Find the value of x. The diagram is not to scale.
A. x=70
B. None of these
C. x=20
D. x=16
Answers
We then have two equal sides:
RS = ST
Thus,
Angle R = Angle T
Then, we have the following equation:
5x = 180- (5x-20)
From here, we clear the value of x:
5x = -5x + 180 + 20
10x = 200
x = 200/10
x = 20
Answer:
the value of x is:
C. x = 20
Related Questions
Two seventh grade math classes are competing in an academic challenge. Each class will randomly select one class member to compete each week. Each class has 26 students, and half of the students in each class are boys.
The classes want to design a simulation that will give the probability of both class members participating in the academic challenge being girls. Two possible simulations are given below.
Simulation 1: Flip a coin 26 times. If it lands on heads, count the flip as a girl. If it lands on tails, count the flip as a boy. Count how many times the coin lands on heads.
Simulation 2: Use two standard decks of cards. Randomly draw one card from each deck. Each diamond or heart drawn will represent a girl. Each spade or club drawn will represent a boy. After the two cards are drawn, they are replaced and the decks are shuffled. Count how many times a heart or diamond is drawn from both decks for 100 trials.
(Simuation 1 or Simulation 2) would be best to use to simulate a girl being randomly selected from each class to participate in the academic challenge. Based on this simulation, the probability that two girls will be selected is about (15%, 50%, 25%, or 75%).
Answers
The best simulation for the probability of selecting two girls is Simulation 2, which uses two standard decks of cards, with hearts and diamonds representing girls. The probability that both selected members are girls is 25%.
To simulate the probability that both class members participating in the academic challenge are girls, Simulation 2 would be more appropriate. Since each class has half boys and half girls, just like a standard deck of cards has half red suits (hearts and diamonds representing girls) and half black suits (spades and clubs representing boys), this simulation effectively mirrors the class demographics.
To calculate the probability of selecting a girl from both classes, consider the probability of drawing a heart or diamond from one deck, which is 1/2 or 0.5. Since the events are independent (what happens in one draw does not affect the other), we can multiply the probabilities for the two events: 0.5 (probability of a girl from Class A) * 0.5 (probability of a girl from Class B) = 0.25. Therefore, the probability of both selected members being girls is 25%.
What will it cost to carpet a rectangular floor measuring 21 feet by 24 feet if the carpet costs $ 31.96 per square yard?
Answers
21 becomes 7, and 24 becomes 8. 7/8 = 56 yards squared.
Multiplied by $31.96, the total comes out to $1789.76.
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. on a certain day, 308 people entered the park, and the admission fees collected totaled 812 dollars. how many children and how many adults were admitted?
Answers
Adult = $4
Total people = 308
Total collected = $812
Assumed all children:
308 x 1.5 = $462
Extra not accounted for:
812 - 462 = $350
Difference in the admin fee:
$4 - $1.50 = $2.50
Find number of adults:
350 ÷ 2.5 = 140 adults
Find number of children:
308 - 140 = 168 children
There were 140 adults and 168 children.
6 students share 4 bagels equally. How many pieces does each person get? (p.s thanks to everyone who answers)
Answers
You would get 1 and a half bagel for each person
6/4 = 1 1/2 or 1.5
Solution:
we are given that
6 students share 4 bagels equally.
we have been asked to find that
How many pieces does each person get?
Here we will have to use the concept of division. Because we are dividing bagels among the students.
So To get the number of pieces each will get divide 6 by 4.
Number of Pieces for each boys [tex] =\frac{6}{4}=\frac{3}{2}=1\frac{1}{2} \\ [/tex]
Consider the quadratic equation y^2-y=6. What is the error with the solution below?
Answers
y^2-y-6=0 => y^2-3y+2y-6=0 => y(y-3)+ 2(y-3)=0 => (y-3) (y+2)=0
y-3=0 or y+2=0 => y=3 or y= -2
Check 1: 3^2 - 3 = 6 => 9-3=6 => 6=6 Identity prove solution
Check 2: (-2)^2 - (-2) =6 => 4+2=6 => 6=6 Identity prove solution
Good luck!!!!
The error in the given solution to the quadratic equation y²-y=6 is identified and corrected step by step.
In the given quadratic equation y²-y=6, the mistake in the solution provided is the incorrect manipulation of the equation. To find the correct solution, follow these steps:
Re-write the equation as y² - y - 6 = 0.
Factor the quadratic equation as (y - 3)(y + 2) = 0.
Solve for y by setting each factor to zero: y = 3 or y = -2.
Convert the following decimal to a common fraction. Reduce to lowest terms 0.2 =
Answers
When finding the lowest terms of a fraction, you want to find the highest number that can go into both numbers, or greatest common factor (GCF), of both the numerator and the denominator. In this case, the greatest common factor would be 2, since it can go into both 2 and 10 without any remainders.
2 can go into 2 once, and into 10 five times, making the reduced term 1/5.
I hope I could help! Feel free to reach out if you need any more help with conversions and reductions.
A farmer has harvested 60% of his crops. If he has harvested 72 acres, how many acres does the farmer have in all?
Answers
Answer:
120 Acres
Step-by-step explanation:
We want to find the total amount of acres that a farmer has given that we know how many acres are in a percentage of his farm.
The farmer has 120 acres in total.
We know that the 60% of the farmer crops is equivalent to 72 acres.
Now we want to find the 100%.
Then we write two equations:
100% = X
60% = 72 acres
Now we want to solve this for X.
To do it, we first take the quotient between the two equations:
100%/60% = X/(72 acres)
Now we solve this for X:
(100%/60%)*(72 acres) = X = 120 acres.
The farmer has 120 acres in total.
If you want to learn more, you can read:
https://brainly.com/question/17409120
A rectangular kitchen floor measures 18 feet by 15 feet. A stove on the floor has a rectangular base measuring 3 feet by 4 feet, and a refrigerator covers a rectangular area of the floor measuring 4 feet by 5 feet. How many square feet of tile will be needed to cover the kitchen floor not counting the area used by the stove and the refrigerator?
Answers
Refrigerator area = 20 square feet
Entire kitchen floor = 270 square feet
12 + 20 = 32 square feet
270 square feet - 32 square feet = 238 square feet
238 square feet will be needed
Number of square feet of tile will be needed to cover the kitchen floor is 238 square feet.
Given that, a rectangular kitchen floor measures 18 feet by 15 feet.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Area of a rectangular kitchen floor
= 18×15
= 270 square feet
Area covered by a stove
= 3×4
= 12 square feet
Area covered by a refrigerator
= 4×5
= 20 square feet
Area covered by tiles
= 270-(12+20)
= 270-32
= 238 square feet
Therefore, number of square feet of tile will be needed to cover the kitchen floor is 238 square feet.
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
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PLEASE HELP WILL GIVE BRAINLIEST!!!******** William invested $7000 in an account that earns 4.5% interest, compounded annually.
Answers
P = 7000 (starting value)
l = 0.045 (rate)
t = 3 (number of years)
A(t) = 7000(1 + 0.045)^3
A(t) = 7000(1.045)^3
After three years, William will have 7988.16
Marco drew 24 pictures he drew 1/6 of them in art class how many pictures did marco draw in art class
Answers
If he drew 1/6 of them ⇒ he drew 1/6 of the 24
1/6 of 24 =1/6 x 24 = 4
So he drew 4 of them.
24 × 1/6 = 24/6 = 4
Marco drew 4 pictures in art class.
Hope this helps!
The annual interest rate on a loan is 10% which can be represented using the expression 1.10t. Write an expression that represents the quarterly interest rate.
Answers
annual rate=10%
quarterly rate=10/4=2.5%=0.025
given time t, this will be represented as :
(1+0.025)t
=1.025t
The rectangular poster shown measures 2w-30 by w. The poster has an area of 5400 cm2. What is the value of w?
Answers
A=lxw
"A" is the area of the rectangle (A=5400 cm²).
"l" is the lenght of the rectangle (l=2w-30).
"w" is the width of the rectangle.
2. When you substitute l=2w-30 into the formula A=lxw, you have:
A=lxw
5400=(2w-30)(w)
5400=2w²-30w
2w²-30w-5400=0
3. Now you have a quadratic equation. When you solve it, you obtain the value of "w". Then:
w=60 cm
A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground. Draw a diagram and find the length of the guy wire. 4.2 yd. 11.0 yd. 23.7 yd.
Answers
The length of the wire will be given by:
cos θ = (adjacent)/(hypotenuse)
thus
cos 65=10/h
h=10/cos 65
h=23.66 yds~23.7 yds
the answer is 23.7 yd
Answer:
23.7 yards
Step-by-step explanation:
Given :A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground
To Find: Draw a diagram and find the length of the guy wire
Solution :
Refer the attached figure
We are given that A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower i.e. AC = 10 yards
We are also given that wire makes an angle of 65° with the ground i.e. ∠BAC = 65°
Now to find the length of the guy wire i.e. AB
We will use trigonometric ratio.
[tex]cos\theta = \frac{Base}{Hypotenuse}[/tex]
[tex]cos 65 ^{\circ} = \frac{AC}{AB}[/tex]
[tex]0.4226= \frac{10}{AB}[/tex]
[tex]AB= \frac{10}{0.4226}[/tex]
[tex]AB= 23.66[/tex]
Thus AB = 23.66 yards ≈ 23.7 yards
Hence the length of the guy wire is 23.7 yards
Two jets leave an airport at the same time, flying in opposite directions. The first jet is traveling at three hundred seventy-seven mph and the other at two hundred seventy-five mph. How long will it take for the jets to be 9128 miles apart?
Answers
For our first jet:
[tex]d_{1}=377t[/tex]
For our second jet:
[tex]d_{2}=275t[/tex]
We know for our problem that after [tex]t[/tex] the jets will be 9128 miles apart, so the total distance will be 9128: [tex]d_{t}=9128[/tex]. Since our jets are traveling in opposite directions, the distance between them will increase over time, so we are going to add [tex]d_{1}[/tex] and [tex]d_{2}[/tex], and set them equal to [tex]d_{t}[/tex] to find our time:
[tex]d_{t}=d_{1}+d_{2}[/tex]
[tex]9128=377t+275t[/tex]
[tex]9128=652t[/tex]
[tex]t= \frac{9128}{652} [/tex]
[tex]t=14[/tex]
We can conclude that our jets will be 9128 miles apart after 14 hours.
Final answer:
To find the time it takes for two jets to be 9128 miles apart, calculate their combined speed and divide the total distance by this speed, resulting in approximately 14 hours.
Explanation:
To find the time taken for the jets to be 9128 miles apart:
Calculate the combined speed of the two jets by adding their speeds together: 377 mph + 275 mph = 652 mph.
Divide the total distance of 9128 miles by the combined speed of the jets to get the time taken: 9128 miles ÷ 652 mph ≈ 14 hours.
At noon, ship a is 30 nautical miles due west of ship
b. ship a is sailing west at 23 knots and ship b is sailing north at 17 knots. how fast (in knots) is the distance between the ships changing at 4 pm?
Answers
.. d = √((30 +23t)² +(17t)²)
.. = √(818t² +1380t +900)
The rate of change of distance with respect to time is
.. d' = (1/2)(2*818*t +1380)/√(818t² +1380t +900)
.. = (818t +690)/√(818t² +1380t +900)
At t=4, this is
.. d' = (818*4 +690)/√(818*16 +1380*4 +900)
.. = 3962/√19508
.. ≈ 28.37 . . . . . knots
The distance between the ships is increasing at about 28.37 knots at 4 pm.
The rate at which the distance between the two ships is changing is approximately 18.86 knots at 4pm.
Explanation:To find the rate at which the distance between the two ships is changing, we can use the concept of relative velocity. Let's consider ship A as the reference point. The velocity of ship A relative to the Earth is given as 23 knots due west, and the velocity of ship B relative to the Earth is given as 17 knots due north. The velocity of ship B relative to ship A can be found by subtracting the velocities.
Using the Pythagorean theorem, we can find the magnitude of the velocity of ship B relative to ship A. This magnitude represents the rate at which the distance between the ships is changing. Therefore, at 4 pm, the distance between the ships is changing at a rate of approximately 18.86 knots.
each side of a square shaped room is 7 ft long what is the rooms area
Answers
A square has four sides, and they have the same length. We must use a formula to calculate the area of a square. The formula is:
A = s^2
It's just the sides squared.
Each side is 7 feet long.
Substitute:
A = 7^2
A = 49
ANSWER:
The area of the room is 49 ft squared.
*Put a small 2 at the end of "ft" to indicate that it is squared!
What is the total surface area of the figure shown
Answers
Answer: The total surface area is 2784 sq. inches.
Step-by-step explanation: We are given to find the total surface area of the given figure.
Let us divide the figure into two two cuboids 1 and 2 as shown in the attached figure.
We know that the surface area of a cuboid with length 'l', breadth 'b' and height 'h' is given by
[tex]S.A.=2(l_1b_1+l_1h_1+h_1b_1).[/tex]
The dimensions of the cuboid 1 are
[tex]length,~l_1=14~\textup{inches},\\\\breadth,~b_1=12~\textup{inches},\\\\height,~h_1=24-10=14~\textup{inches}.[/tex]
The dimensions of the cuboid 2 are
[tex]length,~l_2=30~\textup{inches},\\\\breadth,~b_1=14~\textup{inches},\\\\height,~h_1=10~\textup{inches}.[/tex]
Therefore, surface area of cuboid 1 is given by
[tex]S.A_1\\\\=2(l_1b_1+l_1h_1+h_1b_1)\\\\=2(14\times 12+14\times 14+14\times 12)\\\\=2(532)\\\\=1064~\textup{sq. inches.}[/tex]
And surface area of cuboid 2 is given by
[tex]S.A_2\\\\=2(l_2b_2+l_2h_2+h_2b_2)\\\\=2(30\times 14+30\times 10+14\times 10)\\\\=2(420+300+140)\\\\=2(860)\\\\=1720~\textup{sq. inches}.[/tex]
Thus, the total surface area of the figure is
[tex]S.A.=S.A_1+S.A_2=1064+1720=2784~\textup{sq. inches}.[/tex]
Question 30 Unsaved
What is the net force acting on a golf car traveling at a constant speed of 5 mph?
0 N
10 N
5 N
15 N
Answers
So likely your answer going to be c.
Please make me brainliest.
CAN SOMEONE HELP (AND HELP ME UNDERSTAND)
Answers
Now, consider what happens when Z falls on top of tangent point Y. The angle is still half the measure of arc XY, still 62°.
Selection C is appropriate.
_____
I apologize for any confusion caused by my choice of Z as the name of the point I added. Nothing in my explanation is intended to refer to the Z already shown in the unmodified figure.
Is 2 , -5 a solution to this system equation 2x + 5y = -19, 6y - 8x = -54 .? Justify your answer
Answers
So for 2x + 5y = -19,
2(2) + 5(-5) = -19
4 - 25 = -19
-21 ≠ -19.
You can continue and try it out for 6y - 8x = -54
6(-5) - 8(2) = -54
-30 - 16 = -54
-46 ≠ -54
But since (2, -5) already doesn't work for one equation, it cannot be a solution to the system of equations.
Is this triangle a right triangle?
Answers
2^2 = 4
3^2 = 9
4^2 = 16
9+4 = 13
13 does not = 16
[tex] {x}^{2} = {2}^{2} + {3}^{2} \\ {x}^{2} = 4 + 9 = 13 \\ x = \sqrt{13} [/tex]
it's not a right triangle
Which is a counterexample to this conjecture? The sum of any two consecutive integers is a composite number. A. 16 + 17 = 33 B. 10 + 11 = 21 C. 6 + 7 = 13 D. 7 + 8 = 15
Answers
This is because 33, 21, and 15 are composite numbers, and 13 is not.
Final answer:
The sum of two consecutive integers being composite is disproved by the example 7 + 8 = 15, which is prime.
Explanation:
Counterexample: The sum of any two consecutive integers being a composite number is disproved by the example: 7 + 8 = 15, which is a prime number and not composite.
Explanation: A composite number is a positive integer that has more than two distinct positive divisors. In the case of 7 + 8 = 15, 15 only has divisors 1 and 15, making it a prime number, not composite.
Understanding Conjectures: Counterexamples are essential in mathematics to disprove conjectures by showing cases where the given rule or statement does not hold true.
You are thinking about building a home. You are told that for a particular area, the construction costs for the home should be about four times the cost of the land and the landscaping costs should be about one-third of the cost of the land. If your total budget is $250,000, calculate your budget for the land.
Answers
250k-83k is 167k
Then the land cost is expected to be 3/(12+3+1) = 3/16 of the total cost.
3/16 * 250,000 = 46,875
Your budget for the land should be about $46,875.
Chris bought n packs of pencils. Each pack has 10 pencils. Write an equation to represent the total number of pencils p that Chris bought.
Answers
p = number of pencils
equation: p = 10n
P= total packs
Total packs equals pencils per pack times number of packs.
EQUATION:
P= 10x
Hope this helps! :)
what is the solution of the equation sqrt 5x-7 = sqrt 3x+5 ?
Answers
x=6 loves because it just does
Can someone please help me with these questions I need them ASAP!
Answers
a.Irrational
b. Irrational
c. Rational
d.Irrational
2.
Is Rational
Is an integer
Is a whole number
3.
Is Rational
Is a real number
4.
Is Rational
========================
As far as I can tell you got them all correct, well done :D
Jack is learning to play piano. He knows that a piano has 88 keys and that there are 12 unique keys in each group called octave. How many complete octaves are on a piano?
Answers
Answer:
7 octaves
Step-by-step explanation:
Total number of keys in piano = 88 keys
Numbers of keys in each group called octave= 12 unique keys
We have to find the number of complete octaves on piano
Number of octaves consists of 12 keys= [tex]\frac{Total number of keys}{12}[/tex]
Number of octaves consists of 12 keys= [tex]\frac{88}{12}[/tex]
Number of octaves consists of 12 keys= 7 octaves
Hence, the correct answer is 7 octaves
determine the values of x and y.
DEFG is a parallelogram.
DH = x + 3
HF = 3y
GH = 4x - 5
HE = 2y + 3
A) x = 2 and y = 3
B) x = 3 and y = 2
C) x = 3 and y = 6
D) x = 6 and y = 3
Answers
GE cuts DF at H, then DH = HF
DH = x + 3
HF = 3y
Since DH = HF
x + 3 = 3y
3y - x = 3---->1)
GH = HE
4x - 5 = 2y + 3
4x - 2y = 3 + 5
4x - 2y = 8 ---> 2)
we have a set of simultaneous equations where we have to solve for x and y
3y - x = 3---->1)
4x - 2y = 8 ---> 2)
multiply 1st equation by 4
12y - 4x = 12 ---3)
add 2nd and 3rd equation
10 y = 20
y = 2
substitute y = 2 in 1st equation
3*2 - x = 3
6 - x = 3
x = 3 and y = 2
therefore correct response is B)
Help with this math question please
Answers
Interest rate = r = 7.25% = 0.0725
Time in years = t = 8 years
Amount accumulated = A
Formula for compound interest is:
[tex]A=P e^{rt} [/tex]
Using the given values, we get:
[tex]A=4100 e^{0.0725*8}=7322.76 [/tex]
Rounding of to nearest hundredth, the balance in the account after 8 years will be $7322.76
Noah spent some of his allowance on Monday. He spent 1/6 of his allowance on Tuesday and 3/6 of it on Friday. Noah has none of his allowance money left. What fraction of his allowance did he spend on Monday?
Answers
Let us represent the allowance spent by Noah on Monday by the letter "x".
We know that all the fractions must always add up to 1 in such questions.
Thus, if Noah spent 1/6 of his allowance on Tuesday and 3/6 of it on Friday and he spend x amount on Monday, then these spendings must add up to 1.
In other words,
[tex] x+\frac{1}{6}+\frac{3}{6}=1 [/tex]
[tex] x+\frac{1+3}{6}=1 [/tex]
Thus, [tex] x+\frac{4}{6}=1 [/tex]
[tex] \therefore x=1-\frac{4}{6}=\frac{6-4}{6}=\frac{2}{6}=\frac{1}{3} [/tex]
Thus Noah spent a third or [tex] \frac{1}{3} [/tex] of her allowance on Monday.