Answers
Answer:
Step-by-step explanation:
take 60 degree as reference angle
using sin rule
sin 60=opposite/hypotenuse
[tex]\sqrt{3}[/tex]/2=x/8[tex]\sqrt{5}[/tex](do cross multiplication)
2x=[tex]\sqrt{3[/tex] *8[tex]\sqrt{5}[/tex]
2x=8[tex]\sqrt{15}[/tex]
x=8[tex]\sqrt{15}[/tex]/2
x=4[tex]\sqrt{15}[/tex]
for y
using pythagoras theorem
h^2=p^2+b^2
(8[tex]\sqrt{5}[/tex] )^2=(4[tex]\sqrt{5}[/tex] )^2+b^2
320=80+b^2
320-80=b^2
240=b^2
[tex]\sqrt{240}[/tex] =b
4[tex]\sqrt{15}[/tex]=y
Related Questions
You went to a bake sale and bought a whole bunch of
yummies!
Cookies were $1 and Brownies were $2. You spent
$13 total.
What are three combinations of cookies and brownies
that you could have gotten?
Write an equation that represents this situation.
Answers
Answer:
If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y
∴ $1*(x*1) + $2*(y*1) = $13
Step-by-step explanation:
1) You can buy 4 brownies for $2 each = 2*4 = $8
The rest you can buy cookies = 5 cookies = $5
$8+$5=$13
2) You can buy 5 brownies and 3 cookies = $10+$3 = $13
3) You can buy 3 brownies and 7 cookies = $6+$7=$13
Equation: -
If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y
∴ $1*(x*1) + $2*(y*1) = $13
Select the equivalent expression.
(6-4.8-7)-°
-2
Answers
A bathtub can hold 80 gallons of water. The faucet flows at a rate of 4 gallons per minute.
A) What percentage of the tub will be filled after 6 minutes.
B) How many minutes will it take for the tub to be 75% full?
Answers
Answer:
A) 24 ( 4*6)
B) 15 ( 75%of 80 is 60...
60÷4 is 15)
Answer:
The answer is 30%
Step-by-step explanation:
4 times 6=24
24 divided by 80 times 100 is 30
(That's also how to find your percentage on a test)
Find the derivative of y=2x^2-3x+1 and the slope of the curve at the point where x=3
Answers
The slope of the tangent line to y(x) at any given x is equal to the derivative dy/dx at that point. Differentiate to get
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{4x-3}[/tex]
and evaluate it at x = 3 to get the slope, 4•3 - 3 = 9.
Frosting Mountain cupcake shop is running low on vanilla. They have 2 cups of vanilla left and each batch of cupcakes needs 1 4 of a cup. How many batches of cupcakes can they make before they run out of vanilla?
Answers
Answer:0.143
Step-by-step explanation:
find the mean, median, mode, and range of the data 10, 13, 7, 6, 9, 4, 6, 3, 5
Answers
Show how you use the additive inverse to solve the following.
1. 8-9= 8 + (-9) =
2. +5 - (+14) =
4. -10 - (-9) =
3. -23 - (+10)-(-4) =
6. 16 - (+16) =
5. (+17)-(-20) -(+12) =
8. 5-(+7) -(-8)-3-(-6) =
7. - 200-(-120) -- 25 =
10.-18+ (-22) - (-31) =
9. 53-(-17) + (-6) =
Answers
Answer:
1.8-9=8+(-9)=?
2.+5-(14)= -9
3. -10-(-9)= -1
6.16-(+16)= 0
5.(+17)-(-20)-(12)= 25
8.5-(+7)-(-8)-3-(6)=9
7.-200-(-120)-25=105
10.-18+(-22)-(-31)=9
9.53-(-17)+(-6)=64
that's my answer
A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tallman is walking towards the wall at the rate of 30 feet per second. How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall
Answers
Answer:
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Step-by-step explanation:
Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.
To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?
Proof -
From the given information, the figure becomes
Triangle ABC and Triangle DBE are similar triangle
AC/DE = BC/BE
⇒h/6 = 200/(200-x)
⇒h = 1200/(200 -x)
Now,
Differentiate h with respect to t, we get
[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]
Now,
If the rate of the tip is moving down the wall
At x = 50 feet, dx/dt = 30 feet per second
So,
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]
So, we get
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Find the measure of each angle indicated (quadrilaterals)
Answers
Answer:
The Solar System is the gravitationally bound system of the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun directly, the largest are the eight planets, with the remainder being smaller objects, the dwarf planets and small Solar System bodies.
Step-by-step explanation:
Answer:
its 75
parallel angle degrees always should be 360
just need a bit of help
Answers
Answer:
35A) arc AC = 360-(100+110+80)=
360-290 = 70°
35B) L D = ½× 70 = 35°
35C) L AEC = ½(100+70)=½×170= 85°
35D) L P = ½(100-70) = ½×30 = 15°
if 3/5 of a number is 2 more than 2/3 of the same number, then what is the value if the square of the number
Answers
9514 1404 393
Answer:
900
Step-by-step explanation:
Let x represent the number. The given relationship is ...
(3/5)x = 2 +(2/3)x
-2 = 1/15x . . . . . . . . subtract 2+3/5x from both sides
-30 = x . . . . . . . . . . multiply by 15
Then the square of the number is ...
x² = (-30)² = 900
Find the value of each trigonometric ratio
Answers
№3
[tex]\sin C = \frac{AB}{AC} = \frac{27}{45} = \frac{3 * 9}{5 * 9} = \frac{3}{5}[/tex]
Answer: D (3/5).
№4
[tex]\cos A = \frac{AB}{AC} = \frac{24}{30} = \frac{3 * 4 * 2}{3 * 5 * 2} = \frac{4}{5}[/tex]
Answer: C (4/5).
№5
[tex]\tan C = \frac{AB}{BC} = \frac{32}{24} = \frac{2 * 2 * 2 * 4}{2 * 2 * 2 * 3} = \frac{4}{3}[/tex]
Answer: D (4/3).
Answer:
3.) Sin C = option D, [tex]\frac{3}{5}[/tex]
4.) Cos A = option C, [tex]\frac{4}{5}[/tex]
5.) Tan C = Option D, [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
3.) Sin C = [tex]\frac{opposite}{hypotenuse} = \frac{27}{45} = \frac{3}{5}[/tex]
4.) Cos A = [tex]\frac{adjacent}{hypotenuse} = \frac{24}{30} = \frac{4}{5}[/tex]
5.) Tan C = [tex]\frac{opposite}{adjacent} = \frac{32}{24} = \frac{4}{3}[/tex]
Hope this helps!
A group of students are surveyed about which movie they prefer.
movie a :14
movie b : 9
movie c : 5
movie d : 3
What is the probability that a student prefers Movie A?
Answers
Suppose you wish to test if a number cube (die) is loaded or not. If the die is not loaded, the theoretical probabilities for each roll should be: 1 2 3 4 5 6 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % You roll the die 84 times and come up with the
Answers
Answer:
Goodness of fit
Step-by-step explanation:
Given
The theoretical probabilities
See comment for complete question
Required
The type of test to be use
From the question, we understand that you are to test if the die is loaded or not using the given theoretical probabilities.
This test can be carried out using goodness of fit test because the goodness of fit is basically used to check the possibility of getting the outcome variable from a distribution. In this case, the outcome of the variables are the given theoretical probabilities.
In a nutshell, the goodness fit of test determines if the given data (in this case, the theoretical probabilities) is a reflection of what to expect in the original population.
URGENT... please help
Answers
HELP PLZ I HAVE 5 MIN PLZZ
A box of fruit contains apples, oranges, and bananas. The apples weigh a total of 6 pounds and the oranges weigh a total of 8 pounds.
Let b represent the total weight of the bananas, in pounds.
Create an expression to represent the total weight, in pounds, of the fruit in the box. Move a number, variable, and symbol to the lines to
create the expression.
2
6
8
14
48
b
Lo
Answers
Answer:
6+8
Step-by-step explanation:
Aliyah had $54 to spend on 5 bracelets. After buying them she had $4. How much did each bracelet cost? Each bracelet costs Question Blank type your answer... dollars.
Answers
If using the method of completing the square to solve the quadratic equation x2+14x-14=0, which number would have to be added to "complete the square"?
Answers
Answer:
49
Step-by-step explanation:
the number would simply be
14÷2=7
7²=49
What is the coefficient in this equation? 140 - 6 = 28
Answers
Answer:
There is none there is no variable.
Step-by-step explanation:
Hope this helps!!
Answer:
there is no co efficient a co efficient is the constant before the variable when its attached.
What is the measure of Z ABC ? B 60° 60° c
Answers
Answer:
60°
Step-by-step explanation:
If it a equilateral triangle
find 3/5% of $90,000
Answers
to find a percentage of something, you multiply the percentage and the number, so
60% x 90000 = 54,000
Solve for c.
a(c+b) = d
Answers
Answer:
c = (d/a) - b
Step-by-step explanation:
a(c + b) = d
Divide both sides by a
c + b = d/a
subtract b from both sides
c = (d/a) - b
A family on vacation drove a total round-trip distance of 735.75 miles. They traveled
for 7 hours in one direction and 6.5 hours on the return trip. What was their average
speed for the entire trip?
Answers
Answer:
speed = 54.5 miles/hr
Step-by-step explanation:
speed = distance/time
distaance = 735.75
time = 7 + 6.5 = 13.5
speed = 735.75 / 13.5
speed = 54.5 miles/hr
Which expression has a value of 7/12?
1. 2 1/12 + 5 1/12
2. 6/8 + 1/4
3. 1/3 + 1/4
4. 7/8 + 4
Answers
Answer: 3. 1/3 + 1/4
Step-by-step explanation:
1/3 = 4/12
1/4 = 3/12
4/12 + 3/12 = 7/12
Integration of ∫(cos3x+3sinx)dx
Answers
Answer:
[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx . Now , Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
find the slant height of a cone whose height is 15 cm and whose radius is 8 cm
Answers
Answer:
Right circular cone
Solve for slant height
l=17cm
r Radius
8
cm
h Height
10 gallons to 24 gallons Identify the percent of change as an increase or decrease. Then find the percent of change. Round to the nearest tenth of a percent if necessary.
Answers
Answer:
140%
Step-by-step explanation:
Helen rented a kayak at the lake there is a charge of $6 as an initial fee and then $3 an hour for every hour that she uses the kayak if the total charge is $21 how many hours did she kayak
Answers
Answer:
Helen kayaked for five hours.
Step-by-step explanation: First subtract the initial fee ($6.00) from the total charge ($21), $21 - $6 = $15. Now, divide the $15 she was charged for kayaking by $3 (because it costs 3 bucks an hour to kayak plus the 6 buck initial fee.) 15 divided by 3 = 5. So she kayaked for 5 hours.
Help me out please???
Answers
If G is the incenter of ∆ABC, then GD = GF = GE.
Given, GD is 3x + 5 and GF is 6x - 4.
According to the above statement,
GD = GF
or, 3x + 5 = 6x - 4
or, 5 + 4 = 6x - 3x
or, 9 = 3x
or, 9/3 = x
or, 3 = x
The value of x is 3.
By putting the value of x in GD or GF, we get
GD = 3(3) + 5 = 9 + 5 = 14
GF = 6(3) - 4 = 18 - 4 = 14
Therefore, GE = 14.
At the fair, 2 corn dogs and 3 pretzels cost $13, and 5 corn dogs and 6 pretzels costs $28. How much
would 2 pretzels and a corn dog cost??
Answers
2x+3y=13
5x+6y=28
Multiply the first equation by two so that we can eliminate y.
Subtract:
4x+6y=26
5x+6y=28
-x=-2
x=2
4(2)+6y=26
8+6y=26
6y=18
y=3
3 x 2 = 6
6+2=8
Therefore, 2 pretzels and a corn dog would cost $8.