Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). The coordinates of the intersection point are (1,3).
What is rhombus?
A rhombus is a special type of parallelogram in which all four sides are of equal length. Equivalently, a rhombus is a quadrilateral with four sides of equal length.
Since ABCD is a rhombus, its diagonals AC and BD are perpendicular bisectors of each other, and they intersect at their mutual midpoint M.
The midpoint M of AC is the average of the coordinates of A and C, namely:
M = ((-1+3)/2, (2+4)/2) = (1, 3)
Similarly, the midpoint of BD is the average of the coordinates of B and D. Since we don't know the coordinates of B and D, we need to find them first.
The other two vertices of the rhombus are obtained by reflecting A and C about the midpoint M, since opposite sides of a rhombus are parallel and equal in length. To do this, we subtract the coordinates of M from those of A and C, and then add them to M:
B = 2M - A = 2(1,3) - (-1,2) = (3,4)
D = 2M - C = 2(1,3) - (3,4) = (-1,2)
Now we can find the midpoint of BD:
N = ((3-1)/2, (4+2)/2) = (1, 3)
Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). Therefore, the coordinates of the intersection point are (1,3).
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Please Help!
A plane is located at C on the diagram. There are two towers located at A and B.
The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Unit 8: Right Triangles & Trigonometry
Homework 4: Trigonometric Ratios &
Finding Missing Sides
In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right-angled triangle ABC with drawn with angle B = 90°.
A line BD is drawn which is perpendicular to AC.
The angle BDC is also 90 degrees.
The measure for line segment AD = 12 and CD = 40.
The measure for line segment BD is x.
The side BD is common for triangle ABC and BDC.
So, by the formula of indirect measurement we have -
DC / BD = BD / AD
Substitute the values in the equation -
40 / x = x / 12
x² = 480
x = 21.908
x = 21.91
Therefore, the value of x is obtained as 21.91.
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Answer:
Sin Q
7/25
Cos Q
24/25
Tan Q
7/24
Sin R
24/25
Cos R
7/25
Tan24/7
Step-by-step explanation:
This is 6/6 problems finish them all each is 10 points 60 total.
The angle R is 53.1° by the use of the cosine which is one of the trigonometric ratios that we have.
What is trigonometry?In trigonometry, the three most important trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles of a triangle to the ratios of its sides. For example, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse (the longest side of the right-angled triangle).
Cos R = 3/5
R = Cos-1(3/5)
R = 53.1°
Hence, we can see that the required angle R is obtained as 53.1°
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0.062 in standard form
Answer:
6.2 × 10-2
Step-by-step explanation:
Solve the quadratics attached using the quadratic formula or completing the square
[tex]p^2-6p+8[/tex]
The value of p is 2 and 4.
What is a quadratic equation?
Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Here, we have
Given: p² - 6p + 8
we have to solve the quadratic formula or complete the square.
= p² - 6p + 8
= p² -4p - 2p + 8
= p(p-4) -2(p-4)
= (p-4)(p-2)
(p-4)(p-2) = 0
p-4 = 0,
p-2 = 0
p = 4, 2
Hence, the value of p is 2 and 4,
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please please help its geometry
In response to the given question, we can state that we know that sum of all angles in a triangle is 180. m∠C = 4*11.67+43 = 89.68 = =90
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
we know that sum of all angles in a triangle is 180.
2x - 12 + 4x + 43 + 9x - 26 = 180
15x + 5 = 180
15x = 175
x = 11.67
m∠C = 4*11.67+43 = 89.68 = =90
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Answer:
m∠C = 119°
Step-by-step explanation:
According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
From inspection of the given triangle, the exterior angle is (9x - 26)° and the two non-adjacent interior angles are ∠B and ∠C.
Equate the sum of the two non-adjacent angles to the exterior angle and solve for x:
⇒ (2x - 12)° + (4x + 43)° = (9x - 26)°
⇒ 2x - 12 + 4x + 43 = 9x - 26
⇒ 6x + 31 = 9x - 26
⇒ 57 = 3x
⇒ x = 19
To calculate the measure of angle C, substitute the found value of x into the expression for the angle:
⇒ m∠C = (4x + 43)°
⇒ m∠C = (4(19) + 43)°
⇒ m∠C = (76 + 43)°
⇒ m∠C = 119°
A road race is 6 kilometers long. There is a water station at the halfway mark. How many meters away from from the start line is the water station
Answer: 3000m
Step-by-step explanation:
Half of 6 km is 3 km
To convert to meters multiply 3 times 1000
That will give you 3000m=3km
Each number in the table below represents the number of employees at different stores in
two nearby malls.Part A
Determine the interquartile range for numbers of employees at each mall. Show your work or
explain your reasoning.
Part B
Which mall would you expect to have greater variability in regard to numbers of employees?
Show your work or explain your reasoning.
(A) The interquartile range for numbers of employees at Mall A is 65 and at Mall B is 7.5. (B) Mall B would we expect to have greater variability in regard to numbers of employees.
Part A: To determine the interquartile range (IQR) for numbers of employees at each mall, we first need to find the median for each mall. The median is the middle value of a set of data when arranged in order.
For Mall A:
Arrange the numbers in ascending order: 18, 20, 21, 22, 25, 26, 27, 28, 28, 29
The median is the average of the two middle numbers, which are 25 and 26.
Median = (25 + 26) / 2
= 25.5
Next, we need to find the first quartile (Q1) and the third quartile (Q3). The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.
For Mall A:
Lower half: 18, 20, 21, 22, 25
Upper half: 26, 27, 28, 28, 29
Q₁ = median of the lower half
= (21 + 22) / 2
= 21.5
Q₃ = median of the upper half
= (28 + 28) / 2
= 28
The interquartile range for Mall A is:
IQR = Q3 - Q1
= 28 - 21.5
= 6.5
For Mall B:
Arrange the numbers in ascending order: 19, 21, 23, 24, 25, 26, 27, 29, 30, 33
The median is the average of the two middle numbers, which are 25 and 26.
Median = (25 + 26) / 2
= 25.5
Lower half: 19, 21, 23, 24, 25
Upper half: 26, 27, 29, 30, 33
Q₁ = median of the lower half
= (21 + 23) / 2
= 22
Q3 = median of the upper half
= (29 + 30) / 2
= 29.5
The interquartile range for Mall B is:
IQR = Q3 - Q1
= 29.5 - 22
= 7.5
Part B: To determine which mall would have greater variability in regard to numbers of employees, we can compare the interquartile ranges for each mall. The interquartile range measures the spread of the middle 50% of the data. The larger the interquartile range, the greater the variability.
In this case, Mall B has a larger interquartile range than Mall A (7.5 vs. 6.5). This suggests that there is greater variability in the number of employees at Mall B.
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Frankie is flying to Seattle, Washington from Detroit, Michigan. He
leaves at 12 pm Eastern time. The flight is 5 hours. What time will it be in
Seattle (Pacific time) when he lands
Nancy has twice as many apples as jay. Jay has 3 more apples than Ava. Nancy has 22 apples. How many apples dose Ava have?
Answer:
8 apples
Step-by-step explanation:
Step-by-step explanation:
n = Nancy's apples.
j = Jay's apples.
a = Ava's apples.
n = 22
n = j × 2
j = n / 2 = 22/2 = 11
j = a + 3
a = j - 3 = 11 - 3 = 8
Ava has 8 apples.
Find the distance between the two points.(-6,8) (6,3)
The distance between the two points (-6, 8) and (6, 3) is equal to 13 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(6 - (-6))² + (3 - 8)²]
Distance = √[(12)² + (-5)²]
Distance = √(144 + 25)
Distance = √169 units.
Distance = 13 units.
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hw06-MoreProbability: Problem 11 (1 point) Suppose that you roll two 6 sided dice. a) What is the size of the sample space?
b) What is the probability that the sum of the dice is a 7 ? c) What is the probability that the sum of the dice is at least a 7?
a) Sample space = {36}
b) Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6
c) Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.
We need to find, What is the size of the sample space? Probability of the sum of the dice is a 7 ?Probability of the sum of the dice is at least a 7? Solution a)Sample space is defined as the set of all possible outcomes. Suppose that you roll two 6 sided dice. So, The possible outcomes of each die is {1,2,3,4,5,6}.The total outcomes for rolling two dice are {1,1}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,1}, {2,2}, {2,3}, {2,4}, {2,5}, {2,6}, {3,1}, {3,2}, {3,3}, {3,4}, {3,5}, {3,6}, {4,1}, {4,2}, {4,3}, {4,4}, {4,5}, {4,6}, {5,1}, {5,2}, {5,3}, {5,4}, {5,5}, {5,6}, {6,1}, {6,2}, {6,3}, {6,4}, {6,5}, and {6,6}.Therefore, Sample space = {36}.b)Let E be the event that the sum of the dice is a 7.The events where the sum of the dice is a 7 are {1,6}, {2,5}, {3,4}, {4,3}, {5,2}, and {6,1}.The number of events where the sum of the dice is a 7 is 6.Therefore, Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6.c)Let F be the event that the sum of the dice is at least a 7.Therefore, F = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (2,6), (3,5), (4,4), (5,3), (6,2), (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), and (6,5)}The number of events where the sum of the dice is at least a 7 is 21.Therefore, Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.a) Sample space = {36}.b) Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6.c) Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.
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Alex is a single taxpayer with $80,000 in taxable income. His investment income consists of $500 of qualified dividends and short-term capital gains of $2,000. Use the tables to complete the statement
Due to Alex's salary falling inside the 22% tax bracket, his short-term capital gains would be subject to the same rate of taxation as his income.
What is short-term capital?A profit realized from the sale of a capital asset, such as a piece of personal or investment property, that has been possessed for one year or less is referred to as a short-term gain.
These profits are classified as ordinary income subject to tax at your personal income tax rate. Gain earned by selling assets that are held for a year or less are called short-term capital gains.
Alex is a single taxpayer who has taxable income of $80,000.
His investment income is made up of $2,000 in short-term capital gains and $500 in qualifying dividends.
As a result of his tax rate income falling between 38,601 and 425,800, which is below 15%, his qualifying dividends would be subject to a 15% tax.
Hence, we must deduct 15% of 500 and 22% of 2000 before combining them.
15% x 500
= 15 x 5
= 75
22% x 2000
= 22 x 20
= 440.
The total is = 75 + 440 = 515.
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when predicted errors have a kurtosis of 5, which ols assumption is violated? a. no clustering b. homoskedasticity c. no autocorrelation d. normality e. random sampling f. mean of estimated errors has to be 0
The OLS assumption that is violated when predicted errors have a kurtosis of 5 is normality. The correct option is (d). Kurtosis is a statistical measure of the peak of a probability distribution curve. It measures how the tails of the distribution compare to a normal distribution.
Oridinary Least Squares (OLS) is a regression technique that assumes that the response variable has a linear relationship with the explanatory variable(s) and that the response variable has normal distribution error terms. However, in some cases, such as when the predicted errors have a kurtosis of 5, this assumption of normality is violated. If the distribution has more of its observations in the tails than a normal distribution, it is said to be leptokurtic. If it has fewer of its observations in the tails than a normal distribution, it is said to be platykurtic.
Kurtosis of 5 means that the distribution is leptokurtic and has fatter tails than the normal distribution.Assuming normality of the errors means that the residuals or errors are normally distributed. If the errors are not normally distributed, then the residuals will not be normally distributed either. This will affect the accuracy of the confidence intervals and hypothesis tests. The coefficient estimates may be biased and the confidence intervals may be too wide or too narrow. Therefore, normality of the errors is an important assumption of OLS regression and in this case it has been violated.
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Help,
The Density of
Some Steel is 7.84g/cm³.
What is the mass of 70cm³ of this Steel?
Give your answer to 1 d.p.
Step-by-step explanation:
*change density to kg per cubic meter
*change volume to cubic meter
*rearrange the formula to solve for mass
harrison St thomas St, and Denny Way are parallel. on broad St, the distance between mercer St and Denny way is 0.7 miles. the distance between those same streets on aurora ave is 0.45 miles
The distance between Thomas St and Denny Way on Broad St is 0.1 miles.
How do we calculate?0.45 miles on Aurora Ave is equivalent to the distance between Mercer St and Denny Way on Broad St.
0.2 miles on Aurora Ave is equivalent to the distance between Thomas St and Denny Way on Aurora Ave.
We say X be the distance between Thomas St and Denny Way on Broad St,
and have the following proportion:
0.45 miles / (Mercer St to Denny Way on Broad St) = 0.2 miles / (Thomas St to Denny Way on Broad St)
Solving for x, we get:
x = 0.45 miles x (Thomas St to Denny Way on Broad St) / (Mercer St to Denny Way on Broad St) = 0.45 * 0.2 / 0.7 = 0.1286 miles
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Complete question:
Use the following information and the map of downtown Seattle to answer questions one and two. Harrison St, Thomas St, and Denny Way are parallel. On Broad St, the distance between Mercer St and Denny Way is 0.7 miles. The distance between those same streets on Aurora Ave is 0.45 miles.
a) On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles. What is the distance
between these two streets on Broad St? Round your answer to the nearest tenth of a mile.
Isabella's ice cream parlor uses waffle cones that have a diameter of 5 in. and a height of 6 in. what is the volume of ice cream that completely fills one cone to the top? enter your answer as a decimal in the box. use 3.14 for pi.
The volume of ice cream that fills one waffle cone to the top is 13.09 cubic inches.
The waffle cone has the shape of a circular cone. The volume of a cone is given by the formula [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.
The diameter of the cone is given as 5 inches, so the radius is half of the diameter, or 2.5 inches. The height is given as 6 inches. Substituting these values into the formula, we get:
V = [tex](1/3) * 3.14 * (2.5 inches)^2 * 6 inches[/tex]
V = 13.09 cubic inches
Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches (rounded to two decimal places).
To find the volume of ice cream that fills the waffle cone completely to the top, we first note that the waffle cone has the shape of a circular cone. We use the formula for the volume of a cone, which is [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.
We are given the diameter of the cone, which is 5 inches, and we find that the radius is half of the diameter, or 2.5 inches. We are also given the height of the cone, which is 6 inches. Substituting these values into the formula, we can calculate the volume of the cone as 13.09 cubic inches (rounded to two decimal places). Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches.
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13 Convert 20 to a percentage.
Answer:
13/20 written as a decimal is 0.65 and as a percent is 65%
1) Make the denominator 100 (20 x 5)
2) Multiply by five from the numerator too (13 x 5 = 65)
An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize the surface area?
If a square base has a volume of 4 cubic feet, the dimensions that minimize the surface area are: x = 2√2 and h = 4/x^2 = 1/2.
Let x be the side length of the square base and h be the height of the box. Since the volume is 4 cubic feet, we have:
V = x^2h = 4
Solving for h, we get:
h = 4/x^2
The surface area of the box, A, is given by:
A = x^2 + 4xh
Substituting h in terms of x, we get:
A = x^2 + 4x(4/x^2) = x^2 + 16/x
To minimize A, we take the derivative with respect to x and set it equal to zero:
dA/dx = 2x - 16/x^2 = 0
Solving for x, we get:
x = 2√2
To ensure that this is a minimum, we take the second derivative:
d^2A/dx^2 = 2 + 32/x^3
At x = 2√2, this is positive, indicating a minimum.
The box has a square base with side length 2√2 feet and height 1/2 feet.
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Each day for the next 4 days, there is a 40% chance of a thunderstorm. Use the simulation shown, where the digits 1 through 4 represent days with a thunderstorm, to estimate the probability of a thunderstorm on at least 3 of the next 4 days. Round your anwser to the newrest tenth percent if necessary
Therefore , the solution of the given problem of probability comes out to be there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.
What is probability, exactly?The primary goal of the form of patterns defined as hyper parameters is to calculate the likelihood that a remark is accurate or a specific event will occur. Any number between 0 but instead 1, where 1 usually denotes assurance and range 0 typically connotes possibility, can be used to represent chance. A probability diagram shows the chance that a specific event will occur.
Here,
We must count the number of outcomes in which there are 3 or 4 thunderstorms in order to calculate the chance that a thunderstorm will occur on at least 3 of the following 4 days using the simulation.
We can see from the programme that there are 6 scenarios where there are at least 3 thunderstorms:
=> 1-2-3-4
=> 1-2-4-3
=> 1-3-2-4
=> 1-3-4-2
=> 1-4-2-3
=> 1-4-3-2
Since there are a total of 16 potential outcomes (since a thunderstorm can occur every day or not), the likelihood of at least 3 thunderstorms is:
=> 6/16 = 0.375
This means that there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.
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Below, there is a pattern with its first 5 terms listed. Describe a way to produce each tern from the previous term.
1/2, 1, 2, 4, 8, ...
The formula that describes a way to produce each term from the previous term in the given geometric sequence is: aₙ = ¹/₂(2)ⁿ⁻¹
How to solve geometric sequence?In mathematics, a geometric sequence, is defined as a sequence that consists of non-zero numbers whereby each of the terms after the first is found by multiplying the previous one by a fixed, non-zero number that is referred to as the common ratio.
The formula that is usually utilized in finding the nth term of a geometric sequence is expressed as:
aₙ = arⁿ⁻¹
where:
a is first term
r is common ratio
Thus:
a = 1/2
r = 2/1 = 2
Thus:
aₙ = ¹/₂(2)ⁿ⁻¹
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Todd and Eric went to the book store. Eric spent $15 less than three times the
amount that Todd spent. If the shoppers spent a total of $197 in books, How much
did Eric spend?
$34
$53
$65
$71
$29
$59
$48
If the shoppers spent a total of $197 in books, the amount that Eric spend is $144.
How much did Eric spend?Let's assume that Todd spent x dollars in the bookstore.
According to the problem, Eric spent $15 less than three times the amount that Todd spent, which can be written as:
3x - 15
The total amount spent by both shoppers is $197, so we can set up the equation:
x + (3x - 15) = 197
Simplifying and solving for x, we get:
4x - 15 = 197
4x = 212
x = 53
Therefore, Todd spent $53 in the bookstore.
To find how much Eric spent, we can substitute Todd's value into the expression we derived for Eric's spending:
3x - 15 = 3(53) - 15 = 144
So Eric spent $144 in the bookstore.
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How many whole numbers are in the interval between -5 and 23/6
A:0
B:3
C:4
D:5
Im actually stuck
Answer: i believe its 5
Step-by-step explanation:
Divide round your answer to the nearest set $40. 90 divided by 66
If $40.90 divided by 66, the rounded answer to the nearest set of 40 is given as $0.
To round the answer of $40.90 divided by 66 to the nearest set of 40, we need to perform the division and then round the quotient to the nearest multiple of 40.
First, let's perform the division:
$40.90 / 66 = 0.6206...
The quotient is a decimal, but we need to round it to the nearest multiple of 40. To do this, we need to find out how close the quotient is to each of the multiples of 40 and then round to the nearest one.
The nearest multiples of 40 are 0, 40, 80, 120, etc.
To determine how close the quotient is to each of these multiples, we can subtract the quotient from each multiple and take the absolute value of the result:
|0 - 0.6206| = 0.6206
|40 - 0.6206| = 39.3794
|80 - 0.6206| = 79.3794
The smallest absolute difference is between the quotient and 0, so we round down to 0.
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given f(x)=x^3-x^2-5x-3 and the factor x-3, find the zeros of the function f(x).
PQR is a right angled triangle at P nad ahs PQ
The length QR of the right angle triangle is 26 cm.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of a right angle triangle can be found using Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
24² + 10² = QR²
576 + 100 = QR²
QR² = 676
QR = √676
QR = 26 cm
Therefore,
length of QR = 26 cm
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Rock and Bowl charges $2.75 per game plus $3 for shoe rental. Super Bowling charges $2.25 per game and $3.50 for shoe rental. For how many games will the cost to bowl be approximately the same at both places? What is that cost?
Answer:
1 game, for $5.75
Step-by-step explanation:
To find this answer, all you need to do is create an equation for both Rock and Bowl and the Super Bowling and then set them equal to each other to find out and solve which value of x games makes them equal.
The first equation is 2.75x +3
The second one is 2.25x + 3.5
2.75x + 3 = 2.25x + 3.5
2.75x = 2.25x + .5
From here, you can either solve for x or realize that x being equal to 1 makes both values equal.
So, the answer is 1 game now to plug it into one of our equations, we get
2.75(1) + 3 which we know is equal to the other equation too which is $5.75 dollars
The measures of the angles of a triangle are shown in the figure below. Solve for x.
According to the conditions, in right angled triangle, the value of x is 6.
What is angle ?
In mathematics, an angle is a geometric figure formed by two rays (or line segments) that share a common endpoint, known as the vertex of the angle.
In a right-angled triangle, the sum of the two acute angles is always 90 degrees. Therefore, we can use this fact to find the value of x.
We are given that one of the acute angles is 60 degrees, and the other angle is 7x - 12 degrees. So we can write:
60 + (7x - 12) = 90
Simplifying this equation, we get:
7x + 48 = 90
Subtracting 48 from both sides, we get:
7x = 42
Dividing both sides by 7, we get:
x = 6
Therefore, in right angled triangle, the value of x is 6.
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What amount would you have in a retirement account if you made annual deposits of $375 for years earning 12% compounded annually?
Answer:%40.50
Step-by-step explanation: i tired
a particle moves along the x-axis so that at any time t>0, its velocity is given by v(t)=4-6t^2. if the particle is at a position x=7 at t=1 time, what is the position of the particle at time t=2?
Answer:
-11.
Step-by-step explanation:
We know that the velocity function v(t) is the derivative of the position function x(t).
So, we can integrate v(t) to find x(t) up to a constant of integration:
∫v(t) dt = ∫(4 - 6t^2) dt = 4t - 2t^3 + C
where C is the constant of integration.
We can find the value of C by using the initial condition that the particle is at position x=7 at t=1:
x(1) = 4(1) - 2(1)^3 + C = 7
C = 5
So, the position function is:
x(t) = 4t - 2t^3 + 5
To find the position of the particle at time t=2, we can substitute t=2 into the position function:
x(2) = 4(2) - 2(2)^3 + 5 = -11
Therefore, the position of the particle at time t=2 is -11.