Given tanθ = 4/3 and sin θ =-4/5, based on the Pythagorean identity the cos θ is 3/5.
How do we find the values of cos θ?The sine, cosine, and tangent of an angle are related by the Pythagorean identity sin²(θ) + cos²(θ) = 1.
This means we can solve for cosine given the sine value:
cos²(θ) = 1 - sin²(θ)
We know that sin(θ) = -4/5, so:
cos²θ) = 1 - (-4/5)²
cos²(θ) = 1 - 16/25
cos²(θ) = 9/25
Taking the square root of both sides,
we find that cos(θ) could be ±3/5.
However, we need to consider the quadrant in which theta is located. Since the tangent of theta is positive (4/3) and the sine of theta is negative (-4/5), theta must be in the fourth quadrant (where sine is negative and tangent is positive). In the fourth quadrant, cosine is positive.
Therefore, cos(theta) = 3/5.
Find more exercises on Cosine;
https://brainly.com/question/14360720
#SPJ6
A gift box in the shape of a cube has a volume of 216 cm3 . What is the area of the base of the box
The area of the base of a cube with a volume of 216 cm³ is 36 cm², obtained by first calculating the side length as the cube root of the volume and then squaring that length.
The volume of a cube is calculated by raising the length of one of its sides to the third power (Volume = s³), where s is the length of a side. Given that the volume of the gift box is 216 cm³, we can find the length of a side by taking the cube root of the volume. The cube root of 216 cm³ is 6 cm, which is the length of each side of the box.
Since the base of the cube is a square, the area of the base is simply the length of a side squared (Base Area = s²). Hence, the area of the base of the box is 6 cm × 6 cm, which equals 36 cm².
Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ?
A. The graph of g(x) is the graph of f(x) translated 7 units left.
B. The graph of g(x) is the graph of f(x) translated 7 units up.
C. The graph of g(x) is the graph of f(x) translated 7 units right.
D. The graph of g(x) is the graph of f(x) translated 7 units down.
The statement which correctly describes the relationship between graphs related as g(x)=f(x−7) is; Choice C {The graph of g(x) is the graph of f(x) translated 7 units right}
According to the question; g(x)=f(x−7).
In essence, for every value of x on the graph (g), the value of x on the graph (f) reduces by 7.Put differently; for every value of x on the graph (f), the value of x on the graph (g) increases by 7.However, In graphs: an increase on the x axis is depicted by a movement rightward on the number line.
Therefore, if the relation g(x)=f(x−7) holds;
The graph of g(x) is the graph of f(x) translated 7 units right.
Read more:
https://brainly.com/question/11916980
power negative a b to the third power minus AC if a equals -2 and b equals 3 and C equals negative 8
[tex]\(-ab^3 - ac = 38\)[/tex].
To evaluate the expression [tex]\(-ab^3 - ac\)[/tex] given a = -2, b = 3, and c = -8, we substitute the values into the expression:
[tex]-ab^3 - ac = -(-2)(3)^3 - (-2)(-8)\\= -(-2)(27) - (16)\\= 54 - 16 \\= 38[/tex]
log4 (x - 7) = 3
solve for x
I am so stuck please explain to me how to do this. If you can do this, please do!
Directions: Write each decimal as a fraction or a mixed number.
10.9
00.8
4.125
0.0075
8.016
0.055
grace has 2 cups of strawberries and plans to divide this amout into equal parts to make 3 strawberry pies what fracion of a cup of strawberries will be used for each pie?
George ran 1.1 miles, took a break, and then ran 2.1 more miles. How many meters did George run in all?
plz help me on this question
Evaluate. (1/4)^-2 - (5^0×2)×1^-1
help me please,it will be greatly appreciated
which numbers represents a repeating decimal -2/5, -7, 3/9, 11/12
9n+21−3n−24 simplify
A bar of copper has a mass of 216 g and a volume of 24 cm. what is the density of copper
The density of copper bar is 9g/cm³
Given that :
Mass of copper bar = 216 g
Volume = 24 cm
Density of copper will be :
Recall :
Density = Mass / Volume
Density = 216 g / 24 cm³
Hence, Density of copper bar = 9 g/cm³
Learn more : https://brainly.com/question/18112348
A weight of 15 ounces stretches a spring 10 inches. A weight of 24 ounces stretches the same spring 16 inches. How many inches does the spring stretch per ounce of additional weight?
The spring stretch 0.6 inches per ounce of additional weight.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A weight of 15 ounces stretches a spring 10 inches.
∴ Inches increase of the spring per ounce of weight is the total increase in length divided by the total weight,
= (10/15) inches.
= 0.6 inches of increase in length per ounce.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ5
What does 5/9-2/3x(-1/4)=
Write these portions as percents.
A) 3 tenths and 6 hundredths.
B) 8 hundredths
C) 17 hundredths
D) 11 tenths.
the quotient of eight and a number h is written as
HURRY MATH QUESTION DOWN BELOW
Given f(x)= -4x+7, find f(1)
It costs a family $216 to refinish a wood floor. They want to refinish floor in a larger room. The ratio of corresponding sides is 3:4. How much would it cost to refinish wood floor in the larger room?
A) $396
B) $384
C) $262
D) $288
The cost for the larger room comes out to be $384. Option B) is the correct answer.
The cost of refinishing a wood floor in a room is related to the area of the floor. Since the ratio of the corresponding sides of the two rooms is 3:4, the ratio of their areas is the square of the ratio of the sides, being 9:16 (since 32 = 9 and 42 = 16). To find the cost to refinish the larger room, we can set up a proportion where $216 corresponds to an area with a 'weight' of 9, and x corresponds to an area with a 'weight' of 16.
Mathematically this can be represented as 216/9 = x/16. Solving for x, we calculate x = (216/9) imes 16 = 24 imes 16 = $384. Therefore, the cost to refinish the wood floor in the larger room would be $384, which corresponds to option B).
It cost to refinish wood floor in the larger room is $384. So option (b) is correct.
To solve this problem, we'll use the concept of ratios to find the cost of refinishing the wood floor in the larger room.
First, let's set up the ratio of the areas of the two rooms. Since the ratio of corresponding sides is 3:4, the ratio of their areas will be 3^2 : 4^2, which is 9:16.
Now, since the cost of refinishing the smaller room is $216, we need to find what portion of the total cost that represents. Since 9 parts represent $216, 1 part represents $216 ÷ 9 = $24.
Next, we'll find the total cost of refinishing the larger room. Since the larger room has 16 parts (as per the ratio), the total cost will be 16 parts × $24/part = $384.
So, the correct answer is B) $384.
Here's the detailed calculation:
Find the ratio of areas of the rooms: [tex]\(3^2 : 4^2 = 9 : 16\)[/tex]
Find the cost per part: (216 ÷ 9 = 24)
Find the total cost for the larger room: [tex]\(16 \times 24 = 384\)[/tex]
Simplify fully: √18 / √8
ms.Jackson and 3 of her friends went out for sushi. They order 6 rolls and 4 sodas. The soda is $3.75 less than the rolls. They spent a total of $70.50. What is the cost of one roll, Write and equation and solve.
Mr.hollins determines that he gives away $800 each month. If he gives away 16% of his budget, how much is his overall budget ?
8x+4(x-1) simplify the following expression
If 1 oz of potato chips contains 180 calories, how many ounces would contain 3,180 calories
In 17.66 ounces of chips, 3180 calories are there.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, 1 oz of potato chips contains 180 calories.
∴ No. of ounces of chips that contains 3180 calories can be obtained if we divide total calories by calories in 1 oz which is,
= (3180/180).
= 17.66 ounces.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ2
Rewrite as a square or a cube:
3 3/8 =_____
1 11/25=_____
Answer:
1)
3 3/8= (3/1) + (3/8)=
= (3x8)/8 + (3/8)
=(3x8 +3) / 8 putting both numbers with the same denominator
=27/8
27 is the same as 3³ 3x3x3= 27
8 is the same as 2³ 2x2x2= 8
= 3³÷ 2³
2)
1 11/25= (1/1) + (11/25)
= (25/25) + (11/25) putting both numbers with the same denominator
= (25+11)/25
=36/25
36 is the same as 6² 6x6=36
25 is the same as 5² 5x5=25
6²/5²
Read more on Brainly.com - https://brainly.com/question/6597610#readmore
Step-by-step explanation:
5d - 1 = -11
What is d?
Every day a zookeeper feeds 4 adult gorillas a total of 160 lb of food. At this rate HOW many pounds of food would the zookeeper need everyday to feed 6 adult gorillas
Emily has 300 books if Frank were to double the number of books that he now owns he would still have fewer than Emily has
Frank's current number of books, 'b', satisfies the inequality 2b ≤ 300, and hence, the maximum value for 'b' is 150.
1. Let's assume Frank currently owns 'b' books.
2. According to the given information, if Frank were to double the number of books he now owns, he would still have fewer books than Emily.
3. We know that Emily has 300 books. So, the inequality representing the given information is 2b ≤ 300.
4. To find the maximum value for 'b', we need to solve this inequality.
5. Dividing both sides of the inequality by 2, we get b ≤ 150.
6. This means Frank can own a maximum of 150 books in order to maintain a smaller collection than Emily's 300 books.
The detailed mathematical sentence representing this information is: Frank's current number of books, 'b', satisfies the inequality 2b ≤ 300, and hence, the maximum value for 'b' is 150.
Complete question:
Write a mathematical sentence that expresses the information given below. Use bas your variable name. If necessary: type < = to means or > = to mean . If you need to show multiplication, do not use the letter x. Use the asterisk (*) symbol instead, or simplify your answer. Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Wilbur went to the Halloween costume party at the Teen Center dressed as Romeo. Wendy was at the same party dressed as Juliet. As fate would have it, their eyes met across the crowded room, and they instantly fell in love. (Cheesy, right?) Unfortunately, they never got to talk to each other at the party and have been trying to find each other ever since! Wilbur went back to the Teen center 2 days after Halloween and goes back there every 13th day hoping to find his Juliet. Wendy went back to the Teen Center four days after Halloween and goes back there every 17th day looking for her beloved Romeo. When will they miss each other by just one day?
When will the meet?