Given: ∆AFD, m ∠F = 90°
AD = 14, m ∠D = 30°
Find: Area of ∆AFD
I need an answer asap thanks
Answers
We have the triangle 30° - 60° - 90°.
The sides are in proportion: 2 : √3 : 1
(look at the picture).
[tex]2a=14[/tex] divide both sides by 2
[tex]a=7[/tex]
[tex]a\sqrt3=7\sqrt3[/tex]
The area of a trinagle AFD:
[tex]A_{\Delta}=\dfrac{1}{2}(7)(7\sqrt3)=\boxed{\dfrac{49\sqrt3}{2}}[/tex]
The area of a triangle ADF is 42.46 square units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, in ∆ADF, m∠F=90°, AD = 14 and m∠D=30°
We know that, sinθ= Perpendicular/Hypotenuse
Now, sin A=FD/AD
sin60°=FD/14
⇒ √3/2 = FD/14
⇒ FD=7√3
sin30°=FA/AD
⇒ 1/2 =FA/14
⇒ FA=7
We know that, area of a triangle is 1/2 ×Base×Height
Area of ∆ADF
= 1/2 ×FD×FA
= 1/2×7√3×7
= 42.46 square units
Therefore, the area of a triangle ADF is 42.46 square units.
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Related Questions
please help!!!
A,B,C and D are four towns.
B is 30km due East of A
C is 30km due North of A
D is 45km due South of A
calculate the bearing of D from B
Answers
Answer:
213.7°
Step-by-step explanation:
The bearing of B from D is angle ADB, which is ...
... ∠ADB = arctan(30/45) ≈ 33.7°
The bearing of D from B is that angle plus 180°, so is ...
... 180° +33.7° = 213.7°
_____
We use angle ADB because the reference direction for bearings is North.
The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).
After all of the start-up costs, a company starts with $100 and makes $0.75 on each unit sold. Write a linear equation in slope-intercept form that models this situation using p for profit and n for number of units sold.
Answers
Answer:
y=.75x+100
Step-by-step explanation:
y=mx+b
m=slope (rate)
b=y-intercept (starting point)
y=.75x+100
The linear equation that models this situation, using 'p' for profit and 'n' for number of units sold, is p = 0.75n + 100.
Explanation:The situation described is one of a linear relationship between the number of units sold (n) and the profit (p). In this case, we are given the initial profit (the y-intercept) of $100 (a = 100) and the profit per unit sold (the slope) of $0.75 (b = 0.75). Therefore, the linear equation modeling this situation in slope-intercept form would be p = 0.75n + 100.
In this equation, n represents the number of units sold and p represents the profit. For every unit sold (increase in n by 1), the profit (p) increases by $0.75. The $100 represents the initial profit, or the starting point of sales, which in this case is after covering the start-up costs.
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Write and solve a polynomial equation for the situation described.
A rectangular two-story horse barn is
being designed for a farm. The upper floor will be used
for storing hay, and the lower floor will have horse stalls
that extend 5 feet from both of the longer walls. The barn’s
length is twice the barn’s width, and the lower floor’s
ceiling height is 6 feet less than the barn’s width. What
should the dimensions of the lower floor be if the space
not used for stalls is to have a volume of 1920 cubic feet?
Answers
We can let x represent the width of the barn in feet. Then the length of the barn is 2x. The portion of width not used for stalls is (x-10). The height of that is (x-6).
So, the product of length, width not used for stalls, and height must be 1920 ft³. The equation for that is ...
... 2x(x -10)(x -6) = 1920 . . . . the equation
Solution
I generally find it convenient to use a graphing calculator to find the solutions to higher-order equations. Rearranging this so we're looking for a zero, it becomes ...
... 2x(x -10)(x -6) -1920 = 0
The graph shows one real root, at x = 16.
The dimensions of the lower floor should be 16 feet wide, 32 feet long, and a ceiling height of 10 feet.
_____
Alternate solution
Dividing by 2, we have
... x(x-6)(x-10) = 960
If we look at the factors of 960, we find that it is the product of 16, 10, and 6, which would let us assign x=16.
___
There are 28 divisors of 960. According to the Rational Root theorem, any of them might be a solution. There are arguments that can be made regarding reasonable dimensions that suggest x will be more than 12 (6 ft ceiling, 2 ft aisle). So, the number of trial-and-error possibilities is reduced somewhat.
The dimensions of the lower barn floor should be a width of 8 feet, a length of 16 feet, and a height of 2 feet, determined by setting up and solving a polynomial equation based on the given parameters.
Explanation:The problem can be solved using polynomial equations. First, let's denote the width of the lower barn floor as x. Given that the length of the barn is twice the width, the length is 2x. The height of the lower barn floor is 6 feet less than the width of the barn, so it's x - 6 feet.
The volume of a rectangular solid is given by length times width times height. So according to the information provided, we can set up the following polynomial equation: 2x * x * (x - 6) = 1920.
By simplifying the equation, we get 2x^3 - 12x^2 - 1920 = 0.
This equation can be solved using various methods such as the rational root theorem, synthetic division, or factoring. After solving, we find that the root x = 8 is the only physically meaningful solution (length width and height must be positive). Therefore, the width of the lower floor should be 8 feet, the length should be 2 * 8 = 16 feet, and the height should be 8 - 6 = 2 feet.
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Colin bought a Nissan Sentra that's 3¾ times as expensive as the car his parents bought. If his parents paid $8,000 for theirs, what's the cost of Colin's car?
A. $30,000
B. $28,000
C. $26,000
D. $29,000
Answers
A. $30,000
Step-by-step explanation:Let c represent the cost of Colin's car. Then ...
... c = (3 3/4) × $8000 = (3 × $8000) + ((3/4) × $8000)
... = $24000 + 6000
... c = $30,000
The cost of Colin's car is $30,000.
Answer:
A. $30,000
Step-by-step explanation:
To solve this you just have to do a simple rule of three, where in one side has the price of the car that his parents bought for 8,000 dollars and calculate the money that colin´s car costed in the other side:
[tex]\frac{8000}{1}= \frac{x}{3\frac{3}{4} } \\x=\frac{3,75*8000}{1}\\ x=30000[/tex]
So now we know that the car that Colin bought was 3.75 times as expensive as his parents 8,000 dollar car, that means it costed 30,000 dollars.
please help me asap!
Answers
7. Law of cosines
a² = b² + c² - 2bc cos A
where a is the side opposite to ∠A and b and c are adjacent sides to ∠A.
Here, a=BC= 3.8
b=CA =4.8
c = AB = 3.2
Substituting the values in the formula,
3.8² = 4.8² + 3.2² - 2(4.8)(3.2) cos A
30.72 cos A =23.04 + 10.24 -14.44=18.84
cos A = 18.84/30.72 = 0.6133
∴ cos A =0.6133
8. It is a right angled triangle.
Pythagoras theorem
hypotenuse² = Perpendicular² + base²
Here, hypotenuse = 6.7, base = 5.4
Perpendicular² = 6.7² -5.4²=44.89 - 29.16 =15.73
Perpendicular = √15.73 = 3.966 = 3.97
∴ The length of the missing side is 3.97.
9. Given: Side of new cube = 5 * Side of original cube
Let the side of the original cube measure 1 unit.
So, volume of original cube = side³ = 1
The side of new cube = 5 * 1 =5 units
So, volume of new cube = side³ = 5³ =125
The volume of the bigger cube is 125 times larger than the original cube.
10. Given : Height of the cone = 7 in
Radius of the base of the cone = 2 in
Volume of cone = (1/3) πr²h
=(1/3)π(2²)(7)
=29.32 cubic inches
∴ Volume of the cone is 29.32 cubic inches.
11. The given equation is:
x² -18x +10 =0
(x² -18x + 9²) +10 -9² =0
(x-9)²-71 =0
(x-9)² =71
x-9 =√71
x = 9 + √71
∴ x = 9+√71
Determine the range of the function: (0,2)(2,4)(4,6)(6,8)(8,10) Options: A) y<_10 B) {2,4,6,8,10} C) 2<_y<_10 D) {0,2,4,6,8,10#
Answers
(0, 2), (2, 4), (4, 6), (6, 8), (8, 10)
The domain is the set of the first coordinates of the points.
The range is the set of the second coordinates of the points.
The domain = {0, 2, 4, 6, 8}
The range = {2, 4, 6, 8, 10}
Answer: B) {2, 4, 6, 8, 10}.80 POINTS MATH
In the diagram at the right, in which position are the tips of the scissors farther apart? Explain your reasoning..
Answers
hey mate..
the position at which the tips of the scissors will be FARTHER APART is at position B.
as the angle made by the scissors at the centre is greater in position B.
The lunch platter at one restaurant cost $7. Write an equation that shows the total cost, c, of p people buying the lunch platter?
I’m am not sure how to factor the variables into the equation.
Answers
Answer:
c = 7p
Step-by-step explanation:
If 1 person buys the platter, the bill is c = 1 × $7.
If 2 people buy the platter, the bill is c = 2 × $7.
If 3 people buy the platter, the bill is c = 3 × $7.
(Do you see the pattern yet?)
If "p" people buy the platter, the bill is c = p × $7.
We ususally say "c is in dollars" and drop the "$" sign from the equation. When p is multiplied by 7, we conventionally write it as 7p.
... c = 7p
Given -3x + 2y = 1 and x = 5, solve for y.
a.-7
b.7
c.-8
d.8
Answers
Answer:
d. 8
Step-by-step explanation:
Given: -3x + 2y = 1 and x = 5
Now plug x =5 in the given equation and find the value of y.
-3(5) + 2y = 1
-15 + 2y = 1
2y = 1 + 15
2y = 16
Dividing both sides by 2, we get
y = 8
Thank you.
Answer: [tex]y=8[/tex]
Step-by-step explanation:
1. You already know the value of the variable [tex]x[/tex], which is:
[tex]x=5[/tex]
2. Therefore, you need to substiute the value [tex]x=5[/tex] into the equation [tex]-3x+2y=1[/tex] and then you must solve for [tex]y[/tex], as following:
[tex]-3x+2y=1\\-3(5)+2y=1\\-15+2y=1\\2y=1+15\\2y=16\\y=\frac{16}{2}\\y=8[/tex]
3. The result is: [tex]y=8[/tex]
(2.)are NOT opposite reciprocals
(1.)are NOT equal
(2.) are NOT opposite reciprocals
REALLY NEED HELP WITH BOTH PLEASE FOR GRADE‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️
Answers
The slope of AB is ...
... slope = (change in y)/(change in x) = (-6-(-3))/(8-2) = -3/6 = -1/2
The slope of AD is ...
... slope = (change in y)/(change in x) = (0 -(-3))/(8 -2) = 3/6 = 1/2
We note that the differences have the same magnitudes in both cases (y changes by 6; x changes by 3). This tells us the line segments are the same length. (Each side of the figure is equivalent to the hypotenuse of a right triangle with legs 3 and 6.)
The opposite reciprocal of a number is found by dividing -1 by that number. Thus the opposite reciprocal of the slope of AB is ...
... -1/(-1/2) = (-1/1)·(-2/1) = 2
This value is not the same as the slope of AD, so the slopes are NOT opposite reciprocals.
_____
Plotting the points, we see that we have a rhombus, not a rectangle (or square).
lauren decided to see how many jumping jakes she could do in 10 seconds. She told her mom that she could do 20. she was acually able to complete 15 jumping jacks when the timer went off. what was her percent error.
Answers
Answer:
Her error was overestimating by 33.3%
Step-by-step explanation:
To calculate a relative error (or percent error), we need to identify the absolute error first. In this case, the absolute error is the difference between Lauren's estimate and the actual outcome: 15 jacks - 20 estimated jacks = -5. The fact that this error is negative is only to indicate that Lauren overestimated (as opposed to underestimated). Usually, the absolute value is taken.
As next step, the absolute error is made to a relative one by dividing by the ground truth, which is the actual outcome of 15 jumping jacks. The relative error = |-5|/15 = 1/3. Expressed in percent: 33.3%. Lauren made an error of 33.3% (overestimate).
Which chart shows that the price of a slice of sausage pizza is greater than the price of a slice of mushroom pizza?
Answers
Suppose you have 15 muffins. How many muffins ate left after you give a friend 1/3 of them
Answers
Answer:
10 muffins
Step-by-step explanation:
If you give away 1/3 of your muffins
1/3 * 15 = 5
You will give away 5 muffins
15 -5 =10
You will have 10 muffins left
Christy and Seth are measuring water in a rectangular prism. They know the volume of the container. Christy suggests that they solve for the width of the prism. Transform the formula to find the volume of a rectangular prism to solve for width (w). Solve for w: V = lwh
Answers
Answer:
d) V/(lh) = w
Step-by-step explanation:
The appropriate solution divides the equation by the coefficient of w, which is lh. In answer selection (d), that is done by first dividing by l, then by h.
_____
Comment on the solution
One could just divide by l·h and be done with it.
Find the value of the polynomial:
4x^6y^3–3x^6y^3+2x^2y^2–x^6y^3–x^2y^2+y
x = −2, y = −1
Answers
Answer:
3
Step-by-step explanation:
Terms combine to simplify the expression somewhat.
... = x^6y^3·(4 -3 -1) +x^2y^2·(2 -1) +y
... = x^2y^2 +y
... = (xy)^2 +y
For your given values, this is ...
... ((-2)(-1))^2 +(-1)
... = 2^2 -1 = 3
6(t-2)-76=-142 solve for t
Answers
Answer:
t= -9
Step-by-step explanation:
Add 76 to both sides
6(t-2)= -142+76
Simplify -142+76 to -66
6(t-2)=-66
Divide both sides by 6
t-2= -66/6
Simplify 66/6 to 11
t-2= -11
Add 2 to both sides
t= -11+2
Simplify -11+2 to -9
t= -9
I hope this helps you
6t = 88 -142
6t = -54
t = -9
Hope it helps!
#MissionExam001
PLEASE HELP ASAP please solve for x
Answers
Answer:
x = -11
Step-by-step explanation:
Complimentary so you set them equal to each other.
6x + 185 = 8x + 207
-2x = 22
x = -11
What is the effect on the graph of the function f(x) = x when f(x) is replaced with -1/2 f(x)?
A) vertical reflection over x-axis and vertical stretch
B) vertical reflection over x-axis and vertical compression
C) horizontal reflection over y-axis and horizontal stretch
D) horizontal reflection over y-axis and horizontal compression
Answers
Answer:
The correct option is B.
Step-by-step explanation:
The given function is
[tex]f(x)=x[/tex]
The new function is
[tex]g(x)=-\frac{1}{2}f(x)[/tex]
[tex]g(x)=-\frac{1}{2}x[/tex] .... (1)
It is in the form of
[tex]g(x)=mx[/tex] .... (2)
Where, m is a constant.
If m is negative, then there is a vertical reflection over x-axis. If the constant is greater than 1, we get a vertical stretch and if the constant is between 0 and 1, we get a vertical compression.
From (1) and (2), we get
[tex]m=-\frac{1}{2}[/tex]
Since the value of m is negative and absolute value of m is between 0 and 1, therefore the graph g(x) shows the vertical reflection over x-axis and vertical compression.
Option B is correct.
Final answer:
The graph of f(x) = x, when modified to -1/2 f(x), undergoes a vertical reflection over the x-axis and a vertical compression by a factor of 1/2, resulting in answer B.
Explanation:
When the function f(x) = x is replaced with -1/2 f(x), the effect on the graph is two-fold. Firstly, there is a vertical reflection over the x-axis because of the negative sign.
This means that the graph is flipped over the x-axis, with points that were above the x-axis now being below it, and vice versa.
Secondly, there is a vertical compression by a factor of 1/2 due to the multiplier of -1/2. This compresses the graph towards the x-axis, making it 'flatter' than the original graph of f(x) = x.
Therefore, the correct answer to the question is B) vertical reflection over the x-axis and vertical compression.
Given the following figure, what is the measure of angle B?
Answers
Answer:
132°
Step-by-step explanation:
Sum of the interior angles of a polygon is given by the formula:
[tex](n-2)*180[/tex]
Where [tex]n[/tex] is the number of sides of the polygon.
The figure shows a 5 sided polygon (aka Pentagon). So the sum of all the angles is:
Sum = [tex](5-2)*180\\=3*180\\=540[/tex]
If we add up all the expressions/angles given and equate to 540, we can figure out [tex]x[/tex]. So:
[tex]84+13x+6+9x-16+92+12x=540\\34x+166=540\\34x=540-166\\34x=374\\x=\frac{374}{34}=11[/tex]
But angle B measures [tex]12x[/tex], so plugging in [tex]x=11[/tex], we have:
Angle B = [tex]12x=12(11)=132[/tex]°
Second answer is right.
GUYS HELP PLEASE!!!! I NEED THIS ASAP!!!!!!!
Answers
Answer:
slope = .4
She ran .4 laps per min.
She ran 12 laps in 30 minutes
Step-by-step explanation:
The slope is the rate of change. It can be found by using the formula
slope = (y2-y1)/(x2-x1)
The given points are (11, 4.4) (5.5 ,2.2)
slope = (2.2-4.4(/ (5.5-11)
= -2.2/-5.5
.4
The slope represents .4 laps per min since y is in laps and x is in minutes.
If she ran 30 minutes, we multiply the time by the slope to calculate the laps.
30 * .4 = 12
She ran 12 laps.
A) The slope is the change in Y over the change in X.
Using the 2 points given on the graph (11,4.4) and (5.5, 2.2)
The first number in the parenthesis are the X value and the 2nd numbers are the Y values.
Slope = (4.4 - 2.2) / (11-5.5)
= 2.2 / 5.5
= 0.4
B) From the slope, she ran 0.4 laps per minute.
C) To find the total laps, multiple laps per minute by total minutes:
30 minutes x 0.4 laps per minute = 12 laps.
An eccentric clockmaker built three different clocks. The first clock was a five-minute clock designed with an alarm set to sound each time the hand reached the number 2. The second clock was a six-minute clock designed to sound each time the hand reached the number 3. The third clock was a seven-minute clock designed to sound each time the hand reach the number 4. The clockmaker started the clocks simultaneously on day, and each clock began to sound at its appropriate time. Was there a time when all three clocks sounded their alarms together? If so, tell when it occurred and explain why. If not, explain why not.
Answers
Answer:
Yes, there was a time when the three alarms sounded together. It occurred 3 hours and 27 minutes after the clocks were started, and every 3 hours 30 minutes after that.
Step-by-step explanation:
We assume the clocks are numbered 1–5 on the 5-minute clock, 1–6 on the 6-minute clock, and 1–7 on the 7-minute clock. Then the alarm on each clock goes off 3 minutes before the clock repeats its timing action.
The least common multiple of the clock times is 5·6·7 = 210 minutes, or 3 1/2 hours. All clocks will simultaneously be 3 minutes before their repeat at 3 minutes before this 210-minute period is up.
That is, the clocks will simultaneously alarm 207 minutes after being started, and every 210 minutes after that.
_____
Comment on clock face numbering
If the clock faces are numbered 1–12, so the 5-minute clock alarms 5·(2/12) minutes = 50 seconds after being started, for example, then the alarms can never sound together. The clocks will come together at least once on any/every multilple of 1 minute, but not on any/every multiple of 10 seconds.
The percentage of people accessing the Internet increased from 61 % in 2000 to 87% in 2012. Describe the change as an absolute change in terms of percentage points.
Answers
Answer:
26%
Step-by-step explanation:
We are given that the percentage of people accessing the Internet increased from 61 % in 2000 to 87% in 2012.
So we can describe the change as an absolute change in terms of percentage points by calculating the difference in the two percentages:
Absolute change in terms of percentage = 87 - 61 = 26%
Therefore, there is a 26% absolute change in the percentage of people accessing the internet.
Answer: There is an absolute change of 2.16%.
Step-by-step explanation:
Since we have given that
Percentage of people accessing the internet in 2000 = 61%
Percentage of people accessing the internet in 2012 = 87%
So, there is an increment of some percentage, and we need to find that percent.
so, Absolute change in terms of percentage is given by
[tex]\dfrac{87-61}{2012-2000}\\\\=\dfrac{26}{12}\\\\=2.16\%\\[/tex]
Hence, there is an absolute change of 2.16%.
I need help fast if you can PLEASE HELP
Answers
Answer:
333°
Step-by-step explanation:
Minor arc ST is the difference between minor arc RT and minor arc RS:
... 153° -126° = 27°
Major arc SPT is the remainder of the circle:
... 360° -27° = 333°
On Sunday, a local hamburger shop sold a combined total of 405 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Sunday?
Answers
Answer:
135
Step-by-step explanation:
1 of every 1+2 = 3 items sold was a hamburger.
# of hamburgers = (1/3)·405 = 135
To solve the problem, we first create and solve an algebraic equation. The equation shows that the hamburger shop sold 135 hamburgers on Sunday.
Explanation:The given problem is a classic example of algebraic equations. We know that the total number of hamburgers and cheeseburgers sold was 405. And we know that the number of cheeseburgers sold was two times the number of hamburgers. Let's denote the number of hamburgers sold as H, and the number of cheeseburgers as C. From the information provided, we have two equations:
C = 2HH + C = 405Now, we can substitute the first equation into the second, replacing C with 2H:
H + 2H = 405This simplifies to:
3H = 405Finally, to find H, we divide both sides of this equation by 3:
H = 405 / 3Therefore, 135 hamburgers were sold on Sunday.
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How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?
Answers
Your selection is correct: 180 hours
Step-by-step explanation:The pool is apparently 18000 gallons (= 60 gal/h × 300 h). The combined flow from the two hoses is ...
... (40 gal/h) + (60 gal/h) = 100 gal/h
So, the time required with the two hoses is ...
... 18000 gal/(100 gal/h) = 180 h
Answer:
C) 180 hours
Step-by-step explanation:
Edge 2020
A number is doubled and then 1 is added to it. The answer is divided by 5 and then increased by 16. The final result is 18.
A)Develop an equation that shows the step above
Equation:___________________
B) Solve the equation to determine the value of the number.
Solve the equation. Show your work
Answer: The number is___________
Answers
So let's break down this sentence (Let n = unknown number):
"A number is doubled and then 1 is added to it"; Remember that double means multiplied by 2. With this sentence, we can determine that "2n + 1" is a part of the equation."The answer is divided by 5, and then increased by 16"; The "answer" they refer to is "2n + 1" from the prior sentence. Since this is divided by 5 and then added by 16, we can determine that [tex]\frac{2n+1}{5}+16[/tex] is a part of our equation."The final result is 18"; This means that the prior part of the equation is equal (=) to 18. With this info, our full equation is [tex]\frac{2n+1}{5}+16=18[/tex]B.Now, let's solve our prior equation found in A. To solve for the unknown number, n, we need to isolate the variable onto 1 side of the equation. Firstly subtract both sides by 16 to cancel out the + 16 on the left side:
[tex]\frac{2n+1}{5}=2[/tex]
Next, multiply both sides by 5 to cancel out the division on the left side:
[tex]2n+1=10[/tex]
Next, subtract both sides by 1 to cancel out the + 1:
[tex]2n=9[/tex]
Lastly, divide both sides by 2 to cancel out the multiplication:
[tex]n=\frac{9}{2}\ \textsf{OR}\ 4.5[/tex]
In short, the number is 9/2 or 4.5.
Can someone help me figure out the answer?
Answers
Answer:
f(t) = 5×0.87^t
Step-by-step explanation:
The general form for an exponential function described in this fashion is ...
... f(t) = (starting value) × (1 + (percent change))^t
Here, the "percent change" is -13%, or -0.13.
Then the value (1 + percent change) is (1 + (-0.13)) = 0.87. Putting this and the starting value into the form above, we have ...
... f(t) = 5 × 0.87^t
Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-column proof of the theorem is shown, but the proof is incomplete. A triangle with vertices A is at 6, 8. B is at 2, 2. C is at 8, 4. Segment DE with point D on side AB and point E is on side BC. Statement Reason The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5 By the distance formula Segment DE is half the length of segment AC By substitution Slope of segment DE is −2 and slope of segment AC is −2 Segment DE is parallel to segment AC Slopes of parallel lines are equal Which of the following completes the proof? By definition of congruence Addition property of equality By construction By the slope formula
Answers
The proof can be completed with the concept of the slope formula, which shows that two line segments with identical slopes equate to parallel lines. This fits perfectly in the context of the given two-column proof.
Explanation:In the provided incomplete two-column proof, the statement in question infers that the segment DE is parallel to segment AC because they have the same slope. The reason for this, which completes the proof, would be the slope formula. The slope formula allows us to calculate the steepness, incline, or gradient of a line segment defined by two points in a 2D space. When applied to segments DE and AC, it gives us identical values, indicating that the two line segments are parallel as per the theorem stating that parallel lines have equal slopes.
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To complete the proof, the correct answer is 'By the slope formula'
Explanation:To complete the proof, we need to show that the slopes of segment DE and segment AC are equal. By calculating the slopes using the slope formula, we can determine if they are indeed equal. Therefore, the correct answer is 'By the slope formula'.
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The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 2 multiplied by 1.5 to the power of x. The straight line f of x joins ordered pairs 3, 1 and 2, minus 1 and is extended on both sides. The straight line p of x joins the ordered pairs 1, 3 and 3, 1 and is extended on both sides. Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Answers
A) (3, 1)
B) (3, 1), (2, -1)
C) (1, 3)
Step-by-step explanation:A) The problem statement tells you the point (3, 1) is on both lines.
B) The problem statement tells you the line goes through points ...
... (3, 1) and (2, -1).
C) The problem statement tells you point (1, 3) is a solution to p(x). It also happens that g(1) = 2·1.5¹ = 3, so (1, 3) is also a solution to g(x).
(1, 3) is a solution to p(x) = g(x) because p(1) = 3 = g(1).
Your gross pay is 1,843.45 your involuntary deductions are fica 7.65% federal with holding 9% and state withholding 6.5% how much are you allowed for housing and fixed expenses
Answers
Answer:
1416.71
Step-by-step explanation:
Total Pay= 1843.45
Deductions
Fica = 7.65% of 1843.45 = 141.02
With holding = 9 % of 1843.45 = 165.9
state withholding =6.5 % of 1843.45 = 119.82
total deductions = 141.02 + 165.9 + 119.82
=426.74
Remaining money= 1843.45-426.74
= 1416.71
Answer:
510.01 is the right answer
Step-by-step explanation: