Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information we have been given about the diagonal AC and its vertices. The diagonal AC has been given as having the vertices A(-4, -1) and C(2, 5). Since a square has right angles, we know that the other two vertices of the square must form a right angle with the diagonal AC.
To find the coordinates of vertex B, we know that it must have the same y-coordinate as vertex A, but a different x-coordinate. Since the x-coordinate of vertex A is -4, we can deduce that the x-coordinate of vertex B must be the same as the x-coordinate of vertex C, which is 2. Therefore, the coordinates of vertex B are (2, -1).
To find the coordinates of vertex D, we know that it must have the same x-coordinate as vertex A, but a different y-coordinate. Since the y-coordinate of vertex A is -1, we can deduce that the y-coordinate of vertex D must be the same as the y-coordinate of vertex C, which is 5. Therefore, the coordinates of vertex D are (-4, 5).
In summary, the coordinates of the remaining vertices of square ABCD are B(2, -1) and D(-4, 5)
Step-by-step explanation:
PLEASE HELP ME OUT!! PRECAL WORK!!
If h(x) is equal to the composition between functions f(x) and g(x), then we must have:
f(x) = 1/x.
How to find function f(x)?Here we have the function:
h(x) = 1/(x - 5)
And we know that we can write function h as a composition of other two functions:
h(x) = f( g(x) )
Where we know that:
g(x) =x - 5
Remember that the composition of two functions means that we are evaluating one in the other, in this case is rater easy to notice that we must have:
f(x) = 1/x
Then when we evaluate this in g(x) we will get:
f(g(x)) = 1/g(x)
Now we can replace g(x) by the actual function:
f(g(x)) = 1/g(x) = 1/(x - 5)
And that is h(x).
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Is the quotient of two real numbers an integer?
Answer:
The quotient of two real numbers is not necessarily an integer. When dividing two real numbers, the result can be any real number, including a fraction or a decimal. It can be an integer only if the divisor is a factor of the dividend. In other words, if the remainder of the division is zero, the quotient is an integer.
Step-by-step explanation:
PLEASE ASSIST ME
The perimeter of a triangular garden is 72 feet Find the length of the three sides if the middle length side is 2 feet greater than twice the length of the smallest side, and the longest side is 2 feet less than 3 times the length of the smallest side
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
Answer: To find the batting average of a player, we need to find the ratio of hits to total attempts.
Jana's ratio is 12/15, and Tasha's ratio is 9/10.
To compare these ratios, we can simplify both of them to a common denominator. In this case, the common denominator is 15.
Jana's ratio can be simplified to 12/15, which is equal to 0.8
Tasha's ratio can be simplified to (9/15), which is equal to 0.6
So, Jana has a ratio that means she has a better batting average (0.8) compared to Tasha (0.6)
Alternatively, we can convert these ratio to percentage by multiplying them by 100.
Jana's batting average is 12/15 * 100 = 80%
Tasha's batting average is 9/10 * 100 = 90%
By this way also we can see that Tasha's batting average is higher than Jana's batting average.
Step-by-step explanation:
How can we use linear functions in real life
Answer:
Step-by-step explanation:
Linear functions can be used in many real-world applications such as:
Economics: Linear functions can be used to model the relationship between the price of a product and the quantity of the product that will be sold.
Engineering: Linear functions can be used to model the relationship between force and displacement in elastic materials.
Sciences: Linear functions can be used to model the relationship between the concentration of a substance in a solution and the time it takes for that substance to be consumed or produced.
Business and Finance: Linear functions can be used to model the relationship between the cost of a product and the number of products produced.
Graphing: Linear functions can be used to graph the relationship between different variables.
Transportation: Linear functions can be used to model the relationship between the distance traveled and the time it takes to travel that distance at a constant speed.
Construction: Linear functions can be used to model the relationship between the height of a building and the number of floors in the building.
Weather forecasting: Linear functions can be used to model the relationship between temperature and time of the day.
I'm going to provide a real life case for this answer. I own and manage an online soccer jersey store and the process behind it is quite simple:
1. Receive order
2. Buy jerseys from supplier
3. Resell at an slighly higher price
4. Pay taxes + shipping
Now, say that "x" is the amount of jerseys my store sells in a month. I can use functions to create an expression that tells me what is the total net revenue I get from selling "x" amount of jerseys a month.
For example, say that the jerseys cost $50 and you sell them for 60$. You also need to pay the shipping for each jersey (say it is $5 per jersey). Then, we can form a function like this:
[tex]y=60x-50x-5x[/tex]
As you can tell, the money that comes back to the seller ($60 dollars per jersey) is expressed as a possitive coefficient for variable "x" (number of sold jerseys). And, all the other costs, which is money that you spend in order to sell the jerseys, are expressed with a negative coefficient meaning that they are not net revenue, it isn't profit. Now, to see how much money you can make by selling 2 jerseys, simplify the function and substitute variable "x" (number of sold jerseys) by 1:
[tex]y=60x-55x\\ \\y=5x[/tex]
Say "y" is the net revenue:
[tex]y=5(2)\\ \\y=10[/tex]
You can also use functions to determine things such as, how many jerseys do I need to sell in order to make $750 of net revenue? In that case you do the following:
[tex](750)=5x\\\\x=\frac{750}{5} \\ \\x=150[/tex]
From this analysis, you can conclude that you need to sell 150 jerseys ij order to amke a net revenue of $750.
In conclusion, linear functions can be used to see how a variable value (normally called "x") can affect in the results in multiple daily situations: how many miles can your car run with a full tank, how much time do I need to work so I can buy a product, how much money I can spend in something so I can have saving of "x" amount at the end of the year, etc...
Some IQ test are standardized to a normal model, with a mean of 100 and a standard deviation of 15
(a) in what interval would you expect the central 95% of IQ scores to be found
(b) About what percent should have IQscores above 115
(c) About what percent of people should have IQ scores between 70 & 85
(d) About what percent should have IQ scores above 130%
Answer:
(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115
(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.
(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)
(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.
Step-by-step explanation:
Derive by means of the direct formulas the following functions
The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.
Define the method of direct formula.The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.
Explain the generic steps involved in direct formula method.The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.
To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:
y = (4x+9x^2)(3x-7x^4)
y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4
Using the distributive property, we can simplify the expression by combining like terms:
y = 12x^2 - 28x^5 + 27x^3 - 63x^6
y = (12x^2 + 27x^3) - (28x^5 + 63x^6)
So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6
The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.
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Use computer drawing software to construct a quadrilateral with two pairs of parallel sides and ywo angles measuring 125°. What geometric shape describes this quadrilateral
The geometric shape formed is a rhombus.
What is quadrilateral?A quadrilateral is a four-sided shape enclosed shape, where the sum of the internal angle is 180°.
Here,
It is mentioned in the question, we have to construct a quadrilateral with two pairs of parallel sides and two angles measuring 125°.
So, the construction of a quadrilateral is shown.
As seen in the figure, the figure is of a rhombus.
Thus, the geometric shape formed is a rhombus.
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A man jogs from P to Q to M to R to Q back to P at an average speed of 150 yards per minute. To the nearest tenth of a minute, about how long does it take him to travel the entire distance
The time needed to travel the entire distance is given as follows:
1.27 minutes.
How to obtain the time it took to travel the entire distance?Before obtaining the time, we need to obtain the entire distance.
The distance is the perimeter of the rectangle, which is the sum of all the outer side lengths of the right triangle.
The sides of the right triangle are given as follows:
40 yards and 70 yards.
Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:
h² = 40² + 70²
[tex]\sqrt{40^2 + 70^2}[/tex]
h = 80.6 yards.
Then the total distance is given as follows:
40 + 70 + 80.6 = 190.6 yards.
The time is given by the division of the distance by the velocity of 150 yards per minute, hence:
t = 190.6/150
t = 1.27 minutes.
Missing InformationThe problem is given by the image presented at the end of the answer.
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The results of a survey of students showed that 53 students had a Netflix account, 46 students had a Hulu account and 87 students had a Netflix or a Hulu account. How many students had both a Netflix and Hulu account? Show how you got your answer either by drawing a Venn diagram or by showing the math.
Answer:
12 students
Step-by-step explanation:
The number of students surveyed: 53 + 46 = 99 students
The number of student having both: 99 - 87 = 12 students
area is 7x^5-49x width is 7x units
The length of the rectangle is [tex]x^{4}[/tex]- 7 units.
We know that,
Area of a rectangle = length* width
So, Length = Area/width
According to the question,
Area = [tex]7x^{5} - 49x[/tex]
Width = [tex]7x[/tex]
Length of the given rectangle = Area/width
= [tex]\frac{7x^{5}- 49x}{7x}[/tex]
= [tex]\frac{7x(x^{4}- 7)}{7x}[/tex]
= [tex]x^{4} - 7[/tex]
Hence, the length of the rectangle is [tex]x^{4} - 7[/tex] units.
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The complete question is:
A rectangle has an area of [tex]7x^{5}- 49x[/tex]. Its width is 7x units. What is its length?
sherree recorded her golf scores for the first 8 games of the season. She is using a ar model to predict her scores in future games. Which should be Sheree's golf r on her 12th game according to her model?
Sherree's score on her 12th game is 86.67 in her golf game using equation.
What is a function ?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.
Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs) (Input, Output). In algebra, relationship and function are crucial ideas. They are commonly employed in both real life and mathematics.
At games =2 score was 120
At games = 8 score was 100
so the equation is
y - 2 = (8-2)/(100-120) *(x-120)
⇒ (y-2)*(-20) = 6(x - 120)
⇒ -20y + 40 = 6x -720
⇒ 6x + 20y = 760
⇒ 3x + 10 y = 380
So, for y = 12
3x + 12*10 = 380
⇒ 3x +120 = 380
⇒ x = 260/3 = 86.67
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What type of proofs did Julie and Samuel use
What else is part of the problem?
ages (x) pod essure 56 42 36 47 49 42 60 63 55
blood pressure (Y) 147 125 118 128 145 140 155 160 140 150
a. Determine the least square regression equation of Y on X.
b. Estimate the blood pressure of a woman whose age is 45 years. 72 160
Answer:
Step-by-step explanation:
a. The least square regression equation of Y on X is: Y = 3.08X - 127.82
b. To estimate the blood pressure of a woman whose age is 45 years, we can use the least square regression equation above. Substituting X = 45, we get: Y = 3.08(45) - 127.82 = 143.46. Therefore, the estimated blood pressure of a woman whose age is 45 years is 143.46.
The sum of three consecutive numbers is 120.
a) If x is the smallest of the three numbers,write down the equation that x satisfies.
b) Hence solve for x
Answer:
39
Step-by-step explanation:
x+x+1+x+2=120
3 consecutive numbers leading to x=39 !
Mick's zoo offers a promotional deal: get a free $3 cotton candy and a free
$2 soda with the purchase of five $12 admission tickets. A group of 20
students will each purchase a ticket. If half of them want cotton candy and
14 of them want soda, how many dollars would they save by using the
promotional deal?
The group of 20 students will save $144 by using the promotional deal. Half of the group, or 10 students, will get the free cotton candy, so that's $30 saved. 14 of the students will get the free soda, so that's another $28 saved. Added together the group of 20 students will save $58 on the cotton candy and $28 on the soda for a total savings of $144.
There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson.
Below is a diagram that models this problem using lines. Which of the following could be the equation for the line representing the second road leading from the junction to Garrison?
There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. The road junction to Timpson is option B. 20.57 miles.
How did we get the value?To find the distance between Timpson and the junction point, we can use the Pythagorean theorem. Let's call the distance "d".
d^2 = (60 - 22)^2 + 12^2
d^2 = 38^2 + 144
d^2 = 1444
d = √(1444) = 38.03
So the distance between Timpson and the junction point is 38.03 miles. The distance between the junction point and Ashburn is simply 22 miles, so the total distance from Timpson to Ashburn is 20.57 miles (38.03 + 22).
Therefore, the distance between the road junction to Timpson is option B. 20.57 miles
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The complete question goes thus:
There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. How far is the road junction to Timpson
A. 21.57miles
B. 20.57miles
C. 10.57miles
D. 57.12 miles
The top of a hill rises 64 feet above checkpoint -213. What is the altitude of the hill?
The altitude of the hill whose top rises 64 feet above checkpoint -213, is 277 feet above sea level.
What is the altitude?The altitude refers to the vertical distance or height of an object or point in relation to sea level (true altitude) or ground level (absolute altitude).
The altitude of a hill refers to its height measured from the ground level or the sea level, as the case may be.
In this situation, we can compute the altitude of the hill as the difference between the rise of the hill or mountain above the checkpoint and the given checkpoint.
The rise of the top of a hill = 64 feet
Given checkpoint = -213
The altitude of the hill = 277 feet [64 - (-213)]
Thus, the position or altitude of the hilltop in relation to the ground or sea level is 277 feet.
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A tree is 7 feet 1 inch tall. How tall is it in inches?
Answer:
85 inches
Step-by-step explanation:
7*12+1=84+1=85
A special drill is used at a construction site to dig holes. A hole is dug to a depth of 2.75 feet when the drill hits rock. The progress slows to 56 feet per hour of digging. The depth of the hole must be at least 1012 feet by the end of the day to stay on schedule.
What is the minimum amount of time the drill must continue at its present rate to complete the hole on schedule?
Select from the drop-down menus to correctly complete the statement.
To complete the hole on schedule the minimum amount of time the drill must continue to work is 18 hours
How to determine the minimum length of time the drill must workThe rate of the drill for the remaining part of creating the whole is 56 feet per hour of digging
The remaining depth of the hole = the total hole - the depth before the rock
The remaining depth of the hole = 1012 - 2.75
The remaining depth of the hole = 1009.25
At a rate of 56 feet per hour the number of hours to dig 1009.25
56 feet = 1 hour
1009.25 feet = ?
cross multiplying
? * 56 = 1 * 1009.25
? = 1009.25/56
? = 18
approximately 18 hours will take the drill to reach complete the hole
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A rectangular prism has a square base. The height of the prism is equal to twice the edge length of its base. The base can be completely covered with no overlap by 16 squares that each have an edge length of 1 inch what is the total surface area of the rectangular prism
The total surface area of the rectangular prism is 160 inches².
How to calculate the surface area?Since the base of the rectangular prism is a square, we know that the edge length of the base is the square root of the area of the base. The area of the base is 16 square inches (since it can be completely covered by 16 squares with edge length of 1 inch), so the edge length of the base is 4 inches.
Since the height of the prism is twice the edge length of the base, the height of the prism is 8 inches.
The total surface area of a rectangular prism is given by the formula:
2lw + 2lh + 2wh
Where l is the length, w is the width and h is the height
So, the total surface area of the rectangular prism is:
2(4 inches * 4 inches) + 2(4 inches * 8 inches) + 2(4 inches * 8 inches)
= 160 square inches
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Please look at the picture and answer the question thank you
Answer:
[tex]5y^3-2x^2+2[/tex]
Step-by-step explanation:
I like to start off by rearranging the like terms next to each other, going from the greatest power to the least, so that they are more clear.
So in this case it would be: [tex]2y^3+3y^3+x^2-3x^2+1+5-4[/tex]
Now you can add them together. Remember you can only add/subtract coefficient or variable with the same base and power.
And with that in mind, the final result should be,
[tex]5y^3-2x^2+2[/tex]
Hope this helps!
What type of association does this graph show?
Explanation:
The points do not fall on the same line, but the points trend upward as we move to the right. This means that a straight line can get somewhat close to all of the points to represent the average trend of what's going on.
Answer:
linear :)
Step-by-step explanation:
ive already answered this question and got it right <3
Can someone help me do this problem? Can you do it in a ti-84 calculator? If so how?
Answer:
z = -8/3 - 5i
Step-by-step explanation:
Sorry, I don't know what a ti-84 calculator is.
But, I can solve this question normally.
Let the real part of z be x and the imaginary part be y.
z = x + iy
|z| = √(x²+y²)
z + |z| = x + iy + √(x²+y²) = 3 - 5i
Now, y has to be -5 as |z| is a real number so the only component affecting i is y. Therefore, y = -5.
Now, lets figure out the real part.
Cancel out imaginary part.
x + √(x² + 25) = 3
3 - x = √(x² + 25)
squaring on both sides,
9 + x² - 6x = x² + 25
6x = -16
x = -8/3
Hence the required complex number is -8/3 - 5i
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The top of a hill rises 64 feet above checkpoint -213. What is the altitude of the hill?
The top of the hill have an altitude of 1391 feet above sea level
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
From the table, checkpoint 3 is at 1327 feet above sea level. Since the top of a hill rises 64 feet above checkpoint 3, hence:
Altitude of hill = 1327 + 64 = 1391 feet
The top of the hill is 1391 feet
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Differentiate cos 5x
Answer
[tex] - 5 \sin(5x) [/tex]
I will give brainliest, if you get this correct
Answer: Here it is
Step-by-step explanation:
A.
Arithmetic Mean: 30.57
Median: 32
Mode: 41
Range: 41-23 = 18
B.
Upper Quartile: 39
Lower Quartile: 25
D7: 25
P50: 32
C.
Variance: In order to calculate the variance I would need the data set to be presented in a tabular form with the observations as rows and one column for the data.
Coefficient of Variation: Same as above.
D.
Pearson coefficient of skewness: I would need the data set to be presented in a tabular form with the observations as rows and one column for the data.
Kurtosis: Same as above.
Graph y=3/4x+5 which point lies on the graph of the line
Answer:
Graph is attached below
Step-by-step explanation:
To start off, let's find the y-intercept, which is when x=0
So, when x=0,
[tex]y=\frac{3}{4}(0)+5[/tex], which is y=5.
So we can put a point on (0, 5)
From there, since the slope is 3/4. We can go up 3 and right 4 to plot a point there, you can also do down 3 and down 4 from the y-intercept point, then keep going either, up 3 and right 4 or down 3 and left 4, which should give you a diagonal line that looks something like;
A frame is 10 inches wide and 6 inches tall. If it is reduced to a width of 3 inches then how tall will it be?
Considering the context of the question and the mathematical expression, the height of the frame. after the width is reduced to 3 inches will be 1.8 inches.
What are the Dimensions in MathematicsDimension is a term that is used to describe the measurement of the size or distance of an object or region or space in one direction.
Generally, the term dimension is the measurement of the length, width, and height of anything.
In this case, as given in the question
A frame is 10in wide and 6 in tall.
reduces to a width of 3 in
let us assume that the height of the frame after reducing the width to 3in be = x
then the equation becomes original width/ original length = reduced width/reduced length
put all the value, we get
[tex] = 10 \div 6 = 3 \div x[/tex]
solve the above
[tex]x = (6 \times 3) \div 10 \\ x \: = 1.8in[/tex]
Therefore, in this case, it is concluded that the correct answer is 1.8in, which will be the tall or height of the frame.
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Either Table F or Table G shows a proportional relationship. Plot the points from the table that shows a proportional relationship. Keyboard Instructions Initial graph state The horizontal axis goes from -1 to 11 with ticks spaced every 1 unit(s). The vertical axis goes from -1 to 11 with ticks spaced every 1 unit(s). Table F x 1 2 4 5 y 2 4 8 10 Table G x 3 5 7 9 y 1 3 5 7
Table F shows a proportional relationship and its points are plotted in the graph shown in the image attached below.
What is the graph of a proportional relationship?In Mathematics, the graph of any proportional relationship is represented by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.
Mathematically, a proportional relationship can be represented or modeled by the following linear equation:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2 = 8/4 = 10/2
Constant of proportionality, k = 2.
Therefore, the linear equation for this proportional relationship can be correctly written as follows:
y = kx
y = 7.5x
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