20 Points
The length of the shorter leg of a 30-60-90 Special Right Triangle is 6 cm long. How long is the hypotenuse of the triangle?
Question 2 options:
63–√ cm
6 cm
12 cm
62–√ cm
Answers
Answer:
The answer is 12 cm.
Step-by-step explanation:
Verified by correct test results.
The length of the hypotenuse of the given right triangle would be 12cm.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.The sum of the angles of the triangle is equal to 180 degrees.∠A + ∠B + ∠C = 180°Given is that the length of the shorter leg of a 30-60-90 Special Right Triangle is 6 cm long.
The base length is the shortest distance of the right - angled triangle. We can find the hypotenuse using the cosine function as -
cos(60) = b/h
h ={b/cos(60)}
h = 6/(1/2)
h = 6 x 2
h = 12 cm
Therefore, the length of the hypotenuse of the given right triangle would be 12cm.
To solve more questions on triangles, visit the link-
https://brainly.com/question/2773823
#SPJ3
Related Questions
What is the surface area of this figure?
Enter your answer in the box.
ft²
Answers
Find Tan a and 10 B. Right each answer as a fraction and as I get decimal rounded to the nearest 10th.
Answers
Answer:
[tex]tanA=\frac{12}{20}\\\\tanB=\frac{20}{12}[/tex]
Step-by-step explanation:
[tex]tan(theta)=\frac{Opp}{Adj}[/tex]
Unless you want to solve for A and B plug that into inverse calculator.
A = tan^-1 ( 12/20 ) = 31°
A = 31.0°
B = tan^-1 ( 20/12 ) = 59.0°
B = 59.0°
HELP ASAP
What are the solutions to the following system of equations? 2x − y = 6 y = x2 − 9 (3, 0) and (−1, −8) (3, 0) and (4, 2) (−3, 0) and (−1, −8) (−3, 0) and (4, 2)
Answers
Answer:
I think so none
answer to the following steps below:-
I hope my answer helps.
[tex]$a+a r+a r^{2}+\ldots \infty=15$$a^{2}+(a r)^{2}+\left(a r^{2}\right)^{2}+\ldots \infty=150$. Find $a r^{3}+a r^{4}+a r^{6}+\ldots \infty$[/tex]
Options:
[tex](a) $\frac{1}{2}$\\(b) $\frac{2}{5}$[/tex]
Answers
Let
[tex]S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n[/tex]
where we assume |r| < 1. Multiplying on both sides by r gives
[tex]r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}[/tex]
and subtracting this from [tex]S_n[/tex] gives
[tex](1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}[/tex]
As n → ∞, the exponential term will converge to 0, and the partial sums [tex]S_n[/tex] will converge to
[tex]\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}[/tex]
Now, we're given
[tex]a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a[/tex]
[tex]a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}[/tex]
We must have |r| < 1 since both sums converge, so
[tex]\dfrac{15}a = \dfrac1{1-r}[/tex]
[tex]\dfrac{150}{a^2} = \dfrac1{1-r^2}[/tex]
Solving for r by substitution, we have
[tex]\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)[/tex]
[tex]\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}[/tex]
Recalling the difference of squares identity, we have
[tex]\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}[/tex]
We've already confirmed r ≠ 1, so we can simplify this to
[tex]\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15[/tex]
It follows that
[tex]\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12[/tex]
and so the sum we want is
[tex]ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}[/tex]
which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Please help I’m terrible at math!
Answers
Answer:
5) A - slope is positive, b = 0
6) D - slope is negative, b = 1, function is linear
7) D - b = 0
8) C - slope is negative, b = negative
Step-by-step explanation:
Hope this helps!
rena divides a square into 8 equal part. what unit fraction should she write as a label for each parts?
Answers
The unit fraction is 1/8
A unit fractions one with numerator being 1
She divide the square into 8 and took 1 part out
Hence is 1 out of 8 Represented mathematically as 1/8
If rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.
What is Fraction?A fraction represents a part of a whole.
Given that rena divides a square into 8 equal part.
A division is a process of splitting a specific amount into equal parts.
Let the whole square is divided into eight equal parts.
Which can be represented by 1/8.
Where the numerator 1 represents the whole and eight represents the parts.
The unit fraction for each part is 1/8 because the square is divided into 8 equal parts.
This means each part is one eighth of the whole.
Hence, if rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ2
Can I please get help I don’t know how to use the numbers on the front
Answers
18. Cancellation refers to the procedure for
A. reducing fractions to make multiplying easier.
B. inverting the divisor in a division problem.
C. changing a mixed number to an improper fraction.
D. finding the lowest common denominator for a group of fractions.
Answers
The correct option regarding the operation of cancellation in a fraction is given by:
A. reducing fractions to make multiplying easier.
What is an example of cancellation in a fraction?It happens when two fractions are multiplying each other, and terms are simplified to make the multiplication easier. For example:
[tex]\frac{2}{3} \times \frac{6}{4} = \frac{6}{3} \times \frac{2}{4} = 2 \times \frac{1}{2} = 1[/tex]
The terms 2 and 4, and 3 and 6, were canceled. Hence option A is correct.
More can be learned about cancellation in a fraction at https://brainly.com/question/571030
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Step-by-step explanation:
y - x = 4x (vertically opposite angles)
y = 5x
4x+ y+x = 180
5x+5x = 180
x = 18
y = 90
Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. C. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
Answers
The statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Function g is represented by the table.
x -1 0 1 2 3 4 g(x) 24 6 0 -2The line plotted with these data is shown below where y represent the g(x).
In this line,
X-intercept approaches negative infinity (-∞) to positive infinity (∞).Y-intercept approaches -2.426 to 24.86.Thus, the statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
Learn more about Function here:
https://brainly.com/question/5245372
#SPJ1
Need help DONT understand can someone answer
Answers
Evaluate Grace's new budget.
ОА. Her new budget should have money in every budget category, including debts and medical expenses
OB. Her new budget should have money in medical expenses because she does not know what medical problems she will
encounter in the future.
OC. Her new budget is fine because debts and medical expenses were not needed last month.
OD. Her new budget should have money in debts so that she can afford to go into debt if she has medical expenses.
Answers
let me know
Please help EDGINUITY 2022
Answers
Explanation:
6(103)= 618
618(5)= 3090
write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.
x-2
________
x^2+11x+28
Answers
Answer:
A/(x+7) +B/(x+4)
Step-by-step explanation:
The denominators of the partial fraction expansion are the factors of the denominator of the rational function.
__
Here, the rational function's denominator can be factored as ...
x² +11x +28 = (x +7)(x +4)
Then the form of the decomposition is ...
[tex]\dfrac{x-2}{x^2+11x+28}=\boxed{\dfrac{A}{x+7}+\dfrac{B}{x+4}}[/tex]
_____
Additional comment
Here, A=3. B=-2.
If the factors of the denominator have multiplicity greater than 1, then there is a fraction with each power of that factor up to the multiplicity. For example, if there is a factor (x+4)³, then the decomposition would include fractions A/(x+4) +B/(x+4)² +C/(x+4)³.
Which number is located between 1.2 and 1.4 on the number line
Answers
Researchers would like to assess the overall health of white pine trees in a state park. The park has a paved road that runs through the middle of the park. To select trees to assess for damage, the ranger parks at the side of the road and chooses 100 trees near the road to assess for damage. Which of the following statements best describes the bias that may arise from the results?
Because only 100 trees were selected, the overall damage of trees in the park may be underestimated.
The ranger should take another sample of trees near the road and compare it to the first sample to reduce bias.
Because a random sample of trees was chosen, the sample should provide a suitable estimate of the overall health of the trees.
Trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage of the trees.
Answers
Trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage to the trees.
What is a random sample space?The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive
Given, The ranger parks at the side of the road and chooses 100 trees near the road to assess for damage hence, trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage of the trees.
So, Consequently, the results can exaggerate the total amount of tree damage.
learn more about random samples here :
https://brainly.com/question/29852583
#SPJ6
Evaluate e^-1.6 round your answer to five decimal places
Answers
=> 0.20190
A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green.
After the deck is shuffled, the player is to choose the top card and note its color, replace
the card, shuffle the deck again, and then choose the top card again and note its color.
What is the probability that both cards selected are blue?
A.3%
B.2.25%
C.9%
D.6.25%
Answers
Answer:
B
Step-by-step explanation:
3/20x3/20=
15/100x15/100
The spinner at the right is spun. what is the probability to spin a blue or red? Write your
answer in simplest form
Answers
Answer: The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth.
Step-by-step explanation:
Reduce 1/4 to lowest terms14 is already in the simplest form. It can be written as 0.25 in decimal form (rounded to 6 decimal places). Steps to simplifying fractions find the GCD (or HCF) of numerator and denominator GCD of 1 and 4 is 1 divide both the numerator and denominator by the GCD1 ÷ 14 ÷ 1 reduced fraction: 14Therefore, 1/4 simplified to lowest terms is 1/4.
Find the value of (9/16) ^ - 1/2
Answers
Answer:
4/3
Step-by-step explanation:
Given:
[tex]\displaystyle \large{\left(\dfrac{9}{16}\right)^{-\dfrac{1}{2}}}[/tex]
From the law of exponent:
[tex]\displaystyle \large{a^{-\frac{1}{2}}=\dfrac{1}{\sqrt{a}}}[/tex]
Convert to the form above:
[tex]\displaystyle \large{\left(\dfrac{9}{16}\right)^{-\dfrac{1}{2}}=\dfrac{1}{\sqrt{\dfrac{9}{16}}}}\\\displaystyle \large{\left(\dfrac{9}{16}\right)^{-\dfrac{1}{2}}=\dfrac{1}{\dfrac{3}{4}}}\\\displaystyle \large{\left(\dfrac{9}{16}\right)^{-\dfrac{1}{2}}=\dfrac{4}{3}}[/tex]
Therefore, the solution is 4/3
A study of 110 students who had been awarded University scholarship showed that 40 worked part time jobs, 29 made the dean's list the previous semester and 16 both worked a part time job and made the dean's list the previous semester. What is the probability that a student worked a part time job or made the dean's list.
Answers
Answer:
i dont understand i need pic
On January 1, 2022 Hideki Matsuyama provides services in exchange for a $10,000 zero-interest bearing note due in 4 years. The effective interest rate for a note of this type is 15 percent. How much revenue does Hideki recognize on January 1, 2022?
Answers
Answer:
Revenue=$6000
Step-by-step explanation:
A = PRT
100
A= (10,000×4×15)/100
= (10,000×60)/100
= 600,000/100
=$6000
Hideki recognizes a $17,490.06 revenue.
What is Revenue?Revenue is the total amount of income generated by the sale of goods and services related to the primary operations of the business.
Given that on January 1, 2022, Hideki Matsuyama provides services in exchange for a $10,000 zero-interest bearing note due in 4 years, and the effective interest rate for a note of this type is 15 percent,
To determine how much revenue does Hideki recognize on January 1, 2022, the following calculation must be made:
x = 10000 x 1.15^4
x = 10000 x 1.749
x = 17490.06
Therefore, Hideki recognizes a $17,490.06 revenue.
Learn more about revenue in brainly.com/question/14695611
#SPJ3
8.5 hours in a day what total hours they work in a week
Answers
Answer:
8.5 hrs * 5 day work week = 42.5 hrs. But usually 0.5 hr per day is considered lunch and is usually not payed so theoretically the workweek is only 40 hrs per week (full time)
Step-by-step explanation:
At a concession stand, five hot dog(s) and four hamburger(s) cost $15.25, four hot dog(s) and five hamburger(s) cost $16.25. Find the cost of one hot dog and the cost of one hamburger
Answers
Answer:
0.45
3.25
Step-by-step explanation:
16.25 ÷ 5 = 3.25
15.25 - 3.25 × 4 = 2.25
2.25 ÷ 5 = 0.45
Check Answer:
3.25 × 5 = 16.25
0.45 × 4 = 2.25
3.25 - 2.25 = 1
16.25 - 1 = 15.25
~lenvy~
Find the value of b that would cause the graph of f(x)=b^x to look like the graph with points (0,1) and (2,25)
I am having trouble with this one.
Answers
[tex]f(x)=a(b)^x \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{0}~~,~~\stackrel{y}{1})\qquad 1=a(b)^0\implies 1=a~\hfill \underline{f(x)=1(b)^x} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{2}~~,~~\stackrel{y}{25})\qquad 25=1(b)^2\implies 25=b^2\implies \sqrt{25}=b\implies 5=b \\\\[-0.35em] ~\dotfill\\\\ f(x)=1(5)^x\implies \underline{f(x)=5^x}[/tex]
Please help! I will give Brainliest!!!
Here are 3 receipts for meals at the same restaurant. Fill in the missing values for each recipe.
Answers
(receipt one)
burger = 9
18% tip = 2.16
total with tip = 14.16
(receipt two)
salad = 8
total = 11
total with tip = 12.98
(receipt three)
salad = 8
water = 1.5
total = 9.50
18% tip = 1.71
Step-by-step explanation:
calculator
Martin is saving money to buy a new phone that costs $1,000 by selling trees. He is using an app to manage his
sales, but it keeps a fraction of each sale. His net pay is modeled by the function P(x) = x2 + 20x– 196, where x
represents the number of sales. How many sales does Martin need to make to earn $1,000?
Answers
Answer: 26 sales
Step-by-step explanation:
If you plug in 26 you will get exactly $1,000
Martin needs to sale 8 pieces to make it $1000.
How to elaborate the problem ?
Martin has to save $1000.
He is using an app to manage all the sales, but if keeps fraction of every sales.
The equation which represents his net pay is P(x)=[tex]x^{2}+20x-196[/tex]
How many sales does martin need ?We have to solve the given quadratic equation.
Here, x= (-b±[tex]\sqrt{ b^{2}-4ac }[/tex])/2a
⇒ x= (-20±[tex]\sqrt{400+4*196}[/tex])/2
⇒ x= (-20±[tex]\sqrt{1184}[/tex])/2
⇒ x= -10±[tex]\sqrt{296}[/tex]
⇒ x= -10±17.2
We habe to take the maximum value of x. So we neglect the negative sign.
Hence, x= -10+17.2 = 7.2 = 8 (approx) ,here we can not take 7 because if he sales 7 pieces then the money should less than $1000.
Learn more about Quadratic equation here :
https://brainly.com/question/27272153
#SPJ2
Find the area
(Explain)
Answers
Answer:
960 cm²
Step-by-step explanation:
Area of trapezoid: (a + b)(h)/2
A = (20 + 40)(32)/2
A = 60(32)/2
A = 1920/2
960 cm²
BRAINLIEST please if this helped!Determine the degree of the polynomial −57.
Answers
Answer:
zero (0)
Step-by-step explanation:
The degree of the polynomial -57 is zero (0).
Hope it helps you in your learning process.
Affordable Auto offered to enter people into a drawing for a free car if they shared the company's advertisement on social media. This table gives the total number of times the advertisement was shared since the promotion began. The data can be modeled by a quadratic function.
Length of promotion (days) 2 4 6 8 10 12
Number of shares 1200 3219 6240 10264 15290 21318
What function best models the data?
y=1.2x^2+20.6x+280
y=125.3x^2+183.3
y=1.2x^2+280
y=125.3x^2+257.8x+183.3
Answers
Answer:
D; y=125.3x2+257.8x+183.3
Step-by-step explanation:
I just took the test
have a good day! :)