1. The slope of the line is 3.
2. The direct variation equation is y = 3x
3. The equation in slope-intercept form is:y = 4
4. The equation in slope-intercept form is y = 2/3x + 1.
5. The equation = −2/3 − 1
6. The equation of the parallel line is y = 5x - 11.
1. Slope of the line:
The slope (m) of the line passing through (-1, 2) and (0, 5) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
m = (5 - 2) / (0 - (-1))
m = 3 / 1
m = 3
Therefore, the slope of the line is 3.
2. Direct variation equation:
Since y varies directly with x, we can write their relationship as y = kx, where k is the constant of proportionality. We can find k using the given information:
y = 15 when x = 5
15 = k * 5
k = 3
Therefore, the direct variation equation is y = 3x
When x = 9, y = 3 * 9 = 27.
3. Equation in slope-intercept form: First, calculate the slope using the same formula as in question 1:
m = (4 - 4) / (1 - (-3))
m = 0 / 4
m = 0
Since the slope is 0, the line is horizontal. The equation in slope-intercept form is:
y = 4 (constant y-intercept because it passes through (1, 4))
4. Equation in slope-intercept form using point-slope form:
The point-slope form equation is:
y - y1 = m(x - x1)
Plug in the given values:
y - (-1) = 2/3(x - (-3))
y + 1 = 2/3(x + 3)
3y + 3 = 2x + 6
3y = 2x + 3 (subtract 3 from both sides)
y = 2/3x + 1 (divide both sides by 3)
Therefore, the equation in slope-intercept form is y = 2/3x + 1.
5. Writing the equation in standard form:
The equation = −2/3 − 1 is already in standard form (ax + by = c), where a = -2/3, b = 0, and c = -1.
6. Equation of the parallel line:
Since the parallel line has the same slope (5) as the given line, its equation will be of the form y = 5x + b. To find b, plug the point (2, -1) into this equation:
-1 = 5(2) + b
-1 = 10 + b
b = -11
Therefore, the equation of the parallel line is y = 5x - 11.
An extra large pizza has 12 slices. If there are four people at they table and they each get two slices, how many slices are left?
Answer:
there should be 4 slices left
Hope This Helped
Step-by-step explanation:
Answer:
The most accurate answer is:
*4*
I hope I helped you!
Step-by-step explanation:
Alright, lets examine the problem; *12* slices of pizza are given. We also have *4* guests at the table, and each are given *2* slices. Lets use subtraction to solve: 12 - 2 - 2 - 2 - 2- the *2*'s equal the amount of pizzas given, and the *12* represents our amount of slices of pizza. We also gave 4 people 2 slices, which is why we have *4* *2*'s
[SOLVE]
12 - 2 - 2 - 2 - 2 = 4
which of the following names a diameter of circle A?
Answer:
BC
Step-by-step explanation:
The diameter is the distance across the circle, going through the center
BC or CB is the diameter
PLEASE HELP A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled by this equation:an=500+(k-1)10 Use summation notation to model and evaluate the sales for the first ten years. Explain your steps.
Answer: 131,400$
Step-by-step explanation:
The sale for first month is $500.
The sale increases by $10 each month, as modelled by the equation:
a_k=500+(k-1)10
where, k = 1 (first month)
k = 2 (second month)
.... and so on.
we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)
Total sales = ∑ a_k
∑ a_k = ∑ (500+(k-1)10)
= 500k + ∑ (10k - 10)
= 500k + 10∑k - 10k
= 490k + 10∑k
= 490k + 10 {k*(k+1)/2}
= 490k + 5{k*(k+1)}
= 490k + 5k^2 + 5k
= 5k^2 + 495k
∴∑ a_k = 5k^2 + 495k
For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)
= 5*(120*120) + 495*120
= 72,000 + 59, 400
= 131,400$
Answer:
Distribute 10 to (k – 1) and simplify.
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used. The upper index is 10*12=120.
The values of the summations are 58,800 + 72,600. So, the total sales is $131,400.
Step-by-step explanation:
Jayla buys and sells vintage clothing. She bought 2 blouses for $25 each and later sold them for $38 each. She bought 3 skirts for $15 each and later sold them for $26 each. She bought 5 pairs of pants for $30 each and later sold them for $65 each. Jayla's expenses for purchasing each items were: Her revenue: Total profit:
Answer:
Expenses for purchasing is $245 ,Revenue $479 and Total profit $ 234
Step-by-step explanation:
Cost of two blouses = 2× 25 = $50
Revenue from blouses = 2× 38 = $76
Profit of blouses = 76- 50 = $26
Similarly cost of 3 skirts = 3×15 = $45
Revenue from Skirts = 3×26 =$78
Profit from skirts = 78-45 =$33
Now cost price of pants = 5×30 =$150
Revenue from Pants = 5×65 =$325
Profit from pants = 325-150 = $175
So Jayla's expenses for purchasing = 50+45+150
= $245
Revenue = 76+78+325
= $479
Total Profit = 479 -245
= $234
Jayla's total expenses were $245, she made $479 in revenue through sales, making her resultant profit $234. This is calculated by subtracting the total expenses from the total revenue.
Explanation:The subject of this problem deals with the concepts of expenses, revenues, and profit in a small business setting. Jayla spent $50 on the blouses (2 x $25), $45 on the skirts (3 x $15), and $150 on the pants (5 x $30), adding up to a total expense of $245. She sold these items for total revenues of $76 for the blouses (2 x $38), $78 for the skirts (3 x $26), and $325 for the pants (5 x $65), giving her a total revenue of $479. The total profit can be calculated by subtracting the total expenses from the total revenue, and therefore, Jayla made a profit of $234 ($479 - $245).
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Will all problems adding positive radicals have a rational solution?
Answer:
No
Step-by-step explanation:
Let us consider two positive radicals first,
[tex]\sqrt{3} , \sqrt{5}[/tex]
We know that [tex]\sqrt{3}[/tex] is an irrational number and [tex]\sqrt{5}[/tex] is also an irrational number.
So the sum of two positive radicals does not always have a rational solution.
There are examples when the some of adding positive radicals can get us a rational solution. For example,
[tex]\sqrt{4}+\sqrt{4} =4[/tex]
So if the radicand is a perfect square then the solution is rational.
A parabola has x-int of (-8,0) and (4,0) and a minimum value of -9 in intercept form
Answer:
The function is 1/4x^2 + x - 8
Step-by-step explanation:
In Factor form the function is
a(x + 8)(x - 4) where a is a constant to be found.
= a( x^2 + 4x - 32) Note the coefficient of x is positive because the function has a minimum value.
The line of symmetry is x = (-8+4)/2 = -2.
So the minimum value will be the value of f(x) when x = -2, so we have the equation
a(-2+8)(-2-4) = -9
-36a = -9
a = 1/4.
Nala is escaping from the dragon's lair! She is running toward the entrance of the lair at a speed of 9.29.2 meters per second. The entrance is 180180 meters away. The distance dd between Nala and the entrance of the lair is a function of tt, the time in seconds since Nala began running. Write the function's formula.
Answer: Our function will be
[tex]d=180-9.2t[/tex]
Step-by-step explanation:
Since we have given that
Distance of the entrance = 180 meters
Speed of Nala who is running towards the entrance of the lair = 9.2
As we know the "Distance-Speed formula":
[tex]Time=\frac{Distance}{Speed}\\\\t=\frac{180}{9.2}\\\\t=19.565\\\\t=19.57\ seconds[/tex]
So, our required function will be
[tex]d=180-9.2t[/tex]
As we increase the time distance get reduced from 180 which is the distance of the entrance .
Hence, our function will be
[tex]d=180-9.2t[/tex]
You are in charge of buying the hamburgers and chicken for a party. The hamburgers cost $2 per pound and the chicken is $3 per pound, You have $60 to spend.
Which of the following is a trinomial with a constant term?
A. x3 + 12x2 + x
B. y - 426
C. -x + 42
D. x + 7y + 6
E. x7 - 6
F. y13
Choice A is a trinomial, but it doesn't have a constant term
Choice D is the only other trinomial. This has a constant term, which is 6. The constant is the term without any variables attached to it.
Answer: Choice D
Answer: D. [tex]x+7y+6[/tex]
Step-by-step explanation:
We know that a trinomial is a polynomial with three terms.
From all the given options, only option A. [tex]x^3+12x^2+x[/tex] and option D. [tex]x+7y+6[/tex] are trinomials having three terms .
But option A [tex]x^3+12x^2+x[/tex] does not have any constant term .
On the other hand option D. [tex]x+7y+6[/tex] has a constant term of 6.
Therefore, the option D. [tex]x+7y+6[/tex] represents a trinomial with a constant term.
I need help ASAP PLEASE SOMEONE 100 POINTS IF CORRECT
Answer:
Step-by-step explanation:
84-90=90-96=96-102=102-108=-6
its a sequence where A(1)=84 n A(n+1)-A(n)=6
A(n)=84+(n-1)*6; n=1,2,3,4,5
Answer:
f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...
Step-by-step explanation:
Given 84, 90, 96, 102, 108, ...
the numbers are a sequence with 84 as the initial value and in increment of 6s. So the function can be written as:
f(x) = 84 + 6x where x=0, 1, 2, 3, 4, ...
Alison and Justins father donated $3 every lap they swam in a swim-a-thon.Alison swam 21 laps and justin swam 15 laps.Use the distributive property tp find out the amount of money their father donated/
Answer:
The total amount of money Alison and Justins father donated be $108 .
Step-by-step explanation:
Distributive property.
Let a, b and c be any real numbers.
Thus
a.( b + c ) = a.b + a.c
This is distributive property.
As given
Alison and Justins father donated $3 every lap they swam in a swim-a-thon.
Alison swam 21 laps and justin swam 15 laps.
Total amount of money Alison and Justins father donated = Cost of each lap (Number of laps of Alison father + Number of laps of Justins father )
As
Cost of each lap = $3
Number of laps of Alison father = 21 laps
Number of laps of Justins father = 15 laps
Putting in the above
Total amount of money Alison and Justins father donated = 3(21 + 15)
= 3 × 21 + 3 × 15
= 63 + 45
= $ 108
Therefore the total amount of money Alison and Justins father donated be $108 .
Write the linear equation in slope-intercept form: 5x - y = -17
a: y = -5x + 17
b: x = -1/5y - 17/5
c: y = 5x - 17
d: -5x - 17
In order to express the equation 5x - y = -17 in slope-intercept form (y = mx + b), we need to solve for y. After rearranging, it turns out the correct equation in slope-intercept form is y = 5x + 17.
Explanation:To write the equation 5x - y = -17 in slope-intercept form, we first need to solve the equation for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.
Let's rearrange the given equation: Start by adding 'y' to both sides to get 5x = y - 17. Add 17 to both sides, you will get y = 5x + 17. So, the correct answer is: y = 5x + 17. This aligns with option c.
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Comparing this with the answer choices, the correct option is c: y = 5x - 17.
To write the linear equation 5x - y = -17 in slope-intercept form, you must solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equation:
Add y to both sides to isolate the y-variable on one side: 5x - y + y = -17 + y, which simplifies to 5x = y - 17.Now, subtract 17 from both sides to solve for y: y - 17 = 5x - 17.The equation in slope-intercept form is y = 5x - 17.Comparing this with the answer choices, the correct option is c: y = 5x - 17.
the perimeter of a rectangle of a rectangular field is 76 ft. The length is 12 ft longer than the width. Find the fields dimensions
Answer:
The length is 25 and the width is 13. (25,13)
Step-by-step explanation:
the formula for perimeter is l+l+w+w=76 or 2l+2w=76
and since we know that the length is 12 more than the width, we can create an equation. w+12=l (-l+w=-12)
solve with elimination method:
2l+2w=76
2(-l+w=-12)
2l+2w=76
-2l+2w=-24
4w=52
w=13
Now that we know w=13, add 12 to the width and you get your width (25)
You can check this with the formula 2l+2w=76
2(25)+2(13)=76
50+26=76
and
w+12=l
13+12=25
Hope this helps!
The dimensions of the field will be 13 ft and 25ft.
The perimeter of a rectangle is given as: = 2l + 2w
Length = w + 12Width = wTherefore, the perimeter will be:
2(w + 12) + 2w = 76
2w + 24 + 2w = 76
4w = 76 - 24.
4w = 52
w = 52/4.
w = 13
Width = 13 ft
Length will be: = w + 12 = 13 + 12 = 25
Therefore, the dimensions of the field will be 13 ft and 25ft.
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Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room.
Step-by-step explanation:
10 x 4 = 40$
Samuel earned $6.67 per hour.
Explanation:To calculate how much money Samuel earned per hour, we need to find the total number of hours he spent both mowing the lawn and cleaning his room.
Samuel spent 4 hours mowing the lawn and 2 hours cleaning his room, for a total of 6 hours.
He earned $40 for this time period.
To find how much he earned per hour, we divide the total amount earned by the total number of hours:
$40 divided by 6 hours = $6.67 per hour.
Therefore, Samuel earned $6.67 per hour.
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Simplify. -6i(5+3i) Enter your answer in standard form, in the box
Answer:
Pretty sure the answer is 18-30i
Step-by-step explanation:
-30i - 18i^2
-30i - 18 x (-1)
-30i +18
The expression -6i(5+3i) simplifies to 18 - 30i in standard form of a complex number.
Explanation:The problem asks us to simplify the expression -6i(5+3i). To simplify this, we multiply the complex number (-6i) with the complex number in the parenthesis. This results in (-6i * 5) + (-6i * 3i) which transforms into -30i - 18i^2. Since i^2 is -1, we can simplify further to -30i + 18. So the simplified form in standard form is 18 - 30i.
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The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Subract and simplify.
Answer: C
Step-by-step explanation:
[tex]\dfrac{x+1}{x-5} - \dfrac{x-2}{x+3}[/tex]
= [tex]\dfrac{x+1}{x-5}(\dfrac{x+3}{x+3}) - \dfrac{x-2}{x+3}(\dfrac{x-5}{x-5})[/tex]
= [tex]\dfrac{x^{2}+4x+3}{(x-5)(x+3)} - \dfrac{x^{2}-7x+10}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{x^{2}+4x+3-(x^{2}-7x+10)}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{11x-7}{(x-5)(x+3)}[/tex]
Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x
The correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].
The correct option is (a).
To use the distributive property to simplify the expression (9(x+3) + 15x), we need to distribute the terms outside the parentheses to each term inside the parentheses.
The given expression is [tex]\(9(x+3) + 15x\)[/tex].
1. Distribute 9 to (x) and (3):
[tex]\[ 9(x+3) = 9 \times x + 9 \times 3 \][/tex]
2. Distribute 15 to (x):
[tex]\[ 15x \][/tex]
So, after using the distributive property, the expression becomes:
[tex]\[ 9 \cdot x + 9 \cdot 3 + 15x \][/tex]
Now, let's compare this with the options:
a. [tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex] - This matches our result.
b. [tex]\(9(x+3+15)x\)[/tex] - This option seems incorrect as it doesn't distribute 9 to each term inside the parentheses correctly.
c. [tex]\(9:x+3+15x\)[/tex] - This option doesn't seem to use the distributive property correctly.
d. [tex]\(9x+9 \cdot 3+9 \cdot 15x\)[/tex] - This option distributes 9 correctly but includes an extra term (9x) that doesn't appear in the original expression.
Therefore, the correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].
Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x
a.9· x+9· 3+15x
b.9(x+3+15)x
c.9: x+3+15x
d.9 x+9· 3+9· 15x
Answer:
24x + 15
Step-by-step explanation:
9(x+3)+15x
Use the distributive property.
9*x +9*3 + 15x
9x + 15 + 15x
Combine the like terms.
24x + 15
Which expression are a factor of 36abc-9bcd+24abc
Justin's rice ball recipe uses 100100 grams of rice to make 11 rice ball. Justin has 700700 grams of rice. How many rice balls can Justin make with 700700 grams of rice?
Use your knowledge of insulators and conductors to explain why
cooking pots are usually made of metal with some sort of plastic
handle
Cooking pots are made of metal because metals are good conductors of heat. Plastic is an insulator that is slow at conducting heat. That is why an insulator is used so that we don't burn ourselves.
The cooking pots are good conductor of electricity and sort of plastic
handle are insulator for safety purpose.
Conductors are materials that permit electrons to flow freely from particle to particle. Conductors allow for charge transfer through the free movement of electrons. Conductors are good conduction of electricity.Insulators are materials that does not allow the free flow of electrons from atom to atom and molecule to molecule.Insulator are bad conductor of electricity.Learn more:
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The function h=-16t^2 +1700 gives you the height h, of an object in feet, at t seconds. How long will it take the object to hit the ground ?Round to the nearest hundresth of a second?
Answer:
The object will hit the ground after 10.308 seconds.
Step-by-step explanation:
h(t) = -16t² + 1700
If you graphed this function, the object would be shown hitting the ground when it crosses the x-axis, in other words, when h = 0. So, to find the answer, just set h(t) equal to 0 and solve.
-16t² + 1700 = 0 Plug this into a calculator if you have one.
t = -10.308 and t = 10.308
Since time can't be negative, your answer will be the positive value, 10.308.
The object, described by the equation h(t) = -16t^2 + 1700, will hit the ground after around 10.308 seconds. This is determined by setting h(t) to 0, yielding a valid, positive solution.
The provided equation h(t) = -16t^2 + 1700 describes the height (h) of an object as a function of time (t), taking into account gravitational acceleration. To determine when the object hits the ground, set h(t) to 0 and solve for t:
-16t^2 + 1700 = 0
Solving this equation using the quadratic formula or factoring yields two solutions: t = -10.308 and t = 10.308. However, time cannot be negative in this context, so the only valid solution is t = 10.308.
Consequently, the object will hit the ground after approximately 10.308 seconds. This conclusion is reached by identifying the point where the height function intersects the x-axis, representing ground level. The positive value for t ensures a meaningful interpretation in the temporal context, indicating the time elapsed until the object reaches the ground.
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Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly get in return?
PLEASE HELPPPPPPPPPP!!!!!!!!!
Answer:
11a^2b^8
Step-by-step explanation:
Rule 1: The coefficient (121 in this case) has it's square root taken to derive the side.
Rule 2: If a variable with a power is part of the area of a square, then just divide the power by two
The square root of 121 = 11
The square root of a^4 = a^(4/2) = a^2
The square root of b^16 = b^(16/2) = b^8
A spinner divided into four equal parts, A, B, C, and D, is spun, then is followed by a roll of a standard six-sided die.
1. How many total outcomes are possible?
2. How many outcomes have an ‘A’ and an odd number?
3. What is the probability of getting an ‘A’? Getting an odd number? Getting an ‘A’ and an odd number?
P(A)= P(odd)= P(A and odd)=
4. What is the probability of getting an odd number, given an ‘A’ has already been spun?
P(odd│A)=
5. Since P(odd│A)=P(odd), are the events independent or not independent?
6. What is the probability of getting an ‘A’ or an odd number?
P(A or odd)=
Answer:
1. 24 outcomes
2. 3
3. A= 1/4
Odd = 1/2 (reduced from 12/24 chances)
A/Odd = 1/8
4. 50% the letter chosen doesn't affect the outcome of the roll of the dice
5. i believe they are independent
6. 1/8
Hope that helps!
Answer:
3/4
Step-by-step explanation:
Jack can run a mile in 9, 1/3 minutes. How long will it take for him to run 3, 1/2 miles? What is the answer
Answer:
32, 2/3 minutes.
Step-by-step explanation:
Divide the original mile time by two to get what half a mile would be. Multiply the original mile time by 3, since he is running 3 miles. Add 4 and 2/3, half of a mile time, to that and you're left with 32 minutes and 40 seconds.
HEEEEEEEEEELLLLLLPPPPPPPPPPPPPPPPP ME !
Answer:
B.) 72
Step-by-step explanation:
Because when there is one cup there are 8 fluid ounces, when there are 9 cups there are 9 times more fluid ounces.
Hello :3
To get your answer we would need to multiply.
So, if there's 8 fl. oz. in 1 cup then we need to multiply 8 by 4.
8 x 4 = 32
Your answer would be 32 fl. oz.
Hope This Helps!
Cupkake~
Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away. She is _____ percent closer to the school.
Answer:
Tiffany is 34% closer to the school.
Step-by-step explanation:
Given the statement: Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away.
She lived away from the school = 15 km
as, she moved 9.9 km away.
Now, the distance closer to school from where she lived = 15 -9.9 = 5.1 km
To, find how much percent she is closer to school.
Percent states that a number or ratio expressed as a fraction of 100.
[tex]percent = \frac{5.1}{15} \times 100[/tex] = [tex]\frac{51 \times 100}{150} = \frac{51 \times 10}{15}[/tex]
Simplify:
percent closer to school = 34%
Therefore, she is 34% closer to the school.
Sweet t saved 20% of the total cost of the green-eyed fleas new album let three be fleas on the earth .If the regular price is $30 how much did sweet t save?
Answer:
$6 Sweet t saved on green-eyed fleas new album .
Step-by-step explanation:
As given
Sweet t saved 20% of the total cost of the green-eyed fleas new album .
.If the regular price is $30.
20% is written in the decimal form.
[tex]= \frac{20}{100}[/tex]
= 0.20
Thus
Sweet t saved on green-eyed fleas new album = 0.20 × 30
= $6
Therefore $6 Sweet t saved on green-eyed fleas new album .
Algebra 1 A Semester Exam
30. Write y=-3/4x-6 in standard form using integers. (1 point)
Final answer:
To convert y = -3/4x - 6 to standard form with integers, multiply by 4 to remove the fraction and then arrange the equation as 3x + 4y = -24.
Explanation:
To write the equation y = -3/4x - 6 in standard form using integers, we need to rearrange the terms so that the x and y terms are on the left side of the equation and the constant is on the right side. Moreover, in standard form, the coefficients should be integers. The standard form is typically expressed as Ax + By = C.
Starting with the given equation:
y = -3/4x - 6
Multiply each term by 4 to remove the fraction:
4y = -3x - 24
Now, we need to move the x term to the left side of the equation:
3x + 4y = -24
This is the standard form of the equation, and all the coefficients are integers.