Answer:
[tex]120^{\circ}, 120^{\circ}, 60^{\circ}, 60^{\circ}[/tex]
Step-by-step explanation:
The angles of a quadrilateral add to [tex]360^{\circ}[/tex].
[tex]2h+2h+h+h=360 \\ \\ 6h=360 \\ \\ h=60 \implies 2h=120[/tex]
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kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in., what are the possible lengths of a third rod?
The required length of the third side should be less than the sum of the other two sides or less than 37 in.
As mentioned, Kelsey is welding 3 metal rods to make a triangle. If the lengths of two rods are 15 in. and 22in.,
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the length of the third side,
The property of the triangle states that the sum of the two sides of a triangle is always greater than the length of the third side.
So
x < 15 + 22
x < 37
Thus, the required length of the third side should be less than the sum of the other two sides or less than 37.
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Ron got a cell phone rate of C(a)=0.22+0.10a. Graph the cost per minute. How much will a five minute call cost?
The cost of the five-minute call will be equal to $0.72.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Ron got a cell phone rate of C(a)=0.22+0.10a. The cost of a five-minute call will be calculated as,
Cost = 0.22+0.10a
Cost = 0.22 + ( 5 x 0.10 )
Cost = 0.22 + 0.50
Cost = $0.72
The five-minute call will cost $0.72.
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MATHEMATICAL CONNECTIONS Solve a system of linear equations to find the values of x and y.
The values of x and are 28° and 58° respectively
How to determine the valuesIt is important to note the properties of a trapezium;
Bases are parallel to each otherAdjacent interior angles sum up to 180°Sum of all the interior angles is 360°Length of both diagonals are equalDiagonals intersect each otherWe then have that;
2y + (y + 6) = 180
4x + 2x + 12 = 180
From equation (1), we have;
3y + 6 = 180
collect like terms
3y = 180 -6
3y = 174
y = 58°
From equation (2), we have;
6x = 180 -12
6x = 168
x = 28°
Hence, the values are 28° and 58°
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Solve equation:
-6-3k+8=5
if you solve the equation you get k=-1
what is the answer for 3(m+5)-2(-9+m)=29
solving for m
distribute into parentheses
3m + 15 + 18 -2m = 29
simplify
m + 33 = 29
subtract
m = -4
verify
3(-4+5) -2(-9-4) = 29
3 + 26 = 29
29 = 29
true
m = -4
hope this helps :)
jeron
Convert the quadratic function from vertex form to standard form: g(x)= 1/2 (x+2)^2-8
Answer:
y = 1/2x² - 2x - 6
Please help you get 100 points and brainly
You have points R(2, 10) and S(6, - 8).
There two ways to construct a right triangle with RS being a hypotenuse.
Please see both ways reflected in the attached.
One triangle is RST and another one is RSU with red or blue legs.
Find three integer or decimal solutions to the following equation, and then graph the solution set.
5x+4y=20
Answer:
To find three integer or decimal solutions to the equation 5x + 4y = 20, we can first divide both sides of the equation by the GCF of the coefficients, which is 1. This gives us the equation 5x + 4y = 20/1, which can be rewritten as 5x + 4y = 20. We can then use the substitution method to solve for x in terms of y, by setting 4y = 20 - 5x and solving for x. This gives us x = (20 - 4y) / 5. Substituting this expression for x into the original equation, we get 5((20 - 4y) / 5) + 4y = 20, which simplifies to 20 - 4y + 4y = 20, or 20 = 20. This means that any value of y that satisfies the equation will also satisfy the original equation.
For example, if we choose y = 3, then x = (20 - 4 * 3) / 5 = 2, and the solution (x, y) = (2, 3) satisfies the equation 5x + 4y = 20. Similarly, if we choose y = 0, then x = (20 - 4 * 0) / 5 = 4, and the solution (x, y) = (4, 0) satisfies the equation. Finally, if we choose y = -1, then x = (20 - 4 * -1) / 5 = 5, and the solution (x, y) = (5, -1) satisfies the equation.
The solution set for the equation 5x + 4y = 20 is the set of all ordered pairs (x, y) that satisfy the equation. The three solutions we found are (2, 3), (4, 0), and (5, -1), and these solutions can be plotted on a coordinate grid to show the solution set. The graph of the solution set is a line that passes through the points (2, 3), (4, 0), and (5, -1).
Step-by-step explanation:
Use the normal distribution to the right to answer the questions. (a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? Standardized Test Composite Scores 1921Score mu equals 19.6 sigma equals 5.3 mu x A graph titled "Standardized Test Composite Scores" has a horizontal x-axis labeled "Score" from about 1 to 38 with tick marks at 19 and 21. A normal curve labeled μ = 21.2 σ = 5.4 is centered above the x-axis at 21.2. A vertical line segment labeled μ extends from the normal curve to the x-axis at 21.2. (a) The percent of scores that are less than 19 is nothing %. (Round to two decimal places as needed.) (b) About nothing scores would be expected to be greater than 21. (Round to the nearest whole number as needed.)
a) The percentage of scores that are less than 19 is of: 34.09%.
b) The amount out of the 1500 scores that would be greater than 21 is of: 774.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the scores in this problem are given as follows:
[tex]\mu = 21.2, \sigma = 5.4[/tex]
The proportion of scores that are less than 19 is the p-value of Z when X = 19, hence:
Z = (19 - 21.2)/5.4
Z = -0.41.
Z = -0.41 has a p-value of 0.3409.
Hence the percentage is of 34.09%.
The proportion of scores that are greater than 21 is one subtracted by the p-value of Z when X = 21, hence:
Z = (21 - 21.2)/5.4
Z = -0.04
Z = -0.04 has a p-value of 0.484.
1 - 0.484 = 0.516.
Hence the amount out of the 1500 scores is given as follows:
0.516 x 1500 = 774 scores.
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A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water. What is the velocity of the boat relative to shore?
The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
Define velocity.The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity. Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.
Given
A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
Velocity,
v = √(1.65)² + (10.7)²
v = √2.722 + 114.49
v = √117.212
v = 10.82
The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
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Help pls i need it
Determine which integer will make the inequality 2(n + 1) ≤ 3(n − 2) true.
S:{0}
S:{4}
S:{6}
S:{8}
Vue wonders how long the ball was in the air when it was 54 feet in the air so he writes the equation 54=-16s2+96s. Solve the equation for time(s) to determine how long the ball was in the air when it was 54 feet above the ground . Round your answer to the nearest hundredth of a second . On a piece of paper , Identify which of the following methods you used to solve this question : factoring , completing the square, the Quadratic Formula, using a graph. Then explain how your solution helps Vue answer his question
Answer:
0.63 or 5.37 seconds
Step-by-step explanation:
You want to know how long a ball was in the air when its height is 54 feet, and its height is described by -16s^2 +96s, for time (s) in seconds.
SolutionA graph shows the value of the height function is 54 when s = 0.63 or 5.37.
These solutions mean the ball was in the air 0.63 seconds when it passed 54 feet going up, and it was in the air 5.37 seconds when it was 54 feet in the air on the way down.
A parabola has an axis of symmetry at x = 5/12. The distance between its roots is 13/6. What is the equation of the parabola?
Answer:
The axis of symmetry of a parabola is the line that divides the parabola into two mirror images. This line always passes through the vertex of the parabola. For a parabola with an axis of symmetry at x = 5/12, the vertex of the parabola is at the point (5/12, 0).
The distance between the roots of a parabola is the distance between the x-coordinates of the two points where the parabola crosses the x-axis. In this case, the distance between the roots is 13/6.
To find the equation of the parabola, we can use the vertex form of the equation, which is given by y = a(x - h)^2 + k, where (h, k) is the coordinates of the vertex and a is a constant. In this case, the coordinates of the vertex are (5/12, 0) and the constant a can be determined using the distance between the roots.
To find a, we can use the fact that the distance between the roots of a parabola is equal to the square root of the product of the coefficients of the quadratic terms in the equation. In the vertex form, the coefficient of the x^2 term is a, so we can set up the following equation to find a:
(13/6)^2 = a * (5/12)^2
Solving for a, we find that a = -1/3.
Therefore, the equation of the parabola is y = -1/3(x - 5/12)^2.
A 6-sided polygon is classified as a heptagon.
True
False
Answer:
true 6=hepti
Step-by-step explanation:
One number is two less than a second number. Twice the second number is nine less than three times the first find the two numbers.
Answer:
13 and 15
Step-by-step explanation:
We set up equations.
X=Y-2
2Y=3X-9
We change X=Y-2 into Y=X+2.
Substituting for Y, we get 2Y=2X+4=3X-9
We now solve for x.
2X+4=3X-9 |-2X
4=X-9 |+9
13=X.
X=13
Substituting for Y, we get that Y =15 from the equation Y=X+2.
So, X=13 and Y=15
Find the value of x in this equation
Answer:
x = 4
Step-by-step explanation:
7x = 3x + 16
7x - 3x = 16
4x = 16
4/4 x = 16/4
x = 4
Unit rate reasoning down
In the unit rate between two units, the denominator is always one.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Unit rate is written in a fraction form where the denominator is always one.
Example:
6 miles in 3 minutes.
This can be written as,
6 miles = 3 minutes
Dividing 3 on both sides.
2 miles = 1 minute
= 2 miles per minute
Thus,
In the unit rate between two units, the denominator is always one.
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12. How much tax would I pay on a Nintendo Wii (cost of $150) if the tax is 8%?
Answer:
$162
Step-by-step explanation:
8% of 150 = 12 + 150
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other. PLEASE EXPLAIN WITH WORDS IN TWO SENTENCES I NEED HELP ASAP
Answer:
See below.
Step-by-step explanation:
The given functions f(x) and g(x) are linear functions. Therefore, their inverses are a reflection about the line y = x.
The mapping rule for reflecting a point about the line y = x is:
(x, y) → (y, x)To determine if f(x) and g(x) are inverses of each other:
Input the x-value of the ordered pair into one function.Input the y-value of the ordered pair as the x-value of the other function.If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.
Given functions:
[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]
Ordered pair: (2, 9)
Substitute x = 2 into f(x):
[tex]\implies f(2)=2(2)+5=9[/tex]
Substitute x = 9 into g(x):
[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]
Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.
I want to know what is 2/5 x -3
Answer:
I think your answer is [tex]\frac{2}{5} x-3[/tex]
Step-by-step explanation:
Matthew and some friends are going to a concert. They hire a car service for $75 to drive them to a
restaurant for dinner and then the concert. They divide the $60 cost of the dinner equally. However, since
Matthew's dad provided concert tickets for the group, the friends agree that Matthew doesn't have to help pay
for the car service. The friends divide this cost equally among themselves. If each friend spends a total of $25,
how many friends went to the concert with Matthew?
n represents the number of friends, there must have been 2 friends with Matthew at the concert.
What is the arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Let's call the number of friends n. The cost of the car service for the friends is 75 - 25 = 50 dollars. Since this cost is divided equally among the friends, each friend pays 50/n dollars.
The total cost for each friend, including the cost of the car service and the cost of dinner, is 25 dollars. Therefore, the cost of dinner for each friend is 25 - 50/n dollars.
Since the cost of dinner was divided equally among the friends, each friend paid 60/n dollars for dinner. Therefore, 25 - 50/n = 60/n.
Solving this equation for n, we get:
25 - 50/n = 60/n
50/n - 60/n = -25
10/n = 25
n = 2.5
Hence, n represents the number of friends, there must have been 2 friends with Matthew at the concert.
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I have 3 red balls, 3 blue balls and 3 yellow balls in a box. Total of 9 balls. Let's say that I randomly pick 3 balls, what are the chances of having at least 2 red balls in the 3 that I picked?
The probability of having at least 2 red balls in the 3 that I picked will be 1/3.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.
If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,
P = 3/9
P = 1/3
The probability of having at least 2 red balls in the 3 that I picked will be 1/3.
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A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use b for the base length of the triangular logo.
The inequality that describes the base length of the triangle is b ≤ 28/h
How to determine the inequality that describes the base length of the triangle?From the question, we have the following parameters that can be used in our computation:
Base = bHeight = hArea = At most 14 square feetThe area of a triangle can be calculated using the following formula
Area = 1/2 * Base * Height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * b * h
Evaluate the products
Area = 1/2bh
Recall that
Area = At most 14 square feet
This means that
Area ≤ 14
So, we have
1/2bh ≤ 14
Multiply through by 2
bh ≤ 28
Divide both sides by h
b ≤ 28/h
Hence, the inequality is b ≤ 28/h
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A merchant mixed 20 pounds of a cinnamon tea with 10 pounds of a spice tea. The 30-pound mixture sells for $80. A second
mixture included 12 pounds of the cinnamon tea and 8 pounds of the spice tea. The 20-pound mixture sells for $54. What is the
price per pound of the cinnamon tea?
A.$3.50
B.$2.50
C.$5.50
D.$0.50
Answer:10x+2y=38, where x is the dollar cost of cinnamon and y the dollar cost of the spice.1
6x+8y=80multiply the top by -4-40x-8y=-15216x+8y=80.
Add them and y is eliminated.-24x=-72
Step-by-step explanation:
Consider the following regression model: yi = B0 +B 1xi + ui. If the first four Gauss-Markov assumptions hold true, and the error term contains heteroskedasticity, then _____.a. Var(ui|xi) = 0b. Var(ui|xi) = 1c. Var(ui|xi) = Θi2d. Var(ui|xi) = Θc. Var(ui|xi) = Θi2
If the first two Gauss-Markov assumptions are met and heteroskedasticity exists in the error term, Var(ui|xi) = i2.
What is an example of heteroscedasticity?Examples. When there is a significant disparity in the magnitude of the observations, heteroscedasticity frequently develops. An old-fashioned illustration of heteroscedasticity is the relationship between income and food expenses. The variability of eating habits will rise as income does as well.
Does heteroskedasticity make a difference?Because normal regression model (OLS) regression presumes that all royalties are taken from a population with constant variance, heteroscedasticity is a concern (homoscedasticity). The particles ought to have a standard deviation in order to meet the plugs and be capable of relying on the results.
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Determine whether y = -2x² - 3 is a function.
Answer:yes
Step-by-step explanation:
Please give an answer, and thinking. Thank you.
Answer:
see explanation
Step-by-step explanation:
- 1x + 4y = 12 , that is
- x + 4y = 12 ( add x to both sides )
4y = 12 + x ( divide each term by 4 )
y = 3 + [tex]\frac{1}{4}[/tex] x
Reagan created a model of a rectangular flag.
Her model is 13 inches long.
It is a model of a flag that is 39 inches long.
How many times wider is the actual flag than Reagan's model?
The actual flag is
times wider than Reagan's model.
Actual Flag
39 inches
Reagan's
Model
13 inches
CLEAR
CHECK
The number of times that the actual flag is wider than the Reagan's model would be = 3 times.
What is rectangle?A rectangle is defined as a type of quadrilateral that has opposite sides that are parallel and equal to each other and all four angles are right angles.
The actual length of the rectangular flag = 39 inches long.
The length of Reagan's model = 13 inches.
To find the number of times wider than the actual flag the model is, use the formula:
= Length of actual flag / Length of model
= 39/13 = 3.
Therefore, the number of times that the actual flag is wider than the Reagan's model is 3 times.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
(4,-10)
Step-by-step explanation:
Graphing calculator