Answer:
Step-by-step explanation:The sum of three consecutive odd numbers is 183. Find the numbers. 57; 59; 67 59; 61; 63 60; 61; 62 65; 67; 69.
EASY MATH FROM THE BEGINNING OF 6th GRADE MATH BUT THIS WAS A REVIEW FROM BACK IN 5TH GRADE!!!!GETS BRAINILIST!!The figure below shows the quotient of fraction 1 over 2 divided by fraction 1 over 6. Rectangle divided into six equal parts, where the first part is shaded dark representing one-sixth, the next two parts are shaded light to complete the one-half, and the last three parts are not shaded. The quotient is ____. Numerical Answers Expected! Answer for Blank 1:
Answer:
=3
Step-by-step explanation:
Okay so you 1/2 divided by 1/6
Answer:
3
Step-by-step explanation:
1/2÷ 1/6
=
1/2×6/1
=
1 × 6
2 × 1
=
6/2
=
6 ÷ 2
2 ÷ 2
= 3
Just Divide 1/6 by 1/2
2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.
An open box with a square base is to have a volume of 500 cubic inches. Find the dimensions of the box that will have
minimum surface area. Let x = length of the side of the base.
Show your work:
Answer:
Dimension of box:-
Side of square base = 10 in
Height of box = 5 in
Minimum Surface area, S = 300 in²
Step-by-step explanation:
An open box with a square base is to have a volume of 500 cubic inches.
Let side of the base be x and height of the box is y
Volume of box = area of base × height
[tex]500=x^2y[/tex]
Therefore, [tex]y=\dfrac{500}{x^2}[/tex]
It is open box. The surface area of box, S .
[tex]S=x^2+4xy[/tex]
Put [tex]y=\dfrac{500}{x^2}[/tex]
[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]
This would be rational function of surface area.
For maximum/minimum to differentiate S(x)
[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]
For critical point, S'(x)=0
[tex]2x-\dfrac{2000}{x^2}=0[/tex]
[tex]x^3=1000[/tex]
[tex]x=10[/tex]
Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]
y = 5
Double derivative of S(x)
[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10
[tex]S''(10) > 0[/tex]
Therefore, Surface is minimum at x = 10 inches
Minimum Surface area, S = 300 in²
Find a numerical value of one trigonometric function of x for cos^2x+ 2sin x-2=0
Answer:
x = 90°
Step-by-step explanation:
We are given a trigonometric function of x from which we have to a solution for x.
The function is [tex]\cos^{2} x + 2\sin x - 2 = 0[/tex]
⇒ [tex]1 - \sin^{2} x + 2\sin x - 2 = 0[/tex]
{Since we know the identity [tex]\sin^{2} \alpha + \cos^{2} \alpha = 1[/tex]}
⇒ [tex]\sin^{2} x - 2 \sin x + 1 = 0[/tex]
⇒ [tex](\sin x - 1)^{2} = 0[/tex]
{Since we know the formula (a - b)² = a² - 2ab + b²}
⇒ [tex](\sin x - 1) = 0[/tex]
⇒ [tex]\sin x = 1 = \sin 90[/tex]
⇒ x = 90° (Answer)
To solve cos^2 x + 2sin x - 2 = 0, we convert cos^2 x to 1 - sin^2 x and solve the quadratic equation sin^2 x - 2sin x + 1 = 0, finding that sin x equals 1. Thus, the numerical value of the trigonometric function is sin x = 1.
To find a numerical value of one trigonometric function of x for the equation cos2x + 2sin x - 2 = 0, let's start by expressing everything in terms of sin x:
Using the Pythagorean identity, we know that cos2x = 1 - sin2x. So, we can write:
(1 - sin2x) + 2sin x - 2 = 0
Simplifying, we get:
1 - sin2x + 2sin x - 2 = 0
-sin2x + 2sin x - 1 = 0
This is a quadratic equation in terms of sin x. Let's solve it:
sin2x - 2sin x + 1 = 0
We recognize this as a perfect square trinomial:
(sin x - 1)2 = 0
So, we have:
sin x - 1 = 0
Therefore:
sin x = 1
So, the numerical value of one trigonometric function of x from the given equation is sin x = 1.
The y-intercept is 4 and the line is parallel to the line whose equation is 6x+y=5
Answer:
[tex]\displaystyle 6x + y = 4[/tex]
Step-by-step explanation:
In the Linear Standard Formula [Ax + By = C], C represents the y-intercept, and since the instructions say "parallel line", you keep your '6' the same, and just alter 5 to 4.
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], which was why 6 remained the way it was.
I am joyous to assist you anytime.
what is a equivalent fraction of 10/25, 6/8, 3/5, 1/10
Answer:
Step-by-step explanation:
10/25=20/50=40/100
6/8=3/4=12/16
3/5=6/10=60/100
1/10=10/100
there are 125 students in your class 75 of them are girls what percent all boys percent
Answer:
40%
Step-by-step explanation:
125 - 75= 50
50 ÷ 125 = 0.4
0.4 = 40%
Point A(2, 2) and point B(4, −3) are located on the grid. Which measurement is closest to the distance between point A and point B in units?
A) 5.2 units
B) 5.4 units
C) 5.6 units
D) 5.8 units
Answer:
b
Step-by-step explanation:
5 ft
3 ft
3 ft
2 ft
2 ft
2 ft
3 ft
4 ft
find the area
Answer:
multiply all together
Step-by-step explanation
Which exponential function has an initial value of 2? f(x) = 2(3x) On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (2, 2). f(x) = 3(2x) A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.
Answer:
The correct answer is A. f(x)= 2(3^x)
Step-by-step explanation:
The exponential function y = 2(3)ˣ, has an initial value of 2
Exponential functionAn exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplicative rate of change
Given the exponential function y = 2(3)ˣ, has an initial value of 2
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Ginger adds 15 mL of vitamin C drops to her guinea pig's water everyday. A bottle
of vitamin C drops holds 350mL and costs $4.85. About how much does she spend
on vitamin C drops each year?
A- $70 to $90
B- $50 to $70
C- more than $90
D- less than $50
it is d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
First find how many bottles Ginger will need.
15 mL x 365 day = 5475 mL for 1 yr
5475 mL / 350mL = 16 bottles
Then find the price for the 16 bottles.
16 bottles x $4.85 = $77.60
The graph represents this system of equations y equals 4 - x y equals x - 2 what is the solution to the system of equations
The solution to the system of equations is (3,1)
Step-by-step explanation:
The system of equations represented by graph are:
[tex]y=4-x\\y=x-2[/tex]
Solving the system of equations
Let:
[tex]y=4-x\,\,\,eq(1)\\y=x-2\,\,\,eq(2)[/tex]
Putting value of y from eq(2) into eq(1):
[tex]x-2=4-x\\Simplifying:\\x+x=4+2\\2x=6\\x=6/2\\x=3[/tex]
So, Value of x = 3
Putting value of x into eq(2)
[tex]y=x-2\\y=3-2\\y=1[/tex]
So, value of y= 1
So, The solution to the system of equations is (3,1)
Keywords: System of equations
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Suppose the graph of y=f(x) includes the points (1,5), (2,3), and (3,1).
Based only on this information, there are two points that must be on the graph of y=f(f(x)). If we call those points (a,b) and (c,d), what is ab+cd?
Answer: 17
================================
How I got that answer:
(2,3) and (3,1) have '3' in common in that the y value of the first pairs with the x value of the second.
If you picture a chain, then you start with x = 2, move to y = 3, then move to x = 3 and then y = 1
2 ---> 3 ---> 3 ---> 1
So f(f(2)) = f(3) = 1
If g(x) = f(f(x)), then we know (2,1) is on the graph of g(x)
-------------------------
Repeat for (3,1) and (1,5)
3 ---> 1 ---> 1 ---> 5
f(3) = 1
g(x) = f(f(x)) = f(f(3)) = f(1) = 5
We know that (3,5) is on the graph of g(x)
-------------------------
The two points on g(x) are: (2,1) and (3,5)
Comparing that to (a,b) and (c,d) we can see
a = 2, b = 1, c = 3, d = 5
a*b + c*d = 2*1 + 3*5 = 2 + 15 = 17
#1
Suppose g(a) = 7.6 cos(0.5a).
a. What is the argument of the cosine function? (Enter an expression.)
Answer:
[tex]0.5a[/tex]
Step-by-step explanation:
We have been given a trigonometric function [tex]g(a)=7.6\text{ cos}(0.5a)[/tex]. We are asked to find the argument of the cosine function.
We know that a trigonometric equation is solved for an unknown angle and that unknown angle is known as the argument of the trigonometric function. For example: [tex]\text{cos}(\theta)=0[/tex]. In this equation [tex]\theta[/tex] is the argument of the equation.
Upon looking at our given function, we can see that [tex]0.5a[/tex] is the argument.
the sum of one-half t and one third s
Answer:
5/6
Step-by-step explanation:
Add the fractions by finding the common denominator.
1/2 + 1/3
3/6 + 2/6
5/6
if y varies inversely as x² and x varies directly as z. find the relationship connecting y and z if c is a constant
Answer:
y = c/z²
Step-by-step explanation:
(1) y ∝ 1/x²or
y = a/x² where a is a constant
x ∝ z or x = bz, where b is a constant
Substitute x into (1)
y ∝ a/(bz)² = a/(b²z²) = (a/b²)/z²
a is a constant and b is a constant, so a/b² is a constant.
Let c = a/b². Then
y = c/z²
Train A and Train B leave the station at 2 P.M. The graph below shows the distance covered by the two trains. Compare the speeds of the two trains.
Answer:
Train b is moving faster than a by 45 units an hour
Step-by-step explanation:
25(M-2)=650 what is M ?
Answer:M=24
Step-by-step explanation:
There are 2 ways to do this
---------------------------------------------------
Method 1) Divide both sides by 25, then add 2 to both sides
25(M-2) = 650
M-2 = 650/25
M-2 = 26
M = 26+2
M = 28
---------------------------------------------------
Method 2) Distribute the 25 through to each term inside the parenthesis. Then isolate for M by adding 50 to both sides, and then dividing both sides by 2.
25(M-2) = 650
25M - 50 = 650
25M = 650+50
25M = 700
M = 700/25
M = 28
---------------------------------------------------
Either way the answer is 28Neptune has a gravitational pull 1.2 times that on earth if an object weights 15.3 pounds on earth how much would it weigh on Neptune
Answer:
the object would weigh 18.36
since it is 1.2 times as much you multiply the weight of the object on earth by 1.2 and that's the answer
Step-by-step explanation:
Marquise is 9 years old. In two years, Marquise will be 1/3 of his mother’s age. What is his mother’s age?
Answer:
33
Step-by-step explanation:
9+2=1/3x
11=1/3x
x=11/(1/3)=(11/1)(3/1)=33/1=33
Write 5 over 15 in simplest form.
Answer: 1/3
Step-by-step explanation:
5/15 divided both by 5 is 1/3
Find the range and standard deviation for the set of numbers.
111, 122, 134, 146, 150, 159, 193
Answer:
For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.
Step-by-step explanation:
1. Let's find the range for the set of numbers given:
Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.
Range = 193 - 111
Range = 82
2. For calculating the standard deviation, we should calculate first the mean and the variance, this way:
Mean = Sum of all the terms / Number of the terms of the set
Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7
Mean = 1,015/7
Mean = 145
Now, we proceed to calculate the variance this way:
Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sample
Let's calculate the squared distances of each term in the set from the mean:
111 - 145 = - 34 ⇒ - 34² = 1,156
122 - 145 = - 23 ⇒ - 23² = 529
134 - 145 = - 11 ⇒ - 11² = 121
146 - 145 = 1 ⇒ 1² = 1
150 - 145 = 5 ⇒ 5² = 25
159 - 145 = 14 ⇒ 14² = 196
193 - 145 = 48 ⇒ 48² = 2,304
Now replacing with the real values:
Variance = (1,156 + 529 + 121 1+ 25 + 196 + 2,304)/7
Variance = 4,332/7
Variance = 618.86 (Rounding to two decimal places)
Finally, we can calculate easily the standard deviation:
Standard deviation = √Variance
Standard deviation = √ 618.86
Standard deviation = 24.88 (Rounding to two decimal places)
Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan costs $50 per month and $0.02 per minute. How will the graphs of the monthy costs of the two cell phone plans compare where x represents minutes purchased in a month?
The prepaid phone plan will have a steeper line and lower y-intercept.
The contracted phone plan will have the same steepness and a higher y-intercept.
The prepaid phone plan will have a less steep line and the same y-intercept.
The contracted phone plan will have a steeper line and same y-intercept.
Answer:
The prepaid phone plan will have a steeper line and lower y-intercept.
I hope this is right
Step-by-step explanation:
prepaid phone plan y = .20x
contracted phone plan y = .02x + 50
The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.
We have:
Prepaid
[tex]Rate = 0.20[/tex]
[tex]Monthly = 0[/tex]
Contracted
[tex]Monthly = 50[/tex]
[tex]Rate = 0.02[/tex]
For both plans, the cost function (y) is:
[tex]y =Monthly + Rate \times x[/tex]
Where:
[tex]x \to[/tex] Number of minutes
[tex]Rate \to[/tex] Steepness
So, we have:
Prepaid
[tex]y =0 + 0.20 \times x[/tex]
[tex]y =0.20x[/tex]
The y intercept (i.e. when x = 0) is
[tex]y = 0.20 \times 0 = 0[/tex]
The steep of the function is 0.20The y-intercept is 0Contracted
[tex]y = 50 + 0.02 \times x[/tex]
[tex]y = 50 + 0.02x[/tex]
The y intercept is:
[tex]y = 50 + 0.02 \times 0 = 50[/tex]
The steep of the function is 0.02The y-intercept is 50By comparing the steepness and the y-intercepts,
The prepaid plan is steeper (0.20 > 0.02)The prepaid plan has a smaller y-intercept (0 < 50)Hence, (a) is correct
See attachment for the graphs of both plans
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9-4 (3+6*2)=__+1=
(need answer asap please)
1/8% is what as a decimal
Answer:
[tex]\large\boxed{\dfrac{1}{8}\%=\dfrac{1}{800}}[/tex]
Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\\\\\dfrac{1}{8}\%=\dfrac{\frac{1}{8}}{100}=\dfrac{1}{8}\cdot\dfrac{1}{100}=\dfrac{1}{800}\\\\\text{other method}\\\\\text{Convert the fraction to the decimal:}\\\\\dfrac{1}{8}=0.125\to\dfrac{1}{8}\%=0.125\%\\\\0.125\%=\dfrac{0.125}{100}=\dfrac{0.125\cdot1000}{100\cdot1000}=\dfrac{125}{100000}=\dfrac{125:125}{100000:125}=\dfrac{1}{800}[/tex]
what does x = -6(4x+3) = 6(-4x-3)
Answer:
Infinitely many solutions
Step-by-step explanation:
-6(4x+3)=6(-4x-3)
-24x-18=-24x-18
infinitely many solutions
what is the slope of the line that contains the points (-2,5) and 6,-3)
Answer:
slope = - 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 3)
m = [tex]\frac{-3-5}{6+2}[/tex] = [tex]\frac{-8}{8}[/tex] = - 1
Evaluate x-2 for x=8
Answer:
6
Step-by-step explanation:
8-2=6
If 4 quarts of paint are needed for a 75-foot fence, how many quarts are needed for an
825-foot fence?
Answer:
44 quarts of paint
Step-by-step explanation:
Given,
75-foot fence needs = 4 quarts.
We have to use the unitary method to determine how many quarts will be needed for the fencing system. Hence,
75-foot fence needs = 4 quarts of paint
1-feet fence needs = (4/75) quarts of paint
825-foot fence needs = (4 x 825)/75 quarts of paint
= 3,300/75 quarts of paint
= 44 quarts of paint
Therefore, we need 44 quarts of paint for 825-foot fence.
To determine how many quarts of paint are needed for an 825-foot fence, we can set up a proportion and solve for the unknown quantity.
Explanation:To determine how many quarts of paint are needed for an 825-foot fence, we can use the concept of ratios. Since we know that 4 quarts of paint are needed for a 75-foot fence, we can set up a proportion:
4 quarts of paint / 75 feet = ? quarts of paint / 825 feetTo solve for the unknown quantity, we can cross-multiply and solve for the missing value:
4 quarts of paint * 825 feet = ? quarts of paint * 75 feetDividing both sides of the equation by 75, we get:
? quarts of paint = (4 quarts of paint * 825 feet) / 75 feetBy performing the calculation, we find that quarts of paint is approximately 44 quarts. Therefore, 44 quarts of paint are needed for an 825-foot fence.
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- Suppose y varies directly as x. If y = -7 when x = -14, find x when y = 10.
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
in this problem
For x=-14, y=-7
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
substitute
[tex]k=-7/-14=0.5[/tex]
so
The linear equation is
[tex]y=0.5x[/tex]
Find x when the value of y=10
substitute the value of y in the equation
[tex]10=0.5x[/tex]
solve for x
Multiply by 2 both sides
[tex]x=20[/tex]
Final answer:
In direct variation relationship 'y = kx', using the given y = -7 when x = -14, the constant of variation 'k' is found to be 0.5. To find x when y = 10, we use 'y = kx' to get x = 20.
Explanation:
The student's question revolves around the concept of a direct variation, which is a fundamental topic in algebra. The direct variation relationship between two variables 'x' and 'y' can be expressed as 'y = kx', where 'k' is the constant of variation. To determine the constant 'k', we can use the given condition, which states that when x = -14, y = -7. This equation simplifies to 'k = y/x', so 'k = (-7)/(-14)' which equals 0.5.
Now, we need to find 'x' when y is 10. Using the direct variation equation 'y = kx' and our calculated 'k' value of 0.5, we can set up the equation '10 = 0.5x'. Solving for 'x', we get 'x = 10/0.5' which simplifies to 'x = 20'. Thus, when y equals 10, the corresponding value of x is 20.
Jacob has $1,000 in a checking account and withdraws $40 each week. His account requires a minimum balance of more than $400. Write an inequality to model the number of weeks, x, that he can withdraw $40 to maintain the minimum balance requirement.
Answer:
[tex]1000-40x>400[/tex]
Step-by-step explanation:
Let's call B the balance of Jacob's checking account. Each week he withdraws $40 from his actual balance of $1000, so if x is the number of weeks, the account's balance is
B=1000-40x
The balance must be more than $400, which means
[tex]1000-40x>400[/tex]
That is the inequality to model the situation. If we wanted to know the limit for x, we can solve the inequality. Operating:
[tex]1000-400>40x[/tex]
600>40X
[tex]x<\frac{600}{40}[/tex]
Or x<15
Which means Jacob can withdraw $40 14 times at most to maintain the minimum balance requirement