
there are five couples
These couples have reserved seats in a row for a concert.
So, arrangements of 5 couples can be done in 5! × 2⁵= 3840 ways.
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A circle with a radius of 5 is transformed into the following function:
(x/3)² + (5y)² = 25
What percentage of the original circle's area is the area of the new circle?
A. 60%
B. 167%
C. 36%
D. 278%
The level of the first circle's region is the region of the new circle will be 60%. Then, at that point, the right choice is A.
What is the area?The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
A circle with a sweep of 5 is changed into the accompanying capability:
(x/3)² + (5y)² = 25
The major and minor axes are given as,
(a/3)² = 25
a = 15
(5b)² = 25
b = 1
The percentage of area is given as,
P = [(Area of ellipse) / (Area of the circle)] x 100
P = [(πab) / (πr²)] x 100
P = [(15 x 1) / (5²)] x 100
P = (15/25) x 100
P = 0.6 x 100
P = 60%
The percentage of the original circle's area in the area of the new circle will be 60%. Then the correct option is A.
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The two polygons are similar. Solve for x
Ellen wants to build a sidewalk of uniform width around her pool. Her pool is rectangular,
and its dimensions are 60 feet by 50 feet. She has enough pavers to cover 1000 square
feet and wants to use all the pavers.
Complete the following statement. Round to the nearest tenth
Ellen should make the width of the sidewalk
feet.
Answer:
she should just divide the dimensions by 3
Step-by-step explanation:
Given that the equation of line one (L1) is 2x-y=3 and equation of line two (L2) is kx+2y=3 where k is a constant.
(a) Find the value of k such that L1 and L2 are parallel.
(b) Find the value of k such that L1 and L2 are perpendicular.
This question is related to Linear functions, Answers: (a) k = -4, (b) k=1. Someone pls tell me how to get there though
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given the equation of L1 is
2x - y = 3 ( subtract 2x from both sides )
- y = - 2x + 3 ( multiply through by - 1 )
y = 2x - 3 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes
then slope of L2 is m = 2
given the equation of L2 is
kx + 2y = 3 ( subtract kx from both sides )
2y = - kx + 3 ( divide through by 2 )
y = - [tex]\frac{k}{2}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{k}{2}[/tex]
since slope of L1 and L2 are equal, both 2 , then
- [tex]\frac{k}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )
- k = 4 ( multiply both sides by - 1 )
k = - 4
----------------------------------------------
(b)
given the slope of a line is m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Then
for L2 to be perpendicular to L1
- [tex]\frac{k}{2}[/tex] = - [tex]\frac{1}{2}[/tex] ( multiply both sides by - 1 )
[tex]\frac{k}{2}[/tex] = [tex]\frac{1}{2}[/tex] , thus
k = 1
if my grade is a 92.30% and i got 70% on something that counted for 20% of my grade, what would the final grade be?
If you got a score of 90 percent on the test and the test is worth 20 percent of your overall grade, you would multiply 90 by 0.2 for a value of 18 points out of the possible 20 points.
Is 70 percent a failing grade?
The standard range for grades is 55 to 100. As seen in the chart below, number grades correspond to letter grades. The required passing score is 70. (C). Failure grades are any grades between 55 and 69 (D and F), for which no unit credit is granted.
A Passed grade requires a C or higher; a C- or worse results in a Not Passed mark. Many prerequisites (such as those for General Education and Electives) may be satisfied by a grade of C-, but neither credit nor requirements will be satisfied by a grade of Not Passed.
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