What is the constant of proportionality in the equation 6y=3x6y=3x6, y, equals, 3, x?
If a rectangle measures 8 feet on the short side and 9.8 feet on the long side what is the area of the rectangle in square feet
Find the surface area
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A, toy company manufactures arcade games. They are marketing a new pinball machine to children. It is similar in size to the adult version of the same game.
Adult pinball machine GAME with base ME measuring 35 inches and sides measuring 56 inches. Child pinball machine G prime A prime M prime E prime with base M prime E prime measuring 14 inches
If the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime? Type the numeric answer only in the box below.
Refer to the following illustration to answer this Question.
The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
The answer is (x + 3) 2 + (y − 1) 2 = 81
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If an arithmetic series has a1 equals=44, d equals 5, and n=24, what is sn?
Two angles of a triangle have the same measure and the third angle is 72degrees greater than the measure of the other two. find the measure of each angle.
A right triangle has sides measuring 5 inches, 12 inches, and 13 inches. What is the area, in square inches, of this triangle ?
Final answer:
The area of a right triangle with sides of 5 inches and 12 inches as the base and height, respectively, is 30 square inches, calculated using the formula A = (base × height) / 2.
Explanation:
The area of a right triangle is calculated by multiplying one-half the base by the height: A = (base × height) / 2.
In the case of a right triangle with sides measuring 5 inches, 12 inches, and 13 inches, the 5-inch and the 12-inch sides are the legs and thus can be used as the base and height. Using the formula for the area of a right triangle:
A = (5 × 12) / 2
A = 60 / 2
A = 30 square inches
Therefore, the area of this triangle is 30 square inches.
match each graph with its corresponding equation
The graphs match the equations as follows:
Graph A: (−x+3)^2 -2
Graph B: (x−2)^2+3
Graph C : −(x+2)^2 +3
Graph D : 2(x−2)^2 +3
Equation (−x+3)^2 -2:
This equation is in the form of a quadratic function, y=a(x−h) ^2+k, where (h ,k) is the vertex of the parabola.
The vertex of the parabola is at (3,1), which matches the vertex of Graph A.
The coefficient a is negative, which tells us that the parabola opens downward.
The constant term k is −2, which tells us that the minimum value of the parabola is −2.
Equation (x−2)^2+3 :
This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h, k) is the vertex of the parabola.
The vertex of the parabola is at (2,3), which matches the vertex of Graph B. The coefficient a is positive, which tells us that the parabola opens upward.
The constant term k is 3, which tells us that the minimum value of the parabola is 3.
Equation −(x+2)^2 +3:
This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h, k) is the vertex of the parabola.
The vertex of the parabola is at (−2,3), which matches the vertex of Graph C.The coefficient a is negative, which tells us that the parabola opens downward.
The constant term k is 3, which tells us that the maximum value of the parabola is 3.
Equation 2(x−2)^2 +3 :
This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h ,k) is the vertex of the parabola.
The vertex of the parabola is at (2,3), which matches the vertex of Graph D. The coefficient a is positive and multiplied by 2, which tells us that the parabola opens upward and is stretched vertically by a factor of 2.
The constant term k is 3, which tells us that the minimum value of the parabola is 3.
Gina is a tour boat operator and she wants to know the mean age of all the people in her tour group.
She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34.
What is the best estimate of the mean age of all the people in the tour group?
Round to the nearest whole number.
Find the equation of the line whose x-intercept is 8 and y-intercept is -2. write the equation in slope-intercept form.
To determine the equation of the line with x-intercept 8 and y-intercept -2, the slope is calculated to be 1/4. Thus, the line's equation in slope-intercept form is y = (1/4)x - 2.
To find the equation of a line with an x-intercept of 8 and a y-intercept of -2, we'll first determine the slope of the line (m) and then use the slope-intercept form (y = mx + b).
Two points on this line are (8,0) and (0,-2). The slope (m) of a line is calculated by the change in y divided by the change in x, which in this case is
(0 - (-2)) / (8 - 0) = 2 / 8 = 1 / 4.
Now we know the slope is 1/4 and the y-intercept (b) is -2, so the equation of the line in slope-intercept form is:
y = (1/4)x - 2
At Martina's auto shop, it takes her 15 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Martina can do in at most 3 hours ( 180 minutes).
a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red
[tex] |\Omega|=10\\
|A|=1\\\\
P(A)=\dfrac{1}{10}=10\% [/tex]
Use the graphs of f(x) =2/x and g(x)=1/-3-x to determine the solutions to f(x) = g(x).
A) (-2, -1)
B) (-2, 1)
C) (2, -1)
Steve buys 14 ounces of kiwis and 2 pounds of peaches.How many more ounces do the peaches weigh then the kiwis?
Orville traveled at a speed that was twice as fast as randy, Orville traveled 240 miles in one hour less than it took randy to travel 150 miles. What were the speed and time it took for both Orville and randy?
Please answer will give brainliest
One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time.
Full time Part time
Public Transportation 7 10
Bicycle 4 3
Drive alone 30 31
Carpool 6 9
The probability of getting someone who carpools or someone who works full time is 0.36.
Explanation:To find the probability of getting someone who carpools or someone who works full time, we need to add the probabilities of the two events.
The probability of getting someone who carpools is 6/100 and the probability of getting someone who works full time is 30/100.
So the probability of either event happening is (6/100) + (30/100) = 36/100 = 0.36.
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If two angles are both vertical and supplementary, can we determine the angles? If so, what are they?
Answer:
Step-by-step explanation:
45
What values for xx and yy make △MNO≅△PRT▵MNO≅▵PRT?
Triangles MNO and PRT
Find the 12th term in the following geometric sequence. 0.75, 1.5, 3, 6, . . .
Answer:
1536
Step-by-step explanation:
Given : A geometric sequence 0.75, 1.5, 3, 6, . . .
To Find:Find the 12th term
Solution:
0.75, 1.5, 3, 6, . . .
First term =a = 0.75
Common difference = [tex]r = \frac{a_3}{a_2} =\frac{a_2}{a_1}=\frac{1.5}{0.75}=\frac{3}{1.5}=2[/tex]
nth term of G.P. = [tex]a_n=a r^{n-1}[/tex]
Where a = First term = 0.75
r = common difference = 2
Substitute n = 12
[tex]a_{12}= 0.75 (2)^{12-1}[/tex]
[tex]a_{12}= 0.75 (2)^{11}[/tex]
[tex]a_{12}= 1536[/tex]
Hence the 12th term in the geometric sequence. 0.75, 1.5, 3, 6, . . . is 1536.
For these two rules, the second number in the ordered pair is always three times greater than the first number. If the relationship between the two numbers in each ordered pair is the same, the graph will be: Not graph-able A straight line A circle An exponential curve A parabolic curve
Which graph shows a polynomial function of an even degree?
An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8). Which equation represents this ellipse?
Answer:
D
Step-by-step explanation:
A) how many ways can the letters in the word computer be arranged in a row?
b.how many ways can the letters of the word computer be arranged if the letters co must remain next to each other as a unit?
The permutation is defined as the arrangement number or order in which rearrangement of element in an order list.
(a) The letters in the word computer be arranged in a row is 40320.
(b) The letters of the word computer be arranged 5040 ways.
Given:
The given latter is COMPUTER.
How to find the permutation of latter?(a)
There are 8 letter in word COMPUTER. Calculate the number of ways in which we can arrange 8 letters.
[tex]8!=8\times7\times6\times5\times4\times3\times2\times1\\8!=40,320.[/tex]
Thus, the letters in the word computer be arranged in a row is
(b)
As per the question if we treat CO as a unit then there will only seven letters effective.
[tex]7!=7\times6\times5\times4\times3\times2\times1\\7!=5,040[/tex]
Thus, the letters of the word computer be arranged 5040 ways.
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Mr ong spent $960 of his salary on food and transport.He spent 1/4 of his remaining money on clothes.He then had 1/3 of his salary left.How much was his salary?
A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?
Final answer:
Using trigonometry and the sine function, the maximum height that the ladder can reach when raised to a 75-degree angle with a length of 60 feet is approximately 58 feet.
Explanation:
To determine the maximum height that a fire truck ladder can safely reach when it is extended to 60 feet in length and raised to a maximum angle of 75 degrees with the horizontal, we would use trigonometry, specifically the sine function. The sine of an angle in a right triangle is equal to the opposite side (height in this case) divided by the hypotenuse (the length of the ladder).
Therefore, the maximum height (h) can be calculated using the formula:
h = Ladder Length × sin(Angle)
Where:
Ladder Length is 60 feet
Angle is 75 degrees
Plugging in our values we get:
h = 60 feet × sin(75 degrees)
Using a calculator, we find that:
sin(75 degrees) is approximately 0.9659.
Therefore:
h ≈ 60 feet × 0.9659
h ≈ 57.95 feet
The maximum height the ladder can safely reach when disregarding the height of the fire truck itself is approximately 58 feet.
From 1992 through 2007, the purchasing power of a dollar decreased by about 3.5% per a year. Using 1992, as the base for comparison, what was the purchasing power of a dollar in 2007? Formula: y=C(1−r)t
$0.48
$0.57
$0.44
$0,59
In how many ways can the letters of the word BANANA be rearranged such that the new word does not begin with a B?
First arrange the words in order:
AAABNN
so there are 3 A's, 1 B and 2 N's.
If there were no constraints,
Number of permutations = (3+1+2)!/(3!1!2!)=6!/(6*1*2)=720/(6*2)=60
Number of words that begin with B is to take out the B, that leaves us with
AAANN => 3 A's and 2 N's
=> 5!/(3!2!) = 120/(6*2)=10
Therefore the number of words that do NOT begin with B is
60-10 = 50 ways
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex. which terms describe the degenerate conic section that is formed? select each correct answer. degenerate parabola pair of intersecting lines point line degenerate hyperbola degenerate ellipse
Answer with explanation:
It is given that, a plane intersects a double-napped cone such that the plane intersects both Nappes through the cone's vertex.It also depends on how thick or thickness of the plane:
1.We can surely say that degenerate hyperbola will be formed,whatever be the thickness of Plane.
2. Two parallel lines=pair of intersecting lines ,because both ,A double napped cone and Plane is three dimensional shape.Instead of intersecting lines ,two parallel lines which we call pair of intersecting lines, will be formed.