Answer:
Part A) 170.66$ would be the original price.
Part B) 256$ would be the price that the store paid for the music player.
Part B) What you need to balance is your markup, meaning how much to raise your price, and your markdown or discount, meaning, how to much to decrease prices.
Step-by-step explanation:
Part A) Determining the Original Price
Note: when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.
So, a music player was marked down by 1/4 of the original price, and we have to calculate the original price if the sales price is $128.
Let 'p' be the original price
As a music player was marked down by 1/4 of the original price
So, Markdown = 1/4p
As the sales price is $128
As the Sale price = [tex]p - \frac{p}{4}[/tex] ⇒ [tex]\frac{3p}{4}[/tex]
[tex]128 = \frac{3p}{4}[/tex]
[tex]552 =3p[/tex]
[tex]p =170.66[/tex]
Hence, 170.66$ would the original price.
Part B) Determining the Price that the store paid for the music player
When an amount is added to the cost price of a product or commodity in order to determine the selling price, it means the the product or commodity is being marked up.
So, as the music player was marked up by 1/2 before it was placed on the sales floor and we have to determine the price that store paid for the player.
So, dividing the original price by 2 and adding the result to the original price would give us the price that store had to pay for the music player.
As the original price is 170.66.
So, the price that the store paid for the music player can be calculated as:
price = 170.66 + 170.66/2
price = 170.66 + 85.33
price = 255.99$ ≈ 256$
Therefore, 256$ was the price that the store paid for the music player.
Part C) Determining the difference between the discount price and the price that the store paid for the music
For example, let suppose you are a shopkeeper and have a jeans fabric business. You want to make money from it. But, in order to earn money from selling jeans fabric, you have to make sure that your price must be at the right value price both in terms of generating money and also giving your customer a great value for the money to given them a decent deal.
What you need to balance is your markup, meaning how much to raise your price, and your markdown, meaning, how to much to decrease prices.
In business, the conditions may never always remain favorable due to certain circumstance, hence bad days. Sometimes, the conditions get ideal for business, hence good days.
As I earlier sated that when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.
For example, the cost price of 1 Jeans fabric is 10$, and you want to earn profit. So, you mark up your fabric to 30$. As $30 is $20 more than $10. So, markup value will be 2. In terms of percentage, it means you have a markup of 200%.
But, due to certain issues, your sales are being effected due to certain condition. In order to not affect the sales, you want to markdown the price - a kind of discount. Your starting price was $30 and want to decrease the price to $20. It means the difference is $10. So, you have made a markup or given a discount of $30/$10 = 0.33. In terms of percentage, it is around 33%. So, you have given the discount of 33% to hope for the great sales.
So, in the question, when the music player was marked down by 1/4 of the original price, it means the discount of 1/4 of the original price was provided. As the sale price was $128, and original price was $170.66. So, discount of 1/4 or 25% was offered.
As the original price was $170, and it was marked up by 1/2 by the owner or creator of music player before it was placed on the sales floor. So, 256$ was the price that the store paid for the music player.
Keywords: markdown, markup, discount, price
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The graph of a system of inequalities is shown.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?
y > 2x
x + 2y ≤ –8
y ≥ 2x
x + 2y < –8
y < 2x
x + 2y ≥ –8
y ≤ 2x
x + 2y > –8
Answer:
The system is
[tex]x+2y \leq -8[/tex]
[tex]y> 2x[/tex]
Step-by-step explanation:
Part 1
Find the equation of the first inequality
we know that
The first line is a solid line with negative slope passing through the points (-6,-1) and (0,-4)
The slope is equal to
[tex]m=(-4+1)/(0+6)\\m=-0.5[/tex]
The equation of the solid line in slope intercept form is
[tex]y=-0.5x-4[/tex]
Everything below the line is shaded
so
The inequality is
[tex]y \leq -0.5x-4[/tex]
Convert to standard form
Adds 0.5x both sides
[tex]0.5x+y \leq -4[/tex]
Multiply by 2 both sides
[tex]x+2y \leq -8[/tex] -----> First inequality
Part 2
Find the equation of the second inequality
we know that
The second line is a dashed line with positive slope passing through the points (-2,-4) and (0,0)
This line represent a proportional relationship, because the line passes through the origin
The slope is equal to the constant of proportionality
[tex]k=(-4)/(-2)=2[/tex]
The equation of the dashed line is
[tex]y=2x[/tex]
Everything to the left of the line is shade
so
The inequality is
[tex]y> 2x[/tex] -----> Second inequality
see the attached figure to better understand the problem
The system of inequalities represented by the given graph is y > 2x and x + 2y ≤ –8.
Explanation:The system of inequalities represented by the given graph is:
y > 2xx + 2y ≤ –8We can determine the equations of the lines using the given points:
Line 1: y = mx + b, where m is the slope and b is the y-intercept. Using the points (–6, –1) and (0, –4), we can calculate the slope: m = (–4 – (–1)) / (0 – (–6)) = –3 / 6 = –1/2. Thus the equation of Line 1 is y = –(1/2)x – 3.
Line 2: Using the points (–2, –4) and (0, 0), we can calculate the slope: m = (0 – (–4)) / (0 – (–2)) = 4 / 2 = 2. Thus the equation of Line 2 is y = 2x – 4.
By looking at the graph, we can see that everything below Line 1 (shaded area) satisfies y > 2x, while everything below or on Line 2 (including the line itself) satisfies x + 2y ≤ –8.
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What is the equation of the line that passes through the point
(
−
6
,
−
6
)
(−6,−6) and has a slope of
2
3
3
2
?
Answer:
y+6=2(x+6)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-6)=2(x-(-6))
y+6=2(x+6)
Find the number, if d 12/13 of it is 24
Answer:
26 is the number
Step-by-step explanation:
12/13 x = 24
Multiply by 13 on both sides
12x = 24 * 13
12x = 312
Simplify
x = 26
26
Hope this helps :)
Simplify each expression, and then arrange them in increasing order based on the coefficient of n2. -5(n3 – n2 – 1) + n(n2 – n) (n2 – 1)(n + 2) – n2(n – 3) n2(n – 4) + 5n3 – 6 2n(n2 – 2n – 1) + 3n2
To simplify the expressions and arrange them based on the coefficient of n², combine like terms and perform necessary operations. The expressions, in increasing order, are: 3n + 2, 2n³ - n² + 2n, -5n³ + 6n² - n + 5, and 6n³ - n² + n - 6.
Explanation:To simplify each expression and arrange them in increasing order based on the coefficient of n², we need to combine like terms and perform any necessary operations. Let's go through each expression:
-5(n³ – n² – 1) + n(n² – n) = -5n³ + 6n² - n + 5(n² – 1)(n + 2) – n²(n – 3) = 3n + 2n²(n – 4) + 5n³ – 6 = 6n³ - n² + n - 62n(n² – 2n – 1) + 3n² = 2n³ - 4n² + 2n + 3n² = 2n³ - n² + 2nArranging them in increasing order based on the coefficient of n², we have:
3n + 22n³ - n² + 2n-5n³ + 6n² - n + 56n³ - n² + n - 6Learn more about Simplifying Expressions here:https://brainly.com/question/29003427
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[tex](1 \times 10^{5)(6 \times {10}{4} [/tex]
Note that [tex]10^a\cdot10^b=10^{a+b}[/tex] or more general form, [tex]a^b\cdot a^c=a^{b+c}[/tex].
[tex]10^5\cdot6\cdot10^4=\boxed{6\cdot10^9}[/tex]
Hope this helps.
Dave's sister baked $3$ dozen pies of which a third contained chocolate, a quarter contained marshmallows, a sixth contained cayenne, and one twelfth contained salted soy nuts. What is the smallest possible number of pies that had none of these ingredients?
Step-by-step explanation:
As Dave's sister baked 3 dozen pies.
So, total number of pies = 3 × 12 = 36
Number of pies = 3×12 = 36
Pies which contained chocolate = 1/3×36 = 12
Pies which contained marshmallows = 1/4×36 = 9
Pies which contained cayenne = 1/6×36 = 6
Pies contained soy nut = 1/12×36 = 3
So,
Pies that had none of these ingredients = 36 - (12+9+6+3)
= 36 - 30
= 6 pies
So, total 6 pieces are left that had none of these ingredients.
i.e. 1, 2, 3, 4, 5, 6
Therefore,
The largest possible number of pies that had none of thees ingredients = 6 piecesThe smallest possible number of pies that had none of thees ingredients = 1 pieceKeywords: smallest possible number
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She baked 36 pies. Of these
1/3*36=12 contained chocolate
1/4*36=9 contained marshmallows
1/636=6 contained cayenne
1/12*36=3 contained salted soy nuts.
In order to make the number of pies with none of these ingredients as small as possible, Dave's sister should put all of these ingredients in different pies so that only one of the ingredients is in any pie. If she does this, then 12+9+6+3=30 of the pies will have one of these ingredients. The other 6 pies will have none of these ingredients. At least 6 pies have none of these ingredients.
-Alcumus AoPS Staff
Brainliest would be great!!!
ILL GIVE BRAINLEST AND EXTRA POINTS
Answer:
it's (-3,9 i hope in prey so
Step-by-step explanation:
Answer:
(- 2, - 5 )
Step-by-step explanation:
Note that y = 1 is a horizontal line passing through all points with a y- coordinate of 1
The point (- 2, 7 ) is 6 units above y = 1 (7 - 1 = 6 ), thus
The reflection is 6 units below y = 1, (1 - 6 = - 5 ), hence
P(- 2, 7 ) → P'(- 2, - 5 )
KHAN GEOMETRY QUESTION!!!!!!!!!HELP!!!!!!
Answer:
Arc VU = 44°
Step-by-step explanation:
Given:
Arc SV means ∠SOV = 120°
Arc VU means ∠VOU = ?
We know that, from central angle theorem, central angle made by arc is twice the angle made the same arc at the circumference.
∴ ∠SOU = 2 × ∠STU
⇒ ∠SOU = 2(82°)
⇒ ∠SOU = 164°
Now, from angle addition theorem,
∠SOU = ∠SOV + ∠VOU
⇒ 164° = 120° + ∠VOU
⇒ 164° - 120° = ∠VOU
⇒ ∠VOU = 44°
Therefore, the measure of the arc VU is 44°.
What is 4(x−2)=3(2y−1) in standard form?
Answer: 4x-6y=5
Step-by-step explanation: Using the formula, Ax+By=C, write the equation in standard form.
Hope this helps you out! ☺
The equation 4(x-2) = 3(2y-1) can be converted into standard form by first expanding the equation and then rearranging it. The equation in standard form is 4x - 6y = -5.
Explanation:To convert the equation 4(x-2) = 3(2y-1) into standard form, we first expand both sides of the equation. This results in 4x - 8 = 6y - 3. We can then rearrange the equation to bring all variables to one side which yields 4x - 6y = -8 + 3 or 4x - 6y = -5.
However, in standard form, the coefficients of x and y should be integer and the coefficient of x should be positive. Additionally, the constant should be on the right side of the equation. Therefore, we multiply the whole equation by -1 to get -4x + 6y = 5. Multiplying again by -1 to make the coefficient of x positive, we get 4x - 6y = -5 which is the standard form of the given equation.
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A survey of all beings on planet Tott found that 12 beings preferred
hab juice to all other juices. If 40 beings were surveyed altogether,
what percent of them preferred hab juice?
(step by step)
Answer:
30% of them preferred hab juice.
Step-by-step explanation:
Given:
A survey of all beings on planet Tott found that 12 beings preferred hab juice to all other juices.
40 beings were surveyed altogether.
Now, to find percent of them preferred hab juice.
Total beings surveyed = 40.
Number of beings preferred hab juice = 12.
So, to get the percent:
[tex]\frac{Total\ beings\ surveyed}{Number\ of\ beings\ preferred\ hab\ juice} \times 100.[/tex]
[tex]=\frac{12}{40} \times 100[/tex]
[tex]=0.3\times 100[/tex]
[tex]=30\%.[/tex]
Therefore, 30% of them preferred hab juice.
Given that V= πr^2h. Make r the subject of the formula.
Using the result from the above,find r when V = 81 cm3, π = 4 and h = 9cm
Answer:
The answer is [tex]r=\frac{3}{2}\ cm.[/tex]
Step-by-step explanation:
Given:
V= πr²h.
V = 81 cm3,
π = 4 and
h = 9cm.
Now, making r the subject of the formula using the result from the above, find r.
So, to get the value of r:
[tex]V=\pi r^2h[/tex]
[tex]81=4\times r^2\times 9[/tex]
[tex]81=36r^2[/tex]
Dividing both sides by 36 we get:
[tex]\frac{81}{36} =r^2[/tex]
Using square root on both sides we get:
[tex]\frac{9}{6} =r[/tex]
[tex]\frac{3}{2} =r[/tex]
[tex]r=\frac{3}{2}.[/tex]
Therefore, the answer is [tex]r=\frac{3}{2}\ cm.[/tex]
10 points!
Find the shape resulting from the cross-section of the cylinder.
Answer:
Triangle
Step-by-step explanation:
cross section through the cone perpendicular will be a triangle with the base of the cone's base diameter.
The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [-5, 5] by [-5, 5]
a. r = 2 - 2 sin θ
b. r = 3 - 2 sin θ
c. r = 2 + 2 sin θ
d. r = 1 - 3 sin θ
Answer:
A
Step-by-step explanation:
A limacon curve passes trough the point [tex]\left(\dfrac{\pi}{2},0\right)[/tex], this means when [tex]\theta =\dfrac{\pi}{2},[/tex] the distance [tex]r=0.[/tex]
Note that
[tex]\sin \dfrac{\pi}{2} =1,[/tex]
so, if [tex]r=a+b\sin \theta,[/tex]
then
[tex]r\left(\dfrac{\pi}{2}\right)=a+b=0\\ \\a=-b[/tex]
The only option which shows a = -b is option A.
Answer:
b
Step-by-step explanation:
is y=5x+7 liner, nonlinear, or both
"If two lines intersect, then the intersection is a point." What is the hypothesis? Two lines intersect
Intersection is a point
Points have intersection
Intersection happens at a point
Answer:
Hypothesis is: Intersection happens at a point
Step-by-step explanation:
A hypothesis in science is a suggested explanation of something that has a consequence or leads to an occurrence. Usually it will be written in the form of an "if and then" statement.
Such statement explains what would occur, or follow if the possibility enunciated in the "if" part of the statement happens.
In this case the hypothesis is that if there is intersection of lines, it has to occur at a point. Therefore the closest to that statement among the options given in the problem is the last one: "Intersection happens at a point"
Answer:
Two Line Intersect
Step-by-step explanation:
I got it right on the test :)
Madison’s monthly salary is $1348. If her budget for rent is 32% of salary, then how much is budgeted for rent?
Answer:
$431.36 is budgeted for rent.
Step-by-step explanation:
Given:
Madison’s monthly salary is $1348.
Her budget for rent is 32% of salary.
Now, to find the amount budgeted for rent.
So, salary = $1348.
And, budget for rent = 32% of $1348.
Thus, the budgeted for rent is:
[tex]32\%\ of\ \$1348.[/tex]
[tex]=\frac{32}{100} \times 1348[/tex]
[tex]=0.32\times 1348[/tex]
[tex]=\$431.36.[/tex]
Therefore, $431.36 is budgeted for rent.
Your second mortgage of $31,200 is at a rate of 10.7% compounded quarterly for 8 years. What total will you have paid for your second mortgage after 8 years?
Answer:
The Amount paid after 8 years is $72611.76
Step-by-step explanation:
Given as :
The principal mortgage = p = $31,200
The rate of interest = r = 10.7% compounded quarterly
The time period of mortgage = t = 8 years
Let The Amount paid after 8 years = $A
Now, According to question
From Compounded Interest method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{\textrm 4\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{4\times 100})^{\textrm 4\times t}[/tex]
Or, A = $31,200 × [tex](1+\dfrac{\textrm 10.7}{4\times 100})^{\textrm 4\times 8}[/tex]
Or, A = $31,200 × [tex](1.02675)^{32}[/tex]
Or, A = $31,200 × 2.3273
∴ A = $72611.76
So, The Amount paid after 8 years = A = $72611.76
Hence, The Amount paid after 8 years is $72611.76 Answer
5% tax on $1.50 What us total cost
Answer:
$1.58
Step-by-step explanation:
1.50 multiplied by 1.05
answer is 1.575
rounded is 1.58
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Answer:
2.25
Step-by-step explanation:
just multiply .05 by 1.50 so that would be .075, so then add that by original price so 2.25. Don't Quote me on this its been awile.
runner is compared with the world record
holder during a race. A negative number means the
runner is ahead of the time of the world record holder.
A
positive number means that the runner is behind
the time of the world record holder. The table
shows the time difference between the runner and
the world record holder for each lap. What time
difference does the runner need for the fourth lap
to match the world record?
Answer:
-0.42
Step-by-step explanation:
To match the world record, the runner needs a time difference for the fourth lap that brings the total time difference from all laps to zero. This time difference is calculated based on the sum of time differences of the first three laps.
Explanation:This question is asking about the time difference that the runner needs for the fourth lap in order to match the world record.
Assuming that the total time difference after the first three laps is provided in the table, what you'll do is add these three time differences to get the total difference for the first three laps.
Let's say, for instance, the total after three laps is +15 seconds. Since a positive number means the runner is behind the world record holder's time, we want the fourth lap to compensate for that and bring the total time difference to zero to match the world record. Therefore, the runner will need a -15 seconds time difference on the fourth lap.
Remember that a negative number means the runner ran the lap faster than the world record holder.
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3x +15=75 what is the value of x
Answer:
X=20
you subtract 15 from 75 to get 60 then divide 60 by 3 to get 20
HELP
Find the area of the semicircle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
The area of the semicircle if the radius is 2 in terms of π is 2π.
What is the area of the semicircle?Area of a circle = πr²
Where,
r = radius
A semicircle is half of a circle.
So,
Area of a semicircle = ½πr²
If r = 2
Area of a semicircle = ½ × π × 2²
= ½ × Π × 4
= 4/2π
= 2π
Hence, the area of the semicircle is 2π.
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What is a reasonable distance between two cities? A. 200 km B. 200 m C. 200 cm D. 200 mm
Answer:
A would be best
Step-by-step explanation:
200 km is roughly 124.2 miles
200 m is about 0.12 miles
200 cm and 200 mm is way too small to be distances between cities because 200 cm is like 78.7 inches
200 mm is like 7.8 inches
124.2 miles or 200 km would be a reasonable distances between two cities.
Answer:
A. 200km is your answer
Step-by-step explanation:
I need help on this problem
Answer: [tex]QR=4.04[/tex]
Step-by-step explanation:
For this exercise you must use the followinG Trigonometric Identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
In this case, given the right triangle PQR, you can identify that:
[tex]\alpha=60\°\\opposite=PR=7.0\\adjacent=QR[/tex]
Then, the next step is to substitute those values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]:
[tex]tan(60\°)=\frac{7.0}{QR}[/tex]
And the final step is to solve for "QR" in order to find its value.
So you get that this is:
[tex](QR)(tan(60\°))=7.0\\\\QR=\frac{7.0}{tan(60\°)}\\\\QR=4.04[/tex]
The 3rd term of a geometric sequence is -2 and the 7th is -32. Find the common ratio,the first term, the explicit formula, and the 10th term.
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Both a and r have to be found
Given a₃ = - 2, then
ar² = - 2 → (1)
Given a₇ = - 32, then
a[tex]r^{6}[/tex] = - 32 → (2)
Divide (2) by (1)
[tex]\frac{ar^6}{ar^2}[/tex] = [tex]\frac{-32}{-2}[/tex], that is
[tex]r^{4}[/tex] = 16 ( take the fourth root of both sides )
r = 2 ← common ratio
Substitute r = 2 into (1)
a × 2² = - 2, that is
4a = - 2 ( divide both sides by 4 )
a = - [tex]\frac{1}{2}[/tex] ← first term
Hence
[tex]a_{n}[/tex] = - [tex]\frac{1}{2}[/tex][tex](2)^{n-1}[/tex] ← explicit formula
and
[tex]a_{10}[/tex] = - [tex]\frac{1}{2}[/tex] × [tex]2^{9}[/tex] = - 0.5 × 512 = - 256
Please help!!
1. Solve the following system of equations by graphing.
x + 2y = 8
x + 2y = -4
What is the solution?
(3, 5), no solution, infinite solutions, none of the above
2. The ordered pair (4,2) is a solution to the system of inequalities below.
y>-3x+2
y<2x+1
True or False
3.When solving the system by substitution, what would you plug into the second equation for the letter x?
x+2y=4
2x+2y=6
x = 2, x = 4-2y, x = 4, x = 2y+4
4. There is no solution to the system below.
2x + 4y = 8
x + 2y = 6
True or False
Answer:
(Q.1) No solution
(Q.2) True
(Q.3) x = 4 - 2y
(Q.4) True
========================================
Step-by-step explanation:
(Q.1) As shown in the first attached figure.
By graphing. x + 2y = 8 & x + 2y = -4
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
===================================================
(Q.2) As shown in the second attached figure.
By graphing the system of inequalities y> -3x+2 & y<2x+1
The Shaded area represents the solution of the system of inequalities
And the point (4,2) is inside the shaded area
So, The ordered pair (4,2) is a solution to the system of inequalities.
====================================================
(Q.3) solving the system { x+2y=4 & 2x+2y=6 } by substitution
From the first equation x + 2y = 4
we will find x in terms of y then plug it into the second equation
So, x + 2y = 4 ⇒ x = 4 - 2y
=====================================================
(Q.4) As shown in the third attached figure.
By graphing. 2x + 4y = 8 & x + 2y = 6
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
Round 0.566 to the nearest tenth
Answer:
0.06
Step-by-step explanation:
If you round 0.566 to the nearest tenth it would be 0.06
pls rate and thank me
Answer:
To round 0.566 to the nearest tenth consider the hundredths' value of 0.566, which is 6 and equal or more than 5. Therefore, the tenths value of 0.566 increases by 1 to 6.
=0.6
Step-by-step explanation:
comment how this helps
How do you graph x-y-3=0
Answer:
see explanation
Step-by-step explanation:
To graph the line, we require 2 points
Find the intercepts, that is where the graph crosses the x and y axes
To find the x- intercept let y = 0 in the equation and solve for x
x - 3 = 0 ( add 3 to both sides )
x = 3 ⇒ (3, 0 ) ← x- intercept
To find the y- intercept let x = 0 in the equation and solve for y
- y - 3 = 0 ( add 3 to both sides )
- y = 3 ( multiply both sides by - 1 )
y = - 3 ⇒ (0, - 3 ) ← y- intercept
Plot the points (3, 0) and (0, - 3) and draw a straight line through them
Chloe is painting a room she uses 1/4 gallon of paint to cover 1/3 of a wall if the walls are all the same size how much paint will she need to cover one wall
Answer:
3/4 gallon
Step-by-step explanation:
we know that
Chloe uses 1/4 gallon of paint to cover 1/3 of a wall
so
using proportion
Find out how much paint she will need to cover one wall
Let
x ---> paint needed to cover one wall
[tex]\frac{(1/4)}{(1/3)}=\frac{x}{1}\\\\x=\frac{1}{4} :\frac{1}{3}\\\\x=\frac{3}{4}\ gal[/tex]
What is the equation of the line that passes through the point (-1, -3) and has a slope of -5?
answers y = -5x -16
y = -5x -8
y = -5x +8
y = -5x + 16
Answer:
y = -5x -8
Explanation:
Find b in equation y = mx + b
Insert numbers to find b
-3 = -5· -1 + b
Step 1: Simplify both sides of the equation.
−3=(−5)(−1)+b
−3=5+b
−3=b+5
Step 2: Flip the equation.
b+5=−3
Step 3: Subtract 5 from both sides.
b+5−5=−3−5
b=−8
Insert into equation
y = -5x - 8
o find the minimum value of the quadratic expression −4x2+8x−25,
−
4
x
2
+
8
x
−
25
,
Marla used the following steps to complete the square:
Step 1: −4(x2+8x)−25
−
4
(
x
2
+
8
x
)
−
25
Step 2: −4(x2+8x+16−16)−25
−
4
(
x
2
+
8
x
+
16
−
16
)
−
25
Step 3: −4(x2+8x+16)+64−25
−
4
(
x
2
+
8
x
+
16
)
+
64
−
25
Step 4: −4(x+4)2+39
−
4
(
x
+
4
)
2
+
39
Did Marla use the correct steps to complete the square?
Answer:
Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x
Step-by-step explanation:
we have
[tex]-4x^{2}+8x-25[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Find the vertex
step 1
Factor the leading coefficient -4
[tex]-4(x^{2}-2x)-25[/tex]
step 2
Complete the square
[tex]-4(x^{2}-2x+1-1)-25[/tex]
step 3
[tex]-4(x^{2}-2x+1)-25+4[/tex]
[tex]-4(x^{2}-2x+1)-21[/tex]
step 4
Rewrite as perfect squares
[tex]-4(x-1)^{2}-21[/tex]
the vertex is the point (1,-21)
so
The maximum value of the quadratic equation is (1,-21)
therefore
Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x
Marla correctly completed the square for the expression −4x2+8x−25, arriving at the simplified form −4(x+4)2 + 39 to find the minimum value.
Explanation:To find the minimum value of the quadratic expression −4x2+8x−25, Marla completed the square. Her steps are as follows:
Factor out the coefficient of x2: −4(x2+∼2x−∼) -25Add and subtract (b/2a)2 inside the parentheses: −4(x2+8x+16−16) −25Combine the added 16 with the −4 outside and subtract from −25: −4(x2+8x+16) + 64 −25Factor the perfect square trinomial and simplify: −4(x+4)2 + 39
Marla used the correct steps to complete the square, which simplifies to −4(x+4)2 + 39.