Answer:
\(3\frac{5}{9} or \frac{32}{9}\)
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
If you can buy one bunch of seedless green grapes for $2, then how many can you buy with $18?
If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.
The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.
In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.
⇒ Number of bunches = ($18)/($2) per bunch,
⇒ Number of bunches = 9 bunches;
Therefore, with $18, you can buy 9 bunches of seedless green grapes.
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State the inequalities that satisfy the shaded region.
Answer:
Step-by-step explanation:
\(\Bigg\{ \begin{array}{ccc}2x-y+1&>&0\\x^2+2x-y-15&\leq &0\\\end {array} \right.\)
SOMEONE PLZZ HELP ME! THIS IS DUE TODAY (I WILL GIVE BRAINLIEST)
Alexa is hooked on a new book series, The Galaxy. Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Alexa has cleared off the top shelf of her bookcase to leave room for each of the books as they come out. There is a proportional relationship between the number of books on the shelf, x, and how much shelf space the books take up (in inches), y.
The equation that models this relationship is y=2x.
How many books will take up 16 inches of shelf space? Write your answer as a whole number or decimal.
Answer: 8 books
Step-by-step explanation:
y= how much shelf space take up (inches)
x= # of books
y=2x
in this situation 16=y
16=2x
divide both sides by 2
8=x
can someone translate the points, A- (-3,-6), B- (-5, -1), C- (-10, -9), D- ( -7, -13), E- (-5, -15) to the right?
The first step is to draw the coordinates in the cartesian plane:
Next you have to "Mirror" the points, this means, you check the distance over the X-axis and Y-axis for each point and then move to the next cuadrant and using those lengths you find the mirrored point:
So the mirroed ppoints are:
For A (-3,-6) is A' (3,-6)
For B (-5,-1) is B' (5,-1)
For C (-10,-9) is C' ()
QUESTION 9 1 POINT
Determine the interval(s) for which the function shown below is decreasing.
A function is decreasing if as x-values increase, the y-values decrease. Graphically this means that if you move from left-to-right, the graph goes down.
The downhill portion of this curve is on the interval \((1,\infty)\).
Solve each system of equations below by substitution
1. y = -3x – 16 and 5x – 2y = -23
2. 6y – 3x = -9 and x = -2y + 5
3. y + 4 = 3x and 2y – 6x = -8
Answer:
numero uno, ok
Step-by-step explanation:
Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Hey!
I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.
If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.
Anyways, please show all of your work and explain your thinking! Thanks!
Answer:
A. Cylinder + cone
Volume is the sum of volumes:
V = Vcon + Vcyl = 1/3πr²h₁ + πr²h₂V = 1/3π*9²*12 + π*9²*120 = 31554.2 cm³Surface area of cone:
A = A=πr(r+√(h₁²+r²)) = π*9(9 + √(9²+12²)) = 678.6 cm²Surface area of cylinder minus bases:
A = 2πrh₂ = 2π*9*120 = 6785.8 cm²Total surface area:
678.6 + 6785.8 = 7464.4 cm²-------------------------------------------------
B. Cube+ pyramid
Volume:
V = a³ + (1/3)a²h = a³ + (1/3)a²√(l²-(a/2)²)V = 8³ + (1/3)8²√(10²-4²) = 707.5 cm³Surface area of pyramid:
A = a² + 2al = 8² + 2*8*10 = 224 cm²Surface area of cube minus bases:
A = 4a² = 4(8²) = 256 cm²Total surface area:
A = 224 + 256 = 480 cm²If a = 4 and c = 2 then what is 5ac
Answer:
40
Step-by-step explanation:
by replacing the value and multiplying the numbers and the answer will come 40
Answer:
5ac = 40
Step-by-step explanation: When the letters and the numbers are toghether without a symbol they multiply each other.
So 5 x 4 x 2 = 40
help meeeeeeeeee pleaseee
The domain of the line in the graph is x∈R.
What is a domain?The set of all potential inputs for a function is its domain. For instance, the domain of f(x)=x² and g(x)=1/x are all real numbers with the exception of x=0. Additionally, we can define special functions with more constrained domains. Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, the domain the line is:
From the given graph, we know that y = every time.Which means, in the given graph, y = x = 10.
This also means:
y = x = 9y = x = 11y = x = 10The values of x can go to infinity.
Then the domain will be x∈R.Therefore, the domain of the line in the graph is x∈R.
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PLS HURRY FOR 80 POINTS Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if X′(4, 5).
y-axis
x-axis
y = 1
x = −4
Answer: a
Step-by-step explanation:
The median weekly income for a student who drops out of high school is 451. Someone with a bachelor's degree from college earns 1053 in that same week. Calculate each person's yearly income and then the difference between them.
The difference between their yearly incomes is $31,304.
To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:
For the student who drops out of high school:
Yearly Income = Weekly Income x Number of Weeks
= 451 x 52
= 23,452
For someone with a bachelor's degree:
Yearly Income = Weekly Income x Number of Weeks
= 1053 x 52
= 54,756
The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:
Difference = Bachelor's Yearly Income - Student's Yearly Income
= 54,756 - 23,452
= 31,304
Therefore, the difference between their yearly incomes is $31,304.
It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.
Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.
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please help this ones pretty easy just not sure how to do it
Answer:
-8i + 51
Step-by-step explanation:
(3+5i)(2-9i)
6+10i-18i-45i²
**i² = -1.
6-8i + -45(-1)
= -8i + 51
The x-coordinates of the solutions to a system of equations are 3.5 and 6. Which of the following could be the system? ( )A. y=x+3.5 y=x^2+6B. y=2x-7 y=-(x-6)^2C. y=12x+3 y=-(x-5)^2+7D. y=12x+7 y=-(x-6)^2+3.5
The system of equations that has a solution with x-coordinate of 3.5 and 6 is C. y = 1/2x + 3 and y = -(x - 5)² + 7.
To determine if a coordinate is a solution to a system of equations, substitute the values for the x and y in both equations and check if both resulting equations are true. If both resulting equations are true, then the coordinate is a solution to the system of equations.
A. y = x + 3.5
y = 3.5 + 3.5 = 7
y = x² + 6
7 = 3.5² + 6
7 ≠ 18.25
B. y = x - 7
y = 3.5 - 7 = -3.5
y = -(x - 6)²
-3.5 = -(3.5 - 6)²
-3.5 ≠ -6.25
C. y = 1/2x + 3
y = 1/2(3.5) + 3 = 4.75
y = -(x - 5)² + 7
4.75 = -(3.5 - 5)² + 7
4.75 = 4.75
y = 1/2x + 3
y = 1/2(6) + 3 = 6
y = -(x - 5)² + 7
6 = -(6 - 5)² + 7
6 = 6
D. y = 1/2x + 7
y = 1/2(3.5) + 7 = 8.75
y = -(x - 6)² + 3.5
8.75 = -(3.5 - 6)² + 3.5
8.75 ≠ -2.75
Only the system of equation in option C holds the equations true, hence, C. y = 1/2x + 3 and y = -(x - 5)² + 7 are the system of equations that has the given solution stated in the problem.
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An angle measures 8° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
41° and 49°
Step-by-step explanation:
Complementary angles are angles that sum up to 90°.
Let x represent the smaller angle, then the bigger angle will be represented with x + 8:
x + x + 8 = 90°
Add like terms.2x + 8 = 90°
Subtract 8 from both sides.2x = 82°
Divide both sides by 2.x = 41° this is the measure of smaller angle, then the bigger angle wpis 49°
The answer is:
⇨ 41 and 49Work/explanation:
If two angles are complementary, their measures add to 90°.
So we can set up an equation to find the angles. Let the unknown angle be w, and its complement will be w + 8:
w + w + 8 = 90
Combine like Terms
2w + 8 = 90
2w = 82
w= 41
The other angle measures 8° more than the measure of w:
41 + 8 = 49
Hence, the angles are 41 and 49°.the 4.1 m of concrete is made into the shape of a cylinder. The base has radios 0.5 metres. work out the height of the cylinder ( photo attached)
Answer:
5.22m
Step-by-step explanation:
Rearrange the formula - volume = π × r² × h:
h = volume ÷ (π × r²)
volume = 4.1m³r = 0.5Plug in the numbers:
h = 4.1 ÷ (π × 0.5²)
h = 5.22028... ≈ 5.22m
Hope this helps!
Culver has 1 quarter, 3 dimes and 1 penny. How much money does he have
Answer:
56 cents
Step-by-step explanation:
1 quarter = 25 cents
3 dimes = 30 cents
1 penny = 1 cent -_-
25 + 30 + 1 = 56
A vet is to give a cat 2 grams of medication. So far, 950 milligrams have been given. How many
milligrams still need to be given to the cat?
Answer: 1050 milligrams
Step-by-step explanation: One gram equals 1000 milligrams so 2 grams is 2000 milligrams. Since 950 milligrams have been given then there are 2000-950=1050 milligrams of medication that are meant to be given.
evaluate 24. 5 PLS AND THANK YOU!!!
Answer:
80
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
2⁴ · 5
Step 2: Evaluate
Exponents: 16 · 5Multiplication: 80
Use Substitution to solve each system of equations.
Answer:
x = -3
y = -2
(-3, -2)
Step-by-step explanation:
x - 7y = 11
5x + 4y = -23
-----------------------
-5 (x - 7y = 11)
-5x + 35y = -55
--------------------------
-5x + 35y = -55
5x + 4y = -23
39y = -78
÷39 ÷39
y = -2
-----------------------------
x - 7y = 11
x -7(-2) = 11
x + 14 = 11
-14 -14
x = -3
I hope this helps!
How can I answer this question
Determine a general formula for the solution of the following question
Answer:
general formula: b. θ = -π/6 + πk, or θ = -π/6 + -πk
solutions over [0,2π): θ = 5π/6 or θ = 11π/6
Step-by-step explanation:
First, solve for θ:
\(tan \theta + \frac{1}{\sqrt{3}}=0\) ⇒ \(tan \theta = -\frac{1}{\sqrt{3}}\) ⇒ \(\theta=tan^{-1}(-\frac{1}{\sqrt{3}})=-\frac{\pi}{6}\)
A Bernoulli differential equation is one of the formsdy/dx + P(x)y = Q(x)y^n (*) Observe that, if n 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y^(1-n) transforms the Bernoulli equation into the linear equation du/dx + (1 - n)P(x)u = (1 - n)Q(x). Consider the initial value problem xy’ + y = 2xy^2, y(1) = 4. (a) This differential equation can be written in the form (*) with P(x) = ___,Q(x) =___, and n = ___.(b) The substitution u = ___ will transform it into the linear equation Du/dx + ___ u = ___(c) Using the substitution in part (b), we rewrite the initial condition in part (c) u(1) = ____(d) Now solve the linear equation in part (b). and find the solution that satisfies the initial condition in part (c) U(x) = ____(e) Finally, solve for yy(x) = ____
the answer for this question is i don't know
So , bye
(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.
(b) The substitution u = 1/y will transform it into the linear equation Du/dx + 0u = -2x
(c)Using the substitution in part (b), we rewrite the initial condition in part u(1) = 1/y(1) = 1/4.
(d) the linear equation in part (b) is y = 1/(C - x) and the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,
(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).
What is Bernoulli differential equation?
A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:
dy/dx + P(x)y = Q(x)yⁿ
where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.
These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.
a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.
b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.
c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.
d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e\(\mathrm{(\int -xdx))}\) = -xe\(\mathrm{(\int -xdx))}\) which has the general solution u(x) = Ce\((-x^2/2)\).
Using the initial condition, we find C = 1/4, so u(x) = 1/4e\((-x^2/2)\).
e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e\((-x^2/2)\).
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what is the value of k?
Answer:
(4k+5)+ (6k+10) = 115
Exterior angle of a triangle is equal to the sum of two opposite interior angles
10k=15=115
10k= 100
k = 100/10
k = 10
Step-by-step explanation:
Answer:
k = 10
Step-by-step explanation:
The 3rd angle that's not defined in the equation is supplementary to 115, so the angle is 180-115 = 65.
We can solve for the equation 65+(4k+5)+(6k+10)=180 -> 65+4k+5+6k+10=180 -> 10k+80 = 180 -> 10k = 100 -> k = 10.
To double-check(optional), we can plug k back into the equation, so 65 + 4*10 + 5 + 6*10 + 10 = 180 -> 100 + 65 + 5 + 10 = 180 -> 180 = 180, so we can confirm that k = 10.
Which function has the following characteristics?
- A vertical asymptote at x=3
- A horizontal asymptote at y=2
- Domain: {x ≠ ±3}
A. y= (2x-8) / (x-3)
B. y= (2x^2 - 8) / (x^2 - 9)
C. y= (x^2 - 9) / (x^2 - 4)
D. y= (2x^2 - 18) / (x^2 - 4)
The function has the characteristics is (b) y= (2x^2 - 8) / (x^2 - 9)
How to determine the function?The features are given as:
A vertical asymptote at x=3A horizontal asymptote at y=2Domain: {x ≠ ±3}The function that has the above features is (b).
This is proved as follows:
y= (2x^2 - 8) / (x^2 - 9)
Set the denominator not equal to 0, to determine the domain
x^2 - 9 ≠ 0
Add 9 to both sides
x^2 ≠ 9
Take the square roots
x ≠ ±3 --- domain
Replace ≠ with =
x = ±3 --- vertical asymptote
Set the numerator to 0
2x^2 - 8 = 0
Divide through by 2
x^2 - 4 = 0
This gives
x^2 = 4
Take the square roots
x = 2 ---- horizontal asymptote
Hence, the function has the characteristics is (b) y= (2x^2 - 8) / (x^2 - 9)
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Linear sequence of 35/100,5/10,65/100
The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)
Finding the linear rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
35/100,5/10,65/100
In the above sequence, we can see that 15/100 is added to the previous term to get the new term
This means that
First term, a = 35/100
Common difference, d = 15/100
The nth term is then represented as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation, so, we have the following representation
f(n) = 35/100 + 15/100(n - 1)
So, we have
f(n) = 7/20 + 3/20(n - 1)
Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)
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Rounding Decimals (pt 2)
questions
1) 10.044 (2 decimal place)
2) 5.903 (1 decimal place)
the general formula for the number of decibels corresponding to a change in sound intensity to i2 relative to the former intensity i1 is
Part A: β₂ = β₁ + 10 log₁₀ (f)
Part B: Δβ = 20 log10 (d₁/d₂)
This can be solved using the concept of sound intensity.
What is sound intensity?While amplitude is the distance between a wave's resting position and its crest, sound intensity is defined as the sound power per unit area. The power carried by sound waves per unit area in a direction perpendicular to that region is known as sound intensity or acoustic intensity. The watt per square metre is the SI measure of intensity that includes sound intensity.
Part A:
β₂ - β₁ = 10 log₁₀ (I₂/I₁)
given that : I₂ = f × I₁
hence, I₂/I₁ = f
so the equation becomes:
β₂ - β₁ = 10 log₁₀ (f)
β₂ = β₁ + 10 log₁₀ (f)
Part B:
P = Power by the source
I₁= intensity at distance d1 = P/(4πd₁²)
I₂ = intensity at distance d2 = P/(4πd₂²)
Δβ = β₂ - β₁ = 10 log₁₀ (I₂/I₁)
β₂ - β₁ = 10 log₁₀ ((P/(4πd₂²))/(P/(4πd₁²)))
Δβ = 10log₁₀ ((d₁/d₂)²)
Δβ = 20log₁₀ (d₁/d₂)
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12).What is the angle measure ofL?К.450(x+15) L(2x)O 55O 57O 58360
Answer
Option A is correct.
Angle L = 55°
Explanation
To answer this, we need to note that the sum of angles in a triangle is 180°
So, we can solve for x by summing up the angles of this triangle and equating them to 180°
Angle J + Angle K + Angle L = 180°
2x + 45° + (x + 15)° = 180°
2x + 45° + x + 15° = 180°
2x + x + 45° + 15° = 180°
3x + 60° = 180°
3x = 180° - 60°
3x = 120°
Divide both sides by 3
(3x/3) = (120°/3)
x = 40°
Angle L = x + 15° = 40° + 15° = 55°
Hope this Helps!!!
The scale on a drawing reads 1/16^ prime prime =1^ prime .A2 inch long line represents
A. 8 feet
B. 16 feet
C. 32 feet
D. 64 feet
So
1 in line represents 16ft i e 2^4 ftHence
2in line represents
2(2^4)2(16)32ft