Given:
QR is parallel to RS.
To find:
The value of x.
Solution:
In the given figure, we have,
[tex]PR=12[/tex]
[tex]RT=2x-2 [/tex]
[tex]QS=21[/tex]
[tex]ST=3x-1[/tex]
Using basic proportionality theorem (BPT), we get
[tex]\dfrac{PR}{RT}=\dfrac{QS}{ST}[/tex]
[tex]\dfrac{12}{2x-2}=\dfrac{21}{3x-1}[/tex]
On cross multiplication, we get
[tex]12(3x-1)=21(2x-2)[/tex]
[tex]36x-12=42x-42[/tex]
[tex]36x-42x=12-42[/tex]
[tex]-6x=-30[/tex]
Divide both sides by -6.
[tex]x=\dfrac{-30}{-6}[/tex]
[tex]x=5[/tex]
Therefore, the value of x is 5.
At a factory, light bulbs are packed in boxes that are then placed in a shipping container.
• Each box is in the shape of a cube.
• Each box has an edge length of foot.
• A shipping container has dimensions of feet by 1 foot by 2 feet.
What is the total number of boxes of light bulbs that the shipping container can hold when completely full?
Answer: 144
Step-by-step explanation: You need to find the volume of the shipping container and divide it by the volume of a box.
2 2/3 x 1 x 2 = 16/3
1/3 x 1/3 x 1/3 = 1/27
16/3 divided by 1/27 is 144.
Find 35% of a number is 70 find the number
Answer:
200.
Step-by-step explanation:
35% = 0.35 so
0.35x = 70
x = 70 / 0.35
= 200.
Answer:
200
Step-by-step explanation:
Let the number = x
35% of x = 70
35/100 * x = 70 Multiply by 100
35x = 70 * 100
35x = 7000 Divide by 35
x = 7000/35
x = 200
A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?
Answer:
The probability that the month starts with the letter J or the letter M is 41.66%.
Step-by-step explanation:
Given that a month of the year is chosen at random, to determine what is the probability that the month starts with the letter J or the letter M, the following calculation must be performed:
January - March - May - June - July = 5 months
(5/12) x 100 = X
0.4166 x 100 = X
41.66 = X
Therefore, the probability that the month starts with the letter J or the letter M is 41.66%.
Answer:
5/12
Step-by-step explanation:
Months that start with the letter M are March and May
Months that start with J are January, June, July
So, in total the months that start with J and M are 5 in number.
Total number of months = 12
Therefore the probability = 5/12 or 0.416 (bar on 6)
Hope u understood
Please mark as brainliest
Thank You
An airplane flying into a headwind travels the -mile flying distance between Indianapolis, Indiana, and Phoenix, Arizona, in hours. On the return flight, the airplane travels this distance in hours and minutes. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
Answer:
the airspeed of the plane = 660 miles/hr
the speed of the wind = 60 miles/hr
Step-by-step explanation:
The values are missing in the given information in the question.
To able to solve this question, we will make some assumptions.
Let's assume that:
The airplane heading into the wind travels 1800 miles in 3 hours.
While returning via the same distance, it travels 2 hours 30 minutes.
We are to determine the plane's airspeed as well as the wind speed.
First, let us say that the speed of the plane is p and the wind speed is q
during the time the plane is traveling for 1800 miles in 3 hrs.
Then, we can say
3p -3q = 1800 ----- (1)
However, in 2hours 30 minutes, we have 2.5 hours
So, when the plane is returning, we have the following equation:
2.5p + 2.5q = 1800 ---- (2)
So, to find p and q, we can use the elimination method.
Simply by multiplying equation (1) with 5 and equation (2) with 6
(5)3p - (5)3q = (5) 1800
(6)2.5p + (6)2.5q = (6) 1800
15p - 15q = 9000
+
15p + 15q = 10800
30p - 0 = 19800
30p = 19800
p = 19800/30
p = 660
Since p = 660, then from equation (1) we can obtain the value of q:
So; Using equation (1):
3p -3q = 1800
3(660) - 3q = 1800
1980 - 3q = 1800
-3q = 1800 - 1980
-3q = -180
q = 180/3
q = 60
Therefore, the airspeed of the plane = 660 miles/hr
the speed of the wind = 60 miles/hr
Write the Plural! Spanish, help!!
Can u please answer these two questions
I have 225 in my account I can spend all but 20%
Answer:
20 % is 45 so keep this much remaining
Step-by-step explanation:
Answer:
You can spend 80%. Multiple 225 × 0
80. 225×0.80 = 180. Now you will have $180
Step-by-step explanation:
Have a great day and summer.
PLS HELP ME!!:((( I'm stuck can u pls help me I will give the brainliest pls!!!
Answer:
1. 3/6
2.12/24
3. 6/12
4. 6/12
5.8/16
6. 9/18
7. 12/24
8. 12/24
im not sure if everything is correct
Answer:
To see the shaded regions, check out the attached image below. The shaded regions are in red.
The fractional values for each figure are:
3/612/246/126/128/169/1812/2412/24The fractional answers are in bold. All of those fractions reduce to 1/2. Make sure that you don't reduce any of those fractions.
========================================================
Explanation:
We count out the number of squares for each figure. Then we shade half of them. For problem 1, we just shade the left half (or you can shade the right half, but you can only pick one side). This is because 3 is half of 6.
Problem 2 is a similar story, but we'll shade the first two columns out of the four total columns. You could shade the last two columns if you wanted, but you can't shade everything.
Problem 3 has an odd number of columns, but an even number of rows. I'm shading the first two rows to represent half of the blocks.
The rest are handled in a similar manner.
------------
To form the fractional results, you basically count the number of shaded smaller squares out of the number of squares total.
For example, the answer for problem 1 is 3/6 because we have 3 shaded red squares out of 6 squares total. The rest are handled the same way.
Find the volume of the pyramid. Round to the nearest tenth if necessary.
What is the name of the following net?
Answer:
[tex]\large\colorbox{gold}{sǫᴜᴀʀᴇ ᴘʏʀᴀᴍɪᴅ}[/tex]
If the following picture below was rotated about the y-axis, what 3-D shape would it make? ( HELP PLEASEE )
Rotating the figure about the y-axis results in the creation of a cylindrical figure of radius 2 units and 6 units tall.
The obtuse angle between the hands of a clock at 2.30 a.m is:
A 105°
B 120°
C 135°
D 150°
E 165°
Answer:
c
Step-by-step explanation:
There was a seller of horses, who sold all his horses to three people. To the first man he sold half of all his horses and a half of a horse. To the second man he sold half of what he had left and a half of a horse. To the third man he again sold half of what was left and a half of a horse. How many horses did he have at first? (No horses were harmed!)
Answer:
7
Step-by-step explanation:
3RD MAN: 1
2ND MAN: 2
1ST MAN: 4
3rd Man = 1/2+1/2 = 1
2nd Man = 1+1 = 2
1st Man = 2*2 = 4
Polly had 5 times as many red balloons as many red balloons as blue ones. She had 18 all together. How many of her balloons were blue ones?
Answer: 3 were blue
Step-by-step explanation:
Blue + Red = 18....so.....
B + 5B = 18
6B = 18
B =18 / 6 = 3 blue
-2x +9y=8
x=y+3
Step by step
Choose the best estimate for the multiplication problem below. 56 x 51
A. 2000
B. 3000
C. 4100
Answer:
B
Step-by-step explanation:
PLEASE HELP ME !!! Can anyone help me find the function for this trig graph ?? i need a specific answer for the function , 50 pts and i will mark brainliest !!
Answer:
y = 5 sin (2x) + 4
Step-by-step explanation:
this is sines function,
the amplitude is [9 - (-1)]/2 = 10/2 = 5
the period is 2πx/π = 2x
the x-axis of actual function is at y = 4
so, the function is :
y = 5 sin (2x) + 4
Please help me solve this math problem and explain it. Will give BRANIEST!
(X^2+2xy+y^2)^2
Answer:
I'm sorry hindi ko po alam eh
I WILL MARK BRAINLIEST (PICTURE INCLUDED)A right triangle ABC is shown below: А 3 units B 5 units The area of the triangle above will equal one half of a rectangle that is 5 units long and units wide. (Input only whole numbers, such as 8.)
help? (i mark brainlist)
Answer:
A.
Step-by-step explanation:
Since it says greater than, that means that it cannot be B or D. And ≥ means greater than or equal to and they don't state that in the problem. So the answer would be A.
I HOPE THIS HELPED! :)
Part B: Plot point C(2,7). If M is the midpoint of CD, what are the coordinates of D?
Answer:
[tex]D = (-4,-9)[/tex]
Step-by-step explanation:
Given
[tex]C =(2,7)[/tex]
[tex]M=(-1,-1)[/tex]
Required
The coordinates of D
Represent D with:
[tex]D = (x_2,y_2)[/tex]
Using midpoint formula, we have:
[tex]M(x,y) = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]
So, we have:
[tex](-1,-1) = \frac{1}{2}(2 + x_2, 7 + y_2)[/tex]
Multiply both sides by 2
[tex](-2,-2) = (2 + x_2, 7 + y_2)[/tex]
Compare both sides
[tex]2 + x_2 = -2[/tex]
[tex]7 + y_2 =-2[/tex]
In [tex]2 + x_2 = -2[/tex], we have:
[tex]x_2 =-2-2[/tex]
[tex]x_2 =-4[/tex]
In [tex]7 + y_2 =-2[/tex], we have:
[tex]y_2 = -2 - 7[/tex]
[tex]y_2 = -9[/tex]
So, the coordinates of D is:
[tex]D = (x_2,y_2)[/tex]
[tex]D = (-4,-9)[/tex]
3. Given the bar chart below,
(a) draw a frequency table from the graph.
(b) calculate the mean mark.
(c) what is the modal mark?
(d) find the median mark.
(e) if a student is selected at random, what is the probability that he/she scored
not less than 3 marks?
7
Frequent
п
0
-
0
3
5
N
6
6
Marks
Answer: shehshywhwyw
Step-by-step explanation:
En 9 días, un grupo de trabajadores puede sembrar 72 hectáreas.
¿Cuál es su tasa en hectáreas por día?
Answer:
8 hectáreas por día
Step-by-step explanation:
72 hectares en 9 días por eso divides 72 por 9 para encontrar la repusta es 8
¡Espero que esta te ayudar! :)
(y sí, hablo un poco de español porque he aprendido desde el primer grado)
Two cards are drawn without replacement from an ordinary deck, find the probability that the second is not a black card, given that the first is a black card. What is the conditional probability?
(a) [tex]\frac{26}{51}[/tex]
(b) [tex]\frac{26}{51}[/tex]
Step-by-step explanation:(i) Probability is the likelihood of whether or not an event will occur. It is given by the ratio of the number of favourable outcomes to the number of expected outcomes. i.e
P = number of favourable outcomes / total number of possible outcomes
For drawing a first card which is black,
number of favourable outcomes = 26 (since there are a total of 26 black cards in a deck of card)
total number of possible outcomes = 52 (since the total number of cards in a deck of card is 52)
∴ Probability of drawing the first black card = 26 / 52 = 1 / 13
Since the second card is not a black card, it is a red card.
number of favourable outcomes = 26 (since there are a total of 26 red cards in a deck of card)
total number of possible outcomes = 51 (since a black card has been previously picked from the deck)
∴ Probability of drawing a second black card = 26 / 51
The probability that the second is not a black card is 26 / 51
(ii) The conditional probability of a given event B is the probability that the event will occur knowing that a previous event A has already occurred,
It is given by;
P(B|A) = P(A and B) ÷ P(A)
In this case;
event B is drawing a second card which is not black
event A is drawing a first card which is black
This implies that;
P(A and B) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex]
P(A) = [tex]\frac{1}{13}[/tex]
Substitute these values in the equation for conditional probability as follows;
P(B|A) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex] ÷ [tex]\frac{1}{13}[/tex]
P(B|A) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex] x [tex]\frac{13}{1}[/tex]
P(B|A) = [tex]\frac{26}{51}[/tex]
Therefore the conditional probability is [tex]\frac{26}{51}[/tex]
Is this correct. Please let me know thank you
Answer:
Yes it is correct, the amount of flour is 1.5 times larger than eggs needed
Step-by-step explanation:
A shirt originally cost $15, but it was marked down 5%. How much does the shirt cost now? Don't forget the $ symbol.
===============================================
Explanation:
There are two approaches we can take.
The first approach is finding the amount we save, which is 5% of 15 = 0.05*15 = 0.75 dollars or 75 cents.
So the new price is 15 - 0.75 = 14.25 dollars
----------------
The second approach is to think of it like this: If you save 5%, then you still have to pay the remaining 95% (the two percentages add to 100%).
95% of 15 = 0.95*15 = 14.25
This second approach is handy if you want to chain multiple discounts together. So let's say there's a special 10% off sale on top of the 5% discount. We would multiply by 0.90 to further discount by 10% and get to 0.90*0.95*15 = 12.825 = 12.83. It also works in reverse too and we could chain percent increases along with percent decreases.
what is the answer to this question. i made it 20 pts
Answer:
the second choice
Which is the value of 2.3 - (-2.3)?
Answer:4.6
Step-by-step explanation:2.3-(-2.3) is the same thing as 2.3+2.3 which is 4.6
Answer:
4.6
Step-by-step explanation:
Why does 5(x+20) equal 15x? I'm so confused.
Answer:
Nobody knows its a mistery :'D
Answer:
Because lma/os
Step-by-step explanation:
5 ( x + 20 )
-----------------
1. Simplifly
2. Distribute
3. 5 ( x + 20 )
5 x + 100
Kristy had a piece of fabric that she cut into 8 equal squares. Each square has area 0.625 ft2. What is the area of Kristy's original piece of fabric?
ft2
PLS HELPPP
Answer:
5[tex]ft^2[/tex] is the area of the original piece of fabric.
Step-by-step explanation:
0.625 x 8 = 5