Answer:
Step-by-step explanation:
Lets give a letter value for the chocolate chip and gingerbread cookies. Lets let C= Chocolate chip and G= Gingerbread For Makayla we can set her equation as 8c+12g=364
For John we can leave it as c+4g=93
To solve the equation we would have to substitute the second one into the first one to solve for gingerbread. Lets isolate C to make C=(93-4g)
We can do this because we know that C=93-4g so we can replace the C variable in the first equation with C=93-4g
8(93-4g) + 12g = 364
744 - 32g + 12g = 364
-32g + 12g = 364 - 744
-20g = -380
g = -380/-20
So we know that g=19 dollars. So one gingerbread cookie dough is $19
So now we can plug in the answer of g which was 19 then solve for C
c = 93 - 4(19)
c = $17 for the chip dough
Answer:
The cost per package is $17 for chocolate chip and $19 for gingerbread.
Step-by-step explanation:
Define the variables:
Let x = cost of chocolate chip cookie dough (in dollars)Let y = cost of gingerbread cookie dough (in dollars)Given information:
Makayla sold 8 packages of chocolate chip and 12 packages of gingerbread cookie dough for a total of $364. John sold 1 package of chocolate chip and 4 packages of gingerbread cookie dough for a total of $93.Create two equations using the defined variables and the given information:
[tex]\textsf{Equation 1}: \quad 8x+12y=364[/tex]
[tex]\textsf{Equation 2}: \quad x+4y=93[/tex]
Multiply Equation 2 by 3:
[tex]\implies 3 \cdot x + 3 \cdot 4y=3 \cdot 93[/tex]
[tex]\implies 3x+12y=279[/tex]
Subtract from Equation 1 to eliminate the term in y:
[tex]\begin{array}{lrl}& 8x+12y =&364\\- & (3x+12y =&279)\\\cline{1-3} & 5x \phantom{+12y)} =& \:\:85\end{array}[/tex]
Solve for x:
[tex]\implies 5x=85[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{85}{5}[/tex]
[tex]\implies x=17[/tex]
Substitute the found value of x into Equation 2 and solve for y:
[tex]\implies x+4y=93[/tex]
[tex]\implies 17+4y=93[/tex]
[tex]\implies 17+4y-17=93-17[/tex]
[tex]\implies 4y=76[/tex]
[tex]\implies \dfrac{4y}{4}=\dfrac{76}{4}[/tex]
[tex]\implies y=19[/tex]
Conclusion
Cost per package of chocolate chip cookie dough = $17.Cost per package of gingerbread cookie dough = $19.Learn more about systems of equations here:
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I have no clue how to do this.
A client asked Nathan to design a rectangular garden with an area of 22 square feet. The client also requested that the length of the garden be eight feet less than seven times the width
The length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.
Let the width of the garden be x units.
According to the given question.
The area of the rectangular garden is 22 square feet.
Also, the length of the garden be eight feet less than seven times the width.
⇒ length of the garden = 7x - 8
Thereofore, the area of the rectangular garden is given by
22 = x(7x - 8)
⇒ 22 = 7x^2 - 8x
⇒ 7x^2 - 8x - 22 = 0
⇒ x = [tex]\frac{8 \pm \sqrt{64 + 616} }{14}[/tex]
⇒ x = [tex]\frac{8 \pm \sqrt{680} }{14}[/tex]
⇒ x = [tex]\frac{8\pm 26}{14}[/tex]
⇒ x = 8 + 26/14
⇒ x = 34/14
⇒ x = 2.43 feet
So,
the length of the rectangular garden = 7(2.43) - 8 = 9.01 feet
Hence, the length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.
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an article in forbes noted that the intercounty connector toll road that connects two counties in maryland was not generating as much toll revenue as predicted. at that time, the toll rate was $8 for a passenger car making a round trip from end to end on the tollway during rush hour. what additional information would you need to know in order to determine if the toll should be increased or decreased?
The additional information would you need to know in order to determine if the toll should be increased or decreased is The price elasticity of demand
The additional information required is
In this situation, it is necessary to consider the price elasticity of demand since it demonstrates how changes in price may either increase or decrease a product's consumption.Since the toll road wasn't generating as much toll money as was anticipated in this scenario, it's possible that the toll road's price has increased.The price elasticity of demand will be required in this scenario as extra data.Therefore,The additional information would you need to know in order to determine if the toll should be increased or decreased is The price elasticity of demand
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How do you find the equation of 5x-28=-3
Answer:
Step-by-step explanation:
5x-28=-3
You want to isolate x.
First, add 28 to both sides to isolate 5x, what you do to one side you do to the other, so:
5x= 25
Seperate 5x by dividing it, so 25/5.
x = 5 is your answer.
a concert promoter needs to make $78,700 from the sale of 1780 tickets. the promoter charges $40 for some tickets and $55 for the others. let x represent the number of $40 tickets and y represent the number of $55 tickets.
A concert promoter needs to make $42,000 from the sale of 1800 tickets.
Who is concert promoter?Show advancement is a consuming position, which requires performing business obligations — ordinarily out of an office — by day and going to shows around evening time and toward the end of the week. A show advertiser is answerable for coordinating and publicizing live shows and unique exhibitions. Show Advertisers produce and arrange shows by booking ability, getting settings, employing occasion staff, and promoting their occasions. The most well-known question that surfaces while considering turning into a show advertiser is, how much do they truly make. While taking a gander at certain insights, it shows that the compensation range is $28,000-$187,000 each year.
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Find the equation of the line that passes through the points (1, 3) and (2, 4)
Answer:
y = x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 4 )
m = [tex]\frac{4-3}{2-1}[/tex] = [tex]\frac{1}{1}[/tex] = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 3 )
3 = 1 + c ⇒ c = 3 - 1 = 2
y = x + 2 ← equation of line
Evans favorite hobby is origami he plans to make 100 paper cranes to hang from the ceiling of his bedroom yesterday he made 28 paper cranes and 4 hours today he made 21 paper cranes at the same rate how long did evan spend making paper crates today?
Answer:
Evan spent 3 hours making paper crates today.
Step-by-step explanation:
He made 28 in 4 hours. 28 divided by 4 equals 7. Which means he makes 7 paper crates in 1 hour. Today he made 21. So 21 divided by 7 equals 3.
Someone help please I would really appreciate it :))
The equation that we would use to find the value of x based on the area of a rectangle is:
C. (16 + 2x)(12 + 2x) = 396
What is the Area of a Rectangle?To find the area of a rectangle, find the product of its length and its width. Thus, the area of a rectangle is: (length)(width) = area.
Given the following:
Area of both the walkway and the garden = 396 square meters
Length = x + 16 + x = 16 + 2x
Width = x + 12 + x = 12 + 2x
Using the area formula for a rectangle, we would have:
(16 + 2x)(12 + 2x) = 396.
Therefore, the equation that we would use to find the value of x based on the area of a rectangle is:
C. (16 + 2x)(12 + 2x) = 396
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Find the surface area of the cylinder.
18.84 in² is surface area of cylinder .
What does surface area mean?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.Latitudinally, curvedly, and overall, there are three different forms of surface area.A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².Surface area is the amount of space covering the outside of a three-dimensional shape.sa = 2πr² + 2πrh
= 2 × 3.14 × 1 × 1 + 2 × 3.14 × 1 × 2
= 6.28 + 12.56
= 18.84
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Under his cell phone plan, Carson pays a flat cost of $37.50 per month and $3 per gigabyte. He wants to keep his bill under $40 per month. Which inequality can be used to determine g, the maximum number of gigabytes Carson can use while staying within his budget?
Based on the flat cost paid by Carson for his cell phone plan, and the amount of he wants to keep his bill under, the inequality that can be used to determine g is 37.50 + 40g ≤ 40
How to find the inequality?The inequality that can be used to find the maximum number of gigabytes that Carson can use while staying in his budget can be found as:
Flat cost for the cell phone plan + Cost per gigabyte x Number of gigabytes ≤ Maximum preferred bill by Carson
When we put in the figures from Carson's cell phone plan, we get:
37.50 + 3 x g ≤ 40
37.50 + 3g ≤ 40
In conclusion, the inequality that represents g is 37.50 + 3g ≤ 40.
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Need help with Q6. Kdkdndndnfndndndndndncjndjfjc
Answer:
Because:
30.5^2+73.2^2=79.3^2
=> Right triangle
=> Cos0 = 73.2/79.3 => A
Step-by-step explanation:
a local nonfrofit organization is selling popcorn to raise money for hurrican relief. the organization paid $4 per bag for the popcorn and sold $5 per bag. what was the percent makeup on each bag of popcorn?
The percent makeup on each bag of popcorn is 25%.
When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. The percentages 100%, 50%, 0% indicate all of some quantity, half of the quantity, and none of the quantity respectively.
Popcorn is being sold by a neighborhood nonprofit to support hurricane relief.
The organization paid $4 for each bag of popcorn.
The organization sold each bag of popcorn for $5.
The markup or gain from selling the popcorn is:
$5 - $4 = $1
Therefore, the percent makeup on each bag of popcorn will be:
= ( the gain / the amount organization paid for each bag ) × 100
= ( 1 / 4) × 100
= 0.25 × 100
= 25 %
Hence, the percent makeup on every bag of popcorn is 25%.
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A garden table and a bench cost $987 combined. The garden table costs $87 more than the bench. What is the cost of the bench?
Answer:
$450
Step-by-step explanation:
let the price of the bench = x
Then, the price of the table is x + 87.
x + x + 87 = 987
2x + 87 = 987
2x = 900
x = 450
Answer: $450
please help me solve the problem i took a screen shot to show the problem.
polygon b is a scaled copy of polygon a using a scale factor of 5 . polygon a area is what fraction of polygon b area
The area of polygon A would be a fraction 1/25 of the size of polygon B.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object
The formula of the scale factor is shown as;
Area of Polygon B = (scale factor)²×(Area of Polygon A).
Using a scale factor of 5, we get
(Area of Polygon B) = (5)²× (Area of Polygon A)
(Area of Polygon B) = (25) × (Area of Polygon A)
Area of Polygon A = (1/25) × Area of Polygon B
Therefore, the area of polygon A would be a fraction 1/25 of the size of polygon B.
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Question 8
1 pts
You have $50 in your bank account. You spend $35, deposit $15, and spend $40. How much do you have in our account ? Use negative if the account is over drawn
Answer: $-10
Step-by-step explanation:
The starting value is $50 and you use $35 of it meaning you only have $15 left.
You then deposite $15 meaning you now have $30 in your bank account.
After that, you spend $40 meaning you have $-10 in your bank account.
elect the correct answer from each drop-down menu. Which system of equations is represented by this graph? Graph shows system of equations plotted on a coordinate plane. A line goes through (minus 6, 0) and (0, minus 3). Another line goes through (0, 3) and (minus 4, minus 5). y = x + 3 y = x − 3
The equation of the line traveling through (-6, 0) and (0, -3) is mathematically given as
y = -(1/2)x - 3
The equation of the line traveling through (0, 3) and (-4, -5) is mathematically given as
y = 2x + 3
What exactly is an equation, then?An expression known as an equation is one that illustrates the connection between two or more sets of numbers and variables.
The equation of the line traveling through (-6, 0) and (0, -3) is:
y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))
y = -(1/2)x - 3
The equation of the line going through (0, 3) and (-4, -5) is:
y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)
y = 2x + 3
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Donald and Aaliyah each made a bowl of punch. Aaliyah used 4 times as much lemonade
as Donald did. If Donald used 1 1/2 cups of lemonade, how many cups of lemonade did
Aaliyah use?
Answer: 6 cups of lemonade for Aaliyah
Step-by-step explanation:
If Donald used 1 1/2 cups of lemonade-
And Aaliyah uses 4 times that amount-
Aaliyah does 4 times that amount you will do 1 1/2 *4 which is 1*4=4 and 1/2*4=2 so Aaliyah uses 6 cups of lemonade.
1 1/2 * 4 = 6
MARKING BRAINLEIST If CORRECT BE QUICK!
Answer:
Answer on attached figure
Step-by-step explanation:
Each year a certain amount of money is deposited in an account which pays an annual interest rate of r so that at the end of each
year the balance in the account is multiplied by a growth factor of z=1+r.$500 is deposited at the start of the first year, an
additional $200 is deposited at the start of the next year, and $600 at the start of the following year.
a. Write an expression for the value of the account at the end of three years in terms of the growth factor z
The value of the account at the end of three years of the growth factor z will be $1350.684.
According to the growth factor z, the value of the account after three years is,
Given r, is the yearly interest rate that is compounded by a growth factor z= 1 +r. $500 at the end of each year.
The initial year's deposit is in the amount of $500.
Both the next year and the third-year deposits are made correspondingly, $200 and $600.
As a result, the account will be worth at the end of the three years is:
$(500 x3 + 200 x2 + 600 x) ---(1)
If r= 2%, then x=(1 + 2/100), , substituting the value of x in (1)
The sum will then be:
$(500(1 + 2/100)3 + 200 (1 + 2/100)2 + 600(1+2/100))
Solving the above equation, the amount will be equal to $1350.684.
Hence, The value of the account at the end of three years of the growth factor z will be $1350.684.
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What is the multiplive rate change for the expenstial function f(x)2 5/2-x
0.4 is the multiplive rate change for the Expenstial function .
What exactly makes a function exponential?
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.We have to find the multiplicative rate of change for:
f ( x ) = 2 * ( 5/2 ) ^(-x)
F (X ) = [tex]f(x) = 2 * ( \frac{5}{2} )^{-x}[/tex]
2/5 = 0.4
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please answer this with solution thanks
Answer:
Function 1 is neither odd nor even
Function 2 is odd
Step-by-step explanation:
Here, you must first understand the expression of odd and even functions:
Even: f(x) = f(-x)
Odd: f(-x) = -f(x)
Question 1:
[tex]{ \tt{f(x) = x + 3}} \\ { \rm{when \: x = - x}} \\ { \tt{f( - x) = - x + 3}} \\ { \tt{f( - x) \: is \: neither \: even \: nor \: odd }}[/tex]
Question 2:
[tex]{ \tt{f(x) = - { \green{{3x}^{3} + 6x }}}} \\ { \rm{when \: x = - x}} \\ { \tt{f( - x) = - 3 {( - x)}^{3} + 6( - x) }} \\ { \tt{f( - x) = 3 {x}^{3} - 6x}} \\ { \tt{f( - x) = - \{ { \green{- 3 {x}^{3} + 6x }}}} \} \\ { \tt{f( - x) = - f(x)}}[/tex]
What is the range of the function f(x)=6x^2+x-1/2x^2+x-6
Answer:
Range: [tex]\:f\left(x\right)\ge \:-\frac{68}{11}[/tex]
Interval notation [tex][-\frac{68}{11},\:\infty \:)[/tex]
Step-by-step explanation:
I got a little confused with the x - 1/2x^2 term and I am taking to to be:
[tex]x\:-\frac{1}{2}x^2[/tex] . If this is incorrect please mention the correct term in your comment and I will edit this post. Or you can re-post the question
We have
[tex]f\left(x\right)=6x^2+x\:-\frac{1}{2}x^2+\:x\:-\:6[/tex]
Simplify by grouping like terms:
[tex]=-\frac{1}{2}x^2+6x^2+x+x-6[/tex]
[tex]= \frac{1}{2}x^2+6x^2+2x-6[/tex]
Add similar elements
[tex]-\frac{1}{2}x^2+6x^2[/tex][tex]= -\frac{1x^2}{2}+\frac{12x^2}{2} = \frac{11x^2}{2}[/tex]
So the original function expression becomes
[tex]y=\frac{11}{2}x^2+2x-6[/tex]
This is the equation of a parabola which in standard form is [tex]ax^2 + bx + c[/tex]
Here
[tex]a=\dfrac{11}{2},\:b=2,\:c=-6[/tex]
We can compute the vertex of this parabola using the fact that the x, y coordinates of the vertex are given by
[tex]x_v =-\dfrac{b}{2a}[/tex]
Plugging in values for b and a give us
[tex]x_v =-\dfrac{b}{2a} = -\dfrac{2}{2\left(\dfrac{11}{2}\right)} =-\dfrac{2}{11}[/tex]
Plugging in this value of [tex]x_v[/tex] into the parabola equation will give the value for [tex]y_v[/tex] which is the function value at the vertex
Plug in [tex]x_v = -\frac{2}{11}[/tex] t find the [tex]y_v[/tex] value:
[tex]y_v=\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2}+2\left(-\dfrac{2}{11}\right)-6[/tex]
Simplify
[tex]\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2} =\dfrac{2}{11}[/tex]
[tex]2\left(-\dfrac{2}{11}\right) = -\dfrac{4}{11}[/tex]
Combining the terms we get
[tex]y_v =[/tex] [tex]\dfrac{2}{11}-\dfrac{4}{11}-6[/tex] [tex]= -\dfrac{68}{11}[/tex]
[tex]\textsf{Therefore the parabola vertex is at }[/tex] [tex]\left(-\dfrac{2}{11},\:-\dfrac{68}{11}\right)[/tex]
For a parabola of the form [tex]ax^2 + bx + c[/tex] with vertex [tex]\left(x_v,\:y_v\right)[/tex]
[tex]\circ \;\mathrm{If}\:a < 0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v[/tex]
[tex]\circ \;\mathrm{If}\:a > 0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v[/tex]
Here [tex]a=\frac{11}{2}[/tex] so the range is [tex]f\left(x\right)\ge \:-\dfrac{68}{11}[/tex]
Answer range of f(x) is
[tex]f\left(x\right)\ge \:-\dfrac{68}{11}[/tex]
In interval notation it is [tex][-\frac{68}{11},\:\infty \:)[/tex]
It is much easier if you visualize it in a graph
Hope that helps
The city park has a circular pond with a diameter of 4 yards. What is the pond's circumference?
Use 3.14 for .
If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.
Circumference of the pond
Using this formula to determine or to calculate the pond's circumference
C = π × d
where:
C = Circumference
d = diameter = 4 yards
π = 3.14
Let plug in the formula
C = 3.14×4
C= 12.56 yards
Based on the above calculation the circumference of the pond will be 12.56 yards.
Therefore If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.
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Athena's credit card has an APR of 16.99%. If her current monthly balance, before interest, is $1,567.32, what amount will she be charged for interest?
a)$22.19
b)$26.63
c)$31.19
d) $45.00
The amount that Athena will be charged for interest is $22.19
What is the meaning of APR of 16.99%?
The APR means an annual percentage rate, which means that the 16.99% is annual interest rate compounded monthly, hence, it needs to be divided by 12 in order to determine the equivalent monthly interest rate.
monthly interest rate=16.99%/12
monthly interest rate=0.0141583333333333
The monthly interest charged on the balance of $1,567.32 is computed thus:
monthly interest charged=$1,567.32*0.0141583333333333
monthly interest charged=$22.19
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an airplane flies 2,794 miles in 5.5 hours. what is the speed of the airplane in miles per hour?
Answer:
508 miles per hour
Step-by-step explanation:
First, set up an equation:
miles per hour = # of miles ÷ # of hours
2,794 miles ÷ 5.5 hours = 508 miles/hour
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What is the value of |90|?
Answer:
90
Step-by-step explanation:
|90| = 90
PRACTICING SKILLS & CONCEPTS
1. Solve the shape equation puzzle.
+
+
=
= 10
6=
8 =
The value of box/ square is 5, value of circle is 3 and the value of star is 6.
Let box/ square be denoted by x
let the circles be denoted by y
let the stars be denoted by z
now, let us make three linear equation based on the diagram provided
1. x + x = 10
2. y + z= 9
3. y+ x = 8
solving equation 1
x + x = 10
2x = 10
x = 5
Putting the value of x in equation 3
y + x=8
y + 5 = 8
y = 3
Putting the value of y in equation 2
y + z = 9
3 + z= 9
z = 6
Hence , The value of box/ square is 5, value of circle is 3 and the value of star is 6.
A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C.
A linear equation is an equation with the maximum degree of one. This means that in a linear equation, no variable has an exponent greater than 1. A linear equation's graph is always a straight line.
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Identify the reason for each step in the solution.
3x+6=2x+3
3x+6-2x=2x+3-2x
x+6+3
x+6-6+3-6
x+-3
The reason are as follows:
subtraction of equality i.e., 2xSubtractionsubtraction of equality i.e., 2xSubtractionWhat is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
3x+6=2x+3
3x+6-2x=2x+3-2x (subtraction of equality i.e., 2x)
x+6=3 (Subtraction)
x+6-6=3-6 (subtraction of equality i.e., 6)
x=(-3) (Subtraction)
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solve this answer and get 30 points
Answer:
10
Step-by-step explanation:
[tex]\frac{63}{c}[/tex] + d ( substitute c = 7 , d = 1 into the expression )
= [tex]\frac{63}{7}[/tex] + 1 ← evaluate division before adding
= 9 + 1
= 10