Combined?? The sum of ?
Addends is the word in algebra that means something has been added. Addition is an operation to solve the algebraic problems.
What is algebra?Algebra is a field of mathematics that solves problems by substituting letters for numbers.
Addends refer to the numbers that are being added in an addition issue. An addend is a group of numbers that are added together to generate a sum.
Hence, addends is the word in algebra that means something has been added.
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The equation y = 4x + 4 describes the relationship between the quantities x and y. Are the quantities in a proportional relationship?
Answer:
Yes, because as x grows larger so does y, that means to be in a proportional relationship.
Step-by-step explanation:
Answer: For this to be a proportional relationship, the function would have to be y=4x. Since y=mx+b, this is not a proportional relationship because each time the value of x increases, the value for figure 0 is added on.
So, no. This is not proportional.
Hope this helps!
Each test contains 20 questions. In average, it takes a person to take each test 40 minutes. If I was to get stuck in one out of 5 questions for an additional 2 minutes. How long will it take me to complete 3 of the tests?
I think the answer is 144 minutes
The graph of [tex]f(x) = \frac{1}{4} 3^{x} -6[/tex] is shown below. g(x) is a transformation of f(x). How would you write the equation for the function g(x)?
A. [tex]g(x) = \frac{1}{4}3^{x} +2[/tex]
B. [tex]g(x) = -\frac{1}{4}3^{x} -6[/tex]
C. [tex]g(x) = \frac{1}{3} *4^{x} +3[/tex]
D. [tex]g(x) = 3^{x} +2[/tex]
Answer:
the answer would be like finding the point and then doing the math
after the math u will find you answer on the am going to say either C or D
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
If g(x) is a transformation of f(x), then we can consider function f(x) as parent function.
So, to get the graph of the function g(x), we have to translate the graph of the function f(x) 8 units up.
This translation will give us the function
[tex]g(x)=f(x)+9\\ \\g(x)=\dfrac{1}{4}\cdot 3^x-6+8\\ \\g(x)=\dfrac{1}{4}\cdot 3^x+2[/tex]
Which is the correct inequality for the given graph?
x + 3y < -3
x + 3y > -3
x - 3y < -1
3x + y > -1
Answer:
The correct inequality for the given graph is x + 3y < -3 ⇒ 1st answer
Step-by-step explanation:
* Lets study the graph
- The angle between the positive part of x-axis and the line is obtuse,
that means the slope of the line is negative value
- The shaded part is under the line, that means the solutions of the
inequality are under the line , so the sign of the inequality is <
- The y-intercept is < -1 ⇒ (the value of y when x = 0)
* Now lets check the answers to find the correct answer
- At first we will choose the answer with sign <
∴ The answers are x + 3y < -3 OR x - 3y < -1
- At second lets check the y-intercept (put x = 0)
- Substitute x by 0 in the two answer to choose the right one
∵ x = 0
∴ 0 + 3y < -3 ⇒ ÷ 3 both sides
∴ y < -1
* OR
∵ x = 0
∴ 0 - 3y < -1 ⇒ ÷ -3 both sides
∴ y > 1/3 ⇒ because we divide the inequality by negative number
we must reverse the sign of inequality
∵ the y-intercept is < -1
∴The first equation is right
* To be sure check the slope of each line
∵ y < mx + c, where m is the slope of the line
- Put each inequality in this form
∵ x + 3y < -3 ⇒ subtract x from both sides
∴ 3y < -3 - x ⇒ ÷ 3
∴ y < -1 - x/3
∴ m = -1/3 ⇒ the slope is negative
* OR
∵ x - 3y < -1 ⇒ subtract x from both sides
∴ -3y < -1 - x ⇒ ÷ -3
∴ y > 1/3 + x/3
∴ m = 1/3 ⇒ the slope is positive
∵ The slope of the line is negative
∴ The correct inequality for the given graph is x + 3y < -3
Please please help me please
I believe the answer is 70 degrees. If you divide 360 by 9 (amount of degrees divided by amount of sides) you get 40 and we know that the three angles in a triangle add up to 180 degrees. So if we subtract the 40 we got for the top angle we get 140 degrees. We know the other two angles in the triangle are congruent so we can divide 140 by 2 to get the degree of both angles which is 70. Hope this helps!
A basketball player's probability of making a free throw is 0.9. When the player makes two free throws in a row, X is the number of free throws made.
What is P(X = 2)?
Enter your answer, as a decimal, in the box.
P(X = 2) =
Answer:
0.81
Step-by-step explanation:
P(success) = 0.9
P(failure) = 1 - 0.9 = 0.1
Binomial probability:
P(X=n) = nCr (0.9)^n (0.1)^r
Here, n=2 and r=0:
P(X=2) = ₂C₀ (0.9)² (0.1)⁰
P(X=2) = 0.81
X is the number of free throws made P(X = 2) is 0.81
What is probability?
Probability is a branch of mathematics that deals with the occurrence of a random event.
calculation:-
⇒P( sucess event ) = 0.9
⇒P(failure event) = 1 - 0.9 = 0.1
Binomial probability:
P(X=n) = nCr (0.9)ⁿ (0.1)ˣ
let, n=2 and r=0:
P(X=2) = ₂C₀ (0.9)² (0.1)⁰
P(X=2) = 0.81
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Use the information provided to calculate the different parts of the proposal: The lazy river is basically a large circle that will need to be filled with water. The radius of the outer perimeter is 30 yards. The river is 4 feet deep and it's width is 5 feet. First compute the river's volume in cubic feet and then calculate how many gallons of water it will hold. Remember 1 cubic foot = 7.48 gallons.
Answer:
10,995.6 ft^3.
2300.3 gallons.
(both to the nearest tenth).
Step-by-step explanation:
Area of the surface of the river = area of the outer circle - area of the inner circle.
Radius of the outer circle = 30 *3 = 90 feet.
So the surface area of the river = π(90)^2 - π(85)^2
= 875π ft^2
Also the volume of the river = surface area * depth = 875π*4 = 3500π ft^3
= 10,995.6 ft^3.
Number of gallons of water it will hold = 10,995.6 / 4.78
= 2300.3 gallons.
35 less than seven times a certain number is fifty-three more than 3 times that number. What is the number?
Answer:
70
Step-by-step explanation:
The equation derived from the problem is 7x - 35 = 3x + 53. Solving this equation by combining like terms and isolating the variable x gives us the certain number, which is 22.
We need to find the certain number mentioned in the problem. According to the problem, '35 less than seven times a certain number is fifty-three more than 3 times that number.' We can translate this into an equation:
7x - 35 = 3x + 53
Where 'x' represents the certain number. Now, let's solve the equation step by step:
First, subtract 3x from both sides to move the variable terms to one side of the equation. 7x - 3x - 35 = 3x - 3x + 53 4x - 35 = 53
Next, add 35 to both sides to isolate the variable term. 4x - 35 + 35 = 53 + 35 4x = 88
Finally, divide by 4 to solve for x. 4x / 4 = 88 / 4 x = 22
So, the certain number we are looking for is 22.
Solve For X
A: 10
B:10.5
C:20
D:6[tex]\sqrt{3}[/tex]
The answer is gonna be (B)
If pizzas cost $9.83 per pizza, estimate how much money you would need to buy 18 of them.
Your answer does not need to be exact, so please do NOT use a calculator and please do not put a $ sign in your answer.
Answer:
180
Step-by-step explanation:
because it doesn't has to be exact you can do: 10 × 18 = 180
Answer:
180
Step-by-step explanation:
This is a good question to keep in mind. When you do use a calculator the answer to this estimate will tell you if your work on the calculator is correct.
round the cost of the pizza to 10
18 * 10 = 180 dollars. So you should get an answer that is under 180 dollars -- about 3 dollars short. (0.17 * 18 which is another guess).
Now pick up your calculator and do the math. It comes to 176.94
If you do any grocery shopping, this is a good skill to have.
A wallet contains 34 notes, all of which are either $5 or $10 notes.
The total value of the money is $285. How many $10 notes are there?
Answer:
There are 23 $10 notes and 11 $5 notes
Step-by-step explanation:
x= Number of $10 notes
y= Number of $5 notes
1 x + 1 y = 34 .............1
Total value
10 x + 5 y = 285 .............2
Eliminate y
multiply (1)by -5
Multiply (2) by 1
-5 x -5 y = -170
10 x + 5 y = 285
Add the two equations
5 x = 115
/ 5
x = 23
plug value of x in (1)
1 x + 1 y = 34
23 + y = 34
y = 34-23
y = 11
y = 11
x= 23 Number of $10 notes
y= 11 Number of $5 notes
There are 23 notes of $10.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A wallet contains 34 notes, all of which are either $5 or $10 notes.
let x be Number of $10 notes
let y be Number of $5 notes
x + y = 34 .............(1)
and, 10 x + 5 y = 285 .............(2)
Solving equation (1) and (2), we get
-5 x -5 y = -170
10 x + 5 y = 285
_____________
5 x = 115
x= 11/5/5
x = 23
and, x+ y= 34
y= 34- 23
y= 11
Hence, there are 23 notes of $10.
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A banquet that costs $3,000 at Luci’s serves how many people?
Answer:
the answer will be 125 people
Haya , curra , and Brooke are waiting in line. Brooke is not first in line. Haya is being the oldest in line. Brooke is behind haya. List the girls in order from first to last
haya, brooke, curra is the order, i believe
To line up alphabetically by name, Brooke comes first followed by Curra, and Haya is last.
The question requires organizing the names of three girls in alphabetical order without speaking and within a time limit. Given the names are Haya, Curra, and Brooke, we can determine the alphabetical order by looking at the first letter of each name.
Brooke
Curra
Haya
To line up alphabetically by name, Brooke would be first because 'B' comes before 'C' and 'H' in the alphabet. Curra would be second since 'C' comes after 'B' but before 'H'. Finally, Haya would be last because 'H' comes after both 'B' and 'C'.
Describe the locus in space.
points 4 mm from
Question 34 options:
a sphere of radius 4 cm
two planes parallel to , each 4 mm from
an endless cylinder with radius 4 mm and centerline
two lines parallel to , each 4 mm from
Answer: an endless cylinder with radius 4 mm and centerline
River boat ( ) a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour. it returns by the same route at an average speed of 9 kilometers per hour. what is the average speed for the round-trip in kilometers per hour?
a.7.0
b.7.1
c.7.2
d.7.5
e.8.0
Answer:
Let's suppose the distance between gold town and silver town is 9 kilometers.
The first trip takes 9 km / 6 km / hour = 1.5 hours
The return trip takes 9 / 9 km / hour = 1 hour
TOTAL TRIP = 18 kilometers in 2.5 hours
= 18 / 2.5 = 7.2 hours
Answer is c
Step-by-step explanation:
What is the maximum number of possible solutions for the system shown below?
[tex]x^2+4y^2=64\\x+y=5[/tex]
Answer:
2
Step-by-step explanation:
The first equation is that of a an ellipse. The second equation is that of a line.
Attached is the graphs of both of these equations.
If you think about it, there can only be 2 possible ways of solutions (intersection points) of an ellipse and a line.
1. The line will not intersect the ellipse at all, so no solution
2. The line will intersect the ellipse at 2 points maximum
So, we can clearly see from the reasoning that the maximum number of possible solutions would be 2. The graph attached confirms this as well.
Answer:
The maximum number of solutions that the system can have are 2
Step-by-step explanation:
We have a system of equations composed of an ellipse of equation [tex]x ^ 2 + 4y ^ 2 = 64[/tex] and a line of equation [tex]x + y = 5.[/tex]
The solution to the system of equations gives information about when the values of both equations coincide. In other words, the solutions of the system of equations give information about the number of times that the line [tex]x + y = 5[/tex]. touch or intercept the graph of the ellipse [tex]x ^ 2 + 4y ^ 2 = 64[/tex]
Graphically you can verify that a line can only touch an ellipse once or can intercept an ellipse a maximum of two times, or never touch it
Therefore, the maximum number of solutions that the system can have are 2.
1. A triangle has a side length of 450mm.The scale factor is 1/25.What is the side length of the scale drawing.
Answer:
18 mm
Step-by-step explanation:
To find the side length of the scale drawing, multiply the length of the side by the scale factor
450 * 1/25 =18
The side length in the drawing is 18 mm
Compute the following linear combination.
(79.4, 58.1) + 3(-0.8, 6.3)
Answer:
(77, 77)
Step-by-step explanation:
Carry out the indicated multiplication:
3(-0.8, 6.3) → (-2.4, 18.9)
Next, combine like terms:
(79.4, 58.1) + (-2.4, 18.9). In other words, combine the x terms 79.4 and -2.4 separately and then the y terms 58.1 and 18.9 separately:
(79.4, 58.1) + (-2.4, 18.9) → (77, 77)
The resultant of the following linear combination is:
(77,77)
Step-by-step explanation:We are asked to find the linear combination of the expression:
(79.4, 58.1) + 3(-0.8, 6.3)
We multiply each of the term in the second coordinate by 3 .
i.e. this could also be given by:
(79.4, 58.1) + (3×-0.8, 3×6.3)
= (79.4, 58.1) + (-2.4, 18.9)
Now as there is a addition sign in between the two coordinates i.e. each of the first and the second coordinate will get added
i.e.
= (79.4+(-2.4),58.1+18.9)
= (79.4-2.4,58.1+18.9)
= (77,77)
i.e.
(79.4, 58.1) + 3(-0.8, 6.3)=(77,77)
If x < 5, then which of the following must be true?
-x < -5
-x > -5
-x < 5
-x > 5
Answer:
B
Step-by-step explanation:
x<5
When we multiply by negative number sign of inequality should be changed also.
x*(-1) > 5*(-1)
-x>-5
For this case we have the following expression:
[tex]x <5[/tex]
By definition we have to:
Let [tex]c <0[/tex]. If [tex]a <b,[/tex] then [tex]ac> bc[/tex]
That is to say:
If we multilate on both sides of the inequality by -1, the sign automatically changes direction.
[tex](-1) (x) <(- 1) (5)\\-x> -5[/tex]
ANswer:
Option B
Which of the following equations is the formula of [tex]f(x) = x^{1/3}[/tex] but shifted 2 units to the right and 2 units down?
A. [tex]f(x) = 2x^{1/3} -2[/tex]
B. [tex]f(x) = (x-2)^{1/3} -2[/tex]
C. [tex]f(x) = 2x^{1/3} +2[/tex]
D. [tex]f(x) = (x+2)^{1/3} -2[/tex]
Answer:
[tex]f(x)=(x-2)^{\frac{1}{3}}-2[/tex] ⇒ answer B
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
∵ f(x) = x^1/3
- f(x) shifted 2 units to the right
∴ f(x) = (x - 2)^1/3
- f(x) shifted 2 units down
∴ f(x) = (x - 2)^1/3 - 2
* [tex]f(x)=(x - 2)^{\frac{1}{3}}-2[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Use the probability distribution table to answer the question.
What is P(X ≥ 2)?
Enter your answer, as a decimal, in the box.
Answer: 0.88
Step-by-step explanation:
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(x = 4) + P(X = 5) + P(X = 6)
= 0.21 + 0.35 + 0.21 + 0.06 + 0.05
= 0.88
What is the period of the function?
Answer:
2pi
Step-by-step explanation:
WILL MARK BRAINLIEST
Solve the following equation algebraically:
2x*2=50
a.+0.2
b.+7.07
c.+5
d.+12.5
Divide 50 by 2 so 25 then divide that by 2 so 12.5 =x
The equation 2x² = 50 has two solutions, x = 5 and x = -5.
The equation 2x² = 50 can be solved algebraically by dividing both sides by 2 and then taking the square root of both sides. This gives us two solutions, x = 5 and x = -5.
Another way to solve this equation is to factor the left side. We can see that 2x² = 2(x²). We can also factor x² as (x)(x). This gives us the following equation:
2(x)(x) = 50
Dividing both sides by 2, we get:
(x)(x) = 25
Taking the square root of both sides, we get:
x = ±5
Therefore, the two solutions to the equation 2x² = 50 are x = 5 and x = -5.
We can check our answer by substituting x = 5 and x = -5 back into the original equation.
2(5)² = 50
2(25) = 50
50 = 50
This is true.
2(-5)² = 50
2(25) = 50
50 = 50
This is also true.
Therefore, our solutions are correct.
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Solve 2x2 + 5x = 12.
A. x= three over two and x = −4
B. x = 2 and x = −3
C. x = −6 and x = 5
D. x = one over two and x = one over three
Answer:
A. x= three over two and x = −4
Step-by-step explanation:
2x^2 + 5x = 12
I will use complete the square
Divide each side by 2
2x^2 /2 + 5/2 x = 12/2
x^2 +5/2 x =6
Take 5/2 , divide by 2 and then square it
5/2 ÷2 = 5/2 (5/4) ^2 = 25/16
Add this to both sides
x^2 + 5/2 x + 25/16 = 6 + 25/16
(x+5/4)^2 = 6 *16/16 + 25/16
(x+5/4)^2 = 96/16 +25/16
(x+5/4)^2 = 121/16
Take the square root of each side
sqrt((x+5/4)^2) = sqrt(121/16)
x+5/4 = ±11/4
Subtract 5/4 from each side
x+5/4-5/4 = ±11/4 -5/4
x = ±11/4 -5/4
x = -11/4 - 5/4 and x = 11/4 - 5/4
x = -16/4 = -4 and x = 6/4 = 3/2
Will mark BRAINLIEST!! — Point H is the circumcenter of triangle DEF. Which must be true? Check ALL that apply. See image.
Answer:
A, C, F
Step-by-step explanation:
Definition: The circumcenter is the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. If point H is the circumcenter of the triangle DEF, then the circumcircle passes through its vertices D, E and F (option A is true).
Option B is false, the circumcircle doesn't pass through the points L, M and N. This option is true for inscribed circle, not for circumcircle.
Option C is true, because HD and HE are the radii of the circumcircle.
Option D is false. This option is true for inscribed circle, not for circumcircle.
Option E is false. This option is true for inscribed circle, not for circumcircle.
Option F is true, because both these angles are right angles.
Find all values of the angle θ (in radians, with 0 ≤ θ < 2π) for which the matrix a = cos θ −sin θ sin θ cos θ has real eigenvalues. (enter your answers as a comma-separated list.)
The matrix
[tex]A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}[/tex]
has eigenvalues [tex]\lambda[/tex] such that
[tex]\det(A-\lambda I)=\begin{vmatrix}\cos\theta-\lambda&-\sin\theta\\\sin\theta&\cos\theta-\lambda\end{vmatrix}=0[/tex]
[tex](\cos\theta-\lambda)^2+\sin^2\theta=0[/tex]
[tex](\cos\theta-\lambda)^2=-\sin^2\theta[/tex]
[tex]\cos\theta-\lambda=\pm\sqrt{-\sin^2\theta}[/tex]
[tex]\lambda=\cos\theta\pm\sqrt{-\sin^2\theta}[/tex]
[tex]\sin^2\theta\ge0[/tex] for all values of [tex]\theta[/tex], so we need to have [tex]\sin\theta=0[/tex] in order for [tex]\lambda[/tex] to be real-valued. This happens for
[tex]\sin\theta=0\implies\theta=n\pi[/tex]
where [tex]n[/tex] is any integer, and over the given interval we have [tex]\theta=0[/tex] and [tex]\theta=\pi[/tex].
The matrix a will always have real eigenvalues for any value of θ.
Explanation:To find the values of the angle θ for which the matrix a has real eigenvalues, we need to determine when the determinant of the matrix is greater than or equal to 0. The matrix a can be written as:
a = cos(θ) -sin(θ)
sin(θ) cos(θ)
To calculate the determinant, we use the formula det(a) = cos(θ) * cos(θ) - (-sin(θ)) * sin(θ) = cos²(θ) + sin²(θ) = 1. Since the determinant is always 1, the matrix a will always have real eigenvalues for any value of θ.
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50 POINTS!! PLEASE HELP ASAP
After completing the fraction division 5 divided by 5/3, Miko used the multiplication shown to check her work.
3 x 5/3=3/1 x 5/3 = 15/3 or 5
Which is the most accurate description of Miko’s work?
A. Miko found the correct quotient and checked her work using multiplication correctly.
B. Miko found the correct quotient but checked her work using multiplication incorrectly.
C. Miko found an incorrect quotient but checked her work using multiplication correctly.
D. Miko found an incorrect quotient and checked her work using multiplication incorrectly.
Answer:
D. Miko found an incorrect quotient and checked her work using multiplication incorrectly
Step-by-step explanation:
We are given the equation
[tex]\frac{5}{\frac{5}{3} }[/tex]
This can be rewritten as
[tex]5*\frac{3}{5} =3[/tex]
Miko's work is incorrect as she did not multiply by the reciprocal of denominator's fraction. Instead she just multiplied by that fractions.
Which is the most accurate description of Miko’s work?
After completing the fraction division 5 divided by 5/3, Miko used the multiplication shown to check her work. 3 x 5/3=3/1 x 5/3 = 15/3 or 5
Answer: D) Miko found an incorrect quotient and checked her work using multiplication incorrectly.
I hope this helps you! ☺
What is the mean absolute deviation of the data set?
{12, 10, 10, 8, 6, 7, 7, 12}
.1
.2
.6
.9
Answer:
the mean absolute deviation of the data set is 2.
Step-by-step explanation:
To calculate the mean absolute deviation of a data set, we need to follow the following steps:
Step 1: Calculate the mean.
Step 2: Calculate how far away each data point is from the mean (always keeping a possitive distance).
Step 3: Calculate the mean of the deviations.
Step 1: The mean of the data set is:
Mean = (12 + 10 + 10 + 8 + 6+ 7 + 7 + 12)/8 = 72/8 = 9
Step 2:
{12 -9, 10-9, 10-9, 9-8, 9-6, 9-7, 9-7, 12-9} = {3, 1, 1, 1, 3, 2, 2, 3}
Step 3: (3 + 1 + 1 + 1 + 3 + 2 + 2 + 3)/8 = 2
In conclusion, the mean absolute deviation of the data set is 2. Which corresponds to the option B.
Suppose the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta. What expression represents the hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta? Domain Where a = and b = ln What are the restrictions on ln? ln >
Answer: [tex]ln-10[/tex] is the length of Santa Monica and [tex]ln>10[/tex]
Step-by-step explanation:
Let the length of Nina Pinta be ''ln'
According to question, we have given that
the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta.
and 10 ft shorter than that of Nina Pinta is expressed as [tex]ln-10[/tex]
So, the length of Santa Monica be 'ln'-10'
Restriction on ln is that ln>10.
As Length of Santa Monica cannot be negative or equal to zero.
so, [tex]ln>10[/tex]
Hence, [tex]ln-10[/tex] is the length of Santa Monica and [tex]ln>10[/tex]
The speed of the Santa Monica, given the hull length of Nina Pinta as 'ln' and that Santa Monica is 10 ft lesser in hull length, can be represented by 1.34 * sqrt(ln - 10). The restriction on this is that ln must be greater than 10 ft.
Explanation:The hull length of the Santa Monica is defined as ln - 10, where ln is the hull length of the Nina Pinta. The hull speed of the Santa Monica, according to the hull speed formula, is calculated as 1.34 times the square root of the hull length. Therefore, the hull speed of the Santa Monica in terms of the hull length of the Nina Pinta, ln, can be represented by the expression 1.34 * sqrt(ln - 10) where sqrt stands for 'square root'.
The restriction on the domain is that ln must be greater than 10 as the hull length cannot be negative.
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Jeremy, Sue, and Holly are siblings. Sue was born three years before Holly, and Jeremy was born five years before Sue. The product of Sue's age and Jeremy's age is at most 150.
If x represents the age of Holly, which inequality can be used to find the age of each sibling?
A.
x2 - 11x + 24 ≤ 150
B.
x2 + 8x + 15 ≤ 150
C.
x2 + 8x ≤ 150
D.
x2 + 11x + 24 ≤ 150
Answer:
D is the correct answer
Step-by-step explanation:
Let the age of Holly is x years. Now from the statements of the question we will form the equations.
Sue was born three years before Holly.
Sue = Holly + 3 = x + 3------(1)
Jeremy = Sue + 5
From equation (1)
Jeremy = (x + 3) + 5 = x + 8------(2)
Now statement says the product of Sue's age and Jeremy's age is at most 150.
Sue × Jeremy ≤ 150
(x + 3)(x + 8) ≤ 150
x² + 11x + 24 ≤ 150
Therefore inequality x² + 11x + 24 ≤ 150 can be used to find the age of each sibling.
HAVE AN AMAZING DAY, GLAD TO HELP. ^.^