Let's refer to the chocolate cookies using the variable c, and the oatmeal cookies using the variable o.
Using the information we have, we can set up two equations for the two different transactions.
4c + 9o = 126
8c + 5o = 122
Now, we need to solve for one of the variables in the first equation. I will solve for o.
4c + 9o = 126
9o = 126 - 4c
o = 14 - 4/9c
Next, we'll take this value for o and plug it into the second equation for the variable o. Then we can solve for c.
8c + 5(14 - 4/9c) = 122
8c + 70 - 2 2/9c = 122
5 7/9c + 70 = 122
5 7/9c = 52
c = 9
Finally, we can use the value of c and plug it back into the first equation to solve for o.
o = 14 - 4/9(9)
o = 14 - 4
o = 10
1 dozen chocolate cookies costs $9
1 dozen oatmeal cookies costs $10
Hope this helps!
Miles is putting a fence around his garden. The total area of the garden is 4,864 square feet. The length of the garden is 152 feet. How many feet of fencing does he need to go around the whole garden?
Help pls!!
Fencing required to go around the whole garden = 368 feet
To calculate the fencing needed, given measures in the question,
Total area of the garden is 4864 square feet.Length of the garden is 152 feet.Since, area of a rectangular garden is given by the expression,
Area = Length × Width
4864 = 152 × Width
Width = [tex]\frac{4864}{152}[/tex]
= 32 feet
Since, length of the fence needed = Perimeter of the garden
And Perimeter of a rectangular garden is given by the expression,
Perimeter = 2(length + width)
By substituting the values of length and width of the garden in the expression,
Perimeter = 2(152 + 32)
= 368 feet
Therefore, 368 feet of the fence will be required to go around the whole garden.
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This is my last problem guys please help me
Answer:
Step-by-step explanation:
a) 9.5 feet above the ground
b) max height at of 34.5 feet 5 feet horizontal distance
c) 10.87 feet away
x-1 = [tex]\sqrt{x} -1[/tex]
Answer:
[tex]x = 0[/tex] or [tex]x = 1[/tex].
Step-by-step explanation:
Start by adding [tex]1[/tex] to both sides of this equation:
[tex](x - 1) + 1 = (\sqrt{x} - 1) + 1[/tex].
[tex]x = \sqrt{x}[/tex].
If two numbers are equal, their square should also be equal. Therefore, since[tex]x = \sqrt{x}[/tex], it must be true that [tex]x^{2} = (\sqrt{x})^{2}[/tex]. That is: [tex]x^{2} = x[/tex].
Notice that since [tex]x[/tex] is under a square root, the result must ensure that [tex]x \ge 0[/tex].
Subtract [tex]x[/tex] from both sides of the equation:
[tex]x^{2} - x = x - x[/tex].
[tex]x^{2} - x = 0[/tex].
Factor [tex]x[/tex] out:
[tex]x\, (x - 1) = 0[/tex].
Hence, by the Factor Theorem, [tex]x = 0[/tex] and [tex]x = 1[/tex] would satisfy this rearranged equation. Because of the square root in the original equation, these two value must be non-negative ([tex]x \ge 0[/tex]) to qualify as actual roots of that equation.
In this example, both [tex]x = 0[/tex] and [tex]x = 1[/tex] qualify as roots of that equation.
x-1 = \sqrt{x} -1
Math For Solution#BrainliestBunch
Q:1)A ball is thrown upwards and it goes to the height of 100meter and comes down. What is the net displacement?
Q:2)An athlete completes one round of a circular track of diameter 200m in 30 seconds. Find the distance covered by the athlete at the end of 30 second.
$\sf\underline\bold{Question:1-}$
A ball is thrown upwards and it goes to the height of 100meter and comes down. What is the net displacement?
$\sf\underline\bold{Solution}$
$\sf{According \: to\:the\: question,}$
Displacement for the above situation is 0. As we know, that displacement is the shortest path from the initial to the final point. Here, the initial and the final points are the same, and henceforth, it takes no time to travel. So the displacement is 0.
_________________________$\sf\underline\bold{Question:2-}$
An athlete completes one round of a circular track of diameter 200m in 30 seconds. Find the distance covered by the athlete at the end of 30 second.
$\sf\underline\bold{Solution:}$
$\sf\bold{Given\:parameters:}$
$\sf\small{☆The\:diameter\:of\:the\:circular\:track:200m}$
$\sf{Radius=}$ $\sf\dfrac{200}{2}$ → $\sf\underline{Radius = 100m}$
☆Time taken by an athlete to complete one round : 30 seconds.
$\space$
$\sf\bold{To\:find:}$
❍Distance travelled by an athlete in 30 seconds.
$\space$
❍ AND,Distance travelled by the athlete will be equal to the cumference of the circle.
$\space$
$\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\sf{So,}$
$\mapsto$ $\sf{Circumference\:of\:the\:circle: 2 πr}$
$\space$
$\mapsto$ $\sf{Circumference=2\times}$ $\sf\dfrac{22}{7}$ $\sf{\times 100}$
$\space$
$\mapsto$ Circumference of the circle : $\sf\dfrac{4400}{7}$
$\space$
[tex]\sf\underline\bold{∴Circumference = 628.57m}[/tex]
$\space$
||Therefore,The distance travelled in 30 seconds, by the athlete is 628.57m.||
______________________0 = 1st answer
628.57 m = Question 2 answer.
find the surface area of this cylinder??
Answer:
4
Step-by-step explanation:
A=ch
then,
2ft×2ft
4ft
The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0 and 100. The vertex is (50,1000). The maximum profit of $ dollars is reached when items are produced. The first root tells us that the profit will be 0 when 0 products are produced. The second root says once 100 items are made, the company is no longer making any profit. (They do not have production capacity and have to outsource for anything over 50.)
Answer:
I assume that we want to complete the statement:
"The maximum profit of $__ dollars is reached when __ items are produced"
We know that the profit equation is defined between x = 0 and x = 100, which are the two roots of the equation (so the profit is equal to zero for x = 0 and for x = 100).
Then we can assume that the profit will be positive in this range.
Thus, the quadratic equation should have a negative leading coefficient, which would mean that the arms of the graph go downwards.
If this is the case, we know that the maximum will be at the vertex.
Here we know that the vertex is:
(50, 1000)
Where remember, x represents the number of items and y represents the profit.
So, given that the maximum is at the vertex, and we know that the vertex is (50, 1000) we can conclude that the maximum profit is $1000, and this happens when the number of produced items is 50.
Then the complete statement is:
"The maximum profit of $1000 dollars is reached when 50 items are produced"
if 30% of students like pineapple and 15% of them like banana , how many more students favour pineapple?
Geometry, please answer question ASAP
what is the equation of the line that passes through the points (-8,8) and (4,-1)
Answer:
y = (-3/4)x + 2
Step-by-step explanation:
Find the slope of this line. Note how the first x-coordinate (-8) becomes 4, a jump of 12, and how the first y-coordinate (8) becomes -1, a decrease of 9. Then the slope is
m = (change in y) / (change in x) = -9/12 = m = -3/4
Find the y-intercept from this data using the slope-intercept form:
y = mx + b becomes 8 = (-3/4)(-8) + b when x = -8, y = 8 and m = -3/4.
Solving this equation for b, we get:
8 = 6 + b, so that b must be 2.
The desired equation is y = (-3/4)x + 2.
Circle the graphs of the functions.
How did you know which graphs showed a function?
i will mark brainliest
Answer:
Step-by-step explanation:
Relations are only functions if they do not share any x values at all! The 2 graphs there that do not have any of the same x values are graphs A and D. Notice that on graph B, there are several y values that share the x value of 2; on graph C, there are several y values that share the x value of 2.
Answer:
A and D only
Step-by-step explanation:
A function is a relation where each input has its own output ( each x values has its own corresponding y value ) If an input has more than one output than the relation is not a function.
We can tell if a graph shows a function or not by using the vertical line test. If you draw vertical lines on the graph and more than one point is on the vertical line drawn then the graph does not show a function.
For graph B if you draw a vertical line at x = -2 more than 1 point will be on the line meaning that the graph does not show a function.
For Graph C if you draw a vertical line at x = 2 more than 1 point will be on the line meaning that Graph C also does not show a function.
For Graphs A and D you can draw a vertical line anywhere on the graph and no more than 1 point will be on the line therefore Graphs A and D show functions.
Tricia starts school at 7:00 AM and has lunch at 12:00 PM. She wants to make sure she has something to eat in between. Determine what time she should eat her snack if she is to eat at exactly a time between starting school and eating lunch. (Hint: Set up a horizontal number line as a timeline.) A. A. 9:30 AM
B. 10:00 AM
C. 9:00 AM
D. 10:30 AM
Answer:
D) 9:00 am
Step-by-step explanation:
Because 9:00 is the midpoint of 7 and 12
The polygons in each pair are similar. find the missing side length
If polygons are similar ratio of sides will be same
[tex]\\ \sf\longmapsto \frac{6}{14} = \frac{3}{x} \\ \\ \sf\longmapsto 6x = 14 \times 3 \\ \\ \sf\longmapsto 6x = 42 \\ \\ \sf\longmapsto x = \frac{42}{6} \\ \\ \sf\longmapsto x = 7[/tex]
if A = 1 2 1 1 and B= 0 -1 1 2 then show that (AB)^-1 = B^-1 A^-1
help meeeee plessss
[tex]A = \begin{bmatrix}1&2\\1&1\end{bmatrix} \implies A^{-1} = \dfrac1{\det(A)}\begin{bmatrix}1&-1\\-2&1\end{bmatrix} = \begin{bmatrix}-1&1\\2&-1\end{bmatrix}[/tex]
where det(A) = 1×1 - 2×1 = -1.
[tex]B = \begin{bmatrix}0&-1\\1&2\end{bmatrix} \implies B^{-1} = \dfrac1{\det(B)}\begin{bmatrix}2&1\\-1&0\end{bmatrix} = \begin{bmatrix}2&1\\-1&0\end{bmatrix}[/tex]
where det(B) = 0×2 - (-1)×1 = 1. Then
[tex]B^{-1}A^{-1} = \begin{bmatrix}2&1\\-1&0\end{bmatrix} \begin{bmatrix}-1&1\\2&-1\end{bmatrix} = \begin{bmatrix}-1&3\\1&-2\end{bmatrix}[/tex]
On the other side, we have
[tex]AB = \begin{bmatrix}1&2\\1&1\end{bmatrix} \begin{bmatrix}0&-1\\1&2\end{bmatrix} = \begin{bmatrix}2&3\\1&1\end{bmatrix}[/tex]
and det(AB) = det(A) det(B) = (-1)×1 = -1. So
[tex](AB)^{-1} = \dfrac1{\det(AB)}\begin{bmatrix}1&-3\\-1&2\end{bmatrix} = \begin{bmatrix}-1&3\\1&-2\end{bmatrix}[/tex]
and both matrices are clearly the same.
More generally, we have by definition of inverse,
[tex](AB)(AB)^{-1} = I[/tex]
where [tex]I[/tex] is the identity matrix. Multiply on the left by A ⁻¹ to get
[tex]A^{-1}(AB)(AB)^{-1} = A^{-1}I = A^{-1}[/tex]
Multiplication of matrices is associative, so we can regroup terms as
[tex](A^{-1}A)B(AB)^{-1} = A^{-1} \\\\ B(AB)^{-1} = A^{-1}[/tex]
Now multiply again on the left by B ⁻¹ and do the same thing:
[tex]B^{-1}\left(B(AB)^{-1}\right) = (B^{-1}B)(AB)^{-1} = B^{-1}A^{-1} \\\\ (AB)^{-1} = B^{-1}A^{-1}[/tex]
Mr. Hamilton decorates his U.S. History classroom by putting up pictures of the presidents. The wall is 9.75 feet long. In the center, there is a window that is 5 ¾ feet long.
Each president's picture is 6 inches wide.
4. How would your answer change if the pictures were 10 inches wide? Explain.
Answer:
The number of pictures changes from 8 to 4.
Step-by-step explanation:
I assume the first question was the number of pictures that could be placed when the pictures are 6 inches wide.
Let's first answer the first question.
Wall length: 9.75 ft
Window: 5¾ ft = 5.75 ft
Available wall space for pictures:
9.75 ft - 5.75 ft = 4 ft
Now we convert 4 ft to inches.
1 ft = 12 inches
4 ft = 4 * 12 inches = 48 inches
There is 48 inches of wall space to place pictures that measure 6 inches each.
48 inches / 6 inches = 8
Originally, there is room for 8 pictures.
Question 4.
Each picture is 10 inches wide.
There is still 48 inches of wall space for the pictures.
48 inches / 10 inches = 4.8
There is room for 4.8 pictures. Since Mr. Hamilton will place only whole picture, he can only place 4 pictures now.
Answer: The number of pictures changes from 8 to 4.
Please help, 20 points. Answer choices in the photo
The graph below shows the height of an object that has been launched off a 50 foot high wall. Approximately how long will it take to hit the ground?
Answer:
4.4
Step-by-step explanation:
Answer:
t = 4.4 seconds
Step-by-step explanation:
It hits the ground when the height is equal to zero
This occurs just before 4.5 seconds
t = 4.4 seconds
Calculate the mode of: 4.6, 3, 8.1, 9, 12, 3, 9, 3.5, 7, 3.
Answer:
the Mode Is 3
Step-by-step explanation:
You Have To Put the numbers from ascending order to descending order..The Numbers that appears the most is the mode
Complete the paragraph proof.
Given: and are right angles
Line segment A B is-congruent-to line segment B C Line segment B C is-congruent-to line segment A C
Prove: Line A R bisects Angle B A C
Answer:
wea did tha r come from??
Step-by-step explanation:
it is supposed to be d
1. Sederhanakan dan nyatakan hasilnya dalam bentuk eksponen.
2. Nyatakan soal berikut dalam notasi ilmiah.
Answer:
>
Step-by-step explanation:
A telephone long distance carrier charges customers $0.99 for the first 10 minutes and then $0.09 for each minute beyond 10 minutes. If Mary uses this carrier, how long can she talk for $5.00
Answer:
5 minutes
Step-by-step explanation:
5 * $0.99 = $4.95
Divide the sum of 65/12 and 8/3 by their difference.
Answer:
97/4752
Step-by-step explanation:
So, this problem sounds hard but it is actually simple.
First, add
65/12 + 8/3 = 97/12
Next, subtract
65/12 - 8/3 = 33/12
Then, divide
97/12 ÷ 33/12 = 97/4752
Hope this helps! :)
What is the answer? Don’t give me 4.
Answer:
what?
Step-by-step explanation:
........................................................................
on the unit circle, which of the following angles has the terminal point coordinates of (\sqrt(2))/(2),-(\sqrt(2))/(2)
a)5pi/4
b)pi/4
c)3pi/4
d)7pi/4
Answer:
c)3pi/4
Step-by-step explanation:
The sale price for a jacket that regularly costs $102.00 is now $74.00. With sales tax, a customer pays $82.40.
Please help me anyone
It's very blurry can u retake it?
Fill in the missing statements and reasons in the proof
Answer:
1. Given
2. Vertical angle theorem
3. AB≅DB, EB≅CB, m<ABC≅m<DBE
4. △ABC ≅ △DBE
Hope this helps :D
PLEASE HURRY!!!
Find the area of the region that is NOT shaded.
Answer: 122 square feet
Explanation:
The larger rectangle has area of 14*15 = 210 square feet.
The smaller rectangle has a horizontal dimension of 15-4 = 11 ft and its vertical dimension is 14-6 = 8 ft. Therefore, the area is 11*8 = 88 square feet.
The non-shaded region has area that is the difference of the two previous areas calculated earlier. So that would be 210-88 = 122 square feet
PLEASE HELP ME WITH THIS MATH QUESTION!
Answer:
C
Step-by-step explanation:
First, let's say 4³ is a and 5⁻² is b. We know that (a/b)ⁿ = aⁿ/bⁿ for any n, so
(a/b)⁵ = a⁵/b⁵
= (4³)⁵ /(5⁻²)⁵
Next, one power rule states that (4³)⁵ = 4 ⁽³ˣ⁵⁾ = 4¹⁵ and (5⁻²)⁵ = 5 ⁽⁻²ₓ⁵⁾=5⁻¹⁰, so
(4³)⁵ /(5⁻²)⁵ = 4¹⁵ / 5⁻¹⁰
Next, anything to a negative power (e.g. x⁻ⁿ) is equal to 1 over the absolute value of the power, so x⁻ⁿ = 1/xⁿ. Applying that here, we can say that
5⁻¹⁰ = 1/5¹⁰
4¹⁵ / 5⁻¹⁰ = 4¹⁵ / (1/5¹⁰) = (4¹⁵/1) / (1/5¹⁰) = 4¹⁵ * 5¹⁰
The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle?
20 in.
26 in.
120 in.
138 in.
Answer:
its c 120in
Step-by-step explanation:
The perimeter of the triangle is,
⇒ 138 in.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The hypotenuse of a right triangle is 52 in.
And, One leg of the triangle is 8 in. more than twice the length of the other.
Hence, We get;
Lengths of legs are,
⇒ x
And, ⇒ 8 + 2x
Hence, We can formulate;
⇒ 52² = x² + (2x + 8)²
⇒ 2704 = x² + 4x² + 64 + 24x
⇒ 5x² + 24x - 2640 = 0
⇒ x = 20 and x = - 132/5
For perimeter;
Take x = 20
Hence, The perimeter of the triangle is,
⇒ 52 + x + (2x + 8)
⇒ 52 + 20 + (2 × 20 + 8)
⇒ 52 + 20 + 48
⇒ 138 in.
Thus, The perimeter of the triangle is,
⇒ 138 in.
Learn more about the triangle visit;
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someone please help me I really need help on this or ill fail
Answer:
a. Smart Dot Company: C = 12 + 0.5·t
Communications Plus: C = 2.5·t
b. Please find attached the required tables created using MS Excel cell function tool
c. Please find attached the graph of both relationship created on the same grid with
Step-by-step explanation:
a. The monthly cost of the Smart Dot Company = $12
The hourly cost for internet use on Smart Dot Company = $0.50
The hourly cost of using the Communications Plus = $2.50
Therefore, the total monthly cost, C, for the duration of hours used, t, is given as follows;
Smart Dot Company: C = 12 + 0.5·t
Communication Plus: C = 2.5·t
b. The table of values are created using MS Excel as follows;
[tex]\begin{array}{ll}Smart \ Dot \ Company&\\Time \ (hours)&Cost \ (dollars)\\0&12\\2&13\\4&14\\6&15\\8&16\\10&17\end{array}[/tex] [tex]\begin{array}{ll}Communications\ \ Plus&\\Time \ (hours)&Cost \ (dollars)\\0&0\\2&5\\4&10\\6&15\\8&20\\10&25\end{array}[/tex]
c. Please find attached the graph of both relationship created on the same grid with MS Excel
a polynomial has been factored below but some constants are missing. 2x^3-8x^2-24x=ax(x+b)(x+c)
Answer:
The polynomial is 2x^3 - 8x^2 - 24x
And we can factor out a 2x from each of the three terms:
2x(x^2 - 4x - 12)
Lastly, factor the remaining quadratic:
2x(x+(-2))(x+6)
And we have our answer:
a=2
b=-2
c=6
Let me know if this helps!
Answer:
a =2, b =2, and c = -6
Step-by-step explanation:
We factor the polynomial and then see which value corresponds to what.
2x^3-8x^2-24x
As we see it, all terms are factorable by 2x. So if we take out 2x from every term, we get
2x(x^2 - 4x - 12)
Now we factor the quadratic, which we can do mentally to get
2x(x+2)(x-6)
ax(x+b)(x+c)
Comparing that to ax(x+b)(x+c), we can tell that a =2, b =2, and c = -6.
