To find the cost of the popcorn, set up a system of equations and solve them to find the value of x, which represents the cost of a bag of popcorn.
Explanation:To find the cost of the popcorn, we need to set up a system of equations. Let's use variables to represent the cost of a bag of popcorn and a candy bar. Let x be the cost of a bag of popcorn and y be the cost of a candy bar. We can set up two equations using the given information:
28x + 40y = 282
17x + 20y = 160.50
Now, we can solve this system of equations. Multiply the second equation by 2 to make the coefficients of x in both equations equal:
34x + 40y = 321
28x + 40y = 282
Subtract the second equation from the first equation:
34x - 28x + 40y - 40y = 321 - 282
6x = 39
Divide both sides of the equation by 6:
x = 6.50
Therefore, the cost of a bag of popcorn is $6.50.
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The graph of g(x) is the graph of f(x)=|x| translated 3 units to the left. What is the equation of g(x)?
Answer:
g(x) = |x + 3|
Step-by-step explanation:
The x is replaced by x + 3
The equation of g(x) is | x + 3 | when g ( x ) is translated 3 units to the left
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)
Horizontal shift (also called phase shift):
Left shift by c units: y = f( x + c ) (same output, but c units earlier) Right shift by c units: y = f ( x - c ) (same output, but c units late)Given data ,
The function f(x) = | x | , this function is needed to be translated 3 units to the right. Therefore, the new function can be written as ,
g ( x ) = f ( x + 3 )
= | x + 3 |
Hence, the equation of g(x) is | x + 3 |.
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The salaries of the employees at four companies are summarized below. Answer the questions about them.
Answer:
Range = 24
Step-by-step explanation:
Record of percentage
59, 61, 83, 67, 81, 80, 81
We need to find the range
To find the range , we order the numbers from smallest to largest.
Then Subtract the smallest number from largest number.
When we arrange the numbers it becomes
59, 61, 67, 80, 81, 81, 83
Smallest number is 59 and largest number is 83
Range = 83 - 59 =24
Is a triangle congruent
Answer: Yes
Step-by-step explanation:
When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.
Solve for a. a/g - f = D
Answer:
a = (D+f) * g
Step-by-step explanation:
We want to isolate a
a/g -f =D
Add f to each side
a/g -f+f = D+f
a/g = D+f
Multiply each side by g
a/g *g = (D+f) * g
a = (D+f) * g
[tex]\dfrac{a}{g}-f=D\qquad\text{add f to both sides}\\\\\dfrac{a}{g}=D+f\qquad\text{multiply both sides by }\ g\neq0\\\\\boxed{a=g(D+f)}\qquad\text{use distributive property}\\\\\boxed{a=Dg+fg}[/tex]
There are six houses on Philips Road that each use, on average, between 1.58 units and 1.71 units of electricity for 2 to 4 hours. John estimates the total usage for all six houses to be approximately 28 units. Is this a reasonable estimate?
Answer:no it is not reasonable
Step-by-step explanation: take the Max average number and multiply it by six, it only reaches 10.26
John's estimation of 28 units of electricity usage for the six houses on Philips Road is considered reasonable since it falls within the calculated possible range of 18.96 to 40.08 units.
Explanation:To verify John's estimate, we need to consider the maximum and minimum electricity usage for the houses based on their given range of usage and time. On the high end, each house could use 1.71 units for 4 hours, which gives a total of 6.84 units per house.
Therefore, the total usage for all six houses would be 40.08 units (6 x 6.84 = 40.08). On the low end, each house could use 1.58 units for 2 hours, amounting to 3.16 units per house. The total for all houses would then be 18.96 units (6 x 3.16 = 18.96). Given this, John's estimate of 28 units falls within this range and can be considered reasonable.
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Please answer this question
Answer:
The average rate is 35 miles per hour
Step-by-step explanation:
To get from town A to town B takes 3 hours. The distance is 100 miles
To get from town B to town c takes 1 hours. The distance is 40 miles
To find the average rate , we need to find the total distance and divide by the total time
Total distance = 100 + 40 = 140 miles
Total time = 3 hrs + 1 hr = 4 hours
distance = rate * time
140 miles = rate * 4 hours
140/4 = rate
35 = rate
The average rate is 35 miles per hour
Identify the constant of proportionality in the equation. 3y = 15x
Answer:
5
Step-by-step explanation:
For direct variation y=kx, where k is the constant of proportionality
We need to get the equation in this form
3y = 15x
Divide each side by 3
3y/3 =15x/3
y = 5x
The constant is 5
please help me!!!!!! I cant do it
Average rate of change formula:
[tex]\dfrac{\Delta y}{\Delta x}[/tex]
[tex]\Delta y=6-1=5\\\\\Delta x=4.95-0.40=4.55[/tex]
[tex]\dfrac{\Delta y}{\Delta x}=\dfrac{5}{4.55}=\dfrac{500}{455}=\dfrac{100}{91}\approx1.1[/tex]
Solve for x.
Enter your answer in the box.
An equilateral triangle A B C. Side B C is the base. Sides A B, B C, and A C are equal. Sides A B, B C, and A C are labeled with single tick marks. Angle A is labeled as left parenthesis 2 y right parenthesis degrees, angle B is labeled left parenthesis 25 x minus 15 right parenthesis degrees.
Answer:
3
Step-by-step explanation:
4x-y, when x=5 and y=6
Answer:14
Step-by-step explanation:
(4)(5)−6
=14
Equivalent expression for 3(4m - 2) -2 (m + 5)
Answer:
10m-16
Step-by-step explanation:
3(4m-2)-2(m+5)
Distribute 3 into the equation
12m-6 than do the same with -2
-2m-10
combine like terms
10m-16
simplify
Equivalent expressions are expressions that have equal values
The equivalent expression is [tex]10m - 16[/tex]
The expression is given as:
[tex]3(4m - 2) -2 (m + 5)[/tex]Open the brackets
[tex]3(4m - 2) -2 (m + 5) = 12m - 6 - 2m - 10[/tex]
Collect like terms
[tex]3(4m - 2) -2 (m + 5) = 12m- 2m - 6 - 10[/tex]
Evaluate the like terms
[tex]3(4m - 2) -2 (m + 5) = 10m - 16[/tex]
Hence, the equivalent expression is [tex]10m - 16[/tex]
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evaluate the expression for a=3 and b=10 70/b +5a -2b
Answer:
2
Step-by-step explanation:
evaluate from left to right, substituting the given values into the expression
= [tex]\frac{70}{10}[/tex] + (5 × 3) - (2 × 10)
= 7 + 15 - 20
= 22 - 20
= 2
Substitute the values of a and b to the expression:
[tex]a=3,\ b=10\\\\\dfrac{70}{b}+5a-2b=\dfrac{70}{10}+(5)(3)-(2)(10)\\\\=7+15-20=22-20=\boxed2[/tex]
Sienna published 2/3 of the poems she wrote in a book. Additionally, published 4 different poems in a newspaper. The total numbers of poems she published was 22. How many poems had sienna written?
Answer:
Subtract the 4 additional poems from what was published first:
22 - 4 = 18
Now 18 is 2/3 of what she wrote.
To find the total poems written divide 18 by 2/3:
18 / 2/3 = 27
Sh wrote 27 poems total.
[CALCULUS] [HELP PLEASE]
7. The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm^3. Use tangent line approximation to estimate the percentage error in volume.
0.6%
0.9%
1.2%
1.5%
1.8%
A point on a damped spring has motion given by s(t)=2e^(-1.5t) s in(2(pi)t), where s is measured in centimeters and t is measured in seconds. Choose which of these is the graph for the velocity function for 0 < or equal to t < or equal to 4
Answer:
(7)
error percentage is 0.6%
(8)
Graph-C
Step-by-step explanation:
(7)
we are given cube
Let's assume edge of cube =x
so, volume of cube will be
[tex]V(x)=x^3[/tex]
we are given
V=125000
so, we can find 'x'
[tex]125000=x^3[/tex]
[tex]x=50[/tex]
So,
[tex]a=50[/tex]
now, we can use linear approximation formula
[tex]L(x)=V(a)+(x-a)V'(a)[/tex]
[tex]L(x)=V(a)+(\Delta x)V'(a)[/tex]
we have
[tex]\Delta x=0.1[/tex]
we can plug a=50
[tex]L(x)=V(50)+(0.1)V'(50)[/tex]
[tex]V(x)=x^3[/tex]
we can find derivative
[tex]V'(x)=3x^2[/tex]
now, we can plug x=50
[tex]V'(50)=3(50)^2[/tex]
[tex]V'(50)=7500[/tex]
now, we can plug these values
and we get
[tex]L(x)=V(50)+(0.1)\times 7500[/tex]
[tex]L(x)=V(50)+750[/tex]
[tex]L(x)-V(50)=750[/tex]
so, error is
[tex]error=750[/tex]
now, we can find percentage error
Percentage is
[tex]=\frac{750}{125000}\times 100[/tex]
=0.6%
so, error percentage is 0.6%
(8)
we are given
[tex]s(t)=2e^{-1.5t}sin(2\pi t)[/tex]
We will find derivative
To get velocity , we will find derivative
[tex]s'(t)=\frac{d}{dt}\left(2e^{-1.5t}\sin \left(2\pi t\right)\right)[/tex]
we can use product rule
and we get
[tex]s'(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]
so, we get velocity equation as
[tex]v(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]
now, we can draw graph
we can see that firstly , we get maxima and then minima
so, our graph would be
graph-C........Answer
Final answer:
To estimate the percentage error in volume, use the tangent line approximation and find the derivative of the volume function. Then divide the change in volume by the actual volume and multiply by 100%.
Explanation:
To estimate the percentage error in volume, we need to find the derivative of the volume function with respect to the length of one edge of the cube. The volume of a cube is given by V = a^3, where a is the length of one edge of the cube. So, the volume function is V = a^3.
Using the tangent line approximation, we can approximate the change in volume as the derivative of the volume function multiplied by the change in length of one edge of the cube. The derivative of the volume function is dV/da = 3a^2. The change in length of one edge is ±0.1 cm. So, the change in volume is approximately dV = (3a^2) * (±0.1 cm).
To find the percentage error in volume, we divide the change in volume by the actual volume and multiply by 100%. The actual volume is 125,000 cm^3. So, the percentage error in volume is approximately [(3a^2) * (±0.1 cm)] / (125,000 cm^3) * 100%.
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .
A (5,-4)
B (5,-2)
C (10,-4)
D (10,-2)
If point D divides in the ratio 4 : 5, the coordinates of point D are .
A (62/9,-4)
B (58/9,-4)
C (62/9,-2)
D (58/9,-2)
QUESTION 1
The point C(3.6, -0.4) divides AB in the ratio 3 : 2.
The coordinates of A are (-6, 5).
Let the coordinates of B be [tex](x_2,y_2)[/tex]
We use the formula:
[tex]x=\frac{mx_2+nx_1}{m+n}[/tex] to determine the x-coordinate of B.
We substitute the known values to obtain:
[tex]3.6=\frac{3x_2+2(-6)}{3+2}[/tex]
[tex]3.6=\frac{3x_2-12)}{5}[/tex]
[tex]3.6\times 5=3x_2-12[/tex]
[tex]18=3x_2-12[/tex]
[tex]18+12=3x_2[/tex]
[tex]30=3x_2[/tex]
This implies that:
[tex]x_2=10[/tex]
We also use the formula:
[tex]y=\frac{my_2+ny_1}{m+n}[/tex] to find the y-coordinate.
[tex]-0.4=\frac{3y_2+2(5)}{3+2}[/tex]
[tex]-0.4=\frac{3y_2+10}{5}[/tex]
[tex]-0.4\times 5=3y_2+10[/tex]
[tex]-2-10=3y_2[/tex]
[tex]-12=3y_2[/tex]
[tex]-4=y_2[/tex]
The coordinates of B are (10,-4)
QUESTION 2.
If point D divides CD in the ratio 4 : 5.
Then the coordinates of D are:
[tex](\frac{4(10)+5(3.6)}{4+5}, \frac{4(-4)+5(-0.4)}{4+5})[/tex]
[tex](\frac{58}{9}, \frac{-18}{9})[/tex]
The coordinates of D are [tex](\frac{58}{9}, -2)[/tex]
a jar contains 10 marbles six marbles are red and four marbles are blue if two marbles are chosen one at a time with replacement what is the probability that both marbles will be red
Answer:
30%
Step-by-step explanation:
there is a 60% chance of getting a red marble each time. You need to choose a ball twice. 60/2=30. therefore there is a 30% chance of getting two reds.
Final answer:
To find the probability of drawing two red marbles with replacement from a jar of six red and four blue marbles, we multiply the probability of drawing a red marble (3/5) by itself, resulting in 9/25.
Explanation:
The question asks for the probability that both marbles will be red when two marbles are chosen one at a time with replacement from a jar containing six red marbles and four blue marbles.
To find this, we calculate the probability of drawing a red marble, and since we replace the marble each time, this probability does not change with each draw. With six red marbles out of a total of 10, the probability of drawing a red marble on the first draw is 6/10 or 3/5. Since we replace the marble after each draw, the probability remains the same for the second draw.
Therefore, the probability of drawing two red marbles in a row is (3/5) * (3/5), which is 9/25.
Find the range of f(x) =-x+4 for the domain {-3, -2, -1, 1}
Answer:
{3, 5, 6, 7 }
Step-by-step explanation:
to find the range of f(x) substitute the given values of x from the domain into f(x)
f(- 3) = - (- 3) + 4 = 3 + 4 = 7
f(- 2) = - (- 2) + 4 = 2 + 4 = 6
f(- 1) = - (- 1) + 4 = 1 + 4 = 5
f(1) = - 1 + 4 = 3
range y ∈ {3, 5, 6 , 7 }
23 lb. 14 oz. − 8 lb. 1 oz.
P.S NO WORK NEEDED.
Answer:
15.8125 lb
Step-by-step explanation:
Answer:
15 lb. 13oz.
Step-by-step explanation:
no need
How do you do long division on 0.54?
Answer:
you put your divisor and add Dividend and see what that adds up to and get your answer
Step-by-step explanation:
Answer:
You add more 0
Step-by-step explanation:
what is the simplified form of 15x^5/20y^6*6y^4/5x^2
Answer:
The simplified form of the equation is 9x^3/10y^2 Good Luck!
Step-by-step explanation:
Answer:
if you go to a site called math papa it gives you the answer and how to do it
Step-by-step explanation:
what are the first 4 items of the arithmetic sequence in the graph
Answer:
i dont know
Step-by-step explanation:
What is the sign of − 4 a b −4ab when a > 0 a>0 and b < 0 b<0?
Answer:
The sign is positive.
Step-by-step explanation:
a > 0 and b < 0
So, a·b < 0
⇒ -4·a·b > 0
⇒ -4·a·b - 4·a·b > 0
Hence, the sign will be positive
Answer:
the answer is on top of me
Step-by-step explanation:
my mom is angry at me and im bored
HELP ME WITH THIS AND ILL GIVE YOU BRAINLIST!!!! <3
Answer:
9+8 = 8+991+0 = 91.Step-by-step explanation:
Given expression 9+8.
We need to rewrite it using Commutative Property.
Note: According to Commutative Property of Addition
a + b = b + a
Therefore,
9+8 = 8+9We just need to swap the positions of numbers.
Second expression : 91+0
We need to rewrite it using Identity.
According to Identity property of addition
a+0 = a.
When we add 0 to any number it gives same number.
Therefore,
91+0 = 91.How do I solve this and please be helpful
Answer:
y < 1
Step-by-step explanation:
8y - 5 < 3
To solve this inequality, add 5 to both sides.
8y - 5+5< 3+5
8y < 8
Divide by 8 on both sides
8y/8 < 8/8
y <1
I have no idea how to do this someone helped me with this and got the right answer which is 11/17 but I got a totally different answer!! Please help! Explain.
Answer:
Step-by-step explanation: The reason is is because when adding and subtracting integers, you flip the operation sign that will be used to solve the problem.So when you flip the sign of this equation, you subtract. So that's how your answer was 11/17. Also it is positive because the biggest number is positive so that is what the solution will be.
Please mark brainliest!!!!!!
[tex] \frac{2}{3} - \frac{4}{10} = [/tex]
what is the answer?
Answer:
8/30 (Simplified answer: 4/15)
Step-by-step explanation:
Find common denominators. Note the what you do to the denominator, you do to the numerator.
Multiply 10 to both the denominator & numerator of 2/3, and multiply 3 to both the denominator & numerator of 4/10
(10/10)(2/3) - (3/3)(4/10)
Simplify.
(20/30) - (12/30)
Simplify. Combine the terms
(20/30) - (12/30) = (20 - 12)/30 = 8/30
Simplify the fraction
(8/30)/(2/2) = 4/15
~
bring the fraction: 8/3xy^ 2 to a denominator of 15x^2y^2
If u do dis i really appreciate it!!!!!!!!! thx
Answer:
40x/(15x²y²)
Step-by-step explanation:
8/(3xy²) Multiply by 5/5
= 40/(15xy²) Multiply by x/x
= 40x/(15x²y²)
a store has apples on sale for $3.00 on two pounds . how many pounds of apples can you buy for $9 if an apple is approximately 5 ounces how many apples can you buy for $9 explain your reasoning
Answer: You can get 6 pounds of apples and approximately 19 apples.
Step-by-step explanation:
There are 16 ounces per pound so 6 pounds is 96 ounces
96/5 = 19.2
You can buy 6 pounds of apples for 9, which is approximately 19 apples.
1. First, let's find out how much one pound of apples costs. Since two pounds cost $3.00, one pound would cost half of that, which is $1.50.
2. Now, if one pound costs $1.50, we can find out how many pounds of apples you can buy for $9 by dividing $9 by the cost per pound: [tex]\( \frac{9}{1.50} = 6 \)[/tex]. So, you can buy 6 pounds of apples for $9.
3. Since 1 pound equals 16 ounces, 6 pounds equal [tex]\( 6 \times 16 = 96 \)[/tex]ounces.
4. If one apple is approximately 5 ounces, then the number of apples you can buy for 96 ounces is [tex]\( \frac{96}{5} \).[/tex]
5. Performing the division, [tex]\( \frac{96}{5} = 19.2 \)[/tex]. Since you can't buy a fraction of an apple, you'd round down to the nearest whole number.
6. So, you can buy approximately 19 apples for $9.
Here's the calculation step by step:
1. Cost per pound: [tex]\( \frac{3.00}{2} = 1.50 \)[/tex] dollars per pound.
2. Pounds you can buy for $9: [tex]\( \frac{9}{1.50} = 6 \)[/tex] pounds.
3. Total ounces: [tex]\( 6 \times 16 = 96 \)[/tex] ounces.
4. Apples you can buy: [tex]\( \frac{96}{5} = 19.2 \)[/tex](rounded down to 19 apples).
Which transformation will carry pentagon EFGHI onto itself?
Answer:
D
Step-by-step explanation:
The pentagon has 5 interior angles that add up to 360. To find the angle of rotational symmetry, divide 360 by 5 (you get 72). So if you rotated the shape 72 degrees, it will map onto itself. 72 times 2 is 144, and that's rotating the shape 72 degrees twice, so it will stay the same.
A mathematical transformation that carries a pentagon onto itself is a rotation by 72 degrees or a multiple of 72 degrees, which are the internal angles of a regular pentagon.
Explanation:The question is referring to certain mathematical transformations that can be applied to shapes, specifically a pentagon. A transformation that will carry a shape onto itself, maintaining its form, is a symmetry operation. For a pentagon, one of these transformations could be a rotation. For example, if you rotate the pentagon 72 degrees or a multiple of 72 degrees (such as 144, 216, 288 degrees, etc.), it will land on itself because 72 degrees represents each internal angle of a regular pentagon.
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The measures of the angles of a hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9. What is the measure of the smallest angle in the hexagon?
Answer:
[tex]72^{\circ}[/tex] is the measure of the smallest angle in the hexagon.
Step-by-step explanation:
As, we know that the sum of all the angles is 720 degrees.
Given: The measures of the angles of the hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9.
Let x be the number used to simplify the size of each angle.
Sum of all the measure angles is 720 degrees
⇒[tex]4x+5x+5x+8x+9x+9x = 720^{\circ}[/tex]
Combine like terms;
[tex]40x = 720^{\circ}[/tex]
Divide both sides by 40 we get;
[tex]x = \frac{720}{40} = 18[/tex]
The measure of angles are:
[tex]4x = 4 \times 18 = 72^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\8x = 8 \times 18 = 144^{\circ}\\9x = 9 \times 18 = 162^{\circ}\\9x = 9 \times 18 = 162^{\circ}[/tex]
Therefore; the measure of the smallest angle in the hexagon is, [tex]72^{\circ}[/tex]