Given:
The table of values is
Number of Students : 7 14 21 28
Number of Textbooks : 35 70 105 140
To find:
The rate of change and showing that the ratios of the two quantities are proportional and equivalent to the unit rate.
Solution:
The ratio of number of textbooks to number of students are
[tex]\dfrac{35}{7}=5[/tex]
[tex]\dfrac{70}{14}=5[/tex]
[tex]\dfrac{105}{21}=5[/tex]
[tex]\dfrac{140}{28}=5[/tex]
All the ratios of the two quantities are proportional and equivalent to the unit rate.
Let y be the number of textbooks and x be the number of students, then
[tex]\dfrac{y}{x}=k[/tex]
Here, k=5.
[tex]\dfrac{y}{x}=5[/tex]
[tex]y=5x[/tex]
Hence the rate of change is constant that is 5.
solve each system of equation by elimination
{y=-x+1
{y= 4x-14
Answer:
(3, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -x + 1
y = 4x - 14
Step 2: Rewrite Systems
y = 4x - 14
Multiply everything by -1: -y = -4x + 14Step 3: Redefine Systems
y = -x + 1
-y = -4x + 14
Step 4: Solve for x
Elimination
Combine equations: 0 = -5x + 15Isolate x term: -15 = -5xIsolate x: 3 = xRewrite: x = 3Step 5: Check
Define equation: y = -x + 1Substitute in x: y = -3 + 1Add: y = -2The lunch special at a diner offers you a choice of 5 sandwiches, 2 salads, 3 soups, 6 drinks, and 2 desserts. How many different meals are possible if you choose one item from each category?
Answer:
360
Step-by-step explanation:
there are 360 different meal combos possible if you choose 1 of each because 5×2×3×6×2 is 360
Suppose that three out of five voters support a candidate. If 1,240 voters support the candidate, how many voters participated in the election in all? Round your answer to the nearest whole number.
Answer:
2067 voters
Step-by-step explanation:
Suppose that three out of five voters support a candidate.
This means 3/5 votes support a candidate
Let the total number rod candidates be represented as x
If 1,240 voters support the candidate,
how many voters participated in the election in all?
Hence,
3/5 of x = 1240 voters.
3/5 × x = 1240
3x /5 = 1240
Cross Multiply
3x = 1240 × 5
x = 1240 × 5/3
x = 2066.6666667 voters
Approximately to the nearest whole number:
2067 voters
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Choose one of the following.
Parallel lines have ____________________.
A. one solution
B. 10 solutions
C. infinitely many solutions
D. no solution
D. no solution
Because they never found each other, the point they cross on is the solution.
Answer: D
Step-by-step explanation: it just is
Determine the quadrant point
Answer:
I think b
Step-by-step explanation:
On Wednesday mornings, admission to the park swimming pool is $3.00 per adult and $2.00 per child. Which expression can be used to find the cost of admission to the pool for a group of adults (a) and children (c)?
A. 3ac
B.5+ac
C. 3a+2c
D. 2(3)+ac
WILL GIVE BRAINLIEST I NEED THIS FAST
Answer:
C.) 3a + 2c
Step-by-step explanation:
$3 per adult (a)
$3(a)
+
$2 per child (c)
$2(c)
Answer:
C. 3a+2c
Step-by-step explanation:
It is 3 $ for a adult hence the 3a and 2$ for a child hence 2c
Identify the best method for solving the given
system of equations. DO NOT SOLVE. Justify your
choice using academic vocabulary.
3x + 2y = 0
x - 5y = 17
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.
Part A: Write a system of equations to represent the given scenario. Use the variables "s" for senior citizen tickets and "c" for child.
Part B: Solve the system of equations from Part A algebraically. Show your work.
Part C: Explain what the solution to the system of equations represents in context of the problem. Hint: You will need to put words here, not an equation.
Answer:
The school took in $52 on there second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen
Step-by-step explanation:
20 POINTS
PLEASE HELP!
Find the slope of the line that passes through the pair of points.
(4, –4), (6, –4)
Answer:
0
Step-by-step explanation:
Find the coordinates of midpoint of the line segment p(-5,-1) Q(6,-2)
Answer:
The coordinates of the midpoint of the line segment p(-5,-1) Q(6,-2) would be: (1/2, -3/2)
Step-by-step explanation:
Given
P(-5, -1)Q(6, -2)[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(6,\:-2\right)[/tex]
[tex]=\left(\frac{6-5}{2},\:\frac{-2-1}{2}\right)[/tex]
[tex]=\left(\frac{1}{2},\:-\frac{3}{2}\right)[/tex]
Thus, the coordinates of the midpoint of the line segment p(-5,-1) Q(6,-2) would be: (1/2, -3/2)
Write and solve an equation for seven less than fou
times a number is 29.
what is the x-coordinate of R' ?
Answer:
3
Step-by-step explanation:
Answer:
12
The x-axis is the horizontal one. The full coordinate is (12, 0), which the x-coordinate (or x-intercept) is 12.
Mrs. stone is three times older than her younger daughter, Joyce, but only two times older than her older daughter, Alex. how old is Mrs. stone now, if 9 years ago Alex was two times older than Joyce?
Answer:
54
Step-by-step explanation:
RSM homework lol
made equation, then solved it.
hope this helps!
I’ll mark u as brainlist plss
Answer:
I think C.
Step-by-step explanation:
may someone plz answer this
Answer:
At least 2 weeks
Step-by-step explanation: You divide until you reach 200
1. 6x+4x−1=2(5x+4)
2. 48x+43=47x+43
3. 2(3x+8)=2x+16+4x
4. 0.4(5x−15)=2.5(x+3)
5. 3(4x+2)=20x−9x+2
Answer:
1 . -9 = 0
2 . x = 0
3 . 0 = 0
4 .x = -27
5 . x = -4
Step-by-step explanation:
Can someone explain to me an easy way to divide fractions? I can't seem to understand it.
Answer:
Flip the second fraction and multiply across
ex: 5/4 divided by 3/6
5/4 * 6/3
5*6 / 4*3 = 30/12
5/4 divided by 3/6 = 30/12
Step-by-step explanation:
When loaded with bricks, a lorry has a mass of 11600kg. If the mass of the bricks is three times that the mass of the empty lorry, find the mass of the bricks.
Answer:
8700kg
Step-by-step explanation:
lorry + bricks = 11600kg
bricks = 3(mass of empty lorry)
lorry mass is x
there for bricks = 3x
x+3x = 11600
4x =11600
x= 2900kg
mass of bricks = 3(2900)
=8700kg
A plane travels 3,625.26 miles in 6.9 hours. What is the plane’s unit rate?
Represent this situation with a fraction.
a. Represent this situation using the same units.
b. Estimate the quotient.
c. Express the divisor as a whole number.
d. Use the division algorithm to find the quotient.
e. Use multiplication to check your work
Answer:
The correct answers are:
a) 3625.26 miles OVER 6.9 miles
b) 36252.6 tenths miles÷ 69 tenths hours
c) 3500 miles over 7 hours = 500 miles over hours
d) 3625.26 miles 10 over 6.9 hours 10 = 36252.6 miles over 69 hours
e) 525.4 miles/h
Step-by-step explanation:
Brainliest please?
Let r = unit rate of the plane
r = (3,625.26 miles)/(6.9 hours)
You now have the correct fraction set up to answer a through e.
Take it from here.
Determine the intercepts of the line
Answer:
Step-by-step explanation:
y-intercept: (0 , 2.5)
x-intercept: (3.5 , 0)
Whats The Answer Marking Brainliest, Please explain your answer:D...
.
Answer:
C. 12x
Each box has 12 envelopes.
The number of total envelopes will be the number of envelopes in a box multiplied by the number of boxes. The number of boxes is unknown, so it is replaced by the variable. This gives us 12x
5) James wants to visit his sister Sarah. He
knows C Street is a shorter distance than taking
A Street and B Street. How many miles is C
Street? (GE: 2nd)
Dany has a business selling bracelets for 7.50 each. She only has enough material to make 5 bracelets. If x represents the number of bracelets sold and y represents the total cost, what is the range for this situation.
Answer:
The range is [0,37.5]
Step-by-step explanation:
We start by writing the equation that links x and y
From the question;
y = 7.5x
Now, she has enough material to make 5 only
When we talk of range, we are referring to the values on the y-axis
So the lowest y value is 0
and since the highest number of bracelets is 5;
The total cost of the 5 is 7.5(5) = 37.5
So the range is [0,37.5]
pls help 7th grade math. what is the value of (-4)^2+6÷(3+4)(2)-5?
A Disney world
B the legend of zelda breath of the wild
C Christmas tree
D ELMER'S glue
Answer:
a carrot
Step-by-step explanation:
(-4)^2+6÷(3+4)(2)-5? x 2 +1(2) x 8 equals carrot
Answer:
Mario odyssey
Step-by-step explanation:
Please Help! I'll give Brainliest!
Eshaal is creating a model of a pyramid. The model created will need to be scaled up from the blueprint.
If segments DE and AB are parallel, which of the following expressions will help Eshaal determine the length of segment BC?
BC = CE
BC equals AC times CE all over CD
BC equals AC times DE all over CE
BC = AC
Answer:
See attachment
PS:
Can I have Brainliest?
The correct statement is BC equals to AC times CE all over CD.
We have, If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. this is known as the triangle proportionality theorem.
Given, DE and AB are parallel
So, [tex]\frac{BC}{CE} =\frac{AC}{CD}[/tex]
[tex]BC = \frac{AC\times CE}{CD}[/tex]
Therefore in statement form we say that BC equals to AC times CE all over CD.
For more details on proportionality theorem follow the link:
https://brainly.com/question/2078223
help> ?????? pleaes asdfdfffffffff
Answer:
37.9701
Step-by-step explanation:
I only know the first one?? I'm really sorry cacsknak ik i said id help, but :( it's hard, and i never learned how to do the bottom two.
The longest leg of a right triangle is 12 inches. The hypotenuse is 3 inches longer then twice the shortest leg. How long is the shortest leg and the hypotenuse of the triangle.
Answer:
Shortest Leg: 5 inches, Hypotenuse: 13 inches
Step-by-step explanation:
A right triangle follows the pythagorean theorem, a^2+b^2=c^2. C is the hypotenus. A combination found using this is 5, 12, and 13. To double check this, we know that the hypotenus is 2x+3, where x is the smallest leg.
what does “pi” equal?
Answer:
here!
Step-by-step explanation:
"In decimal form, the value of pi is approximately 3.14."
hope this helps! :)
Answer:
pi equal 3.141492654 ................. and more but that is the standard answer
Step-by-step explanation:
Evaluate the expression below
if a = -8, b = 17, and c = 21
a2 –(b+c)
Answer:
-54
Step-by-step explanation:
first fill in the numbers
next do the parentheses 17 + 21=38
then find -8×2 which equals -16
then subtract -16 from 38 and get -54
The value of the expression a² - (b + c) at a = -8, b = 17, and c = 21 will be 26.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ a² - (b + c)
The value of the expression at a = -8, b = 17, and c = 21 will be
⇒ a² - (b + c)
⇒ (-8)² - (17 + 21)
⇒ 64 - 38
⇒ 26
The value of the expression a² - (b + c) at a = -8, b = 17, and c = 21 will be 26.
More about the value of expression link is given below.
https://brainly.com/question/23671908
#SPJ2
8x – 12y = 48
Find the x-intercept and y-intercept
Answer:
my answer came out to x = 6 + 1.5y
Step-by-step explanation: