A rhombus, which is a quadrilateral with 44 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are: (5,3)5,3, (2,-1)2,-1, (-3,-1)-3,-1, (0,3)0,3. How long is each side of the rhombus?
Answers
The length of one side of the rhombus is 5 units, hence all the other sides are also 5 units each.
Related Questions
The following two-way table shows the number of students of a school who have a video game and/or have a laptop:
Have Video Game Do Not Have Video Game Total
Have Laptop
15
50
65
Do Not Have Laptop
50
15
65
Total
65
65
130
Based on the table, how many students have both a laptop and a video game?
15
50
65
130
Answers
have laptop 15 50 65
dont have 50 15 65
total 65 65 130
have both a laptop and a game : 15
Based on the table given, the number of students who have both a laptop and a video game is 15 students.
Which students have both laptops and video games?In order to solve this question, look at the part of the table where the row on students who have laptops intersects with the column on those who have video games.
That part of the table has 15 in the cell. This means that 15 students have both video games and laptops.
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Find two positive numbers such that their product is 192 and their sum is a minimum pre-calc
Answers
xy = 192
Let's rearrange this to make the equation explicit: y = 192/x
Then, the other equation is for the sum. Let S be the sum of the two positive numbers.
S = x + y
Now, substitute the other equation into this one:
S = x + 192/x
Here's where we apply calculus. We can determine the minimum S by getting the first derivative of S with respect to y and equating to zero. Thus,
dS/dx = 1 - 192x⁻² = 0
1 = 192x⁻²
x² = 192
x = +/- √192
But since we are finding the positive number, x = + √192
Then, we use this to the first equation:
y = 192/√192 = √192
Therefore, the two positive numbers are equal which is √192 or 13.86.
The two numbers with a product equal to 192 such that their sum is minimized are:
A = √192 and B = √192
How to find the two numbers?
Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:
A*B = 192.
Now, the sum of these two numbers is:
A + B.
And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:
A = 192/B
Replacing this in the sum, we get:
192/B + B
To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.
The differentiation is:
-192/B^2 + 1
Then we need to solve:
-192/B^2 + 1 = 0
192/B^2 = 1
192 = B^2
√192 = B
To get the value of A, we use:
A = 192/B = 192/√192 = √192
Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:
A = √192 and B = √192.
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If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possible value of n
Answers
Since 990=2*3²*5*11 ==>n=11
How do I simplify this problem?
Answers
(15x^2h+15xh^2+5h^3)/h= 15x^2+15xh+h^2
juanita and lauren are painting a circular mural on one wall of the community center. the area of the mural is 66 square meters. what is the radius
Answers
Final answer:
The radius of Juanita and Lauren's circular mural with an area of 66 square meters is approximately 4.58 meters.
Explanation:
Juanita and Lauren's mural has an area of 66 square meters, and we need to find the radius of the circular mural. To find the radius, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Since the area of the mural is 66 square meters, we have:
66 = πr²
To solve for the radius (r), we divide both sides of the equation by π:
r² = 66 / π
Then, take the square root of both sides to get:
r = √(66 / π)
Using a calculator to compute this, we find:
r ≈ 4.58 meters (rounded to two decimal places)
Therefore, the radius of the circular mural is approximately 4.58 meters.
Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike?
Answers
80d≤320 divide both sides by 80
d≤4
So the maximum number of days it can take them to build the bicycle so that $480 will cover the cost.
Solve x3 = 64 over 27.
±8 over 3
8 over 3
±4 over 3
Answers
Cube root the answer
³√x³=³√64/27
x=4/3.
Check:
x=4/3
x³=(4/3)³
x³=64/27. As a result, the correct answer is 4/3 or 4 over 3. If you wonder why don't I choose the answer as ±4 over 3 because of this
±4/3
Choose positive first
(4/3)²=64/27 Correct. However, then choose negative signs
(-4/3)³=-64/27 Incorrect. Hope it help!
The solution of the given equation is ±8/3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is x³= 64/27
x=±∛(64/27)
x=±∛(8³/3³)
x=±8/3
Therefore, the solution of the given equation is ±8/3.
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What are the phase shift and period for the function y = 3cos[4(θ + 60°)] − 2?
Phase shift = right 60°, period = 90°
Phase shift = right 60°, period = −90°
Phase shift = left 60°, period = 90°
Phase shift = left 60°, period = −90°
Answers
The length of a rectangular lawn is measured to twice its width. the perimeter of the lawn is given as 30 m. find the length and width of the lawn.
Answers
Which sample fairly represents the population? CHECK ALL THAT APPLY.
--measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school
--calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment
--observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses
--sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town
--taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch
Answers
Answer:
The population is defined by: The set of all possible individuals who are likely to be selected for a study and who also share some observable characteristic. In this way, the correct answer is:
Taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch
Step-by-step explanation:
(30 Points) Paysly is studying a mosquito with a mass of 2.5×10^-6 kilograms and a housefly with a mass of 2×10^-5 kilograms. Which statement is true?
Answers
B.The housefly is 8 times the mass of the mosquito.
Triangle XYZ is a right triangle. Angle Z is a right angle and m∠X = 68°. What is m∠Y?
Answers
< X + < Y + < Z = 180
68 + Y + 90 = 180
158 + Y = 180
Y = 180 - 158
Y = 22 <==
m∠Y is 22°
What is right triangle?Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
Given,
ΔXYZ is a right triangle
m ∠Z = 90°
m∠X = 68°
Let m∠Y = x,
∵ Addition of interior angles of a triangle is 180°
So, m∠X + m∠Y +m ∠Z = 180°
Subsitute the values,
68° + x + 90° = 180°
x = 180 - 158
x = 22
Hence, m∠Y = 22°
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How many different selections of 4 books can be made from a bookcase displaying 12 books?
Answers
(12 x 11 x10 x9) / (4 x3 x 2 x 1) = 495
there are 495 different ways to select 4 books
Start with a square piece of cardboard to produce a box that is 8 cm deep and whose capacity is exactly 1 liter. how large must the original square be
Answers
The formula for the volume of a square prism or box is calculated using the formula:
V = s^2 * h
where,
s is the measure of the sides of a square
h is the height of the prism or box = 8 cm
We are given that the volume capacity of the box must be 1 Liter. We know that 1 Liter is equivalent to 1000 cm^3. Therefore calculating for s:
1000 cm^3 = s^2 * (8 cm)
s^2 = 125 cm^2
s = 11.18 cm
Therefore the measure of the sides of the square must be about 11.18 cm. If the problem ask for the area of the square, A = s^2 = 125 cm^2.
Planes Q and R are parallel. Explain how you know lines a and b are skew.
Sample Response: Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew
Answers
Sample Response:
Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.
The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7
Answers
P(t) = 5,000 (1-7%)t
P(t) = 5,000 (0.93)t
The annual depreciation rate is 7%
Answer:
Option 4 - 7%
Step-by-step explanation:
Given : The function [tex]P(t) = 5000 (0.93)^t[/tex] is the value of a motor scooter t years after it is purchased.
To find : Which of the following values show the annual depreciation of the value of the motor scooter?
Solution :
We are given a function p(t) which is represented as:
[tex]P(t) = 5000 (0.93)^t[/tex]
Where, p(t) is the value of a motor scooter t years after it is purchased.
Depreciation is the amount that has been deducted from the cost of an item.
The rate of change is 1-0.93=0.07 i.e. 7%.
So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.
Therefore, The annual rate of depreciation is 7%.
So, option 4 is correct.
cot^2x-csc^2x=-1 for all values of x true or falsse
Answers
sin²x + cos²x =1
1 + tan²x = sec² x
1 + cot² x = csc² x
These are all derived from circle geometry on the cartesian plane. Now, the useful trigonometric property to be used is the third one. Rearranging this, we come up with
cot²x - csc²x = -1
This coincided with the given equation. Therefore, this is true. This is because it is already established from the pythagorean theorems.
The original equation cot^2x - csc^2x = -1 is true for all values of x.
How to determine if cot^2x-csc^2x=-1 for all values of xThe equation cot^2x - csc^2x = -1 is true for certain values of x, but not for all values of x.
To see why, let's break down the equation using trigonometric identities:
cot^2x - csc^2x = -1
Using the reciprocal identities, we can rewrite cot^2x and csc^2x in terms of sine and cosine:
(cos^2x / sin^2x) - (1 / sin^2x) = -1
Now, let's simplify:
(cos^2x - 1) / sin^2x = -1
Using the Pythagorean identity cos^2x + sin^2x = 1, we can substitute cos^2x with (1 - sin^2x):
(1 - sin^2x - 1) / sin^2x = -1
-sin^2x / sin^2x = -1
Now, we can cancel out the sin^2x terms:
-1 = -1
This equation holds true for all values of x. Therefore, the original equation cot^2x - csc^2x = -1 is true for all values of x.
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What are the zeros of the polynomial function f(x) = x3 − x2 − 12x?
a. 0, −4, −3
b. 0, −4, 3
c. 0, 4, −3
d. 0, 4, 3
Legit answer plz
this is important
Answers
x(x^2-x-12)=0 factor parenthetical expression
x(x^2-4x+3x-12)=0
x(x(x-4)+3(x-4))=0
x(x+3)(x-4)=0
So x=-3, 0, 4
So c) 0, 4, -3
Answer:
The correct option is c.
Step-by-step explanation:
The given function is
[tex]f(x)=x^3-x^2-12x[/tex]
Taking out the common factors.
[tex]f(x)=x(x^2-x-12)[/tex]
Now, factorize the parenthesis.
[tex]f(x)=x(x^2-4x+3x-12)[/tex]
[tex]f(x)=x(x(x-4)+3(x-4))[/tex]
[tex]f(x)=x(x-4)(x+3)[/tex]
Equate the function equal to 0, to find the zeros of the polynomial function f(x).
[tex]f(x)=0[/tex]
[tex]x(x-4)(x+3)=0[/tex]
Using zero product property, we get
[tex]x=0[/tex]
[tex]x-4=0\Rightarrow x=4[/tex]
[tex]x+3=0\Rightarrow x=-3[/tex]
The zeros of the polynomial function f(x) are 0,4,-3. Therefore the correct option is c.
PLEASE HELP!!!!!!!
f(x)=x^2−3x+9
g(x)=3x^3+2x^2−4x−9
Find (f−g)(x)
Select one:
a. −3x^3−x^2+x+18
b. 3x^3+3x^2−7x
c. 3x^3+x^2−x−18
d. 3x^3−x^2−x
Answers
-----------------------------
Work Shown:
(f-g)(x) = f(x) - g(x)
(f-g)(x) = [ f(x) ] - [ g(x) ]
(f-g)(x) = [ x^2-3x+9 ] - [ 3x^3+2x^2-4x-9 ]
(f-g)(x) = x^2-3x+9 -3x^3-2x^2+4x+9
(f-g)(x) = -3x^3+(x^2-2x^2)+(-3x+4x)+(9+9)
(f-g)(x) = -3x^3-x^2+x+18
What is the approximate area of a circle whose radius is 7? steps?
Answers
So plug in your numbers to get
3.14 * 7^2 = 153.94^2
The coordinates of a point are (4, –1). which matrix expression represents translating the point 3 units to the left and 7 units up?
Answers
| 4 |
| |
|-1 |
Please, understand that the three vertical | represent a continuous line, which is the matrix representation.
The traslataion of 3 units to the left and 7 units up means that you have to add the matrix:
|- 3|
| |
|7 |
So the representation is:
|4 | |-3 | |1 |
| | + | | = | |
|-1 | |7 | |6 |
The line y = x − 6 y=x−6 has exactly one point in common with the circle x 2 + y 2 = r 2 x2+y2=r2. what is the value of r 2 r2?
Answers
y = x - 6 (1)
for the line
x² + y² = r² (2)
for the circle
When the line intercepts the circle, the x and y values will be equal.
Equate the values of y by substituting (1) into (2).
x² + (x - 6)² = r²
x² + x² - 12x + 36 = r²
2x² - 12x + 36 = r²
Answer: r² = 2x² - 12x + 36
The French club is sponsoring a bake sale. If their goal is to raise at least $135, how many pastries must they sell at $2.50 each in order to meet that goal? Write and solve an inequality.
Answers
X * 2.5 ≥ 135
X ≥ 54
So answer will be 54 pastries
The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
Answers
31 = C*11
C = 31/11 = 2.8 radians to nearest tenth
2.8 radians is the answer.
Please help with this question! thanks :)
Answers
the tallest line in the graph is 3
so 3 would be the answer
18 divided by 5593 equals 31-5400 = 193 what number should be placed in the box to help complete the division calculation?
Answers
The number that should be placed in the box to complete the division calculation is -7.
To find the number that should be placed in the box to complete the division calculation, let's analyze the given information:
- Dividend: 5593
- Divisor: 18
- Quotient: 31 (hundreds place is 3 and tens place is 1)
- When 5400 is subtracted from 5593, the result is 193.
- The box represents an unknown number in the ones place of the quotient.
To find the value in the box, we need to consider the units place. Since 5400 is subtracted from 5593 to give 193, the difference between the units places should be the value in the box.
193 - 5400 = -5207
So, the number that should be placed in the box to complete the division calculation is -7.
Correct question is:
What number should be placed in the box to help complete the division calculation?
Long division setup showing an incomplete calculation. 18 is in the divisor, 5593 is in the dividend, and 3 hundreds and 1 tens is written in the quotient.
5400 is subtracted from 5593 to give 193.
An unknown value represented by a box is being subtracted from 193.
Please show work on how you got the answer
Answers
[tex]x+2x=15[/tex]
[tex]3x=15 \newline x=5[/tex]
The lower segment is 10 feet long. The vaulter's right hand is 1.5 feet above her left, so it is 10 + 1.5 = 11.5 from the bottom of the pole.
The masses, in kg, of some bags on an airplane are shown below: 7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3 Jack made the following box plot to represent the masses: box plot shows minimum at 5.8, first quartile at 6.1, median at 6.3, third quartile at 6.8 and maximum at 7 Which of the following did Jack show incorrectly on his box plot?
Answers
Answer:
The value that Jack show incorrectly on his box plot is:
Median ( As he showed median is 6.3 but median is 6.2)
Step-by-step explanation:
We are given the mass of the bags as:
7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3
On arranging the data in the increasing order we have:
5.8 6.1 6.1 6.2 6.2 6.2 6.3 6.8 6.8 7
There are a total of 10 data points.
Also, the minimum value is: 5.8
Maximum value is: 7
The median is the central tendency of the data and lie in the middle of the data.
Hence, Median lie between 6.2 and 6.2
Hence, Median=6.2
Also, the lower set of data is: 5.8 6.1 6.1 6.2
The lower quartile or first quartile is the median of lower set of data is: 6.1
Also, the upper set of data is: 6.3 6.8 6.8 7
The upper quartile or Third quartile is the median of lower set of data is: 6.8
Hence, he showed median incorrectly in the box plot.
:)
Solve log2(6-2x)-log2x=3
Answers
Join logarithms (always):
log2(6-2x)-log2(x) = log2( (6-2x/x) )
Then get rid of it! :)
(6-2x)/x = 2^3=8,
Solve the equation:
6-2x=8x ---> 10x=6 ---> x = 3/5.
find the solution to the two equations shown below y=16x-9 y=-4x+21
Answers
Answer: (1.5, 15)
Step-by-step explanation:
The given system of equations :-
[tex]y=16x-9...................(1)\\\\y=-4x+21..................(2)[/tex]
Substituting the value of y from equation (1) in equation (2), we get
[tex]16x-9=-4x+21[/tex]
Now, Adding 4x and 9 on both the sides , we get
[tex]16x+4x=21+9\\\\\Rightarrow\ 20x=30\\\\\Rightarrow\ x=\dfrac{3}{2}=1.5[/tex]
Substitute the value of x in equation (1), we get
[tex]y=16(1.5)-9=15[/tex]
Hence, the solution to the given system of equations : (1.5, 15)
The solution to the given system of equation is (1.5, 15).
The given system of equations are
y=16x-9 ---------(i)
y=-4x+21 ---------(ii)
From equation (i) and (ii), we get
16x-9=-4x+21
16x+4x=21+9
20x=30
x=30/20
x=1.5
Substitute x=1.5 in equation (i), we get
y=16×1.5-9
y=24-9
y=15
Therefore, the solution to the given system of equation is (1.5, 15).
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