The expression 40t - 16 is factored completely by first identifying the greatest common factor, which is 8, then factoring it out to get the result 8(5t - 2).
To factor the expression 40t - 16 completely, we need to find the greatest common factor (GCF) of the terms. The GCF of 40t and 16 is 8. Therefore, we can factor out 8 from both terms:
40t - 16 = 8(5t) - 8(2) = 8(5t - 2)
So, the completely factored form of the expression 40t - 16 is 8(5t - 2).
What is the slope of the graph shown below?
Answer: The correct option is (A) 4.
Step-by-step explanation: We are given to find the slope of the graph shown in the figure.
We can see that the graph is a straight line.
Also, the line passes through the points [tex](0,-3)[/tex] and [tex]\left(\dfrac{3}{4},0\right).[/tex]
We know the slope of a straight line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
Therefore, the slope of the given line is
[tex]m=\dfrac{0-(-3)}{\frac{3}{4}-0}\\\\\\\Rightarrow m=\dfrac{3}{\frac{3}{4}}\\\\\\\Rightarrow m=3\times\dfrac{4}{3}\\\\\\\Rightarrow m=4.[/tex]
Thus, the required slope of the graph is 4.
Option (A) is correct.
Of the 304 people who attended the school play,5/8 were students.How many of the people who attended were students?
Need help with number 9 please, thanks.
What is the next expression in the following pattern: 4n; 8n; 16n???
A local hamburger shop sold a combined total of 712 hamburgers and cheeseburgers on Tuesday. There were 62 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?
Final answer:
To find how many hamburgers were sold, we set up an equation and solve for H, the number of hamburgers. After forming the equations, simplifying, and solving, it turns out that 325 hamburgers were sold on Tuesday.
Explanation:
The student is asking how many hamburgers were sold on Tuesday given that a total of 712 hamburgers and cheeseburgers were sold, with there being 62 more cheeseburgers sold than hamburgers. To solve this, we can set up an equation. Let's denote the number of hamburgers sold as H and the number of cheeseburgers as C. According to the problem,
C = H + 62 and H + C = 712.
By substituting the first equation into the second, we get:
H + (H + 62) = 712
Simplifying, we have
2H + 62 = 712
Subtracting 62 from both sides, we get-
2H = 650
Dividing both sides by 2, we find -
H = 325
Therefore, 325 hamburgers were sold on Tuesday.
The vertices of triangle ABC are A(−6,−3) and B(2,−3). Which coordinates of the third vertex allow the triangle to have an area of 24 square units?
The third vertex C of triangle ABC with vertices A(-6,-3) and B(2,-3) and area 24 square units can have coordinates (0,3) or (0,-9).
Explanation:
Given the vertices of triangle ABC are A(−6,−3) and B(2,−3). The coordinates of point C will form the third vertex of the triangle. The distance from A to B is the base of the triangle and can be calculated as follows: AB = sqrt[(2 -(-6))^2 + ((-3) - (-3))^2] = 8 units. The area of a triangle is calculated by the formula: 1/2*base*height=area. Given that the area of the triangle ABC is 24 square units, we can set up the following equation: 1/2*8*height=24. Solve for height to get the y-coordinate of point C as 6 units above the line AB (which lies on y = -3), for C(0,3) or 6 units below line AB for C(0,-9). Therefore, the third vertex C can be at coordinates (0,3) or (0,-9) for the triangle to have an area of 24 square units.
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A satellite is 18 meters wide. A model of it was built with a scale of 1 centimeter: 3 meters. How wide is the model?
Answer: 6 centimeters
Step-by-step explanation: I took the test and got this answer correct :)
does 3/4 have the same value as the expression 4 ÷ 3 answer
Two sides of an isosceles triangle have lengths of 6 inches and 15 inches, respectively. What is the length of the third side?
instruction: You must show all of your work bysl setting up the problem using combinatorics and simplifying completely.
question: There are 5 red marbles and 9 blue marbles in a bag. suppose two of the marbles are cracked. how many ways can four marbles be selected so that either no cracked marbles are selected or just one cracked marble is selected?
1. A parallelogram with four congruent sides is a? 2. A polygon with all angles congruent is a? 3. Angles of a polygon that share a side are? 4. A blank is a quadrilateral with exactly one pair of parallel sides?
What is the volume of the pyramid to the nearest whole unit?
A. 1,134 yd^3
B. 567 yd^3
C. 378 yd^3
D. 284 yd^3
A rectangular football field is 64 meters wide and 100 meters long. A player runs from one corner of the field in a diagonal line to the opposite corner. How far did the player run? Round your answer to the nearest meter.
The distance covered by a player on a rectangular football field will be 118.73 meters.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A rectangular football field is 64 meters wide and 100 meters long. A player runs from one corner of the field in a diagonal line to the opposite corner.
Then the distance covered by a player on a rectangular football field will be given by the Pythagoras theorem.
H² = 100² + 64²
H² = 10000 + 4096
H² = 14096
H = 118.73 meters
The distance covered by a player on a rectangular football field will be 118.73 meters.
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how do you write this in numerical expression and in a answer statement
What symbol should be placed in the blank to make the equation true? 3 + 10___ 2 - 4 = 4
Ieda and Thanh both offer piano lessons. Ieda charges an initial fee of $8.50 and an hourly rate of $11.00. Thanh charges an initial fee of $10.00 and an hour rate of $10.50. At how many hours of instruction will the price for each instructor be the same?
A student used the equation below to create a table.
y = –3x – 5
The student used –2 as one of the values for the input. Which ordered pair could be taken from the table?
A. (–11, –2)
B. (–2, –11)
C. (–2, 1)
D. (1, –2)
You deposit $350 in a savings account. The account earns 2.5% simple interest per year. What is the balance after 2 years?
Answer:
Balance = $367.5
Step-by-step explanation:
The 2.5% of $350 is,
→ (350/100) × 2.5
→ 3.5 × 2.5
→ $8.75
The balance after 2 years is,
→ $350 + (2.5%) × 2 years
→ 350 + 8.75 × 2
→ 350 + 17.5
→ $367.5
Hence, the answer is $367.5.
The balance after 2 years on principle amount of $350 at the rate of 2.5% will be $525.
What is Simple interest?The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money.
Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.
As per the information in the question,
Principle amount, p = $350
Rate, r = 2.5%
Time, t = 2 years.
Use the formula of simple interest,
[tex]S.I = (p*r*t)/100[/tex]
S.I = (350 × 2.5 × 2)/100
S.I = 17500/100
S.I = 175
Now, the total amount will be,
$350 + 175 = $525
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macy is trying to construct an isosceles triangle. She assigns and angle measurement of 40 degrees to the unique angle of the triangle. She wants the length fo the opposite side (the base) to be 6 centimeters. How many isosceles triangles can macy construct using this information? A. 3 cm B. 10 centimeters, C. 12 Centimeters D. 14 centimeters, E. 18 centimeters
Answer:
the awnser is 2
Step-by-step explanation:
if she makes more that 2 the 3rd one wont be an isosoceles triangle
25 POINTS TO WHO EVER ANSWERS!!!
1. An ice cream store owner randomly samples 50 customers each day on three separate days to give their opinion about which flavors should be flavor of the month.
Vanilla | Chocolate | Rocky Road | Cheesecake
Day 1: 13 | 12 | 11 | 14
Day 2: 12 | 15 | 11 | 14
Day 3: 15 | 7 | 8 | 20
Select from drop-down menu to complete the statement using the information in the "table".
Based on the results of the survey, if the ice cream store owner asks 2300 people, ____ will most likely pick vanilla to be flavor of the month.
2. The line plots show the results of a survey of 10 boys and 10 girls about how many hours they slept the previous night.
x
x
x x
x x x x x x
<-+-+-+-+-+-+-+-+-+-+->
1 2 3 4 5 6 7 8 9 10
x x
x x x
x x x x x
<-+-+-+-+-+-+-+-+-+-+->
1 2 3 4 5 6 7 8 9 10
Select from the drop-down menus to complete each statement.
The range ________. The mean __________.
1. answers: 40, 150, 460, or, 613
2 A. answers: is greater for boys, is greater for girls or, us the same for both sets of data
2 B. answers: is the same for both sets of data, is greater for the boys or, is greater for the girls
What is the equivalent factored form of 12x^4-42x^3-90x^2
A rectangular prism has a length of 3 1/2 inches, a width of 5 inches, and a height of 1 1/2 inches.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
Answer:
26.25
Step-by-step explanation:
I took the test.
e vertices of a trapezoid are shown below. P(0, 0), Q(2, 0), R(2, 5), S(0, 10) This trapezoid is dilated about the origin by a scale factor of 3. What is the location of point Q'?
The location of point Q' after the dilation is (6, 0).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
To dilate the trapezoid by a scale factor of 3 about the origin, we need to multiply the coordinates of each vertex by 3.
The coordinates of Q are (2, 0), so to find the coordinates of Q' after the dilation, we multiply both the x and y coordinates by 3:
Q' = (32, 30) = (6, 0)
Therefore, the location of point Q' after the dilation is (6, 0).
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What is 14.281 rounded to the nearest one?
two numbers have a difference of 0.7 and a sum of 1 what are the numbers
When a class took a math test, 15% of the class failed, 25% made some mistakes (but didn’t fail), and 24 students got perfect scores. How many students were in the class?
a $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
To calculate the balance in the account after 4 years, use the compound interest formula.
Explanation:To calculate the balance in the account after 4 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the balance after the specified time period
P is the principal amount (initial deposit)
r is the interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal is $4,000, the interest rate is 5% (written as 0.05), the interest is compounded annually (n = 1), and the time period is 4 years (t = 4). Plugging in these values, we get:
A = $4,000(1 + 0.05/1)^(1*4)
A = $4,000(1.05)^4
A = $4,000(1.2155)
A ≈ $4,862.20
The balance in the account after 4 years is approximately $4,862.20.
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15 POINTS!! HELP ME PLZ!!!
In conducting a survey of voters, a pollster selected every tenth name on a list of registered voters.
Which sampling technique did the pollster use?
a) convenience sampling
b) stratified sampling
c) systematic sampling
d) voluntary sampling
The answer is C: systematic sampling
Answer:
The awnser is C
Step-by-step explanation:
combine the like terms 10 y + 1 x - 4y + 4x
how to solve this ? the question asked, the distance between two houses P&Q is 200 kilometer. Joe travel by car from P to Q at average speed of x km/h
a) write down an expression in terms of X for the number of hours he took to travel from P to Q.
b) he returned from Q to P at an average of (x + 5) km/h. write down an expression in terms of X for the number of hours he took to travel from Q to P
c) the total time he took to go from P to Q & to return from P to Q was 8 hours