The function into vertex form is m(d) = -4(d -2 )^2 - 24
Given in the question:
m(d)= - 4d^2 + 16d -40
and, Convert the function into vertex form.
Let's Know:
How do you change a function into vertex form?
m(d) = - 4d^2+16d-40 Convert the function into vertex form.
To convert standard form to vertex form, Convert y = ax2 + bx + c into the form y = a (x - h)2 + k by completing the square. Then y = a (x - h)2 + k is the vertex form.
Come to the solution:
m(d)= - 4d^2 + 16d -40
take out the leading coefficient;
m(d)= - 4(d^2 - 4 x d ) -40
Complete the square
m (d) = - 4(d^2 +(2 x(-2))x d + (-2)^2) + (-40 - (-4 x (-2)^2))
Express the function in vertex form :
m(d) = -4(d -2 )^2 - 24
Hence, The function into vertex form is m(d) = -4(d -2 )^2 - 24
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a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits in . no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in . a set of plates in which each possible sequence appears exactly once contains license plates. find .
The value of N/10 is 372.
The characters can be chosen from the word "AIME" or the number "2007".
There are 7 different characters that can be picked, with 0 being the only number that can be repeated twice.
There are two possible cases.
The first case is given below :
If 0 appears 0 or 1 time in the sequence, the number of possible sequences is 7!/(7-5)!.
If 0 appears 0 or 1 time in the sequence, the number of possible sequences is 2520.
The second case is given below :
If 0 appears twice in the sequence, the number of places to fill 0 is 5C2.
If 0 appears twice in the sequence, the number of places to fill 0 is 10.
The number of ways to place the remaining three characters is 6!/(6-3)!.
The number of ways to place the remaining three characters is 120.
The total number of ways in the second case is 10*120 = 1200.
The total number of ways is 2520 + 1200.
The total number of ways is 3720.
N = 3720
We have to find the value of (N/10).
N/10 = 3720/10
N/10 = 372
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what are the maximum dimensions of a div with the following properties?div.container { min-height: 150px; max-height: 600px; min-width: 300px; max-width: 900px;
Write an equation in slope-intercept form for each line described.
18.) passes through (5,-3), perpendicular to y=-2x+4
19.) passes through (-2,4), parallel to y=9
20.) passes through (3,5), perpendicular to y=1/3x+12
The equation of the line in slope-intercept form passes through (5,-3), parallel to y = - 2x + 4 is y = - 2x + 8 and equation of the line passes through (3,5), perpendicular to y = 1/3x + 12 is y = - 3x + 18.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know that parallel lines have same slopes and perpendicular lines have slopes that are negative reciprocals of each other.
Given a line passes through (5,-3), perpendicular to y = - 2x + 4.
The slope of this line is - 2 and hence line parallel to it will also have a
slope of - 2.
∴ The equation of the line in slope-intercept form is,
- 3 = 5(-2) + b.
- 3 = - 10 + b.
b = 8.
The required line is y = - 2x + 8.
Given a line passes through (3,5), perpendicular to y = 1/3x + 12.
The given line has a slope of 1/3 so the line perpendicular to it will have a slope of - 3 ( as the negative reciprocal of 1/3 is - 3/1 = - 3 ).
∴ The equation of the line in slope-intercept form is,
3 = 5(-3) + b.
3 = - 15 + b.
b = 18.
So, y = - 3x + 18.
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To solve a system of equations _______________ means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: _______________ and _______________.
To solve a system of equations algebraically means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: elimination and substitution.
The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics.
Computational methods for getting the solutions, which are essential to the disciplines of engineering, physics, biochemistry, computer science, and economics, are included in numerical linear algebra. It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computational modelling of a relatively complex system (see linearization).The easiest method for resolving a system of linear equations is to repeatedly remove variables. This method is described in the sentences that follow.The first equation's variables should each be solved for in relation to one another.In the following equations, substitute this expression in its place. As a result, the system of equations contains one less equation and unknown.Hence the two ways an algebraic equation can be solved is by elimination and substitution.
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Write the coordinates of the vertices after a rotation 270° clockwise around the origin.
The coordinates of the vertices when rotated 270° counterclockwise around the origin are:
K' = ( 4, 1 )
L' = ( 7, 1 )
M' = ( 7, 0 )
N' = ( 4, 0 )
When a point P( a, b ) is rotated 270° counterclockwise around the origin, we flip a and b and reverse the sign of a.
Therefore,
The rule to rotate a point P ( a, b ) after a rotation 270° counterclockwise around the origin is:
P ( a, b ) → P' ( b, - a )
Now, consider the points on the graph:
L = ( - 1, 7 )
K = ( - 1, 4 )
N = ( 0, 4 )
M = ( 0, 7 )
When the coordinates are rotated 270° counterclockwise.
L ( - 1, 7 ) → L' ( 7, 1 )
K ( - 1, 4 ) → K' ( 4, 1 )
N ( 0, 4 ) → N' ( 4, 0 )
M ( 0, 7 ) → M' ( 7, 0 )
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Which property of equality should you apply to keep the equation 22 . a = 242 in balance when solving?
The division property of equality
The subtraction property of equality
The reflexive property
The substitution property of equality
A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.
What is the subtraction property of equality?In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
Based on the information provided above, we can logically deduce the following equation:
22 . a = 242
22 × a = 242
By applying the division property of equality, we have the following:
a = 242/22
a = 11.
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1/2+3/6=
what will the answer be
The value of the fraction expression 1/2 + 3/6 is 1.
The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.
The smallest number (non-zero) that is a multiple of all the numbers is known as the least common multiple of two or more numbers.
Consider the expression,
1/2 + 3/6 = x
Consider the fraction 3/6,
The factors of 3 are 1 and 3.
The factors of 6 are 1, 2, 3, and 6.
Therefore, the GCF or greatest common factor is 3.
Therefore,
3/6 = ( 3 ÷ 3 ) / ( 6 ÷ 3 ) = 1/2
So, the value of the expression will be:
x = 1/2 + 3/6
x = 1/2 + 1/2
As the denominators of the fractions are equal.
x = ( 1 + 1 )/ 2
x = 2/2
x = 1
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Write an equasion of the line that passes through (0,-2) and (4,10)
Answer:
12.649
Step-by-step explanation:
we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).
So, we just need to find the length of the two sides:
Vertical side: 12
Horizontal side: 4
Thus;
[tex]4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)[/tex]
On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles?
When a scale of 1 inch to 40 miles apart then distance = 112 miles .
We have been give that
If 1 inch = 25 miles,
Then 2.8 inches would be 25 miles multiplied by 2.8 since each of those 2.8 inches is 25 miles.
2.8 x 25 = 70.
70 miles.
The same two cities be on a map that has a scale of 1 inch to 40 miles
Then 1 inch= 40 miles,
then 2.8 inches would be 40 miles multiplied by 2.8 since each of those 2.8 inches is 40 miles.
2.8 x 40 = 112.
112 miles.
Hence , Distance equals 112 miles when measured on a scale of 1 inch to 40 miles apart.
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An A.P has 17 terms and a common difference of -4 determine the first and the last termif the A.P is 107.1
Answer:
Below in bold.
Step-by-step explanation:
The sum of 17 terms is 107.1.
Sn = (n/2)[2a + (n-1)d] where a = first term and d = common difference
(17/2) (2a + (17-1)(-4)) = 107.1
8.5(2a -64) = 107.1
17a - 544 = 107.1
17a = 651.1
a = 38.3 = First term
The last term is the 17th so
L = a + (n - 1) d
= 38.3 + 16*-4
= -25.7.
What is the surface area of this rectangular pyramid? 4 mm
4 mm 4 mm
The formula for calculating the total surface area of a rectangular pyramid using its length, width, and height is provided as T.S.A. = lw + l[(w/2)2 + h2] + w[(l/2)2 + h2], where l is the length of the rectangular base, w is its width, and h is its height.
What is the Rectangular Pyramid?Pyramids are three-dimensional constructions with triangle-shaped faces and a base with a polygonal shape. A pyramid is referred to as a rectangular pyramid if its base is also rectangular. All pyramids have triangular sides, despite the fact that their bases are rectangular. The height of the pyramid is indicated by the top vertex, also known as the apex. The volume of a rectangular pyramid can be calculated using the formula V=1/3lwh, where l denotes the length of the base, w its width, and h its height.To learn more about Rectangular Pyramid refer :
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if you cant read it it says : Use the distributive property for the expression 4(m + 7) - 6(4-) and simplify
Explanation
The distributive property tells us how to solve expressions in the form of a(b + c)
[tex]a(b+c)=ab+ac[/tex]Then,
Step 1
apply distributive property operate
[tex]\begin{gathered} 4(m+7)-6(4-m) \\ 4\cdot(m)+4\cdot7-6(4)+6(m) \\ 4m+28-24+6m \end{gathered}[/tex]
Step 2
add similar terms
[tex]\begin{gathered} 4m+28-24+6m \\ 10m+4 \end{gathered}[/tex]so, the answer is
[tex]D)10m+4[/tex]I hope this helps you
8x^4+7x^3+2x^4+6+4x^3
You have the following algebraic expression:
[tex]\begin{gathered} 8x^4+7x^3+2x^4+6+4x^3 \\ \end{gathered}[/tex]The previous expression can be simplified by taking into account, that for the simplification you sum or subtract (depending of signs) similar terms. Remind that similar terms are those one which has the same variable with the same exponent. In this case you have similar terms with variable x and exponent 4, furthermore you have similar terms with variable x and exponent 3. Then you sum this terms and you obtain:
[tex]\begin{gathered} 8x^4+7x^3+2x^4+6+4x^3 \\ =8x^4+2x^4+7x^3+4x^3+6 \\ =10x^4+11x^3+6 \end{gathered}[/tex]where you have summed 8x^4 + 2x^4 = 10x^4, and 7x^3 + 4x^3 = 11x^3.
Hence, the simplied expression is 10x^4 + 11x^3 + 6
Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies. Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether. Graphically solve a system of equations in order to determine the number of donuts, x, and the number of cookies, y, that Autumn bought.
Autumn bought 4 Donuts and 2 Cookies worth of 5 dollars.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies.
Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether.
Let us denote no. of Donuts by x and no. of Cookies by y.
∴ x + y = 6...(i) and x + 0.5y = 5...(ii).
Subtracting eqn(ii) from eqn(i) we get y = 2 and substituting the value of y in eqn(i) we get x = 4.
Autumn bought 4 Donuts and 2 cookies with 5 dollars.
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if y=-2 when x=4, find y when x =7
As x and y vary inversely as each other , if x=7 then y = -8/7.
in the question ,
it is given that
x and y vary inversely ,
So , x * y = k
given that , when x = 4 , the value of y = -2 .
Substituting , 4 * (-2) = k
k = -8
so , the constant of variation (k) = -8 .
in order to find value of y when x = 7 ,
we substitute x=7 and k = -8 in the relation xy = k
we get , 7 * y = (-8)
Dividing both sides by 7 we get
7y/7 = -8/7
on simplifying we get ,
y = -8/7
Therefore , as x and y vary inversely as each other , if x = 7 then y = -8/7 .
The given question is incomplete , the complete question is
If y varies inversely as x, and y = -2 when x = 4 find y when x = 7 .
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A particle travels along the x-axis such that its position at time t is given by the function x(t) = 2t2 + t. What is the average speed of this particle over the interval 2 ≤ t ≤ 10?
4
25
32
200
Answer:
25.
Step-by-step explanation:
At time 2, x(t) = 2(2)^2 + 2 = 10
At time 10, x(t) = 2(10)^2 + 10 = 210.
Average speed for this interval
distance / time
= (210 - 10) / (10 - 2)
= 200/8
= 25.
A store owner paid $225 wholesale price for a TV. They need to make a 65% profit on the sale of the TV. What will a customer pay for the TV after it is marked up 65% and they pay sales tax of 9%?
The customer will pay $391.5 after it is marked up to 65% and the sale tax of 9%.
When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
The wholesale price paid by a store owner is $225.
The store owner needs to make a profit of 65%.
Then, the profit will be:
= 225 × 65% = $146.25
And, amount of tax the customer will pay will be:
= $225 × 9% = $20.25
Therefore, the price at which the customer will buy the TV will be:
= $225 + profit + sales tax
= $225 + $146.25 + $20.25
= $391.5
Hence, the customer will pay $391.5 for the TV.
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Brady loves to go fishing he goes every weekend this weekend he caught 4 less fish than he did last weekend he caught 7 fish this weekend write and solve and equation to determine how many fish he caught last weekend let f represent the number of fish
Solve the system of equations by elimination.-2x + 2y + z = 143x - 2y + z = -5-x + y - 2z = -8c
x= -3, y = 1, z = 6
Explanation:
-2x + 2y + z = 14 ....equation 1
3x - 2y + z = -5 ....equation 2
-x + y - 2z = -8 ....equation 3
Note: Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
Subtract equation 2 from 1:
-2x - 3x +2y -(-2y) + z - z = 14 -(-5)
-5x + 2y + 2y + 0 = 14 + 5
-5x + 4y = 19 ....equation 4
Due to the first equation we derived where we only have x and y. We need to solve the second equation in such a way we get only x and y.
This means we find a way to eliminate z in the second subtraction.
To do this, we multiply 1 by 2. Then we add both equations to eliminate z
-4x + 4y + 2z = 28 ....equation 1
-x + y - 2z = -8 ....equation 3
Add equation 3 and 1:
-4x + (-x) + 4y + y + 2z + (-2z) = -8 + 28
-4x - x + 5y + z + 2z - 2z = 20
-5x + 5y = 20 ....equation 5
-5x + 4y = 19 ....equation 4
-5x + 5y = 20 ....equation 5
subtract equation 4 from 5 (we will be eliminating x):
-5x -(-5x) + 5y - 4y = 20 - 19
-5x + 5x + y = 1
y = 1
we substitue the value of y in any of the equation between 4 and 5:
using equation 4:
-5x + 4(1) = 19
-5x + 4 = 19
-5x = 19-4
-5x = 15
x = 15/-5
x = -3
we substute for both y and x in any of the initial equation to get z:
using equation 2:
3(-3) -2(1) +z = -5
-9 - 2 + z = -5
-11 + z = -5
z = -5 + 11
z = 6
NEED DONE ASAP
The diameter of a speck of dust is about 0.00002 inches. Which of these is an appropriate estimate for the diameter of the speck of dust?
A
2×10−5in.
B
2×10−4in.
C
2×104in.
D
2×105in.
The diameter of the speck of dust is written as;
⇒ 2 × 10⁻⁵ inches.
Option A is true.
What is Number system?
A way for system of writing to express the number is called number system.
Given that;
The diameter of the speck of dust = 0.00002 inches.
Now,
Find the estimate number of the diameter of speck of dust as;
Since, The diameter of the speck of dust = 0.00002 inches.
The number = 0.00002 inches
It can be written as;
0.00002 inches = 2 × 10⁻⁵ inches.
Therefore,
The diameter of the speck of dust is written as;
⇒ 2 × 10⁻⁵ inches.
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How do you decide which operations to use when writing an equation?
Answer:The order of operations tells us the order to solve steps in expressions with more than one operation.
Step-by-step explanation: First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.
While shopping for supplies for the party, she is trying to decide which soda is the better deal. She can buy a 138 ounce bottle of soda for $3.20 or she can buy twelve 12ounce cans of cola for $3.60. Find the unit rate for the bottle.
Find the unit rate for the cans.
Answer:
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
Step-by-step explanation:
Cans oz/can Total oz Price ($) Cost ($/oz)
1 138 138 3.20 $0.023
12 12 144 3.60 $0.025
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
Find the difference: (2x − 8) - (x + 5)
An algebraic expression is described as 7 less than the product of 22
and the sum of t and 18. What is the value of this expression when
t = 13?
Step-by-step explanation:
22×(t + 18) - 7
t = 13
so,
22×(13 + 18) - 7 = 22×31 - 7 = 682 - 7 = 675
A karaoke machine regularly costs $153 and is on sale for 25% off. What is the discount?
A karaoke machine regularly costs $153 but due to a discount on sale of 25%, it will cost $114.75 due to a reduction of $38.25.
What is a discount?Discounts are sums of money or percentages taken off of a product's usual selling price. A good or service's price is decreased by the discount.
Discount describes the circumstance when the price of a bond will be less than its face value.
According to the question, the given values are :
Original Price of the Karaoke machine = $153
Discount = 25%
So, the reduction will be :
= 153 ×(25/100)
Reduction = $38.25
Hence, the discount he gets on the karaoke machine is $38.25 or we can say that the karaoke machine will cost $114 after a reduction of 25%.
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Answer:
its 38.25
Step-by-step explanation:
I did the 3.07 test on flvs and got it right
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help! (functions) I don’t understand how to do this
A function from set A to set B is a relation that pairs each element of set A to exactly one element of B.
Here, we are given two functions as shown in the figure. We can answer the questions as follows-
1. a. the given function represents the countries to which the chocolate companies belong to.
b. the function represents the square of the a number
2. Both the relations are functions because for every value in the first circle there is one and only one unique value in the second circle. This, is the basic property of a function.
3. a. Domain: (Neuhaus, Cote d'Or, Leonidas, Toblerone, Lindt, Hershey's, Baci)
Range: (Belgium, Switzerland, USA, Italy)
b. Domain: (1, -1, 2, -2, 5, -5)
Range: (1, 4, 5)
4. a. (Neuhaus, Belgium) is one ordered pair of the given function
b. (1, 1) is one ordered pair of the given function
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On Monday morning, Mr. Descartes asked his Algebra II students whether they had gone to the carnival in town over the weekend.
"I did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20."
"I went on those rides, too!" exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25."
"I did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."
Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters, plus two rides on the Spinning Vortex, all for - "
"You don't need to say," interrupted Mr. Descartes. "I know how much you spent."
How much are the rides? How much did Marc spend?
• A. Teacups: $2; rollercoaster: $5; Spinning Vortex: $6; Marc spent $26.
• B. Teacups: $2; rollercoaster: $5; Spinning Vortex: $6; Marc
spent $28.
• C. Teacups: $3; rollercoaster: $4; Spinning Vortex: $6; Marc
spent $29.
• D. Teacups: $3; rollercoaster: $4; Spinning Vortex: $6; Marc spent $30.
Answer:
C.
Step-by-step explanation:
You can assign each variable a ride, let's say the teacup is t, the roller coaster is r, and the spinning vortex is s. Now we can create algebraic expressions to find the values of each ride :
Kristen: 2t+2r+s=20
Jorge: t+r+3s=25
Lakesha: 5t+2r+s=29
Now we can use elimination to find each variable:
2t+2r+s=20
-2t-2r-6s=-50
The t and r cancel out, so find s
-5s=-30
s=6, so the spinning vortex is $6.
Now, substitution
2t+2r+s=20 -5t-2r-s=-29
2t+2r+6=20 -5t-2r-6=-29
2t+2r=14 -5t-2r=-23
2t=-2r+14
t=-r+7
Now plug in for t
-5(-r+7)-2r=-23
5r-35-2r=-23
3r=12
3r/3=12/3
r=4, which means the roller coaster is $4
Now we can just plug in both of those and solve for t with any equation
t+r+3s=25
t+4+3(6)=25
t+4+18
t+22=25
t=3
Now we know that the teacups have to be $3, the rollercoaster has to be $4, and the spinning vortex has to be $6. Marc's equation is:
3t+2r+2s = Money marc spent
Plug in the values
3(3) + 2(4) + 2(6) = Money marc spent
9+8+12 = Money marc spent
29 = Money marc spent
Marc spent $29, your answer is C
can someone help me...........
Answer:
?=5
Step-by-step explanation:
8
[tex] {8}^{4 - 2 +3} = {8}^{?} \\ {8}^{5} = {8}^{?} \\ 5 = {?}[/tex]
if a test yields almost identical scores when it is retaken after a two-month interval, we can say that the test is
Yield testing is a technique for figuring out the precise quantity of raw materials required to make a specific quantity of finished product.
What exactly is a yield test?The amount of food material available for consumption after it has been prepared, processed, and changed into the completed product is referred to as yield.Yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of final product.AP weight minus waste equals EP weight.Calculate your yield percentage by dividing the edible product weight by 100. EP weight x AP weight x 100 = yield% is the formula.Therefore, yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of the final product.
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Darren and his two siblings' ages are three consecutive odd numbers. if the sum of their ages is 51, what are the three ages?
Darren age is 15
and 1st sibling is x+2= 17 yrs
2rd sibling is x+4 = 19 yrs
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, it is given that :
Darren and his two siblings' ages are three consecutive odd numbers and the sum of their ages is 51.
Let Darren age be x
and since they are odd consecutive numbers, his two siblings age will be
1st sibling age will be = x+2
2rd sibling age will be = x+4
If the sum of their ages is 51
that is,
x+x+2+x+4= 51
solving for x:
3x+6 = 51
3x+6-6=51-6
3x = 45
3x/3 = 45/3
x = 15 yrs
Therefore, x is 15, therefore Darren age is 15
and 1st sibling is x+2= 17 yrs
2rd sibling is x+4 = 19 yrs
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