A triangle is a three-edged polygon with three vertices. The height of the triangle can be written as h = (2A)/b.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The complete question is:
Given the equation of the area of a triangle. how did you find the height of the triangle? A=(1/2)b x (h)
(Hint: Solve the equation for h)
Given the equation of the area of the triangle. Therefore, the height of the triangle can be written as,
A=(1/2)b x (h)
2A = b x h
h = (2A)/b
where h is the height of the triangle and b is the length of the base of the triangle.
Hence, the height of the triangle can be written as h = (2A)/b.
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Given: FB ║ CG ∠BFE and ∠C are supplementary. Prove CA ║ FE
Answer:
Step-by-step explanation:
1) [tex]FB \parallel CG[/tex], [tex]\angle BFE[/tex] and [tex]\angle C[/tex] are supplementary (given)
2) [tex]\angle ABF \cong \angle C[/tex] (corresponding angles theorem)
3) [tex]\angle BFE[/tex] and [tex]\angle ABF[/tex] are supplementary (supplements of congruent angles are congruent)
4) [tex]CA \parallel FE[/tex] (converse of the same-side interior angles theorem)
If cos a = 0.871 and cos ß= 0.338 with both angles' terminal rays in Quadrant-I, find the values of
tan(a + 3) =
Your answers should be accurate to 4 decimal places.
Answer:
tan(α+β) ≈ -5.8688
Step-by-step explanation:
You can use the formula for the tangent of the sum of angles, or you can use a calculator to find the angles. The latter is much simpler.
Calculator solutiontan(α+β) = tan(arccos(0.871) +arccos(0.338))
tan(α+β) ≈ -5.8688
Note that the two angles total slightly more than 90°, so the tangent of their sum is a large negative number.
Trig identity solutionThe use of trig identities also requires a calculator, and many more steps.
The tangent of the angle can be found from the cosine using ...
tan(x) = √((1/cos(x))² -1)
tan(α) = √((1/0.871)² -1) ≈ √(1.1481056² -1) ≈ 0.56404479
tan(β) = √((1/0.338)² -1) = √(2.9585799² -1) ≈ 2.7844559
And the tangent of the sum of angles is ...
tan(α +β) = (tan(α) +tan(β))/(1 -tan(α)tan(β))
tan(α+β) = ((0.56404479 +2.7844559)/(1 -(0.56404479)(2.7844559))
tan(α+β) = 3.3485007/(1 -1.5705579)
tan(α+β) ≈ -5.8688
__
Additional comment
The approximate angles are ...
α ≈ 29.4249°
β ≈ 70.2448°
Then α+β ≈ 99.6699°
Pls help! Geometry
Find the area
how many 4 digit numbers can I make only using the numbers 5533?
Is the relation depicted in the chart below a function?
The true statement is (a) it is a function
How to determine the relation?For a relation to be a function, the following must be true:
Each x value must be paired with exactly one y value
From the table of values, all x values have exactly one y value
This means that the relation is a function
Hence, the true statement is (a) it is a function
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The correct option regarding whether the relation is a function is:
It is a function.
When does a relation represents a function?A relation represents a function if each input X is mapped to only one output Y.
In this problem, this statement is true(input 3 is mapped to output 10 twice, same output so ok), hence it is a function.
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In a plane, line b is parallel to line f, line f is parallel to line g, and line h is perpendicular to line b.
The statement that cannot be true is that g cannot be parallel to h (g ║h)
How to know parallel lines in a plane?On the plane ,
line b is parallel to line f.
Therefore,
b ║ f
line f is parallel to line g,
Therefore,
f ║ g
line h is perpendicular to line b.
h ⊥ b
Therefore,
Since line h is perpendicular b, line b is perpendicular to h.
b can be parallel to g on the plane.
g cannot be parallel to h because h is perpendicular to b.
h can be perpendicular to f because b is parallel to f.
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Boating: A paddleboat moves at a rate of 12 mph in still water. If the rover’s current moves at a rate of 3 mph, how long will it take the boat to travel 36 miles downstream and 36 miles upsteam? (Two answers)
The time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
A paddleboat moves at a rate of 12 mph in still water. If the rover’s current moves at a rate of 3 mph.how long will it take the boat to travel 36 miles downstream and 36 miles upstream?The time taken by the boat upstream will be calculated as:-
( B + W ) Td = D
( 12 + 3 ) Td = 32
( 15 ) Td = 32
Td = 32 / 15 = 2.1 hours
The time taken by the boat downstream will be calculated as:-
( B - W ) Tu = D
( 12 - 3 ) Tu = 32
9 Tu = 32
Tu = 32 / 9 = 3.56 hours.
Therefore the time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.
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Jack pays 1.74$ for 6 packs of gum. How much does he pay for one
Answer:
$0.29 and if you want to round it up then it is going to be $0.30
Step-by-step explanation:
You are asking what 1 pack of gum costs. We already know that 6 packs of gum costs $1.74 and we need to find the unit rate which is basically what one pack of gum costs so in order to do that we need to [tex]\frac{1.74}{6}[/tex] which is 0.29 and that is the cost of 1 pack of gum. Hope that helps and also can you please mark me as brainlist. Thank you
A rectangular lot is 80 yards long and 50 yards wide.
Give the length and width of another rectangular lot that has the same perimeter but a larger area.
Answer:
55 Wide and 75 Long works.
Step-by-step explanation:
Since the Perimeter of the original is likely 80 + 80 +50 + 50 = 260 since it it a rectangular lot, 55 + 75 + 55 + 75 = 260 as well, meaning no change in perimeter. Now when we look at the area 80 x 50 = 4000, but
55 x 75 = 4125, leading to a larger plot
The total interest on a discounted loan is $80. If James received $880 into his bank account on drawdown, and the loan lasts for 6 months, what is the (simple) interest rate? Give your answer as a percentage to the nearest tenth of a percent.
With the use of formula, the interest rate is 18.2%
How can Simple Interest be Calculated ?The Interest is the product of the principal, time and the rate in percentage. That is, I = PTR / 100
Where
P is the Principal = $880T is the time = 6 months = 0.5 yearR is the rate = ?I is the interest = $80Substitute all the parameters into the formula
80 = (880 x 0.5R)/100
cross multiply
8000 = 440R
R = 8000/440
R = 18.2%
Therefore, the (simple) interest rate is 18.2%
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if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places. x2,3,4,5,6 y73,77,85,101,133
A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706
The regression equation is (d) log(y) = 0.064x + 1.706
How to determine the regression equation?The table of values is given as:
x 2 3 4 5 6
y 73 77 85 101 133
Calculate the logarithm of the y values.
So, we have:
x 2 3 4 5 6
log(y) 1.86 1.89 1.93 2 2.12
Next, we enter the above values in a regression calculator.
From the calculator, we have the following summary:
Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63The regression equation is then represented as:
log(y) = bx + a
Where:
b = SP/SSX = 0.64/10 = 0.064
a = MY - bMX = 1.96 - (0.064*4) = 1.706
So, we have:
log(y) = 0.064x + 1.706
Hence, the regression equation is (d) log(y) = 0.064x + 1.706
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The function g(x) is graphed on the coordinate grid. What is the domain of g(x)? x≥5 x>5 x≥0 x>0
The domain of the function g(x) is x >= 5
How to determine the domain?The complete question is added as an attachment
From the graph, we have the smallest value of x to be 5.
And the value of x increases to the right
This means that:
x >= 5
Hence, the domain of the function g(x) is x >= 5
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Select the properties of a square? please answer, I'm desperate
Answer:
all are the properties of square
Step-by-step explanation:
all are correct
City planners are planning to build a new community park. They agree that the park will be rectangular in shape, but the proposed
dimensions changed. At the most recent meeting, it was determined that the length would remain at 21.6 meters but that the width
would increase by 4.7 meters. So, the park would now cover an area of 714.96 square meters.
Which equation can be used to determine the original width of the park?
Answer:
(c) 714.96 = 21.6(w +4.7)
Step-by-step explanation:
The area of the rectangular park will be the product of its length and width. This relation is used to write an equation to find the original width of the park.
WidthLet w represent the original width of the park in meters. The new width is 4.7 meters more, so is represented by (w +4.7).
Other dimensionsThe length of the park is given as 21.6 meters. The area is given as 714.96 square meters.
Area formulaThe various dimensions of the park are related by the area formula:
A = LW
714.96 = 21.6(w +4.7)
Answer: The answer is C i took the k12 5.21 unit test
Step-by-step explanation:
Explain a detailed solution to the advanced function 4096^x = 8
The value of x in 4096^x = 8 is 0.25
How to solve the equation?The equation is given as:
4096^x = 8
Express 4096 as 8^4
8^(4x) = 8
Cancel the common base
4x = 1
Divide by 4
x = 0.25
Hence, the value of x in 4096^x = 8 is 0.25
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0
Fantastic Catering completed the following selected
transactions during May 2016:
• May 1: Prepaid rent.for three months, $2,700
• May 5: Received and paid electricity bill, $240
• May 9: Received cash for meals served to
customers, $2,700
•
May 14: Paid cash for kitchen equipment, $2,400
May 23: Served a banquet on account, $2,900
May 31: Made the adjusting entry for rent (from
May 1).
•
• May 31: Accrued salary expense, $1,800
• May 31: Recorded depreciation for May on
kitchen equipment, $730
To see what to study next, go to your Study Plan.
Based on the type of transaction that Fantastic Catering completed, the types of accounting basis they are in will be:
Cash Basis Accrual Basis
May 1 (2,700) 0
May 5 (240) (240)
May 9 2,700 2,700
May 14 (2,400) 0
May 23 0 2,900
May 31 0 (1,800)
May 31 0 ( 900 )
May 31 0 ( 730)
When are the cash and accrued basis used?The cash basis is used for when cash transactions have happened. There has to be cash changing hands for this to be recorded like the prepaid rent and the payment for kitchen equipment.
The accrual basis is used for all payments and revenue including both cash transactions and those that are recorded on account such as the banquet on May 23 and accrued salaries.
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What is the value of "y" that satisfies the expression below?
1 y + 12 = 6 ( 1 y + 1 )
Round your answer to 2 decimal points (i.e. #.##)
Answer:
1.20Step-by-step explanation:
1y + 12 = 6 (1y + 1)
1y + 12= 6y + 6
12 - 6 = 6y - 1y
6 = 5y
y = 6/5
y = 1.2
I don't what you meant by rounding to 2 decimal points so my answer is
1.20Giving brainliest to whoever can accurately solve these questions first.
Question 1. Suppose $30,000 is deposited into an account paying 3.5% interest, compounded annually.
How much money is in the account after ten years if no withdrawals or additional deposits are made?
A. 41,878.94
B. 42,317.96
C. 44,350.50
D. 40,500.00
Question 2.
To collect data on the signal strengths in a neighborhood, Pamela must drive from house to house and take readings. She has a graduate student, Kevin, to assist her. Pamela figures it would take her 12 hours to complete the task working alone, and that it would take Kevin 20 hours if he completed the task by himself.
How long will it take Pamela and Kevin to complete the task together?
A. 4.6 hours
B. 5.5 hours
C. 8.2 hours
D. 7.5 hours
1. The amount of money in the account after 10 years is 42,317.96 dollars.
2. it will take Pamela and Kevin 7.5 hours to complete the task together
How to find compound interest?Question(1)
Using compound interest formula,
[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where
p = principalr = raten = number of timest = timeTherefore,
p = 30,000
r = 3.5% = 0.035
t = 10
n = 1
Therefore,
[tex]A = 30000(1+\frac{0.035}{1} )^{1X10}[/tex]
A = $42,317.96
Question 2:
Pamela takes 12 hours to complete a task.
Kelvin takes 20 hours to complete same task.
The time it will take both of them can be computed as follows:
using rate principle,
let
x = time it will take both of them to do the work together.
[tex]\frac{1}{x}=\frac{1}{12} + \frac{1}{20}[/tex]
[tex]\frac{1}{x}=\frac{20+12}{240}[/tex]
[tex]\frac{1}{x}=\frac{32}{240}[/tex]
cross multiply
240 = 32x
x = 240 / 32
x = 7.5 hours
Therefore, it will take Pamela and Kevin 7.5 hours to complete the task together
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Pls Help (question is in pic)
1. If the function holds true, in what year would the cost of mailing a first class letter reach 60 cents.
2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since 1991?
Based on the function given, the year when the cost of mailing a first class letter would reach 60 cents is 2007.
If the cost of mailing a first-class letter is 41 cents, then the inflation rate has not stayed constant.
What year does the cost reach 60 cents?0.60 = 0.29 (1.046)^t
0.60 / 0.29 = (1.046)^t
log (2.07) = t x log (1.046)
t = 16 years
Added to 1991:
= 1991 + 16
= 2007
The cost of mailing a first-class ticket was 41 cents however which means that inflation was not constant.
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log2(1/128)=x, then x =
The value of x will be -7. The expression is solved using the identity.
What is the definition of a logarithm?Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
Given expression;
[tex]\rm log_2(\frac{1}{128}) = x[/tex]
The expression is solved using the identity as;
[tex]\rm log_e1 = x\\\ e^x=1[/tex]
Apply the identity;
[tex]\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7[/tex]
Hence the value of x will bed -7.
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please help! :(
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get?
a. 4^2 - 3^3
b. 3^3 + 4^2
c. 4 - 3^3
d. 3^3 - 4^2
e. 3^2 - 4^3
Answer:
d.
Step-by-step explanation:
k gets 3^3
a gets 4^2
subtract 3^3-4^2=d.
select the value of y in terms of x.
please help
Answer: A
Step-by-step explanation:
By the exterior angle theorem,
[tex]x+y=138\\\\\implies y=138-x[/tex]
The quotient of a number and 4, minus 2, equals 5/4.
Find the number.
Answer:
n=16
Step-by-step explanation:
If a bond is trading at a premium, what is the relationship between the bond's coupon rate, current yield and yield to maturity?
A bond purchased at a premium, it will have a yield to maturity and current yield that is lower than its coupon rate.
What is a Premium bond?This is usually above its face value which may be as a result of the interest rate being higher than the current market interest rates.
When a bond is traded at a premium, the yield to maturity and current yield will be lower than its coupon rate.
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QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:
1.
p=M/V. by rearranging this formula you get
V=M/p
V=560kg/7kg/m³
=80m³ b/c kg canceled kg
2.
p=M/V
=352kg/220m³
=1.6kg/m³
A cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-sixth its height, what portion of the volume of the cup is filled with water?
Answer:
1/216
Step-by-step explanation:
The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.
Linear scale factorIf the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.
Volume scale factorThe scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...
(1/6)³ = 1/216
The volume of the filled portion of the cup is 1/216 of the volume of the cup.
3 red balls, 4 white balls, and 1 green ball are in a bag. Balls are drawn without replacement. Find the probability that the red balls can be drawn before the green ball is drawn.
The probability that the red balls can be drawn before the green ball is drawn is 3/8.
What is Probability?The probability is the measure of the likelihood of an event to happen.
Given:
red balls= 3
white balls = 4
green balls = 1
So, Probability of red balls
=3/8
Probability of green balls
=1/7
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What is the range of function g?
Using it's concept, the range of function g is given by:
B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]
What is the range of a function?The range of a function is the set that contains all possible output values for the function. In a graph, it is the values of y.
In this graph, y assumes all values except y = -3 and y = -4, hence the range is given by:
B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 60 pounds each, and the small boxes weigh 25 pounds each. There are 105
boxes in all. If the truck is carrying a total of 4550 pounds in boxes, how many of each type of box is it carrying?
Answer: The truck is carrying 55 large boxes and 60 small boxes
Step-by-step explanation:
Let x represent the number of large boxes
Therefore,
The number of small boxes = 115 - x
[tex]\therefore[/tex] According to the question
60x + 25(105 -x) = 4550
60x + 2625 - 25x = 4550
35x = 4550 - 2625
35x = 1925
x = 55
Number of large boxes = x = 55
Number of small boxes = 115 - 55 = 60
Thomas traveled north 24 miles and then 15 miles west. Find the shortest distance between the start and end points. 15 miles O 24 miles 28.3 miles 32.8 miles Thomas traveled north 24 miles and then 15 miles west . Find the shortest distance between the start and end points . 15 miles O 24 miles 28.3 miles 32.8 miles
The distance between the start and end points is 28.3 miles.
How to find the distance?
Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_2 -y_1)^2}[/tex]
Here the initial point is (0mi, 0mi).
If we define the north as positive y-axis and east as the positive x-axis, after that Thomas travels 24 miles north and 15 miles west his new position is:
(-15mi, 24mi).
The distance is then:
[tex]d = \sqrt{(-15mi - 0mi)^2 + (24mi - 0mi)^2} = 28.3mi[/tex]
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