Apply the 30°-60°-90° Triangle Theorem to find the length of the longer leg of a triangle if the length of the shorter leg is 5√3 inches.
Answer:
15 inches
Step-by-step explanation:
The shortcut for finding the side lengths on a 30°-60°-90° triangle is that the long leg is
the short leg × √3.
So for your question:
5√3 × √3
= 5 × √3 × √3
= 5 × 3
= 15
Just in case it comes up next, the other shortcut is that the hypotenuse is double the short leg. Hypotenuse =
2 × 5√3 = 10√3
What is an equation of the line that passes through the point ( 2 , − 3 ) (2,−3) and is perpendicular to the line 2 x + 5 y = 10 2x+5y=10?
Answer: y=-[tex]\frac{5}{2}[/tex]x+2 or 5x+2y=4
Step-by-step explanation:
let’s make l1: 2x+5y=10,
then 5y=-2x+10
then y=-[tex]\frac{2}{5}[/tex]x+2
So k1=-[tex]\frac{2}{5}[/tex]let’s make the unknown line equals l2: y=k2*x + bBecause l2 is perpendicular to l1, so k2*k1=-1then who can calculate k2=-[tex]\frac{5}{2}[/tex]Because l2 passes the point (2,-3),so when x=2, we can know y=-3we can get an equation is -3=-[tex]\frac{5}{2}[/tex]*2 +bSo b=2l2: y=-[tex]\frac{5}{2}[/tex]x +2 or 5x+2y=4A suit is being sold for 194.49, discount is 73% from the original price.
What’s the original price?
The original price is $720.33 .
What is original price ?
Convert the percent discount to a decimal by dividing by 100% . Step 2: Set up the equation P=(1−d)x P = ( 1 − d ) x to find the original price of the item where P is the sale price, d is the discount as a decimal, and x is the original price of the item.You need to be aware of the selling price as well as the discount % in order to determine the item's original cost. The calculations contain a straightforward method that divides the sale price by the percentage-based result of 1 minus the discount. To determine an item's original or list price, use this formula.
SInce $194.49, is what is owed after the discount you will want to subtract 73 from 100 to get the percent of what is owed. Then you will set it up like a percent equation. 27/100 = 194.49/X where X = the original price. You will then multiply 194.49 by 100 and divide that answer by 1.9449. This equals $720.33 as the original price.
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Please help me I’m so sad
Answer:
Sym
Step-by-step explanation:
A school is arranging a field trip to the zoo. The school spends 746.34 dollars on passes for 40 students and 2 teachers. The school also spends 352.40 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Each pass costs $17.77 and each student's lunch costs $8.81
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The school spends 746.34 dollars on passes for 40 students and 2 teachers.
So, Each pass costs = 746. 34/ 42 = $17.77
Now, The school also spends 352.40 dollars on lunch for just the students.
= 352.40/ 40
= $8.81
Hence, Each pass costs $17.77 and each student's lunch costs $8.81
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The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
Answer: The value 550 represents the initial balance in the account, which means the account started with $550.
Step-by-step explanation:
The 550 represents the start balance that was put into the account. The (1+0.05t0 is the interest being added every t years/months.
in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time. group of answer choices true false
in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time is a True statement.
In a simple linear regression equation, the independent variable is the one that is used to predict the dependent variable. In this case, time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.A linear regression equation is used to describe the relationship between two variables, where one is the independent variable and the other is the dependent variable. The independent variable is the one that is used to predict the dependent variable. In this case, time series data is being used to forecast the trend in sales, so time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.
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Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?
Answer:
it may be not
take an example x=(1) y={123) and define a relation of R as the set of pairs (1,1) (1,2)(1,3) so this not a function
Graph y=2x-3-5. Algebra 2 connection unit 2 test
Answer: Slope: 2, y-intercept: (0,-8)
Step-by-step explanation:
x | y
0 -8
1 -6
Please answer quickly
1) The length of AC is 14.
2) The length of AB is 8.
3) The length of BC is 17.
4) The length of AB is 29.1.
5) The length of BC 53.
6) The measure m∠C is 53.8°
What is sine rule of a triangle?
AB/sin C = BC/ sin A = AC / sin B
1)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
22° + 118° + ∠C = 180°
∠C = 40°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 24, ∠C = 40°, and ∠B = 22°:
AB/sinC=AC/sin B
24/sin 40° = AC/ sin 22°
AC = 13.98
AC ≈ 14
2)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 7, ∠B = 44°, and ∠C = 53°:
AC/sin B=AB/sin C
7/sin 44° = AB/ sin 53°
AB = 8.047
AC ≈ 8
3)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
39° + ∠B + 51°= 180°
∠B = 90°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 27, ∠B = 90°, and ∠A = 39°:
BC/sinA=AC/sin B
BC/sin 39° = 27/ sin 90°
BC = 16.99
BC ≈ 17
4)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
∠A + 101° + 63°= 180°
∠A = 16°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting CB = 9, ∠A = 16°, and ∠C = 63°:
AB/sinC=BC/sinA
AB/sin 63° = 9/ sin 16°
AB = 29.09
AB ≈ 29.1
5)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
93° + ∠B + 58° = 180°
∠B = 29°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 16, ∠B = 29°, and ∠A = 93°:
AC/sinB=BC/sin A
16/sin 29° = BC/ sin 93°
BC = 32.95
BC ≈ 33
6)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 21, ∠A = 88°, and BC= 26:
AB/sinC=BC/sinA
21/sin C = 26/ sin 88°
sin C/21 = sin 88°/26
C = 53.82
C ≈ 53.8
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Which equation can be used to find d, the number of dollar coins Giuliana has?
The equation of the number of dollar cins giuliana has, is found to be
0.25(22 – d) + d = 10.75.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Giuliana has 22, quarters and dollar coins worth a total of $10.75.
Let the number of dollar coins be represented by d, while the number of quarter coins be represented by (22-d). Therefore, the sum of the total amount that is with Giuliana can be written as,
(1 x d) + (0.25 x (22-d)) = 10.75
d + 0.25(22-d) = 10.75
Hence, the equation can be used to find d, the number of dollar coins Giuliana has is 0.25d + 22 – d = 10.75.
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Identify a value of k that transforms finto g, where g(x) = f(x) + k.
7 is a value of k that transforms f into g, where g(x) = f(x) + k. Using the concept of x and y-axis:
What is x-axis and y-axis?A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.
The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.
From the graph it is observe that,
Graph of Function f(x) cut at y axis in the point 3
graph of function g(x) cut y axis in the point 4
So, the difference between the cut of y axis is k
Thus, {g(x)-f(x)=k}
Hence, k = [4 - (-3)] = 7
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Pls Help ASAP) Willing to give 25 points) Pls show your work) If you don't know pls don't answer.
From the given statements about the linear graph, the correct ones are statements 1, 2 and 3 while the incorrect one is statement 4
How to interpret Linear Graphs?The slope of a linear graph is simply the change in the y-values divided change in the corresponding x-values.
Now, from the graph, if we take two coordinates, we can easily say that;
Slope = (18 - 16)/(0 - 100)
Slope = -2/10 = -1/5
Statement 1; From the graph, the y-intercept is $18. This means that this is the cost of the book as that is where the cost starts decreasing for each weed she pulls. Thus, it is true.
Statement 2; The slope as we saw earlier was -1/5. Thus, it means that her grandma pays $1 for every 5 weed she pulls.
Statement 3; The x-intercept is 90 and it means after 90 weeds pulled, she no longer has to use her own money at all for the book. This is correct.
Statement 4; This is wrong because she needs to pull at least 90 weeds for her not to use her money.
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Under a translation 2 units to the right on the coordinate plane, point A maps to A’ and point B maps to B’
The correct statement as regards the transformation involving translation is
AB = A'B'What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation point A and point B made are all translation which is a type of rigid transformation, the dimension of the length will remain same
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what is the slope of a line that is perpendicular to y = 2x + 3
a. 2
b. -2
c. 1/2
d. -1/2
Answer: The answer is: a
Find the measure of angle A
Answer:
45°
Step-by-step explanation:
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for the length of the room are
(b) y²-5y=750 , (c) 750-y(y-5)=0 and (e) (y+25)(y-30)=0
Given that:
The area of rectangular room is 750 square feet.
Let the length of the rectangular room be y feet.
Since the width of the rectangular 5 less than the length of the room.
Then the width of the given rectangular room is (y-5) feet.
We know the area of a rectangular plot is = Length×width.
Thus , the area of the rectangular room is = y(y-5) square feet
According to problem,
area of the rectangular room = 750 square feet
⇒ y(y-5) =750.........(1)
⇒ y²-5y=750 .......(2)
⇒ y²-5y-750=0
⇒ y²-30y+25y-750=0
⇒ y(y-30)+25(y-30)=0
⇒ (y-30)(y+25)=0 ......(3)
⇒ y-30=0 or, y+25=0
⇒ y= 30, -25
∵ the length of a rectangle can't be negative.
So, y=30.
We can rewrite the equation (1) in form of
(i)
y(y-5) =750
⇒750= y(y-5)
⇒750-y(y-5)=0.......(4)
(ii)
y(y-5) =750
⇒y(y-5) -750=0.......(5)
Hence , the equations that can be used to solve for the length of the room are
(b) y²-5y=750 , (c) 750-y(y-5)=0 and (e) (y+25)(y-30)=0
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help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Step-by-step explanation:
part (a) - you plug 25 into the given function they give you and that'll be your answer
part (b) - 200 is your original amount given by the function so what is half of 200? 100. So set 100 on the right side of your function and solve for t to find the year
NEED HELP! 50 POINTS!
If you move the quadratic parent function, f(x) = x2, left 3 units, what is the equation of the new function?
g(x) = x2 - 3
g(x) = (x - 3)2
g(x) = (x + 3)2
g(x) = 3x2
Answer: [tex]g(x)=(x+3)^2[/tex]
Step-by-step explanation:
When shifting a function left [tex]3[/tex] units, [tex]f(x) \to f(x+3)[/tex].
Therefore, [tex]g(x)=(x+3)^2[/tex].
4.) Describe a series of transformations
(translate, rotate, reflect and dilate) that
takes triangle ABC to triangle CEF. Give all specific details.
The series of transformations of triangle ABC to triangle CEF is shown.
Explain the term transformation?A point, line, or geometry figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.For the given transformations from triangle ABC to triangle CEF are-
Translation:
1 unit to the right2 units upward.Rotation: There is no rotation taken place.
Reflection: There is no reflection of the given triangle ABC.
Dilation: The dilation of the 2 times the original coordinates is taken place.
Thus, the series of transformations of triangle ABC to triangle CEF is shown.
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Select ALL equations that have no solution.
A 6x – 2 – 3x = 3x – 2
B 6x – (3x + 8) = 16x
C 10 + 6x = 15 + 9x – 3x
D 11 + 3x – 7 = 6x + 5 – 3x
E 12x + 2 = 2 + 12x
The equations have no solution.
6x – 2 – 3x = 3x – 2
10 + 6x = 15 + 9x – 3x
11 + 3x – 7 = 6x + 5 – 3x.
We have determine from the given option which option has no solution.
When an equation has a solution?
An equation with no solution will be an equation when simplified, which will be a false statement.
The equation, 6x – 2 – 3x = 3x – 2
add like terms,
3x-2=3x-2
So we get,This equation has no solution
10 + 6x = 15 + 9x – 3x
10+6x=15+6x
add like terms we cannot find the value of x.
Therefore the given equation has no solution.
11 + 3x – 7 = 6x + 5 – 3x.
add like terms,
4+3x=3x-5
we cannot find the value of x.
So this equation has no solution.
Therefore, The equations 6x – 2 – 3x = 3x – 2,10 + 6x = 15 + 9x – 3x and 11 + 3x – 7 = 6x + 5 – 3x have no solution.
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Find f(1), f(2), f(3), f(4), and f(5) if fen) i defined recurively by f(O) = 3 and for n 0,1,2,. A) fen I) = -2f(n). B) fen I) = 3f(n) 7. C) fen I) = f(n)2 2f(n) 2. D) fen 1) = )f(n)/3
Given recursion function in options we have calculated values of f(1),f(2),f(3),f(4),f(5).
Find f(1), f(2), f(3), f(4), f(5) if f(0) = 3.
First recursive Function is given as
a) f(n+1) = -2*f(n)
f(1) = -2*f(0) = -2*3 = -6
f(2) = -2*f(1) = -2*(-6) = 12
f(3) = -2*f(2) = -2*12 = -24
f(4) = -2*f(1) = -2*(-24) = 48
f(5) = -2*f(4) = -2*(48) = -96
Second recursive Function is given as
b) f(n+1) = 3*f(n)+7
f(1) = 3*f(0)+7 = 3*3+7 = 16
f(2) = 3*f(1)+7 = 3*16+7= 55
f(3) = 3*f(2)+7 = 3*55+7 = 172
f(4) = 3*f(3)+7 = 3*172+7 = 523
f(5) = 3*f(4)+7 = 3*523+7 = 1576
Third recursive Function is given as
c) f(n+1) = [tex]f(n)^2-2*f(n)-2[/tex]
f(1) = f(0)*f(0)-2*f(0)-2 =3*3 - 2*3 - 2 = 1
f(2) = f(1)*f(1) - 2*f(1) - 2 = 1*1 - 2*1 - 2 = -3
f(3) = f(2)*f(2) -2*f(2)- 2 =-3*(-3) - 2*(-3) - 2 = 13
f(4) = f(3)*f(3) -2*f(3)- 2 = 13*13 - 2*13 - 2 = 141
f(5) = f(4)*f(4) -2*f(4)-2 = 141*141 - 2*141 - 2 = 19597
Fourth recursive Function is given as
d) f(n+1) = [tex]3^(f(n)/3)[/tex]
f(1) = 3^((f(0)/3) = 3^1 = 3
f(2) = 3^((f(1)/3) = 3^1 = 3
f(3) = 3^((f(2)/3) = 3^1 = 3
f(4) = 3^((f(3)/3) = 3^1 = 3
f(5) = 3^((f(4)/3) = 3^1 = 3
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Which expression is equivalent to (m^−2 n^−3)−3?
m6n9
m−6n−9
m−5n−6
1 over the quantity m raised to the fifth power times n raised to the sixth power end quantity
Answer:
(a) m^6·n^9
Step-by-step explanation:
You want to know an expression equivalent to (m^-2·n^-3)^-3.
Rules of exponents(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
Application[tex](m^{-2}n^{-3})^{-3}=m^{(-2)(-3)}n^{(-3)(-3)}=\boxed{m^6n^9}[/tex]
If it takes 5 hours to drive 62 miles how fast are you going
Answer:
12.40mph
Step-by-step explanation:
Is this a function? Explain, why or why not!
Answer:
No
Step-by-step explanation:
A function can have only output for each input. The input 3 has two outputs 3 and 5.
The input 4 has two outputs 4 and 6.
Simplify (28x102)-(69x10 Write the final answer in scientific notation
6.62x10-9
6.62x10-8
41x10
41x10
5. Two burgers and one hotdog cost $4.82. At the
same price, one
burger and two hotdogs cost $3.70.
How much does a hotdog cost?
Hello!
Let's use 'x' to represent the cost of the burger, and 'y' to represent the cost of the hotdog.
2x + y = 482
× + 2y = 370
2x + 47 = 740
-3y = -258
y = 86 cents
2x + 86 = 482
2x = 396
x = 198
A burger costs $1.98 and a hot dog costs $.86
I hope this didn't confuse you, I'm not very good at explaining!
Which relation is also a function?
Answer:
Step-by-step explanation:
I am not 100% positive but I am 75% positive it is B.
The last time Barry checked, his dog weighed 30 kilograms. Barry just measured his dog again and found out that it weighs 10% less now. How much does the dog weigh now?
27kg is the weight of Barrys dog now,
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The weight of dog last time when Barry checked is 30kilograms.
Barry just measured his dog again and found out that it weighs 10% less now.
We need to find the weight of Barrys dog.
Convert 10% to decimal value
10/100=0.1
0.1×30=3
Now subtract 3 from 30
30-3
27
Hence, currently Barrys dog weight is 27kg.
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Write at least four more addition or multiplication equations for 2 in which all
the fractions have a denominator of 8.
Answer:
Step-by-step explanation:
2 + 3/8 = 7/8
2 x 7/8 = 7/4
2 + 5/8 = 9/8
2 x 9/8 = 9/4
2 + 6/8 = 8/8
2 x 8/8 = 16/8
2 + 7/8 = 15/8
2 x 15/8 = 15/4