The sum of twice a number and half the number is 10 ???
2.5% TAX, $679 SEMIMONTHLY: FIND THE LOCAL TAX DEDUCTED.
Answer:
$16.98
hope this helps you! good luck ;)
A bank contains 35 coins, all nickels and quarters. The total value of coins is $8.15. How many of each coin does the bank contain?
n + q = 35
n = 35-q
0.05n + 0.25q = 8.15
0.05(35-q) +0.25q = 8.15
1.75 -0.05q + 0.25q =8.15
1.75 + 0.20q = 8.15
0.20q = 6.40
q = 6.40 / 0.20 = 32
32 quarters and 3 nickels
At the beginning of a basketball season, the Panthers won 40 games out of 60 games. At this rate, how many games will they win in a normal 110-game season? Round answer to the nearest game.
The Panthers are expected to win approximately 73 games out of 110 based on their current win rate.
To find out how many games the Panthers will win in a normal 110-game season based on their current winning rate from the beginning of the season, we use a simple proportion. Initially, they won 40 games out of 60, which gives us a winning ratio.
The ratio can be written as:
40 wins / 60 games = number of wins / 110 games
To find the number of wins, we cross-multiply and solve for the unknown:
(40 wins / 60 games) * 110 games = number of wins
After the calculation:
40 * 110 / 60 ≈ 73.33
As we need to round to the nearest game, it gives us approximately 73 games out of 110.
A delivery truck travels 21 blocks north, 12 blocks east and 26 blocks south. what is its final displacement from the origin? assume the blocks are equal length.
The truck's displacements in the North-South and East-West directions are calculated separately. The final displacement is 5 blocks South and 12 blocks East.
Explanation:To solve this problem, we need to consider the truck's displacement in the North-South direction and the East-West direction separately.
Starting with the North-South direction, the truck moves 21 blocks North and then 26 blocks South. Thus, its total displacement in the North-South direction is 21 - 26 = -5 blocks. The negative sign indicates that the truck is 5 blocks South from its starting point.
Considering the East-West direction, the truck moves 12 blocks East. Therefore, its total displacement in the East-West direction is +12 blocks.
Overall, the displacement of the truck from the origin is 5 blocks South and 12 blocks East.
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You buy 12 tickets and the total is $120. a student ticket is $9 and an adult ticket is $12. how many student tickets did you buy
Terry had $43 in a checking account. If Terry writes a check for $62, what is the new account balance? a. $105 c. -$19 b. $19 d. -$9
How many two-person conversations can occur at a party with 150 people?
---------------- conversations
Final answer:
There can be a total of 11,175 two-person conversations at the party.
Explanation:
In a party with 150 people, the number of two-person conversations that can occur can be calculated using the formula for combinations. Since each conversation involves two people, we need to choose 2 people from the total of 150. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of people and r is the number of people we need to choose. Plugging in the values, we have:
C(150, 2) = 150! / (2!(150-2)!)
C(150, 2) = (150 ×149) / (2 ×1)
C(150, 2) = 11175
Therefore, there can be a total of 11,175 two-person conversations at the party.
Final answer:
At a party with 150 people, there can be 11175 unique two-person conversations, calculated using the combination formula 150C2.
Explanation:
The question is asking how many two-person conversations can occur at a party with 150 people. This is a classic combination problem where we need to calculate the number of unique pairs that can be made from 150 people. Since the order in which the pair is chosen does not matter, we use the combination formula nCr = n! / (r!(n-r)!), where 'n' is the total number of people and 'r' is the group size (in this case, 2 for a two-person conversation).
For 150 people, the calculation is:
150C2 = 150! / (2!(150-2)!) = 150! / (2! x 148!) = (150 x 149) / (2 x 1) = 11175.
Therefore, there can be 11175 unique two-person conversations at a party with 150 people.
Please help me , algebra math !!
Determine the value of r so that the line through (5, 2) and (7, r) has a slope of m= -1/2
Final answer:
The value of r that makes the line through (5, 2) and (7, r) have a slope of -1/2 is 1.
Explanation:
To determine the value of r so that the line through the points (5, 2) and (7, r) has a slope of m= -1/2, we use the slope formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is (5, 2) and (x2, y2) is (7, r).
Slope calculation:
-1/2 = (r - 2) / (7 - 5)
-1/2 = (r - 2) / 2
Multiplying both sides by 2 to isolate the variable r:
-1 = r - 2
r = 2 - 1
r = 1
Therefore, the value of r that makes the slope -1/2 is 1.
what is 2.31 divided by 3?
The selling price, s, of an item is s = c + mc, where c is the cost of the item and m is the percent markup based on cost. What is the formula solved for m?
Answer:
[tex]m=\frac{s-c}{c}[/tex]
Step-by-step explanation:
The given expression is
[tex]s=c+mc[/tex]
Now, to find the expression for [tex]m[/tex], we just have to isolate it. First, we have to move the term [tex]c[/tex] to the other side of the equation, and then to move the coefficient [tex]c[/tex], which is gonna pass to the other side dividing.
[tex]s=c+mc\\s-c=mc\\\frac{s-c}{c}=m\\m=\frac{s-c}{c}[/tex]
Therefore, the percent markup is defined as the difference between the selling price and cost, divided by that cost.
What are the steps for using a compass and straightedge to construct an equilateral triangle?
Drag the steps and drop them in order from start to finish.
Construct a point at one of the two intersection points of circle E and circle F and label this point G
.Construct EG¯¯¯¯¯ and FG¯¯¯¯¯ .
Construct EF¯¯¯¯¯
.Construct a circle with point E as the center and a circle with point F as the center with each circle having radius EF .
What is the equation of the line with an x-intercept of -2 and a y-intercept of 1?
A.y = -1/2x + 1
B.y = 1/2x + 1
C.y = 2x + 1
Find the Missing part of the unit rate: 40 students over 5 groups = ? Students over group
The missing part of the unit rate in the given situation is 8 students per group. This is obtained from dividing the total number of students (40) by the total number of groups (5).
Explanation:To find the missing part of the unit rate, we'll need to divide the total number of students (40) by the total number of groups (5). This is because a unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
So in this case, the unit rate would be 40 ÷ 5 = 8. Therefore, the missing part of the unit rate is 8 students per group.
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calculate the distance between the points A (-4,2) and B (15,6)
Distance between the points A (-4, 2) and B (15, 6) is 19.41.
Here,
The points are A (-4, 2) and B (15, 6).
We have to find the distance between the points A (-4, 2) and B (15, 6).
What is Distance between two points?
Distance between two points A (x₁, y₁) and B (x₂, y₂) is given by:
[tex]D_{AB} = \sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]
Now,
Distance between the points A (-4, 2) and B (15, 6) is;
[tex]D_{AB} = \sqrt{(15-(-4))^2+(6-2)^2}[/tex]
[tex]= \sqrt{19^2+4^2}[/tex]
[tex]= \sqrt{361+16}[/tex]
[tex]= \sqrt{377}[/tex]
[tex]= 19.41[/tex]
Hence, Distance between the points A (-4, 2) and B (15, 6) is 19.41.
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What equation models the data in the table if d = number of days and c = cost?
Days Cost
2 44
3 66
5 110
6 132
c = 22d
d = 22c
c = d + 22
c = d + 22d
The equation that models the data in the table is:
[tex]c=22d[/tex]
Step-by-step explanation:The table that represent the days and cost is given by:
Days Cost
2 44
3 66
5 110
6 132
We see that the cost is a constant multiple of the number of days.
i.e. the equation is given by:
c=22d
i.e. the relationship is linear.
( Since, when d=2
we have: c=22×2=44
when d=3 we have:
c=22×3=66
and so on )
If f(x)=3x^2-2x+4 and g(x)=5x^2+6x-8 find (f+g)(x)
What is the equation for the line of reflection that maps the trapezoid onto itself? x = 0 x = 3 y = 3 y = 0?
The correct answer is option 3. The equation for the line of reflection that maps the trapezoid onto itself is y = 3.
To determine the line of reflection for a trapezoid that maps onto itself, we need to identify the axis of symmetry.
We can analyze each one:
1. x = 0 represents a vertical line of reflection. If the trapezoid were reflected over this line, the left and right sides would be swapped. This would not map the trapezoid onto itself unless the trapezoid is symmetric about the y-axis, which is not specified.
2. x = 3 also represents a vertical line of reflection. This would reflect the trapezoid over a vertical line three units to the right of the y-axis. Again, this would not map the trapezoid onto itself unless the trapezoid is symmetric about the line x = 3, which is not specified.
3. y = 3 represents a horizontal line of reflection three units above the x-axis. If the trapezoid has its bases parallel to the x-axis and the midline of the trapezoid is at y = 3, then reflecting over this line would indeed map the trapezoid onto itself. This is because the top half of the trapezoid would be a mirror image of the bottom half across the line y = 3.
4. y = 0 represents a horizontal line of reflection along the x-axis. Reflecting the trapezoid over the x-axis would flip it upside down, which would not map the trapezoid onto itself unless the trapezoid is symmetric about the x-axis, which is not typical for a trapezoid.
The complete question is:
What is the equation for the line of reflection that maps the trapezoid onto itself?
1. x = 0
2. x = 3
3. y = 3
4. y = 0
if you have 2 dollars 5 pennies and three quarters how much money do you have
You and 2 friends have a job washing cars. you split the money you make so that you each get the same amount. on the first day, you earn $75. the second day, you earn $84. the third day, you earn $105. how much money will you each get for those 3 days?
Final answer:
Each friend would receive $88 from the total earnings of $264 over three days, after splitting the amount equally.
Explanation:
The question asks how much money each person would get from a total earning of $75 on the first day, $84 on the second day, and $105 on the third day after splitting it equally among three friends. To find this out, first, we need to calculate the total earnings by adding the amounts from all three days, and then we divide the total by three, since there are three friends.
The total earnings over the three days are $75 + $84 + $105 = $264. To find out how much each person gets, we divide this amount by 3:
$264 ÷ 3 = $88
So, each friend would get $88 for their work over those three days.
Find the value of b if it is known that the graph of y=−3x+b goes through point: M(−2, 4)
Factor this Polynomial completely. X^2-12x-36
this cannot be factored.
there are no 2 numbers that when added will equal - 12 and when multiplied together would equal -36
Suppose you kick a football and its movement can be modeled by a parabola. after 1 second its height is 15 feet above ground, after 2 seconds its height is 14 feet above ground, and after 3 seconds its height is 9 feet above ground.
a.find the equation of the parabola that models this behavior. y = -2x2 + 5x +12
b.after how many seconds does the ball hit the ground? 4 seconds
The equation of the parabola that models the movement of the football is y = -2x² + 5x + 12. The time at which the ball hits the ground is x = 4 seconds.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
a. We know that the general form of the quadratic equation is y = ax² + bx + c, where a, b, and c are constants.
We are given three points that the football passes through: (1, 15), (2, 14), and (3, 9).
We can substitute these points into the quadratic equation and solve for a, b, and c.
For the first point, we have: 15 = a(1)² + b(1) + c
For the second point, we have: 14 = a(2)² + b(2) + c
For the third point, we have: 9 = a(3)² + b(3) + c
Solving this system of equations using elimination gives us:
a = -2
b = 5
c = 12
Therefore, the equation of the parabola that models the movement of the football is y = -2x² + 5x + 12.
b. To find the time at which the ball hits the ground, we can set the value of y equal to 0 and solve for x.
y = -2x² + 5x + 12
0 = -2x² + 5x + 12
-12 = -2x² + 5x
-2x² + 5x - 12 = 0
We can use the quadratic formula to solve for x:
x = (-5 +/- √(5² - 4(-2)(-12)))/(2(-2))
x = (-5 +/- √(25 + 96))/(-4)
x = (-5 +/- √(121))/(-4)
x = (-5 +/- 11)/(-4)
Therefore, x = 4 or x = -3/2.
The time at which the ball hits the ground is x = 4 seconds.
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M(3, 4) is the midpoint of mc010-1.jpg The coordinates of S are (4, 1). What are the coordinates of R?
Answer:
its c
Step-by-step explanation:
(WILL MARK AS BRAINLIEST) Consider the graph of quadrilateral WXYZ.
Which statements about quadrilateral WXYZ are true? Check all that apply.
The slope of ZW is .
The slope of YX is .
The length of ZY is .
The length of WX is 5.
Quadrilateral WXYZ is a square.
Answer:
The slope of ZW is [tex]\frac{2}{5}[/tex]
The lenght of ZY is [tex]\sqrt{29}[/tex]
Quadrilateral WXYZ is a square
Step-by-step explanation:
Statements
case A) The slope of ZW is [tex]\frac{2}{5}[/tex]
The statement is True
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]Z(-3,1),W(2,3)[/tex]
substitute
[tex]m=\frac{3-1}{2+3}[/tex]
[tex]m=\frac{2}{5}[/tex]
case B) The slope of YX is [tex]-\frac{5}{2}[/tex]
The statement is False
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]Y(-1,-4),X(4,-2)[/tex]
substitute
[tex]m=\frac{-2+4}{4+1}[/tex]
[tex]m=\frac{2}{5}[/tex]
case C) The lenght of ZY is [tex]\sqrt{29}[/tex]
The statement is True
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]Z(-3,1),Y(-1,-4)[/tex]
substitute
[tex]d=\sqrt{(-4-1)^{2}+(-1+3)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
case D) The lenght of WX is [tex]5[/tex]
The statement is False
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]W(2,3),X(4,-2)[/tex]
substitute
[tex]d=\sqrt{(-2-3)^{2}+(4-2)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
case E) Quadrilateral WXYZ is a square
The statement is True
Because sides ZW and YX are parallel sides (has the same slope)
Slope ZY
we have
[tex]Z(-3,1),Y(-1,-4)[/tex]
[tex]m=\frac{-4-1}{-1+3}[/tex]
[tex]m=-\frac{5}{2}[/tex]
so
ZW and ZY are perpendicular sides (the product of their slopes is equal to minus one)
[tex]-\frac{5}{2}*\frac{2}{5}=-1[/tex]
Slope WX
we have
[tex]W(2,3),X(4,-2)[/tex]
[tex]m=\frac{-2-3}{4-2}[/tex]
[tex]m=-\frac{5}{2}[/tex]
ZY and WX are parallel sides (has the same slope)
distance ZW
we have
[tex]Z(-3,1),W(2,3)[/tex]
[tex]d=\sqrt{(3-1)^{2}+(2+3)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
distance YX
we have
[tex]Y(-1,-4),X(4,-2)[/tex]
[tex]d=\sqrt{(-2+4)^{2}+(4+1)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
The four sides are congruent
case F) [tex]YZ=\sqrt{(-3-(-1))^{2}+(1-4)^{2}}[/tex]
The statement is False
[tex]YZ=\sqrt{(-2)^{2}+(-3)^{2}}[/tex]
[tex]YZ=\sqrt{13}[/tex] ----> is not correct
the value of YZ is [tex]\sqrt{29}[/tex]
You want to convert a measurement of 800 milliliters to centiliters using back-to-back conversion factors.
The conversion factors you will need are:
1 milliliter = 1/1000 liter
1 centiliters = 1/100 liters
The image shows you the template of the equation.
What is the order of the conversions you must perform?
How many inches are there in 62 centimeters? there are 2.54 centimeters in 1 inch?
Write the equation of the line that passes through the points (1,4) and (5,8) in standard form.
Question 8 options:
x + 4y = 1
5x + 8y = 4
-2x + y = 5
-x + y = 3
What is the answer to X2+16x+60=0