Answer:
3x² - 12x - 36
= 3(x - 6)(x + 2)
Step-by-step explanation:
3x² - 12x - 36 Find any common factor. All terms are divisible by 3.
= 3(x² - 4x - 12) Find two numbers that sum to -4 and whose product is -12. Replace -4 with these two numbers.
= 3(x² - 6x + 2x - 12) Group the terms splitting from the middle
= 3( (x² - 6x) + (2x - 12) ) Find the common factor in each group.
= 3( x(x - 6) + 2(x - 6) ) The groups have a common factor (x - 6).
= 3( (x - 6)(x + 2) ) Remove the extra brackets
= 3(x - 6)(x + 2) Fully factored
what is 4.14x10*9 in standard form
Answer:
372.6
Step-by-step explanation:
Tom is thinking of two numbers,a and b,where a is a positive and b is negative. write to inequalities that Tim can use to compare a and b
Explain
Final answer:
Two inequalities that Tim can use to compare a positive number, a, and a negative number, b, are |a| > |b| and a > 0 and b < 0.
Explanation:
To compare two numbers, a and b, where a is positive and b is negative, we can use two inequalities:
The magnitude of a must be greater than the magnitude of b. This can be represented as |a| > |b|.
The value of a must be greater than 0 and the value of b must be less than 0. This can be represented as a > 0 and b < 0.
These inequalities help Tim compare the positive and negative numbers a and b based on their magnitudes and values.
The sum of two numbers is 33.the larger number is 3 more than two times the smaller number.what are the numbers?
Answer: 10 and 23
Step-by-step explanation:
Let the first number be x and the second number be y.
Also , let x be the bigger number and y the smaller number.
From the first statement;
x + y = 33 ............................. equation 1
From the second statement
twice the smaller number = 2y
so, if the bigger number is 3 more than two times the smaller number, this means that
x = 2y + 3 .................................... equation 2
Solving the resulting linear equations by substitution method .
substitute x = 2y + 3 into equation 1 , that is
x + y = 33 becomes :
2y + 3 + y = 33
3y + 3 = 33
3y = 30
y = 10
Substitute y = 10 into equation 2 , that is
x = 2y + 3 becomes
x = 2(10) + 3
x = 20 + 3
x = 23
volume of a regular quadrilatral pyramid is 400 cm^3.and it's height is 12 then it's lateral surface area=?
Answ For Lateral Area : When all the side faces are the same: Multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is "base times height divided by 2"er:
Step-by-step explanation:
Marco drew 20 pictures .He drew 3/4 of them in art class.How many pictures did Marco draw in art class
Answer: 15
5,10,15,20
3/4 is 15
what is f (6) for the quadratic function graphed here
Answer:
-2.5
Step-by-step explanation:
We are given that a quadratic function graph f(x).
We have to find the value of f(6).
The given graph is parabolic .
The vertex of the graph is at (3,-2).
The graph cut the x -axis at point (1,0) and (5,0).
The graph cut the y-axis at point (0,-2.5).
To find the value of f(6) we will find the value of y corresponding to x=6.
When we draw a vertical line x=6 then we see that it cuts the given graph at point (6,-2.5).
Therefore, the value of f(6)=-2.5
Hence, the f(6) for the quadratic function graph=-2.5
Is there a series of rigid transformations that could map A
KLP to AQNM? If so, which transformations?
No, AKLP and A QNM are congruent but A KLP cannot
be mapped to A QNM using a series rigid
transformations
No, AKLP and A QNM are not congruent.
Yes, A KLP can be reflected across the line containing
KP and then translated so that Pis mapped to M.
Yes, AKLP can be rotated about P and then translated
so that Lis mapped to N.
Answer:
Yes, A KLP can be reflected across the line containing KP and then translated so that Pis mapped to M.
Step-by-step explanation:
The figure shows two congruent by HA theorem (they have congruent hypotenuses and a pair of congruent angles adjacent to the hypotenuses) triangles KLP and QNM.
A rigid transformation is a transformation which preserves lengths. Reflection, rotation and translation are rigit transformations.
If you reflect triangle KLP across the leg KP and translate it up so that point P coincides with point M , then the image of triangle KLP after these transformations will be triangle QNM.
Triangle KLP can be reflected across the line containing KP and then translated so that P is mapped to M
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane.
Triangle KLP can be reflected across the line containing KP and then translated so that P is mapped to M
Find out more on Transformation at: https://brainly.com/question/1548871
Find the length of the missing side of a rectangle if the diagonal is 13 cm and the shortest side is 5cm
And please show the steps and explain
Answer:
12 cm
Step-by-step explanation:
I drew a picture of a rectangle with a diagonal measurement of 13 units and what appear to be the shortest side to be 5 units. (This picture was not drawn to scale.) We were has to find the longest side which I said was b. Notice the diagonal cuts the rectangle into right triangles.
We will need to use Pythagorean Theorem to find the length of the longer side of the rectangle.
[tex]5^2+b^2=13^2[/tex]
[tex]25+b^2=169[/tex]
Subtract 25 on both sides:
[tex]b^2=144[/tex]
Take square root of both sides:
[tex]b=\sqrt{144}[/tex] (I did not worry about the negative answer to this because we are dealing with lengths.)
[tex]b=12[/tex]
GDP is the most often cited measure of how our economy is doing. The U.S. Bureau of Economic Analysis reported that U.S. Real GDP grew at an annual rate of 1.9% in the third quarter of 2019. 1) Where did the growth come from? 2) Using GDP as your reference, how is the economy doing and how will it do in 2020?
1. Growth came from personal and government spends and other investments.
2. Economy is slowing down and reflects weaker outlook in 2020
Explanation:1. Real Gross Domestic Product showed increment at the rate of 1.9% annually by the end of 3rd quarter of 2019. This estimate was released by Bureau of economic analysis. They also had estimated that Real GDP was increased by approximately 2.0% when 2nd quarter of 2019 ended.
Factors that contributed the increase in real GDP by the end of 3rd quarter included expenditures and consumption of the common people for personal use, expenditure of federal government along with local and state governments, investments in fixed residential assets, and also exports.
2. International Monetary Fund estimated and projected a slower growth rate for United States in 2019 and 2020 and revised the growth rate as downward of 0.3% for both 2019 and 2020. This shows us that GDP will now grow at the rate of 7% and 7.2% , which reflects a very weak outlook for domestic demand, weaker than expected. Global trade tension poses a threat to the economic outlook.
12. The equation for line G is given by
5y = -2x - 20. Suppose line G is parallel to line R, and line E is perpendicular to line G. Point (-10,8) lies on both line R and line E.
Part A: Write an equation in slope-
intercept form for line R.
Part B: Write an equation in slope-
intercept form for line E.
Answer:
Step-by-step explanation:
line G :
5y = -2x - 20...put in slope intercept form (y = mx + b)
y = -2/5x - 4....the slope(m) = -2/5
Part A.) slope intercept form for line R...since R is parallel to G, it will have the same slope....so slope(m) = -2/5
(-10,8)...x = -10 and y = 8
slope(m) = -2/5
y = mx + b
8 = -2/5(-10) + b
8 = 4 + b
8 - 4 = b
4 = b
so ur equation is : y = -2/5x + 4 <=== part A answer
since line E is perpendicular to line G, it will have a negative reciprocal slope...all that means is flip the slope and change the sign....so the slope of line E is : (flip -2/5.....-5/2.....change the sign......5/2)
(-10,8)...x = -10 and y = 8
slope(m) = 5/2
y = mx + b
8 = 5/2(-10) + b
8 = -25 + b
8 + 25 = b
33 = b
so ur equation is : y = 5/2x + 33 <== part B answer
The equation for line R is y = -2/5x + 12. The equation for line E is y = 5/2x + 33.
Explanation:Part A: To write the equation for line R in slope-intercept form, we need to find the slope and the y-intercept. Since line R is parallel to line G, it will have the same slope. The slope of line G can be determined by dividing the coefficient of x by the coefficient of y: -2/5. We can use the point-slope form, y - y1 = m(x - x1), to find the equation. Substituting the coordinates of the point (-10,8), the equation for line R is y - 8 = (-2/5)(x + 10). Simplifying, we get the equation for line R: y = -2/5x + 12.
Part B: To write the equation for line E in slope-intercept form, we need to find the slope and the y-intercept. Since line E is perpendicular to line G, its slope will be the negative reciprocal of the slope of line G. The slope of line G is -2/5, so the slope of line E will be 5/2. Using the point-slope form and substituting the coordinates of the point (-10,8), the equation for line E is y - 8 = (5/2)(x + 10). Simplifying, we get the equation for line E: y = 5/2x + 33.
Learn more about Equations of Lineshttps://brainly.com/question/25128481?referrer=searchResults
#SPJ2
4 adult and 10 student tickets cost 58$ overall on the first day on the second 5 adult and 1 student cost 38$ overall how much is each ticket sold for
Cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3
Solution:
Let "a" be the cost of 1 adult ticket
Let "s" be the cost of 1 student ticket
Given that,
4 adult and 10 student tickets cost 58$ overall on the first day
So we can frame a equation as:
4 adult ticket x cost of 1 adult ticket + 10 student ticket x cost of 1 student ticket = $ 58
[tex]4 \times a + 10 \times s = 58[/tex]
4a + 10s = 58 ------ eqn 1
On the second 5 adult and 1 student cost 38$ overall
So we can frame a equation as:
5 adult ticket x cost of 1 adult ticket + 1 student ticket x cost of 1 student ticket = $ 38
[tex]5 \times a + 1 \times s = 38[/tex]
5a + 1s = 38 ------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "s"
Multiply eqn 2 by 10
50a + 10s = 380 ---- eqn 3
Subtract eqn 1 from eqn 3
50a + 10s = 380
4a + 10s = 58
( - ) --------------------
46a = 322
a = 7Substitute a = 7 in eqn 1
4a + 10s = 58
4(7) + 10s = 58
28 + 10s = 58
10s = 58 - 28
10s = 30
s = 3Thus cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3
which expression is equal to (x+5)(-3x^2+15x-1)?
a. -3x^3+74x-5
b. -3x^3+30x^2-76x-5
c. -3x^3-76x-5
d. -3x^3+30x^2+74x-5
Answer:
-3x^3+74x-5
Step-by-step explanation:
(x+5)(-3x^2+15x-1)
-3x^3+15x^2-x-15x^2+75x-5
-3x^3+15x^2-15x^2+75x-x-5
-3x^3+74x-5
The given expression can be simplified to obtain -3x³ + 74x - 5. The correct option is (a).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given algebraic expression is (x + 5)(-3x² + 15x - 1).
It can be evaluated as follows,
(x + 5)(-3x² + 15x - 1)
⇒ x(-3x² + 15x - 1) + 5(-3x² + 15x - 1)
⇒ -3x³ + 15x² - x - 15x² + 75x - 5
⇒ -3x³ + 74x - 5
Hence, the product of the given expression is -3x³ + 74x - 5.
To know more about algebraic expression click on,
brainly.com/question/953809
#SPJ2
(PLEASE ANSWER...I FORGOT TO DO THIS OVER BREAK)
What is the value of x in the equation −x = 4 − 3x + 6? (5 points) Group of answer choices 5 10 −5 −10
Answer:
so the solution is in the picture please mark me brainliest.
the Answer is 5
Answer:
-x+3x=4+6 because when we collected liketerms
2x=10 now divided both side by 2
2x/2=10/2
x=5 so the value of x is 5
a pulley 18 inches in diameter is driven by a belt at the rate of 90 revolutions per minute. what is the angular velocity of the pulley in radians per minute? what is the speed of the belt in feet per second?
Answer:90*2π，90/60*18/2
Step-by-step explanation:
You received partial credit in th
A lottery ticket has a grand prize of $44.8 million. The probability of winning the grand prize is 000000020.
Determine the expected value of the lottery ticket. (Round your answer to 3 declmal places.)
Expected value
Answer:
Expected value would be $ 0.896
Step-by-step explanation:
Given,
The price of the lottery ticket = $44800000,
Also, the probability of winning the grand prize = .000000020,
Thus, the expected value of the lottery ticket = value of the lottery ticket × probability of getting the lottery ticket
= 44800000 × .000000020
= $0.896
Note : value of lottery ticket = prize amount - cost of each ticket,
Here the cost price of a ticket is not given,
That's why we did not consider it.
Final answer:
The expected value of a lottery ticket with a grand prize of $44.8 million and a winning probability of 0.00000002 is $0.896, assuming the ticket has no cost.
Explanation:
To calculate the expected value of a lottery ticket, we need to consider both the payout and the probability of each outcome. Given that the grand prize is $44.8 million with a probability of winning of 0.00000002, we can compute the expected value.
To find the expected value (EV) of the lottery ticket, we use the following formula:
EV = (Payout × Probability of winning) - (Cost of ticket × Probability of losing)
Plugging in the values, we get:
EV = ($44,800,000 × 0.00000002) - ($0 × (1 - 0.00000002))
EV = $0.896.
Since the cost of the ticket is not given, we assume it's $0 for the purpose of this illustration. The expected value of the lottery ticket when rounded to three decimal places is $0.896.
What is the greatest whole number m for which 2m < 11 ?
While at the gym levon spent 25 minutes on the treadmill and 35 minutes lifting weight what is the ratio of the levon spent on the treadmill to the time he spent lifting?
The ratio of the time levon spent on the treadmill to the time he spent lifting is 5/7 or 5:7
Step-by-step explanation:
Given
Time spent on treadmill = [tex]T_t = 25\ min[/tex]
Time spent on weight lifting = [tex]T_w = 35\ min[/tex]
We have to find the ratio of the time Levon spent on the treadmill to the time he spent lifting
The ratio will be denoted by r
[tex]r = \frac{T_t}{T_w}\\=\frac{25}{35}\\[/tex]
Simplifying the fractions
[tex]=\frac{5*5}{7*5}\\=\frac{5}{7}[/tex]
The ratio of the time levon spent on the treadmill to the time he spent lifting is 5/7 or 5:7
Keywords: Ratio, fraction
Learn more about fractions at:
brainly.com/question/7287774brainly.com/question/726990#LearnwithBrainly
a container shaped like a right circular cylindar having diameter 6cm and height 7.5cm is full of ice cream.The ice cream is to be filled into cones of height 6cm and diameter 3cm,having a hemispherical shape on the top.Find the number of cones which can be filled with ice cream
Answer:
Step-by-step explanation:
Cylinder:
d= 6cm; r =6/2 = 3cm
h =7.5cm
Volume of ice cream in cylinder = πr²h
= π * 3 * 3 * 7.5 = 67.5 π cubic cm
Cone:
h = 6 cm;
d = 3cm ; r = 3/2 = 1.5cm
Volume =(1/3)πr²h
= (1/3) * π * 1.5 * 1.5 * 6
= π * 1.5*1.5 * 2 = 4.5π cu. cm
Hemisphere on top:
r = 1.5cm
Volume = (2/3)πr³
=(2/3)* π * 1.5 *1.5 * 1.5
= 2 *π * 0.5*1.5*1.5
= 2.25π cu.cm
Volume of ice cream in each cone = 4.5 π + 2.25π = 6.75π cubic cm
No of cones = volume of cylinder/ Volume of ice cream in each cone
=π *67.5 / 6.75 * π
= 67.5 * 100 / 6.75 * 100
= 6750 / 675
= 10
number of cones which can be filled with ice cream = 10 cones
Jamie says that the expression s6x-2x+4 and 4(x+1)are not equivalent because one expression has a term that is subtracted and the other does not. Do you agree? Explain
Answer:
I do not agree. When the expressions have like terms collected and are factored, they are the same.
Step-by-step explanation:
Make 6x-2x+4 the same as 4(x+1):
6x - 2x + 4 Collect the like terms 6x and -2x
= 4x + 4 Factor. Divide each term by 4 and take it out of a bracket
= 4(x + 1)
4(x+1) = 4(x+1)
They are equivalent expressions, just written differently.
Answer:
No Jamie is incorrect
Step-by-step explanation:
No, because in the expression 4(x+1) you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.
Also in the expression 6x-2x+4 ,you will first need to subtract 2x from 6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4
Our final answer is:
6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4
simplify the following expression -12[ 3y - 4x] - 10y
Answer:
-46y+48x
Step-by-step explanation:
Answer:
-46y + 48x
Step-by-step explanation:
-12(3y - 4x) -10y
-36y + 48x - 10y
-36y - 10y + 48x
-46y +48x
Ms. Clark spends $89.85 on science kits that cost of each plus $4.85 tax on the total bill, how many kits did she buy?
Mrs. clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?
Answer:Mrs. Clark bought 17 science kits
Solution:Given that Mrs. clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill
To find: number of kits she bought
Cost of one kit = $ 5
Tax amount = $ 4.85
Total amount spend including tax = $ 89.85
Lets first get rid of the tax in the total amount
Amount without tax = Total amount spend including tax - Tax amount
Thus amount without tax = $ 89.85 - $ 4.85 = $ 85
Since we know that each kit costs $5, we would divide 85 by 5 to see find how many kits she bought
[tex]\begin{array}{l}{\text { number of kits bought }=\frac{\text { amount spent }}{\text { cost of one kit }}} \\\\ {\text { number of kits bought }=\frac{85}{5}=17}\end{array}[/tex]
Thus Mrs. clark has bought 17 science kits
Answer:
Ms. Clark bought 17 science kits
Step-by-step explanation:
how to solve 3a - ( -1 ) = -5
The perimeter of a rectangle is 53 inches. The length of the rectangle is 5 less than twice it’s width. Solve the system using 2 equations.
Answer:
length of rectangle=16 inches
width of rectangle=10.5 inches
Step-by-step explanation:
given ,perimeter of rectangle=53 inches
let ,length of rectangle= l=2b-5
width of rectangle=b
p=2(l+b)
53=2(2b-5+b)
26.5=3b-5
31.5=3b
b=[tex]\frac{31.5}{3}[/tex]
b=10.5 inches
l=21-5=16 inches
Find original price.
Swimsuit discounted 65% on sale for $20.30
Answer:
58 dollars
Step-by-step explanation:
(100% - 65% = 35% or 0.35)
x(0.35) = 20.30
divide both sides by 0.35
x = 58
The swimsuit was originally 58 dollars.
Answer:
$58
Step-by-step explanation:
Comparing and ordering integers
Answer:
what about it?
Step-by-step explanation:
find <ABC + <ADC
help... ASAP! :)
Answer:
Option D. 124°
Step-by-step explanation:
step 1
Find the measure of angle AOC
The triangle AOC is an isosceles triangle, because OA=OC=radius
so
[tex]m\angle OAC=m\angle OCA=28^o[/tex]
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
[tex]m\angle OAC+m\angle OCA+m\angle AOC=180^o[/tex]
substitute the given values
[tex]28^o+28^o+m\angle AOC=180^o[/tex]
[tex]56^o+m\angle AOC=180^o[/tex]
[tex]m\angle AOC=180^o-56^o[/tex]
[tex]m\angle AOC=124^o[/tex]
step 2
Find the measure of arc AC
we know that
[tex]arc\ AC=m\angle AOC[/tex] ----> by central angle
we have
[tex]m\angle AOC=124^o[/tex]
therefore
[tex]arc\ AC=124^o[/tex]
step 3
we know that
The inscribed angle is half that of the arc comprising
[tex]m\angle ABC=\frac{1}{2}[arc\ AC][/tex]
[tex]m\angle ADC=\frac{1}{2}[arc\ AC][/tex]
so
[tex]m\angle ABC=m\angle ADC[/tex]
therefore
[tex]m\angle ABC+m\angle ADC=2m\angle ABC=arc\ AC[/tex]
substitute the value of the arc AC
[tex]m\angle ABC+m\angle ADC=124^o[/tex]
How many solutions does the equation -3+3a+6=7 have
Answer: The equation has No Solution.
Step-by-step explanation:
Given the following equation:
[tex]-3a+3a+6=7[/tex]
You can simplify it by adding the like terms.
It is important to remember the, by definition, the like terms have the same variable and the same exponent.
In this case, you can identify that the term [tex]-3a[/tex] and the term [tex]3a[/tex] are "like terms", because their variables and their exponents are the same.
So, if you add them, you get:
[tex]-3a+3a=0[/tex]
Then:
[tex]0+6=7\\\\6=7\ (FALSE)[/tex]
Therefore, since there is no value that satisfies the equation, you can conclude that the equation has No Solution.
4cos+4sin^2=5 find cos
Answer:
cos θ = 1/2
Step-by-step explanation:
4 cos θ + 4 sin² θ = 5
Use Pythagorean identity.
4 cos θ + 4 (1 − cos² θ) = 5
4 cos θ + 4 − 4 cos² θ = 5
0 = 4 cos² θ − 4 cos θ + 1
0 = (2 cos θ − 1)²
0 = 2 cos θ − 1
cos θ = 1/2
Answer:
60° and 300°
Step-by-step explanation:
Before beginning to answer this question, you'll need a quick formula that will be very helpful trying to answer questions like this one:
[tex]sinx^2 + cosx^2 = 1[/tex]You'll see why this formula is useful soon.
Work:
[tex]4cosx+4sinx^2=5[/tex]
The way we want to go about answering this question is very similar to what we've learned in the past: factoring. In order to be able to factor though, we need to have only [tex]cosx[/tex] in our equation instead of both [tex]sinx[/tex] and [tex]cosx[/tex] like the above equation has. this is where the formula I showed earlier comes into play.Using the equation I showed earlier, we are going to get rid of the [tex]sinx[/tex].[tex]sinx^2+cosx^2=1[/tex]
We are going to isolate [tex]sinx^2[/tex] and then substitute what its equal to into the equation.[tex]sinx^2=-cosx^2+1[/tex]
Now Substitute this back into the original equation.[tex]4cosx+4(-cosx^2+1)=5[/tex]
Put this into standard form. Then we can factor.[tex]4cosx-4cosx^2+4=5[/tex]
[tex]-4cosx^2+4cosx+4=5[/tex]
[tex]4cosx^2-4cosx-4=-5[/tex]
[tex]4cosx^2-4cosx+1=0[/tex]
Let [tex]cosx[/tex] be [tex]u[/tex].[tex]4u^2-4u+1=0[/tex]
Look familiar? We could have factored before just the same, but this ensures there will be fewer mistakes while factoring.[tex](2u-1)^2=0[/tex]
Now let's change [tex]u[/tex] back to [tex]cosx[/tex][tex](2cosx-1)^2=0[/tex]
Set [tex]2cosx-1[/tex] equal to 0.[tex]2cosx-1=0[/tex]
[tex]2cosx=1[/tex]
[tex]cosx=1/2[/tex]
Hopefully if your teacher taught you unit circle properly, you will know that [tex]cosx=1/2[/tex] is asking for an angle. In this case, I know the angle because of memorization, but sadly the only way to learn this stuff is memorization, so I wont be able to show work for how I got my final answer. I'll have to just show calculator-wise how its done.[tex](cos^-^1)cosx=1/2(cos^-^1)[/tex]
[tex]x=60[/tex] [tex]x=300[/tex]
Find the y - intercept of y=3x+15 and then interpret it
Answer:
The y-intercept to the given line equation y=3x+15 is (0,15).
Step-by-step explanation:
Given line equation is y=3x+15
To find the y-intercept from the given line equation y=3x+15:
y-intercept when x=0
That is substitute x=0 in the given line equation
y=3x+15
y=3(0)+15
y=0+15
y=15
Therefore y=5
The point (0,15) on the graph where the line y is intersected is y-intercept.
In other words y-intercept is the point (0,15) where the given line equation y=3x+15 crosses the y-axis.
Therefore the y-intercept to the given line equation y=3x+15 is (0,15).
Final answer:
The y-intercept of y=3x+15 is 15 and it represents the value of y when x is zero.
Explanation:
The y-intercept, b, of the equation y=3x+15 is 15. It represents the value of y when x is equal to zero. In other words, when x is zero, y is equal to 15.
Interpretation: In the context of the equation y=3x+15, the y-intercept of 15 means that when there is no input or x-value, the output or y-value is 15. This suggests that when the x-value is zero, the value of y is 15. This can be visualized on a graph as the point where the line intersects the y-axis at the coordinate (0, 15).
Catera has found that as she increases her price, p, the quantity she sells q, decreses.
The following equation relates q, the quantity she sells, to p, the price she charges.
p = 284 - 4q Catera's price is $232.
what is the quantity that she sells? Show your work.
Answer
The quantity "q" sold by Catera is 13
Solution:
Given that Catera has found that as she increases her price, p, the quantity she sells q, decreases
The following equation relates q, the quantity she sells, to p, the price she charges:
p = 284 - 4qWhere, "p" is the price and "q" is the quantity she sells
Given that Catera price is $ 232
To find: quantity she sells
Substitute p = 232 in given equation
232 = 284 - 4q
4q = 284 - 232
4q = 52
[tex]q = \frac{52}{4} = 13[/tex]
q = 13
Therefore the quantity she sells is 13