A line contains L(-4, -4) and M(2, 3). Line q is in the same coordinate plane but does not intersect IM. Line q contains point N. (Can someone please look at the picture and help me)
Answers
The line q passes through (2, 0) and (-7, -4)
How to find line LM?If line Q does not intersect the line LM, then these lines are parallel, thus, have the same slope.
The slope of line LM is given by:
s = (3 + 4)/(2 + 4) = 7/6
Now we know that the line Q contains point N (2, 0) ( i will assume is this because in the image the points don't have the correspondent names).
Then the line also passes through another point (a, b) such that:
s = (0 - b)/(2 - a) = 7/6
Then:
b = -7
a = -4
The line q passes through (2, 0) and (-7, -4)
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Related Questions
marking brainliest if a/2-3/2+22 what is A
Answers
The value of a cannot be determined because the expression is not an equation
How to determine the value of a?The expression is given as:
a/2 - 3/2 + 22
The above is an expression, and not an equation
For the value of the variable a to be solved, the expression must be an equation
Equations are mathematical expressions that are represented by the equal to or equality sign i.e =
Examples of equations are:
a + b = c
y = mx + c
Ax + By = C
y = ax^2 + bx + c
y = x
Hence, the value of a cannot be determined because the expression is not an equation
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Find the value of x in each case 40 points!!!
Answers
The values of x associated with each case are listed below:
1911How to find the variables behind angles in a geometric systemHerein we find two cases of geometric systems generated by two parallel lines and auxiliary line segments, wherein we must use the concept of supplementary angles and triangle properties to determine the value behind angles. Now we proceed to determine the value of the variable x for each case:
Case 1
m ∠ DCA = m ∠ CBE = 3 · x Alternate internal angles between parallel linesm ∠ CAD + m ∠ ADC + m ∠ DCA = 180° Internal angles in trianglesm ∠ ADC = 180° - 95° = 85° Supplementary angles.2 · x + 85° + 3 · x = 180° Steps 1 & 35 · x = 95° Algebrax = 19 Algebra / ResultCase 2
m ∠ BFE = 180° - 147° = 33° Supplementary anglesm ∠ FEB = 180° - 4 · x Supplementary anglesm ∠ BFE + m ∠ FEB + m ∠ EBF = 180° Internal angles in triangles33° + (180° - 4 · x) + x = 180° Steps 1 & 23 · x = 33° Algebrax = 11 Algebra / ResultTo learn more on triangles: https://brainly.com/question/2269348
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You can find the equation of a line through two points even if one point is not the y -intercept. Find the slope m of the line passing through the two points.Using either point, substitute for x, y , and m into y=m x+b . Solve for b and rewrite y=m x+b for the values of m and b . Write an equation in slope-intercept form for the line passing through each pair of points.
c. (-2,17) and (2,1)
Answers
1 = -4(2) + 9 is an equation in slope-intercept form for the line passing through points (-2,17) and (2,1)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We have been asked to write an equation in slope-intercept form for the line passing through (-2,17) and (2,1)
First we will find the slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-2,17) and (2,1)
⇒ m = [tex]\frac{1- 17}{2 - (-2)}[/tex]
⇒ m = [tex]\frac{-16}{4}[/tex]
⇒ m = -4
We know that the equation for slope(m) and y - intercept(b) of a line is given by :
y = mx + b
Here lets take equation 1 = -4(2) + b .Here x and y is substituted with the second two points.
⇒ 1 = -4(2) + b
⇒ 1 = -8 + b
⇒ b = 1 +8
⇒ b = 9
The equation in the slope intercept is as follows:-
1 = -4(2) + 9
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2. Open Response The table shows the amount
spent on tomatoes at three different stands
at a farmer's market. Which stand sold their
tomatoes at the least expensive price per
pound, and what is that price? Round to the
nearest cent, if necessary. (Lesson 1)
Stand Weight (lb) Cost ($)
A
2.00
B
C
100
NATA/W
3.45
14.85
Answers
Stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.
The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have to determine the price of sold tomatoes at the least expensive price per pound.
The price of sold tomatoes at stand A:
⇒ 2/(3/4) = 2/0.75 = 2.67 per pound.
The price of sold tomatoes at stand B:
⇒ 3.45/(5/4) = 3.45/1.25 = 2.76 per pound.
The price of sold tomatoes at stand C:
⇒ 14.85/(11/2) = 14.85/5.5= 2.70 per pound.
Here is the least expensive price per pound at stand C.
Hence, the stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.
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Peter and Patty are very competitive and they both are saving money in their piggy banks. Peter has $90 and
Patty has $120. Patty's mom gives her a bonus of 20% of what she already has and Patty adds it to her piggy
bank. Peter's dad tells him that he will give him a bonus so that Peter has the same total as Patty. What percent of
Peter's money must the bonus from his dad be?
Answers
that would mean peter’s dad would need to give him $54 which is 60% of $90
so the answer would be 60%
Find the coordinates of the centroid of the triangle with the given vertices. X(5,7), Y(9,-3), Z(13,2)
Answers
The coordinates of the centroid of the triangle with the given vertices X (5, 7), Y (9, -3), Z (13, 2) is (13 - 4,2) or (9, 2).
What is meant by the centroid of a triangle?The centroid is the object's center point. The centroid of a triangle is the point where the three medians of the triangle intersect. It is also defined as the point at which all three medians intersect. A median line connects the midpoint of a side and the opposite vertex of a triangle.
The midpoint D of XY is [tex]$\left(\frac{5+9}{2}, \frac{7-3}{2}\right)$[/tex] or (7, 2).
Note that DZ is a line that connects the vertex Z and D, the midpoint of XY. The distance from D(7, 2) to Z(13, 2) is 13 - 7 or 6 units.
If P is the centroid of the triangle XYZ, then [tex]$P Z=\frac{2}{3} D Z$[/tex].
So, the centroid is [tex]$\frac{2}{3}(6)$[/tex] or 4 units to the left of Z. The coordinates of the centroid (P) are (13 - 4, 2) or (9, 2).
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16-x=x-16
I don't know what to do first for this equation
Answers
Answer:
16
Step-by-step explanation:
the first thing is to rearrange terms
Solve each system by elimination.
3x + 2 =10 , 6 +4y = 15
Answers
By elimination, the system of equations, 3x + 2y = 10 , 6x + 4y = 15, has no solutions.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
First, multiply the first equation by 2.
3x + 2y = 10 ⇒ 6x + 4y = 20 (equation 1)
6x + 4y = 15 (equation 2)
Since the new equation of equation 1 has the same coefficients with those in equation 2, but different constants, then the two lines are in parallel.
Hence, the system of equations has no solutions.
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solve the equation and show the process
2 + 2 x 45/5
Answers
Answer:
20
Step-by-step explanation:
2+2x45\5
=2+90/5
=2+18
=20
A school has a total of 900 pupils .400 pupils are boys and the rest of the girls.find the ratio of boys to girls .give the ratio in the simplest form
Answers
If a school has a total of 900 pupils and 400 pupils are boys and the rest are girls, then the ratio of the boys to the girls in the simplest form is 4:5.
A ratio in mathematics can be defined as the number of times a number contains another number or is contained in another number to express the connection between two or more things in quantity or size.
To find the ratio of boys to girls, first, we calculate the number of girls in the school. The number of girls can be found by subtracting the total number of pupils which is 900 from the number of boys which is 400.
Hence,
number of pupils that are girls = total number of pupils - number of boys
number of pupils that are girls = 900 - 400
number of pupils that are girls = 500
Hence the ratio of boys to girls can be given as,
400 : 500
Simplifying,
400/100 : 500/100
4:5
Hence, the simplest ratio of boys to girls is 4:5.
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You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?c. Explain the difference between an explicit formula and a recursive formula. Use your formula from part (a) as part of your explanation.
Answers
Money received in tenth month: $104
Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Money received in first four months: $50, $52, $55, %59.To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
(b) Difference between explicit formula and recursive formula of an arithmetic progression:
The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is [tex]a_n=a_{n-1}+d[/tex]. A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation [tex]a_n = a_1 + (n-1)d[/tex].To learn more about arithmetic Progressions, refer to the link: https://brainly.com/question/6561461
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More math help please its urgent
Answers
Answer:
LMK and QPM
Step-by-step explanation:
When two lines are crossed by another line (called the transversal), the angles in matching corners are called corresponding angles.
John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
(lol please help, I don't know how to format this-)
Answers
Based on the graph (see attachment), John's speed on each section of the walk are as follows:
At the first interval, John's speed is equal to 4 km/h.At the second interval, John's speed is equal to 0 km/h.At the third interval, John's speed is equal to 1.5 km/h.What is speed?Speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured as meter per seconds.
What is distance?Distance can be defined as the amount of ground covered (travelled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.
How to calculate the speed?Mathematically, speed can be calculated by using this formula;
Speed = distance/time
Based on the graph (see attachment), John's speed on each section of the walk can be calculated as follows.
For the first interval, we have:
Speed = 6/1.5
Speed = 4 km/h.
For the first interval, we have:
Speed = 6/1.5
Speed = 4 km/h.
For the second interval, we have:
Speed = 6/0
Speed = 0 km/h.
For the third interval, we have:
Speed = 6/4
Speed = 1.5 km/h.
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Which linear equation has no solution? clear submit 23(9x 6)=6x 4 5x 12=5x−7 4x 7=3x 7 −3(2x−5)=15−6x
Answers
The linear equation which has no solution is 5x+12=5x-7
Given set of linear equations are:
23(9x+6)=6x+4, 5x+12=5x-7, 4x+7=3x+7, -3(2x-5)=15-6x.
We try to solve each equations one-by-one.
Consider the first equation:
23(9x+6)=6x+4
⇒207x+138 = 6x+4
⇒201x = -134
⇒ x =-134/201.
So this linear equation has a solution.
Now consider the second linear equation:
5x+12=5x-7
⇒12 = -7, which has no meaning.
Therefore, this linear equation has no solution.
Now consider 3rd linear equation:
4x+7=3x+7
⇒x = 0
It has a solution.
Consider the 4th linear equation:
-3(2x-5)=15-6x.
⇒ -6x+15=15-6x
⇒ 0=0
In this case, any value for x is a solution. So there are infinitely many solutions.
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Write 35 - 9 as the product of the GCF of 35 and 9 and another sum. Make sure you check your work.
Answers
Answer:
Step-by-step explanation:
Assume our initial amount is $1000, the rate is 5% and it will only compound once per year. Our equation would look something like this:
Answers
The amount of money available after x number of years is given by y = 1000(1.05)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the amount of money after x years. Assume our initial amount is $1000, the rate is 5% (0.05) and it will only compound once per year. The equation is given by:
y = 1000(1 + 0.05)ˣ
y = 1000(1.05)ˣ
The amount of money available after x number of years is given by y = 1000(1.05)ˣ
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i need help bad because my teacher didn't even teach this to my class and make sure its correct
Answers
Based on the information, it can be inferred that the number that is the change in height of the elevator is 12 feet.
How to complete the table?To complete the table we must take into account the height of the elevator at a given time of seconds. Additionally, we must take into account that the elevator goes down 12 ft every second. So the table would look like this:
12 × 3 = 36180 - 36 = 14412 × 6 = 72180 - 72 = 10812 × 9 = 108180 - 108 = 72What is the height of the basement with respect to the first floor?
To calculate the height of the basement with respect to the first floor, we must take into account the following information:
Every second the elevator descends 12ft.The elevator takes 4 seconds to go down from the first floor to the basement.To calculate this height we must multiply the time it takes for the elevator to go down to the basement by the distance it travels each second.
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1) A lunch service takes 3 ½ hours to complete. If the chef is getting pains $24.80, per hour, what is the total amount earned?
Answers
Answer:
The answer is $86.80. The lunch service gains $86.80 in 3 1/2 hours if they get $24.80 per hour.
Step-by-step explanation:
You have to multiply how much they earn per hour, $24.80, by the number of hours they work, 3 1/2. $24.80 times 3 1/2 equals 86.80 so the lunch service earns $86.80 in 3 1/2 hours.
Hope this helps!
if jimmy has 99 cups of cofe and drinks 50 how many does jimmy have
Answers
Answer:
jimmy
Step-by-step explanation:
ALGEBRA Which is a factor of x²+19 x-42 ?
F x+14
G x+2
H x-2
J x-14
Answers
The factors of x²+19x-42 are (H) (x-2).
What is factorization?Factorization is the process of reducing a quadratic equation's bracket rather than expanding the bracket and converting the equation to a product of factors that cannot be reduced further. Consider factoring (x2+5x+6) to (x+2) (x+3). In this case, (x+2) (x+3) is the factorization of a polynomial (x2+5x+6).To find the factors:
x²+19x-42x²+x(21 - 2)-42x² + 21x - 2x - 42x(x + 21) - 2(x + 21)Factors are: (x-2) and (x+21)
Therefore, factors of x²+19x-42 are (H) (x-2).
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Find the sum of -4x^{2}-3x-3−4x
2
−3x−3 and -4x^{2}-9x−4x
2
−9x.
Answers
The sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex].
We have two expressions.
We have to add them.
What is Expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it.
According to the question -
f(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex]
g(x) = [tex]-4x^{2} -9x -4x[/tex]
Now -
h(x) = f(x) + g(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex] + ( [tex]-4x^{2} -9x -4x[/tex])
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
Hence, the sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
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Sarah works as a nanny and charges different rates for working during the week and the weekend. One week, she earned 902.50 working 45 hours, of which 5 hours were during the weekend. The following week she earned 1045 working 50 hours, of which 10 hours were during the weekend. What does Sarah charge per hour, in dollars, for working during the week?
Answers
Sarah's charges per hour for working during the week will be $9.5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.
Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be
45x + 5y = 902.5 ...1
50x + 10y = 1045
25x + 5y = 522.5 ...2
Subtract equation 2 from equation 1, then we have
45x - 25x = 902.5 - 522.5
20x = 380
x = 19
And the value of y will be
25 (19) + 5y = 522.5
475 + 5y = 522.5
5y = 47.5
y = 9.5
Sarah's charges per hour for working during the week will be $9.5.
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The population of Smalltown was 3,187 in 2016. In 2017, 148 more people moved to Smalltown. In 2018, 219 more people moved to Smalltown. What was the population of Smalltown in 2018
Answers
The population of Smalltown in 2018, using the mathematical operation of addition, was 3,554.
What is an addition?An addition is one of the basic mathematical operations involving combining two or more numbers or values to form a single value.
Additions are used to find the sum or total of a group of numbers.
Data and Calculations:2016 population of Smalltown = 3,187
2017 addition to the population of Smalltown = 148
The total population of Smalltown in 2017 = 3,335 (3,187 + 148)
2018 addition to the population of Smalltown = 219
The total population of Smalltown in 2018 = 3,554 (3,335 + 219)
Thus, in 2018, the total population of Smalltown was 3,554, 219 more than the population in 2017.
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Find the value of y.
(14y-4)
(3x + 11)
(x+21)
Answers
The simplified value of y in the equation is x = 38 + -3.5y
Simplifying
[tex](14y + -4) + (3x + 11) + (x + 21) = 180[/tex]
Reorder the terms:
[tex](-4 + 14y) + (3x + 11) + (x + 21) = 180[/tex]
Remove parenthesis around (-4 + 14y)
[tex]-4 + 14y + (3x + 11) + (x + 21) = 180[/tex]
Reorder the terms:
[tex]-4 + 14y + (11 + 3x) + (x + 21) = 180[/tex]
Remove parenthesis around (11 + 3x)
[tex]-4 + 14y + 11 + 3x + (x + 21) = 180[/tex]
Reorder the terms:
[tex]-4 + 14y + 11 + 3x + (21 + x) = 180[/tex]
Remove parenthesis around (21 + x)
[tex]-4 + 14y + 11 + 3x + 21 + x = 180[/tex]
Reorder the terms:
[tex]-4 + 11 + 21 + 3x + x + 14y = 180[/tex]
Combine like terms: -4 + 11 = 7
[tex]7 + 21 + 3x + x + 14y = 180[/tex]
Combine like terms: 7 + 21 = 28
[tex]28 + 3x + x + 14y = 180[/tex]
Combine like terms: 3x + x = 4x
[tex]28 + 4x + 14y = 180[/tex]
Solving
[tex]28 + 4x + 14y = 180[/tex]
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-28' to each side of the equation.
[tex]28 + 4x + -28 + 14y = 180 + -28[/tex]
Reorder the terms:
[tex]28 + -28 + 4x + 14y = 180 + -28[/tex]
Combine like terms: 28 + -28 = 0
[tex]0 + 4x + 14y = 180 + -28\\4x + 14y = 180 + -28[/tex]
Combine like terms: 180 + -28 = 152
[tex]4x + 14y = 152[/tex]
Add '-14y' to each side of the equation.
[tex]4x + 14y + -14y = 152 + -14y[/tex]
Combine like terms: 14y + -14y = 0
[tex]4x + 0 = 152 + -14y\\4x = 152 + -14y[/tex]
Divide each side by '4'.
[tex]x = 38 + -3.5y[/tex]
Simplifying
[tex]x = 38 + -3.5y[/tex]
Therefore, we can simplify that the value of y can be expressed as x = 38 + -3.5y
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Evaluate each finite series for the specified number of terms. 1+2+4+ . . . . ; n=5
Answers
Solving the question with the help of geometrical progression, we get that the value of this finite series is 31.
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
As we know the formula for geometric progression is:
aₙ = a₁ r ⁿ⁻¹
Where , a₁ is the first term and r is the ratio , and n is the number of terms.
Here, the ratio is 4/2 = 2
Here, a₅ = 1 . 2⁵ ⁻ ¹ = 2⁴ = 16
a₄ = 1 . 2⁴ ⁻ ¹ = 2³ = 8
Now, We should calculate the value 1 + 2 + 4 + 8 + 16 = 31.
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Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm . The box must be 4cm high. What dimensions give the maximum volume?
a. How can you model the volume of the box with a quadratic function?
Answers
The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
Imagine you work for a packaging firm and are building a box with a 36 cm-long rectangular bottom. The box has to be 4 cm tall.
The perimeter is given as,
36 = 2 (L + W)
W = 18 - L
Then the volume is given as,
V = L x W x H
V = L x (18 - L) x 4
V = 72L - 4L²
For the maximum volume, V' = 0
V' = 0
72 - 8L = 0
8L = 72
L = 9
Then the width will be
W = 18 - 9
W = 9
The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².
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D Number of Sheets (x) Total Cost (y) 3 Cost of Stickers $10.25 $26.65 19
Answers
Answer: 5=10.25, 13=26.65, 19=38.95
Simplify each complex fraction.
1/1+ x / y
Answers
The simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to
(y)/ (y +x).
As given in the question,
Given complex fraction is equal to [tex]\frac{1}{1+\frac{x}{y} }[/tex]
Simplify the given complex fraction by taking the least common multiple of the denominator,
[tex]\frac{1}{1+\frac{x}{y} }\\\\\\= \frac{1}{\frac{y+x}{y} } \\\\\\=\frac{ (1)(y)}{y+ x} \\\\= \frac{y}{y+x}[/tex]
Therefore, the simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to (y)/ (y +x).
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Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Write a function f(x) that presents the total cost of the candy, where x is the weight of the less expensive candy.
Answers
Answer:
10 times 3.50 + 10x= f(x)
Step-by-step explanation:
35+28
f(x)= 63
The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Let x be the number of pounds of caramel candies and (10 - x) be the number of pounds of chocolate candies. Then the equation is given as,
f(x) = 2.80x + 3.50(10 - x)
f(x) = 2.80x + 35 - 3.50x
f(x) = 35 - 0.70x
The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.
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Point B is the center of a circle, tangent to the y -axis, and the coordinates of Point B are (3,1) . What is the area of the circle?
A π units ² D 6 π units²
B 3 π units² E 9 π units²
C 4 π units ²
Answers
The area of the circle with center located at Point B (3, 1) and tangent to the y-axis is 9π units^2. The answer is E.
The area of a circle is the area enclosed by the circle. It is the product of the square of the radius and the constant π. The Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Area of circle = πr^2
To know the radius of a circle given its center and tangent line to it, find the distance between the the center and the point of tangency. As the radius is the distance from the center of the circle to any point in the circumference of the circle
If the circle is tangent to y-axis, then the radius is the absolute value of the x-coordinate.
r = 3 units
Using the formula for the area of a circle:
Area of circle = πr^2
Area of circle = π(3 units)^2
Area of circle = 9π units^2
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