Answer: 12 and 36
Step-by-step explanation: The best way to approach a word problem like this is to break it down sentence by sentence.
We know that the sum of two numbers is 48 so we can move on to the next sentence. Now, let's take a look at the second sentence. One number is 3 times as large as the other.
This sentence tells us what variables we are going to use to represent our numbers.
So if we use x to represent one of our numbers, and one number is 3 times as large as the other, we can use 3x to represent our other number. Also, make sure to always label your variables.
X ⇒ first number
3x ⇒ second number
Now let's look back at the first sentence. "The sum of two numbers is 48". This sentence tells us how we will set up our equation. "The sum" if our variables are X and 3x will be X + 3x = 48.
Keep in mind, the word "is" means equal.
Now we have the following equation and we can solve for X.
X + 3x = 48
We start by simplifying on the left side to get 4x.
Now we have the following equation.
4x = 48
÷4 ÷4 ← divide both sides of the equation by 4
X = 12
So our first number, X, is 12 and our second number will be 3 × 12 or 36.
Therefore, our two numbers are 12 and 36.
The function f(x) = –x2 + 16x – 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points
please help
Final answer:
The vertex of the profit function f(x) = -x^2 + 16x - 60 is (8, 4), meaning the maximum profit is $4 when 8 candles are sold. The x-intercepts are (6,0) and (10,0), indicating zero profit when either 6 or 10 candles are sold.
Explanation:
The function given is a quadratic equation of the form f(x) = ax2 + bx + c, where the constants are a = -1, b = 16, and c = -60. To find the vertex of the parabola, we can use the formula -b/(2a) for the x-coordinate of the vertex.
Calculate the x-coordinate of the vertex: x = -b/(2a) = -16/(2 * -1) = 8.
Substitute x = 8 into the original function to find the y-coordinate: f(8) = -(8)2 + 16(8) - 60 = -64 + 128 - 60 = 4.
The vertex is at the point (8, 4). In the context of the problem, this point represents the maximum daily profit of $4, which occurs when 8 candles are sold.
To determine the x-intercepts, we set f(x) to zero and solve for x, which represents the number of candles sold when the profit is zero.
Set the function equal to zero and solve for x: 0 = -x2 + 16x - 60.
Apply the quadratic formula x = [-b ± sqrt(b2 - 4ac)]/(2a) to find the x-intercepts. In this case, a = -1, b = 16, and c = -60.
Calculate the discriminant, sqrt(162 - 4(-1)(-60)) = sqrt(256 - 240) = sqrt(16) = 4.
Find the two x-intercepts: x = [16 ± 4]/(2 * -1) which yields x = 6 and x = 10.
The x-intercepts (6,0) and (10,0) indicate the number of candles sold at which the profit would be zero, specifically at 6 and at 10 candles sold.
Read the following statement: If two angles are acute, their sum is never a straight line. The hypothesis of the statement is:
their sum is never a straight line.
two angles are acute.
If two angles are acute they are straight lines.
None of the choices are correct.
The correct option is (3).
What is acute angle?An acute angle is defined as an angle that measures less than 90 degrees that is measure between 0° to 90°.
Given that if two angles are acute, their sum is never a straight line.
The hypothesis of this would be the one which would satisfy the opposite of the given statement
1) their sum is never a straight line which is Incorrect.
2) two angles are acute which is incorrect because this is given.
3) If two angles are acute they are straight lines which is right.
Hence, the correct option is (3).
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Which represents a quadratic function? f(x) = −8x3 − 16x2 − 4x f (x) = x 2 + 2x − 5 f(x) = + 1 f(x) = 0x2 − 9x + 7
Answer: The correct answer is [tex]f(x)=x^2+2x-5[/tex]
Step-by-step explanation:
A Quadratic equation is defined as the equation in which the highest power of the variable is 2. The general form of this equation represents:
[tex]ax^2+bx+c=0[/tex]
where, [tex]a\neq 0[/tex]
From the given options:
1. [tex]f(x)=-8x^3-16x^2-4x[/tex]: Here, the highest power of the variable is 3. Therefore, it is not a quadratic equation.
2. [tex]f(x)=x^2+2x-5[/tex]: Here, the highest power of the variable is 2. Therefore, it is a quadratic equation.
3. [tex]f(x)=+1[/tex]: Here, the highest power of the variable is 0. Therefore, it is not a quadratic equation.
4. [tex]f(x)=0x^2-9x+7[/tex]: Here, the highest power of the variable is 1. Therefore, it is not a quadratic equation.
Hence, the correct answer is [tex]f(x)=x^2+2x-5[/tex]
5v + 7f =28.70 if f is 2.85
5v+7(2.85)=28.70
5v+19.95 = 28.70
5v = 8.75
v = 1.75
Find the length of the diameter of a sphere with a surface area of 452.39^2 ft.
surface area = 4*pi*r^2
using 3.14 for pi
452.39 = 4*3.14*r^2=
452.39=12.56* r^2
r^2 = 452.39/12.56 = 36.0
sqrt(36) = 6= r
diameter = 2r = 6*2= 12
diameter = 12 feet
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Check all that apply.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 24
x2 + (x + 2)2 = 100
Please help me quickly, I really need the help. I'll even mark brainiest if you do it correctly. I really need this and I need whoever does this to pay attention to the whole "Check all that apply". I'm adding the picture below.
The equation that can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex]
Given thatThe area of the right triangle shown is 24 square feet.
We have to determine
Which equations can be used to find the lengths of the legs of the triangle?
According to the question
From the given figure the base of the triangle is x.
And the height of the triangle is (x+2).
What is the area of a triangle?The area of the triangle is given by half the product of the height and base.
[tex]\rm Area = \dfrac{1}{2} \times base \times height\\ [/tex]
Substitute all the values in the formula;
[tex]\rm Area \ of \ right \ triangle= \dfrac{1}{2} \times base \times height\\ \\ \rm 24= \dfrac{1}{2} \times x \times (x+2)\\\\ \rm 0.5(x)(x + 2) = 24[/tex]
The equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].
Hence, the equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].
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3+-1/1/3 the first half is 3+-1 the second half is 1/3
Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event
Answer: False
Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.
A. True
B. False
Suppose i pick a jelly bean at random from a box containing two red and ten blue ones. i record the color and put the jelly bean back in the box. if i do this three times, what is the probability of getting a blue jelly bean each time? (round your answer to three decimal places.)
The city of Lakeside has a population of 22,000 people and is decreasing at a rate of 1.5% The population in 3 years would be
A)Approximately 21,000 people
B)None of the choices are correct
C)Approximately 20,000 people
D)Approximately 25,000 people
E)Approximately 19,000 people
Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer. y3 - 2y2 + 3y + 5, y3 - 4y2 + 2y - 5, y3 - 4y2 + 2y + 5, y3 - 8y2 + 8y + 5.
Answer:
[tex]y^3 - 8y^2 + 8y+5)[/tex]
Step-by-step explanation:
Take [tex]2y^2 - 3y - 5[/tex] from [tex]y^3 - 6y^2 + 5y[/tex]
Subtract [tex]2y^2 - 3y - 5[/tex] from [tex]y^3 - 6y^2 + 5y[/tex]
[tex]y^3 - 6y^2 + 5y-(2y^2 - 3y - 5)[/tex]
Multiply negative sign inside the parenthesis
[tex]y^3 - 6y^2 + 5y- 2y^2 + 3y +5[/tex]
Combine like terms
[tex]y^3 - 8y^2 + 8y+5[/tex]
Answer:
Step-by-step explanation: y3 - 8y2 + 8y + 5 (Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer.)
Why might algebra tiles not be a good tool to use to factor x2 + 18x + 80? Explain.
Algebra tiles are used to factorize a polynomial. The factorization of the given trinomial will be very difficult to perform using the algebra tiles due to the large number of tiles used.
The given quadratic polynomial or trinomial is [tex]x^2 + 18x + 80[/tex].
The algebra tiles required to solve the given trinomial are,
1 x-squared tile.18 x-tiles.80 unit tiles.So, the total number of times required will be 1+18+80 or 99 tiles.
Now, it will be very difficult to drag or arrange so many tiles on the board. Also, the space could be a problem in this case.
Therefore, the factorization of the given trinomial will be very difficult to perform using the algebra tiles due to a large number of tiles used.
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Julio paid 1.3 times his normal hourly rate for each he works over 31 hours in a week. Last week he worked 35 hours and earned $448.88. What is julios normal hourly rate ?
Solve the equation: 2.6 = -0.2t
In how many ways can 2 singers be selected from 4 who came to an audition?
A. 6
B. 2
C. 12
D. 4
In a batch of 280 water purifiers, 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary.
A. 4.3%
B. 5.6%
C. 95.7%
D. 71.8%
Answer: A. 6
A. 4.3%
Step-by-step explanation:
The total number of singers = 4
To choose singers = 2
The number of ways to choose 2 singers from 4= [tex]^4C_2=\frac{4!}{2!(4-2)!}=3\times2=6[/tex]
Hence, A is the right option.
The total number of water purifiers T= 280
The number of defective purifiers D= 12
The probability that a water purifier chosen at random will be defective (in percent)=[tex]\frac{\text{T}}{\text{D}}\times100[/tex]
[tex]=\frac{12}{280}\times100\\=0.042857\times100\\=4.2857\%\approx4.3\%[/tex]
Hence, A is the right option.
Apply the distributive property to factor out the greatest common factor. 45+75=
Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously, how much money will she have in nine months?
Identify the value of y
24^2 = 18 * (18 +y)
576 = 324+18y
252 =18y
y = 252/18 =14
y = 14
The value of y is 14.
What is a circle?'A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant'
According to the given problem,
We know,
⇒ 18 ( 18 + y ) = 24²
⇒ 324 + 18y = 576
⇒ 18y = 576 - 324
⇒ 18y = 252
⇒ y = 252/18
⇒ y = 14
Hence, we can conclude, the value of y is 14.
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The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12).
The equation of the parabola is y =
x2 +
x +
.
The equation of the parabola with a vertex at (-2, -20) and a y-intercept at (0, -12) is y = 2x^2 + 8x - 12.
Explanation:To find the equation of the parabola, we can use the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola, and 'a' is a coefficient that determines the parabola's width and direction. Since we have the vertex (-2, -20) and the y-intercept (0, -12), we can plug in these values to solve for 'a':
y = a(x - (-2))^2 - 20
Using the y-intercept:
-12 = a(0 - (-2))^2 - 20
-12 = 4a - 20
8 = 4a
a = 2
The equation of the parabola is therefore:
y = 2(x + 2)^2 - 20
Expanding the equation:
y = 2(x^2 + 4x + 4) - 20
y = 2x^2 + 8x + 8 - 20
y = 2x^2 + 8x - 12
The final quadratic equation of the parabola is:
y = 2x^2 + 8x - 12
Given the equation 5x + 23 = − 2x − 12, which order of operations completely solves for x?
a.Subtract 5x, then subtract 23, lastly divide by −7
b. Subtract 2x, then add −23, lastly divide by 7
c.Add 5x, then subtract 12, lastly divide by 7
d. Add 2x, then subtract 23, lastly divide by 7
16% of what number is 17 ?
Step-by-step explanation:
To find out what 16% of 17 is, we create a cross multiply equation
16/100=17/x
Cross multiply
(16 * x = 16x)
(100 * 17 = 1700)
16x = 1700
1700/16 = 106.25
if ∠1 and ∠2 are complementary and m∠1= 17°, what is m∠2?
173 degrees
90 degrees
73 degrees
77 degrees
(02.05 MC)
Triangle ABC is transformed to obtain triangle A′B′C′:
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC.by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees
A new machine can make 10,000 aluminum cans three times faster than an older machine. with both machines working, 10,000 cans can be made in 9 hours. how long would it take the new machine, working alone, to make the 10,000 cans?
Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.
Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.
The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.
When both machines are working together, they can make 10,000 cans in 9 hours.
Now, we can set up an equation based on the work rates of the two machines:
Work rate of the older machine + Work rate of the new machine = Combined work rate
The work rate is the amount of work (number of cans made) per unit of time (hours).
For the older machine:
Work rate of the older machine = 10,000 cans / t hours
For the new machine:
Work rate of the new machine = 10,000 cans / (t/3) hours
Combined work rate when both machines work together:
Combined work rate = 10,000 cans / 9 hours
Now, the equation becomes:
10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours
To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:
t/3 is the same as (1/3)t. So the equation becomes:
10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours
Now, to combine the fractions, we find the common denominator, which is 3t:
(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours
(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours
Combine the terms on the left side of the equation:
40,000t / (3t^2 hours) = 10,000 cans / 9 hours
Now, cross-multiply to solve for "t":
40,000t * 9 hours = 10,000 cans * 3t^2 hours
360,000t hours = 30,000t^2 hours
Now, rearrange the equation:
30,000t^2 - 360,000t hours = 0
Divide by 30,000t to simplify the equation:
t - 12 = 0
Now, solve for "t":
t = 12 hours
Therefore, it takes the older machine 12 hours to make 10,000 cans.
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A store's cost for a stereo was $27. The markup was 75%. A customer purchased it on sale at 40% off the markup price. What was the purchase price of the stereo
(02.03 MC)
The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A'B'C'?
A.. A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down
B. A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin
C. A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
D. A translation 5 units to the right, followed by a 270-degree counterclockwise rotation about the origin
True or False...
P^2+2pq+q^2= 1
Answer:
defiantly a false!!
Step-by-step explanation:
PLEASE HELP ASAP!!! A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 243 81 27 9 3 Compute the average rate of change of f(x) from x = 1 to x = 4 and describe what it represents.
A) −78 contestants per round, and it represents the number of contestants who will reach the final round
B)−234 contestants per round, and it represents the number of contestants who will reach the final round
C)−234 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
D) −78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
Answer:
D
Step-by-step explanation:
Given the following data
x 1 2 3 4 5
f(x) 243 81 27 9 3
The rate of change between the second and the first points is computed as
(f(x2) - f(x1))/(x2 -x1) = (81 - 243)/(2-1) = -162
Analogously, between 3rd and 2nd points and between 4th and 3rd points:
27 - 81 = -54
9 - 27 = -18
Therefore, the average rate of change is (-162 -54 -18)/3 = -78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round .
I don't understand this and would appreciate an explanation as well :)
Solve for the variable in the equations below.
Round your answers to the nearest hundredth.
Do not round any intermediate computations.
e^x = 6
4^(y+3) = 3
[tex]e^x = 6[/tex]
[tex]4^y^+^3 = 3 [/tex]
Which of the following triangles are right triangles? Check all that apply
A triangle with side lengths 4, 5, 6
A triangle with side lengths 6 inches, 8 inches, 10 inches
A triangle with side lengths 8, 15, 17
A triangle with side lengths 5, 12, 13
In this exercise we have to apply the Pythagorean theorem to know that it is possible to form a certain triangle, so we have:
A) No
B) Yes
C) Yes
D) Yes
Knowing that the Pythagorean theorem is given by:
[tex]a^2 = b^2 +c^2[/tex]
They are putting the values informed we have:
A) [tex]6^2 = 4^2 + 5^2[/tex]
B) [tex]10^2 = 6^2 + 8^2[/tex]
C) [tex]17^2=15^2+8^2[/tex]
D) [tex]13^2 = 12^2 + 5^2[/tex]
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