Final answer:
To solve for angle B in triangle ABC, you can use the Law of Cosines. Rearrange the equation to isolate the cosine of angle B and then take the inverse cosine to find the value of angle B. The value of angle B is approximately 99.99 degrees.
Explanation:
To solve for angle B in triangle ABC, you can use the Law of Cosines. The Law of Cosines states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.
In this case, you are given the lengths of sides AB, BC, and AC as 4.1 cm, 2.7 cm, and 4.5 cm respectively. You are also given the equation 4.1 = 4.5 + 2.7 - 24.3cos B. To solve for angle B, you can rearrange the equation to isolate the cosine of angle B and then take the inverse cosine to find the value of angle B.
Let's go step-by-step:
Start with the equation 4.1 = 4.5 + 2.7 - 24.3cos B
Subtract 4.5 and 2.7 from both sides: 4.1 - 4.5 - 2.7 = -3.1 - 24.3cos B
Combine like terms: -3.1 - 24.3cos B = -7.1
Add 7.1 to both sides: -3.1 - 24.3cos B + 7.1 = -7.1 + 7.1
Simplify: -3.1 + 7.1 - 24.3cos B = 0
Subtract -3.1 + 7.1 from both sides: -3.1 + 7.1 - 3.1 + 7.1 - 24.3cos B = -3.1 + 7.1
Simplify: -24.3cos B = 4.0
Divide both sides by -24.3 to isolate cos B: (-24.3cos B) / -24.3 = 4.0 / -24.3
Simplify: cos B = -0.1645
Take the inverse cosine of -0.1645 to find the value of angle B: B = cos-1(-0.1645)
Using a calculator, you can find that angle B is approximately 99.99 degrees.
For every $4 Gillian makes, her friend Lucas makes $5.
Lucas makes $54,000 each year. How much does Gillian
make in a year?
Answer:
67500
Step-by-step explanation:
4-----54000
5-----x
4x=54000*5
x=67500
Answer:
43,200
Step-by-step explanation:
4/5=x/54000
(brainliest)Armando found the volume of the figure below by using the steps shown. A rectangular prism with a length of 18 inches, width of 5 inches, and height of 8 inches. A triangular prism with a base of 18 inches and height of 6 inches. The prism has a height of 5 inches. Total Volume = Volume of rectangular prism + volume of triangular prism = 5 (8) (18) + one-half (6) (18) (8) = 720 + 432 = 1,152 cubic inches. What mistake, if any, did Armando make? Armando determined the volume correctly. Armando used the wrong formula for the total volume. Armando used the wrong dimensions for the triangular prism. Armando did not apply the order of operations correctly.
Answer: Armando used the wrong dimensions for the triangular prism.
Step-by-step explanation:
Hi, to answer this question we have to analyze Armando’s work.
Total Volume = Volume of rectangular prism + volume of triangular prism
Total Volume = 5 (8) (18) + one-half (6) (18) (8)
Total Volume= 720 + 432
Total volume = 1,152 cubic inches.
He made a mistake in the second step, where used h=8 for the triangular prism instead of h= 5 . (h=height)
The correct way to solve this is.
Total Volume = 5 (8) (18) + one-half (6) (18) (5)
Total Volume= 720 + 270
Total volume = 990 cubic inches.
Answer:
Armando used the wrong dimensions for the triangular prism.
Step-by-step explanation:
A Ferris wheel has a radius of 20 feet and is rotating at a rate of 4 revolutions per minute. When t = 0 (measured in seconds), a chair at the lowest point on the wheel is 6 feet above the ground. Write a model for the height, h, of the chair as a function of time.
Answer:
the model for the height, h, of the chair at a function of time is [tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]
Step-by-step explanation:
To answer the question, we note that the height of the Ferris will varies proportionately to the angle of rotation, hence we can model the height according to he sine function as follows;
y = a·sin(b·x+c) + d
Where: a = Amplitude = Maximum displacement = r = 20 ft
or [tex]a = \frac{maximum - minimum}{2} = \frac{44 - 4}{2} = 20 \, ft[/tex]
The period, [tex]\frac{2\pi }{b}[/tex] = Time for one complete revolution, for a Ferris wheel making 4 revolutions per minute, we have
Period = 1 minute/4 = 15 seconds
Therefore, [tex]\frac{2\pi }{b}[/tex] = 15 seconds or [tex](b =\frac{2\pi }{15})[/tex]
d = the vertical shift is given by minimum + amplitude or maximum - amplitude = 6 + 20 = 26 ft
c = Phase shift since we want the chair to be at the minimum at t = 0 we put c = π/2
x = Independent variable, which in the case of the question is time, t
Therefore, the model for the height, h, of the chair at a function of time is as follows
[tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]
i.e. y = -20×sin(2π/15 + π/2) + 26.
Final answer:
To model the height of the chair as a function of time on a Ferris wheel, use the equation h(t) = 20 × cos((8π/60)t) + 6, where t is in seconds and h(t) is in feet.
Explanation:
To write a model for the height, h, of the chair as a function of time, t, for a Ferris wheel with a radius of 20 feet and a rotation rate of 4 revolutions per minute, we must consider the motion of the wheel. Since the Ferris wheel completes one rotation in 15 seconds (60 seconds/4 minutes), the chair's height above the ground will depend on the cosine of the angular position of the chair. Including the initial condition of the chair being 6 feet above the ground at its lowest point, the mathematical model will be:
h(t) = 20 × cos(ωt + ϕ) + 6
where angular velocity ω is calculated from the rotation rate (4 revolutions per minute) and phase shift ϕ accounts for the initial position. Since t = 0 corresponds to the lowest point, ϕ is 0 degrees or 0 radians (cos(0) = 1). The angular velocity in radians per second is:
ω = 2π × rotation rate = 2π × 4 / 60 = 8π/60 rad/s
Thus, the final equation for the height of the chair as a function of time is:
h(t) = 20 × cos((8π/60)t) + 6
where t is in seconds and h(t) is in feet.
What is the side length of a square with a perimeter of 80 meters?
The side length is
meters.
Answer:
20
Step-by-step explanation:
A square has four sides and if the perimeter is 80 then you divide the perimeter by four to find the length of each side
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Solve the equation:
5x + 65 = 25
What is the value of x
Answer: -8
Step-by-step explanation:
Answer:
x = -8
Step-by-step explanation:
If you multiply -8 by 5 you get -40. Then if you add 65 to -40 you get 25.
Hope this helps.
Factor the expression using the GCF.
60 – 36 =
Answer
12 (5 - 3)
Step-by-step explanation:
The greatest common factor is the largest number that will divide both numbers evenly. As an example, 6 is a common factor because it divides both 60 and 36. However, it is not the greatest common factor.
If I break 60 into it's prime factors, I would get 2 * 2 * 3 * 5.
If I break 36 into it's prime factors, I would get 2 * 2 * 3 * 3.
The two number have the factors, 2, 2, and 3 in common.
The greatest common factor is then: 2 * 2 * 3, or 12.
The expression can be factored as: 12 ( 5 - 3)
To factor the expression 60 - 36, we need to find the GCF of the numbers. The GCF is 12, so the factored form is 24.
Explanation:To factor the expression using the Greatest Common Factor (GCF) 60 - 36, we need to find the largest number that evenly divides both 60 and 36. The GCF of 60 and 36 is 12.
Therefore, we can rewrite the expression as 12 * (5 - 3). Simplifying further, we get 12 * 2 = 24.
So, the factored form of 60 - 36 is 24.
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Multiply the binomials (3x - 5) and (4x + 6).
A)
12x2 + 38x + 30
B)
12x2 + 38x - 30
C)
12x2 - 2x + 30
D)
12x2 - 2x - 30 PLS ANYONE ANSWER
Answer:
12x² - 2x - 30
Step-by-step explanation:
(3x - 5)(4x + 6)
12x² + 18x - 20x - 30
12x² - 2x - 30
The Multiplication of the binomials (3x - 5) and (4x + 6) will be 12x² - 2x - 30. Then the correct option is D.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The binomails are given below.
(3x - 5) and (4x + 6)
Multiply the binomials (3x - 5) and (4x + 6), then we have
⇒ (3x - 5) · (4x + 6)
⇒ 3x · (4x + 6) - 5 · (4x + 6)
⇒ 12x² + 18x - 20x - 30
⇒ 12x² - 2x - 30
The Multiplication of the binomials (3x - 5) and (4x + 6) will be 12x² - 2x - 30. Then the correct option is D.
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Need help please one this one
Answer: each triangle is 1/3 of the whole
Step-by-step explanation: If you add an upside down triangle to the two triangles below you would get the whole.
three triangles make that whole so one third of the whole is only one of the triangles.
(hope this helps)
In a standard 52−card deck, half of the cards are red and half are black. The 52 cards are divided evenly into 4 suits: spades, hearts, diamonds, and clubs. Each suit has three face cards (jack, queen, king), and an ace. Each suit also has 9 cards numbered from 2 to 10.
Dawn draws 1 card, replaces it, and draws another card. Is it more likely that she draws 2 black cards or 2 face cards?
It is more likely that she draws 2
cards.
Answer:
more likely she draws 2 face cards
Step-by-step explanation:
there is a 50% chance of drawing a black card because there are 26/52 black cards but there aee only 12/52 face cards
will give brainliest if answered correctly!!!
So the right answer is 13.
Look at the attached picture
Hope it will help you
Solve the equation for y: -8x + 4y = 20
21 Points
Answer:
y = 5 + 2x
Step-by-step explanation:
[tex]-8x+4y=20\\ 4y=20+8x\\ y=5+2x[/tex]
Add 8x on both sides
Divide by 4 on both sides
Simplify
The rate of collection by a solar panel decreased steadily throughout the day due to increasing cloud cover until it reached a constant amount. Later in the day, there were two short periods where the Sun appeared, only for the cloud cover to return.
Which graph models the amount of energy collected depending on the time since the cloud cover began?
ANSWER: B
Answer:
Second graph
Step-by-step explanation:
In the second graph we can see how the rate of collection decreases steadily at 0 < x < 7.5; at x = 7.5 it becomes constant; and later in the day, there were two short periods (about x = 12.5 and x = 22.5) where the rate of collection has two peaks.
y = 9x - 12. What is the slope of the equation?
Answer:
Step-by-step explanation:
the correct answer is the last option on the bottom
Answer:
Slope: 9 y-intercept (0,-12)
Step-by-step explanation:
y=mx+b
m is always the slope
b is always the y-intercept
y=9x-12
you can see 9 is m and -12 is b
Mr.Prieto wants to buy pizza that costs $14 each and 5 sodas for $2 each. He has $94. Write and solve an equation to find out how many pizzas he can buy.
Answer:
Mr. Prieto can buy 6 pizzas
Step-by-step explanation:
Cost of 5 soda's = 5 * 2 = $ 10
Remaining amount with him after buying 5 soda's= 94 - 10 = $ 84
Number of pizza's = Remaining amount/cost of 1 pizza
[tex]=\frac{84}{14}[/tex]
= 6 pizzas
Answer:
he can buy 6 pizzas
Step-by-step explanation:
5 x 2 = 10
94-10 = 84
84 divided by 14 = 6
he can buy 6 pizzas.
Can someone tell me what is 6=2(y+2)
Distribute the 2 through the parentheses
on the right side of the equation.
2(y) is 2y and 2(2) is 4.
So the problem now reads 6 = 2y + 4.
Now we can subtract 4 from both
sides of the equation to get 2 = 2y.
Now divide both sides of the
equation by 2 and 1 = y.
Answer:
the answer is attached to the picture
A student drove 9,500 miles in his car last year. Fixed costs totaled $1,215.
Variable costs totaled $1,985. What is the total annual cost? What was the
cost per mile? (Enter answer: $-----; $-----)
Answer: $7,81; $4.78 per mile
Step-by-step explanation:
To get the cost per mile we have to divide 9,500 by the cost.
(The total cost annual was $3,200)
9,500 divided by $1,215 = $7.81
9,500 divided by $1,985 = $4.78
I hope this helps!
A table is 3 feet wide. The length of the table can be adjusted as needed. You need at least 24 square feet of space on the table. Write and solve an inequality to represent the minimum length the table should have.
The minimum length of a table that is 3 feet wide to have at least 24 square feet of space is found by solving the inequality 3L ≥ 24, which results in a minimum length of 8 feet.
The question involves finding the minimum length of a table to achieve a certain area, which requires understanding and solving an inequality. Given that the table is 3 feet wide and we need at least 24 square feet of space, we can set up the inequality as follows:
Let L be the length of the table in feet.
The area A of a rectangle is calculated as A = length × width.
Thus, A = L × 3 square feet.
To satisfy the condition of having at least 24 square feet, we have the inequality 3L ≥ 24.
Dividing both sides by 3 to solve for L, we get L ≥ 8.
Therefore, the minimum length the table should have is 8 feet.
The net of a triangular prism is shown. Which measurement is closest to the total surface area of the triangular prism in square centimeters?
A
6 cm2
B
8 cm2
C
14 cm2
D
20 cm2
Answer:
is the anwser a?
Step-by-step explanation:
The total surface area of the triangular prism will be 14 square centimeter.
Option C is correct.
Total surface area :
From the given diagram of triangular prism,
It is observed that, The total surface area of the triangular prism will be the summation of area of two triangle and area of large rectangle.
Area of one triangle =(1/2)*3*2 = 3 square centimeters
So that, area of both triangle =2 * 3=6 square centimeters
Area of large rectangle=(2.5+3+2.5)*1=8*1=8 square centimeters
total surface area of the triangular prism =8+6=14 square centimeters
Therefore, total surface area of the triangular prism is 14 square centimeters.
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−3−4x≤21 pls help me
Answer:
-7x<21
i think, I'm not fully sure what it's asking.
Step-by-step explanation:
Answer:
x ≥ - 6
Step-by-step explanation:
Given
- 3 - 4x ≤ 21 ( add 3 to both sides )
- 4x ≤ 24
Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.
x ≥ - 6
The solution to an inequality is 5 ≤ = x < 9 What is the smallest value of x that will make the original inequality true? ___________.
Answer:
5 is indeed correct
Step-by-step explanation:
The smallest value of x will be 5 that will make the original inequality true.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The solution to an inequality is,
⇒ 5 ≤ x < 9.
Now,
Since, The solution to an inequality is,
⇒ 5 ≤ x < 9.
Hence, The value of x = { 5, 6, 7, 8 }
Thus, The smallest value of x = 5
Therefore, The smallest value of x will be 5 that will make the original inequality true.
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What is the value of x?
(Srº
The value of x of the missing angles is: 45
How to find the missing angle?
A linear pair of angles is a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary, which means their measures add up to 180 degrees.
Some properties of linear pairs of angles include:
The angles in a linear pair are adjacent.
Their non-common arms are opposite rays and form a straight line.
They together form a straight angle.
Two angles forming a linear pair have a common vertex and a common arm. Their non-common sides are opposite rays that form a line.
Thus:
3x + x = 180
4x = 180
x = 180/4
x = 45
The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their
sum?
A) 5 squared
B) 8
C) 20
D) 6
The magnitude of their sum is 6 units
ResultantThe formula for calculating the resultant vector is given as:
[tex]V=\sqrt{(\sum V_x)^2+(\sum V_y)^2}[/tex]From the given figure, the resultant is calculated as:
[tex]V=\sqrt{[(4cos45)+(2sin45)]^2+((4sin45)+2cos45)^2} \\V=\sqrt{[2\sqrt{2}+\sqrt{2}]^2 +[2\sqrt{2}+\sqrt{2}}]^2\\V=\sqrt{18+18} \\V= 6 units[/tex]
Hence the magnitude of their sum is 6 units
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If a vertical plane sliced a sphere, what would be the 2-D cross section?
square
rectangle
circle
triangle
I WILL MARK YOU THE BRAINLIEST OF YOU ANSWER FIRST PLS AND FAST!!
[Deleted Because Incorrect]
The equation for the graph obtained when the graph of y= 1/x is compressed vertically by a factor of 0.25, translated 4 units right and then translated 3 units up
Answer:
y= (0.25)1/x-4 +3
Step-by-step explanation:
You just multiply the compression by mx. then you would add the translation (-4 since it goes to the right). and +3 since it moves up on the y axis
The graph of g(x) = (x + 2)2 is a translation of the
graph of f(x)
by
units.
DONE
X
-2
2
4
2
h = 1
y = (2-1)
Answer:
The graph of g(x) = (x + 2)2 is a translation of the
graph of f(x) ✔ left by 2 units.
The graph of h(x) = (x − 3)2 is a translation of the
graph of f(x) ✔ right by 3 units.
100% Correct
Step-by-step explanation:
Can someone help me again on this.
Which graph represents the solution set to this system of equations? –x + 2y = 6 and 4x + y = 3 On a coordinate plane, a line goes through (negative 1, negative 1) and (0, 3) and another line goes through (1, 4) and (2, 2). On a coordinate plane, a line goes through (negative 4, 0) and (0, 4) and another line goes through (negative 1, 1) and (0, negative 3). On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (1, 0). On a coordinate plane, a line goes through (0, 0) and (4, 3) and another line goes through (2, 5) and (4, 4).
Answer:
On a coordinate plane, a line goes through (0, 3) and (2, 4) and another line goes through (0, 3) and (0.75, 0).
This answer almost coincide with option C. I suppose there was a mistype.
Step-by-step explanation:
The system of equations is formed by:
–x + 2y = 6
4x + y = 3
In the picture attached, the solution set is shown.
The first equation goes through (0, 3) and (2, 4), as can be checked by:
–(0) + 2(3) = 6
–(2) + 2(4) = 6
The second goes through (0, 3) and (0.75, 0), as can be checked by:
4(0) + (3) = 3
4(0.75) + (0) = 3
On a coordinate plane, a line goes through (-6, 0) and (0, 3) and another line goes through (0.75, 0) and (0, 3).
Given :
The system of equation -- (-x + 2y = 6) and (4x + y = 3)
The following steps can be used in order to determine the graph represents the solution set to this system of equations:
Step 1 - Write the given system of equations.
-x + 2y = 6 --- (1)
4x + y = 3 --- (2)
Step 2 - The x-intercept of equation (1) is:
-x + 0 = 6
x = -6
Step 3 - The y-intercept of equation (1) is:
0 + 2y = 6
y = 3
Step 4 - The x-intercept of equation (2) is:
4x + 0 = 3
x = 3/4
Step 5 - The y-intercept of equation (2) is:
0 + y = 3
y = 3
On a coordinate plane, a line goes through (-6, 0) and (0, 3) and another line goes through (0.75, 0) and (0, 3).
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If a person's eye level is h meters above sea level and he can see d kilometers to the horizon, then d=3.57h. Suppose the person's eye level is 15.21 meters
above sea level. How far can he see to the horizon?
Round your answer to the nearest tenth.
Answer:
54.3m
Step-by-step explanation:
h = distance above sea level
d = distance he can sea above sea level
d = 3.57h
h = 15.21m
d = ?
d = 3.57 × 15.21
d = 54.2997m approximately 54.3m
The person can see up to a distance of 54.3m
Answer:
d = 7.5
Step-by-step explanation:
d = 3.57[tex]\sqrt{h}[/tex]
= 3.57[tex]\sqrt{4.41}[/tex]
= 3.57( 2.1)
= 7.497
d = 7.5!
How would you describe "plate motion" to someone else? (In other words, how
do plates move?) *
Will mark as Brainliest plz help