Caden needs to use 126 cubes to fill the box without empty space.
How many cubes does he use to fill the boxThe volume of the box is:
42 in. x 1 in. x 3 in. = 126 cubic inches
The volume of each small cube is:
1 in. x 1 in. x 1 in. = 1 cubic inch
To fill the box, the number of cubes needed is the volume of the box divided by the volume of each cube:
126 cubic inches ÷ 1 cubic inch per cube = 126 cubes
Therefore, Caden needs to use 126 cubes to fill the box without empty space.
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Yolanda rented a truck for one day. There was a base fee of $10.75, and there was an additional charge of 6 cents for each mile driven. The total cost, C (in dollars), for driving x miles is given by the following.
Answer:
The total cost, C (in dollars), for driving x miles is given by:
C = 0.06x + 10.75
where x is the number of miles driven.
To find the total cost for driving a certain number of miles, simply substitute that value for x in the equation and solve for C.
A certain type of cable has a mean breaking point of 150 pounds with a standard deviation of 8 pounds. What weight should we specify so that we expect 95% of the cables not to break supporting that weight?
Answer:
171.76 Pounds
Step-By-Step Explanation:
So the explanation to how I got the answer is in the link below.
find the limiting value or horizontal asymptote of y= 2x/4x-5
The limiting value or horizontal asymptote of the function y = 2x/4x-5 is y = 0.5
Finding the limiting value or horizontal asymptoteFrom the question, we have the following parameters that can be used in our computation:
y = 2x/4x-5
The limiting value or horizontal asymptote can be calculated by graph
So, we start by plotting the graph of y = 2x/4x-5
See attachment for the graph
From the graph, we can see that
The function does not have a defined value at y = 0.5
This means that the limiting value or horizontal asymptote is y = 0.5
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Tres amigos van de compras, Juan gasta el doble que Alicia y Ana gasta el triple de Alicia. Si entre los tres han gastado L.
720.00, ¿Cuánto ha gastado cada uno?
the three friends spent L.120.00, L.240.00, and L.360.00, respectively.
How to solve the problem?
Let's denote the amount that Alicia spends as "x". According to the problem statement, we know that Juan spends twice as much as Alicia, which means he spends 2x. Similarly, we know that Ana spends three times as much as Alicia, which means she spends 3x.
We also know that the three friends together have spent L.720.00. So, we can set up an equation to represent this:
x + 2x + 3x = 720
Simplifying this equation, we get:
6x = 720
Dividing both sides by 6, we get:
x = 120
So, Alicia spent L.120.00, Juan spent twice as much as Alicia, which is L.240.00, and Ana spent three times as much as Alicia, which is L.360.00.
Therefore, the three friends spent L.120.00, L.240.00, and L.360.00, respectively.
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The venue for an outdoor summer concert was divided into 35 sections. The event planner randomly chose 8 sections and counted the number of ice chests in the section, as shown below.
45, 57, 30, 62, 57, 45, 30, 57
Assuming that the sample was representative of the entire venue, what was the mean number of ice chests in a section?
A.
48.5
B.
51
C.
47.875
D.
44.125
please answer
Answer:
C is correct
Step-by-step explanation:
express the function graphed on the axis below as a piecewise function
The function graphed on the axis above should be expressed as a piecewise function as follows;
f(x) = x + 1 {x < -5}
= 5x - 10 {x > 1}
How to determine the piecewise function?In order to determine the piecewise function, we would determine an equation that represent each of line shown on the graph. Therefore, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-7 + 4)/(-8 + 5)
Slope (m) = -3/-3
Slope (m) = 1.
At data point (-5, -4) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 4 = 1(x + 5)
y = x + 1
1, -5 2 0
For the second line, we have:
Slope (m) = (0 + 5)/(2 - 1)
Slope (m) = 5/1
Slope (m) = 5.
At data point (2, 0) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 5(x - 2)
y = 5x - 10
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graph of the function h(x)=(x^2-3x-4)/x-4
Plotting the graph of the function h(x) = [tex](x^2 - 3x - 4) / (x - 4)[/tex], we get y- intercept = 1, vertical asymptotes at x=4 and horizontal asymptotes at y=1.
What does graph of any function represents?The connection between a function's input values (usually written as x) and output values (often indicated as y) is represented by the function's graph. It gives insights on the function's characteristics, including its domain, range, intercepts, asymptotes, and general form, as well as a visual representation of how the function acts.
Steps to plot the graph of the give function h(x) =[tex](x^2 - 3x - 4) / (x - 4)[/tex]:
Put the numerator [tex](x^2 - 3x - 4)[/tex] equal to zero and solve for x to discover the x-intercepts, if any, to determine the x-intercepts.Finding the y-intercept To get the y-intercept, set x = 0 in the function and solve for y, which gives y- intercept=1.To locate any vertical asymptotes, set the denominator (x - 4) equal to zero and solve for x, which gives x=4.Find horizontal asymptotes: To find the horizontal asymptote, compare the degrees of the numerator and denominator (s). There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote lies at y = ratio of the leading coefficients if the degree of the numerator and denominator are equal. The horizontal asymptote is at y = 0 if the degree of the numerator is smaller than the degree of the denominator, for given problem it is at y=1.Draw the graph of the function h(x), highlighting the x-intercepts, y-intercept, vertical asymptotes, and horizontal asymptotes using the knowledge gained from the aforementioned phases (s). Take attention to how the function behaves as x gets closer to positive or negative infinity.Name the graph, including the x- and y-axes, x- and y-intercepts, vertical and horizontal asymptotes, and any other interesting points.Learn more about Graphs here:
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The table is completed as below
Interested in NOT Interested in Total
Athletics Athletics
Interested in
Academic Clubs 26 58 84
Not Interested in
Academic Clubs 118 38 156
Total 144 96 240
How to fill the tableTo fill in the table, we start with the total number of students, which is 240.
We know that 35% of students are interested in athletics, so we can find the number of students interested in athletics as:
0.35 x 240 = 84
Similarly, we know that 3/5 of students are interested in academic clubs, so we can find the number of students interested in academic clubs as:
(3/5) x 240 = 144
We also know that 26 students are interested in both athletics and academic clubs, so we can fill in that cell as 26.
To fill in the remaining cells, we can use the fact that the row and column totals must add up correctly. For example, in the "Interested in athletics" row, we know that there are a total of 84 students interested in athletics. We also know that 26 of these students are interested in both athletics and academic clubs. Therefore, the number of students interested in athletics but not academic clubs is:
84 - 26 = 58
We can use similar reasoning to fill in the remaining cells. For example, in the "Not interested in athletics" column, we know that there are a total of 214 students who are not interested in athletics. We also know that 144 students are interested in academic clubs. Therefore, the number of students who are not interested in athletics but are interested in academic clubs is:
144 - 26 = 118
Let x represent "not interested in academics club" and "not interested in athletic". Using the total in the horizontal (bottom row) we have:
144 + 58 + x = 240
x = 240 - 202
x = 38
Hence 58 + 38 = 96 and 118 + 38 = 156
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Which of the following do not belong to the group of numbers
The number that does not belong to the set of numbers is given as follows:
B. Three
What are even and odd numbers?Numbers are classified as even or odd depending on whether they are divisible by 2 or not, as follows:
Even numbers are divisible by 2, that is, their last digit is either 0, 2, 4, 6 or 8.Odd numbers are not divisible by 2, that is, their last digit is either 1, 3, 5, 7 or 9.For this problem, we have that the number five does not belong to the set of even numbers, as the numbers two, four and six do.
Missing Information?The options are:
A.Two
B.Three
C.Four
D.Six
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A bag contains 3 gold marbles, 8 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
To calculate the expected value of playing this game, we need to multiply the probability of winning each amount by the corresponding payout and then sum them up.
Let's start by calculating the probability of selecting each type of marble:
Probability of selecting a gold marble: 3/34
Probability of selecting a silver marble: 8/34
Probability of selecting a black marble: 23/34
Now, let's calculate the expected value of playing the game:
E(x) = (3/34) * $3 + (8/34) * $2 + (23/34) * (-$1)
E(x) = $0.26
So the expected value of playing this game is $0.26. This means that over many plays of the game, we would expect to win an average of $0.26 per play. However, it's important to remember that this is just an average, and in any individual play of the game, you could win more or less than this amount.
Writing With Tens and Ones
rite each number described.
1) Write a number with eight tens and one one
2) Write a number with five tens and five ones
3)
Write a number with eight tens and nine ones
) Write a number with five tens and eight ones
O Write a number with one ten and seven ones
O Write a number with five tens and two ones
Write a number with six tens and two ones
Write a number with three tens and zero ones
Write a number with four tens and five ones
A number with eight tens and one one is = 81.
A number with five tens and five ones is = 55.
A number with eight tens and nine ones is 89.
A number with five tens and eight ones = 58.
A number with one ten and seven ones is 17.
A number with five tens and two ones is 52.
A number with six tens and two ones is 62.
A number with three tens and zero ones is 30.
A number with four tens and five ones is 45.
What is the Number about?The phrase "eight tens and one one" denotes a numerical value featuring the digit 8 in the tens position and 1 in the ones position. This is equal to the sum of 80 and 1, resulting in a total value of 81.
Therefore "a numerical figure composed of 5 tens and 5 units" indicates a number where 5 is in the tens position while 5 is in the ones position, resulting in a total of 50 + 5, which equals 55.
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if 123=2, then what is 354=
if 1 2 3 = 2
then 3 5 4 = 5
hope it helps:)
Surface area of triangular prism
Please answer, this as quick as possible, it’s very important for me, I’ll give brainliest if it’s correct, and try not to use chatgpt or you’ll get reported
Answer:
Your calculator should be in radian mode.
a)
[tex]f(x) = 56 \sin( \frac{2t\pi}{12} + \frac{\pi}{2} ) + 4[/tex]
b)
[tex]f(x) = 56 \cos( \frac{2t\pi}{12} - \frac{\pi}{2} ) + 4[/tex]
c)
The height of the wheel's central axle is 32 meters.
f(x) = 56sin((2(x + 4)π/12) - (π/2)) + 4
Two mountain peaks are known to be 17 kilometers apart. A person located at a vista point such that a right angle is spanned when he looks from one peak to the other
is told that the distances from the vista point to each peak differ by 7 kilometers. How far is the vista point from each mountain peak?
The person is looking at each peak on a leg of a right triangle. The hypotenuse is the distance between the mountains.
How far is the vista point from each mountain peak?The distance is determined by
x^2+(x+5)^2=25^2
x^2+x^2+10x+25=625
2x^2+10x-600=0
x^2+5x-300=0
(x+20)(x-15)=0
only positive root is x=15
x+5=20
The vista point is 15 miles from one mountain peak and 20 miles from the other.
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What is the domain of the function in the graph?
graph on the h-g axis, between the points (6, 80) and (11, 40)
A. 6≤g≤11
B. 40≤g≤80
C. 40≤h≤80
D. 6≤h≤11
Answer:
D
Step-by-step explanation:
The domain of a function refers to the set of all possible input values (independent variable) for which the function is defined. In this case, the graph has points (6,80) and (11,40), which means that the function is defined for the values of g (the independent variable) between 6 and 11. Therefore, the domain of the function is:
D. 6≤g≤11
The domain of the function in the given graph is 6≤h≤11, as it includes all possible values of h between and including 6 and 11 on the horizontal (h) axis. So the correct option is D.
The domain of a function refers to the set of all possible input values for the function. In the given graph, which is plotted on the h-g axis and includes points (6, 80) and (11, 40), we are interested in determining the valid range for the independent variable, h.
The lowest h-value on the graph is 6, corresponding to the point (6, 80), and the highest h-value is 11, corresponding to the point (11, 40). These are the boundaries that define the domain of the function. Any value of h that falls within this range is a valid input for the function, and any value outside this range is not represented on the graph.
Therefore, the domain of the function is 6≤h≤11, as it includes all values of h between and including 6 and 11. This range encompasses all possible inputs for this function as depicted in the graph.
In summary, the domain represents the valid input values, and in this case, it is limited to the interval from 6 to 11 on the h-axis.
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Turner helped his grandfather build a raised garden bed for Tanner’s grandmother. The bed is shaped like a rectangular prism that is 4 1/2 feet wide and a half of a foot tall. Turner and his grandfather use 18 bags of topsoil, each containing three force of a cubic foot, to feel the bed completely. How long is the garden?
The length of the garden containing the soil is L = 24 feet
Given data ,
Volume = Length x Width x Height
Width = 4 1/2 feet
Height = 1/2 foot
Total volume of topsoil used = 18 bags x 3 cubic feet/bag = 54 cubic feet
So , the length of the garden is
54 = Length x 4 1/2 x 1/2
On simplifying , we get
54 = Length x 9/2 x 1/2
Now, let's simplify the right-hand side by multiplying the numerator and denominator by 2
54 / (9/2 x 1/2) = The length of the garden
The length of the garden = 54 /9 x 4
The length of the garden = 6 x 4
The length of the garden = 24 feet
Hence , the length of the garden bed is 24 feet
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Using a table, find the range of the function for the given domain:
f(x)=2x+7 with domain: x = {2, 3, 5, 9}
A. y = {9, 10, 12, 16}
B. y = {11, 13, 17, 25}
C. y = {4, 6, 10, 18}
D. y = {-11, -13, -17, -25}
The range of the function is y = {11, 13, 17, 25}.
What is range of function?In mathematics, the range of a function refers to the set of all possible output values that the function can produce when given a set of input values. It is also known as the image of the function. The range of a function can be found by evaluating the function for all possible input values, or by analyzing the properties of the function.
According to given information:To find the range of the function, we need to substitute each value of the domain into the function and record the corresponding output values.
For x = 2, f(2) = 2(2) + 7 = 11.
For x = 3, f(3) = 2(3) + 7 = 13.
For x = 5, f(5) = 2(5) + 7 = 17.
For x = 9, f(9) = 2(9) + 7 = 25.
Therefore, the range of the function is y = {11, 13, 17, 25}.
The answer is A. y = {9, 10, 12, 16} is not the correct range for this function with the given domain.
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what 95% confidence interval for a standard normal distribution
A 95% confidence interval for the standard normal distribution is typically given by (-1.96, 1.96) . mean that correspond to the upper and lower bounds of the interval
what is mean ?
In statistics, the standard deviation is a measure of the amount of variation or dispersion in a set of data. It is the square root of the variance and is denoted by the symbol σ (sigma). The standard deviation is expressed in the same units
In the Given question :
A 95% confidence interval for the standard normal distribution is typically given by (-1.96, 1.96)
This means that we are 95% confident that the true value of a normally distributed variable falls within this range. The values of -1.96 and 1.96 represent the number of standard deviations from the mean that correspond to the upper and lower bounds of the interval, respectively. This interval is often used in statistical inference to estimate the population mean or proportion based on a sample.
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what 95% confidence interval for a standard normal distribution then what is the number of standard deviations from the mean that correspond to the upper and lower bounds of the interval ?
Juan wants to see the Grand Cayon, so he is taking a vacation in Arizona. He drove south from his house for 280 miles. Then, He drove east 64 miles.
a. Draw a diagram illustrating Juans Trip
b. How many total miles did Juan travel?
c. If a road was built directly from Juans home to the grand canyon, how long would it be? Round to the nearest mile.
d. Approximately how much shorter would Juans trip be if he was able to take the direct route?
Juan traveled approximately 288.24 miles.
The direct road would be approximately 288 miles long.
Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.
We have,
a.
Here is a diagram illustrating Juan's trip:
Grand Canyon
|
|
|
Juan's | x
house --------->
y
b.
To find the total distance Juan traveled, we can use the Pythagorean theorem:
distance² = x² + y²
Juan drove 280 miles south (y direction) and 64 miles east (x direction), so we have:
distance² = 280² + 64²
distance² = 78,976 + 4,096
distance² = 83,072
Taking the square root of both sides, we get:
distance ≈ 288.24 miles
c.
To find the length of the direct road, we can use the Pythagorean theorem again:
distance² = x² + y²
The direct road forms a right triangle with legs of 280 miles and 64 miles, so we have:
distance² = 280² + 64²
distance² = 78,976 + 4,096
distance² = 83,072
Taking the square root of both sides, we get:
distance ≈ 288.24 miles
d.
To find how much shorter Juan's trip would be if he took the direct route, we can subtract the distance he traveled from the direct road distance:
288 - 288.24 ≈ -0.24
Thus,
Juan traveled approximately 288.24 miles.
The direct road would be approximately 288 miles long.
Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.
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When Caroline runs the 400 meter dash, her finishing times are normally distributed with a mean of 68 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 99.7% of her finishing times in the 400 meter race.
The empirical rule to determine the interval middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds
Given data ,
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the middle 99.7% of data falls within three standard deviations of the mean, we can calculate the upper and lower limits of this interval as follows:
Lower limit = Mean - (3 x Standard Deviation)
Upper limit = Mean + (3 x Standard Deviation)
Plugging in the values for mean and standard deviation:
Lower limit = 68 - (3 x 1.5) = 68 - 4.5 = 63.5 seconds
Upper limit = 68 + (3 x 1.5) = 68 + 4.5 = 72.5 seconds
Hence , the interval of times that represents the middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds
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Can you help with this please?
The p-value associated with the test statistic of z = 2.566 is 0.0045, accurate to four decimal places.
Based on the given information, we can conduct a one-tailed right-sided test using a normal distribution calculator to find the p-value associated with the test statistic of z = 2.566.
What is a one-tailed right-sided test?In hypothesis testing, a one-tailed right-sided test is a statistical test where the alternative hypothesis (H1) is specified to detect a change typically towards larger values.
Using a normal distribution calculator, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 2.566.
The CDF gives us the probability that a randomly selected value from a standard normal distribution is less than or equal to a given value.
Using a normal distribution calculator:
CDF at z = 2.566 = 0.9955 (rounded to four decimal places)
Since we are conducting a one-tailed right-sided test, we are interested in the probability of getting a value greater than the test statistic. Therefore, the p-value for the given test statistic is:
p-value = 1 - CDF at z = 2.566 = 1 - 0.9955 = 0.0045 (rounded to four decimal places)
Thus, the p-value associated with the test statistic of z = 2.566 is 0.0045, accurate to four decimal places.
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Use the formula for n^p r to evaluate the following expression
Answer:
Use Formula nPr, to solve the following question
6P4 = 360
Find the partial fraction decomposition of x^3-x/x^4+2x^2+1
the partial fraction decomposition of x^3-x/x^4+2x^2+1 is (x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1)
How to find the partial fraction decompositionTo find the partial fraction decomposition of x^3-x/x^4+2x^2+1, we first factor the denominator:
x^4 + 2x^2 + 1 = (x^2 + 1)^2
So we can write:
(x^3 - x)/(x^4 + 2x^2 + 1) = A/(x^2 + 1) + B/(x^2 + 1)^2
Multiplying both sides by the denominator, we get:
x^3 - x = A(x^2 + 1) + B
Now we can solve for A and B by choosing appropriate values for x. Let's choose x = 0 first:
0 - 0 = A(0^2 + 1) + B
B = 0
Now let's choose x = 1:
1 - 1 = A(1^2 + 1) + 0
A = -1/4
So the partial fraction decomposition of x^3-x/x^4+2x^2+1 is:
(x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1) + 0/(x^2 + 1)^2
or
(x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1)
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12. The measures of alternate exterior angles are
Answer:
The same, Congruent
Step-by-step explanation:
The measures of alternate exterior angles are equal when two parallel lines are intersected by a transversal line. That is, if we have two parallel lines l and m intersected by a transversal line t, then the alternate exterior angles are congruent, which means that they have the same measure. More formally, if angle 1 and angle 2 are alternate exterior angles, then:
angle 1 = angle 2
The reason for this is that when the parallel lines are intersected by the transversal line, they form a Z-shape pattern, and the alternate exterior angles are located on opposite sides of the transversal line, but outside of the two parallel lines. The angles are congruent because they are formed by a pair of corresponding angles and a pair of vertical angles.
Have a Great Day!-
What is the measure of angle A in this triangle?
Enter your answer in the box.
Answer:
m∠A = 50°
Step-by-step explanation:
The ∑ of all interior angles of any given triangle is 180°. Set all angle measurements equal to 180:
[tex](x + 30) + (2x - 10) + 70 = 180[/tex]
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex](x + 2x) + (30 - 10 + 70) = 180\\(3x) + (90) = 180[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 90 from both sides of the equation:
[tex]3x + 90 = 180\\3x + 90 (-90) = 180 (-90)\\3x = 180 - 90\\3x = 90[/tex]
Next, divide 3 from both sides of the equation:
[tex]3x = 90\\\frac{(3x)}{3} = \frac{(90)}{3}\\ x = \frac{90}{3}\\ x = 30[/tex]
Plug in 30 for x in the given angle measurement of A and simplify:
[tex]m\angle{A} = 2x - 10\\m\angle{A} = 2(30) - 10\\m\angle{A} = (60) - 10\\m\angle{A} = 50[/tex]
50° is your answer for m∠A.
~
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Answer:
m∠A = 50°
Step-by-step explanation:
The ∑ of all interior angles of any given triangle is 180°. Set all angle measurements equal to 180:
[tex](x + 30) + (2x - 10) + 70 = 180[/tex]
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex](x + 2x) + (30 - 10 + 70) = 180\\(3x) + (90) = 180[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 90 from both sides of the equation:
[tex]3x + 90 = 180\\3x + 90 (-90) = 180 (-90)\\3x = 180 - 90\\3x = 90[/tex]
Next, divide 3 from both sides of the equation:
[tex]3x = 90\\\frac{(3x)}{3} = \frac{(90)}{3}\\ x = \frac{90}{3}\\ x = 30[/tex]
Plug in 30 for x in the given angle measurement of A and simplify:
[tex]m\angle{A} = 2x - 10\\m\angle{A} = 2(30) - 10\\m\angle{A} = (60) - 10\\m\angle{A} = 50[/tex]
50° is your answer for m∠A.
~
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Can someone help me with this question? thank you ^^
Solve the inequality.
4g ≤ 10
(Middle school)
The value of the inequality is g≤2.5
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
The given inequality is 4g≤10
To solve the inequality, divided bo sides of the inequality by the coefficient of g which is 4
This gives the value
4g/g≤10/4
⇒ that g = 2.5
Therefore the value of the inequality is g≤2.5
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y=9/5X+6. find the equation of the line that is parallel to this line and passes through the point (-5,-2)
Answer:
9/5x+7
Step-by-step explanation:
You can keep the slope the same, because it is parallel, but the y-intercept must change to plus seven in order to go through (-5, -2)
Which is the distance between the point with the coordinates (1, 2) and the line with the equation 2x-3y = -2?
a. √13
c. 3√13
13
13
9-
b. 2√13
13
d. 6√13
13
Please select the best answer from the choices provided
A
B
C
D
0
Answer:
To find the distance between a point and a line in a plane, we can use the formula:
distance = |Ax + By + C| / √(A^2 + B^2)
where A, B, and C are the coefficients of the general form of the line equation (Ax + By + C = 0), and (x,y) are the coordinates of the point.
First, we need to rewrite the given line equation in the standard form (y = mx + b):
2x - 3y = -2
-3y = -2x - 2
y = (2/3)x + 2/3
Now we can identify the slope (m) and y-intercept (b) of the line:
m = 2/3
b = 2/3
Next, we can find the equation of the perpendicular line that passes through the point (1,2), since the distance between the point and the line will be the length of the segment connecting the point to the intersection of these two lines. The slope of a line perpendicular to a line with slope m is -1/m, so the equation of the perpendicular line passing through (1,2) is:
y - 2 = (-3/2)(x - 1)
y = (-3/2)x + (7/2)
Now we need to find the intersection of the two lines by solving the system of equations:
y = (2/3)x + 2/3
y = (-3/2)x + (7/2)
(-3/2)x + (7/2) = (2/3)x + 2/3
(-13/6)x = -5/6
x = 5/13
y = (2/3)(5/13) + 2/3
y = 11/13
So the intersection point of the two lines is (5/13, 11/13). Now we can use the distance formula to find the distance between this point and the given point (1,2):
distance = √[(5/13 - 1)^2 + (11/13 - 2)^2]
distance = √[(36/169) + (25/169)]
distance = √(61/169)
distance = √61/13
The closest answer choice is (A) √13, but the simplified expression is actually √61/13. Therefore, none of the answer choices provided are completely accurate.
Step-by-step explanation:
A nursing student can be assigned in how many different ways?
The total number of different ways that the student can be assigned during a 4-day work week is 81 different ways.
What is student?A student is a person who is enrolled in an educational institution, such as a college, university, or trade school. Students are typically required to attend classes and complete assignments to gain knowledge and develop skills related to their field of study. Depending on their level of education, students may also be required to participate in research or internships in order to gain practical experience.
There are 3 possible floors that the student can be assigned to, so for each day of the 4-day week, there are 3 possible assignments.
Therefore, the total number of different ways that the student can be assigned during a 4-day work week is 3 x 3 x 3 x 3
= 81 different ways.
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