Angles a and b are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of b if b < α. sin(7x − 15) = cos(3x + 5)
In order for the sine and cosine to be equal, the angles must be complementary
sin (7x-15) = cos (3x+5)
7x-15+3x+5 =90 (because sum of both angles a and b must be 90)
10x -10 = 90
10x = 100
x =10
One angle = 7x-15= 7*10-15 = 70-15 =55
Other angle = 3x +5 = 3*10+5 = 30+5 = 35
Since B is less than A, A = 55 degrees and B = 35 degrees
Since we need B, B = 35 degrees
(a) An angle measures 43 . What is the measure of its complement? (b) An angle measures 81 . What is the measure of its supplement?
The complement of a 43-degree angle is 47 degrees, and the supplement of an 81-degree angle is 99 degrees.
To find the complement and supplement of an angle, you need to subtract the given angle from specific values. For a complement, this value is 90 degrees, and for a supplement, it is 180 degrees.
(a) To find the measure of the complement of a 43-degree angle, you subtract the angle from 90 degrees:
90 degrees - 43 degrees = 47 degreesSo, the complement is 47 degrees.
(b) To find the measure of the supplement of an 81-degree angle, you subtract the angle from 180 degrees:
180 degrees - 81 degrees = 99 degreesTherefore, the supplement is 99 degrees.
Find the volume of each composite figure. Round to the nearest tenth
To calculate the volume of a composite figure, individual volumes of simple geometric shapes that make up the figure are calculated using dimensionally consistent formulas and then summed up to find the total volume.
Explanation:To find the volume of a composite figure, we must analyze each part of the figure separately and then combine their volumes. Volume is a measure of how much space an object occupies and for common shapes like cylinders, prisms, and cones, there are specific volume formulas. According to the information given, dimensionally consistent volume formulas would be those where volume is calculated by combining length measurements in such a way that the result has dimensions in cubic units. For example, for a cylinder, the volume is found by multiplying the area of the base by the height (V = πr²h), which is dimensionally consistent because it's the product of an area (with units squared) with a length (with a unit), resulting in units cubed, i.e., cubic units which represent volume.
For example, if we are to find the volume of a cylinder with a radius 'r' and height 'h', we would use the formula V = πr²h, where π is approximately 3.14159. If the radius is 2 cm, and the height is 5 cm, then the volume would be V = 3.14159 * (2²) * 5 cm³, which simplifies to V = 3.14159 * 4 * 5 cm³ = 62.8 cm³, after rounding to the nearest tenth.
As per the subject of composite figures, when the figure is made of multiple simple geometric shapes, we first find the volume of each part separately and then sum them all up to get the total volume of the composite figure. Understanding the dimensional analysis principles helps identify and correct potential errors in geometric formulas by ensuring that the dimensions on either side of an equation are consistent.
To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.
The formula to find the volume of a cube is V = s^3, where s is the length of the side. It is shown in the figure that the length is 8 feet. Substitute this into the formula to find the volume of the cube.
V = s^3
= (8 ft)^3
= 512 ft^3
The formula to find the volume of a cylinder is V = πr^2h, where "r" is the radius and "h" is the height of the cylinder. It is shown in the figure that the diameter of the cylinder is 8 feet and its height is 8 feet. However, we need the value of the radius, not the diameter. To find the radius, we will divide the length of the diameter by 2 since the radius is half the length of the diameter.
r = d/2
= 8/2
= 4 ft
We already solve the length of the radius. Substitute the length of the height and radius to the formula to find the volume of the cylinder.
Volume (V) = πr^2h = π(4 ft)^2(8 ft) = π(16 ft^2)(8 ft) = 128π ft^3
We have solved the volume of the cube, which is 512 ft^3, while the volume of the cylinder is 128π ft^3. To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.
V = V_cube - V_cylinder
V = 512 ft^3 - 128π ft^3
V = 109.9 ft^3
What is an equation for a sine curve with amplitude 2, and period 4pi symbolradians?
If someone runs 4 miles in 30 minutes how many will they run in 48 minutes
15 Points!
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
The dimensions of a rectangle has aa width of three more than three times its lenght.Find the dimensions if the area of the rectangle is 36m to the second power.
Helppp how do u do 34
The width of a rectangle is half the length. the perimeter of the rectangle is 54 in. what is the length of the rectangle?
The equation of the linear regression line represents the relationship between the number of cars washed for charity, x, and the amount earned for charity, y. yˆ=10x+20 How much money can the charity expect to earn if 50 cars come in for a wash?
a $3
b $20
c $720
d $520
By substituting 50 for x in the given linear regression equation, we find that the charity can expect to earn $520 if 50 cars come in for a wash.
The equation of the linear regression line given is y=10x+20, which represents the relationship between the number of cars washed for charity (x) and the amount earned for charity (y). To find how much money the charity can expect to earn if 50 cars come in for a wash, we substitute x with 50 in the equation: y = 10(50) + 20 = 500 + 20 = 520. Therefore, the charity can expect to earn $520 if 50 cars come in for a wash.
When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?
a. it is taller and narrower than the normal distribution.
b. there is no consistent relationship between the t distribution and the normal distribution.
c. it is almost perfectly normal.
d. it is flatter and more spread out than the normal distribution?
The surface inside the circles will be painted green. The surface outside the circles will be painted white. What is the ratio of green paint to white paint?
A. π : (4 - π)
B. (4 - π) : π
C. π : (π - 4)
D. π^2 : (4 - π^2)
Answer:
The ratio of green paint to white paint is A. [tex]\pi:(4-\pi)[/tex]
Step-by-step explanation:
To find the ratio of green paint to white paint we need to divide the surface that will be painted green by the surface that will be painted white.
In the graph we can see 4 equal circles. Let be ''R'' the radius of the circles.
We can also see a square. The side of the square is 4R (because the length of the side is 4 times the radius of any circle).
The surface of a circle which radius is ''R'' is equal to :
[tex]\pi .R^{2}[/tex]
The surface inside this 4 circles is equal to :
[tex]4.\pi .R^{2}[/tex]
The surface [tex]4.\pi .R^{2}[/tex] will be painted green.
The surface outside the circles is equal to [tex]4.\pi .R^{2}[/tex] subtracted to the area of the square.
The area of the square is :
[tex](4R)^{2}=16R^{2}[/tex] ⇒
[tex]16R^{2}-4.\pi.R^{2}[/tex] is the surface that will be painted white.
If we make the division between the surfaces :
[tex]\frac{GreenSurface}{WhiteSurface}[/tex] ⇒
[tex]\frac{4.\pi .R^{2}}{16R^{2}-4.\pi .R^{2}}[/tex]
[tex]\frac{(4R^{2}).\pi}{(4R^{2}).(4-\pi)}=\frac{\pi}{4-\pi}[/tex]
We find that the ratio of green paint to white paint is [tex]\pi:(4-\pi)[/tex]
A dog is standing 12 feet from a tree looking at a bird in the tree. the angle of elevation from the dog to the bird is 50°. how far above the ground is the bird? round to the nearest tenth of a foot.
a___ is a solid consisting of a polygon, a point not in the same plane as the polygon, and all points between them.
A pyramid is the correct answer
How do you find zeros when given a quadratic relation in vertex form
In order to find the zeros in a quadratic in vertex form, you need to follow a number of steps. They have been outlined for you along with a sample problem.
y = (x - 2)^2 - 16
After getting the original form, you can place a 0 in for y. In is where the graph will cross the x-axis, so it is where you will find both of your zeros.
0 = (x - 2)^2 - 16
Now take the constant and add it to both sides. In this equation, -16 is your constant. So, we'll add 16 to both sides to begin to solve.
16= (x - 2)^2
Now we can take the square root of both sides. After we do so, we take both the positive and negative version of what we get. This is because both 4 and -4 squared is equal to 16.
+/-4 = x - 2
Now we add 2 to both sides to get us what is left of x.
2 +/- 4 = x
Now that we have a final form such as this, we can separate and get two answers for our two zeros.
2 + 4 = 6
2 - 4 = -2
What is 15% of 60? Create a model to prove your answer.What is 15% of 60 ?
A density curve for all of the possible weights between 0 pounds and 1000 pounds is in the shape of a rectangle. What is the value of the density curve in this interval?
Answer:
The area under the curve is one.
Step-by-step explanation:
A density curve for all of the possible weights between 0 pounds and 1000 pounds is in the shape of a rectangle. What is the value of the density curve in this interval?
The area under the curve is one.
Reason
Lets draw an histogram. On the vertical axis is the frequency distribution. horizontal axis is the weights. the interval between the bars will be 1.
the height of the bars will be the frequency distribution.
we get the area of the bars by multiplying the bars width and height. add up all with the other weight.
we get 1
9 students ask to visit the counselor and each visit includes one student. how many ways can they be scheduled?
Please explain, not just answer!
given that f(x)=x^2+2x+3 and g(x)=x+4 over 3 solve for f(g(x)) when x=2
A jar of dimes and quarters is worth $4.55. If there are the same number of dimes as quarters, what is the value of only the dimes?
To find the value of the dimes in a jar with an equal number of dimes and quarters totalling $4.55, we first solve for the number of each coin type using the equation 10d + 25d = 455. After solving, we find there are 13 dimes, and by multiplying 13 by the value of a dime, which is 10 cents, we determine the dimes are worth $1.30.
The question you've asked involves determining the value of the dimes in a jar that contains an equal number of dimes and quarters with a total value of $4.55. Let's solve this step by step.
First, we need to establish the value of each coin type. A dime is worth 10 cents and a quarter is worth 25 cents. Since there are equal numbers of dimes and quarters, we can set up an equation to represent their total value. Let the number of dimes and quarters be represented by d. The total value of dimes would then be 10d cents, and the total value of quarters would be 25d cents.
The combined value of the dimes and quarters is 455 cents (since $4.55 is equivalent to 455 pennies). So, our equation would be: 10d + 25d = 455. Simplifying the equation, we get 35d = 455. Dividing both sides by 35 gives us d = 13. This means there are 13 dimes and 13 quarters in the jar.
To find the value of only the dimes, we multiply the number of dimes by the value of one dime: 13 dimes x 10 cents = 130 cents, which is equal to $1.30. Therefore, the value of only the dimes is $1.30.
Charlie walk 9 blocks to school after school he walked 3 blocks to soccer practice he walks 7 blocks back home how many total blocks did Charlie walk in one day
Answer:
19 blocks
Step-by-step explanation:
9+7=16
16+3=19
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).
A. –x^2 + 2x – 6
B. –x^2 + 2x + 8
C. x^2 – 2x – 8
D. 2x^2 – 15
alyssa wants to build a fence around her garden to keep deer and rabbits out. the length of the fence must be at least 50 ft, but she only has 140 ft for entire perimeter
Alyssa must design a fence within a 140 ft perimeter to keep out deer and rabbits, requiring heights and depths appropriate for each animal. She may use a combination of high electric fencing for deer and buried hardware cloth for rabbits, being mindful of her perimeter constraint.
The student, Alyssa, needs to build a fence around her garden and requires the length to be at least 50 ft with a total available perimeter of 140 ft. To keep deer and rabbits out, she might consider different fence designs.
For preventing deer from entering, it's suggested to use electric fencing at least 8-10 feet tall or two parallel fences that are about 4 feet high and spaced 3 feet apart.
For rabbits, a two-foot high fence made of hardware cloth or chicken wire should be used, extended at least five inches below the ground. This will discourage rabbits from digging under the fence and protect the garden effectively.
Since Alyssa has a limited amount of fencing material, she will need to calculate the perimeter carefully to maximize the enclosed area while keeping within the 140 ft limitation. She might use lengths of sides that meet her minimum requirement and stay within her total available perimeter.
Add. Express your answer in simplest mixed-number form.
2 3/4 + 4 3/4
A dog chases a squirrel. The dog is originally 200 feet away from the squirrel. The dog’s speed is 150 feet per minute. The squirrel’s speed is 100 feet per minute. How long will it take for the dog to get the squirrel?
How do you do it????
What are the coordinates of the point that corresponds to -7x/4 on the unit circle
An event that is made up of two or more outcomes is called.....
let f(x)=x*2+2x-1 and g(x)=2x-4 find 2f(x)-3g(x)
Composite functions involve combining more than one functions
The value of 2f(x) - 3g(x) is [tex]2x^2 -2x-+ 10[/tex]
We have:
[tex]f(x) = x^2 + 2x - 1[/tex]
[tex]g(x) =2x - 4[/tex]
The value of 2f(x) - 3g(x) is calculated as follows:
[tex]2f(x) - 3g(x) = 2 \times f(x) -3 \times g(x)[/tex]
Substitute the values of f(x) and g(x)
[tex]2f(x) - 3g(x) = 2 \times (x^2 + 2x -1) -3 \times (2x - 4)[/tex]
Open brackets
[tex]2f(x) - 3g(x) = 2x^2 + 4x -2 -6x + 12[/tex]
Collect like terms
[tex]2f(x) - 3g(x) = 2x^2 + 4x -6x-2 + 12[/tex]
[tex]2f(x) - 3g(x) = 2x^2 -2x-+ 10[/tex]
Hence, the value of 2f(x) - 3g(x) is [tex]2x^2 -2x-+ 10[/tex]
Read more about composite functions at:
https://brainly.com/question/19695569
Your favourite Tv station has ten minutes of commercials per hour. What is the expected number of times you could randomly select this channel without hitting a commercial?
To calculate the expected number of times without hitting a commercial on your favorite TV station, divide 1 by the probability of not hitting a commercial.
Explanation:To calculate the expected number of times you could randomly select this TV station without hitting a commercial, we need to find the probability of not hitting a commercial in one selection. Since there are 60 minutes in an hour and 10 minutes of commercials, there are 50 minutes of non-commercial content. Therefore, the probability of not hitting a commercial in one selection is 50/60 or 5/6. To find the expected number of times without hitting a commercial, we can use the formula:
Expected number = 1 / Probability of not hitting a commercial
Expected number = 1 / (5/6) = 6/5 = 1.2 times
Learn more about probability here:https://brainly.com/question/22962752
#SPJ11
Answer:
5
Step-by-step explanation:
Reword the question: "Select this channel without hitting a commercial" = "How many selects until hitting a commercial"
Success (p) = hit
Failure (q) = no hit
p (probability of hitting a commercial): 10/60
q (probability of not hitting a commercial): 50/60
E(x) = q/p
E(x) = 50/60 / 10/60
E(x) = 5
Therefore, five selects without hitting a commercial