(17) The value of x would be 20 degrees.
(18) The value of x would be 21.25 degrees.
(20) The value of x would be 6 degrees.
What is the sum of the angles of a triangle?
The sum of the angles of a triangle is 180 degrees. This is a fundamental property of triangles and is known as the triangle sum theorem.
(17)
By using the property of the sum of angles of a triangle, we get
(x+6) + (3x+9) + (4x+5) = 180
Simplifying the left side of the equation gives:
8x + 20 = 180
Subtracting 20 from both sides of the equation gives:
8x = 160
Dividing both sides of the equation by 8 gives:
x = 20°
(18) In a right triangle, one angle is a right angle, which measures 90 degrees. If we know the measures of the other two angles in the triangle, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to find the value of x.
(2x-4) + (6x+14) + 90 = 180
Simplifying the left side of the equation gives:
8x + 10 = 180
Subtracting 10 from both sides of the equation gives:
8x = 170
Dividing both sides of the equation by 8 gives:
x = 21.25
(20) To find the value of x, we can use the fact that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. We can write an equation using this fact and the measures of the three angles given in the problem:
(2x+13) + (15x+19) = (7x+92)
Simplifying the left side of the equation gives:
17x + 32 = 7x + 92
Subtracting 7x from both sides of the equation gives:
10x + 32 = 92
Subtracting 32 from both sides of the equation gives:
10x = 60
Dividing both sides of the equation by 10 gives:
x = 6
Hence,
(17) The value of x would be 20 degrees.
(18) The value of x would be 21.25 degrees.
(20) The value of x would be 6 degrees.
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3. The vertices for A LML are L(-4,0), M(-2,0) and N(-3,-3). Its image is L'(1,1), M'(3,1) and
N'(2,-2). What is the translation rule that maps the preimage to the image?
The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)
How to determine the translation rule of the transformationFrom the question, we have the following parameters that can be used in our computation:
Pre-image: L(-4,0), M(-2,0) and N(-3,-3)
Image: L'(1,1), M'(3,1) and N'(2,-2)
The translation rule is calculated as
(x, y) = L' - L
Substitute the known values in the above equation, so, we have the following representation
(x, y) ⇒ (x + 1 + 4, y + 1 - 0)
Evaluate
(x, y) ⇒ (x + 5, y + 1)
Hence, the translation is (x, y) ⇒ (x + 5, y + 1)
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Write an equation of the line that passes through the points.
4.(-3,0), (-2, 3)
5. (-6, 10), (6, -10)
4.
find slope;
3 - 0/-2 -(-3) = 3/1 = 3
y = 3x + b
0 = (3)(-3) + b
0 = -9 + b
b = 9
y = 3x + 9
Help me pls pls I been stuck om this question for 5 hours now help me pls
The volume of the tunnel is 225.476cm³
How to find volume of objects?We should know that the volume of an object entails the quantity of things it can hold at a particular time.
The volume of the tunnel = Volume of semi circle + volume of the rectangle
This is given by
V=3/4[tex]\frac{4}{3} \pi r^{3}[/tex] + lbh
volume of the tunnel = 4/3*3.142*(5/2)³ + 4*5*8
Simplifying the expression
(65.476 + 160)cm³
Volume = 225.476cm³
Given that the car exhaust at 10m³
226cm = 2.26m
Note that 60 seconds = 1 Minute
Therefore 10*2.26=22.6m
=22.6/60 = 3 hours, 46 mins and 2 seconds.
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1. 5x - 8 < 17
It needs to be graphed on a number line.
Answer: x < 5
What does this mean?
This simply means that any point that is five or below is going to be outlined.
How do I do it?
It's as simple as drawing a point at value 5, and everything below is going to contain a line.
Representation
-----------------------------------------------o
a vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a
A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.
The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.
To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.
Bidirectional chi-square is one of several tests of goodness of fit between the actual values of two nominal or ordinal variables and the values expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.
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help me pleasee asappp
The median of the data sets 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32 is 21.
How to find median?The Median is the "middle" of a sorted list of numbers. In other words, Median, in statistics, is the middle value of the given list of data when arranged in an order.
Therefore, let's find the median of the data sets.
Firstly, we have to sort the data in ascending order before we can find the median in the data set.
10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32
Hence, the sorted data set is 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32.
Therefore,
median = 21
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What i cot of tiling a rectangular plot of land 500m long and 200m wide at the rate r 8 per q m
The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
Area of rectangle = length × breadth
Area of rectangular plot = 500× 200 = 1,00,000 sq m
Cost of tilling 1 sq m of land = Rs. 8
Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000
Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
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an item is regularly priced at . it is on sale for off the regular price. how much (in dollars) is discounted from the regular price?
An item is regularly priced at, 1.98$ is discounted from the regular price.
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given that,
First, change the percentage into decimal:
Let us assume,
Sale of regular price = 1%
1% = 1/100 = 0.01
Assume, item regular price is = 2$
Multiply 2 with 0.01:
2 * 0.01 = 0.02
Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02
2 - 0.02 = 1.98
Therefore,
An item is regularly priced at, 1.98$ is discounted from the regular price.
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When Lisa increased her speed in letter c,
the increase took two seconds. What was her acceleration?
Lisa's change in speed is 4 miles per hour.Lisa's acceleration is 2 miles per hour.
What was her acceleration?According to the question,
The speed of Lisa is = 3 miles per hour
A dog starts to chase her, and she speeds up to seven miles per hour.
The change in speed after dog chase her is,
= 7 miles per hour - 3 miles per hour
= 4 miles per hour
Lisa's change in speed is 4 miles per hour.
When Lisa increased her speed in letter c, the increase took two seconds.
Then,
The Lisa acceleration is,
Acceleration = Change in speed/Change in time
Acceleration = 4/2
Acceleration = 2 per mail.
Hence, Lisa's acceleration is 2 miles per hour.
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If Santa Claus ate two cookies from every child on Earth, how many cookies would he eat over one Christmas Eve?
Answer:
three billion eight hundred million
Step-by-step explanation:
Which is equal to 1/58^8 ? a.58^-8 b.-1/58^-8 c.58^8 d.1/(58)^-8
a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
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suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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HELPPPPP ME NOW PLEASE
Write y=1/8x+7 in standard form unsung integers.
A. 8x-y=56
B. -x+8y=56
C. -x-8y=56
D. -x+8y=56
Answer:
-x + 8y = 56
Step-by-step explanation:
.................
An online furniture store sells chairs for $100 each and tables for $400 each. Every
day, the store can ship no more than 18 pieces of furniture and must sell no less than
$2900 worth of chairs and tables. Also, the store must sell a minimum of 10 tables. If
a represents the number of tables sold and y represents the number of chairs sold,
write and solve a system of inequalities graphically and determine one possible
solution.
PLS INCLUDE THE INEQUALITIES
y ≥ 0 , Zero possible solution.
What is inequality ?
In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.
According to question
a represents the number of tables sold and y represents the number of chairs sold
Using a and y as variables, we get
a + y ≤ 18
100y + 400a ≥ 2900
Simplified,
100(y + 4a) ≥ 2900
y + 4a ≤ 29
Given the minimum number of tables that need to be sold, we evaluate using a = 10
y + 4(10) ≥ 29
y ≥ -11
y represents the number of chairs sold
therefore, y ≥ 0
Since we can't purchase -11 chair, we round up our result giving us y ≥ 0
Now
the store must sell a minimum of 10 tables and tables for $400 each
then
10*400 = $4000
which is more than worth of chairs and tables $2900
hence Zero possible solution.
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Rectangle ABCD is dilated with a center at (0, 0) and a scale factor of 1. What is the perimeter of the dilated rectangle? Enter the answer as a whole number in the box.
units
Answer:
12 units
Step-by-step explanation:
You want to know the perimeter of rectangle ABCD after it has been dilated by a factor of 1.
PerimeterThe original rectangle ABCD has a perimeter of ...
P = 2(L +W) = 2(4 +2) = 12
The perimeter of the dilated rectangle is the original perimeter multiplied by the dilation factor:
P' = 12·1 = 12
The dilated rectangle has a perimeter of 12 units.
__
Additional comment
Dilation by a factor of 1 changes nothing at all. The center of dilation is irrelevant.
Last winter, a store sold 408 coats in
3 months. This winter, the store plans to sell
coats for 4 months. Based on the average
number of coats sold each month last winter,
how many total coats should the store plan to
sell this winter?
Total coats should the store plan to sell this winter is 952.
Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.
What is sell?
Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.
3month = 408 coats
1 month = 408/3 =136 coats
Then, 4 months = 136*4 = 544 coats
Total coats should the store plan to sell this winter = 544+408 = 952.
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Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
2. How many points of inflection will f(x) = 3x5+2x4 - 5x - 12 have?
5
3
2
4
2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.
What is Inflection points definition?
An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.
If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.
[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]
Show Steps
Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]
Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]
(0,-12)
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give a point estimate (mean) for the average height of all people at the place where you work. start by putting the 20 heights you are working with into the blue data column of the spreadsheet. what is your point estimate, and what does this mean?
A point estimate (mean) for the average height of all people at the place where you work is 62.26
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
Given,
Number of observations = 20
Mean = sum of all observation / number of observations
Mean = 66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20
Mean = 1245.2 / 20 = 62.26
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what is the value of the expression 3^{2}*(2^{3} +4)-22
Answer:
86
Explanation:
3² × (2³ + 4) - 22
9 × (8 + 4) - 22
9 × 12 - 22
108 - 22
86
One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
What is the value of y in the equation?
6y + 2 = 4p - 10
3. Solve the
proportion
x : 15 = 29 : 9.6
The required value of x for the given proportion is 45.31
What is proportion?
Proportion is a mathematical relationship or ratio between two or more values. It is used to compare the size, quantity, or degree of two or more objects or measurements. Proportion can be expressed as a fraction, decimal, or percentage. It is often used in geometry, algebra, and calculus to determine the size of a shape or to solve an equation. Proportion is also used in statistics to compare data sets. In everyday life, proportion is used to make sure that items are in good balance with each other. For instance, proportions are used when baking a cake or making a recipe to ensure that the ingredients are properly combined.
Given, the proportion
x : 15 = 29 : 9.6
or, x = [tex]\frac{29}{9.6}[/tex] × 15
or, x = 45.31
Hence, the required value of x for the given proportion is 45.31
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Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1
Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute
The equation of line in point-slope form of the line, is y = 5x - 1.
What is point - slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
The line passes through the points (1, 4) and (2, 9).
We have to find the equation of line in point - slope form.
First to find the slope from the given points.
Since,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]
So, [tex]m = \frac{9-4}{2-1} = 5[/tex]
Now consider, the point slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]
⇒
[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
Hence, the equation of line in point-slope form of the line, is y = 5x - 1.
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12. What is the maximum value of a periodic
function with amplitude 6.5 and minimum
value 7?
The maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.
What is a periodic function?
The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
The maximum value of a periodic function with amplitude 6.5 and minimum value 7 is equal to the sum of the amplitude and the minimum value.
The amplitude of a periodic function is defined as the maximum distance that the function deviates from its centerline. In this case, the amplitude of the function is 6.5.
The minimum value of a function is the lowest value that the function takes on over a given period. In this case, the minimum value of the function is 7.
To find the maximum value of the function, we need to add the amplitude and the minimum value. The maximum value is equal to 6.5 + 7 = 13.5.
Hence, the maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.
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Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:
Part A: Determine which integer(s) in the solution set makes the equation false. Show all work. (8 points)
Part B: Use a complete sentence to explain how you were able to determine which values make the equation false. (4 points)
A) The integers that make the equation false are {2, 54, 86}
B) We found that by solving the linear equation.
Which integer makes the equation false?
Here we have the following linear equation:
7m - 11 = 5m + 43
And the set of the possible solutions is S: {2, 27, 54, 86}
The simplest way to see which integer makes the equation false, we just need to replace the values of the possible solution sets and see which ones give a false equation.
Another method is to simplify the equation, and i will do that:
7m - 11 = 5m + 43
7m - 5m = 43 + 11
2m = 54
m = 54/2
m = 27
So the equation has a single solution, m = 27.
Then the integers that make the equation false are {2, 54, 86}
B) We determined the only true solution for the linear equation, and thus, all the other possible integers aren't solutions, thus, make the equation false.
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Tabatha and Horatio each leave their separate houses and drive to a restaurant to meet for dinner. Tabatha lives 15 miles from the restaurant, and she drives at a rate of 3 miles every 2 minutes. The graph represents Horatio’s distance, in miles, y, from the restaurant after driving for x minutes.
Tabatha drives 1/12 mile more per minute than Horatio drives.
Tabatha drives 1/6 mile more per minute than Horatio drives
Tabatha drives 3 miles more per minute than Horatio drives.
Tabatha drives 9 miles more per minute than Horatio drives.
Answer:
Tabatha drives 1/6 mile more per minute than Horatio drives
Step-by-step explanation:
What is the value of 24 + x ÷ 12 when x = −180?
17
9
−13
−178
If you don't know the answer please do not type random stuff or you'll see what ima do
The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?From the question, we have the following parameters that can be used in our computation:
24 + x ÷ 12
Also, we have the value of the variable to be
x = −180
Substitute the known values in the above equation, so, we have the following representation
24 - 180 ÷ 12
Evaluate the quotient in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 24 - 15
Evaluate the difference in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 9
Hence, the value of the expression is (b) 9
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Two angles are complementary. The measure of the larger angle is 26 degrees less than 3 times the measure of the smaller angle. The measure of the smaller angle is ________ degrees, and the larger angle is ________ degrees.
Answer:
29, 61
Step-by-step explanation:
x = smaller
y = larger
y = 3x - 26
x + y = 90
x + 3x - 26 = 90
4x - 26 = 90
4x = 116
x = 29
x + y = 90
29 + y = 90
y = 90 - 29
y = 61
Answer:
smaller angle = 29°
larger angle = 61°
Step-by-step explanation:
Let x be the larger angle and y be the smaller angle
Larger angle is 26° less than 3 times the smaller angle
i. e x = 3y-26°
Since x and y are complementary angles, we can write,
x + y = 90°
or, (3y - 26°) + y = 90°
or, 4y = 90° + 26°
or, y = 116°/4
or, y = 29°
So,
x = 3 * 29° - 26° = 61°