The length of the hypotenuse is: [tex]\[ c = \sqrt{61} \][/tex]
To find the length of the hypotenuse of a right triangle with legs measuring 6 and 5, we use the Pythagorean theorem, which states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Given:
a = 6
b = 5
We need to find c . Plugging the values into the Pythagorean theorem, we get:
[tex]\[ 6^2 + 5^2 = c^2 \][/tex]
Calculating the squares:
[tex]\[ 36 + 25 = c^2 \][/tex]
Adding the numbers:
[tex]\[ 61 = c^2 \][/tex]
To find c , we take the square root of both sides:
[tex]\[ c = \sqrt{61} \][/tex]
Therefore, the length of the hypotenuse is:
[tex]\[ c = \sqrt{61} \][/tex]
The rectangle below has an area of x^2-15x+56 x 2 −15x+56 x, start superscript, 2, end superscript, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters. what expression represents the width of the rectangle
The expression that represents the width of the rectangle is x - 8
Area of a rectangle:area = lwl = length
w = width
area = x² + 15x + 56
length = x - 7
Therefore,
x² - 15x + 56 = (x - 7) w
divide both sides by x - 7
w = x² - 15x + 56 / x - 7
w = (x - 7)(x - 8) / x - 7
w = x - 8
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Triangle XYZ is a right triangle. Angle Z is a right angle and m∠X = 68°. What is m∠Y?
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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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
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
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.
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
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.
For large parties, a restaurant adds a 15% service charge to the bill. how much would be added to a bill of $638.40?
Answer:
Service charge added to a bill of $638.40 is $95.76 .
Step-by-step explanation:
As given
For large parties, a restaurant adds a 15% service charge to the bill.
Bill of the parties is $638.40 .
15% is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Thus
Service charge = 0.15 × Bill of the parties .
= 0.15 × $638.40
= $ 95.76
Therefore service charge added to a bill of $638.40 is $95.76 .
How many different selections of 4 books can be made from a bookcase displaying 12 books?
(12 x 11 x10 x9) / (4 x3 x 2 x 1) = 495
there are 495 different ways to select 4 books
WILL GIVE A BRAINLIEST IF UR CORRECT PLEASE HELP!!
Find three solutions of the equation.
y = –3x
a.
(3, –9), (0, 0), (–1, 4)
c.
(–2, 6), (3, –9), (2, –7)
b.
(0, 0), (–3, 7), (–2, 6)
d.
(–2, 6), (3, –9), (–4, 12)
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.
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
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:
Please help with this question
(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?
triangle abc is a right triangle. If AC = 4 and BC = 10, find AB. Leave your answer in simplest radical form.
find the solution to the two equations shown below y=16x-9 y=-4x+21
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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The coordinates of a point are (4, –1). which matrix expression represents translating the point 3 units to the left and 7 units up?
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
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.
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?
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.
:)
cot^2x-csc^2x=-1 for all values of x true or falsse
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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18 divided by 5593 equals 31-5400 = 193 what number should be placed in the box to help complete the division calculation?
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.
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?
What is the approximate area of a circle whose radius is 7? steps?
The distance between points (3, 7) and (x1, y1) is the square root of (x1 - 3)2 + (y1 - 7)2. A. True B. False
Answer:
true
Step-by-step explanation:
took the test hope this helps
Solve x3 = 64 over 27.
±8 over 3
8 over 3
±4 over 3
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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Is the sqr root of 1.21 rational or irrational?
Solve log2(6-2x)-log2x=3
Please help with this question! thanks :)
the tallest line in the graph is 3
so 3 would be the answer
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
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.
What is the answer and steps if x=6
Please show work on how you got the answer
What is the image of point (0,3) for mapping (x,y) (x-2,y-3)