Answer: The answer is A
Step-by-step explanation: Add the coefficient of x to the both sides.
X²+4x=12
X²+4x+4=12+4
X²+4x+4=16
X²+2x+2x+4=16
X(x+2)+2(x+2)=16
(X+2)(x+2)=16
(X+2)²=16
The equivalent equation is (x+2)²=16
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: The expression x²+4x-12=0
Thus simplifying the equation we get
x²+2.2x+4-12-4=0
(x+2)²-4²=0
(x+6) (x-2)=0
x=-6,2
or the equation can also be rewritten as (x+2)²=16
Thus the equivalent equation is (x+2)²=16
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The radius of a cylindrical gift box is (4x + 1) inches. The height of the gift box is three times the radius. What is the surface area of the cylinder? Write your answer as a polynomial in standard form.
Answer:
S = 128πx² + 64πx + 8π
Step-by-step explanation:
Suraface area of a cylinder is given by:
S = 2πrh + 2πr²
We know that the height is 3 times as big as the radius, hence:
h = 3r
so we can plug in the new h value and rewrite the S equation as:
S = 2πrh + 2πr²
S = 2πr(3r) + 2πr²
S = 6πr² + 2πr²
S = 8πr²
We're given in the question that the radius is (4x + 1) inches, so plug that into r.
Given: r = 4x + 1
Therefore,
S = 8πr²
S = 8π(4x + 1)²
S = 8π(16x²+8x+1)
S = 128πx² + 64πx + 8π
Answer:
The answer to your question is 128πx² + 64πx + 8π
Step-by-step explanation:
Data
radius = (4x + 1)
height = 3(4x + 1)
Formula
Area = 2πrh + 2πr²
Substitution
Area = 2π(4x + 1)(3)(4x + 1) + 2π(4x + 1)
Simplification
Area = 6π(4x + 1)² + 2π(4x + 1)²
Area = 6π(16x² + 8x + 1) + 2π(16x² + 8x + 1)²
Area = 96πx² + 48πx + 6π + 32πx² + 16πx + 2π
Area = 128πx² + 64πx + 8π
Sally and Adam work at different jobs. Sally earns $5 per hour and Adam earns $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
Answer:
10 hrs
Step-by-step explanation:
sally earns $5/hr while Adam earns $4/hr
let the number of Hour sally works be 'x'
From question Adam work 2 hrs more than sally,
therefore Adam works (x + 2)hrs also the both earn same amount per week
therefore;
4 x [tex](x + 2)[/tex] = 5 x [tex]x[/tex]
4x + 8 = 5x
5x - 4x = 8
x = 8hrs
Adam works for (8+2)hrs = 10hrs
A square park has a diagonal walkway from one corner to another. If the walkway is 120 meters long, what is the approximate length of each side of the park?
Answer:
85 m
Step-by-step explanation:
The diagonal of a square is √2 times the length of the side. The park will have a side length of 120/√2 m ≈ 84.85 m, about 85 meters.
_____
The relations are ...
diagonal = (√2)×(side length)
side length = diagonal/√2 . . . . . . . . . divide the above equation by √2
Solve each equation below for x show all work and check your answer by substituting it back into the equation and verifying that it makes the equation true
The solutions to the equations:
(a) x/3 = 6 => x = 18 (Verified)
(b) (5x + 9)/2 = 12 => x = 3 (Verified)
(c) x/4 = 9/6 => x = 6 (Verified)
(d) 5/x = 20/8 => x = 2 (Verified)
To solve the equation, follow these steps: identify the equation with one unknown, isolate x, substitute known values and solve, and check the solution.
The equations are
(a) x/3 = 6
(b) (5x + 9)/2 = 12
(c) x/4 = 9/6
(d) 5/x = 20/8
The answers to the question are
(a) x = 18
(b) x = 3
(c) x = 6
(d) x = 2
Step-by-step explanation:
(a) x/3 = 6
Therefore x = 3×6 = 18
x =18
Substituting the value of x in the above equation, we have
18/6 = 3 verified
(b) (5x + 9)/2 = 12
Multiplying both sides by 2 gives
(5x + 9)/2 × 2 = 12×2 = 24
5x + 9 = 24 or x = (24-9)/5 = 3
Substituting the value of x in the above equation, we have
(5×3 + 9)/2 = 24/2 = 12 verified
x = 3
(c) x/4 = 9/6
Multiplying both sides by 4, we have
x/4×4 = 9/6×4 = 6
x = 6
Substituting the value of x in the above equation, we have
(6/4 = 9/6 = 3/2 verified
(d) 5/x = 20/8
Inverting both equations, we have
x/5 = 8/20
Multiplying both sides by 20 we have x/5 × 20 = 8/20 × 20 or 4x = 8 and x = 2
Substituting the value of x in the original equation, we have
2/5 = 2/5 = 8/20 verified
x = 2
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Interpret the average rate of change of -14/7 that you found previously. What does this mean in terms if the waterslide, from x=0 to x=15
Answer:
1. The vertical components decrease by 14 units while the horizontal component increase by 3 units
2.it therefore means that the vertical component decreases by 70units
Step-by-step explanation:
Slope of a graph is change in the vertical axis over the the change in the horizontal axis
in the above question, if the average rate of change is -14/7 it therefore means that the vertical components decrease by 14 units while the horizontal component inc rfease by 3 units
what does that mean if the waterslide from x=0, and x=15
it means that the vertical components decrease why there is an increment distance in the horizontal axis
mathematically, we say
-14/3=-y/[tex]s= \frac{dy}{dx} , slope=s\\-14/3=\frac{-y}{15-0}[/tex]
14/3=y/15
y=70
it therefore means that the vertical component decreases by 70units
Answer:
On average, the slide drops 14 feet for every 3 feet of horizontal distance.
On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.
Step-by-step explanation:
on edg... Good Luck!!!
Verify that parallelogram ABCD with vertices A(-5, -1), B(-9, 6), C(-1, 5) and D(3, -2) is a rhombus by showing that it id a prallelogram sith perpendicular
Answer:
Step-by-step explanation:
The diagonals of the parallelogram are A(-5, -1), C(-1, 5) and B(-9, 6), D(3, -2).
Slope of diagonal AC = (5 - (-1)) / (-1 - (-5)) = (5 + 1) / (-1 + 5) = 6 / 4 = 3/2
Slope of diagonal BD = (-2 - 6) / (3 - (-9)) = -8 / (3 + 9) = -8 / 12 = -2/3
For the parallelogram to be a rhombus, the intersection of the diagonals are perpendicular.
i.e. the product of the two slopes equals to -1.
Slope AC x slope BD = 3/2 x -2/3 = -1.
Therefore, the parallelogram is a rhombus.
When you add their numbers together you get 207 . Jen's number is 9 more than Carrie's, and Fran's number is 3 less than Jen's number. What is Fran's number?
Final answer:
By defining equations based on the relationships between Jen's, Carrie's, and Fran's numbers and solving them, we find that Carrie's number is 64, Jen's number is 73, and Fran's number is 70.
Explanation:
To solve for Fran's number, we need to use the information given: Jen's number is 9 more than Carrie's, and Fran's number is 3 less than Jen's number. Their total sum is 207. We can set up equations to solve this. Let Carrie's number be c, Jen's number be c + 9 (since it is 9 more than Carrie's), and Fran's number be c + 9 - 3 (since it is 3 less than Jen's).
The equation to express the sum of their numbers will be: c + (c + 9) + (c + 9 - 3) = 207.
Now let's solve the equation:
Combine like terms: 3c + 15 = 207Subtract 15 from both sides: 3c = 192Divide both sides by 3: c = 64Now that we have Carrie's number, we can find Fran's number:
Carrie's number, c, is 64.Jen's number is c + 9, which is 64 + 9 = 73Fran's number is c + 9 - 3, which is 73 - 3 = 70Therefore, Fran's number is 70.
A jar contains only pennies, nickels, dimes, and quarters. There are 14 pennies, 28 dimes, and 16 quarters. The rest of the coins are nickels. There are 70 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n?
Answer:
Step-by-step explanation:
Let n represent the number of nickels in the jar.
The jar contains only pennies, nickels, dimes, and quarters. There are 14 pennies, 28 dimes, and 16 quarters. This means that the total number if pennies, dimes and quarters would be
14 + 28 + 16 = 58
This means that the number of coins that are not nickel is 58
The total number of coins in the jar is 70. Therefore, the equation that can be used to find n is
n + 58 = 70
n = 70 - 58
n = 12 nickels
According to the U.S. Census bureau, 23.5% of people in the United States are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18. Which one of the following statements is true?
1. 23.5% and 28% are statistics, 250 and 18 are parameters
2. 23.5% and 28% are parameters, 250 and 18 are statistics
3. 23.5% and 28% are parameters, 18 is a statistic
4. 28% is a parameter and 23.5% is a statistic
5. 23.5% is a parameter and 28% is a statistic
Answer:
Option 5) 23.5% is a parameter and 28% is a statistic
Step-by-step explanation:
We are given the following in the question:
"According to the U.S. Census bureau, 23.5% of people in the United States are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18."
Population is the collection of all the observation of individual of interest.Population of interest:
People in the United States
Parameter is any value that describes the population.Parameter:
23.5% of people in the United States are under the age of 18
Sample is a subset of a population and is always smaller than the population.Sample:
Random sample of 250 residents of a small town in Ohio
Statistic is any value that describes a sample.Statistic:
28% of the sample was under 18
Thus, the correct answer is
Option 5) 23.5% is a parameter and 28% is a statistic
The drawing plan for an art studio shows a rectangle that is 19.2 inches by 6 inches. The scale in the plan is 3 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio.
Answer:
321.24 ft²
Step-by-step explanation:
If 3in = 5ft
1in = x
5/3 = 1.6
So 1in = 1.67 ft
Actual dimensions will be;
L = 19.2*1.67 = 32.06ft
W = 6*1.67 = 10.02ft
Area = 32.06 * 10.02 = 321.24 ft²
To find the length and width of the actual studio, set up a proportion to convert the given dimensions from the scale to the actual dimensions. Then, find the area of the actual studio by multiplying the length and width.
Explanation:To find the length and width of the actual studio, we need to convert the given dimensions from the scale to the actual dimensions. Since the scale is 3 in.: 5 ft, we can set up the proportion:
3 in / 5 ft = 19.2 in / x ft
Cross multiplying and solving for x, we get:
x = 32 ft
The length of the actual studio is 32 ft. Similarly, we can find the width:
3 in / 5 ft = 6 in / y ft
Solving for y, we get:
y = 10 ft
The width of the actual studio is 10 ft.
To find the area of the actual studio, we multiply the length and width:
Area = length x width = 32 ft x 10 ft = 320 ft²
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Delegates from 10 countries, including Russia,
France, England, and the United States, are to
be seated in a row. How many different seating arrangements are possible if the French and
English delegates are to be seated next to each
other and the Russian and U.S. delegates are not
to be next to each other
Answer:
564,480
Step-by-step explanation:
The appliocation of factorial n! = n(n-1)(n-2)(n-3).....
Arrangement when french and English delegates are to seat together ;
since we have 10 delegates, Freench and english will be treated as 1 delegates as such we have 9groups. The number of ways of arranging 9groups = 9! and if the french and English are to be treated as a group = 2!
Hence, number of ways of arrangement = 9! x 2! = 725,760
In this case, English and french are to be seated next to each other while russia and US delegates are not to seat nect to each other ; both groups will be treated as 2 as such we have 8groups, the number of ways of arranging 8groups = 8!
french and english together = 2!
Russia and US together = 2!
The number of ways of arrangement = 8! x 2! x 2! = 161,280
hence the number of ways of arranging 10 delegates if french and english are to be seated next to each other and Russia and US are not to be seated next to each other;
N = 725,760 - 161,280 = 564,480
There are 282,240 different seating arrangements possible if the French and English delegates are to be seated next to each other and the Russian and U.S. delegates are not to be next to each other.
Explanation:To determine the number of different seating arrangements, we can treat the French and English delegates as a single entity. Therefore, we have 9 entities overall (Russia, (France and England), United States, and the 6 remaining countries).
The number of arrangements of these 9 entities is 9! (9 factorial) which is equal to 362,880. However, since the Russian and U.S. delegates cannot be seated next to each other, we need to subtract the number of arrangements where they are together.
Let's consider the Russian and U.S. delegates as a single entity as well. Now we have 8 entities to arrange (Russian and U.S., (France and England), and the 6 remaining countries). The number of arrangements of these 8 entities is 8! which is equal to 40,320.
Finally, we need to consider the arrangements of the Russian and U.S. delegates within their entity. The Russian and U.S. delegates can be arranged in 2! (2 factorial) ways, which is equal to 2.
Therefore, the total number of different seating arrangements is 362,880 - (40,320 * 2) = 362,880 - 80,640 = 282,240.
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How do you do this question?
Answer:
E) 13
Step-by-step explanation:
∫₀⁴ f'(t) dt = f(4) − f(0)
8 = f(4) − 5
f(4) = 13
The residents of a downtown neighborhood designed a triangular-shaped park as part of a city beautification program. The park is bound by streets on all sides. The second angle of the triangle is 7° more than the first. The third angle is 7° less than seven times the first. Find the measures of the angles.
The measure of the first, second and third angles are 20°, 27° and 133°.
What is an exterior angle of a triangle ?An exterior angle of a triangle is the sum of two opposite interior angles.
According to given question
The residents of a downtown neighbourhood designed a triangular-shaped park as part of a city beautification program.
Let us assume the first angle to be x°.
Therefore from the given data second angle is (x + 7)° and the third angle is (7x - 7)°.
We know that the sum of all the interior angles of a given triangle is 180°.
∴ x + (x + 7) + (7x - 7) = 180°
9x = 180°
x = 180°/9
x = 20°.
So, The first angle of the triangular park is 20°, The second angle is 27° and the third angle is 133°.
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Buck rented a truck for $39.95 plus $0.32 per mile. Before returning the truck, he Filled the tank with gasoline, which cost $9.85. If the total cost was $70.23. How far was the truck driven?
Answer:
Step-by-step explanation:
Let x represent the distance that the truck was driven.
Buck rented a truck for $39.95 plus $0.32 per mile. This means that the total cost of driving x miles with the truck would be
39.95 + 0.32x
Before returning the truck, he Filled the tank with gasoline, which cost $9.85. This means that the total amount that he spent is
39.95 + 0.32x + 9.85
If the total cost was $70.23, it means that
39.95 + 0.32x + 9.85 = 70.23
49.8 + 0.32x = 70.23
0.32x = 70.23 - 49.8 = 20.43
x = 20.43/0.32 = 63.8
Approximately 64 miles
Helppp i need answer asap
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
BC represents the hypotenuse of the right angle triangle.
With m∠B as the reference angle,
AB represents the adjacent side of the right angle triangle.
AC represents the opposite side of the right angle triangle.
To determine BC , we would apply the Sine trigonometric ratio which is expressed as
Tan θ = opposite side/hypotenuse. Therefore,
Sin 44 = 10/BC
0.695 = 10/BC
BC = 10/0.695
BC = 14.4 to 1 decimal place.
Use the function f(x) = x2 + 6x + 6 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8 15 12 9 3
The answer is 15,
because F(X)'s minimum value is (-3, -3)
and G(X)'s maximum value is (12, 3)
So when you subtract -3 from 12, you get a number that is greater then both. (because of the negative 3)
12 - (-3) = 15
Answer:
A. 15
Step-by-step explanation:
I got it rigth on the test :)
Have a great day fam!
What is the common difference between the terms in the following sequence?
{17,11,5,−1,−7...}
Answer:
-6
Step-by-step explanation:
Take a couple of differences and see:
11 -17 = -6
5 -11 = -6
The common difference is -6.
Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Select all that apply: A. (20−4)÷6 B. 16(20−4) C. 20−6−4 D. 20÷6−4 E. 1/6(20−24) F. (20−24)÷6
Option D: [tex]20 \div 6-4[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Option E: [tex]\frac{1}{6} (20-24)[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Option F: [tex](20-24) \div 6[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Explanation:
The expression is [tex]6(x+4)=20[/tex]
Let us find the value of x.
[tex]\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}[/tex]
Now, we shall find the expression that is equivalent to the value [tex]x=-\frac{2}{3}[/tex]
Option A: [tex](20-4) \div 6[/tex]
Simplifying the expression, we have,
[tex]\frac{16}{6}=\frac{8}{3}[/tex]
Since, [tex]\frac{8}{3}[/tex] is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-4) \div 6[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option A is not the correct answer.
Option B: [tex]16(20-4)[/tex]
Simplifying the expression, we have,
[tex]16(16)=256[/tex]
Since, 256 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]16(20-4)[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option B is not the correct answer.
Option C: [tex]20-6-4[/tex]
Simplifying the expression, we have,
[tex]20-10=10[/tex]
Since, 10 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20-6-4[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option C is not the correct answer.
Option D: [tex]20 \div 6-4[/tex]
Using PEMDAS and simplifying the expression, we have,
[tex]$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20 \div 6-4[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option D is the correct answer.
Option E: [tex]\frac{1}{6} (20-24)[/tex]
Simplifying the expression, we have,
[tex]$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]\frac{1}{6} (20-24)[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option E is the correct answer.
Option F: [tex](20-24) \div 6[/tex]
Simplifying the expression, we have,
[tex]$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-24) \div 6[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option F is the correct answer.
To solve 6(x + 4) = 20, we isolate x to get x = -2/3. The correct expressions representing the solution are E. 1/6(20 - 24) and F. (20 - 24) / 6.
To solve the equation 6(x + 4) = 20, we need to isolate x.
First, distribute the 6 on the left-hand side:
6x + 24 = 20
Next, subtract 24 from both sides:
6x = -4
Finally, divide by 6:
x = -4/6 = -2/3
Now, let's analyze the given choices:
A. (20 - 4) ÷ 6: This simplifies to 16 / 6, which does not match x = -2/3.B. 16(20 - 4): This simplifies to 16 × 16, which is incorrect.C. 20 - 6 - 4: This simplifies to 10, which is incorrect.D. 20 ÷ 6 - 4: This simplifies to 10/3 - 4, which is incorrect.E. 1/6(20 - 24): This simplifies to 1/6(-4) = -2/3, which matches the solution.F. (20 - 24) / 6: This simplifies to -4/6 = -2/3, which matches the solution.Therefore, the correct choices are E and F.
Speed cell wireless offers a plan of $40 for the first 400 minutes, and an additional $0.50 for every minute over 400. Let t represent the total talk time in minutes. Write a piecewise-defined function to represent the cost C(t)
The function that represent cost is c(t) = 40 + 0.5(t -400).
For the first 400 minutes [tex](\(0 \leq t \leq 400\))[/tex], the cost is a flat rate of $40.
T represents the overall conversation time in minutes in the provided question.
Speed cell wireless offers a $40 package for the first 400 minutes.
Additional $0.50 per minute for remaining time
Time remaining = (t - 400) minutes
So, the cost for more beyond 400 minutes is 0.5(t -400). $
Thus, the entire cost, c(t), is 40 + 0.5(t -400).
Find the volume of a cube with side length of 7 in.
A: 147 in³ B: 49 in³
C:215 in³ D: 343 in³
Answer: 343 in³
Explanation: In this problem, we're asked to find the volume of a cube.
It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.
Volume = length × width × height
In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.
So the formula for the volume of a cube is side × side × side or s³.
So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).
7 x 7 is 49 and 49 x 7 is 343.
So we have 343 in³.
So the volume of the given cube is 343 in³.
Answer:
343 in³
Step-by-step explanation:
HELP ASAP FOR BRAINLIEST:
Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3
Thank you sooo much! Show work!
Answer:
The answer is 12
Step-by-step explanation:
t5 = 24 = a × r⁴
t8 = 3 = a × r⁷
We divide one by the other
r³= 1 / 8
r = 1 / 2
t6 = a × r⁵ = t5 × r = 24 × (1/2) = 12.
Therefore the sixth term of the geometric sequence is 12
In a certain corporation, 2/3 of the employees are men and 1/3 are women. Of the men, 5/8 are college-educated and 3/8 are not. Of the women, 2/5 are college-educated and 3/5 are not. What percentage of the employees are college-educated? What percentage of the college-educated employees are women?
Answer:
55% and 24%
Step-by-step explanation:
Firstly, we need an arbitrary number to serve as the number of students.
Let the total number of students be 120.
Firstly we need college-educated percentage.
Men are two-thirds, women are one-third
Men = 2/3 * 120 = 80
Women = 1/3 * 120 = 40
5/8 of men are college educated = 5/8 * 80 = 50
2/5 of women are college educated = 2/5 * 40 = 16
Total college educated = 50+ 16 = 66
% college educated = 66/120 * 100 = 55%
Percentage of college educated that are women.
Total college educated = 66
The % is 16/66 * 100 = 24%
The least number of customers in a shop at any time during the day was 15. Fran represented this situation with the inequality c > 15, where c is the number of customers in the shop. Is Fran correct? Explain.
Answer:
Fran was incorrect.
Correct representation: [tex]c \geq 15[/tex], where c is the number of customer during any time of day.
Step-by-step explanation:
We are given the following in the question:
Fran used the given inequality to represent the number of customers in a shop at any time.
[tex]c > 15[/tex]
where c is the number of customer during any time of day.
The least number of customers in a shop at any time during the day was 15.
Thus there could be 15 or greater than 15 customers in shop during any ime of day.
Thus, Fran was incorrect.
The correct representation is given by the inequality
[tex]c \geq 15[/tex]
where c is the number of customer during any time of day.
Answer:
Fran is incorrect.
The inequality is c ≥ 15
Step-by-step explanation:
One container is filled with a mixture that is 30%acid a second container is filled with a mixture that is 50%acid the second containet is 50%larger than the first and that twocontainers are are emptied into a third what percent of acid is the third container
Answer:
The amount of acid in third container is =42%
Step-by-step explanation:
Given , one container is filled with a mixture that is 30% acid a second container filled with a mixture that is 50% acid and the second container 50% larger than the first .
Let, the volume of first container is = x
Then , the volume of second container = (x+ x of 50%)
= x + 0.5 x
= 1.5 x
Therefore the amount of acid in first container [tex]=x \times \frac{30}{100}[/tex] = 0.3 x
The amount of acid in second container [tex]=1.5x \times \frac{50}{100}[/tex] = 0.75x
Total amount of acid= 0.3x + 0.75x = 1.05 x
Total amount of solution = x+1.5x = 2.5x
The amount of acid in third container is = [tex]\frac{1.05x}{2.5x} \times 100%[/tex] %
= 42%
Final answer:
By calculating the total acid content and total volume when two containers with different acid concentrations are mixed, we find that the third container has an acid concentration of 42%.
Explanation:
The question involves mixing two solutions of different acid concentrations and calculating the final concentration of acid. Let's assume the first container has 1 unit of volume. Since the second container is 50% larger, it has 1.5 units of volume. The first container has 30% acid, so it contains 0.3 units of acid. The second container has 50% acid, resulting in 0.75 units of acid. Together, the total volume of the solution is 2.5 units, and the total amount of acid is 1.05 units.
Therefore, the percentage of acid in the third container is calculated by dividing the total acid by the total volume: (1.05 units of acid / 2.5 units of volume) x 100% = 42%.
what is the solution to the following expression if x=5
The value of given expression is 16
Solution:
Given expression is:
[tex]\sqrt{x^2} + \sqrt{x} \times \sqrt{x} + 6[/tex]
We have to find the value of expression when x = 5
Substitute x = 5
[tex]\sqrt{x^2} + \sqrt{x} \times \sqrt{x} + 6\\\\\sqrt{5^2} + (\sqrt{5} \times \sqrt{5}) + 6[/tex]
We know that,
[tex]\sqrt{a} \times \sqrt{a} = a[/tex]
Therefore, the above equation becomes,
[tex]\sqrt{5^2} + 5 + 6\\\\\sqrt{25} + 5 + 6\\\\5 + 5 + 6 = 10 + 6 = 16[/tex]
Thus the value of given expression is 16
Question 5 options: What is the approximate area of a circle with a radius of 11 cm? Use 3.14 for π. ______ cm2
The area of circle is 379.94 cm².
Step-by-step explanation:
Given,
Radius of circle = 11 centimeters
We have to calculate the area of circle.
We know that;
Area of circle = [tex]\pi r^2[/tex]
Here;
π = 3.14 , r = 11
Area of circle = [tex]3.14*(11)^2[/tex]
Area of circle = 3.14*121
Area of circle = 379.94 squared centimeters
The area of circle is 379.94 squared centimeters.
Keywords: area, circle
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A pitcher throws a baseball straight into the air with a velocity of 72 feet/sec. If acceleration due to gravity is -32 ft/sec^2, how many seconds after it leaves the pitcher's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet.
t= 2.25 secs
Step-by-step explanation:
Step 1 :
Equation for motion with uniform acceleration is v = u+ at
where v is the final velocity
u is the initial velocity
a is the acceleration due to gravity
and t is the time
Step 2 :
Here , v = 0 because at the highest point final velocity is 0.
u = 72 feet/sec
a = -32 ft/sec^2
We need to find the time t.
Substituting in the equation we have,
0 = 72 -32 * t
=> 32 t = 72
=> t = 72/32 = 2.25 secs
A line perpendicular to another line or to a tangent line is called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curve at the given point P.
Y=x^2-3x
P (7, 28)
The equation of the normal line at P(7, 28) is:
Answer:
The equation of the normal line to the curve y = x² - 3x at the point (7, 28) is 11y + x - 315 = 0
Step-by-step explanation:
First, we need to find the slope of the line tangent to the curve at the point (7, 28).
To do this, we need to differentiate y with respect to x and evaluate at the point x0 = 7.
Given y = x² - 3x
dy/dx = 2x - 3
So, the slope, m of the tangent line is dy/dx at x = 7:
m = 2(7) - 3 = 11
Slope, m = 11
The slope, m2 of the line perpendicular to the tangent is given as m2 = -1/m
m2 = −1/11
Finally, given the slope m of a line, and a point (x0, y0) on the line, we can use the point-slope form of the equation of a line:
y - y0=m(x - x0)
The perpendicular line has slope m2 = -1/11, and (7, 28) is a point on that line, the desired equation is:
y - 28 = (-1/11)(x - 7)
Or multiplying by 11, we have
11y - 308 = -x + 7
11y + x - 315 = 0
The slope of the curve at point (7,28) is 11, found by differentiating the given function. The slope of the normal line is the negative reciprocal of that, -1/11. Inserting these into the line equation, we get y - 28 = -1/11 * (x - 7).
Explanation:To find the equation of the line perpendicular to the tangent line, we first find the slope of the tangent line. The derivative of the given function y = x^2 - 3x tells us the slope of the curve at any point, so let's find the derivative:
y' = 2x - 3
Now, let's find the slope of the tangent line at the point (7,28) by plugging 7 into the derivative:
y'(7) = 2*7 - 3 = 11
The slope of the line perpendicular to this (the normal line) is the negative reciprocal of the tangent line's slope, so it's -1/11.
The equation of the line with slope m that goes through the point (x1, y1) is:
y - y1 = m*(x - x1)
Substitute the slope of -1/11 and the point (7,28) into this equation to get the equation of the normal line:
y - 28 = -1/11 * (x - 7)
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Mr.Nguyen bought a suit that was on sale for 40% off the original price.He paid 9% sales tax on the sale price. The original price of the suit was 260$ how much did he pay for the suit, including tax, to the nearest dollar?
Answer: The total amount that he paid for the suit is $170
Step-by-step explanation:
The original price of the suit was $260.
Mr.Nguyen bought a suit that was on sale for 40% off the original price. This means that the amount of discount in the suit is
40/100 × 260 = 0.4 × 260 = $104
The sale price would be
260 - 104 = $156
He paid 9% sales tax on the sale price. This means that the amount of sales tax that he paid is
9/100 × 156 = 0.09 × 156 = $14.04
The total amount that he paid for the suit, including tax is
156 + 14.04 = $170 to the nearest dollar
The range for a list of measurements equals the greatest measurement minus the least measurement. The two lists of measurements, X and Y, combined consist of 30 measurements with a range of 25. What is the range for the measurements in list X?
Answer:
Insufficient information
Step-by-step explanation:
The information provided us isn't sufficient to determine the range for the measurements in list X. Because we need to be given the range for the measurements in Y at least. We also need the number of measurements in both X and Y.