20 POINTS!
Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
What is the length of one of the diagonals of the rectangle?
Anna is selling tickets to her tennis tournament. An adult ticket costs $20 and a student ticket costs $16. Anna collects $1020 for a total of 55 tickets. How many adult and how many student tickets has Anna sold?
Anna sold 35 adult tickets and 20 student tickets.
Explanation:Let's assume that Anna sold x adult tickets and y student tickets. From the given information, we can form the following equations:
Equation 1: x + y = 55 (total number of tickets)
Equation 2: 20x + 16y = 1020 (total amount collected)
We can solve this system of equations using the substitution method or the elimination method. Let's use the elimination method. First, multiply Equation 1 by 16 so that the coefficients of y cancel out when added to Equation 2:
16x + 16y = 880 (equation obtained by multiplying Equation 1 by 16)
20x + 16y = 1020 (Equation 2)
Now subtract Equation 1 from Equation 2:
20x + 16y - (16x + 16y) = 1020 - 880
4x = 140
Divide both sides of the equation by 4:
x = 35
Substitute the value of x into Equation 1:
35 + y = 55
y = 55 - 35
y = 20
Simplify the expression x^2+3x-28/x^2-7x+12
Answer:
[tex]\frac{x+7}{x-3}[/tex].
Step-by-step explanation:
We have been given an expression. We are asked to simplify our given expression.
[tex]\frac{x^2+3x-28}{x^2-7x+12}[/tex]
Let us factor numerator and denominator by splitting the middle term.
[tex]\frac{x^2+7x-4x-28}{x^2-4x-3x+12}[/tex]
[tex]\frac{(x^2+7x)+(-4x-28)}{(x^2-4x)+(-3x+12)}[/tex]
Factor out GCF of each group:
[tex]\frac{x(x+7)-4(x+7)}{x(x-4)-3(x-4)}[/tex]
[tex]\frac{(x+7)(x-4)}{(x-4)(x-3)}[/tex]
Cancel out common factor [tex](x-4)[/tex]:
[tex]\frac{(x+7)}{(x-3)}[/tex]
Therefore, the simplified form of the given expression would be [tex]\frac{x+7}{x-3}[/tex].
Divide. (359)÷(−223) Enter your answer as a mixed number, in simplified form,
Answers
the answers is-3.245 hope this helps subscribe to my channel Elite_Raider Perez
Answer:
-3.245 I hope this helped hun! :3
Describe the translation from AB TO AB
Answer: I got A.
Step-by-step explanation:
Please Hurry!! Use any model you choose to solve the story problem. Macy is making a border out of strips of wall boarder placed end to end along the 12-foot wall in her room. Each strip 1/3 is foot long. How many strips of wall border will Macy need?
Macy needs 36 strips of wall border to cover a 12-foot wall, calculating by multiplying the wall's length by the reciprocal of 1 strip's length.
To solve how many strips of wall border Macy will need, we divide the total length of the wall by the length of each strip. Macy's wall is 12 feet long, and each strip is 1/3 foot long. So, we divide 12 by 1/3 or multiply 12 by the reciprocal of 1/3.
Here is the calculation step by step:
Convert 1/3 to its reciprocal by flipping the numerator and denominator, which gives us 3/1 or just 3.Multiply the length of the wall, 12 feet, by 3.Which of the following expressions represents the value, in dollars, of a certain number of dimes, d, and pennies, p?
0.01d + 0.10p
0.10d + 0.01p
0.11dp
0.11d + p
A) choose the linear model that passes through the most data points on the scatterplot.
a. true. choose the linear model that passes through the most data points on the scatterplot.
b. false. the line usually touches none of the points. minimize the sum of the squared errors.
c. false. all of the data points either touch the line or fall below the line.
d. false. the linear model line usually passes through exactly half of the data points.
Final answer:
The correct statement relating to the selection of a linear model is that the line of best fit is found using the least-squares method to minimize the sum of squared errors. This involves plotting data points, calculating the least-squares regression line, and determining if the linear model fits the data appropriately.
Explanation:
The question pertains to the selection of a linear model based on a provided scatterplot. The correct choice is b. false. the line usually touches none of the points. minimize the sum of the squared errors. This statement refers to the concept of least-squares regression, a mathematical method used to find the line of best fit by minimizing the squared differences (errors) between the observed values and the values predicted by the model. This line is intended to predict the dependent variable based on the independent variable. The process includes plotting the data, calculating the least-squares line, and determining if the linear model is appropriate for the data set.
After plotting the data points on a scatter plot, we use a calculator or statistical software to compute the least-squares regression line, represented as ŷ = a + bx, where a is the y-intercept, b is the slope, and ŷ is the predicted value of the dependent variable for any given value of the independent variable. The line may not pass through the most data points, but instead represents the trend of the data points in a way that minimizes the overall error of the model.
During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph?
whats the bisector of an obtuse angle forms
acute angles
right angles
obtuse angles
straight angles
Answer:
A.Acute angle
Step-by-step explanation:
We are given that an obtuse angle
We have to find that which type of angle of bisector of an obtuse angle.
Bisector of an obtuse angle means it is divided into two equal parts.
Obtuse angle is that angle whose measurement is greater than 90 degrees and less than 180 degrees.
Suppose, we have an obtuse angle =100 degrees
After bisection , it divides into two equal parts
Let x and x are two equal parts of given obtuse angle
[tex]x+x=100[/tex]
[tex]2x=100[/tex]
[tex]x=\frac{100}{2}=50[/tex]
Each angle measurement=50 degrees < 90 degrees
The angle which is less than 90 degrees and greater than zero degrees is called acute angle.
Hence, the bisector of an obtuse angle forms acute angles.
Answer:A.Acute angle
HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL
-x -y -z = -8
-4x + 4y + 5z = 7
2x + 2z = 4
I'm not sure how to work this out.
Helpp me with this word problem number one
Estimate the unit rate
What is the expression phrase of the sum of a number x and 4, all divided by 3?
Manuel rode his bicycle at an average speed of 13 miles per hour for 1 hours. of d = the total distance he rode, which choice is the most reasonable value for d?
What is the greatest common factor of 125, 50, and 275?
Answer:
25 is the greatest common factor.
Step-by-step explanation:
We are given the following information in the question:
We have t find the greatest common factor of 125, 50 and 275.
We can use the method of prime factorization.
[tex]125 = 5\times 5\times 5\\50 = 5\times 5\times 2\\275 = 5\times 5\times 11[/tex]
Hence, the common factor of the the three numbers are:
[tex]5\times 5 = 25[/tex]
Hence, the greatest common factor 125, 50, 275 is 25.
The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume of the prism, l and w are the length and width of the base of the prism, respectively, and h is the height of the prism.
Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known.
Answer:
[tex]w=\frac{V}{lh}[/tex]
Step-by-step explanation:
As per the statement:
The volume of a rectangular prism is calculated using the formula:
[tex]V = lwh[/tex] ....[1]
where, V is the Volume of the prism
l is the lenght
w is the width
h is the height of the prism respectively.
We have to Rewrite the formula to find the width of the base of the prism.
Divide equation [1] by [tex]lh[/tex] to both sides we have;
[tex]\frac{V}{lh} = \frac{lwh}{lh}[/tex]
Simplify:
[tex]\frac{V}{lh} = w[/tex]
or
[tex]w=\frac{V}{lh}[/tex]
Therefore, the the formula to find the width of the base of the prism,if the volume, length of the base, and height of the prism are already known is:
[tex]w=\frac{V}{lh}[/tex]
To find the width of a rectangular prism when the volume, length, and height are known, you can rearrange the formula V = lwh to solve for width, resulting in the formula w = V / (lh).
Explanation:The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. If we know the volume (V), the length of the base (l), and the height of the prism (h), and we want to find the width (w), we can rearrange the formula to solve for width.
To do this, you divide both sides of the equation by the length and the height. As a result, the formula to find the width when the volume, length, and height are known is w = V / (lh). By dividing the volume by the product of the length and the height, you can find the width of the base of the prism.
Learn more about Rectangular prism here:https://brainly.com/question/32444543
#SPJ2
Find the average rate of change of the function defined by the following table.
x y
-2 -5
2 35
6 75
10 115
A careful examination of the data in the table shows that for each 4 unit increase in x, y increases by 40.
It's valid to surmise that the average rate of change is 40/4, or 10. This is the slope of the line thru the given points.
Answer:
1/10
Step-by-step explanation:
The x goes up by 4 and the y goes up by 40
= 4/40 = 1/10
Please rate & thank : )
One third of the sum of two consecutive odd integers is five less than the smaller integer
the diagram below shows a rectangle inside a regular hexagon . the apothem of the hexagon is 19.05 units . to the nearest square unit . what is the area of the shaded region
A. 1257
B.861
C.442
D.1653
Answer:
B. 861.Step-by-step explanation:
In the figure attached, you can observe that the shaded area can be found by calculating the difference between the area of the regular hexagon and the area of the rectangle inside.
The area of a regular hexagon is defined as
[tex]A_{hexagon} =\frac{Pa}{2}[/tex]
Where [tex]P[/tex] is the perimeter and [tex]a[/tex] is the apothem.
By given, we know that the side of the hexagon is 22 units.
Remember that the perimeter is the sum of all sides, in this case would be
[tex]P_{hexagon}=22(6) =132[/tex].
The perimeter of the hexagon is 132 units.
Therefore, the area is
[tex]A_{hexagon} =\frac{132(19.05)}{2}=\frac{2514.6}{2}=1257.3 u^{2}[/tex]
On the other hand, the area of the rectangle is defined as
[tex]A_{rectangle}=bh[/tex], where [tex]b[/tex] is the base and [tex]h[/tex] is the height. We know, by given
[tex]b=22\\h=18[/tex]
Replacing these values, we have
[tex]A_{rectangle}=bh=22(18)=396 u^{2}[/tex]
As we said before, the shaded are is defined by the following difference
[tex]A_{shaded}=A_{hexagon}-A_{rectangle}[/tex]
Replacing each area, we have
[tex]A_{shaded}=A_{hexagon}-A_{rectangle}\\A_{shaded}=1257.3u^{2} -396u^{2}=861.3 u^{2}[/tex]
Therefore, the right answer is B. 861.
Greg, marcia, peter, jan, bobby and cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. if marcia and jan will not sit next to each other, in how many ways different arrangements can the 6 people sit?
If it took eight men ten hours to build a wall, how many hours would it take four men to build it?
A figure drawn in the coordinate plane has the coordinates J(‒1,5), K(6,5), L(9,1) and M(2,1).
1) Use what you have learned in this unit to prove that the figure is either a parallelogram, rectangle, square or a rhombus.
2) Use what you have learned in this lesson to find the area and perimeter of the figure.
The sum of the angle measures of a polygon with n sides is 1440. find n
The number of sides of the polygon that has a sum of the angles 1440° will be 10.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let 'n' be the number of sides of the polygon. Then the sum of the interior angles of the polygon is given as,
Sum of angles = (n - 2) × 180°
The sum of the angle measures of a polygon with n sides is 1440. Then the number of sides of the polygon is given as,
(n - 2) × 180° = 1440°
(n - 2) = 1440° / 180°
(n - 2) = 8
n = 8 + 2
n = 10
The number of sides of the polygon that has a sum of the angles 1440° will be 10.
More about the polygon link is given below.
https://brainly.com/question/17756657
#SPJ2
If it's 8:23 pm now... What time would it be in 45 min? ( I want to see what everyone comes up with)
Which equation describes a line with a slope of -8 and includes the point (-4, 7)?
It takes 69 pounds of seed to completely plant an 8 -acre field. how many acres can be planted per pound of seed? math
(6r^3s^5)(-2rs^3)(-r^2s)
A1 Plumbing Service charges $35 per hour plus a $25 travel charge for a service call. Good Guys Plumbing Repair charges $40 per hour for a service call with no travel charge. How many hours must a service call be for it to be better for you to call A1 Plumbing Service?
A1 = 35x+25
Good guys = 40x
35x+25 = 40x
subtract 3x x from each side
25 = 5x
divide each side by 5
x = 25/5 = 5
so 5 hours they would be the same cost, anything over 5 hours and A1 would be better
so X>5 for A1 to be the better price
Consider the following three statements:
As children grow older, their weight increases.
As children grow older, they expand their vocabulary.
As children's weight increases, their vocabulary expands.
Does statement #3 describe a correlational relationship? A causal relationship? Explain your answer.
Actually the third
statement would only be classified as correlational relationship.
Correlational relationship means that the one occurrence can
occur at the same time with another; they could be associated but does not
really imply that one causes the other.
Answer:Actually the third statement would only be classified as correlational relationship.
Correlational relationship means that the one occurrence can occur at the same time with another; they could be associated but does not really imply that one causes the other.
Step-by-step explanation: