Michael and Ashley bought same amount of turkey and ham.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Michael and Ashley each buy x pounds of turkey and y pounds of ham.
Michael purchased from store A.
Cost of turkey per pound at store A = $3
Cost of ham per pound at store A = $4
Michael spends $18 at store A.
3x + 4y = 18
Ashley purchased from store B.
Cost of turkey per pound at store B = $4.50
Cost of ham per pound at store B = $6
Ashley spends $27 at store B.
4.5x + 6y = 27
We get two linear equations,
3x + 4y = 18
4.5x + 6y = 27
Multiplying the first equation throughout with 4.5 and the second equation throughout with 3, we get,
13.5x + 18y = 81
13.5x + 18y = 81
Since both the equations coincide, Michael and Ashley bought same amount of Turkey and Ham.
Hence Michael and Ashley bought same amount of turkey and ham.
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Write the equation of the line which passes through (5, −2) and (3, 4) in standard form.
The equation of the line is 3x + y = 1
How to determine the equation of the line?The points are given as:
(5, −2) and (3, 4)
Start by calculating the slope (m)
m =(y2 - y1)/(x2 - x1)
This gives
m = (4 + 2)/(3 - 5)
Evaluate
m = -3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = -3(x + 2) +5
So, we have:
y = -3x - 6 + 5
Evaluate the like terms
y = -3x - 1
Rewrite as:
3x + y = 1
Hence, the equation of the line is 3x + y = 1
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pls help :,)
What is the area of this triangle?
units²
Answer:
6 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.
A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6
Which is the graph of a quadratic equation that has a positive discriminant?
Answer:
CORRECT graph is Graph C.
________________________________
HOPE IT HELPS
Revenue function: r(x) = 60x cost function: c(x) = 12 + 7x profit function: p(x) =
Profit function : p(x) = 53 x - 12
Cost is the total cost of producing the output.
The cost function consists of two different types of costs:
- Variable costs
- Fixed costs.
Variable costs vary with output (number of units produced). Total variable costs can be
expressed as the product of variable costs per unit and the number of units produced. If there are multiple items
manufactured costs are higher.
Fixed costs usually do not vary with performance.
Revenue is the total payment received from the sale of goods or the provision of a service.
The revenue function R() reflects the revenue from selling “” quantity of output items at price
"p" after item.
() =
Profit functions
The profit function P() is the difference between the revenue function R(x) and the total cost function C()
So P() = R() – C()
=−
Now, Profit = Revenue - Cost
= 60 x - ( 12 + 7 x)
= 60 x -12 -7 x
Profit = 53 x - 12
Hence, Profit function : p(x) = 53 x - 12
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Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
1 2 5 8 10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter
Answer:
4.35
Step-by-step explanation:
The expected value can be defined as: [tex]\sum{x_i*p_i}[/tex] where x_i = the payout, and p_i = the probability of it occurring.
This gives us the expression: [tex](1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 0.35 + 0.4 + 0.5 + 1.6 + 1.5 = 4.35[/tex]
So the expected payout is 4.35
determine the slope of the line
Answer:
2
Step-by-step explanation:
We can find the slope of the line by using the slope formula
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y1) are points on the line
Using the points (0,-4) and (2,0)
m = ( 0 - -4)/ ( 2 - 0)
= ( 0+4)/( 2-0)
= 4/2
= 2
Ben has typed 180 and can type 30 words per minute. millie has typed 60 and can type 50 words per minute. how many minutes will it take for millie to catch up with ben.
The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
We assume the minutes taken by Millie to catch up with Ben to be x minutes.
The number of words Ben has already typed = 180.
The unit rate for Ben for the typing of words = 30 per minute.
Therefore, words typed by Ben in x minutes = 30x words.
Therefore, the total number of words typed by Ben = 180 + 30x words.
The number of words Millie has already typed = 60.
The unit rate for Millie for the typing of words = 50 per minute.
Therefore, words typed by Millie in x minutes = 50x words.
Therefore, the total number of words typed by Millie = 60 + 50x words.
As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.
To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:
60 + 50x = 180 + 30x,
or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},
or, 60 + 20x = 180 {Simplifying},
or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},
or, 20x = 120 {Simplifying},
or, 20x/20 = 120/20 {Dividing both sides by 20},
or, x = 6 {Simplifying}.
Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
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Rewrite each equation in factored form and solve using zero product property. Find the solutions of each equation. Use the notes about r * k = c and r + k = b. In the first problem c is 6 and b is -7. So you need the same r and k that multiply to be 6 but also add to be -7. The numbers you find will be the solutions
The factored form of the equation are as follows;
(d - 6)(d - 1) = 0(x + 9)(x + 9) = 0(u + 12)(u - 5) = 0How to write equation in factored form?Converting a quadratic function to factored form is called factoring.
Therefore,
let's factor the equation,
a.
d² - 7d + 6 = 0
d² - d - 6d + 6 = 0
d(d - 1) - 6(d - 1) = 0
(d - 6)(d - 1) = 0
b.
x² + 18x + 81 = 0
x² + 9x + 9x + 81 = 0
x(x + 9) + 9(x + 9) = 0
(x + 9)(x + 9) = 0
c.
u² + 7u - 60 = 0
u² - 5u + 12u - 60 = 0
u(u - 5) 12(u - 5) = 0
(u + 12)(u - 5) = 0
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A badminton net is tethered to the ground with a strand of rope that forms a 50 angle with the ground. What is the length of the rope, x? Write an equation and show work below. Round to the nearest tenth.
Answer:
5.4 ft to nearest tenth.
Step-by-step explanation:
We know the adjacent side of the right triangle and we need the hypotenuse so we use the cosine:
cos 50 = 3.5/x
x = 3.5 / cos 50
= 5.445 ft.
What is the first step in the construction of a line perpendicular to and passing through an external point m? assume that the construction uses only a compass and a straightedge. a. place the compass needle on m and, keeping the compass width the same, draw two arcs that intersect . b. place the compass needle at any point on , and set the compass width to m. c. draw a line from point m passing through , and mark the point of intersection. d. place the compass needle at any two points on , and draw two arcs through m.
The first step in the construction of a line perpendicular to line AB and passing through an external point m is:
a. place the compass needle on m and keeping the compass width the same, draw two arcs that intersect the line AB
What are the steps to construct a perpendicular line from an external point?To construct a perpendicular line, a compass and a scale are used.
Consider a line AB and an external point M.
Step 1:
Place the compass needle on M and keeping the compass width the same, draw two arcs that intersect the line AB.
Step 2:
Name the two intersecting points on line AB as X and Y.
Draw the arcs from these two points to the opposite side of point M with the same compass width.
Step 3:
Name the intersecting point of two arcs as N.
Draw a line connecting the two points M and N using scale.
Step 4:
Using a protractor, measure the angle of the line MN with the line AB.
The angle must show 90°.
Thus, the line MN perpendicular to line AB and passing through an external point M is constructed.
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Answer:
a. place the compass needle on m and keeping the compass width the same, draw two arcs that intersect the line AB
Step-by-step explanation:
Help me with alg 2 please!
The probability that 5 boys would be selected would be 5/6720
How to determine the probabilityFrom the information given, the probability can be calculated using permutation
The formula for permutation is given as;
Permutation = [tex]\frac{n!}{n - r!}[/tex]
Where;
n is number of sets = 8r is the number of objects selected = 5Substitute the values into the formula
Permutation = [tex]\frac{8!}{8 - 5!}[/tex] = [tex]\frac{8!}{3!}[/tex] = [tex]\frac{40, 320}{6}[/tex] = 6720
The probability that 5 boys would be selected is 5/6720
Thus, the probability that 5 boys would be selected would be 5/6720
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20pts and brainliest !! please help quick
Answer:
y = -1.3x + 10
Step-by-step explanation:
x_avg = (-2 + -1 + 1 + 2 + 3 + 4)/6 = 1.166666...
y-avg = (21 + 8.6 + 1 + 1 + 5 + 14.3) = 8.48333...
x y x-x_avg y-y_avg (x-x+avg)² (x-x_avg)(y-y_avg)
-2 21 -3.1666 12.51666 10.02777 -39.63611
-1 8.6 -2.1666 0.11666 4.69444 -0.252777
1 1 -0.1666 -7.48333 0.02777 1.247222
2 1 0.83333 -7.48333 0.69444 -6.236111
3 5 1.8333 -3.48333 3.3611111 -6.386111
4 14.3 2.8333 5.81666 8.02777 16.480555
sum of (x-x_avg)(y-y_avg) = -34.858
sum of (x+x_avg)² = 26.8333
slope = [(x-x_avg)(y-y_avg)/[(x+x_avg)²]
slope = -34.858/26.8333
slope = -1.29907
y = mx + b
y_avg = m(x_avg) + b
8.48333 = -1.3(1.1666) + b
b = 9.9989
y = -1.3x + 10
If f(x) = x-2, what is f¹(x)?
f¹(x) = 9x + 18
ƒ²¹(x) = x + 2
f¹(x) = 9x+2
ƒ¹ (x) = -2x +
Interchange x and y
[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]
Solve for y[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]
[tex]\\ \tt\leadsto y=9(x+2)[/tex]
[tex]\\ \tt\leadsto y=9x+18[/tex]
That's the inverse[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]
Answer:
[tex]f^{-1}(x)=9x+18[/tex]
Step-by-step explanation:
[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is its reflection in the line y = x.
Given function:
[tex]f(x)=\dfrac{1}{9}x-2[/tex]
To find the inverse of the given function:
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=\dfrac{1}{9}x-2[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+2=\dfrac{1}{9}x[/tex]
[tex]\implies 9(y+2)=x[/tex]
[tex]\implies x=9y+18[/tex]
Replace x with [tex]f^{-1}(x)[/tex] and y with x:
[tex]\implies f^{-1}(x)=9x+18[/tex]
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Compared to the graph of f(x) = x², the graph of g(x) = (x − 2)² +3
is the result of translating f(x)
Answer:
Vertical shift up 3
Horizontal shift to the right 2
Brainliest, please :)
Answer:
Step-by-step explanation:
f(x) is moved 2 units to the right followed by 3 units up,
Clark works for Acme Bank and asks for your assistance. He wants you to look at a property that's about to go into foreclosure and provide him with a report on its current marketability and an approximate market value. What's Clark most likely asking you to provide
The information that Clark is asking me to provide for him regarding the property is called Brokers Price Opinion (BPO).
What is BPO?
The term BPO refers to Brokers Price Opinion. It is the opinion of a genuine real estate professional regarding the accurate pricing of a property.
The information that Clark is asking me to provide for him regarding the property is called Brokers Price Opinion (BPO).
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11 points
please help me
Answer:
40%
8%
15%
37%
Step-by-step explanation:
The solutions are in the image
Solve the simultaneous equations x - 5y = 0 and 15x + 10y = 17
The solutions of the equations x - 5y = 0 and 15x + 10y = 17 at x and y is 1 and 1/5 respectively.
Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.
Given that:
The linear equations are:
x - 5y = 0
15x + 10y = 17
Solve the equations using elimination method:
Multiply equation 1 by 2
2(x - 5y) = 0
15x + 10y = 17
This can be solved as:
2x-10y = 0.....(1)
15x + 10y = 17....(2)
On subtracting equation 1 from 2
17x = 17
x = 1
The value of x is 1.
Substitute the value of x in equation (1)
2(1)-10y = 0
2=10y
y = 1/5
Thus, the value of x and y is 1 and 1/5 respectively.
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I need help! ASAP
As shown in the figure below, a || b and c is the transversal, m∠1= 40°, m∠2= 70°.
Question: m∠3= ?
Answer:
Step-by-step explanation:
your answer will be 110degrees
Which expression can be used to find the volume of the sphere?
A sphere with diameter 10 inches.
V = four-thirds pi r squared = Four-thirds (3.14) (5) squared
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
V = four-thirds pi r cubed = Four-thirds (3.14) (10) cubed
V = four-thirds pi r squared = Four-thirds (3.14) (10) squared
I think its (B)
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
Select the correct answer from each drop-down menu. a comic-strip writer churns out different numbers of comic strips each day. the writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set. 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8 the data in the distribution is . if the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is .
Mean = 3.5
Median = 3
Distribution is negatively skewed.
What is skew in the distribution?
The distribution has no skewness if the mean and median are equal.
The median exceeds the mean in a favorably skewed distribution.
The distribution is also negatively skewed if the median is lower than the mean.
Given,
Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
Mean = [tex]\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}[/tex]
Mean = [tex]\frac{56}{16}[/tex]
Mean = [tex]3.5[/tex]
Median = mid value of the data set when the values are arranged in ascending order
Here,
the two mid values = [tex]3, 3[/tex]
Median = [tex]\frac{3+3}{2}[/tex]
Median = [tex]\frac{6}{2}[/tex]
Median = [tex]3[/tex]
Now, as the mean is larger than the median therefore the distribution will be skewed negatively.
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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.
ヾ(•ω•`)o
Find the value of X. Round to the nearest tenth HELP ASAP!!!!
Answer: 22.5
Step-by-step explanation:
[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]
can someone help me i know nothing about graphs
Answer:
The answer is B.
Step-by-step explanation:
The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.
if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.
if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.
someone please help with this please
Answer:
b = 21
Step-by-step explanation:
In general for these trig problems look for the angle whose measure you are given or need to find and for the sides you are given lengths or whose sides you need to find.
Given:
side AB = 10 cm
m<C = 25°
Find:
side AC
The angle of interest here is <C whose measure is 25°.
Now look at the given side and the side you are looking for with respect to angle C, the given angle.
For angle C, AC is the adjacent leg.
For angle C, AB is the opposite leg.
Which trig function relates the opposite leg to the adjacent leg?
It is the tangent, since, in general, tan X = opp/adj.
tan C = opp/adj
tan 25° = AB/AB
tan 25° = 10 cm/b
Solve for b.
b × tan 25° = 10 cm
b = 10 cm / tan 25°
Using your calculator, divide 10 by the tangent of 25°.
b = 21.44506...
Answer: b = 21
Answer:
[tex]b = \bf 21 \space\ cm[/tex]
Step-by-step explanation:
• To solve for a side using SOH CAH TOA, first check the angle whose measure is given.
In this case, we know ∠ C is 25°.
• Next we have to figure out the relationships between the given angle and two sides: one side whose length we know, and the other whose length we have to find.
In this case, the side opposite to ∠ C is known to be 10 cm, and the side adjacent to ∠ C is AC, whose length, b, we have to find.
• The trigonometric ratio that relates the adjacent and opposite sides of an angle is tan, where:
[tex]\boxed{tan \theta = \frac{opposite}{adjacent} }[/tex] .
We can use this relationship to calculate the value of b:
⇒ [tex]tan (25 \textdegree) = \frac{10}{b}[/tex]
Solving for b:
⇒ [tex]b \cdot tan (25 \textdegree) = 10[/tex]
⇒ [tex]b = \frac{10}{tan (25 \textdegree)}[/tex]
⇒ [tex]b = 21.45[/tex]
⇒ [tex]b \approx \bf 21 \space\ cm[/tex] (rounded to the nearest whole number)
Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.
The cost of 2 chairs is = $30
The cost of 1 table = $60
Step-by-step explanation:
Let a table represent x
A chair represents y
4x + 3y = 225.......eq 1
3x + 4y = 195........eq 2
Use elimination method
x - y = 30
x= 30 + y...... Eq 3
Substitute the value of x into equation 1
4(30+ y) + 3y= 225
120 + 4y + 3y= 225
7y + 120= 225
7y= 225-120
7y= 105
y= 15
Substitute the value of y in eq 2
3x + 15 = 195
3x= 195-15
3x= 180
x= 60
Therefore, the cost of 2 chairs is 15 * 2= $30
The cost of 1 table = $60
Answer:
65
Step-by-step explanation:
Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Relations and Functions” Below is an example of this.
——————————————————————
Example :
Is the set of ordered pairs below a function? Yes or no, explain your reasoning.
{(4,6),(10,-2),(13,7),(15,8),(10,11)}
——————————————————————
2. Answer each question and show a brief step by step process on how you got the answer to each of your questions.
As per definition
In. a function every domain has an unique range of it
f(x)=yHere
f(4)=6f(10)=-2f(13)=7d(15)=8f(10)=11f(10) has two corresponding values hence it's not a function
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 7. Express the probability as a simplified fraction. Group of answer choices
Answer:
12/13
Step-by-step explanation:
there are 4 7's in a 52 card deck, that means the other 48 cards are not 7's. 48/52 = 12/13
this table shows how many students fro two high schools attended a football game. A student is randomly selected. what is the probability that a student attended the game, given that the student if fro North Beach? Round your answer to two decimal places.
Using it's concept, the probability that a student attended the game, given that the student if fro North Beach is:
B. 0.65.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 170 people attended the game, out of which 110 are from North Beach, hence the probability is:
p = 110/170 = 0.65.
Hence option B is correct.
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Answer:0.55 is the correct answer
Step-by-step explanation:
Rosa goes to the home of Mr. and Mrs. Johnson twice a week to work with their 4-year-old on his letters and numbers. Rosa is providing
Rosa is providing home-based tutoring.
What is Home-based tutoring?
At-home tutoring is a type of tutoring that takes place in the student's house. Tutoring is frequently related to an academic subject or test preparation. This is in contrast to tutoring centers or after-school programs that give tutoring.A home tutor is an instructor who conducts classes in the convenience of your own home. Because they give personalized attention, these classes are frequently more expensive than those offered at tuition centers. In-home tutoring typically has fewer pupils, and the lessons are even more exclusive.Tutoring's goal is to help students help themselves, or to aid or guide them to the point where they are independent learners and no longer require a tutor.Therefore, Rosa is providing home-based tutoring.
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A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
(0, –2)
(2, –1)
(4, 0)
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
A possible critical point of the function f(x) is given by: (0,-2)
What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
At these points, the function can change from decreasing to increasing, or vice-versa.
For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).
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i need help with this page
Answer:
See picture below.
Step-by-step explanation: