3. What is the exact area of triangle ABC? Use special right triangles to help find the base of the triangle. Show your work.
Answers
The exact area of triangle ABC is 93.51 cm².
The given parameters;
Height of the triangle, h = 18 cmThe base of the triangle is calculated by using trigonometry ratio as follows;
[tex]tan (30) = \frac{b}{18} \\\\[/tex]
where;
b is the base of the triangle ABC[tex]b = 18 \times tan(30)\\\\b = 10.39 \ cm[/tex]
The area of the triangle ABC with the calculated base and given height is calculated as follows;
[tex]A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 10.39 \times 18\\\\A = 93.51 \ cm^2[/tex]
Thus, the exact area of triangle ABC is 93.51 cm².
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Related Questions
2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^2at
Hint: Turn tan(x) = e^at and e^y = 1 + e^2at into expressions suited to your calculation.
Answers
I assume a is a constant. If tan(x) = exp(at) (where exp(x) means eˣ), then differentiating both sides with respect to t gives
sec²(x) dx/dt = a exp(at)
Recall that
sec²(x) = 1 + tan²(x)
Then we have
(1 + tan²(x)) dx/dt = a exp(at)
(1 + exp(2at)) dx/dt = a exp(at)
dx/dt = a exp(at) / (1 + exp(2at))
If exp(y) = 1 + exp(2at), then differentiating with respect to t yields
exp(y) dy/dt = 2a exp(2at)
(1 + exp(2at)) dy/dt = 2a exp(2at)
dy/dt = 2a exp(2at) / (1 + exp(2at))
By the chain rule,
dy/dx = dy/dt • dt/dx = (dy/dt) / (dx/dt)
Then the first derivative is
dy/dx = (2a exp(2at) / (1 + exp(2at))) / (a exp(at) / (1 + exp(2at))
dy/dx = (2a exp(2at)) / (a exp(at))
dy/dx = 2 exp(at)
Since dy/dx is a function of t, if we differentiate dy/dx with respect to x, we have to use the chain rule again. Suppose we write
dy/dx = f(t)
By the chain rule, the derivative is
d²y/dx² = df/dx
d²y/dx² = df/dt • dt/dx
d²y/dx² = (df/dt) / (dx/dt)
d²y/dx² = 2a exp(at) / (a exp(at) / (1 + exp(2at)))
d²y/dx² = 2 (1 + exp(2at))
The initial balance of a savings account was $275 Adter which transactions will the balance of the savings account be the same as the initial balance?
A. a withdrawal or $232 followed by a deposit of $132
B. a deposit of $278 followed by a withdrawal of $278
C. a withdrawal of $115 followed by a deposit of $312
D. a deposit of $205 followed by a withdrawal of $317
Answers
The transactions that would leave the initial balance the same are a deposit of $278 followed by a withdrawal of $278.
The transactions that would leave the initial balance the same are transactions that net to zero. Withdrawals reduce the balance in the account. Deposits increase the value of the balance in the account.
Option A: Net balance
$275 - $232 + 132 = $175
Option B: Net balance
$275 + $278 - $278 = $275
Option C: Net balance
$275 - $115 + $312 = $472
Option D: Net balance
$275 + $205 - $317 = $163
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POINTS AND BRAINLIEST IF YOU GAVE ME THIS CORRECT!!!
To rent a moving truck for the day, it costs, $33 plus $1 for each mile driven.
a. Write an expression for the cost to rent the truck.
b. You drive the truck 300 miles. How much do you pay?
Answers
Answer:
a) x + 33
Step-by-step explanation:
x is the number of miles driven. Therefore, the answer for b is $333
Because it is the miles driven plus 33
It took Erika 8 games to score 30 points. At that rate, how many games will it take her to score 45 points?
Answers
Answer : 12 games
Step - by - step explanation :
In - order to find out how many games it will take Erika to get 45 points we need to find out how many points she normally gets in 1 game . . .
What is 30 divided by 8 ? 3.75 ( So Erika gets 3.75 points per game ! )
What is 45 divided by 3.75 ? 12 ( So Erika had to play 12 games in - order to get 45 points ! )
The cylindrical container shown below can be completely filled with 24 litres of water. The base area of the container is 600 cm2. What is the height of the container? PLEASE FAST!!
Answers
Answer:
40cm
Step-by-step explanation:
volume of a cylinder= πr²h
V=24litres, Area=πr²=600cm², height=?
converting litres to cm³
1litre=1000cm³
24litres= 24×1000
=24000cm³
24000=600× h
h= 24000/600
= 40cm
which statement best describes the first step to the equation -11-3x=44-2x
A. add 3 to both sides
B add 2 to both sides
C.get the variables on one side
Answers
Get the variables on one side statement best describes the first step to the equation -11-3x=44-2x
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -11-3x=44-2x
Minus eleven minus three x equal to forty four minus two times of x
To solve this, we need to seperated the variable on one side
-3x+2x=44+11
-x=55
x=-55
Get the variables on one side is the first step to the equation -11-3x=44-2x
Hence, get the variables on one side statement best describes the first step to the equation -11-3x=44-2x
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Evaluate.
(jk−1)÷j when j=−4 and k=−0.7
Enter your answer as a decimal in the box.
Answers
Answer:
(jk - 1) / j
jk = (-4 x -0.7) = 2.8
(2.8 - 1) / - 4
1.8 / -4 = -0.45
Answer is -0.45 when j = -4 and k = -0.7
Select the correct answer.
Why would someone choose to invest rather than depend only on savings?
A. An investment account provides regular income, while money held in a savings account may decrease.
B. An investment account has the potential to earn more money than a savings account.
C. An investment account has a fixed maturity date, but a savings account doesn't.
D. There's less risk of losing money held in an investment account than in a savings account.
Answers
Answer:
B
Step-by-step explanation:
Money invested in stock or something else has the potential to grow exponentially (at the risk of losing most of it) vs money in the bank will grow very slowly and may not even keep up with inflation making it worth less than it used to be.
mayam bought potato chips to school she share 1/4 of her chips with friends and 1/8 of her chips with her teacher how many has she shared in all?
Answers
[tex]\huge\underline\mathtt\colorbox{cyan}{3/8}[/tex]
[tex]\huge\mathsf\colorbox{white}{}[/tex]
Step-by-step explanation :Total shared part:
1/4 + 1/8
Taking LCM and adding:
2/8+1/8
Adding gives:
3/8
Helppp for a math exammm
Answers
Answer:
d.
Step-by-step explanation:
Robin is making floral arrangements for a party. Each arrangement has 8 roses and 10 carnations. Each carnation costs $0.75 and each rose costs $1.85. Which expression represents the total cost for one arrangement? A 8 + 10 + (0.75 + 1.85) B (8 + 0.75)(10 + 1.85) C 10(0.75) + 8(1.85) D 8(0.75) + 10(1.85)
Answers
Full explanation and answers on these 2 questions please. Also only answer if u know what ur doing.
Answers
Step-by-step explanation:
Q3
25 - (x-8)²/4 = [100 - (x-8)²]/4
[100 - (x²- 16x + 64)]/4
(100 - x² + 16x - 64)/4 = (-x² + 16x + 36)/4
(36 + 16x - x²)/4 = (36 - 2x + 18x - x²)/4
[2(18 - x) + x(18 - x)]/4 = [(2 + x)(18 - x)]/4
....proved
Q4
3(ax + 7) - 2(x + b) = 4x + 29
expanding,
3ax + 21 - 2x - 2b = 4x + 29
3ax - 2x + 21 - 2b = 4x + 29
Comparing terms; x terms,
3ax - 2x = 4x
3a - 2 = 4
3a = 6
a = 6/3
a = 2
constant terms,
21 - 2b = 29
21 - 29 = 2b
2b = -8
b = -8/2
b = -4
.... proved
Hi can someone please send me answers?
Answers
Answer:
61 campers will focus on hockey.
Step-by-step explanation:
86+53=139
139-200=61
Function h gives the height of a tennis ball, in feet, t seconds after it is tossed straight up in the air. The equation h(t) = -16t2 +12t+10 defines function h
Answers
See picture attached
Sebastian said that if a number is a perfect square. then the number is even. Provide two examples that show that the statement is false.
Answers
Below!
Step-by-step explanation:You can take 25 as one example and 49 as the second example.
Let's factorize.
=> 25 = 5 x 5 = 5² (Which is odd)=> 49 = 7 x 7 = 7² (Which is odd)Conclusion:Hence, the statement is not true.
Hoped this helped.
SOMEONE PLEASE HELP QUICKLY
A commercial claims that 8 out of 10 dentists recommend a certain brand of toothpaste. To test this claim, a random sample of 85 dentists is obtained. Of these 85 dentists, 73 indicated that they recommend that brand of toothpaste. Using a significance level of 5%, test the claim to see if the proportion of dentists who recommend this toothpaste is not 8 of 10.
a) State the null and alternative hypotheses
b) State the p value
c) Make a conclusion about the claim
Answers
Answer:
rgb
Step-by-step explanation:
wrtbtrb
a) The null hypothesis is: p = 0.8 and the alternative hypothesis is p ≠ 0.8.
b) p-value is 0.0838
c) We accept the null hypothesis
What are null and alternative hypothesis?The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
What is p-value?A p-value is a statistical measurement used to validate a hypothesis against observed data.
a. Let p be the proportion of 8 out of 10 dentists.
The null hypothesis is
[tex]H_0 : p=\frac{8}{10}=0.8[/tex]
The alternative hypothesis is
[tex]H_1:p\neq 0.8[/tex]
b. The sample proportion [tex]\hat p=\frac{73}{85}\approx 0.86\\[/tex]
Z-score, the test statistic is
[tex]Z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}}{n} } \\\\Z=\frac{0.86-0.8}{\frac{\sqrt{0.8(1-0.8)}}{85} }\\ \\Z=\frac{0.06}{0.043386}\\ \\Z=1.3829\\\\Z\approx 1.38[/tex]
P(Z > 1.38) = 1 - P(Z < 1.38)
∴ P(Z > 1.38) = 1 - 0.9162 = 0.0838
p-value is 0.0838
c. Since the p-value is greater than the level of significance α=0.05, we reject the alternative hypothesis and accept the null hypothesis
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graph y + 2 = -3/4 (x+4)
Answers
Answer:
Use a website called desmos and type in y=-3/4(x+4)-2
Step-by-step explanation:
1) isolate y by subtracting 2 on both sides
y=-3/4(x+4)-2
Answer:
Clue: two points : (0,-5) ( 4 , -8)
Step-by-step explanation:
Look at the graph.
The equation of a line is given below.
2x + 5y = -5
Find the slope and the y-intercept.
Then use them to graph the line.
Answers
Answer:
y=-2/5x-1
Step-by-step explanation:
2x+5y=-5
Step 1: Add-2x to both sides.
2x+5y=-5
+-2 +-2
5y=-2x-5
Step 2: Divide both sides by 5.
5y ÷ 5 = -2x-5÷5
y=-2/5x-1
QUESTION 18 PLEASE HELP ME ASAPP
Answers
Answer:
constant over time
Step-by-step explanation: for every 3 cookies the cost goes up 2 dollars
How do you add fractions with a whole number? Please explain the rules of it too! To be marked as brainliest
Answers
9/4 = 21/4 therefore, 9/4 = 21/4
24/10 try to reduce the numerator and denominator by a common denominator 24/10 divided 2/2 = 12/5
16/2 divided 2/2 = 8/1 = 8
I hoped that help!<3
Find an equation in the form y=ax^2+bx+c for the parabola passing through the points.
(3,25) (1,3) (-5,-15)
Thanks for the help! :)
Answers
Answer: [tex]x^2+7.0x-5.0x[/tex]
Step-by-step explanation:
Help help help help math math
Answers
Step-by-step explanation:
Relation
Hope it correct!!!
Help me pleaseeeeeeeeeee
Answers
Carry learning!
Stay safe!
Last oneeee helpppp pleaseeeee
Answers
[tex]13-4x = 13 -4(-8) = 13 +32 = 45[/tex]
=> 13 - 4x
=> 13 - 4(-8) ..(when x = (-8))..
=> 13 - (-32) ..( (-) , (-) = + )..
=> 13 + 32
=> 45
_ _ _ _ _ _ _ _ _ _ _☆ Final Answer ☆45_ _ _ _ _ _ _ _ _ _ _☆- PhysicsMaths - ☆
Find the inverse of the function.
f(x) = x^3 - 3
Answers
5-x=3
Work out the value of 3x2
Answers
Answer:
No
Step-by-step explanation:
5-X=3
X=5+3
X=8
5-8=3
Charlie surveyed his class to determine favorite colors. By examining his results in this chart, which numbered choice represents the fraction of the class that
Color
Number of
Students
red
9
white
4
blue
10
green
8
listed blue as their favorite color.
Answers
Hey! I really need help with this question:
Giving out brainiest to best answer and 100 points. <3
Please help.
Question: How do I memorize words faster and better? And- how do I study faster and quicker?
Answers
Answer:
Idea one, if you want to memorize words fast and better, you can put part of it in your password of something and then try to log in to whatever you set the password on everyday. Idea two, if you want to study fast and quicker you need to spend big half of the day learning what you need to learn and reading books.
Hope this helps!
The best way I could explain this is that everyone has there own pace at doing things. Like me I learn very fast but I have to read over something to memorize them.
The only way I could say is that maybe take more notes and go over them everyday. It helped me a lot when I wanted to learn more and get better grades. Also another way is taking you time at first and when you get use to it you'll be able to read faster learn quicker but you have to go slow first to go fast.
Please hurry!! This assignment is almost due!!
Answers
Answer:
x = 23
Step-by-step explanation:
8x-27 = 7x-4
8x-7x = -4+27
x = 23
Help a brother out.ill give brainlist
Answers
[tex]\text{a. cm}^2\\\\\text{b. cm}^3\\\\\text{c. cm}\\\\\text{d. cm}^2\\\\\text{e. cm}^3\\[/tex]