The Isosceles triangle length of a² will be equal to (32 - 16√2).
What is an isosceles triangle?
The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.
A triangle that has at least two sides of equal length is said to be isosceles. Sometimes it is stated to have exactly two sides that are the same length, while other times it is stated to have at least two sides that are the same length, with the latter version mentioning the equilateral triangle as an exception.
It is given that in an isosceles triangle abc has a=π/4 and b=c=4. Then the value of a² will be calculated as below:-
Using the cosine formula to calculate the value of a².
a² = b² + c² -2bc cosФ
a² = 16 + 16 - 2(4)(4)cos(π/4)
a² = 32 - ( 32 x {√2/2})
a² = 32 - 16√2
Therefore, the length of a² will be equal to (32 - 16√2).
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Answer:
4^2(2-root2)
Step-by-step explanation:
Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations. If required enter negative values as negative numbers (to 2 decimals).
Z-score of 10 is -1.25; Z-score of 20 is 1.25; Z-score of 12 is -0.75; Z-score of 17 is 0.50; and Z-score of 16 is 0.25.
How do we calculate the Z-scores of each observation?To calculate this, we use the following notations and formulas:
Mean = (sum of the values) / n
Variance = ((Σ(x - mean)^2) / (n - 1)
SD = Standard deviation = Variance^0.5
Z-score = (x - Mean) / SD
Where;
n = number of obsrvations = 5
x = each observation
We now proceed as follows:
Mean = (10 + 20 + 12 + 17 + 16) / 5 = 15
Variance = ((10-15)^2 + (20-15)^2 + (12-15)^2 + (17-15)^2 + (16-15)^2) / (5-1) = 64 / 4 = 16
SD = Variance^0.50 = 16^0.5 = 4
Z-score of 10 = (10 – 15) / 4 = –1.25
Z-score of 20 = (20 - 15) / 4 = 1.25
Z-score of 12 = (12 - 15) / 4 = –0.75
Z-score of 17 = (17 - 15) / 4 = 0.50
Z-score of 16 = (16 - 15) / 4 = 0.25
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The sets J and I are given below.
J=(-2, 3, 4, 5, 6, 8)
I=(-2, 0, 4, 8)
Find the union of J and I. Find the intersection of J and I. Write your answers using set notation (in roster form).
The intersection is the set of all elements in both sets, so the answer is {-2, 4, 8}.
The union is the set of all elements in at least one of the sets, so the answer is {-2, 0, 3, 4, 5, 6, 8}.
after raining for 3/4 of an hour a rain gauge is 2/5 filled. if it continues to rain at that rate for 15 more minutes, what fraction of the rain gauge will be filled?
Answer:8/15 part of rain gauge is filled after 1 hour.
Step-by-step explanation:
question 9: please help me asap !!!!
Answer:
8a-2ab
Step-by-step explanation:
5a-2b+2b+3a-2ab
Simplify 'a'
5a+3a=8a
Simplify 'b'
2b+2b=4b
8a-2ab
The average professional hockey player makes $2.78 million a year. They play an average of 82 games
much does the average hockey player make per game?
The harvest was cornucopian as it was 45 percent greater than last year. If the yield was 140795 bushels, how many bushels were harvested last year
After solving for x in the constructed equation, 97100 bushels were harvested last year.
What is an equation?
A mathematical statement known as an equation is consisting of two expressions joined together by an equal sign.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.The point-slope form, standard form, and slope-intercept type are the three main types of linear equations.Constructing equation to determine no. of bushels.
Bales from the previous year = x + 0.45 x
= 140795 1.45 x
= 140795 X
= 97100 bales
After solving for x in the constructed equation, 97100 bushels were harvested last year.
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Answer:97100
Step-by-step explanation:
The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For amonth in which the executive's cellular phone bill was $83.80, how many minutes did the executive use the phone?
Answer:
1022 minutes
Step-by-step explanation:
Let x be the number of minutes the executive used the phone
There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute
So total bill A = 35 + 0.4(x-900)
We know the bill was $83.80
So we can rewrite the equation as
35 + 0.4(x-900) = 83.30
and solve for x
To make it easier for computational purposes
1) Multiply both sides by 10
[tex]35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10[/tex]
2) Perform individual multiplication
[tex]350+4\left(x-900\right)=838[/tex]
3) Subtract 350 from both sides
[tex]350+4\left(x-900\right)-350=838-350[/tex]
4) Simplify
[tex]4\left(x-900\right)=488[/tex]
5) Divide both sides by 4
[tex]\frac{4\left(x-900\right)}{4}=\frac{488}{4}[/tex]
6) Simplify
[tex]x-900=122[/tex]
7) Add 900 to both sides to isolate x
[tex]x-900+900=122+900[/tex]
8) Simplify to obtain x
[tex]x=1022[/tex]
Answer: The executive used the phone for 1022 minutes that month
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
O all real numbers greater than or equal to -3
The domain of the function given on the graph is basically all numbers which are real and greater than or equal to -3.
Given a graph of a function.
We are required to choose the correct domain of the function from the options.
Function is basically a relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain of that function and the values that we get from the function are known as part of range of that function.
Because the lowest point on x axis on which the curve starts is -3 and it continuously increases, so the domain of the function given on the graph is basically all real numbers which are greater than or equal to -3.
Hence the domain of the function given on the graph is all real numbers which are greater than or equal to -3.
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Question is incomplete as it should include the attached figure.
Luis is helping to make tacos for a school fundraiser. He needs to buy tortillas. Happy Grocery sells small packs of 20 tortillas for $4.40 and large packs of 45 tortillas for $8.55. Luis has been given $48 to spend on tortillas. Fill in the blanks to complete the statements. Tortillas The unit price for the small pack is $ A per tortilla. The unit price for the large pack is $ B per tortilla.
Answer:
A. $0.22 per tortilla
B. $0.19 per tortilla
Step-by-step explanation:
A. All you gotta do is divide the money by the amount of product.
4.40 ÷ 20 = 0.22
B. All you gotta do is divide the money by the product.
8.55 ÷ 45 = 0.19
Therefore, the best pack to spend your money on would be the larger pack B.
HELPP
You want to enclose a rectangular region with an area of
1200 square feet and a length of 40 feet, 50 feet, or 60 feet.
Find the perimeter for each possible region. Explain why
you might rewrite the area formula to find the solutions.
The possible perimeters are 140 feet, 148 feet and 160 feet.
In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.
What are the possible perimeters?A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.
Area of a rectangle = length x width
Width = area / length
1200 / 40 = 30 feet
1200 / 50 = 24 feet
1200 / 60 = 20 feet
Perimeter of a rectangle = 2 x (length + width)
Perimeter when width is 30 feet : 2(40 + 30) = 140 feet
Perimeter when width is 24 feet : 2(24 + 50) = 148 feet
Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet
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Can someone pls help me with this i only have a little bit of time left pls hurry
A rectangular solar panel has a length that is 12 inches shorter than 3 times its width. If the perimeter of the panel is 132 inches what are the dimensions of the panel?
Answer: 46.5 by 19.5
Step-by-step explanation:
P=perimeter of panel. L=length. W=width
L=3W-12
P=2L+2W
132=2(3W-12)+2W
132=6W-24+2W
132=6W+2W-24
132=8W-24
156=8W
W=19.5
P=2L+2W
132=2L+2(19.5)
132=2L+39
2L=93
L=46.5
46.5 by 19.5
Give the equation of the resulting function.
The function f(x)= 3^x is reflected across the y-axis
The function which results from the reflection of the given function; f(x) = 3^x is; f(x) = 3^(-x).
What is the equation of the resulting function?It follows from the task content that the function given is; f(x) = 3^x.
The function in discuss is reflected across the y-axis, hence, it follows from transformation rules that the resulting function involves multiplying x by -1 as follows;
f(x) = 3^(-1×x)
f(x) = 3^(-x).
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28% of 80 is what number?
Answer:
22.4
Step-by-step explanation:
28% of 80 = [tex]\frac{28}{100}[/tex] of 80
=[tex]\frac{28}{100}[/tex] of 80 = [tex]\frac{28}{100}[/tex]*80
cut the zeros
=[tex]\frac{28}{10}[/tex]*8
=[tex]\frac{28}{5}[/tex]*4
=[tex]\frac{112}{5}[/tex]
=22.4
there is a stack of old algebra books in the library. Each book is 1 1/4 inches thick. let b represent the number of books in a stack and s(b) represent the total height of the stack in inches. what is the equation?
The equation which represents the height of the books is [tex]s(b)=\frac{5}{4} b[/tex]
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation between two sums of monomials of degree 0 or 1 is known as a linear equation.
The books are stacked one above the other and each book is [tex]1\frac{1}{4}[/tex] inches thick.
So to calculate the total height of the stack we have to multiply the number of books in the stack with the thickness of each book.
The total thickness is represented in the from of a function as
s(b) and the thickness of each book is [tex]1\frac{1}{4}=\frac{5}{4}[/tex] inches
total height=[tex]\frac{5}{4}\times b[/tex]
Therefore the required equation is [tex]s(b)=\frac{5}{4} b[/tex].
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A college football team will play 14 games next fall each game can result in 2 possible outcomes find the total possible number of outcomes for the season
There will be an outcome of 16380 times.
What is an outcome?
An outcome is a potential consequence of an event or trial in probability theory. A specific experiment can have any number of outcomes, and they are all distinct and unrelated to one another.The football team will play 14 games
and each game can result in one of 2
Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].
Now, let us explain
Let the result can be represented by an 'ordered set" i.e. 14- box.
|1|2|3|4|5|6|7|8|9|10|11|12|13|14|
Hence, the first box can be filled in 2 ways.
Similarly, all boxes.
Hence, the total number of cases will be,
2*2*2*2.... 14 times
= [tex]2^{14}\\[/tex]
=16380 times.
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√38 I’m not sure how to solve these kinds of equations
Answer:
√38
Step-by-step explanation:
√38
step 1: Check which squared numbers can be multiplied by another number to get 38.
Start with these numbers: 4, 9, 16, and 25
Step 2: Testing out the numbers
√25 × __ = 25 can't be divided by 38
√16 × ___ = 16 can't be divided by 38
√9 × ____ = 9 can't be divided by 38
√4 × ____= 4 can't be divided by 38
Step 3: Answer
After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38
I hope this helps!
What is the measure of Lx?
30°
45
x
Answer:
75 =x
Step-by-step explanation:
We can use angle addition to find the measure of angle x
30 + 45 = x
75 =x
Answer:
x = 75°
Step-by-step explanation:
x = 30° + 45°
x = 75°
Find the area of the figure. (Sides meet at right angles.)
Answer:
70in²Step-by-step explanation:
Find the area of the figure. (Sides meet at right angles.)
1 rettangle on a square
Area Rectangle
(2+2+5)*5=
9*5=
45in²
Area of the Square
5*5=
25in²
sum
45+25=
70in²
The winning times for the 200-meter dash can be approximated by f(x)=-0.05577x+146.2, where x is the year what is the slope of f
The slope of f is m= -0.05577.
Given : The winning times for the 200-meter dash can be approximated by f(x) = - 0.05577x+146.2 , where x is the year.
To find : The slope of f
Solution : Using slope intercept form a linear function is represented as
y = mx+b
where, m is the slope and b is the y-intercept.
We can write the function as f(x) = - 0.05577x+146.2
Comparing with slope intercept form,
m= -0.05577 and y-intercept = 146.2
Therefore, The slope of f is m= -0.05577
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Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression. Answer exactly.
(sin60∘+cos60∘)^2=
help please question is in picture
HELP ASAP!!!
Determine the direction in which the graph of the function f(x)=x^2+x-2 opens.
A.upward
B.downward
C.to the left
D.to the right
Answer:
A
Step-by-step explanation:
Since the leading coefficient of the function is greater than 0, then it opens upward.
|3k| >30 what is the compound inequality
Answer:
k < - 10 or k > 10
Step-by-step explanation:
inequalities of the type | x | > a have solutions of the form
x < - a or x > a , then
3k < - 30 or 3k > 30 ( divide each interval by 3 )
k < - 10 or k > 10
What is the unit rate?
For the given proportional relationship, it is found that the unit rate is of 1.5 inches per second, and the meaning of the points is given as follows:
(0,0): 0 inches in 0 seconds.(1, 1.5): 1.5 inches in 1 second.(3, 4.5): 4.5 inches in 3 seconds.What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality, also called the unit rate.
For this problem, the unit rate is given as follows:
k = 4.5/3 = 1.5/1 = 1.5 inch per second.
The meaning of the points are given by:
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Find the first five terms of the recursive sequence. Show all your work. an = 3a n-1 - 6 where a1 = 7
======================================================
Work Shown:
First replace every copy of n with 2
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_2 = 3*(a_{2-1}) - 6\\\\a_2 = 3*(a_{1}) - 6\\\\a_2 = 3*(7) - 6\\\\a_2 = 21 - 6\\\\a_2 = 15\\\\[/tex]
Notice how the second term [tex]a_2[/tex] relies on the first term [tex]a_1[/tex]
Then repeat for n = 3
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_3 = 3*(a_{3-1}) - 6\\\\a_3 = 3*(a_{2}) - 6\\\\a_3 = 3*(15) - 6\\\\a_3 = 45 - 6\\\\a_3 = 39\\\\[/tex]
Same goes with n = 4
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_4 = 3*(a_{4-1}) - 6\\\\a_4 = 3*(a_{3}) - 6\\\\a_4 = 3*(39) - 6\\\\a_4 = 117 - 6\\\\a_4 = 111\\\\[/tex]
Finally plug in n = 5
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_5 = 3*(a_{5-1}) - 6\\\\a_5 = 3*(a_{4}) - 6\\\\a_5 = 3*(111) - 6\\\\a_5 = 333 - 6\\\\a_5 = 327\\\\[/tex]
-----------------------------------
We have this summary:
[tex]a_1 = 7\\\\a_2 = 15\\\\a_3 = 39\\\\a_4 = 111\\\\a_5 = 327\\\\[/tex]
The first five terms are: 7, 15, 39, 111, 327
The cost of producing 390 calculators is $3100. Producing 490 calculators would cost $3700. Assuming the total cost is a linear function, write an equation for the cost of producing x calculators?
Answer:
y = 6x + 760
Step-by-step explanation:
In the problem you are given two pairs of numbers. These are both a pair of inputs and outputs, (x, y):
(390, 3100) also,
(490, 3700)
Write an equation by finding and filling in m and b in the following equation:
y = mx + b
To find m, which is the slope of the line, subtract y-y and put that on top. Then subtract x-x and put that on the bottom. See image.
Next, find b by use EITHER pair of numbers to find b.
I used (390, 3100).
see image.
m = 6 and b = 760
Fill these into
y= mx + b
y = 6x + 760
In case they ask, this means each calculator takes $6 to make and it costs $760 to set up your operation even before you have made any calculators.
A researcher who is interested in the behavior of chimps believes that temperature is related to aggression in this species of animal. She goes out to her local zoo during a particular weekend and adjusts the temperature of their climate-controlled habitat to 50-degrees, 70-degrees and 90-degrees Fahrenheit over the course of three days, noting the number of aggressive acts she observes at each temperature level.
A) What is the independent variable?
B) What is the dependent variable?
C) Is the dependent variable discrete or continuous?
D) What scale of measurement (nominal, ordinal, interval or ratio) is used to measure the dependent variable? What research method is being used (experimental or observational), and why?
The experimental research conducted by the scientist takes into account the following factors:
a)The change in temperature is the independent variable.
b) The effect of temperature on the chimp's act of aggression is the dependent variable.
c)The dependent variable is continuous.
d)The scale of measurement used to measure the dependent variable is interval.
e) The research method being used here is experimental.
In the above experiment the researcher wants to see the change in the aggression of the chimp when there is a change in temperature in the zoo.
In this experiment there are two variables that are being used, independent and dependent.The independent variable is the change in temperature as it is regulated by the researcher.The dependent variable is the change in the aggressive nature of the chimps, as the change in nature is directly affected by the change in temperature. The dependent variable(mood of the chimp) is continuous, as the value cannot be defined separately.Since the data is not discreet but continuous , the scale of measurement used is interval.The research method being used is experimental , because the researcher is controlling the variable temperature to see the effect of the temperature change on the chimps. So the researcher is directly experimenting on the chimps by changing an external factor. So the experiment is not observational.To learn more about research experiment and variables:
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(a)A tram moved downward 21meters in 7 seconds at a constant rate. What was the change in the tram's elevation each second?
(b)In a lab, a substance was heated by 4 Celisse each hour for 40hours. What was the total change in temperature?
(a) The change in the tram's elevation (speed) each second is 3 meters/Sec
(b) The total change in temperature of the substance was 160 Celsius.
(a) The tram moves downward 21 meters in 7 second. So, the speed of the tram is 21/7 = 3 meters/Sec, which is the tram’s elevation each second.
We know that, speed = (total distance travel)/(Total travelling time)
(b) The substance was heated by 4 Celsius each hour for 40hours.
Therefore, the total change in temperature is = (4x40) = 160 celcius.
The degree Celsius is the unit of temperature on the Celsius scale, originally known as centigrade scale
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Answer:
(a) The change in the tram's elevation (speed) each second is 3 meters/Sec
(b) The total change in temperature of the substance was 160 Celsius.
Step-by-step explanation:
If you only have a 1/3 measuring cup and a recipe calls for 12 2/3 cups of flour, how many 1/3 cups would you need to use? 1/3 * t th cups
If we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.
Given that we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour.
We are required to find the number of cups that are needed.
Fraction is the combination of two numbers,one above the division sign and other one below the division sign. The number which is above the division sign is known as numerator and the number which is below the division sign is known as denominator.
Measuring cup=1/3
Number of cups needed in recipe=12+2/3=38/3
Number of cups needed=38/3/1/3
=38 cups
Hence if we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.
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