The problem is a simple algebraic equation that, when solved, shows there were 175 roses.
To solve the problem given by the student, we need to set up an equation based on the information provided. We are told that the number of roses was 15 greater than twice the number of prunes, and together they totaled 255.
Let the number of prunes be p. Then the number of roses can be represented as 2p + 15. Adding these amounts must total 255, so we can write the following equation:
2p + 15 + p = 255
Combining like terms:
3p + 15 = 255
Subtracting 15 from both sides of the equation:
3p = 240
Dividing both sides by 3:
p = 80
Now that we have the number of prunes, we can find out the number of roses:
Roses = 2p + 15 = 2(80) + 15 = 160 + 15 = 175
Therefore, the student had 175 roses.
I need to solve this problem in my exam:
Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x^2. Find the average cost per radio of producing the first 35 radios. ...?
The area of a rectangle is 48 square centimeters and the length of the rectangle is 8 centimeters longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
8w = 48
w + 8 = 48
w(w+8)=48w(w+8)=48
w + 8w = 48
One airplane is approaching an airport from the north at 124 km/hr. A second airplane approaches
from the east at 223 km/hr. Find the rate at which the distance between the planes changes when
the southbound plane is 34 km away from the airport and the westbound plane is 15 km from the
airport.
The distance between the planes is increasing at a rate of approximately 252 km/hr when the southbound plane is 34 km from the airport and the westbound plane is 15 km from the airport.
Explanation:Identify the relative motion: We need to find the rate of change of the distance between the planes, which is a relative motion problem.
Calculate individual velocities: Since the planes are approaching from different directions, we need to consider their velocities as vectors. The southbound plane has a southward velocity of 124 km/hr, and the westbound plane has an eastward velocity of 223 km/hr.
Apply Pythagorean theorem: At the given moment, the distance between the planes is the hypotenuse of a right triangle formed by their individual velocities. Using the Pythagorean theorem:
Distance^2 = Southbound velocity^2 + Westbound velocity^2
Distance^2 = (124 km/hr)^2 + (223 km/hr)^2
Distance ≈ 258.5 km
Differentiate distance equation: To find the rate of change of the distance, we need to differentiate the distance equation with respect to time. This gives us the relative velocity between the planes.
Calculate relative velocity: Taking the derivative of the distance equation and plugging in the individual velocities:
Rate of change of distance = (Southbound velocity * Eastward velocity) / Distance
Rate of change of distance ≈ (124 km/hr * 223 km/hr) / 258.5 km ≈ 252 km/hr
Therefore, the distance between the planes is increasing at a rate of approximately 252 km/hr when the southbound plane is 34 km from the airport and the westbound plane is 15 km from the airport.
The function f(x) is represented by the table below. What are the corresponding values of g(x) for the transformation g(x) = 4f(x)?
$250 at 5% simple interest for 3 years
How many meters are in 7.2 kilometers?
I included a photo with the information! Here are the questions. A thorough explanation and diagram would help IMMENSELY. Thank you so much!
Question 1: reate a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Question 2: Create a labeled diagram of the Egyptian. Use x to represent the length of a side of the base of the candle. Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Question 3: 1. To impress management, you decide to propose your own original candle design based on solid figures. Make your candle design attractive and make sure it will be practical to manufacture. Draw the candle in the space below and label the drawing with dimensions. Then write an equation for the volume of the candle in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in standard form.
Answer:
1) Labeled diagram in the first figure attached
Volume of the rectangular prism: x^2*(x-1) = x^3 - x^2 ; x in cm, volume in cm^3
2) Labeled diagram in the second figure attached
Volume of the right square pyramid: (1/3)*(x^2)*21 = 7*x^2, x in cm, volume in cm^3
3) A cylinder is proposed, where x is the radius of the base and the height is 4 times the radius. Labeled diagram in the third figure attached .
Volume of the cylinder: π*x^2*(4*x) = 4*π*x^3, x in cm, volume in cm^3
f(x)=2x- 1 what is odd number
How do you solve this one 10x^2-25=x^2
Average speed of Car 1 = 35 mph. Average speed of Car 2 = 55 mph. Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
How long before Car 2 overtakes Car 1? ___________ hour.
Answer:
.525
Step-by-step explanation:
35(t+18/60) = 55t
35t +10.5 = 55t
10.5 = 20t
0.525 = t
X^3+512=0 real or imaginary solution by factoring
Find the difference. (-ab+8a-5)-(-8ab-4)
Is 4yards greater, less, or equal to 13feet
What is the length of arc AB if the radius is 14
A country's population in 1991 was 136 million. In 2000 it was 141 million. Estimate the population in 2016 using the exponential growth formula. Round your answer to the nearest million. ...?
A car travels at 65 mph going through construcion it travels at 3/5 this speed write this fraction as a decimal an the find the speed
The daily fat allowance is 70g, the dinner has 48g. What percentage of her total daily allowance of fat will the dinner be?
help please!!!!!!!!!!!!!!!!!!!!!
Whenever you sign a lease for an apartment, you typically have to pay a security deposit before you even move in; this is in case something happens while you are occupying the apartment and repairs have to be made. One apartment building has apartments that rent for $900 a month and a security deposit of $600. Write an equation to represent the situation described. F(x) = 600x + 900 F(x) = 600x - 900 F(x) = 900x - 600 F(x) = 900x + 600
Which graph best represents the solution to the following system?
5x - 2y < (less than or equal to) 10
x + y < 5
The graph that best represents the solution to the given system is:
Graph A.
Step-by-step explanation:We are given a system of inequalities as:
[tex]5x-2y\leq 10[/tex]
and [tex]x+y<5[/tex]
i.e. the graph of first inequality is a solid straight line( since the inequality is not strict) that passes through (2,0) and (0,-5) and the shaded region is towards the origin( since it passes the zero point test)whereas the graph of second inequality is a dotted straight line(since the inequality is strict) that passes through (0,5) and (5,0) and the shaded region is towards the origin( since it passes the zero-point test)Hence, the graph is:
Graph A.
Hue is 56in.tall. His friend is 42in.tall. Hue's shadow is 24in.long. How long is his friend's shadow at the same time?
By setting up a proportion based on the concept of similar triangles, we can solve for the length of Hue's friend's shadow, which is 18 inches.
Explanation:To find the length of Hue's friend's shadow, we can use the concept of similar triangles. The ratio of Hue's height to his shadow's length is the same as the ratio of his friend's height to his friend's shadow's length, assuming the sun's rays are parallel and create similar angles with respect to the ground for both individuals.
Hue's height to shadow length ratio is 56 inches to 24 inches. Let's denote the length of his friend's shadow as x inches. We can set up a proportion:
56 inches (Hue's height) / 24 inches (Hue's shadow) = 42 inches (friend's height) / x inches (friend's shadow)
Solving for x, we get: 56/24 = 42/x, which simplifies to x = (42 * 24)/56 = 18. Therefore, Hue's friend's shadow is 18 inches long.
Which of the following is not a cost of being financially irresponsible?
You are late to work because you forgot to set the alarm.
You have no money to pay the cable bill, but you have a new flat screen television.
You can't afford to go to the movies.
You end up paying more for things because of credit card interest.
what is the domain of this function p(w) 2/3w^9
...?
You have a fractions, so the only thing you must be sure of is that the denominator is not zero.
In your case, the denominator is given by the function f(w)=3w9. You need to find out the values of w for which f(w)=0. You have
f(w)=0⇔3w9=0⇔w9=0⇔w=9√0=0
So, your only problem is w=0, and all other numbers are fine.
Your domain is thus given by the set {x∈R∣x≠0}
The domain can also be written as (−∞,0)∪(0,+∞).
On a certain map 3/4 inch represents one mile, what distance, in miles is represented by 1 3/4 inches
In the function y=-2(x-1)^2+4, what effect does the number 4 have on the graph, as compared to the graph of the function y=x^2?
A. It shifts the graph 4 units to the right.
B. It shifts the graph down 4 units.
C. It shifts the graph up 4 units.
D. It shifts the graph 4 units to the left. In the function y=-2(x-1)^2+4, what effect does the number 4 have on the graph, as compared to the graph of the function y=x^2?
A. It shifts the graph 4 units to the right.
B. It shifts the graph down 4 units.
C. It shifts the graph up 4 units.
D. It shifts the graph 4 units to the left.
Answer:
it shifts the graph up four units
Step-by-step explanation:
it shifts the graph up four units because its outside of the phranthasies, in y=a(x+h)k k is the shift vertically
In the function y=-2(x-1)²+4, the number 4 represents a vertical translation, shifting the graph up by 4 units when compared to the function y=x². Option C) is the correct answer.
In the function y=-2(x-1)²+4, the number 4 acts as a vertical translation of the graph. Comparing this function to the standard parabola y=x², the addition of 4 to the equation represents shifting the entire graph of the parabola upwards by 4 units. Therefore, the correct answer to the effect of the number 4 on the graph, as compared to the graph of the function y=x² is: C. It shifts the graph up 4 units.
Understanding graph transformations is key in analyzing how different parts of the function equation affect the function's graphical representation.
A positive constant added to a function results in a vertical shift of the graph in the upward direction. This means that every point on the graph y=x² is moved 4 units higher on the y-axis to create the graph of y=-2(x-1)²+4.
Integrate sin^9(x)dx ...?
A cannery processed 1,445 pounds of strawberries in 4.5 hours. The cannery processed 2,320 of strawberries in 7 hours. Write a linear equation to model the relationship between the weight of strawberries S and time T. How many pounds of strawberries can be processed in 11 hours?
The linear equation to model the relationship between the weight of strawberries and time can be found using the slope and y-intercept. The equation is S = 690T - 560.5. In 11 hours, the cannery can process 7109.5 pounds of strawberries.
Explanation:To write a linear equation to model the relationship between the weight of strawberries S and time T, we need to determine the slope and the y-intercept. The slope represents the rate at which strawberries are processed per hour, while the y-intercept represents the initial amount of strawberries processed.
Using the given information, we can use the formula for calculating the slope (m) of a line: m = (y2 - y1) / (x2 - x1). Plugging in the values, we have: m = (2320 - 1445) / (7 - 4.5) = 690 pounds/hour.
Next, we can calculate the y-intercept (b) using the formula: b = y - mx. Plugging in the values for one of the points (1445 pounds in 4.5 hours), we have: 1445 = 690(4.5) + b. Solving for b, we get: b = -560.5 pounds.
Therefore, the linear equation to model the relationship between the weight of strawberries S and time T is: S = 690T - 560.5. To find the number of pounds of strawberries that can be processed in 11 hours, we can substitute T = 11 into the equation: S = 690(11) - 560.5 = 7109.5 pounds.
Learn more about Linear equation here:https://brainly.com/question/32634451
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Which expression is equivalent to 3x(-4x^2+5x-8)-6(x^2-5x+7)?
A. 12x^3-9x^2+6x-42
B.-12x^3-54x^2+6x-42
C.-12x^3+9x^2+6x-42
D.-27x^3-6x^2+6x-42
In the normal distribution, values in the distribution being measured are close to the mean (high or low values are infrequently found). true or false ?
Answer: True.
Step-by-step explanation:
Hi, the statement "In the normal distribution, values in the distribution being measured are close to the mean (high or low values are infrequently found)." is true.
The normal distribution is a probability function that how the values of a measure are distributed. Most of the values cluster around the mean, it’s a symmetric distribution.
Normal or Gaussian distributions Means that many variables have similar characteristics. So, middle values have higher probability or are more likely to occur, and extremely low or high values are more infrequent.
assume 1 card is drawn from a standard deck of 52 cards.find the probability of drawing a 6 or a face card