The length and width of the rectangular field are determined using algebra by setting up and solving two equations which represent the relationships between the length, width, and perimeter of the field. The dimensions are found to be 46 yards for the width and 137 yards for the length.
Explanation:The dimensions of the rectangular playing field can be found using algebra, specifically the formulas for the dimensions and perimeter of a rectangle. The problem can be translated into two equations reflecting the relationships of the field's width and length to the perimeter.
The first equation is: L = 3W + 5, which represents the relationship that the length is 5 yards longer than triple the width.
The second equation is derived from the formula for the perimeter of a rectangle (P = 2L + 2W), which given the problem's perimeter of 346 yards gets us: 2L + 2W = 346.
Substitute the first equation into the second to solve for the width, then use that result to find the length. The solution indicates that the width of the rectangular playing field is 46 yards, and the length is 137 yards.
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(02.05)The figure shows three quadrilaterals on a coordinate grid:
A coordinate plane is shown. Figure Q is a quadrilateral with sides measuring 5 and 2. Figure S is a quadrilateral with sides measuring 5 and 2. Figure W is a quadrilateral with sides measuring 10 and 4.
Which of the following statements is true about the three quadrilaterals?
Q and W are similar but not congruent.
W and S are similar and congruent.
W and Q are similar and congruent.
Q and S are similar but not congruent.
Answer:
The correct option is A) Q and W are similar but not congruent.
Step-by-step explanation:
Consider the provided graph.
Figure Q is a quadrilateral with sides measuring 5 and 2
Figure S is a quadrilateral with sides measuring 5 and 2.
Figure W is a quadrilateral with sides measuring 10 and 4.
Two figures are similar if the shape of the figures are same but not necessarily same size.
Two figures are congruent if the size and shape of the figure are same.
Note: If two figures are congruent, then they are also similar, but converse is not true.
The dimensions of Q is equals to the corresponding dimensions of the rectangle S. Thus, Q and S are similar and congruent as they have the same shape and the same size.
The dimension of quadrilateral W is 2 times of quadrilateral Q and S. Thus the dimensions of W is proportional to dimensions of Q.
That means quadrilateral W is similar to Q and S but not congruent.
Thus, the correct option is A) Q and W are similar but not congruent.
The chord XY is a diameter of of O. True or false?
Answer:
False
Step-by-step explanation:
XY is the diameter of the circle with the centre of this circle being O.
But O on it's own is just a coordinate, and not the circle.
Answer:
False, XY is not a diameter
Step-by-step explanation:
To be a diameter, it must go through the center of the circle, which is point O
The chord XY does not pass through the point O, so XY cannot be a diameter
The volume of a rectangular prism is (x^4+4x^3+3x^2+8x+4), and the area of its base is (x^3+ 3x^2+8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism
Answer:
height of prism = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex]
Step-by-step explanation:
Volume of rectangular prism = (x^4+4x^3+3x^2+8x+4)
Area of its bases = (x^3+ 3x^2+8)
Height of prism = ?
Volume of rectangular Prism = Area of its bases * Height of prism
(x^4+4x^3+3x^2+8x+4) = (x^3+ 3x^2+8) * height of prism
=> height of prism = (x^4+4x^3+3x^2+8x+4) /(x^3+ 3x^2+8)
=> height of prism = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex]
The division of (x^4+4x^3+3x^2+8x+4) /(x^3+ 3x^2+8) is shown in the attached figure.
Answer:
Step-by-step explanation:
what is the purpose of graphing linear equations? and how can we use it in everyday life?
variable costs, rates, marketing and budgeting are completely dependant on linear graphs it can be used to display a steady flow of something, or even and increase of a specific subject over time. if you were a market manager or banker, you'd probably deal with them.
can 3,2,5 be the lengths of a triangle
Answer:
No
Step-by-step explanation:
In a triangle, sum of any two sides is always grater than the third side.
Here,
[tex]3 + 2 = 5 \ngtr \: 5 \\ [/tex]
Hence, 3,2,5 can no tbe the lengths of a triangle
Enter the explicit rule for the geometric sequence. 60,12,12/5,12/25,12/125,...
Answer:
60(1/5)^(n-1).
Step-by-step explanation:
The common ratio r is 12/60 = 12/5 / 12 = 12/25 / 12/5 = 1/5.
The first term a1 = 60 so the explicit rule is
a1 * r^(n-1)
= 60(1/5)^(n-1).
aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .This can be obtained by using the formula of geometric sequence.
What is a geometric sequence?Sequence is s collection of objects in a particular order and repetitions are allowed.
Geometric Sequence:
a, ar, ar¹, ..., arⁿ⁻¹ is a geometric sequence, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.Common ratio, r = aₙ/aₙ₋₁In the given question, first term a=60
Common ratio r = a₂/a₁ = 12/60 = 1/5 ⇒ r = 1/5
By definition, arⁿ⁻¹ = (60)(1/5)ⁿ⁻¹ is the required explicit rule for the geometric sequence.
Hence aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .
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The number of lattes sold daily for two coffee shops is shown in the table:
Lattes
55
52
50
47
68
48
53
53
Based on the data, what is the difference between the median of the data, including the possible outlier and excluding the possible outlier?
Answer:
0.5
Step-by-step explanation:
Sort the given data in ascending order:
47, 48, 50, 52, 53, 53, 55, 68
Possible outlier is number 68. Check whether this number is an outlier:
[tex]Q_1=49\\ \\Q_2=52.5 \\ \\Q_3=54[/tex]
The interquartile range is
[tex]Q_3-Q_1=54-49=5[/tex]
Multiply it by 1.5:
[tex]1.5\cdot 5=7.5[/tex]
and add to third quartile:
[tex]7.5+54=61.5[/tex]
Since [tex]68>61.5,[/tex] number 68 is an outlier.
The median of the sample with outlier is [tex]Q_2=\dfrac{52+53}{2}=52.5[/tex]
The median of the sample without outlier is 52
The difference between the median of the data, including the possible outlier and excluding the possible outlier is 52.5-52=0.5
Answer:
0.5
Step-by-step explanation:
i finished the assignment and it was right so yeah it’s 0.5
d – 10 – 2d + 7 = 8 + d – 10 – 3d
Answer:
d=1
Step-by-step explanation:
Let's start by combining like terms.
-3-d=-2-2d
+d. +d
-3= -2-d
+2 +2
-1= -d
/-1. /-1
d=1
Which histogram correctly represents the data given in this frequency table
Answer:
The right histogram is the second one.Step-by-step explanation:
The image is blurred.
The given frequency is showing only 4 intervals, that means there should be only 4 bars in the right histogram, that lead us only to the first or second choice as right answers.
Now, according to the frequency table the first interval is larger than the second interval and the third interval is larger than the fourth interval. This means the first bar must be taller than the second bar, and the third bar must be taller than the fourth bar, and the second histogram is showing this.
Therefore, the right histogram is the second one.
f(1)=-1.5
f(n+1)=f(n)+0.5
what is f(10)?
Answer:
Step-by-step explanation:
3.
Final answer:
To find f(10) using a recursive formula, we can calculate intermediate values starting from f(1) and applying the given rule to find f(10) as 2.
Explanation:
The function is defined as follows:
f(1)=-1.5
f(n+1)=f(n)+0.5
To find f(10), we can use the given recursive formula to calculate subsequent values:
f(2) = f(1) + 0.5 = -1.5 + 0.5 = -1
f(3) = f(2) + 0.5 = -1 + 0.5 = -0.5
Continuing this pattern, we find f(10) = 2
Solve the proportion.8/d = -12/30
A. -45
B. -20
C. -3.2
Answer:
B. -20
Step-by-step explanation:
8/d = -12/30
We can use cross products to solve
8 * 30 = d* -12
240 = -12 d
Divide each side by -12
240/-12 = -12d/-12
-20 = d
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why JKZ QRS?
Check all that apply.
A. HA B.LA C.SAS D.HL E.LL F.SSS
Step-by-step explanation:
C. SAS the sides and angles are similar in both hence they are similar
F. SSS all sides equal
Answer:
SSS, SAS, LL, HL
Step-by-step explanation: because I got it incorrect by the last guy who tried to answer and I found out the hard way.. good luck everyone
How would you answer this math question please this is my last question
Answer:
Shorter sides: 270 feet.
Larger side: 540 feet.
Greatest possible area: 145800 square feet.
Step-by-step explanation:
So we need fencing around the garden except along the river.
The opposite sides of a rectangular are congruent.
So the sides perpendicular to the river in the picture are both of the same length, let's call it x. The length opposite the river is y.
So the perimeter excluding the side along the river is
x+x+y or 2x+y or 1080 is how much fencing we want.
So we have the equation:
2x+y=1080
The area of rectangle can be found by multiplying it's dimensions:
xy=A
We want to find the dimensions that provide us with the maximum area.
This is our area function so for:
A=xy
We need the area to be in terms of one variable.
Let's use our condition that 2x+y=1080.
2x+y=1080
Subtract 2x on both sides:
y=1080-2x
or
y=-2x+1080
We are going to plug this into:
[tex]A=xy[/tex]
[tex]A=x(-2x+1080)[/tex] : I replaced y with -2x+1080 since y=-2x+1080.
[tex]A=-2x^2+1080x[/tex] : I distribute.
Let's find the x-coordinate of the vertex.
To do this we need to determine [tex]a[/tex] and [tex]b[/tex] in the comparison of
[tex]A=ax^2+bx+c[/tex].
[tex]a=-2[/tex]
[tex]b=1080[/tex]
[tex]c=0[/tex]
The formula for the x-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-b}{2a}=\frac{-1080}{2(-2)}=\frac{1080}{4}=270[/tex]
We could plug this into our area Area function in terms of to find maximum area.
We could also wait til later. I think I will do both for a later check.
[tex]A=-2x^2+1080x[/tex] with [tex]x=270[/tex]
[tex]A=-2(270)^2+1080(270)[/tex]
[tex]A=145800[/tex]
So we one dimension of the rectangle so for which is 270 feet.
We have the maximum area which is 145800 square feet.
Now recall y=-2x+1080.
y=-2x+1080 with x=270
y=-2(270)+1080
y=540
So we have one dimension of the rectangle is 270 feet.
Another dimension is 540 feet.
And the area of the rectangle is 145800 square feet.
Does 270(540) equal 145800? 270(540)=145800 so yes.
Let's check to see if we have 1080 feet of fencing.
So we have 2 small sides of 270 and 270 feet.
We have a larger side which is 540 feet.
270+270+540=10180 so everything checks out.
the number that is x more than 2x+1
Answer:-1
Step-by-step explanation:x>2x+1=x-2x>1
-x>1,x<- 1
Answer:
-1
Step-by-step explanation:
Question 4(Multiple Choice Worth 5 points)
(04.03 MC)
What is the slope of the line joining (8, 1) and (24, 9)?
1 H
&
M
Answer:
1/2
Step-by-step explanation:
The slope between two points is found by
m = (y2-y1)/(x2-x1)
= (9-1)/(24-8)
= 8/16
= 1/2
Answer:
1/2.
Step-by-step explanation:
The slope = rise / run
= difference in y coordinates / corresponding differences in x coordinates
= (9 - 1) / (24 - 8)
= 8 / 16
= 1/2.
The tail of an airplane is 62 feet, 10 inches tall. How many inches tall is the tail
Answer:
754 inches
Step-by-step explanation:
you have to convert the 62 feet into inches which will be 62*12=744. You then add 10 to it to get 754 as your answer.
Find the coordinates of P so that P partitions the segment AB in the ratio 6:2 if A(−4,12) and B(9,−4).
A. (13.75, -24)
B. (5.75, 0)
C. (-16, 13)
D. (9.75, -12)
ANSWER
B. (5.75, 0)
EXPLANATION
If the point P(x,y) partitioned
[tex]A(x_1,y_1)[/tex]
and
[tex]B(x_2,y_2)[/tex]
in the ratio m:n, then
[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]
[tex]y=\frac{my_2+ny_1}{m + n} [/tex]
If the coordinates are A(−4,12) and B(9,−4), then:
[tex]x = \frac{6 \times 9+2 \times - 4}{6 + 2} [/tex]
[tex]x = \frac{54 - 8}{8} [/tex]
[tex]x = \frac{46}{8} [/tex]
[tex]x = 5.75[/tex]
[tex]y= \frac{6 \times - 4+2 \times 12}{6 + 2} [/tex]
[tex]y = \frac{24 - 24}{8} [/tex]
[tex]y = \frac{0}{24} = 0[/tex]
The correct choice is
[tex]B. (5.75, 0) [/tex]
The dishes have been sorted into cups and plates. The number of plates is four less than two times the number of cups. The dishes are 60% plates. How many cups are there?
a) 3
b) 6
c) 8
d) 9
Answer:
Option C) 8 cups
Step-by-step explanation:
Let
x----> the number of cups
y ---> the number of plates
we know that
y=2x-4 -----> equation A
60%=60/100=0.60
y=0.60(x+y) ----> equation B
Substitute equation A in equation B and solve for x
2x-4=0.60(x+2x-4)
2x-4=0.6x+1.2x-2.4
2x-4=1.8x-2.4
2x-1.8x=4-2.4
0.2x=1.6
x=1.6/0.2
x= 8 cups
From looking at the question, the answer is C. 8
How many solutions are there to the equation x2 + 7x – 6 = 0?
Answer:
two real roots
Step-by-step explanation:
x^2 + 7x – 6 = 0
We can use the discriminant
This is in the form ax^2 +bx+c=0
b^2 -4ac
If b^2 -4ac> 0 there are 2 real roots
If b^2 -4ac = 0 there is one real root
If b^2 -4ac <0 there are two complex roots
7^2 -4(1)*(-6)
49 +24
73
Since 73 > 0 there are two real roots
Answer:
The graph of the equation intersects the x-axis at two points. Therefore, it has two solutions.
Step-by-step explanation:
Subtract the following polynomials.
3.1x + 2.8z
4.3x - 1.2z
PLEASE HELP
Answer:
3.1x+2.8z
3.1 over 10x +14 over 15 z
1 over 10 x (3.1x + 2.8z)
4.3x - 1.2z =
43 over 10x - 6 over 5z
1 over 10 x (43x-12z)
Answer:−1.2x+4z
Step-by-step explanation:
What is the length of line segment BC?
Answer:
24
Step-by-step explanation:
hbdhdjjdjchchcbndndnxnndjdjdjdjjsjdhjdjxjxjjdjcncnncnfjfjdjdnndndnd
What type of polynomial is: 2a−4b+7c
The expression 2a−4b+7c is a trinomial and a first-degree polynomial.
The expression 2a−4b+7c is a linear polynomial because each term has a variable (a, b, c) with an exponent of one.
It is also a first-degree polynomial since the highest power of any variable is 1.
The price of pebbles are 4.50/kg.
A) How many kilograms of pebbles can be bought with $10?
Answer:
2.222222222222222222222222222222222222222222222222222222kg
or 2.2kg rounded :)
Step-by-step explanation:
10/4.50 = 2.2222222222222222222222222222222222222222222222222
so if you multiply both sides by 2.22222 you get (4.50 *2.222222 = 10)(kg*2.222222 = 2.222222222kg)
The u-drive rent-a-truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000 , each small truck $30,000 , and large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?
Answer:
They can buy 160 commercial vans, 80 small trucks and 40 large trucks.
Step-by-step explanation:
The company plans to spend $8 million on 280 new vehicles.
Commercial van = $25,000
Small truck = $30,000
Large Truck = $40,000
Let 'x' be commercial van, 'y' small truck and 'z' large truck. Therefore:
x + y + z = 280
Also, we know that x = 2y
Therefore: 3y + z = 280
Also we know that:
25,000x + 30,000y + 40,000z = 8,000,000
50,000y + 30,000y + 40,000z = 8,000,000
80,000y + 40,000z = 8,000,000
Therefore, we need to solve the following system of equation:
3y + z = 280 [1]
80,000y + 40,000z = 8,000,000 [2]
We have that the results are: y=80, z=40 and x=160.
Therefore, they can buy 160 commercial vans, 80 small trucks and 40 large trucks.
What is the median of the data set given below?
42, 20, 12, 15, 18, 15, 29, 33
ОА. 19
с. 15
Answer:
19
Step-by-step explanation:
Hey diddle diddle the medians in the middle you add then divide for the mean. the mode is the one that appears the most and the range is the difference in between.
Median: you have to organize the numbers from least to greatest then eliminate one by one.
12, 15, 15, 18, 20, 29, 33, 42
eliminate 12, and 42
15, 15, 18, 20, 29, 33
eliminate 15, and 33 ... so on
once you get to the median you end up with two numbers.
18, 20
because you can only have one median you find the number between, which in this case would be 19
Answer:
19
Step-by-step explanation:
The median is the middle value of the data in ascending order. If there is no exact middle then it is the average of the two values either side of the middle.
Arrange in ascending order
12, 15, 15, 18, 20, 29, 33, 42
The middle is between 18 and 20
median = [tex]\frac{18+20}{2}[/tex] = [tex]\frac{38}{2}[/tex] = 19
which representation has a constant of variation of -2.5
Answer:
Step-by-step explanation:
This is direct variation, and the pertinent equation is y = -2.5x, where -2.5 is the constant of variation.
Complete the toble below.
Percent = Decimal
11% =
6.5% -
0.26
-0.195
-111
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
Answer:
Step-by-step explanation:
This is a question that uses the Pythagorean Theorem.
a = 35 feet
b = x which is the height of the tree.
c = 3*x + 1 so we are trying to find x. Substitute into a b and c
a^2 + b^2 = c^2
35^2 + x^2 = (3x + 1)^2
35^2 + x^2 = 9x^2 + 6x + 1 Subtract x^2 from both sides.
35^2 = 8x^2 + 6x + 1 Subtract 35^2 from both sides.
0 = 8x^2 + 6x + 1 - 35^2
0 = 8x^2 + 6x - 1224
Does this factor?
(x + 12.75)(x - 12)
x - 12 = 0 is the only value that works.
x = 12
The tree is 12 feet high.
Note: I used the quadratic formula to solve this.
Answer:
12 ft
Step-by-step explanation:
Let the height of the tree is h.
So the distance of top of the tree = 3 h + 1
Distance of base of tree = 35 ft
So, by use of Pythagoras theorem
[tex]\left ( 3h+1 \right )^{2}=h^{2}+35^{2}[/tex]
[tex]8h^{2}+6h-1224=0[/tex]
[tex]4h^{2}+3h-612=0[/tex]
[tex]h=\frac{-3\pm \sqrt{9+4\times 4\times 612}}{8}[/tex]
[tex]h=\frac{-3\pm 99}{8}[/tex]
Take positive sign
h = 12 ft
Thus, the height of tree is 12 ft.
162*0.967=what? {this is multiplication}
Answer:
156.654
Step-by-step explanation:
162*.967=156.654
To multiply 162 by 0.967, use a calculator or perform the multiplication manually to get approximately 156.654.
The product of 162 and 0.967, you can multiply these two numbers together. When you multiply a whole number by a decimal, you're essentially combining that many groups of the decimal number. In this case, you are combining 162 groups of 0.967.
Here is the step-by-step calculation:
Write down the numbers: 162 and 0.967.
Multiply the whole number by the decimal: 162 * 0.967.
Use a calculator or long multiplication to find the product.
If you use a calculator, the answer you would get is approximately 156.654.
Write an equation for a line parallel to y=−4x+5 and passing through the point (4,-21)
Answer:
Y=-4x-5
Step-by-step explanation:
-21=-4(4)+b
-21=-16+b
b=-5
y=-4x-5
Answer:
y = - 4x - 5
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 )
y = - 4x + 5 is in this form with slope m = - 4
• Parallel lines have equal slopes, hence
y = - 4x + c ← is the partial equation of the parallel line
To find c substitute (4, - 21) into the partial equation
- 21 = - 16 + c ⇒ c = - 21 + 16 = - 5
y = - 4x - 5 ← equation of parallel line