The expression 36a - 16 to write an equivalent expression in which all coefficients and constants are integer values is; 4(9a - 4)
How to factor Algebraic expressions?We are given the expression as; 36a - 16
Now, we want to write an equivalent expression of 36a - 16.
However, according to question, 36 and 16 are both divisible by 4. Thus, we will divide both sides by 4 to get;
36/4 = 9 and 16/4 = 4
Now, factorize the given expression 36a - 16.
Taking 4 as a common factor, we get,
36a - 16 = 4(9a - 4)
Therefore, 4(9a - 4) is the factor to write an equivalent expression 36a - 16.
Read more about factoring expressions at; https://brainly.com/question/14271086
#SPJ1
This is a multi-part Item. Make note of your answer(s) to this part for use in the remaining part(s).Kara and Nathan participated in a 60-minute maze race.Kara:32 minutesNathan:40 minutesPart AUse ratio notation and decimal notation to describe the relationship between Kara's time and the total time of the race.Enter the correct answers in the box. For the decimal, enter the digit that repeats 3 times.Hint(s): Write the ratio of Kara's time over the total time.Use long division to write the fraction as a decimal.ratio:decimal:
Answer:
Kara's rate over the total time is 0.5333
Step-by-step explanation:
Kara finished the race in 32 minutes.
The total duration of the race was 60 minutes.
So the ratio is:
32/60 = 16/30 = 8/15 = 0.5333
Kara's rate over the total time is 0.5333
The bedroom floor is in the shape of a rectangle. It is 14 feet long and 16 feet wide. Your client has requested that you install either oak flooring or maple flooring. The oak flooring costs $5.25 per square foot for materials. The maple flooring costs $7.00 per square foot for materials. The cost you charge for labor will be the same for either flooring options.
How much money will your client save if you install oak flooring instead of maple flooring?
========================================================
Explanation:
The room is 14 ft by 16 ft.
The floor area is 14*16 = 224 sq ft.
Since oak costs $5.25 per sq ft, this means the total cost of an oak floor is 5.25*224 = 1176 dollars.
Meanwhile, maple flooring will have a total cost of 7*224 = 1568 dollars
If you go with the cheaper option (oak), then the savings is 1568-1176 = 392
----------
Alternative Route:
The difference in per sq ft costs is 7.00-5.25 = 1.75, meaning you save $1.75 per sq ft if you go with the cheaper option.
Multiply this with the total floor area to get 1.75*224 = 392
what is 11/15 + (- 3/5)
we have
11/15 + (- 3/5)
step 1
REmove the parenthesis
11/15-3/5
Remember that
3/5(3/3)=9/15 ------> is the same number
substitute
11/15-9/15 -----> the fractions have the same deniominator
so
(11-9)/15
2/15
Use the graph below for this question: graph of parabola going through 2, negative 3 and 3, negative 1. What is the average rate of change from x = 2 to x = 3? (1 point) a) 2 b) 3 c) 0 d)5
From x = 2 to x = 3 the average rate of change is 2.
The graph of the parabola passes through 2, negative 3 and 3, negative 1 or ( 2, - 3) and ( 3, - 1 ).
Let's say y = f(x) represents the function of the parabola.
Then f( 2 ) = - 3 and f( 3 ) = - 1
Now, for a function y = f(x) the average rate of change from x = a to x = b is given by the expression [ f( b ) - f( a ) ] / ( b - a)
When x changes from x = 2 to x = 3,
The average rate of change will be:
[ f( 3 ) - f( 2 ) ] / ( 3 - 2 ) = [ - 1 - ( - 3 ) ] / 1 = 2
The average rate of change from x = 2 to x = 3 is 2.
The correct option is (a).
Learn more about function here:
brainly.com/question/11624077
#SPJ1
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would liketo travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket
We have that the price of a train ticket has an initial fee of $5 and $2.75 per stop.
Then, we can represent this using the next inequality:
[tex]5+2.75\cdot S\leq21[/tex]In the inequality, we have some restrictions:
• Julia only has $21, no more than that.
,• In the inequality, we need to talk about the same units. If we have units in money on one side of the inequality, we need to have the same units on the other side of the inequality.
,•
Therefore, the scenario can be described by the inequality presented in the first option (option A).
What is f(6) for the quadratic function graphed shown below?
In order to find the value of f(6) we look in the graph for the point of the curve in the position of x = 6, then we see with wich value of the y axis its correspond. We see that the value of y is y = 6.
So the answer is: f(6) = 4
Hello all the info I was given is right there
11.
We can determine the number of real solutions checking the number of times the graph crosses the x-axis, therefore, we can conclude from the graph that the function has 2 real solutions
If P = 3x^2 + xy - 5y^2, Q = 2x^2 - xy + 3y^2 and R = -6x^2 + 4xy -7y^2what is P + Q - R ?
To find what is P + Q - R
From the equation given
[tex]\text{ p = 3x}^2+xy-5y^2[/tex][tex]\Q=2x^{2\text{ }}-xy+3y^2[/tex][tex]\R=-6x^2+4xy-7y^2[/tex][tex]\P+Q-R=3x^2+xy-5y^2+(2x^2-xy+3y^2)-(-6x^2+4xy-7y^2)[/tex]Now we will simplify the equation by first opening the parentheses
Values of Q will remain the same even after opening the parenthesis because it's addition but for the values of R, the signs will be affected because it's a subtraction.
That is :
[tex]3x^2+xy-5y^2+2x^2-xy+3y^2+6x^2-4xy+7y^2[/tex]So the next is to rearrange them according to their powers
[tex]3x^2+2x^2+6x^2+xy-xy-4xy-5y^2+3y^2+7y^2[/tex]Then we will add or subtract variables that are the same accordingly(depending on their signs)
[tex]11x^2-4xy+5y^2[/tex]Therefore
[tex]\P+Q-R=11x^2-4xy+5y^2[/tex]Question Let f(x) = -531+4. Evaluate f(-1). Do not include 'f(-1) =' in your answer.
Note that the function f(x) = -531+4 is a function that doesn't depend on x. Hence, it is a constant function. We have that f(x) = -531+4 = -527. This means that the function assigns to any input value the number -527. So, in this case
f(-1) = -527.
2f = -12f=??[tex]2f = - 12 \\ \\ f = [/tex]
Given:
2f = -12
We are required to find the value of f.
To find f, divide both sides of the equation by 2.
We have:
[tex]\begin{gathered} \frac{2f}{2}=-\frac{12}{2} \\ \\ f\text{ = -6} \end{gathered}[/tex]ANSWER:
f = -6
HELP!!!!!!!
they are 10 to 10. my screen isn't big enough to screenshot it.
A B C or D
The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the table,
The values of x = 0 , 1 , 2
The values of y = 4 , 2 , 0
Now,
The coordinates are;
(x , y) = (0, 4) , (1, 2) and (2, 0)
Here, For the value of x shows the coordinates for x - axis.
The value of y shows the coordinates for y - axis.
So, The points (0, 4) , (1, 2) and (2, 0) are draw on the graph as given in figure.
Thus, The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
Learn more about the coordinates visit:
https://brainly.com/question/25099398
#SPJ1
A point representing the location of a library is shown on the coordinate grid. A museum is located 3.75 units from the library.
We are going to plot the library located at coordinate (3,4)
Then let's plot the museum which is located at 3.75 units.
Find compatible numbers to find two estimates.
2518 divided by 32
Answer: 78.6875
Step-by-step explanation:
math
Help pls 10 points thx
The probability of getting 6 or a odd number is [tex]\frac{2}{3}[/tex]
What is probability?Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Probability can range from 0 to 1, with 0 meaning the event is impossible and 1 meaning the event is likely to occur.
For illustration: The number that appears first when a fair dice is rolled is one through six. Let's say we roll the dice once to see if three might come up.
For instance : When a fair dice is rolled, the number that comes up top is a number between one to six. Assuming we roll the dice once, to check the possibility of three coming up.
Number of possible outcomes = 6
Number of outcomes to get three = 1
The probability of getting three = Number of outcomes to get three/Number of possible outcomes=1/6
Similarly in this question :
Sample space ; { 1, 2 , 3, 4, 5, 6}
Event : (E) : { Probability of 6 or odd number }
Thus n(E )= {1, 3, 5, 6}
Thus P(E)= [tex]\frac{ favorable number of outcomes}{the total number of possible outcomes}[/tex]
= [tex]\frac{4}{6}[/tex]
P (E )= [tex]\frac{2}{3}[/tex]
To know more about probability visit:
https://brainly.com/question/22597778
#SPJ13
I need some help to tell whether a table is a linear or non linear function
A linear equation has the form:
[tex]y=mx+b[/tex]Let's find a linear equation using the table, and let's check if it satisfy all the points:
[tex]\begin{gathered} x=0,y=-1 \\ -1=b \\ ------ \\ x=1,y=1 \\ 1=m+b \\ 1=m-1 \\ m=2 \end{gathered}[/tex]so:
[tex]y=2x-1[/tex]Let's check the other points:
[tex]\begin{gathered} x=-3 \\ y=2(-3)-1=-6-1=-7_{\text{ }}True \\ ------ \\ x=-2 \\ y=2(-2)-1=-4-1=-5_{\text{ }}True \\ ------ \\ x=-1 \\ y=2(-1)-1=-2-1=-3_{\text{ }}True \end{gathered}[/tex]Therefore, we can conclude it is a linear function.
Which picture shows a properreflection across the red dashed line?АB
When you reflect a point across the red dashed line y = x, the x-coordinate and y-coordinate change places;
If you reflect over the red dashed line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
Thus, the picture that shows a proper reflection across the red dashed line is B
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
Drag each choice into the boxes to correctly complete the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Parallel Perpendicular Neither
y=−12x−5−2x+y=−4−x+2y=2x+2y=−2
Answer:
Step-by-step explanation:Base line: x + 2y = 6
Parallel: Continous, never touching
Perpendicular: Create a right angle when touching
y= -1/2x -5 : Parallel
-2x+y=-4 : Pependicular
-x+2y=2 : Neither
x+2y=-2 : Parallel
Alyssa paints 3 walls blue. Each of the walls is 8.3 feet tall and 7.5 feet wide. Round the length and width to the nearest whole number. Then estimate the area that Alyssa will paint. Write equations to show your work. Once, you have done everything find the exact area. Write equations to show your work. Then, compare your estimate to the exact answer. Why is your answer reasonable?
The equation to show the area Allysa will paint is Area = 3(Height x Width) = 3( 8.3ft * 7.5ft) and the area is 186.75 ft²
How to solve Algebraic Word Problems?We are given the dimensions of wall as 8.3ft by 7.5ft.
Thus;Height of wall = 8.3 ft
Width of wall = 7.5 ft
Now, there are total 3 walls in the bedroom to be painted blue.
The formula to calculate the area of one wall is;
A = Height x WidthFormula to calculate the area of four walls will be;
Area = 3(Height x Width) = 3( 8.3ft * 7.5ft)
= 3 (62.25 ft²)= 186.75 ft²
Thus, an area that Alyssa will paint = 186.75 ft²
Read more about Algebraic Word Problems at; https://brainly.com/question/13818690
#SPJ1
negative 45 minus negative 19
Answer:
-26
Step-by-step explanation:
Answer:
The answer to this problem is -26
In the expression 5^2, the 2 represents the _________________.
A: product
B: sum
C: base
D: exponent
The number, 2, in the given expression represents the exponent. The correct option is D: exponent
The exponent in a mathematical expressionFrom the question, we are to determine what the number, 2, represents in the given expression
The given expression is
5^2
That is,
5²
An exponent is a number or letter written above and to the right of a mathematical expression called the base
In the given expression, the number 2 is written above and to the right of 5. The number 5 is the base in the expression.
Thus,
The 2 represents the exponent
Learn more on Exponent in a mathematical expression here: https://brainly.com/question/23275698
#SPJ1
A drama club is selling tickets to a play. The cost of each adult ticket is $8, and the cost of each student ticket is $4. One customer purchased 8 tickets andspent a total of $56. The system of equations shown can be used to model this situation.y = 8 - 28x + 4y = 56Which equation can be used to find 2, the number of adult tickets the customer purchased?O 8 (8 – 2) + 4y = 56O 8x +4(8 - x) = 568.2 + 4y - 56 = 8 - 3
Given the system of equations below, to eliminate y,
[tex]\begin{gathered} y=8-x\text{ (1)} \\ 8x+4y=56\text{ (2)} \\ \text{Substitute 8-x for y into equation (2)} \\ 8x+4(8-x)=56 \end{gathered}[/tex]Hence, the answer is 8x + 4( 8 - x) = 56
Given a triangle with a = 1, A = 17°, and B = 32°, what is the length of c? Round to the nearesttenth.
a=1
A=17°
B=32°
c=?
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex][tex]C=180-17-32=131[/tex][tex]\frac{1}{\sin 17}=\frac{c}{\sin 131}[/tex][tex]\frac{1}{0.2924}\cdot0.7547=c[/tex][tex]2.58=c[/tex]There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.40). What is the slope of the graph? What is the unit rate? Complete the explanation The slope is passes through the point (1 The unit rate is $ Vmin. If the graph ofa proportional relationship r), then r equals the slope and unit rate.
Let:
(x1,y1)=(0,0)
(x2,y2)=(1,3.40)
The slope is:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{3.40-0}{1-0}=\frac{3.40}{1}=3.40[/tex]The unit rate is:
[tex]\frac{3.40}{\min }[/tex]elenas bed measures 3‘ x 6‘ on the scale drawing what are the actual measurements of her bed
Using proportions, supposing a scale of 1 inch = 3 feet, the actual measurements of her bed are given by: 9 ft x 18 ft.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division, from the relations built in the problem.
One example of application of proportions is for scale problems, as the actual scale and the drawing length are compared to find the actual length of the object drawn.
In the context of this problem, the scale is given by:
1 inch = 3 feet.
The drawn length of the bed is given by:
3 inches x 6 inches.
Hence the actual length is given by:
9 feet x 18 feet.
As:
3 x 3 = 9.6 x 3 = 18.What is the missing information?The scale of the drawing is missing, hence we are going to suppose that it is 1 inch = 3 feet.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
I need to find the point of intersection Y=.5x+3 & Y=2x-9
SOLUTION:
Step 1:
In this question, we are meant to find the point of intersection of the two lines:
[tex]\begin{gathered} \text{y = 0. 5 x + 3 -- equation 1} \\ \text{and } \\ \text{y = 2x -9 -- equation 2} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
From the graph, we can see the point of intersection of the two lines
is at:
[tex]\begin{gathered} \text{ x= 8} \\ y=\text{ 7} \end{gathered}[/tex]
Manuel's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Manuel $5.80 per pound, and type B coffee costs $4.55 per pound. This month, Manuel made 115 pounds of the blend, for a total cost of $585.75. How many pounds of type A coffee did he use?
92.75 pounds of type A are used and 22.25 pounds of type B coffee are used.
It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Let "a" denote the quantity of type A utilized in pounds, and "115-a" denote the quantity of type B used. Hence, the equation is:
$585.75 = 5.80 a + 5.9(115-a)
-92.75 = 5.80 a - 5.90 a
0.1a = 92.75
a = 92.75
solving for the number of pounds of type A
So type B coffee is obtained as,
= 115 - 92.75
= 22.25
Thus,92.75 pounds of type A are used and 22.25 pounds of type B are used.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ1
Saquon Barkley lost 7 2⁄3 yards on the first play, and gained 9 5⁄8 yards on the next play. What was the total gain or loss for the running back during the first two plays?
If Saquon Barkley lost [tex]7\frac{2}{3}[/tex] yards on the first play, and gained [tex]9\frac{5}{8}[/tex] yards on the next play, then the total gain for the running during the first two plays is [tex]1\frac{23}{24}[/tex] yards
The amount he lost on the first play = [tex]7\frac{2}{3}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]7\frac{2}{3}[/tex] yards = 23/3 yards
The amount he gained on the second play = [tex]9\frac{5}{8}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]9\frac{5}{8}[/tex] yards = 77/8 yards
The total gain for the running during the first two plays = The amount he gained on the next play - The amount he lost on the first play
Substitute the values in the equation
= 77/8 - 23/3
= 47/24 yards
Convert the simple fraction to the mixed fraction
47/24 yards = [tex]1\frac{23}{24}[/tex] yards
Hence, if Saquon Barkley lost [tex]7\frac{2}{3}[/tex] yards on the first play, and gained [tex]9\frac{5}{8}[/tex] yards on the next play, then the total gain for the running during the first two plays is [tex]1\frac{23}{24}[/tex] yards.
Learn more about total gain here
brainly.com/question/14350453
#SPJ1
Add − 0 . 25 + 3 1 6 + 2 1 12 . Write in simplest form.
On addition, the simplest form of the given equation is results in 2427.75.
Addition - In math is a process of combining two or more numbers.
OR
the process of finding the total, or sum, by combining two or more numbers
RULES IOF ADDITION
It is always positive to add two positive integers. It is always negative to add two negative values. Two positive integers can be subtracted in either a positive or negative way.thus
= − 0 . 25 + 3 1 6 + 2 1 12
= -0.25 + 2428
= 2427.75
On addition, the simplest form of the given equation is results in 2427.75.
To know more about addition
https://brainly.com/question/20658817
#SPJ1
Do the ratios 3 4 and 7 8 form a proportion?
no
No, the ratios are not proportional because they are not equivalent.
We are given a table which has the values of the "x" column and the corresponding "y" column.The values in the "x" column are 3 and 7.The values in the "y" column are 4 and 8.The ratio of the first corresponding values in each column is 3/4 = 0.75.The ratio of the second corresponding values in each column is 7/8 = 0.875.The ratios for all the corresponding values in the table are not equivalent.Hence, they are not proportional because the ratios are not equivalent to a single value.To learn more about ratio, visit :
https://brainly.com/question/13419413
#SPJ1
45 POINTS PLEASE BE FAST 18-22 !! <33 (sorry if its blurry)
Answer:
18. Aileen
19. Edward
20. 25 seconds
21. 40 seconds
22. 55 seconds or 3 minutes, 20 seconds - 4 minutes, 15 seconds
Step-by-step explanation:
Hello! Alright, let's start breaking down the answers one by one!
18.
To begin with 18, we just have to simply compare everyone's time to the actual time! (3 minutes and 46 seconds). To make this easier for us, we should convert everyone's time into the form of minutes/seconds. So it would be:
Aileen: 3 minutes, 50 secondsAlejandra: 4 minutesChris: 3 minutes, 20 secondsDavina: 3 minutes, 40 secondsEdward: 4 minutes, 15 secondsAs you can compare here, the closest person here would be Aileen being 4 seconds off from the actual time.
19.
Based off of what we did in 18, we can use that chart to compare, we just have to find the time differences to see who is more off from the actual time and that would be:
Aileen: +4 secondsAlejandra: +14 secondsChris: -26 secondsDavina: -6 secondsEdward: +29 secondsHere in this case, Edward's estimate would be the farthest away with +29 seconds.
20.
To calculate the time difference between these two, we simply just take the data from 18 and compare Aileen and Edward. In this case, it would be a difference of 25 seconds.
21.
Again, we take a look at Alejandra and Chris's estimate and compare the time difference. In this case, it would be 40 seconds.
22.
Finally, to figure out the range, we essentially just need to figure out the time difference between the lowest time and the highest time estimated. So that would be Chris's time (3 minutes, 20 seconds) and Edward's time (4 minutes, 15 seconds) and that would be 55 seconds.
