Answers
Part A
The yard is a quadrilateral with the following corner points
(0,0)(0,40)(40,50)(50,0)I'll label those points A through D in the order presented above.
From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.
In short: side AB is 40 feet long.
The length of side BC is not as simple. We'll need the distance formula.
[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]
Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.
Use the distance formula again to find the distance from point C(40,50) to D(50,0)
[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]
Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.
We have these side lengths:
AB = 40
BC = 41.2311 (approximate)
CD = 50.9902 (approximate)
AD = 50
Add up those four sides and we'll get the perimeter of the quadrilateral.
AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213
Answer: About 182.2213 feet===================================================
Part B
The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).
This 15 by 20 rectangle has an area of 15*20 = 300 square feet.
The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.
The area of the trapezoid is
A = h*(b1+b2)/2
A = 15*(20+35)/2
A = 412.5
That decimal value is exact.
Add it onto the area of the rectangle
412.5+300 = 712.5
Answer: 712.5 square feet exactlyRelated Questions
Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can
be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the
constraints on the values of x and y?
O y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
O y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to
5.5.
O y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
O y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to
5.5.
Answers
This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is the equation for this situation?It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:
y = x + 5.5
The possible values are
x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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Answer: y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
The data below represents the weight, in kilograms, of 15 containers shipped from a factory in one week.
Match the letter with the correct term that would be necessary to complete the box and whisker plot.
Answers
Box and whisker plot has shown in the picture which shows different measures of the data set.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have data:
45, 51, 53, 55, 55, 65, 75, 81, 84, 87, 93, 93, 95, 96, 100
Sample size: 15
A = (c) The Lowest value (45)
B = (e)Lower quartile Median (55)
C = (b) Median (81)
D = (d) Upper quartile (93)
E = (a) The Highest value (100)
Thus, box and whisker plot has shown in the picture which shows different measures of the data set.
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Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t) = 16t^2 where is time in seconds. The height of a certain tower is 878 feet. How long would it take an object to fall to the ground from the top of the building?
Answers
Answer:
7.4 seconds
Step-by-step explanation:
878 = 16 t^2 divide both sides of the equation by 16
54.875 = t^2 take positive sq rt
7.4 seconds
7513% [tex]\frac{5}{3x^{2} }[/tex] x³ Find the Product Show All work!
Answers
[tex]\\ \rm\Rrightarrow \dfrac{7513/100\times 5x^3}{3x^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{75.13(5)x^3}{3x^2}[/tex]
[tex]\\ \rm\Rrightarrow {125.22x}[/tex]
3. If you are just building your payment history, how many points from a perfect score will you possibly miss
A. 280 points
B.
80 points
240 points
D. 120 points
Answers
a) 280 points
b) 80 points
c) 240 points
d) 120 points
correct option :A) 280 points9. Use the distance formula to find the distance between the points (-4,-4) and (4,4).
Answers
Answer:
16
Step-by-step explanation:
Distance formula = [tex](x_{1}-x_{2})+(y_{1}-y_{2})[/tex]
Depending on which point is A and Which point is B, the answer is one of the two.
However, there is no such thing as negative distance, so your answer is 16 points in a certain direction.
Which of these is an example of similar terms
Answers
Answer:
sorry if this is wrong, I don't take algebra two and I won't have to, but maybe a polynomial with three turns
A couple is looking for a mortgage to purchase a house for $256,000. If the bank requires a 5% down payment, what is the amount to be mortgaged?
$128000
$12800
$243200
$25600
Answers
Multiply $256,000 by 5%
I need a genuine answer. Don't answer if you don't know. Need a proper explanation.
Answers
Answer:
Step-by-step explanation:
If m and n are both 1 then
Minimum value = 10^(1+1) * 3^(1-1) * 225
= 325.
If m and n have to be different, then m = 2 and n = 1
Minimum value = 10^3 * 3^1 * 15^2
= 675,000.
If m >= n then N will also be natural which is a subset of rational numbers.
If m < n then 3^(m - n) will be less than 1 and N will need to be written as a fraction, which are still rational.
The minimum values for both m and n are 1 by definition.
I need this problem solved
Answers
Answer:
x = 50
Step-by-step explanation:
∠ BAC and 135° are adjacent angles and sum to 180° , then
∠ BAC = 180° - 135° = 45°
∠ BCA = 180° - 45° - 85° = 180° - 130° = 50° ( sum of angles in triangle )
x and ∠ BCA are alternate angles and are congruent , then
x = 50
Solve this system of equations by
using the elimination method.
3x + 3y = 18
2x+y = 4
([?], [ ])
Answers
Answer:
solution: (x,y)=(-2,8)
Step-by-step explanation:
1) 3x+3y=18
2x+y=4
2) -x-y=-6
2x+y=4
3) x=-2
4) 2x(-2)+y=4
5) y=8
6) (x,y)=(2,8)
and that is :D
The charge for electricity consumption E is partly constant and partly varies as the number N of units used. The charge for 82 units is N 3,655 while the charge for 42 units is N 2055:
a) calculate the charge per unit of electricity
b) obtain a formula for E in terms of N
Answers
The charge per unit of electricity is #415
The formula for E in terms of N is E = 375 + 40N
What is variation?Variation is a mathematical term that establishes the relationship between quantities and variables in an equation.
Analysis:
E = K + CN
where K and C are constants
When E = 3655, N = 82 and when E = 2055, N = 42
3655 = K + 82C ---------------1
2055 = K + 42C----------------2
subtract equation 2 from 1
40C = 1600
C = 40
substitute C in equation 1
3655 = K + 82(40)
3655 = K + 3280
K = 3655 - 3280 = 375
charge per unit is N = 1
E = 375 + 40(1) = #415
Formula for E in terms of N is E = 375 + 40N
In conclusion, the charge per unit of electricity is 415 and the equation connecting E and N is E = 375 + 40N
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We randomly select 100 Pell grant recipients from two states. State A is a relatively small state with approximately 4,000 Pell grant recipients. State B is a large state with approximately 200,000 Pell grant recipients. Suppose that the mean and standard deviation in individual Pell grants is approximately the same for both states: μ = $2, 600 and σ = $800. For which state is the sample mean for our 100 Pell grant recipients most likely to be within $80 of $2,600?a. State A because the sample represents a larger segment of this small population. b. State B because there is less variability in larger populations so estimates from samples are more accurate. c. Equally likely because σ = $800 for both states.
Answers
Using the Central Limit Theorem, the state that the sample mean would most likely be within $80 of $2,600 is given by:
c. Equally likely because σ = $800 for both states.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that for both states, [tex]\sigma = 800, n = 100[/tex], hence they have the same standard error, being equally as likely to be within $80 of $2,600, meaning that option C is correct.
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Four students, Adrian, Claire, Jackson, and Wyatt, line up one behind the other. How many different ways can they stand in line?
Hannah is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange, and flips a coin?
Answers
The bumper car ride at the state fair has 3 red cars, 4 green cars, and 5 blue cars. Michelle is first in line for the ride and is assigned a car at random. Garth is next in line and is randomly assigned a car. What is the probability that both Michelle and Garth will drive a red bumper car? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Answers
Answer:
4.5 %
Step-by-step explanation:
Answer:
4.5%
Explanation:
1) red = 3
2) green = 4
3) blue = 5
Total bumper cars: (3 + 4 + 5) = 12 cars
Michelle gets red car:
3/12 = 1/4Remaining red cars: 3 - 1 = 2
Remaining total cars: 12 - 1 = 11
Garth get red car:
2/11Probability they both get red cars:
1/4 × 2/11 = 1/22 ≈ 4.5%Find the output for the graph
y=-3x +11
when the input value is -4.
y = [?]
Answers
Answer:
Y = 23
Step-by-step explanation:
In the equation (y = -3x + 11) the X is the input value. When you replace this by -4 you will multiply -4*-3 which will give you 12 and then you will want to add 11 as that is your y intercept. Giving the value of your Y a 23, or the point would be (-4,23)
Please help me solve for X
Answers
Answer:
[tex]\boxed{\sf x = 8.67}[/tex]
Step-by-step explanation:
[tex]\sf 6(6 + x) = 4(4 + 18)[/tex]
Use the distributive property to multiply 6 by (6+x).
[tex]\sf 36+6x=4(4+18)[/tex]
Let's add 4 and 18 = 22.
[tex]\sf 36+6x=4 \times 22[/tex]
Multiply 4 and 22 = 88.
[tex]\sf 36+6x=88[/tex]
Subtract 36 from both sides.
[tex]\sf 6x=88 - 36[/tex]
[tex]\sf 6x=52[/tex]
Divide both sides by 6.
[tex]\sf x = 8.67[/tex]
How many ways can a president, vice president, and secretary be selected from a class of 30 students? a. 90 b. 2,068 c. 4,060 d. 24,360
Answers
Answer:
the answer to your question should be 2,068
Step-by-step explanation:
i hope i am right but i think so
If m(x) = x2 3 and n(x) = 5x 9, which expression is equivalent to (mn)(x)?
Answers
These are functions inside another function. The resulting composite function is given as (5x+9)^2 + 3
Composite functionsThese are functions inside another function. Given the following functions
m(x) = x^2 +3
n(x) = 5x +9
We are to solve for the function m(n(x))
m(n(x)) = m(5x+9)
Substitute 5x +9 into m(x) to have:
m(n(x)) = (5x+9)^2 + 3
Hence the resulting composite function is given as (5x+9)^2 + 3
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Timothy draws three isosceles triangles. In each figure, he measures a pair of angles.
What is a reasonable conjecture for Timothy to make by recognizing a pattern and using inductive reasoning?
In an isosceles triangle, two of the angles are congruent.
In an isosceles triangle, one angle is always obtuse.
In an isosceles triangle, all of the angles are congruent.
In an isosceles triangle, two of the angles are obtuse.
Answers
Answer: I believe that the answer would be "In an isosceles triangle, two of the angles are congruent."
Step-by-step explanation:
Answer:
In an isosceles triangle, two of the angles are congruent.
hope this helps :)
The map uses a scale 1 inch = 880 ft. On the map, How many inches represent 2 miles?
PLS HURRY
Answers
Answer:
[tex]12\ inches[/tex]
Step-by-step explanation:
Step 1: Determine how many ft are in 2 miles
[tex]1\ mile = 5280\ ft[/tex]
[tex]2\ miles = 5280\ ft * 2[/tex]
[tex]2\ miles = 10560\ ft[/tex]
Step 2: Determine how many 880 ft's are in 10560 ft
[tex]10560\ ft / 880\ ft[/tex]
[tex]12[/tex]
Answer: [tex]12\ inches[/tex]
what are the roots of x^2+7x+12
A:6&2
B:-6&-2
C:3&4
D:-3&-4
Answers
Answer:
D
Step-by-step explanation:
x² + 7x + 12
to find the roots equate the expression to zero
x² + 7x + 12 = 0
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)
the factors are + 3 and + 4 , since
3 × 4 = 12 and 3 + 4 = 7 , then
(x + 3)(x + 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 4 = 0 ⇒ x = - 4
Answer:
D -3, -4.
Step-by-step explanation:
x^2 + 7x +12 = 0
12 = 3*4 and 7 = 3 + 4 so we write:
(x + 3)(x + 4) = 0
x + 3 = 0 , x + 4 = 0
So x = -3, -4.
Billy has been on a diet for
22
weeks. He has averaged a loss of
0.73
pounds each week.
How many total pounds has Billy lost?
Answers
Answer:
16.06 lbs
Step-by-step explanation:
I believe, I did~ 0.73x22
Thank you for answer, if you do
Answers
The majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.
What is the meaning of dot plot?The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.
The data given in the table is-
3.01, 3.26, 3.26, 3.79, 4.26, 4.34, 5.17, 5.94, 5.94, 5.94, 5.94, 7.14, 7.54, 7.90, 8.03, 9.15, 10.25, 11.98, 12.84, 19.86
The majority of data is between 3.01 to 7.90. The percentage of these data values to total data is 70%.
When data is represented in dot plot, then the distribution is a normal distribution. The data set has the value of median and mode equal to 5.94.
Median=5.94
Mode=5.94
Thus, the majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.
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Which is Greater, negative 2 and 2 fifths or negative 2 and 1 forth?
Answers
Answer:
-2 and 1/4
Step-by-step explanation:
1/4 is equal to 0.25
2/5 is equal to 0.40
Because it is negative, 1/4 is considered greater.
For the following sequence.
1/2 2/3 3/4 4/5 5/6
Describe the term to term rule.
...............................................
Calculate the 10th term
.............................................
Answers
Answer:
Term-to-term rule: Adding one to the numerator and the denominator
10th term: 10/11
Step-by-step explanation:
the vertices of figure ABC are A(-4,1), B(5,3), and C(4,-2). If figure ABC is reflected over the line x=2, find the coordinates of vertex B'.
Answers
The coordinates of vertex B' are (-1,3)
What is reflection?Reflection is a mathematical transformation in which a image of an object is formed by flipping it over a reflection line a distance equal to the distance of the object from the reflection line.
Analysis:
When an object is reflected along the y-axis, only the the x-coordinate changes , if reflected along the x-axis, only the y-coordinate changes.
So vertex B' is a reflected vertex along the y- axis since it is at x=2
The distance of the x-coordinate of vertex B from the mirror line is 5-2 = 3
so the x-coordinate of vertex B' is going 3 units away from the mirror line which is at -1.
So the coordinates of vertex B' are (-1,3)
In conclusion, the coordinates of vertex B' reflected over the line X= 2 are (-1,3)
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Point b has coordinates (1,2). the x-coordinate of point a is negative −11. the distance between point a and point b is 15 units. what are the possible coordinates of point a?
Answers
can some please help me
Answers
Answer:
2.3 cm
Step-by-step explanation:
[tex]\textsf{Area of a trapezium}=\dfrac{1}{2}(a+b)h \quad \textsf{(where a and b are the bases and h is the height)}[/tex]
Given:
base a = 3.8 cmbase b = 6.1 cmh = x cmSubstituting the given values into the formula and solving for x:
[tex]\implies \dfrac{1}{2}(3.8 + 6.1)x=11.385[/tex]
[tex]\implies \dfrac{1}{2}(9.9)x=11.385[/tex]
[tex]\implies 9.9x=22.77[/tex]
[tex]\implies x=2.3[/tex]
Area of trapezoid 1/2(sum of parallel sides)(Height)
1/2(6.1+3.8)x=11.3851/2(9.9)x=11.3859.9x=22.77x=22.77/9.9x=2.3Write the number shown in standard notation. 1.02 x 10 A. 1,020,000 B. 102,000,000 C. 102,000 D. 10,200,000
Answers
i think its c
Step-by-step explanation:
don't count me on this
Your answer should be A please mark brainlest