Answer:
huh i dont understand can u post a pic
In the diagram, ABC is a triangle in which AB = 4 cm, BC = 6 cm and angle ABC = 150°. The line CX is perpendicular to the line ABX.
(i) Find the exact length of BX and show that angle CAB = tan^-1 (3/4+3√3)
(ii)
Show that the exact length of AC is √52 + 24√3 cm.
Part (i)
Angle ABC is 150 degrees. The angle CBX is supplementary to this, so,
(angleABC)+(angleCBX) = 180
angle CBX = 180-(angleABC)
angle CBX = 180-150
angle CBX = 30 degrees
Because of the right angle marker at point X, we can find that triangle CBX is a 30-60-90 triangle. This special type of right triangle has its hypotenuse twice as long as the short leg, which we'll call y. The long leg is equal to y*sqrt(3) units.
The diagram shows BC = 6 is the hypotenuse, so the short leg is y = 6/2 = 3. The longer leg is y*sqrt(3) = 3*sqrt(3) which is the distance from B to X.
In summary so far,
CX = 3
BX = 3*sqrt(3)
We have enough information to find the tangent of angle CAB, and then find the actual angle itself.
tan(angle CAB) = opposite/adjacent
tan(angle CAB) = (CX)/(AX)
tan(angle CAB) = 3/(4+3*sqrt(3))
angle CAB = arctan( 3/(4+3*sqrt(3)) )
I'm using arctan in place of tan^(-1) which is the same basic function, just different notation.
========================================================
Part (ii)
Focus on triangle AXC. The legs we found were
AX = 4+3*sqrt(3)
CX = 3
Use the Pythagorean theorem to find the hypotenuse AC
a^2 + b^2 = c^2
(AX)^2 + (CX)^2 = (AC)^2
(AC)^2 = (AX)^2 + (CX)^2
(AC)^2 = (4+3*sqrt(3))^2 + (3)^2
(AC)^2 = (4+3*sqrt(3))(4+3*sqrt(3)) + 9
(AC)^2 = 4(4+3*sqrt(3))+3*sqrt(3)(4+3*sqrt(3)) + 9
(AC)^2 = 16+12*sqrt(3)+12*sqrt(3)+27 + 9
(AC)^2 = 52+24*sqrt(3)
AC = sqrt( 52+24*sqrt(3) )
Note that AC is a length so AC is positive. We don't have to worry about the plus minus.
This is known as a nested radical since one square root is buried in another.
We can write that as [tex]AC = \sqrt{52 + 24\sqrt{3}}[/tex] if you're curious as to how that looks on paper.
Using your calculator, you should find that,
[tex]\sqrt{52+24\sqrt{3}} \approx 9.673118[/tex]
David's bowling score is 6 less than 3 times Aaron's score. The sum of their scores is 214. Find the score of each student. Use the variable a for Aaron's score.
plz help
Step-by-step explanation:
Let aron's variable be = a
Let davids variable be( 6 less tan 3 times aron) = 3×a-6
Thier sum is =214
So,
3×a-6 + a = 214
3a -6 +a = 214
(transpose)
3a + a = 214 + 6
4a = 220
a = 220/4
a= 55
Thus,aron's score is = 55
And davids score is (3×a-6) = 3×55-6 = 159
Checking,
Aron score + david score = 214
55 + 159 = 214
SO, ITS CORRECT
HOPE IT HELPS :)
20
16
12
Cost (dollars)
8
4
0
4 8 12 16 20
Amount of Tea (ounces)
Which equation models this relationship?
Oy=
Oy = 40
#thisisacryforhelp!!!
Answer:
y=4x
Step-by-step explanation:
you just have to find the slope!
pls help!! would be greatly appreciated<3
Answer:
x=7
Step-by-step explanation:
Expand and simplify 3(2x + 1) +2(x + 4)
Answer:
8+11
Step-by-step explanation:
Answer:
3(2x + 1) +2(x + 4)
6x + 3 + 2x + 8
8x + 11
Step-by-step explanation:
Correct 25.0457 to 2 significant figure
9514 1404 393
Answer:
25.
Step-by-step explanation:
The first two significant figures are 2 and 5. The next figure is 0, so we don't need to round up. The number to 2 significant figures is 25.
The total U.S. apple production increased during the 1973-1988 period from 6.2 to 9.l billion pounds. To the nearest tenth of a percent, what was the percent of increase in apple production in the United States from 1973-1988? plzzzzz help
Subtract to find the difference in the amounts:
9.1 - 6.2 = 2.9
Divide the change by the starting amount:
2.9/6.2 = 0.46774
Multiply by 100 to get the percentage and round to the nearest tenth:
0.46774 x 100 = 46.8 %
Answer: 46.8%
plzzzzzz helpppppp plzzz
Answer:
D. 6
Step-by-step explanation:
Answer:
B, 6
I think! hope it helped
Translate the number equation into a written equation: 2p + 4 = 20
Answer:
p is 8
Step-by-step explanation:
4 - 20
then 2 divided by 16
then you get 8
Answer:11. g. 10. 3g. 12. 2p. 4q. 20 g plus 10 is the same as. Twice p plus 4 times q is 20. 3 times g. 13. 4(a b). 9a. 14. 8.
Step-by-step explanation:
i think thats the answer
A math book comprises of two sections: arithmetic and geometry in the ratio 5:3. How much of each type of content will be needed to make a book of 480 pages?
Answer:
Arithmetic content = 300 pages
Geometric content = 180 pages
Step-by-step explanation:
Arithmetic : Geometry = 5 : 3
Total pages of book = 480
How much of each type of content will be needed to make a book of 480 pages?
Total ratio = arithmetic + geometric
= 5 + 3
= 8
Arithmetic content = 5 / 8 × 480
= 0.625 × 480
= 300
Arithmetic content = 300 pages
Geometric content = 3 / 8 × 480
= 0.375 × 480
= 180
Geometric content = 180 pages
If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete? 8r 8(5) r (5)
Hello soldier!! The answer is D! Have a great day <3
Answer:
The answer is: D / 1/8(5)
Step-by-step explanation:
Last one , will mark brainliest !!!!
Answer:
Step-by-step explanation:
Part 1:y=426x+4298
y=223x+6129
Part 2: x=9.020 (x is the number of months and y is the miles)
Part 3: y=8140.394, or 8,140 since it's rounding to the nearest mile
Answer:
See answers in explanation below
Step-by-step explanation:
1. 4298 + 426t = 6129 + 223t
2. Basically get into the graphing page and find "function" section then select "f(x) = mx + b", then graph f(x) = 426x + 4298 and f(x) = 223x + 6129
and find the answer at where these two lines intersect with each other, x=9.0197 (months)
3. sub x=9.0197 into any of the two equation and f(x) = 8140 (miles)
The chart shows number of minutes students spent studying for a test and their grade on the test. Draw a scatter plot of the data.
Which equation is closest to the line of best fit?
A) y=-1/3x-52
B) y= 1/3x + 52
C) y=-52x + 1/3
D) y=52x-1/3
Answer:
the answer is A). y=1/3×-52
PLEASE HELP!! I’LL GIVE BRAINLIEST AND 10 POINTS !! FOR THE CORRECT ANSWER
Answer: -9
Step-by-step explanation:
You count down the distance from T to K
Answer:
-9
Step-by-step explanation:
you are counting from t to k but its going to the left of the number line to its negative.
The diagram shows a triangle.
3t
2t–50°
2t–50°
What is the value of t?
t =
Doreen Schmidt is a chemist. She needs to prepare 28 ounces of a 8% hydrochloric acid solution. Find the amount of 14% solution and the amount of 7% solution she should mix to get this solution
Let, amount of 14% solution required is x ounces.
So, amount of 8% solution will be ( 28 - x ) ounces.
Now, mathematical equation is :
[tex]\dfrac{14x}{100}+\dfrac{7(28-x)}{100}= \dfrac{8\times 28}{100}\\\\14x + 196 - 7x = 224\\\\7x = 28\\\\x = 4\ ounces[/tex]
Therefore, amount of 14% solution and 8% solution required is 4 ounces and 24 ounces respectively.
Hence, this is the required solution.
Substitute to solve
Brainliest for correct answer
Answer:
4x-1y=3xy
Step-by-step explanation:
because 3-2=1 and add the y on and the do 4x-1y and that will = 3xy
Answer:
x=4, y=6
Step-by-step explanation:
hope that helps :)
Evaluate:
7 - 3 + 10
Answer:
14
Step-by-step explanation:
7-3 = 4 4+10=14 therfore 14 would be the answer hope this helps
3(x + 3) – 2 < 4 or 1 – x ≤ –1
Answer:
eu singer nuştiu
terog scuză
50% of 320 is equal to 80% of what number?
Answer:
128
Step-by-step explanation:
PLS HELP I WILL GIVE BRAINLIEST
Answer:
6x-2
Step-by-step explanation:
the side lengths are x+2, x+2, 2x-3 and 2x-3
(the other two are the same as the ones shown because it's a rectangle)
when you combine like terms you get 2x+4 and 4x-6
combine like terms again and you get 6x-2
hope this helps :)
Logan weighed two buckets of sand for a geology project. The first bucket weighed 5.19 pounds. The other bucket weighed 9.01 pounds. How much do the two buckets of sand weigh all together?
Answer:
14.2
Step-by-step explanation:
you just have to add both of the numbers shown in the question
what is 2350 million in standard from
Answer:
2350000000
Step-by-step explanation:
quick i need hellppppp!!!!
Answer:
D
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Read the problem. Tamir baked cookies for his mother's birthday. He mixed the cookie batter, scooped it into mounds on a cookie sheet, and then put the cookie sheet in the oven. After 20 minutes in the oven, 15 of the 20 cookies were fully baked. Shade the grid to show the fraction of the cookies that were fully baked after 20 minutes in the oven. What percent of the cookies were fully baked? You can use your model to help.
Answer:
Percentage baked= 75%
Step-by-step explanation:
Giving the following information:
After 20 minutes in the oven, 15 of the 20 cookies were fully baked.
First, the fraction of cookies baked:
Fraction of cookies= 15/20= 3/4
Now, to calculate the percentage, we need to use the following formula:
Percentage baked= (15/20)*100
Percentage baked= 75%
what is the volume of a A prism with a base area of 34 m2 and a height of 6 m.
Answer:
34 * 6 = 204
Thank you and please rate me as brainliest as it will help me to level up
Classify the following triangle based on its shape.
Answer: a right triangle
Step-by-step explanation:
what's the answer? 4/5×1/3?
Answer:
4/15
Step-by-step explanation:
what's the answer? 4/5×1/3?
A school set a goal to collect at least $360 from a book sale. They have already collected $180. The school receives $3 for each book sold. Write an inequality to show the number of books the school needs to sell to meet their goal.
Use substitution to solve the following system of equations. What is the value of y?
6x + 2y = 4
3x - 5y = 44
A. y = 7
B. y = -7
C. y = -4.5
D. y = 4.5
Answer:
B
Step-by-step explanation: