true or false.
The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. ...?
Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether he following statement is true or false :
"The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. "
Let us consider the right-angled triangle ABC as shown in the attached figure below.
With respect to acute angle C, we can see that
perpendicular, p = AB
base, b = BC
and
hypotenuse, h = AC.
We know that
sine of an angle in a right-angled triangle is equal to the ratio of the perpendicular to the base.
So, we must have
[tex]\sin \angle C=\dfrac{p}{h}\\\\\\\Rightarrow \sin \angle C=\dfrac{AB}{AC}.[/tex]
Since AB is the opposite side to angle C, not adjacent, therefore
sine of any angle in a right-angled triangle is the ratio of the length of the OPPOSITE SIDE to length of the hypotenuse.
Thus, the given statement is FALSE.
Final answer:
The statement is false; sine is the ratio of the opposite side to the hypotenuse, not the adjacent side to the hypotenuse.
Explanation:
The statement is false. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse, not the adjacent side to the hypotenuse. Therefore, the sine of angle A would be expressed as sin(A) = opposite/hypotenuse. The ratio of the adjacent side to the hypotenuse, on the other hand, defines the cosine of the angle, which is cos(A) = adjacent/hypotenuse.
(4x+20)+(x-10)=180 how do you solve this?
Verify the identity.
tan^5x = tan^3xsec^2x -tan^3x
What can you say about the end behavior of the function f(x)= 5x-3x+332
Answer:
B.
The leading coefficient is positive so the left end goes down.
done
C.
f(x) is odd so both ends go in opposite directions.
Step-by-step explanation:
APEX
FIND MISSING ANGLES
D1=
D2=
D3=
D4=
D5=
D6=
How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8 percent compounded annually? $117,817.20 or $454,144.00 or $112,817.20 or $549,144.
Please help
F(x)=x^2 +1, g(x)=5x how to solve
You need to have at least $100 in your checking account to avoid a low balance fee. You have $247 in your account, and you make withdrawals of $20 per week. What are the possible numbers of weeks that you can avoid paying the fee? Solve this problem using two different methods. PLEASE HELP
7 WEEKS is how long you can last.
First off, you need at least $100 in your account to avoid the fee and you currently have $247. With that being said, you're taking out $20 every week.
The first thing you can do would be to start at $147 (since that's $100 less than what you can use) and divide that by 20 (since that's what you're taking out every week) 147 / 20 = 7.35. That's 7 weeks because you have to round down to the nearest whole number.
Second What you can do to find how many weeks you can take this out by starting at $100 and adding $20 for every week. So 120, 140, 160, 180, 200, 220, 240. This also gives you 7.
You can take $20 out of your account for 7 WEEKS until you have to pay the low-balance fee.
May I have brainliest please? :)
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division
The possible number of weeks to withdraw avoiding the low balance fee is 7 weeks.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total amount in account = $247
Amount withdrawals per week = $20
Amount needed in account to avoid low balance fee = $100
The possible number of weeks to withdraw avoiding the low balance fee:
= (247 - 100) ÷ 20
= 147÷ 20
= 7.35
This means 7 weeks.
Thus,
The possible number of weeks to withdraw avoiding the low balance fee is 7 weeks.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
James is no longer able to feel the same effect from his drug of choice with his regular dose; he needs to increase the amount of the drug to feel the desired effect this demonstrates this demonstrates
a.withdrawal
b. tolerance
c. adjustment
d. intolerance
Which statement describes the graph of f(x) = 4x2 + 20x + 25?
The graph does not intersect the x-axis.
The graph touches the x-axis at (–2.5, 0).
The graph intersects the x-axis at (–0.4, 0) and (0.4, 0).
The graph intersects the x-axis at (2, 0) and (5, 0).
The graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0)
Graph of a quadratic functionThe given function is f(x) = 4x² + 20x + 25
The table of values for the function from -1 to -4 is
x -1 -2 -3 -4
f(x) 9 1 1 9
The graph of the function is attached below
From the graph, we can observe that the graph touches the x-axis at the point (-2.5, 0)
Hence, the graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0).
Learn more on Graph of a quadratic function here: https://brainly.com/question/13724583
Write 1 ft. 7 in. in inches.
a girl has a coloring book with 60 pages in it. she uses 5 pages every 3 days. How many days will it take her to finish the coloring book?
Im totally lost! A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon 14 of a contemporary living sample. Estimate the age of the sample ...?
Final answer:
The sample from the refuse deposit near the Strait of Magellan, with 60% carbon-14 remaining compared to a contemporary living sample, is estimated to be approximately 7777 years old, based on the known half-life of carbon-14 being 5730 years.
Explanation:
The age of a sample can be estimated using radiocarbon dating, which measures the decay of carbon-14 (14 C). Since the half-life of 14 C is known to be approximately 5730 years, we can use this information to estimate the age of the sample. Radiocarbon dating works on the principle that living organisms continually replenish carbon while alive, maintaining a constant level of 14 C relative to 12 C. When an organism dies, it no longer absorbs carbon, and the 14 C begins to decay at a known rate.
In the case of the refuse deposit near the Strait of Magellan, the sample had 60% of the carbon-14 of a contemporary living sample. To determine the age, we use the half-life formula, which is Time = Half-life / log2 (Starting amount / Remaining amount). Here, starting amount is 100% (contemporary living sample), the remaining amount is 60%, and the half-life is 5730 years.
So the calculation will be: Age of sample = 5730 / log2 (100/60). Calculating this, we get:
Age of sample = 5730 / log2 (1.6667)
Age of sample = 5730 / 0.737
Age of sample ≈ 7777 years
Thus, the sample from the refuse deposit near the Strait of Magellan is estimated to be approximately 7777 years old.
lizzy is tiling the kitchen floor for the first time. she had a tough time at first and placed only 5 tiles the first day. she started to go faster, and by the end of day 4 she had places 35 tiles. she worked at a steady rate after the first day. use an equation in point slope form to determine how many days lizzy took place all of 100 tiles needed to finish the floor
Answer:
10.5 days
Step-by-step explanation:
Point slope form
y-5=10(x-1)
Substitute for y
100-5=10(x-1)
Distribute the 10
100-5=10x-10
Combine like terms
95=10x-10
Add ten to both sides
105=10x
Divide by 10
X = 10.5
Mel Company has a net income, before taxes, of $95,000. The treasurer of the company estimates 45 percent of net income will have to be paid for federal and state taxes. The tax for both federal and state is: ...?
Jenny's Bakery sells carrot muffins for $2.00 each. The electricity to run the oven is $120.00 per day and the cost of making one carrot muffin is $1.40. How many muffins need to be sold each day for the bakery to break even?
Answer:
D. 200 muffins
Step-by-step explanation:
Break even is a condition where the total production cost is same as the profit produced. In this question, the carrot muffin cost is $1.4 and sold at $2. Then the profit for every muffin should be: $2- $1.4= $0.6/muffin
The electricity cost is $120/day. Then to cover this cost, the muffin need to sold would be:
cost= muffin profit * muffin sold
$120= $0.6/muffin * muffin sold
muffin sold= $120 / ($0.6 / muffin)= 200 muffin
Simplify (x − 4)(x2 + 3x − 1).
A.x^3-x^2+11x+4
B.x^3-x^2-13x+4
C.x^3+7x^2+11x+4
D.x^3+7x^2-13x+4
Final answer:
To simplify (x - 4)(x^2 + 3x - 1), use the FOIL method to distribute each term and combine like terms, resulting in x^3 - x^2 - 12x + 4 (option B).
Explanation:
To simplify the expression (x − 4)(x2 + 3x − 1), we need to use the distributive property, also known as the FOIL method, which stands for First, Outside, Inside, Last. We will multiply each term in the first binomial by each term in the second binomial.
Multiply the first terms: x * x2 = x3.Multiply the outside terms: x * 3x = 3x2.Multiply the inside terms: (-4) * x2 = -4x2.Multiply the last terms: (-4) * (3x) = -12x.Multiply the last terms: (-4) * (-1) = 4.Combine like terms:
x3 + 3x2 - 4x2 - 12x + 4
Simplify the expression by combining 3x2 and -4x2:
x3 - x2 - 12x + 4
Therefore, the simplified form of the expression is x3 - x2 - 12x + 4, which corresponds to option B.
if sin theta =1/4, theta in quadrant II, find the exact value of cos[theta +pi/6]
The exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II is (-√(45) - 1)/8, found by using the Pythagorean identity and the angle sum identity.
To find the exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II, we can use trigonometric identities and properties of angles. First, we use the Pythagorean identity to find cos θ. Since θ is in the second quadrant, cos θ is negative and solving for cos θ gives cos θ = -√(1 - sin² θ) = -√(1 - (1/4)²) = -√(15)/4.
Next, we apply the angle sum identity for cosine, which is cos(α + β) = cos α cos β - sin α sin β. Using this identity, we find:
cos(θ + π/6) = cos θ cos(π/6) - sin θ sin(π/6) = (-√(15)/4)(√(3)/2) - (1/4)(1/2) = -√(45)/8 - 1/8 = (-√(45) - 1) / 8.
The two interior angles that are not adjacent to an exterior angle are called ________.
remote exterior angles
remote interior angles
alternate exterior angles
corresponding angles
Answer: Second option is correct.
Step-by-step explanation:
The two interior angles that are not adjacent to an exterior angle are called "Remote interior angles"
As remote interior angles are those interior angles that are inside the are inside the triangle but opposite to the exterior angles.
Hence, Second option is correct.
What is the value of the expression when a = 4, b = 3 ,and c = 10? 3a4b−c
Answer:
9yb
Step-by-step explanation:
Five cards are randomly selected without replacement from a standard deck of 52 playing cards. what is the probability of getting 5 hearts? round your answer to four decimal places
The probability of getting 5 hearts from the deck of cards is 0.0962.
We need to find the probability of getting 5 hearts.
What is in a 52 deck of cards?A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suite contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
P(E)=Number of favourable outcomes/Total number of outcomes.
Now, P(E)=5/52=0.0962
Therefore, the probability of getting 5 hearts from the deck of cards is 0.0962.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ2
If Tucson's average rainfall is 12 1/4 and Yumas is 2 3/5 inches, how much more rain, on an average does Tucson get? ...?
Answer:
[tex]9\frac{13}{20}\text{ inches}[/tex]
Step-by-step explanation:
Given,
Tucson's average rainfall = [tex]12\frac{1}{4}\text{ inches}=\frac{49}{4}\text{ inches}[/tex]
Also, Yumas's average rainfall = [tex]2\frac{3}{5}\text{ inches}=\frac{13}{5}\text{ inches}[/tex]
Difference between Tucson's average rainfall and Yumas's average rainfall
[tex]=\frac{49}{4}-\frac{13}{5}[/tex]
[tex]=\frac{245-52}{20}[/tex]
[tex]=\frac{193}{20}[/tex]
[tex]=9\frac{13}{20}[/tex]
Hence, Tucson gets [tex]9\frac{13}{20}[/tex] inches more rainfall.
Proportion is ________________
Proportion is a mathematical concept that describes the relationship between two or more quantities. It is often represented using ratios and can be used to solve for unknown values, scale measurements, and interpret data.
Explanation:Proportion is a mathematical concept that describes the relationship between two or more numbers or quantities. It is a way of expressing that one quantity is equal to another quantity, or that one quantity is a fraction or multiple of another quantity. Proportions can be represented using ratios, which compare the relative sizes of different quantities.
For example, if we have two ratios, such as 1:2 and 3:6, we can determine if they are proportional by cross-multiplying and checking if the products are equal. In this case, 1 × 6 = 2 × 3, so the ratios are proportional.
Proportions are used in many different areas of mathematics, such as solving for unknown values, scaling up or down, and interpreting data. They are also used in real-world applications, such as finding the missing side length of a similar triangle or calculating the unit price of a product.
What is 528−−√+63−−√528+63 in simplest radical form?
Answer: [tex]13\sqrt{7}[/tex]
Step-by-step explanation:
In the simple radical form there are no square root is remain to find.
Since, the given expression,
[tex]5\sqrt{28} + \sqrt{63}[/tex]
[tex]5\sqrt{4\times 7} + \sqrt{9\times 7}[/tex]
[tex]5\sqrt{4} \times \sqrt{7} + \sqrt{9}\times \sqrt{7}[/tex]
[tex]5\times 2 \times \sqrt{7} + 3\times \sqrt{7}[/tex]
[tex]10 \sqrt{7} + 3\sqrt{7}[/tex]
[tex](10 + 3)\sqrt{7}[/tex]
[tex]13\sqrt{7}[/tex]
Since, we do not need to find further square root of 7.
Thus, the required radical form of [tex]5\sqrt{28} + \sqrt{63}[/tex] is [tex]13\sqrt{7}[/tex].
Answer:
[tex]13\sqrt{7}[/tex]
Step-by-step explanation:
[tex]5\sqrt{28} +\sqrt{63}[/tex]
To simplify the given expression we simplify each radical
[tex]5\sqrt{28} = 5\sqrt{4*7} = 5*2\sqrt{7} =10\sqrt{7}[/tex]
[tex]\sqrt{63} = \sqrt{9*7} =3\sqrt{7}[/tex]
[tex]5\sqrt{28} +\sqrt{63}[/tex]
[tex]10\sqrt{7}+3\sqrt{7}[/tex]
[tex]13\sqrt{7}[/tex]
2 1/2 divided by 4. can you please answer i need help
Answer:
5/8
Step-by-step explanation:
What is 666 divided by 22?
Answer:
30.27272727272727 and repeating.
Step-by-step explanation:
The hu family goes out for lunch and the price of the meal is $45 the sales tax on the meal is 6% and the family also leaves a 20% tip on the pre-tax amount what is the total cost of the meal ?
The first step in solving 7/8 = 3x - 5/11 is to subtract 5/11 from both sides of the equation.
True
False
Answer:
false
Step-by-step explanation:
<3
If Martha earns $6.50 per hour for babysitting, how much will she earn in: 1.5 hours? 2.5 hours? 3.5 hours?
Martha earns $6.50 per hour, so for 1.5 hours, she will earn $9.75; for 2.5 hours, she will earn $16.25; and for 3.5 hours, she will earn $22.75. We simply multiply her hourly wage by the number of hours to find the total earnings for each duration.
If Martha earns $6.50 per hour for babysitting, we can find out how much she will earn for different numbers of hours by multiplying her hourly rate by the number of hours worked.
For 1.5 hours: $6.50 * 1.5 = $9.75For 2.5 hours: $6.50 * 2.5 = $16.25For 3.5 hours: $6.50 * 3.5 = $22.75As a result:
Martha will earn $9.75 for 1.5 hours of babysitting.Martha will earn $16.25 for 2.5 hours of babysitting.Martha will earn $22.75 for 3.5 hours of babysitting.
The ratio of trumpet players to tuba players at a high school is 5:2 Which statement is true?
A.2/5 of the total tuba and trumpet players are tuba players.
B.The number of trumpet players is 2.5 times the number of tuba players.
C.There are 2 trumpet players for every 5 tuba players.
D.If there are a total of 100 trumpet and tuba players, 52 of them are tuba players.
The correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.
Let's analyze each statement and determine which one is true:
A. "2/5 of the total tuba and trumpet players are tuba players."
To find out if this statement is true, we need to determine what portion of the total number of players are tuba players. Since the ratio of trumpet players to tuba players is 5:2, for every 5 + 2 = 7 players, 2 are tuba players. So, the proportion of tuba players is 2/7, not 2/5. Therefore, Statement A is false.
B. "The number of trumpet players is 2.5 times the number of tuba players."
According to the given ratio, for every 5 trumpet players, there are 2 tuba players. Thus, the number of trumpet players is indeed 2.5 times the number of tuba players. Therefore, Statement B is true.
C. "There are 2 trumpet players for every 5 tuba players."
This statement matches the given ratio, so it is true. However, it doesn't provide any additional information beyond what's already given in the initial problem.
D. "If there are a total of 100 trumpet and tuba players, 52 of them are tuba players."
To verify this statement, we can calculate the number of tuba players using the given ratio. Since the total ratio parts is 5 (trumpet) + 2 (tuba) = 7, and the total number of players is 100, we can find the number of tuba players as (2/7) * 100 = 28. Thus, Statement D is false.
Therefore, the correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.