The midpoint of the line segment given is (1, 4.5)
Midpoint of a LineIn geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment equally into two halves.
The formula of midpoint of a line is given as
[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]
A = (-2, 7)B = (4, -2)Substituting the given values;
[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\\M_x_y = \frac{-2+4}{2}, \frac{7+2}{2} \\M_x_y = 1, \frac{9}{2} \\M_x_y = 1, 4.5[/tex]
The midpoint of the line AB is equal to (1, 4.5)
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A piggy bank contains $2.65 in nickles and dimes. if the number of nickles is 7 less than three times the number of dimes. how many of each are there
In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes. Then There are 29 nickels and 12 dimes in the piggy bank.
We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.
Let x be the number of nickels and y be the number of dimes.
We know that, 1 dollar = 20 nickels
and 1 dollar = 10 dimes
So, we get an equation
0.05x + 0.1y = 2.65 ...........(1)
Also the number of nickels is 7 less than three times the number of dimes.
x = 3y - 7 .................(2)
Substitute above value of x in equation (1)
0.05(3y - 7) + (0.1)y = 2.65
0.15y - 0.35 + 0.1y = 2.65
0.25y = 2.65 + 0.35
0.25 y = 3
y = 12
Substitute above value of y in equation (2)
x = 3(12) - 7
x = 29
Therefore, there are 29 nickels and 12 dimes in the piggy bank.
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Find the area of ABCD with vertices A(-5,2), B(-3,2), C(-2,-5),
D(-4,-5).
Answer:
14 units²=============================
Given Vertices A(-5,2), B(-3,2), C(-2,-5), D(-4,-5)To find The area of ABCDSolutionWe can observe that:
1. AB and CD are horizontal segments, since both endpoints have same y-coordinates:
A and B have y = 2, C and D have y = - 52. AB and CD are of same length:
AB = - 3 - (-5) = 2,CD = - 2 - (-4) = 2.It means the ABCD is a parallelogram, since two opposite sides are parallel and of same length.
The area of parallelogram is:
A = bh, where b- base length, h - heightWe know the length of the base, it is found above, 2 units.
The height is the difference of y- coordinates:
h = 2 - (-5) = 7The area is:
A = 2*7 = 14 units²Use I = PTR to solve
(time is in years)
I=$252
R=7% find T.
P=$900
The time period in years T = 4 years
The simple interest amount = $252
The rate of interest per year as percentage = 7%
The principal amount = $900
The simple interest I = PTR
Where I is the interest amount
P is the principal Amount
T is the time period involved in years
R is the rate of interest per year as a percent
Substitute the values in the equation
252 = 900 × T × (7 / 100)
252 = 900 × T × 0.07
252 = 63 × T
Move the 63 to other side
T = 252 / 63
T = 4 years
Hence, the time period in years T = 4 years
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Why is the denominator of each fraction 12?
Pls help me
Answer: because it is out of 12
Step-by-step explanation:
1. Henry wants to go on a vacation. He knows it will cost $300 per
day that he's on vacation plus $650 for miscellaneous activities. He
has $2750 dollars in his savings account. How many days can he go
on vacation?
The number of days Henry can go on vacation is 7 days.
Given that, Henry knows it will cost $300 per day that he's on vacation plus $650 for miscellaneous activities.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of days be x.
Henry has $2750 dollars in his savings account.
So equation is 300x+650=2750
The obtained equation can be solved as follow
300x=2750-650
⇒ 300x = 2100
⇒ x = 2100/300
⇒ x = 7
Therefore, the number of days Henry can go on vacation is 7 days.
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5. The table shows how far a car is from its destination after x hours.
Hours
Miles
1
150
2
100
50
لیا
3
The function f(x) = 210-60x represents a second trip, where f(x) is the number of miles
the car is from its destination after x hours. Which trip takes less time? Explain.
Answer:
the trip represented by f(x) takes less time
Step-by-step explanation:
Given a table of time and distance to go, and a function f(x) = 210-60x representing the same for a different trip, you want to know which trip takes less time.
TableThe table has values ...
(time in hours, remaining distance in miles) = (1, 150), (2, 100), (3, 50)
This shows you the remaining distance decreases by 50 miles for every hour added to the travel time. That means the remaining 50 miles will be reduced to zero after 4 hours.
The trip represented by the table takes 4 hours.
EquationThe function f(x) = 210-60x will have a value of zero when ...
0 = 210 -60x
0 = 3.5 -x . . . . . . divide by 60
x = 3.5 . . . . . . . . add x
The trip represented by the function f(x) takes 3.5 hours.
The second trip takes less time.
standard form. (-3,0) and (0,8)
Answer:
8x−3y=−24
Step-by-step explanation:
ASAP!!
3x + 9x = 6x + 42
Solve the equation for X and include all steps for Branliest.
Answer:
x = 7
Step-by-step explanation:
3x + 9x = 6x +42
12x = 6x +42
12x - 6x = 6x -6x +42
6x = 42
[tex]\frac{6x}{6} = \frac{42}{6}[/tex]
x = 7
WILL GIVE BRAINLIST IF ANSWERED CORRECTLY!!
Answer: 9 units to the right and 5 units down
Step-by-step explanation:
1) Measure the length.
You can find that you can match point C with point W. Next find how much it goes to the right and left.
Right from (C->W): 9 squares
Down from (C->W): 5
2) Fill in the blank
9 units to the right and 5 units down
Answer:
ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.
Step-by-step explanation:
The triangles are congruent as the measures of their corresponding sides and angles are the same.
To determine the translation of ΔABC to ΔNKW, find the change in the x and y values from one of the points of ΔABC to its corresponding point of ΔNKW.
Point C = (0, 0)Point W = (9, -5)Therefore:
ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.
a) Find the value of 8*1/3
b) Find the value of 8*2/3
c) Find the value of 164*3/4
1. 8/3
2. 16/3
3. 123
*some words for 20 symbols*
plssssss helpppppppppppppppppp
ou have three jars of gumballs. the first jar has 100 white gumballs and 25 green, the second jar has 50 white and 150 blue, and the third jar contains 500 white and 10 red. if you randomly draw one gumball from each jar, what is the probability for at least one white gumball?
The probability for at least one white gumball is 0.196
Consider the following:
First jar:100 whites, 25 green
Total=100+25
=125 gumball
P(White)=100/125=0.8
Second jar:50 whites, 150 blue
Total=50+150
=200 gumballs
P(White)=50/200=0.25
Third jar:500 whites, 10 red
Total=500+10
=510
P(White)=500/500=0.98
Now, probability for at least one white is
=P(white in jar 1)*P(white in jar 2)*P(white in jar 3)
=0.8*0.25*0.98
=0.196
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will give 30 points if its right need asap please
Answer:
2y + 1 maybe??????
Step-by-step explanation:
hope its correct if not please tell me
What is the complete factorization of 2 - 2ab + b2?
F. (a - b)(a + b)
G. (a + b)(a + b)
H. (a + b)(-a-b)
J. (a - b)(a - b)
Answer:
J
Step-by-step explanation:
assuming the 2 is a squared s a*a is a2 2*a*-b is -2ab
and -b* -b is b2
Given the function:
g(x)=8-2.5x
Find the following values.
a) g(6)
b) g(0)
c) g(-6)
A) g(6)
g(6) = 8 -2.5*6
g(6) = 8 - 15
g(6) = -7
B) g(0)
g(0) = 8 -2.5*0
g(0) = 8 - 0
g(0) = 8
C) g(-6)
g(-6) = 8 -2.5*-6
g(-6) = 8 + 15
g(-6) = 23
Tina's taco truck sold 3 times as many veggie tacos in August than in September. She sold twice as many in September than in October. She sold 927 veggie taco during the three months
The number of tacos sold in August, September and October is 103, 206, 618 respectively.
Let the number of veggie tacos sold by Tina in October be x
Then, number of veggie tacos sold in September is twice that of veggie tacos sold in october = 2x
Number of veggie tacos sold in August is thrice that of veggie tacos sold in September = 3 x 2x = 6x
Total veggie taco during the three months by Tina = 927
6x + 2x + x = 927
9x = 927
x = 927/9
x = 103
Tacos sold in August = 6x = 618
Tacos sold in September = 2x = 206
Tacos sold in October = x =103
Therefore, the number of tacos sold in August, September and October is 103, 206, 618 respectively.
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An 8-foot roll of butcher paper costs $6.72. What is the price per inch?
Answer:
$0.84
Step-by-step explanation:
To solve this problem, divide 6.72 by 8.
6.72/8=0.84
It costs $0.84 per inch.
Hope this helps! :D
Simplify
8(x + 3)2/2(x + 3)
Answer:
4x + 12Step-by-step explanation:
[tex] \sf \cfrac{8(x + 3)^{2} }{2(x + 3)} [/tex]
Cancel out 2(x+3) in both numerator and denominator:
[tex]\sf 4(x + 3)[/tex]
Use the distributive property to multiply 4 by x+3:
[tex]\sf 4x + 12[/tex]
》》》》》》》》》》》》》》
Hope this helps!!
Have a nice day
Write an equation that represents the line.
Use exact numbers.
y=1.5x+3
Observing the graph
Let,
A(0,3) -----> this point is the y-intercept of the line
B(2,6)
We know that
The equation of the line into slope intercept form is equal to
y = mx + c
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem
b=3
Find the slope of the line m
The formula to calculate the slope between two points is equal to
m = y2-y1 / x2-x1
substitute the values
m = 6-3 / 2-0
m = 3/2
m = 1.5
The equation of the line is
y= 1.5x+3
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Ivan has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Using combinations, there are a total of 20 distinct voting combinations.
We now have five bands. We'll refer to them as A, B, C, D, and E.
John will choose two bands from the available five if he is required to vote for his favorite and second-favorite.
We must pair bands and discover every possible combination in order to determine the TOTAL number of different possibilities.
The results/totals are as follows:
AB, AC, AD, AE
BA, BC, BD, BE
CA, CB, CD, CE
DA, DB, DC, DE
EA, EB, EC, ED
Thus, there are a total of 20 distinct voting combinations.
Since you already know that each of the five initial bands (A, B, C, D, and E) will result in a multiple of four, you may accomplish it more simply without listing by taking the five bands.
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Which postulate could we use to prove that the angles
Answer:
you can use the angle addition postulate I think that's what it's called
Pls help ASAP
The question is in the picture
Answer:
1. x = 0 , x = 3
2. x = -2 , x = 2
3. (x - 1)²
The measure of a base angle of an isosceles triangle is 20 degrees. What is the measure of the vertex?
Answer:
140 degrees
Step-by-step explanation:
isosceles triangle so two angles are equal 20 and 20
ALL of the angles sum to 180 degrees
20+ 20 + vertex = 180
vertex = 140°
The length of the rectangle is 5 more than twice the width. If the perimeter is 10 times that of the width, what is the width, length, and perimeter of the rectangle?
Width of the rectangle is 2.5, Length is 10 and perimeter is 25
Given
Length of rectangle is 5 greater than double of width
let us say width = w
According to the question length L = 5 + 2w
Perimeter is 10 times the width
P= 10w
we know that perimeter of a rectangle is 2(L+W)
Substituting the values in the formula we get
10w = 2(5+2w + w)
10w = 10 + 6w
w= 2.5
From this length L = 5+2(2.5)
L = 10
Perimeter P = 10W
P= 10(2.5)
P= 25
Hence the length is 10, width is 2.5 and perimeter is 25
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7/3y = 21 solve for y simplify your answer as much as possible
Answer: y = 1/9
Step-by-step explanation:
7/3y=21
7= 21 x 3y
7/21 = 3y
1/3 = 3y
1/9 = y
1-2p=-4p-9 solve equation
Answer: p= -5
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
carry the one over to the right side and subtract it to get an amount of -10.
then carry the -4p to the left and add it with -2p. which comes out to be 2p
now the equation reads as 2p=-10
continue to divide 2 to get p alone and divide -10 by 2 as well.
now p=-5 because a negative divided by a postive is a negative.
HELP ASAP!!
Solve the inequality divided by negative 3. 2 is greater than or equal to 7. 6 for r.
A. ) r ≥ −24. 32
B. )r ≤ −24. 32
C. )r ≥ 2. 375
D. ) r ≤ −2. 375
Answer:
B. )r ≤ −24. 32
Step-by-step explanation:
Write an equation in standard form for the line that passes through the given points
(3,0) and (0, -2)
Equation of a line in the standard form that passes through the points (3, 0) and (0, -2) will be [y = (2/3)x - 2].
As per the question statement, a straight line passes through the points (3, 0) and (0, -2).
We are required to determine the equation of the above mentioned line in it's standard form.
To solve this question, we need to know the formula to write the standard equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as [tex][(y-y_{1})=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}(x-x_{1})][/tex].
Here, let (x₁, y₁) be (3, 0) and (x₂, y₂) be (0, -2).
Therefore, equation of our concerned line passing through the two points (3, 0) and (0, -2), by substituting [(x₁, y₁) = (3, 0)] and [(x₂, y₂) = (0, -2)] in the above mentioned formula, will be [(y - 0) = {(-2 - 0)/0₂ - 3)}(x - 3)]
Or, [y = {(-2)/(-3)}(x -3)]
Or, [y = (2/3)(x - 3)]
Or, [y = (2/3)x - 2]
Equation: In mathematics, an equation is a statement that expresses the relation of equality between two expressions, by connecting them with the "equal to" sign (=).Line: In geometry, a line is an infinitely long one-dimensional object or shape with no width, depth, or curvature.To learn more about Equations and lines, click on the link below.
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One teacher wants to give each student 4/9 of a slice of pizza. if the teacher has 4 slices of pizza, then how many students will she be able to hand out pizza to?
How do solve this in geometry?
Answer:
x=0.4
Step-by-step explanation:
Put both equations equal to each other:
16x+2=7x+6
Now, Solve:
16x+2=7x+6 Set the equation
16x-7x=6-2 Move like terms together
9x=4 Subtract like terms
x=4/9 Simplify
x=0.4 Answer