Solve the problems below. Please answer with completely simplified exact value(s) or expression(s). Given: ΔАВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 60°,BC = 6 cm Find CD, Area of ΔABC
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Answers
Answer:
[tex]CD=3\sqrt{3}\ cm,\\ \\A_{ABC}=18\sqrt{3}\ cm^2[/tex]
Step-by-step explanation:
Triangle ABC is right triangle. Since m∠ACB = 90° and m∠ACD = 60°, you get m∠BCD = 90°-60°=30°.
Triangle BCD is rigth triangle, then the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,
[tex]BD=\dfrac{1}{2}BC=\dfrac{1}{2}\cdot 6=6\ cm.[/tex]
By the Pythagorean theorem,
[tex]CD^2=BC^2-BD^2=6^2-3^2=36-9=27,\\ \\CD=3\sqrt{3}\ cm.[/tex]
Then
[tex]CD^2=AD\cdot BD,\\ \\27=3\cdot AD,\\ \\AD=9\cm.[/tex]
Hypotenuse AB of the triangle ABC is equal to
[tex]AB=AD+BD=9+3=12\ cm.[/tex]
The area of the triangle ABC is
[tex]A_{ABC}=\dfrac{1}{2}\cdot AB\cdot CD=\dfrac{1}{2}\cdot 12\cdot 3\sqrt{3}=18\sqrt{3}\ cm^2.[/tex]
CD is √3 cm, and the area of right-angled triangle ABC, with ∠ACB = 90° and ∠ACD = 60°, is 9 cm², obtained by applying the Pythagorean Theorem and area formula.
The given triangle is right-angled at C (as per the given condition m∠ACB = 90°), and ∠ACD is 60°.
Thus, we know that ΔACD is a 30-60-90 triangle because the remaining angle of the triangle (∠ADC) would have to be 30° (since all angles in any triangle sum up to 180°).
In a 30-60-90 triangle, the ratio of the sides opposite to these angles respectively is 1 : √3 : 2. This tells us AC is 2 times the length of CD and AC is √3 times the length of AD.
We don't have the lengths of AC, AD, or CD yet, but we can solve for CD using the Pythagorean Theorem in triangle ABC. Since it's a right triangle, the square of the hypotenuse (AC in our case) is equal to the sum of the squares of the other two sides. We can express this as:
AC² = BC² - CD²
Substituting AC = 2CD into this equation, we get:
(2CD)² = 6² - CD²
Solving this equation yields CD = BC / (2 √3) = 6 / (2 √3) = √3 cm
So the length of CD is √3 cm.
Now let's find the area of triangle ΔABC. The area is typically given by the formula 0.5 * base * height.
In this case, BC is the base of triangle ABC, and CD is the height due to its perpendicular nature to side AB by the given condition (CD ⊥ AB). So, the calculation would go as follows:
Area = 0.5 * BC * CD = 0.5 * 6 cm * √3 cm = 3 √3 cm².
But by rationalizing the denominator, which is a common practice especially when having square roots in the denominator, we get Area = 3√3 * √3 * √3 cm² = 3 * 3 cm² = 9 cm².
Therefore, CD = √3 cm and the area of ΔABC is 9 cm².
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Related Questions
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
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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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.
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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H= 62.4NS/33,000 solve for N
Answers
Answer:
N = 33,000H/(62.4S)
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of N.
... N = 33,000H/(62.4S)
Answer:
33,000
Step-by-step explanation:
Which chart shows that the price of a slice of sausage pizza is greater than the price of a slice of mushroom pizza?
Answers
Given the following figure, what is the value of x? PLZ HELP ASAP WILL MARK BRAINIEST
Answers
Answer:
The value of x = 11
Step-by-step explanation:
It is given that, the figure shows a pentagon.
The sum of angle of pentagon = 540
So we can equate these 5 angles to 540
To find the value of x
13x + 6 + 9x - 6 + 92 + 12x + 84 = 540
34x + 166 = 540
34x = 540 - 166
34x = 374
x = 374/34 = 11
Therefore the value of x = 11
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:
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
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
Devonte opens a savings account by making a deposit of $249.45. Every week, he deposits another $31.75 in the account. Which expression shows the amount of money that will be in the account 'w' weeks after the account is opened?
Answers
To find the total you would need to multiply the 31.75 by w to get the total amount of his weekly deposits, then that would get added to the initial amount of 249.45
The equation would be 249.45 + 31.75w
249.45 +31.75w
Step-by-step explanation:When w = 0, the amount is 249.45. This eliminates the first two choices.
When w = 1, the amount is 31.75 greater than 249.45. This eliminates the last choice.
The remaining choice is the correct one:
... 249.45 +31.75w
It shows the account balance is initially 249.45 and increases with increasing w at the rate of 31.75 per week.
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.
Problem 3 among the cast aluminum parts manufactured on a certain day, 80% were flawless, 15% had only minor flaws, and 5% had major flaws. find the probability that a randomly chosen part
a.has a flaw (major and minor).
b.has no major flaws.
Answers
Answer:
A) P(flaw) = 0.2
B) P(No major flaws) = 0.95
Step-by-step explanation:
A)To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:
P(no flaw) = [tex]\frac{80}{100}[/tex] = 0.8
So then:
P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2
P(flaw) = 0.2
B)First, we need to find the probability of major flaws:
P(major flaws) = [tex]\frac{5}{100} = 0.05[/tex]
P(Major flaws) = 0.05
So to find the probability of no major flaws:
P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95
P(No major flaws) = 0.95
Hope this helps!
According to known percentages, it can be concluded that the probability a part has a flaw is 20% (0.20), and the probability a part has no major flaws is 95% (0.95).
Explanation:This question is about probability in Mathematics. Specifically, it's based on the principles of probability distribution. Given that we know the percentages for flawless, minorly flawed, and majorly flawed parts, we can calculate the requested probabilities as follows:
The probability that a part has a flaw (major or minor) is the sum of the probabilities of a part having minor flaws and major flaws, so 15% + 5% = 20%, or 0.20 when expressed as a decimal.The probability of a part having no major flaws includes both flawless parts and parts with minor flaws. Therefore, its probability equals 80% + 15% = 95%, or 0.95 in decimal form.Learn more about Probability here:https://brainly.com/question/22962752
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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).
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%.
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!
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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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What is the best approximation of the length of segment QS? (Note: cos 80° = 0.17)
(Round your answer to the nearest tenth.)
Answers
Answer:
Length of the segment QS = 11.76 cm
Step-by-step explanation:
We are given with right angle triangle QRS
Angle S is 80 degree and RS = 2 cm
We need to find out QS
RS is adjacent to angle S, so we use cos formula
[tex]Cos (A) = \frac{adjacent}{hypotenuse}[/tex]
[tex]Cos (S) = \frac{RS}{QS}[/tex]
Plug in the angle and RS
[tex]Cos (80) = \frac{2}{QS}[/tex]
Given cos(80) = 0.17
[tex]0.17= \frac{2}{QS}[/tex]
Multiply by QS on both sides
0.17 * QS = 2
Divide by 0.17 on both sides
QS= 11.76470588
Length of the segment QS = 11.76 cm
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.
i will give the brainliest
Answers
Answer:
option 3
Step-by-step explanation:
sin45° = 11/BC
=>1/√2 = 11/BC
=>BC = 11√2
For this case we must find the hypotenuse (H) or the BC side of the rectangular triangle shown in the figure.
We have to:
[tex]Tangent (B) = \frac {Cathet \ opposite} {Cathet \ adjacent}\\Tangent (45) = \frac {11} {BA}[/tex]
By clearing BA we have:
[tex]BA = \frac {11} {Tangent (45)}\\BA = \frac {11} {1}\\BA = 11[/tex]
The Pythagorean theorem, which states:
[tex]BC = \sqrt {(CA) ^ 2 + (BA) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {2 * 11 ^ 2}\\BC = 11 \sqrt {2}[/tex]
Answer:
[tex]BC = 11 \sqrt {2}[/tex]
Option C
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
Please answer ASAP!! which of the following is closest to 0.25 and why?
A) 9/40 B)5/16 C) 9/32 D) 0.28 E) 15/64
Answers
Answer:
E) 15/64
Step-by-step explanation:
To compare the numbers, it works best to express them all using a common denominator. One possibility is 1600, another is 1,000,000.
9/40 = 360/1600
5/16 = 500/1600
9/32 = 450/1600
0.28 = 448/1600
15/64 = 375/1600
The number we're comparing to is 0.25 = 400/1600, so we want to find the closest number to 400 in the set ...
... {360, 500, 450, 448, 375}.
The magnitude of the differences of these numbers from 400 is ...
... {40, 100, 50, 48, 25}.
Clearly, the last number, 15/64 = 375/1600 has the smallest difference from 0.25.
Hey there!
“Which of the following is closest to[tex]0.25[/tex] and why?”
Options
A. [tex]\frac{9}{40}[/tex]
B. [tex]\frac{5}{16}[/tex]
C.[tex]\frac{9}{32}[/tex]
D. [tex]0.28[/tex]
E. [tex]\frac{15}{64}[/tex]
Process of elimination
Well,
Option A can’t be your answer because, [tex]\frac{9}{40}[/tex]equals [tex]0.225[/tex] in decimal form
Option B can’t be your answer because [tex]\frac{5}{16}[/tex] equals [tex]0.3125[/tex] in decimal form
Option C can’t be your answer because [tex]\frac{9}{32}[/tex] equals [tex]0.234375[/tex] in decimal form
Option D. Could be your answer because it’s a tad bit closer by a tad bit but let’s check for option E
Option E can but can’t be your because[tex]\frac{15}{64}[/tex] equals [tex]0.234375[/tex]
This leaves us with [tex]\boxed{OptionE. \frac{15}{64} }[/tex] as your result
Good luck on your assignment and enjoy your day
~LoveYourselfFirst:)
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.
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
What is the value of sin 0 given that (-3,7) is a point on the terminal side 0
Answers
Answer:
[tex]\frac{7\sqrt{58}}{58}[/tex]
Step-by-step explanation:
[tex]\\\text{Given that a point on the terminal side of }\theta \text{ is }(-3,7)\\\\\text{so the terminal side is in Quadrant II}\\\\\text{In the right triangle OMN, using Pythagorean theorem, we get}\\\\\text{ON}=\sqrt{(MN)^2+(OM)^2}\\\\\Rightarrow ON=\sqrt{(7)^2+(-3)^2}\\\\\Rightarrow ON=\sqrt{49+9}\\\\\Rightarrow ON=\sqrt{58}\\[/tex]
[tex]\\\text{we know that in Quadrant II, sine and cosecant are positive.}\\\text{so using the trigonometric ratios, we get}\\\\\sin \theta=\frac{\text{Opposite }}{\text{Hypotenus}}\\\\\Rightarrow \sin \theta=\frac{7}{\sqrt{58}}\\\\\Rightarrow \sin \theta=\frac{7\sqrt{58}}{58}\\[/tex]
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]
In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
Answers
Answer:
ADE = 34°
Step-by-step explanation:
To solve a question in which a shape is described, the first step must be to draw a diagram based on the information provided. Based on the information provided in a diagrammatic form, it can be seen clearly that lines DE and BA are parallel. Therefore, angle ADE and DAB are equal. It is also mentioned that line AD is the bisector of angle CAB. From the information provided, below correlations are determined.
CAB - 34 = ADE
ADE = DAB
DAB = DAC
CAB = DAB + DAC
This gives:
CAB = 2xDAB = 2xADE
When the above equations are reduced,
CAB - 34 = ADE
2xADE - 34 = ADE
ADE = 34°
n trapezoid STUV, SW is an altitude. Which is equivalent to the measure of angle m + n + p if m angle VSW = 65 degrees?
Answers
Answer:
The measure of angle m+n+p is equivalent to 205° (Fourth option)
Step-by-step explanation:
In a quadrilateral, the sum of the interior angles must be equal to 360°:
S=m+n+p+m<VSW+m<WST=360°
m<VSW=65°
Like SW is an altitude, m<WST=90°
Replacing the known values in the formula above:
m+n+p+65°+90°=360°
Adding like terms:
m+n+p+155°=360°
We want m+n+p, then subtracting 155° both sides of the equation:
m+n+p+155°-155°=360°-155°
m+n+p=205°
Answer:
4th Option is correct.
Step-by-step explanation:
Given: STUV ia a trapezoid that is ST is parallel to UV
SW is altitude that is m∠ SWV = 90°
m∠ VSW = 65°
To find: measure of m + n + p
Since, ST is parallel to UV.
⇒ n + p = 180° because Sum of Interior Angle on the same side of traversal is 180°
Now, In ΔSVW
∠SVW + ∠SWV + ∠WSV = 180° (Angle sum property of triangle)
m + 90° + 65° = 180°
m + 155 = 180
m = 180 - 155
m = 25°
Thus, m + n + p = 25 + 180 = 205°
Therefore, 4th Option is correct.
Round the numbers to the nearest cent and then to the nearest dollar. 23. $62.756 24. $38.415
Answers
Answer:
23. $ 62.76 to the nearest cent
$63.00 to the nearest dollar
24. $ 38.42 to the nearest cent
$38.00 to the nearest dollar
Step-by-step explanation:
When we round to the nearest cent we round the second number after the decimal. We look at the third number after the decimal. If it is 5 or above we round up.
When we round to the nearest dollar, we round the number befroe the decimal. We look at the number after the decimal. If it is 5 or above we round up.
23. $62.756 we round the 5 so we look at the 6 6>= 5 so we round up
$ 62.76 to the nearest cent
$62.756 we round the 2 so we look at the 7 7>= 5 so we round up
$63.00 to the nearest dollar
24. $38.415 we round the 1 so we look at the 5 5>= 5 so we round up
$ 38.42 to the nearest cent
$38.415 we round the 8 so we look at the 4 4< 5 so we leave alone
$38.00 to the nearest dollar