Linear Equations
word problems
Mrs. Dyal starts the year with 150 pencils and
gives away an average of 10 pencils per week.
Represent with a function Represent with a graph
f(x)
Domain =
Range =
140
120
100
Pencils remaining
80
When will Mrs. Dual run
out of pencils?
Answer:
Part 1
The given information represented as a function, f(x) is;
f(x) = 150 - 10·x
Part 2
Please find attached the given information represented as a graph is created with Microsoft Excel
Part 3
Mrs. Dyal will run out of pencils after giving away pencils for 15 weeks
Step-by-step explanation:
The word problem relates to linear functions of the form f(x) = y = m·x + c
The given parameters are;
The number of pencils Mrs. Dyal has at the start of the year = 150 pencils
The number of pencils Mrs. Dyal gives away per week = 10 pencils
Part 1
Let "x" represent the number of weeks at which Mrs. Dyal is giving away the pencils
Given that she gives away 10 pencils each week, we have the function that represent the number of pencils remaining after "x" weeks is given as follows;
f(x) = 150 - 10×x.
The number of weeks, "x", that passes before Mrs. Dyal runs out of pencil (f(x) = 0) is given as follows;
f(x) = 0 = 150 - 10 × x
∴ 150 Pencils = 10 Pencils/Week × x
x = 150 Pencils/(10 Pencils/Week) = 15 Weeks
x = 15 Weeks
Therefore Mrs. Dyal will run out of Pencil at when x = 15 Weeks
Part 2
The function can be represented as a graph using the table of values as follows ;
Pencil remaining [tex]{}[/tex] Number of weeks
150 [tex]{}[/tex] 0
140 [tex]{}[/tex] 1
130 [tex]{}[/tex] 2
120 [tex]{}[/tex] 3
110 [tex]{}[/tex] 4
100 [tex]{}[/tex] 5
90 [tex]{}[/tex] 6
80 [tex]{}[/tex] 7
70 [tex]{}[/tex] 8
60 [tex]{}[/tex] 9
50 [tex]{}[/tex] 10
40 [tex]{}[/tex] 11
30 [tex]{}[/tex] 12
20 [tex]{}[/tex] 13
10 [tex]{}[/tex] 14
0 [tex]{}[/tex] 15
The domain = 0 ≤ x ≤ 15 {x ∈ N including 0}
The range = 0 ≤ f(x) ≤ 150
From the graph of the function created with Microsoft Excel, Mrs Dyal has no more Pencils left when x = 15 weeks
find the value of x
A) 3
B) 14
C) 5
D) 2
Answer:
C) 5
Step-by-step explanation:
The measure of angle TSU is 75°. (180° - 105° because it is a flat angle)
The sum of all the angles of a triangle is 180° as well.
You can write an equation to solve for x.
12x + 9x + 75 = 180
Isolate x.
12x + 9x = 180 - 75
12x + 9x = 105
Add the 12 and the 9.
21x = 105
Find what x is.
x = 105 ÷ 21
x = 5
given g(x)=-3x-5, find g(-4)
Answer:
7
Step-by-step explanation:
Answer:
i got 7
Step-by-step explanation:
Someone pls help ??:)
If f(x)=x-6 and g(x)=x^1/2(x+3) , find g(x) X f(x) .
Answer:
(B).
Step-by-step explanation:
√x(x + 3)(x - 6) = √x(x² - 3x - 18) = [tex]\sqrt{x^{5} }[/tex] - 3[tex]\sqrt{x^{3} }[/tex] - 18√x
A model baseball bat was designed using a scale factor of 1:3. If the
model bat is 10 inches long, how many inches long is the real bat?
Is the following sequence arithmetic?
-14, 86, 186, 286, ...
A.No
B.Yes
Par quelle fraction est multipliée l'aire d'un rectangle si l'on augmente sa longueur de son cinquième et sa largeur de son tiers ?
Répondre:
8/15
Explication étape par étape:
Prendre:
Longueur = x
Largeur = y
Zone du rectangle = Longueur * largeur
Un cinquième de longueur = x / 5
Un tiers de largeur = x / 3
Zone d'origine = xy
Nouvelle dimension:
Longueur = x + x / 5 = (5x + x) / 5 = 6x / 5
Largeur = x + x / 3 = (3y + y) / 3 = 4y / 3
Nouvelle zone = 6x / 5 * 4y / 3
Nouvelle zone = (24/15) xy
Fraction de la nouvelle zone par rapport à la zone d'origine:
(24/15) xy: xy
24/15: 1
24/15
= 8/5
Use the Rational Zeros Theorem to write a list of all potential rational zeros.
Answer:
Your potential zeros are ± 1/2, ± 3/2, ± 1, and ± 2.
Help please I need this asap :’)
Answer: Line C
Step-by-step explanation:
Because when you use the slope formula on it you get a negative slope. Also the line in going down unlike the other lines which are goign up.
Elaina misses 2 free throws for every 10 attempts. How many free throws can you expect Elaina to make if she shoots 15 free throws in a game? Input your answer as a number with NO spaces!
Answer:
12
Step-by-step explanation:
Tracy ran a lap around the school track in 74.2 seconds. Malcolm ran a lap in 65.92 seconds. Estimate the difference in the times in which the students completed the lap.
Answer:
8.28 is the difference in times in which the students completed the lap.
Step-by-step explanation:
Subtract 74.20 and 65.92 and that gives you your answer.
1. Sara bought cartons of raspberries that cost $1.50 and cartons of blackberries cost $2. Sara spent $11 buying raspberries and blackberries. She bought a total of 6 cartons. How many cartons of blackberries did she buy?
Sara brought a total of 5 cartons of blackberries. Since it said that Sara brought 6 cartons and you know that the cost of the blackberries are $2, you multiply 6 with 2 but its 12. But if Sara brought 2 cartons of raspberries it will be $3. Now you subtract 6 with 2 since you used 2 cartons on raspberries and now multiply $2 with 4 and get 8. 8+3=11, which is exactly how much she needs. This means that Sara brought 4 cartons of blackberries.
(4x2 + 6) + (2x2 + 6x + 3)
(x + 3)2 – (2x – 1)2
Answer:
-2x+8
Step-by-step explanation:
Please help me with the correct answer
Answer:
y=2(-2)+3
y=-1
y=2(-1)+3
y=1
y=2(0)+3
y=3
y=5
y=7
Answer:
(From left to right)
1st y (output): -1
2nd y (output): 1
3rd y (output): 3
4th y (output): 5
5th y (output): 7
Step-by-step explanation:
Substitute each x (input) into the given equation and solve. For example, to get the first y (output), substitute "-2" into the "x" in the equation, giving you "y = 2(-2) +3", then solve it.
Multiply 2(-2) to get -4, then add 3 to get -1.
x + 23 = −4 need help
Answer:
-27
Step-by-step explanation:
x+23−23=−4−23
x=−27
10+8+5+ ? HELPPPPPPPPPPPPPP
Answer: the answer is 23
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
10+8+5=23
Gerardo divides 1/2 by 2, and then divides the quotient by 2 again. Draw a circle to represent one whole. Then use it to explain how Gerardo's work is similar to dividing 1/2 by 4.
Answer:
Kindly check attached picture for circle illustration.
Step-by-step explanation:
The whole circle = 1
Half the circle = semicircle = 1/2
Half the semicircle = 1/4
Half of 1/4 = 1/8
Hence, Geraldo would obtain 1/8
Normal calculation:
1/2 ÷ 2
1/2 * 2/1 = 1/4
Quotient = 1/4
Quotient / 2
1/4 ÷ 2
1/4 * 1/2
= 1/ 8
Which function had the same y-intercept as the function y= 2/3 x-3
Answer:
y-intercept of the function [tex]y=\frac{2}{3}x-3[/tex] is -3.
Step-by-step explanation:
We need to find the function that had the same y-intercept as the function [tex]y=\frac{2}{3}x-3[/tex]
(Note: Since the options are not given, so I will find the y-intercept of the given equation and you can match it with the functions and find the y-intercept of the required function)
The equation given [tex]y=\frac{2}{3}x-3[/tex] is written in slope-intercept form i.e [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
Comparing equation [tex]y=\frac{2}{3}x-3[/tex] with [tex]y=mx+b[/tex] we get the value of b = -3
So, y-intercept of the function [tex]y=\frac{2}{3}x-3[/tex] is -3.
Now, for the options (not included) in the question, you can find y-intercept and function that have y-intercept = -3 will be the answer.
What is the equation, in standard form, of a parabola that models the values in the table?
x= -2, 0, 4
f(x)= 2.5, 1.5, -60.5
Answer:
y=-2.5[tex]x^{2}[/tex]+4.5x+1.5
Step-by-step explanation:
standard form of equation of parabola is,
y=a[tex]x^{2}[/tex]+bx+c
For x=0
1.5=0a+0b+c
1.5=c
For x=-2,
2.5=4a-2b+c
substituting the value of c
2.5=4a-2b+1.5
on solving,
4a-2b=1____________(1)
For x=4,
-60.5=16a+4b+c
substituting the value of c,
-60.5=16a+4b+1.5
on solving,
16a+4b=-62_______(2)
Multiplying equation 1 by 2,
8a-4b=2_______(3)
adding equation 2 and 3
16a+4b+8a-4b=-62+2
24a=-60
on solving,
a=-2.5
substituting the value of a in equation 1,
10-2b=1
2b=9
b=4.5
hence, equation of parabola in standard form is,
y=-2.5[tex]x^{2}[/tex]+4.5x+1.5
Answer for the points
6 − (9 − 2) + 3 × 6
Answer:
17
Step-by-step explanation:
USING BIDMAS (Brackets Indices Division Multiplication Addition Subtraction)
6 − (9 − 2) + 3 × 6
9-2=7
3x6=18
6-7+18=17
Use the tables to help you compare the two ratios.
2 tables. One table has 2 rows. The first row has entries 3, 6, 9. The second row has entries 10, 20, 30. The second table has 2 rows. The first row has entries 1, 2, 3. The second row has entries 5, 10, 15.
Compare the ratios 1:5 and 3:10.
The ratio 1:5 is less than 3:10
The ratio 1:5 is greater than 3:10
The ratio 1:5 is equal to 3:10
The ratios cannot be compared
Given the data from the question, the correct statement is: the ratio 1:5 is less than 3:10
Data obtained from the questionFirst table:Row 1 = 3, 6, 9Row 2 = 10, 20, 30Second table:Row 1 = 1, 2, 3Row 2 = 5, 10, 15Comparison of ratio 1:5 and 3:10 =?How to determine the comparison of ratio 1:5 and 3:10To otain the comparison of both ratios, we shall determine the value of each ratio. This is illustrated below:
1 : 5 = 1 / 5
1 : 5 = 0.2
3 : 10 = 3 / 10
3 : 10 = 0.3
SUMMARY
1 : 5 = 0.23 : 10 = 0.3Thus, we can conclude that 1:5 is less than 3:10
Learn more about ratios:
https://brainly.com/question/2462048
#SPJ1
Please answer this question
Answer:
I think the scale factor would be 1/6
Answer:
1/6
Step-by-step explanation:
3 feet = 3*12 = 36
Scale factor = 6/36 = 1/6
ella purchased 9 rews & umpts for about $24. Rews are $1 each and umpts are $6. write a system of equations in standard form to model relationship between rews (x) and umpts (y)
HELP PLS ILL MARK AS BRAINIEST !!!!
Answer:
Slope is -3/4
Y intercept is 7
y= -3/4x+7
Find the value of 42 - (-10)
*explain how to solve*
Answer: 52
Step-by-step explanation:
42-(-10) first since your multiplying the two negative signs with each other it turns into a positive and looks like 42+10 and 42+10=52
Write an algebraic expression for the verbal expression: three times the sum of X and Y increase by five times the product of x and 3y.
Answer:
3(x+y)+15xy
Step-by-step explanation:
Write an algebraic expression for the verbal expression: three times the sum of X and Y increase by five times the product of x and 3y.
Sum of x and y = x+y
three times the sum of X and Y = 3(x+y)
product of x and 3y = x(3y) = 3xy
five times the product of x and 3y = 5(3xy) = 15xy
Three times the sum of X and Y increase by five times the product of x and 3y will be expressed as;
3(x+y) + 15xy
Hence the required algebraic expression is 3(x+y)+15xy
Help plz and please tell me how u got the answer
Answer:
I think is 2/3
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
COP is slope which is rise over run.
Use the Distributive Property. -9(2x-4y)
Answer:
-18x-36y
Step-by-step explanation:
Distributive Property:
-9*2x=-18x
-9*4y=-36y
-18x-36y
