Answer:
Each geometry book costs $6, each algebra book costs $8.
Let a=cost of one algebra book and g=cost of one geometry book. We have:
2a + 3g = 34-------->6a + 9g = 102
3a + 2g = 36-------->6a + 4g = 72
-------------------
5g = 30
g = 6
2a + 3(6) = 34
2a + 18 = 34
2a = 16--->a = 8
Question: John paid $34 for two algebra and three geometry books. He paid $36 for three algebra and two geometry books. What is the cost of each book?
Answer: The cost of each algebra book is $8 and the cost of each geometry book is $6.
Step-by-step explanation:
a= algebra book cost
g= geometry book cost
Here's what we know:
2a + 3g = 34 (the 2 alg and 3 geo comes to $34)
3a + 2g = 36 (the 3 alg and 2 geo comes to $36)
This is a classic elimination method problem. I suggest that we multiply the first equation by -2 and the second by 3. This way, we can eliminate the variable g and still keep the other parts of the problem in the positive range:
-4a - 6g = -68
9a + 6g = 108
-------------------
5a = 40
Divide by 5:
a = 8
Now to solve for g:
2 * 8 + 3g = 34
16 + 3g = 34
3g = 18
g = 6
check (by using the second equation):
3 * 8 + 2 * 6 = 36
24 + 12 = 36
Can someone help please
Answer:
-18a⁸
Step-by-step explanation:
-2a²(-3a³)²
-2a²*9a⁶ (Opening the square)
-18a⁸
You are in charge of purchasing breakfast for an upcoming service activity involving about 50 people.
You have the choice to pick one of the following food items:
donuts ($0.30/each)
muffins ($0.50/each)
bagels ($0.40/each)
You have the choice to pick one of the following drinks:
individual cartons of milk or chocolate milk ($0.50/each)
individual bottles of orange juice or apple juice ($0.75/each)
You must stay within a budget of $100.
Write the following in your notebook.
What food item did you choose? What drink did you choose? Why?
Write an inequality to represent the cost of the items (less than or equal to $100) in standard form. Use x to represent the number of food items and y to represent the number of drinks.
Solve the inequality for y (slope-intercept form). Interpret the slope in context of the drinks and food items that are being purchased.
Graph the inequality and describe your graph and the process you used; for example, is your line dotted, solid, or shaded up or down? What does the shaded region represent?
What are the x and y-intercepts? Explain what these would represent in this situation.
What are the domain and range in this problem? Explain why you would or would not use the minimum and maximum values of the domain and range. How are the domain and range in the context of this problem different from the domain and range of any linear equation? What are the limits?
The limits of the domain and the range are 0 to 200, respectively; and you would use the minimum and maximum values of the domain and range because the graph of the inequality uses a solid line.
The items chosenThe items selected here could be any of the listed drinks and food items.
To solve this question, we use the following selection:
Muffins ($0.50/each) -- xindividual cartons of milk or chocolate milk ($0.50/each) -- yBudget of $100The inequality of the cost of itemsIn this case, we use the less than or equal to inequality.
So, we have:
0.5x + 0.5y ≤ 100
Solve the inequality for y (slope-intercept form).In (b), we have:
0.5x + 0.5y ≤ 100
Subtract 0.5x from both sides
0.5y ≤ -0.5x + 100
Divide through by 0.5
y ≤ -x + 200
This means that the slope is -1, and it means that for every food item bought, there is a decrement of 1 in the drink.
The graph of the inequalitySee attachment for the graph of the inequality
The features of the graph include
Straight and solid lineIt is shaded downThe shaded region represents the acceptable solutionsWhat are the x and y-intercepts?From the attached graph, we have:
x-intercept = 200y-intercept = 200This means that you can buy 200 food items, when you buy no drinks or buy 200 drinks when you buy no food item
What are the domain and range in this problem?These are the acceptable x and y values of the graph.
From the attached graph, we have:
Domain: 0 ≤ x ≤ 200Range: 0 ≤ y ≤ 200The domain and range are different from the domain and range of any linear equation because the domain and the range of a linear equation is the set of all real numbers, while this domain and range are limited to 0 to 200
Read more about linear inequality at:
https://brainly.com/question/371134
#SPJ1
6) What will be the new position of the given
point (0, 6) after translation of 6 units down
and 3 units right?
a) (6, 3)
b) (3, 0)
c) (-6, 3)
d) (-3,0)
Please help omg
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
Answer:
[tex]29i[/tex]
Step-by-step explanation:
From this information, we can write the following equation: [tex](2-5i)(2 + 5i)(i)[/tex]
We can see that there is the factorization of the difference of squares, so we can first expand that. The equation will become the following: [tex](4+25)(i)[/tex]
= [tex]29i[/tex]
hope this helped! :)
A bag contains 7 red marbles, 12 orange marbles, 18 yellow marbles, and 5 purple marbles. a marble is drawn at random from the bag. what is the probability that the marble drawn will not be orange? 130 112 27 57
Answer:
its 5/7
Step-by-step explanation:
no of marbles that r not orange = 30
no of total marbles = 42
probability = 30/42
= 15/21
= 5/7
I hope my answer is helpful
A rectangular plot measures 140m by 20m find the area in ares
Answer:
28ares
Step-by-step explanation:
that's the correct way.i hope you will understand it. if there's any question feel free to ask. nice day.
Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?
The values of n does either player have a winning strategy is; Player B has a winning strategy for all n ≥ 2.
How to predict winning probability?Let us use an example to solve this question. The game is played on the complete graph Kₙ (n ≥ 2), which consists of n vertices, each pair of vertices joined by an edge.
Now, Initially all edges are unpainted. At each turn, A chooses an edge, which B paints blue or red. Now, B will win if, after the last edge is painted, there is a vertex which is joined to all other vertices by blue edges. If that doesn't happen, then A wins.
The winning strategy of B is described by 3 rules which are;
Rule 1; Paint the last edge blue.Rule 2. Never paint an edge red if that would result in two red vertices being joined by an unpainted edge.Rule 3. Use red paint whenever permitted by Rules 1 and 2.Thus, if n >2, the first edge will always be painted red, the second will always be painted blue.
In conclusion, when we apply that same scenario to our question it is the same result and as such Player B has a winning strategy for all n ≥ 2.
Read more about probability at; https://brainly.com/question/24756209
#SPJ2
need help on this geometry problem
which of the following is a true statement
Answer:
b
Step-by-step explanation:
[tex] = \frac{68}{5} - \frac{18}{5} \\ [/tex]
[tex] = \frac{50}{5} \\ [/tex]
Change into lowest term
[tex]10...[/tex]
What is the slope of a line that goes through (2, -2) and (5, 6)
8/3
4/3
3/4
3/8
Answer:
correct option is A i.e. 8/3
please hepl will give brainly, 30 points
Answer:
∠G = 53°
∠H = 90°
∠I = 37°
Step-by-step explanation:
∠H = 90° because it is a right angle and all right angles = 90°
The sum of all angles in a triangle = 180°
∠H + ∠G + ∠I = 180°
90° + (5x - 7)° + (3x + 1)° = 180°
5x - 7 + 3x + 1 = 90° Subtract 90° from both sides
8x - 6 = 90 Adding like terms
8x = 96 Adding 6 to both sides
x = 12 Dividing both sides by 8
Now solve for ∠G and ∠I using 12 as the value for x
∠G = (5x - 7)° ∠I = (3x + 1)°
∠G = 5·12 - 7 ∠I = 3·12 + 1
∠G = 53° ∠I = 37°
What is the equation?
There is no answer? So how am I supposed to answer it?
Answer:
Yeah How am I supposed to answer it?
Step-by-step explanation:
Riya's biking app says that she rides at a speed of 5 miles per hour.
At this speed, how far does Riya ride in 1 hour?
At this speed, how far does Riya ride in 3 hours?
Write an equation for the relationship between Riya's distance biked, d,and time t
Answer:
Step-by-step explanation:
Formula
d = speed * time
d = s * t
Givens
t = 1 hour
t2 = 3 hours
s = 5 miles / hour
Solution
t = 1 hour
d = s * t
d = 5 mph * 1 hour
d = 5 miles
t = 3 hours
d = s * t
d = 5 miles / hour * 3 hours
d = 15 miles
Answer
d = s * t
d = 5 miles
d = 15 miles
A campaign manager is creating campaign signs that advertise his political candidate. The campaign manager would like to maximize the surface area of the signs so that passersby have the greatest chance of seeing them. In keeping with local campaign laws, the campaign signs must have a perimeter of 160 inches. Explain how the campaign manger can find the width and height of the signs that maximize area. Round your values to the nearest tenth of a square inch.
Will mark brainliest please help!!
So if length be L and width be B
We know
Perimeter
2(L+B)So if he wants to create a rectangle advertisement
2(L+B)=160L+B=80The sum of length and breadth must be 80
If it's square
4S=160S=40inIt should have side as 40in
Mrs. gellar works at a diner. at the end of
her shift, she was putting away pies in the
display case. there were 5 pies, and of 3/8
each pie left. what fraction of the pies did
mrs. gellar put away?
The diameter of a ceiling fan, blade tip to blade tip, is 120 centimeters.
a) about how many whole revolutions does it take for the fan to move 1000 meters?
_______
b) if the fan rotates at 40 revolutions per minute, about how long does it take to move 1000 meters? round to the nearest minute.
_______
The number of whole revolutions for 1000 meters is 265, while the time taken to move 1000 meters with a speed of 40rev/min is 7minutes.
What is a revolution?This is the number of times a body moves round a circular path.
A revolution is equal to the circumference of a circle.
Analysis:
r = 120/2 = 60cm
1 revolution of a circle = 2πr
Let n be the number of revolutions
so that 2πr x n = 1000 x 100 since 100 cm = 1 m
n = 100000/2πr = 265 revolutions
If the Fan turns 40 rev / minute
Then it 265 revolutions = 1000 meters, 265/40 = 7 minutes
In conclusion, the number of revolutions for 1000 meters is 265 and the time taken for 265 revolutions is 7 minutes.
Learn more about revolutions : brainly.com/question/16533738
#SPJ1
Can anyone tell me the formula or way to solve this problem
[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]
can someone help me pls
Answer:
90
Step-by-step explanation:
Formula : 180 ( n - 2 ) / n n being the amount of sides
180 ( 4 - 2 ) / 4 = 90
How many participants will make 45 handshakes in total
Is 1000 a sequence in 50 65 80 95
Answer: yes
Step-by-step explanation:
it’s the 41st term
Select the correct answer from each drop-down menu.
Three students used factoring to solve a quadratic equation.
x²+17x+72=12.
Jordan's Solution x² + 17x + 72 = 12, (x + 8)(x + 9)= 12, x+8=12 & x+9=12
Keith's Solution x² + 17x + 72 =12, x² + 17x +60 =0, (x +5)(x +12) =0 x + 5 = 0 & x + 12 =0.
Randall's Solution x² +17x +72 = 12,x2 +17x = -60,x(x +17) = -60, -60 & x +17 = -60.
he equation was solved correctly by ____. The solutions of the equation are____.
Answer:
Keith's Solution-5-12Step-by-step explanation:
x + 5 =0 & x + 12 =0
:- x = -5 & -12
What is the longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide, and 11cm tall?
The longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide and 11cm tall is 19.1cm.
What is a right rectangular prism?A right rectangular prism is a three dimensional solid shape formed by 6 rectangles.
it is also called the cuboid.
Analysis:
The diagonal of the face of the prism with dimensions 14cm long and 13cm wide is the longest line segment that can be drawn.
Since rectangles have 90° on each vertex, we can use Pythagoras theorem to calculate for the length of the diagonal.
[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](13)^{2}[/tex]
= 196 + 169 = 365
[tex](diagonal)^{2}[/tex] = 365
diagonal = [tex]\sqrt{365}[/tex] = 19.1cm
In conclusion, the length of the longest diameter is 19.1cm
Learn more about Right rectangular prism: brainly.com/question/3317747
#SPJ1
A soup can, shaped like a cylinder, has a diameter of 3.5 inches and a height of 5 inches. Each serving of soup is 15 cubic inches. If a can of soup this size costs $1.99, what is the cost for each serving of soup? Round to the nearest cent.
Answer: The answer to your question is Cost of a serving = $0.62
Step-by-step explanation:
Data
diameter = 3.5 in
height = 5 in
each serving = 15 in³
Cost of the can = $1.99
Process
1.- Calculate the volume of the can
Volume = πr²h
-Substitution
Volume = (3.14)(3.5/2)²(5)
-Simplification
Volume = (3.14)(3.062)(5)
-Result
Volume = 48.08 in³
2.- Use proportions and cross multiplication to find the cost of a serving.
48.08 in³ ---------------- $1.99
15 in³ ---------------- x
x = (15 x 1.99)/48.08
x = 29.85/48.08
x = $0.62
(3x+8) (x + 4) need help solving the problem
Answer:
3x^2 [squared] + 20x + 32 (If your factoring)
Step-by-step explanation:
3x X x = 3x^2
3× X 4 = 12x
8 X x = 8x
8 X 4 = 32
Find the lateral surface area of the triangular prism.
Answer:
672
[tex]A_L = (a+b+c)h = (12+10+20)*16 = 672[/tex]
Find the MAD:
98, 140, 220, 150
Answer:
I'm not too sure but I think It's 34
Step-by-step explanation:
Rusty in that particular area of math
PLEASE HELP!!
(look at picture!)
Answer:
a. 35, 34
b. 25, 18
Step-by-step explanation:
Evaluate the indefinite integral.
Answer:
[tex]\frac{1}{3} x^3 - x^2 + 4x[/tex]
Step-by-step explanation:
All this takes is the use of the power rule, which, for integrals, says that
∫[tex]x^n[/tex] = [tex]\frac{1}{n+1}x^{n+1}[/tex].
With this in mind, we can integrate:
∫[tex]x^2 - 2x + 4[/tex]
= [tex]\frac{1}{3} x^3 - x^2 + 4x[/tex].
We can also check our answer by differentiating our answer:
[tex]\frac{d}{dx} (\frac{1}{3}x^3 - x^2 + 4x)\\\\ = x^2 - 2x + 4[/tex]
so we are correct!
hope this helped!
Mrs. Purdue needs to pick three random students in her class to be representatives on the student council. Explain how Mrs. Purdue could use slips of paper to generate a random sample.
Answer:
See below
Step-by-step explanation:
She could have each student in the class write his or her name on a slip of paper and put it in a bowl. Then, she could shake the bowl and pull out any slip of paper with a student's name on it. After 3 times, the random sample would be over, and Mrs. Purdue would have her 3 representatives.
please help me It's pythagorean theorem
Answer: 4
Step-by-step explanation:
3^2 + b^2 = 5^2
9 + b^2= 25
b^2 = 16
b = ±4
Answer:
The simple answer is 4 inches for steps look below
Step-by-step explanation:
According to pythagoras theorem
[tex] {5}^{2} = {3}^{2} + {x}^{2} \\ \\ \\ 25 - 9 = {x}^{2} \\ \\ x = 4[/tex]
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE