Ben has $3.40 consisting of quarters and dimes. How many coins of each kind does he have if he has 22 coins?
Show a system of equation to represent the word problem.
Answers
There are 8 quarters and 14 dimes.
Step-by-step explanation:Let there are x quarters.
and y dimes.
Also as we know,
1 quarter= 0.25 dollar
Hence, x quarter= $ 0.25x
and 1 dime= $ 0.10
Hence, y dimes= $ 0.10y
Ben has $3.40 consisting of quarters and dimes.This means that:
0.25x+0.10y=3.40
Also, in non-decimal form it could be written as:
25x+10y=340
He has 22 coinsThis means that:
x+y=22
Now on solving it graphically we see what is the point of intersection of the two lines or system of linear equations.
We get the point of intersection as: (8,14)
i.e. x=8 and y=14
Hence, there are 8 quarters.
and 14 dimes.
Related Questions
The mean number of hours that Raphael worked over the past four weeks is 37.75. If he works 40 hours this week, what will the mean number of hours be that he will have worked over the five-week period?
What is the five-week mean?
Answers
37.75 x 4 = 151
Then, add 40 to that total to get the new total.
151 + 40 = 191
Now, divide that number by 5 (as in 5 weeks, the new number of parts).
191/5 = 38.2 hours
Total hours in 4 weeks / 4 = average of four weeks.
Total hours in 4 weeks = 37.75 x 4
= 151
Total hours in 5 weeks = 151 + 40
= 191
5-week mean = 191 / 5
= 38.2
Simplify (8j3 + 5j2 – 3) – (5j3 + 7j2 – 12j + 7) ...?
Answers
8j^3 + 5j^2 - 3 - 5j^3 - 7j^2 + 12j - 7
3j^3 - 2j^2 + 12j - 10
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
3j^3 - 2j^2 + 12j - 10
Step-by-step explanation:
I took the test and got a 100%
A surveyor, standing 100 ft. from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
Answers
= 373.205 Ft
dH/da = 100sec^2(a)
Fractional change in height = dH/H = 0.04
0.04 = 100 sec^2 a da/H
da = 0.04 H / 100 sec^2a
da = 0.01
Hope this helps
Wendy wants $15,000 saved in 6 years to make a down payment on a house. How much money should she invest now at 4.65% compounded annually in order to meet her goal?
Answers
A=$15000, n=6 years, R=4.65
Therefore,
15000=P(1+4.65/100)^6
15000=P(1.3135)
P=15000/1.3135
=$11420 (to the nearest dollars)
Solve for x. Enter your answer in interval notation using grouping symbols.
x^2+4x<45 ...?
Answers
-9,5
A brownie recipe requires one and one third cups of sugar to one cup of chocolate chips. If four and two thirds cups of sugar is used, what quantity of chocolate chips will be needed, according to the recipe?
...?
Answers
Final answer:
To find the number of chocolate chips needed for four and two-thirds cups of sugar, we use the given ratio of 4/3 cups of sugar to 1 cup of chocolate chips and set up a proportion. Solving it gives us 3.5 cups of chocolate chips.
Explanation:
To determine the number of chocolate chips needed when using four and two-thirds cups of sugar according to the brownie recipe, we must first understand the ratio given in the recipe, which is one and one-third cups of sugar to one cup of chocolate chips. This ratio can be simplified to a fraction for easier calculation: 4/3 cups of sugar : 1 cup of chocolate chips.
With this ratio, we can set up a proportion to find the amount of chocolate chips needed for four and two-thirds cups of sugar:
(4/3 cups of sugar) / (1 cup of chocolate chips) = (14/3 cups of sugar) / (x cups of chocolate chips)To solve for x, we cross-multiply and solve the resulting equation:
(4/3) * x = (14/3) * 1x = (14/3) * (3/4)x = 14/4x = 3.5The quantity of chocolate chips needed is 3.5 cups when using four and two-thirds cups of sugar.
What is the best approximation of the sine of 50°?
A. 0.2624
B. 0.6428
C. 0.7660
D. 1.1918
Answers
As I calculated it, sine 50 is equivalent to 0.2623748537.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
The graph of y = x2 is shown below.
If graphed on the same grid, which of the following could be the graph of y = 0.4x2?
Answers
The answer is third graph (middle one)
Answer:
The answer is in the attachment.
Step-by-step explanation:
Coefficient in front of x^2 is 0.4. What that means is that for same increase of x now we will have less increse of y. If you picture that we can also say that graph would be wider. The graph will stay on positive side of y axis because x^2 is always positive and 0.4 times that is again always positive.
The answer is third graph (middle one)
Miss fernandez built two rectangular gardens the length of garden a is 2 feet longer than twice its width the list of garden b is 1 foot less than the width of garden a the length of garden b is 2.5 times its width the two gardens have the same perimeter what are the dimensions of the gardens
Answers
For garden B, let width = x, length = y
So we are given the following:
L = 2+2w
x = w - 1
y = 2.5x
2w+2L = 2x+2y ------> w+L = x+y
Ok lets do some substituting into the perimeter equation
[tex]w + (2+2w) = (w-1) + 2.5(w-1)[/tex]
adding like terms...
0.5w = 5.5
w = 11
This means that:
L = 2+2(11) = 24
x = 11-1 = 10
y = 2.5x = 2.5(10) = 25
Final solution:
Garden A is 11 by 24
Garden B is 10 by 25
PLEASE HELP!!
Oscar entered y=−0.4^x+3y=−0.4^x+3 into an online graphing tool.
What function did he graph?
y=(−0.4)x+3y=(−0.4)x+3
y=(−0.4)x+3y=(−0.4)x+3
y=−(0.4)x+3y=−(0.4)x+3
y=−(0.4)x+3
Answers
Among the choices provided above the function the Oscar graph is
y=(−0.4)x+3y=(−0.4)x+3
During World War I, the Germans had a gun
called Big Bertha that was used to shell Paris.
The shell had an initial speed of 2.41 km/s at
an initial inclination of 61.5 to the horizontal.
The acceleration of gravity is 9.8 m/s2 .
How far away did the shell hit?
Answer in units of km
How long was it in the air?
Answer in units of s
Answers
2.41 km/s = 2410m/s\
To solve the second part
First we have to find Vy Vy = 2410 m/s * sin 61.5 = 2410 m/s * 0.8788 =2117.908 m/s.
When the shell reaches it's maximum height the vertical velocity component will be zero
based on that theorem let's apply linear motion equation
V = u + at
0 = 2117.908 m/s - 9.8 m/S^2 * (t)
t = 216.1130 s
As the shell has to go upward and comes back to earth the shell will require a same amount of time in order to reach earth again so the total time that shell will spend on the air will be
2*t = 432.226 s
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
To find the distance the shell hit and the time it was in the air, we need to determine the total time it takes for the shell to hit the ground. The horizontal component of the shell's initial velocity remains constant, while the vertical component is affected by gravity. By solving for the time using the vertical component, we can then multiply it by the horizontal component to find the distance and convert it to kilometers.
Explanation:To find the distance that the shell hit, we need to determine the time it was in the air. We can do this by finding the total time it takes for the shell to hit the ground. The shell's initial velocity is given as 2.41 km/s at an angle of 61.5 degrees. We can break down the initial velocity into its horizontal and vertical components. The horizontal component remains constant, while the vertical component is affected by gravity. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the time it takes for the shell to reach the ground.
Find the horizontal component of the initial velocity using the equation horz_vel = init_vel * cos(angle).Find the vertical component of the initial velocity using the equation vert_vel = init_vel * sin(angle).Using the vertical component, solve for the time it takes for the shell to reach the ground using the equation -vert_vel = 0 + 0 * t - 0.5 * acceleration * t^2.The time calculated in step 3 will give us the total time the shell was in the air.Multiply the total time by the horizontal component of the initial velocity to get the distance that the shell hit.Convert the distance from meters to kilometers by dividing by 1000.So, the shell hit a distance of [distance] km away and was in the air for [time] s.
Learn more about Calculating the distance and time a shell travels in the air here:https://brainly.com/question/24196077
#SPJ3
If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful
launches? ...?
Answers
0.97 ^ 3 = 0.91
= 91%
Answer: The required probability of three consecutive successful launches is 91.27%.
Step-by-step explanation: Given that a satellite launch has a 97% chance of success.
We are to find the probability of three consecutive successful launches.
Let P(A) denotes the probability of the event of the success of the satellite launch.
Then, according to the given information, we have
[tex]P(A)=97\%=\dfrac{97}{100}=0.97.[/tex]
Therefore, the probability of three consecutive successful launches will be
[tex]p\\\\=P(A)\times P(A)\times P(A)\\\\=0.97\times0.97\times0.97\\\\=0.912673\\\\=0.912673\times100\%\\\\=91.2673\%\\\\=91.27\%.[/tex]
Thus, the required probability of three consecutive successful launches is 91.27%.
half a pepperoni pizza plus three fourths a ham-and-pineapple pizza contains 765 calories. One fourth of a pepperoni pizza plus a whole ham-and-pineapple pizza contains 745 calories. How many calories are in each kind of pizza?
Answers
1. D (4,5)
2. C
3. D
4. A
5. C
6. D
7. B
8. C
9. A
10. B
OR
1. B (2,6)
2. A
3. A
4. C
5. D
6. A
7. A
8. B
9. C
10. A
Don't deny it, you came here for the answers ;)
Final answer:
A half pepperoni pizza contains 660 calories and a ham-and-pineapple pizza contains 580 calories.
Explanation:
Let's represent the number of calories in half a pepperoni pizza as x, and the number of calories in a ham-and-pineapple pizza as y. We can set up a system of equations to represent the given information:
0.5x + 0.75y = 765 -- Equation (1)
0.25x + y = 745 -- Equation (2)
We can solve this system of equations using the method of substitution:
From Equation (2), y = 745 - 0.25x
Substitute this value of y into Equation (1):
0.5x + 0.75(745 - 0.25x) = 765
Simplify and solve for x:
0.5x + 558.75 - 0.1875x = 765
0.3125x = 206.25
x = 660
Now substitute the value of x back into Equation (2) to find y:
0.25(660) + y = 745
Simplify and solve for y:
165 + y = 745
y = 580
Therefore, there are 660 calories in a half pepperoni pizza, and 580 calories in a ham-and-pineapple pizza.
Wally bakes muffins. in each batch of 12 muffins, he bakes 8 bluberry muffins write in simplest form the fraction of muffins that are not blue berry
Answers
Answer:
probably 4/12 = 1/3 muffins are not blueberry
Step-by-step explanation:
Find the missing length. The triangle in each pair are similar.
Answers
B/c 27/45=.6
.6*65=39
Answer:
39 UNIT
Step-by-step explanation:
According to similar triangle.
Let's call NG "X"
45/27 = 65/x
X=( 65*27)/45
X= 1755/45
X = 39
4sin(x)−4=0
solve for x
Answers
4sin(x) - 4 = 0
4sin(x) = 4
sin(x) = 1
Now use the unit circle and you'll see that the only solution in the interval [0,2pi) is x = pi/2
If you want to ignore the restriction and consider all solutions, then x = (pi/2) + 2pi*n where n is any integer
A truck carried 3 1/3 ton of sand, but lost 1/4 ton of sand along the way. how many tons of sand were survived
Answers
3 1/3=3.3+1/3=10/3
10/3-1/4
10.4/3.4-3.1/4.3
40/12-3/12
37/12
3 1/12
What is d if p equals 15 in d=-3p^2+168p-315
Answers
so your equation will look like d=3(15)^2+168(15)-315
then you will simplify
to get d= 2025+2520-315
simplify again
to get d=4230
-3(15^2)+168(15)-315=
-3(225)+2520-315=
-675+2205=
1530
d=1530 when p=15
Which of the following is not a way to prove a quadrilateral is a parallelogram?
Answers
The way to not prove a quadrilateral is a parallelogram is; Show one set of opposite sides of the quadrilateral is congruent.
Parallelogram and CongruenceA parallelogram is a quadrilateral which has opposite sides to be congruent and parallel as the name implies and hence, opposite angles of the parallelogram are congruent.
However, showing one set of opposite sides of the quadrilateral is congruent is not a confirmatory test for a parallelogram, as it evades the parallel law of opposite sides of the Parallelogram.
Read more on parallelogram;
https://brainly.com/question/17167464
A car Purchased for $18,500. After each year, the resale value decreases by 30%. What will the resale value be after 4 years
Answers
A = amount of money
P = Principle amount
r = annual rate of interest
t = number of years
what is the area of a right triangle with side lengths 6, 8, and 10? a. 48 b. 40 c. 30 d. 24
Answers
The legs are 6 and 8, and the hypotenuse is 10 (the longest side).
Since 6 and 8 are the legs (i.e. the base and height),
area = 1/2 • base • height
= 1/2 • 6 • 8 = 24
What is a soliloquy? ...?
Answers
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Which of the following is a result of shifting a circle with equation (x + 3)² + (y - 2)² = 36 left 3 units?
Answers
(x + 6)^2 + (y - 2)^2 = 36
Answer:
The answer is [The x-coordinate of the center of the circle decreases by 3.]
Step-by-step explanation:
A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?
Answers
t=d/v
Substitute your variables and solve.
65 mi/hr = 65 / 3600 mi/second
25 mi / ( 65/3600) = 1384.6 seconds
Answer:
Step-by-step explanation:
A vehicle travels at a rate of 65 m/h, How long does it take the vehicle to travel at 25 miles?
Apply the "distance formula":
d = rt
25 = 65t
25/65 = t
5/13 hour = t
or
0.385 hour = t
or
23.08 minutes = t
21/80 in a simplified fraction
Answers
What is the solution to the equation?
5(8 + 7) = 5 • x + 5 • 7
A.
x = 1
B.
x = 5
C.
x = 7
D.
x = 8
Answers
A furniture company misprinted a sales ad for a living room set but honors the advertised price. For each customer who purchases the living room set, the company suffers a loss of $125. Write a function to represent the company's total loss. What is the value of the function for an input of 50, and what does it represent? ...?
Answers
So,
f (x) = 125x
To get how much money the company loses, we can make x equal to 50.
f (50) = 125(50) = 6250
The company loses $6,250 when 50 customers purchase the furniture.
An Antique vase is projected to be worth $1000 in 2 years and $1,300 after 5 years. If the value continues to appreciate at the same rate, what will it be worth in 8 years?
Answers
The value of the antique vase after 8 years with a consistent appreciation rate, it would amount to $1,600.
An antique vase:
Value after 2 years: $1,000
Value after 5 years: $1,300
To find the value after 8 years, we can assume a constant rate of appreciation:
In 8 years, the value will be: $1,000 + ($1,300 - $1,000) = $1,300 + ($1,300 - $1,000) = $1,600
A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?
Answers
To maximize profit, the candy manufacturer should use mathematical linear programming. The decision variables are the amounts of Candy A (x) and Candy B (y). The profit function P = 285x + 260y is to be maximized subject to constraints arising from available stock of dark chocolate, caramel, and walnuts, leading to a typical linear programming problem.
Explanation:To solve this problem, we need to use Linear Programming, a mathematical model that helps in making optimal decisions. The candies are what we call decision variables. Our decision variables here are Candy A and Candy B.
Candy A: x kilograms (dark chocolate and caramel in equal parts).
Candy B: y kilograms (two parts of dark chocolate and one part of walnut).
We want to maximize the profit function P = 285x + 260y subject to constraints arising from the available stock of dark chocolate (DC), caramel (C), and walnuts (W).
DC constraint: A uses DC in equal parts, and B uses two parts DC. Therefore, x + 2y ≤ 360.C constraint: A uses equal parts C, x ≤ 430 (as B doesn't use C).W constraint: B uses one part W, y ≤ 210 (as A doesn't use W).
The next step is to solve these inequalities graphically or using mathematical methods to get values of x and y that maximize P while respecting constraints. This case, where we want to optimize a certain function with respect to constraints, is a typical linear programming problem in mathematics.
Learn more about Linear Programming here:https://brainly.com/question/34674455
#SPJ12
is 87 a prime or composite
Answers
Answer:
Prime
Step-by-step explanation:
77 is composite
It has other factors besides 1 and itself
68 -composite
52-composite (it is even)
31 -prime
59-prime