Label XY with 3.
Label angle X with 53 degrees.
Label angle Y with 90 degrees.
Label angle C with 37 degrees.
Label angle A with 53 degrees.
Label BC with 4.
Label AC with 5.
Answer: i don't know if you want degrees or the lengths so i did both
∠ACB = 37°
∠BAC = 53°
∠ZXY = 53°
∠XYZ = 90°
∠XZY = 37°
∠ABC = 90°
BC = 4
AC = 5
AB = 3
YZ = 4
XY = 3
XZ = 5
Step-by-step explanation:
37 + 90 = 127
180 - 127 = 53
37 + 90 + 53 = 180
Which one of the following is not equivalent to the statement "There is a 40% chance of rain today"?
A) The odds against rain today are 4 to 10
B) The probability of rain today is 0.4
C) On a day like today, 4 out of 10 times it rained
D) The probability of rain today is 25
E) There is a 2 in 5 chance of rain today
The probability of indifferent forms will be 0.4, 4/10, or 2/5. Then the correct options are B, C, and E.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
There is a 40% opportunity of a downpour today. Then the probability is given as,
P = 40% / 100
P = 0.40
Convert it into a fraction, then we have
P = 4 / 10
P = 2 / 5
The probability of indifferent forms will be 0.4, 4/10, or 2/5. Then the correct options are B, C, and E.
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find the missing side. round to the nearest tenth
The required angle is 24.5°.
Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,
To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.
In this case, the perpendicular side is 16 and the base is 35.
Let's denote the acute angle as θ.
Using the tangent function, we can set up the equation:
tan(θ) = perpendicular side / base
tan(θ) = 16 / 35
To find the value of θ, we can take the inverse tangent of both sides:
θ = tan⁻¹(16 / 35)
θ = 24.5°
Hence the required angle is 24.5°.
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Consider the line y=-8x+6.
Find the equation of the line that is parallel to this line and passes through the point (7, 5).
Find the equation of the line that is perpendicular to this line and passes through the point (7, 5).
The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.
What is the equation of line parallel and perpendicular to the given line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line:
y = -8x + 6
Using the slope intercept:
Slope m = -8
Since the desired line is parallel, it will have the same slope.
Therefore, the slope of the parallel line is also -8.
Plug in the slope m = -8 and the poin (7,5) into the point-slope form:
( y - y₁ ) = m( x - x₁ )
( y - 5) = -8( x - 7 )
Simplify
y - 5 = -8x + 56
y = -8x + 56 + 5
y = -8x + 61
The equation of the parallel line is y = -8x + 61.
For the perpendicular line:
The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.
Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:
( y - y₁ ) = m( x - x₁ )
\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)
Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).
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A population of 130,000 grows 5% per year for 14 years. How much will the population be after 14 years?
There are 5 dogs playing at the dog park. Tyrone has 4 biscuits to share equally among the dogs. Tyrone wants to know how many dog biscuits each dog will get.
Find the slope of the line graphed below.
Answer:
Step-by-step explanation:
To find the slope you would get two points and then you'd use your slope formula. Which is y2-y1 over x2 - x1. The two points I got are (2, -2) and (-3,2), I got this points from the graph. I plugged them in for the x's and y's in the formula and had 2-(-2) on top and -3-2 at the bottom. When I solved the top one which is 2-(-2) I got positive 4. After I solved -3-2 which is in the denominator I got -5. So then I ended with 4/-5. I divided and got -0.8. meaning that 4/-5 or -0.8 is your slope.
(If wrong, I'm sorry might've gotten the points wrong/confused..)
Helppppppppppppppppppppppppppppppppppppppppp
Answer:
2
Step-by-step explanation:
( \(\frac{1}{2}\) × 4 ) × 5 - 2³ = 10 - 8 = 2
7/8 ^2
Choose the correct expanded form for the following expression .
Evaluate 7/8^2
The correct expanded form for the following expression is 7/8 × 7/8.
What is expanded form?The division of numbers into their component ones, tens, hundreds, thousands, ten thousand, and so forth creates the expanded form of the number. The expanded version of the number is the sum of each digit times its place value, which is used to represent the number. A number is broken down to show the value of each of its digits in order to be written in expanded form. 144 would then be converted to 100 + 40 + 4 = 144. It can be used to compute sums as well. When a number is expanded to show the value of each digit, it is written in expanded form. The numerical value of each digit in the number we are writing is represented using extended form.
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50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 which of the following histograms is the best representation of the data?
The best way to represent histograms is by decreasing to increasing order.
The mean is the arithmetic mean and is calculated by adding a group of numbers and dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
Given the values:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
We have that:
(22+24+28+28+30+31+31+32+32+35+36+37+38+41+42+42+44+44+45+46+46+47+47+49+50)/25=37.88.
The average age that a large construction company wants to know is 38.
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Find the open intervals on which the function f(x)= x+10sqrt(9-x) is increasing or decreasing.
The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).
To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.
Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.
f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)
= 1 - 5√(9 - x) / √(9 - x)
= 1 - 5 / √(9 - x).
To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.
Setting f'(x) = 0:
1 - 5 / √(9 - x) = 0
5 / √(9 - x) = 1
(√(9 - x))^2 = 5^2
9 - x = 25
x = 9 - 25
x = -16.
The critical point is x = -16.
We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.
Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).
For x < -16:
Plugging in a test value, let's say x = -17, into the derivative:
f'(-17) = 1 - 5 / √(9 - (-17))
= 1 - 5 / √(9 + 17)
= 1 - 5 / √26
≈ 1 - 0.97
≈ 0.03.
Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).
For -16 < x < 9:
Plugging in a test value, let's say x = 0, into the derivative:
f'(0) = 1 - 5 / √(9 - 0)
= 1 - 5 / √9
= 1 - 5 / 3
≈ 1 - 1.67
≈ -0.67.
Since f'(0) is negative, the function is decreasing in the interval (-16, 9).
For x > 9:
Plugging in a test value, let's say x = 10, into the derivative:
f'(10) = 1 - 5 / √(9 - 10)
= 1 - 5 / √(-1)
= 1 - 5i,
where i is the imaginary unit.
Since the derivative is not a real number for x > 9, we cannot determine the sign.
Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).
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Properties to Know and Identify Commutative, Associative, Distributive
Answer:
Commutative Laws: a + b = b + a a × b = b × a2. Associative Laws: (a + b) + c = a + (b + c) (a × b) × c = a × (b × c)
3. Distributive Law: a × (b + c) = a × b + a × c
Can someone help me with this problem please
Suppose M is a matrix of size 9x10, c is a scalar, and the matrix computation cM is defined. What is the size of matrix cM?
----------------
If the size of matrix "M" is 9×10, and a scalar "c" is multiplied by matrix, then the size of "cM" will be 9×10.
We know that when a scalar is multiplied to a matrix, each element of the matrix gets multiplied by that scalar.
In this case, the scalar "c" is multiplied with the Matrix "M";
So if a scalar "c" is multiplied by a matrix "M" of size 9×10, then the resulting matrix "cM" will also have the same number of rows and columns as the original matrix "M".
Therefore, the size of "cM" will also be 9×10.
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4. plot (2, 3) and (4, 5). Explain how the input-output values relate to the equation and the graph of the line.
Any point in the cartesian coordinate system has two components, one in the X-axis and one in the Y-axis, they are always symbolized:
P(XY)
I'll call the first point A with coordinates (2,3) and the second point B with coordinates (4,5). The coordinate sof both points are positive, this means that they'll be in the first quadrant of the system (upper right)
For point A, the X-coordinate is 2 and the Y-coordinate is 3, where these two values cros, you mark the point.
For B. the X-coordinate is 4 and the Y-coordinate is 5, where these two values cross paths you have to mark the point.
The question is in the picture.
Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16
How do you pronounce B"?
Answer:
bee
Step-by-step explanation:
Heather opened a lemonade stand on her street. It costs her $5.25 to buy the supplies each day, and she sells lemonade for $1.50 a cup. If she wants to make at least $100.00 in profits (sales - expenses) each day, what is the minimum number of cups of lemonade Heather needs to sell? Input your answer as a whole number.
Answer:
Answer: 71 cups
Step-by-step explanation:
71 x 1.5 = 106.5 - 5.25 = 101.25
Plz mark me brainliest
Answer:
100=1.50x-5.25
105.25=1.50x
x=70.167
so to get at least $100 a day she'd have to sell 71 cups
what is the value of 7x-3y-1 for x = -2 and y = 4?
\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)
what is the value of 7x-3y-1 for x = -2 and y = 4?
\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\)
Replace x with -2 and y with 4:-
\(\sf{7(-2)-3(4)-1}\)
On simplification,
\(\sf{-14-12-1}\)
On further simplification,
\(\sf{-27}\)
Good luck with your studies.\(\rule{300}{1}\)
dibuja una línea desde cada ecuación hasta la propiedad de igualdad que ilustra
By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.
What does Property of Equality means?The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.
As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.
Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"
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5 cm
6 cm
13 cm
Help me find the area of this please
The area should be 47.5 CM.
Answer:
Step-by-step explanation:
The figure you see here is a trapezoid.
Area = \(\frac{(a + b)h}{2}\) = \(\frac{(6 + 13)(5)}{2}\) = \(\frac{(19)(5)}{2}\) = \(\frac{95}{2}\) = 47.5 cm
please help ASAP !!!
Transform 2 exponential functions
f(x) = e^ (2x)
g(x) = e^(2(x - 6))
Apply exponents rule:
A^ (B-C) = A^B/A^C
Then
e^(2(x - 6)) = e^2x / e^12
Now transform x to (x-6)
Shift x 6 units to the left, because have minus sign
Therefore OPTION C is right answer
While rolling, a wheel with a diameter of 7/2 ft makes 112 revolutions. Find the distance that is traveled by the wheel. Use 22/7 for π.
Answer:
1232 is the answer
Step-by-step explanation:
distance= 22/7 ×7/2 ×112
=1232
Answer:
1232 ft.
Step-by-step explanation:
Distance travelled = circumference of the wheel * number of revolutions
= 7/2 * 22/7 * 112
= 22/2 + 112
= 11 * 112
= 1232 ft.
Write the equation of the line with slope 5/2 through the point (8, -2) in slope intercept
Answer:
Y = 5/2x - 22
Step-by-step explanation:
The equation of the line with slope 5/2 through the point (8, -2) in slope intercept will be y = (5/2)x – 22.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The slope is 5/2, then the equation will be
y = (5/2) x + c
The equation of line passing through (8, -2).
-2 = (5/2)(8) + c
-2 = 20 + c
c = -22
Then the equation will be
y = (5/2)x – 22
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If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
C) 3 years
D) 308 years
Answer:
approx 32years so pick answer A
Step-by-step explanation:
22000x4=88000
22000x1.045^t
22000x1.045^31=84,104
22000x1.045^32=89,979
B(n)=1 (-2)^n-1
What is the 4th term in the sequence
Answer:
The fourth term of the sequence B(4) =-8
The sequence is 1,-2,4,-8...
Step-by-step explanation:
Explanation:-
Given that the sequence
B(n) = 1(-2)ⁿ⁻¹
Put n=1
B(1) = 1(-2)¹⁻¹ = 2⁰ =1
Put n=2
B(2) = 1(-2)²⁻¹ = (-2)¹ =-2
Put n=3
B(3) =1(-2)³⁻¹ = (-2)² =4
Put n=4
B(4) = 1(-2)⁴⁻¹ =(-2)³ =-8
The sequence
1,-2,4,-8...
Each square below represents one whole.
What percent is represented by the shaded area?
Answer:
any picture?
Step-by-step explanation:
I can't see the shaded area
Find the sum of the first 36 terms of the following series, to the nearest integer.
2, 5,8,...
Answer:
Step-by-step explanation:
Comment.
You need to use the addition formula when the last term is not given. Mind you, you could find it, but it is just as easy to get the answer without it.
Givens
a1 = 2
d = 3
n = 36
Formula
Sum = n(a1 + (n - 1)* d)/2
Solution
Sum = 36(2 + (36 - 1)*3 )/2 Combine the brackets
Sum = 36 (2 + 35*3 )/2
Sum = 36(2 + 105) /2 Combine the brackets
Sum = 36 * 107/2
Sum = 3852 /2
Sum = 1926
Answer
1926
Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays the other. For example, if Deven owes Laura 189 dollars, he can give her 6 Harry Potter stickers ($6 \cdot 49 = 294$ dollars), and she can return 3 Twilight stickers ($3 \cdot 35 = 105$ dollars). This trade is like a transfer of $294-105=189$ dollars. What is the smallest positive debt, in dollars, that can be paid off using sticker trading?
The smallest positive debt that can be paid off using sticker trading is $7$ dollars.
To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.
Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.
The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.
In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.
Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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determine the amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST
The total amount of cash collected is $10,418.6.
What is a percentage?A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.
The amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST is,
Rate of interest on the sales amount is 13%
13% of 9220 = \(\frac{13}{100}*9220=1198.6\)
Here, sales price = $9,220
The total amount of cash collected = 1198.6+9220
= 10,418.6
Hence, the total amount of cash collected is $10,418.6.
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what's the answer for this? CLASS 6 MATHS I NEED HELP ASAP!!!
Answer:
20:
3 5/12 or 41/12
21:
-9 5/8 or -77/8