the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number
Answer:
the numbers are 4, 8, 14
Step-by-step explanation:
If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.
The first number is 4.
The second number is 2×4 = 8.
The third number is 8 + 6 = 14.
Statistics??? Construct a 95% confidence interval for the population mean. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.
AB and BC are tangent to circle D. Find x if AB = 2x + 9 and BC = 3x + 6. Find x.
Answer:
the value of X comes out to be equal to 3
Step-by-step explanation:
since AB and BC are tangent to the circle D
then the length of the tangent will be same
AB will be equal to BC
where,
AB = 2 x + 9
and
BC = 3 x + 6
2 x + 9 = 3 x + 6
3 x - 2 x = 9 - 6
x = 3
hence, the value of X comes out to be equal to 3
How can you tell whether a rational expression is in simplest form? Include an example with your explanation.
Rational numbers are numbers that are written as a ratio of two integers.
Let a and b be integers, hence a rational expression can be expressed as a/bIn order to tell whether a rational expression is in its simplest form, we need to ensure no integer can go in both the numerator and the denominator.
For instance, given the rational number 10/15, the simplest form of the rational number will be expressed as (5*2)/(5*3) = 2/3
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An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is cubic inches. This is cubic inches less than the volume of the new chamber. NextReset
Answer:
added pictures of all the questions on this test
Step-by-step explanation:
Find the take home percent of the gross pay: net pay $298.76, gross pay $402.38. round to the nearest percent.
In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.
Answer:
Rectangle and Square.
Step-by-step explanation:
To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.
In other words, two or more angles are said congruent if and only if they have the same measurement.
What is the inverse of f(x)=70x^3/4 ?
The inverse of the function [tex]f(x) = 70x^{(3/4)[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)[/tex].
Explanation:The inverse of the function [tex]f(x) = 70x^{(3/4)}[/tex] can be found by interchanging the roles of x and y and solving for y. The goal is to isolate y on one side of the equation.
Step 1: Replace f(x) with y: [tex]y = 70x^{(3/4)}[/tex]
Step 2: Swap x and y: [tex]x = 70y^{(3/4)}[/tex]
Step 3: Solve for y: Divide both sides of the equation by 70 and raise both sides to the power of 4/3 to undo the exponent: [tex]y = (x/70)^{(4/3)}[/tex]
Therefore, the inverse of [tex]f(x) = 70x^{(3/4)}[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)}[/tex].
1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!
Helpppppppppp me!!!!!!!!!
A) w/9=6
w=9*6
w=54
B) 5q=15
q=15/5
q=3
C)2s-3s=20
-1s=20
s=20/-1 = -20
s=-20
D)4-a=-12
a= 4+12 = 16
a=16
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0
Sandy can assemble a particular type of light fixture in 3/8 hour. it takes her 2/3 hour to hang the fixture and another 1/6 hour to wire the fixture once it is hung. how many fixtures could sandy install in 29 hours?
Sandy can install a maximum of 24 fixtures in 29 hours.
Explanation:To calculate the number of fixtures Sandy can install in 29 hours, we need to determine the amount of time it takes for Sandy to complete one installation process (excluding assembly time).
Sandy takes 2/3 hour to hang the fixture and another 1/6 hour to wire it, totaling
2/3 + 1/6 = 7/6 hour.
Therefore, Sandy takes 7/6 hour per fixture.
Next, we can calculate the number of fixtures by dividing the total time available (29 hours) by the time it takes for one installation process.
Number of fixtures = Total time available / Time per fixture
Number of fixtures = 29 / (7/6) = 29 * (6/7) = 174/7 = 24.86
Since we can't have a fraction of a fixture, Sandy can install a maximum of 24 fixtures in 29 hours.
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2. A ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. This mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. When the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak?
Part I: Sketch a figure to illustrate the scenario above. Label the vertices and the lengths that are given in the question. (3 points)
Part II: Using your sketch from Part I, write an equation using a trigonometric ratio to find the distance a tourist will travel from the base of the mountain to its peak. Round your answer to the nearest 100th. Show your work. (2 points)
3. Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB = 10 feet, and BE and BD trisect ∠ABC, what is the perimeter of the deck area to the right of the beam of light (△BDC)?
Part 1: What other angles or sides of △BDC can you label given that side AB is 10 feet, BE and BD trisect ∠ABC? Label the diagram accordingly, and explain your reasoning. (4 points)
Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of △BDC. Show your work. (3 points)
Part 3: Use the Pythagorean Theorem to calculate the length of side BD. Does this method verify the length you found using trigonometric ratios? (2 points)
Part 4: What is the perimeter of the area to the right of the beam of light on Darcy's deck (△BDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)
4. Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph. Which car will reach the intersection first?
Part I: Use the law of cosines to determine how far Car B has to travel to reach the intersection. (2 points
Part II: Use to determine the time necessary for Car A to reach the intersection. Round your answer to the nearest hundredth of an hour. (1 point)
Part III: Use to determine the time necessary for Car B to reach the intersection. (1 point)
Part IV: Which car reaches the intersection first, and by how many hours? (2 point
5. Solve for the missing length and the other two angles in the triangle below.
Part I: Use the law of cosines to find the missing third side. (2 points)
Part II: Use either the law of cosines or the law of sines to find the measure of angle C. (2 points)
Part III: Use any method you like to find the measure of angle B. (1 point)
6. Solve the triangle below.
Part I: Use the law of cosines to find the measure of angle B. (2 points)
Part II: Use the law of sines to find the measure of angle C. (2 points)
Part III: Use any method you like to find the measure of angle A. (1 point)
7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and Suzie to be . Suzie approximates the angle formed by the lead boat, herself, and Swanson to be . How far is the boat from Swanson?
Part I: What is the missing angle in this triangle? (1 point)
Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)
8. Solve the following triangle for all missing sides and angles.
Part I: Find the measure of angle B. (1 point)
Part II: Use the law of sines to find the length of side a. (2 points)
Part III: Use any method to find the length of side c. (2 points)
Answer:
156
Step-by-step explanation:
You are given the mountain that has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. You are asked to find how many yards will a tourist travel from the base of the mountain to its peak. You can solve this using trigonometric function. More importantly, imagine that the mountain has a 90 - degree vertical height so that when you connect the peak of the mountain down to its base and then connected to the ski, you can form a right triangle.
Use the sine function.
sine β = opposite side / hypotenuse side
the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain
sine 40° = 100 yards / hypotenuse side
hypotenuse side = 100 yards / sine 40°
hypotenuse side = 156 yards
On a recent trip, I took a cab from the airport to my hotel. These were the cab fares posted on the door of the cab: $2.20 for the first 1⁄2 mile and 30 cents for each additional 1/5 mile. How far did I travel if my fare was $17.20? What would my fare be if I were to travel 16.8 miles? What would my fare be if I were to travel n miles? What kind of relationship is this? Justify your response and provide a visual representation (a graph) of the relationship.
Angle C is an inscribed angle of circle P. Angle C measures (5x-7) degrees and arc AB measures (2x) degrees. Find x.
List all your possibility of outcomes (there are 36 outcomes) if you roll a dice containing numbers 1-6 two times. Determine the probability of each outcome.
In triangle abc, the measure of angle b is 29 degrees° more than three times the measure of angle
a. the measure of angle c is 61 degrees° more than the measure of angle
a. find the measure of each angle.
Answer:
∠a = x
∠b = 3x + 29
∠c = x + 61
x + 3x + 29 + x + 61 = 180
5x = 180 - 29 - 61
5x = 90
x = 90/5
x = 18° ← ∠a
∠b = 3x + 29 = 3*18 + 29 = 83°
∠c = x + 61 = 18 + 61 = 79°
Step-by-step explanation:
in how many ways can a judge award first, second, and third place in a contest with 10 entries
720. just multiply 10 9 and 8 because first, second, and third, that is means three and that's how many numbers you multiply from 10,so it equals 720.
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At a certain university the student to teacher ratio is 16:1. If there are 2,000 students enrolled, how many teachers must be employed to maintain this ratio?
A. 28,000 B. 200 C. 215 D. 125
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Answer:
D. 125
Step-by-step explanation:
Ratio between students and teacher = 16:1 , 16/1 =2000 /x , x = 2000/16 = 125 teachers
The number of teachers in the school will be 125. The correct option is D.
What are ratios and proportions?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3.
Given that at a certain university the student-to-teacher ratio is 16:1. If there are 2,000 students enrolled.
The number of teachers will be calculated as,
16 / 1 = 2000 / t
t = 2000 / 16
t = 125 teachers
Therefore, the count of teachers in the school is 125.
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BARNEY'S BICYCLE SHOP IS SELLING T-SHIRTS AT THE LOCAL HEALTH FAIR. THEY PLAN ON SELLING SHIRTS FOR $8 EACH. TO HAVE THE SHIRTS MADE, BARNEY'S BICYCLE SHOP PAYS THE SHIRT MAKER $3.50 PER SHIRT PLUS AN INITIAL FEE OF $63. HOW MANY SHIRTS MUST BARNEY'S BICYCLE SHOP SELL BEFORE THEY CAN MAKE A PROFIT?
A. 9 SHIRTS
B. 8 SHIRTS
C. 14 SHIRTS
D. 11 SHIRTS
Barney's Bicycle Shop must sell at least 14 shirts before they can make a profit. Among the given options, the correct answer is C. 14 shirts.
To determine the number of shirts Barney's Bicycle Shop must sell before making a profit, we need to consider the cost of producing the shirts and the revenue generated from selling them.
For each shirt sold, the shop earns $8 in revenue. However, they incur costs to have the shirts made. The shirt maker charges $3.50 per shirt and an initial fee of $63.
Let's calculate the total cost per shirt:
Cost per shirt = $3.50 + ($63 / number of shirts)
To break even or make a profit, the revenue from selling the shirts must exceed the cost per shirt.
Let's calculate the revenue per shirt:
Revenue per shirt = $8
Now we can set up the equation to find the number of shirts needed to break even or make a profit as inequality:
Revenue per shirt ≥ Cost per shirt
$8 ≥ $3.50 + ($63 / number of shirts)
To solve this inequality, we can subtract $3.50 from both sides:
$4.50 ≥ $63 / number of shirts
Multiplying both sides by the number of shirts:
$4.50 x number of shirts ≥ $63
Simplifying the equation:
Number of shirts ≥ $63 / $4.50
Number of shirts ≥ 14
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Factor the expression.
4r^2 – 64
1)(4r + 5)(r – 16)
2)4(r – 4)(r – 4)
3)(4r – 5)(r + 16)
4)4(r + 4)(r – 4)
How do I do this someone please explain I need help
Directions: Describe the transformation. (x,y) -> (5x,5y)
The transformation (x, y) -> (5x, 5y) is a scaling transformation that dilates a point by a factor of 5 in both the x and y directions, making the entire figure five times larger while preserving its shape.
Explanation:The transformation described by (x, y) -> (5x, 5y) is a scaling transformation or dilation in both the x and y directions by a factor of 5. What this means is that any point on the plane, when subjected to this transformation, will move five times further away from the origin along both axes. For example, if you begin with the point (1, 1), applying this transformation will result in the point (5, 5). This dilation affects all points equally, meaning that the relative distances between points are preserved, but the entire figure is made larger by a factor of 5. Therefore, if you have a figure with dimensions of length and width, after the transformation, both dimensions will be increased by five times their original measure.
Final answer:
The transformation (x, y) -> (5x, 5y) represents a dilation, enlarging a figure by a factor of 5 along both the x-axis and y-axis, which alters size but not shape.
Explanation:
The transformation described by the rule (x, y) -> (5x, 5y) is a geometric transformation known as a dilation or scaling. This type of transformation alters the size of a figure without changing its shape. Specifically, the coordinates of each point in the figure are multiplied by 5, which means that the figure is enlarged by a factor of 5 in both the x-axis (east-west direction) and the y-axis (north-south direction). If, for example, we apply this transformation to a point (1, 2), the resulting coordinates will be (5, 10), and similarly, applying it to (3, 7) would yield (15, 35). This illustrates the dependence of y on x as each x-coordinate and y-coordinate are scaled by the same factor, maintaining the shape but increasing the size.
Harry Hoodeen made $24,567.00 net pay last year. His monthly expenses averaged $1,980.00. How much was left over for savings for the year?
What is the slope of the line below
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Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.
From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet
How to work with trigonometric ratios?We are told that you are standing 30 ft from the base of a tree.
Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.
Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;
h/30 = tan 37
h = = 30 * tan 37
h = 22.61 ft
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1. Given f(x)=3x+8f(x)=3x+8 and g(x)=6x+6g(x)=6x+6 then what is (f+g)(−1))(f+g)(−1)) ?
2. Given f(x)=6x+4f(x)=6x+4 and g(x)=3x+7g(x)=3x+7 then what is (f−g)(1)) ?
Two trucks leave a warehouse at the same time. one travels due north at an average speed of 4747 miles per hour, and the other travels due south at an average speed of 5050 miles per hour. after how many hours will the two trucks be 388388 miles apart?
What is another name for angle 2?
Angle 2 could refer to different things, such as an angular velocity, a direction angle, or a contact angle, depending on its context within a mathematical or physical scenario.
Explanation:In mathematical terms, angle 2 refers to a particular position or orientation, typically specified in degrees. For instance, if points 1 and 2 rotate through the same angle (AO), angle 2 might move through a greater arc length because it is farther from the center of rotation. This concept is related to the mathematical definition of angular velocity, defined as radians per unit time.
Alternatively, angle 2 could also refer to the direction angle, which is the angle measured counterclockwise from the positive direction on the x-axis to a vector. This term is often used when calculating vector components. In this context, a positive angle indicates a counterclockwise rotation, whereas a negative angle implies a clockwise rotation.
Finally, angle 2 might specify the contact angle, which is the angle between the tangent to the liquid surface and the surface itself. To figure out the precise name for angle 2 in your particular context, I would need further information about the specific scenario or diagram you're referring to.
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