Answer:
There is one unique solution (-3, 6)
Step-by-step explanation:
Desmos graphing calculator helps a lot with this stuff
Answer: b) there is only one unique solution (-3, 6)
Step-by-step explanation:
15. A pool can hold 850 gallons. It now has 598 gallons of
water and is being filled at the rate shown. How many
more minutes, m, can water continue to flow into the
pool before it overflows? Write and solve an inequality.
Then graph the solutions.
The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let
x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of
$500 and wanteho purchase as many DVDs as possible, which values of x and y could represent the number of new
release and classie movies bought?
O x= 8, y = 45
O x= 10, y = 22
O x = 16. Y = 22
Ox= 18, y=18
Mark this and return
Save and Exit
Next
Submit
The Correct answer is option (C) x = 16. Y = 22 . number of new-release movies on DVD is 16 and the number of classic movies on DVD is 22 .
What is linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given,
To find the values of X and Y,
Let x = number of new releases
Let y = number of classics.
The equation to solve the question is ,
20x + 8y = 500
When x= 16 and y = 22
= 20x + 8y
= 20(16) + 8(22)
= 320 + 176
= 496
Therefore, the number of new-release movies on DVD is 16 and the number of classic movies on DVD is x= 16, y = 22
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simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6
The simplified value of x is 44 / 15 or 7 / 5 and value of y is -2
What is simplification?Simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Given that, simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6
1) 2(y-1) / 3 - 3(y-2) / 4 = 1
Multiplying by 12 to both sides,
8(y-1) - 9(y-2) = 12
8y-8 - 9y+18 = 12
-y + 10 = 12
y = -2
2) 3x = 44 / 5 = 2x+6
3x = 44 / 5
Multiplying by 5 to both sides,
15x = 44
x = 44 / 15
or,
44 / 5 = 2x + 6
Multiplying by 5 to both sides,
44 = 10x + 30
14 = 10x
x = 7 / 5
Hence, the simplified value of x is 44 / 15 or 7 / 5 and value of y is -2
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ES = ___ units
Round your answer to the nearest tenth.
Answer:
15
Step-by-step explanation:
Can you help me with this
Dalis' employer pays $2,150 in health insurance and $86
in life insurance per year. She also gets $3,520 in paid time
off per year. Her monthly gross pay is $4,370. What are
Dalis' total job benefits?
Answer: chiki
Step-by-step explanation:
Please hurry it's timed i need help
The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given the function as;
cosx - √(3 - 3cos³x) = 0
cosx = √(3 - 3cos³x)
Taking square root on both sides.
cos ²x = √(3 - 3cos³x) ²
cos ²x = (3 - 3cos³x)
For solving for x in
cos ²x = (3 - 3cos³x)
cos ²x = 3 (1 - cos³x)
(1 - cos³x) = cos ²x/3
x= π/6 + 2πn
or
x=11π/6 + 2πn
where n is an integer.
30° + 360° n, 330° + 360°n
The correct answer is C.
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A company has two manufacturing plants with daily production levels of 5x +14 items and 3x - 5 items, respectively. The first plant produces how many more items daily than the second plant?
Answer:
21x
Step-by-step explanation:
5x+14=19x
3x-5=-2x
-2x-19x=21x
Your friend has read 6 more than twice as many pages as your
sister has read. Let 4
be the number of pages that your sister has
read. Write an expression for the number of pages that your friend
has read
Answer:
Expression: 2s + 6
# of Pages Friend Read: 14 pages
Step-by-step explanation:
Let's call the number of pages your sister has read, s, and the number of pages your friend has read, f. We will make our equation first. If your friend has read 6 more than twice as many pages as your sister has, your equation would look like this:
f = 2s + 6
That is your equation for how many pages your friend read, your expression would be just 2s + 6. Now, we will substitute in 4 for s, and we get:
f = 2 * 4 + 6
Multiplying gives:
f = 8 + 6 = 14
So your friend has read 14 pages.
Hope this helped!
The total number of books sold from 2010-2015 from
Amazon can be modeled by the function
3
2
f(x) = 40x + 8x + 14824x + 33000and the number of kinds
of books at Amazon from that same time period can be modeled
as g(x): =
10x + 22, where x is the number of years since
2010. What is the average number of each kind of book
Amazon sold?
Answer:
If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.
Step-by-step explanation:
How do you find the slope of two points on a graph?
To find the slope of two points on a graph, use the formula:
[tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]
Substitute the coordinates of the two points into the formula and solve for the slope.
Finding the Slope of Two Points on a GraphThe slope of two points on a graph is a measure of how steep the line connecting the two points is. To find the slope, you can use the slope formula: [tex]Slope =\frac{y2 - y1}{x2 - x1}[/tex]
This formula requires the coordinates of the two points, which can be found on the graph. Once you have the coordinates, you can substitute them into the formula and solve for the slope. This will give you the slope of the line connecting the two points.
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what value of x would prove that the following triangle is a right angle? Answers x=7 x=2 x= 14 x= 10
Step-by-step explanation:
Pythagoras' TheoremFor Pythagoras' Theorem to be valid, the triangle must be a right-angled one.
The formula is:
c^2 = a^2 + b^2
Where c is the longest side. While a,b are the side lengths.
SolutionUsing the above formula and the measurements given in the question, we can find the value of x.
By Pythagoras' Theorem,
26^2 = (5x)^2 + (12x)^2
676 = 25x^2 + 144x^2
169x^2 = 676
x^2 = 676 ÷ 169
x^2 = 4
x = 2
A large helium balloon is tethered to the ground by two taut lines. One line is 100 ft. Long and makes an 80 degree angle with the ground. The second line makes a 40 degree angle with the ground. How long is the second line?
The second line is 153ft long.
We are making a figure out of the given statment. Where we have the Triangle ABC and other two Triangle ADB and ADC inside Triangle ABC. Here Angle ADC = 80 degress and Angle ACD = 40 egress.
According to given statement and figure,
In triangle ABO, AD= 100 ft
Hence, BD/AD = Cos80
or, BD = (100 * Cos80)
or, BD = 17.36 ft
Now, AB/AD = Sin80
or, AB = (100* Sin 80)
or, AB = 98.48
Now, In case of triangle ABC
AB/AC = Sin40
or, AC = AB/ Sin 40
or, AC = 98.48/ Sin40
or, AC = 153.2 ft (nearly equal to 153 ft)
The second line is 153ft long.
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What it means when a function and its inverse is the same?
Step-by-step explanation:
it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.
it means that the function applied to itself gives x.
f(f(x)) = x
e.g.
f(x) = 5 - x
f(f(x)) = 5 - (5 - x) = 5 - 5 + x = x
so, this f(x) is its own inverse.
solve the following equations for values of theta between 0 degrees and 360 degrees. 1. 2tan^2 theta - 7 sec theta + 8 = 0
The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.
How to solve a trigonometric equation
In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.
First, write the complete expression:
2 · tan² θ - 7 · sec θ + 8 = 0
Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:
2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0
2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0
2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0
6 · cos² θ - 7 · cos θ + 2 = 0
Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:
6 · u² - 7 · u + 2 = 0
u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]
u = - 7 / 12 ± (1 / 12) · 1
u = - 7 / 12 ± 1 / 12
There are two possibilities:
u₁ = - 2 / 3, u₂ = - 1 / 2
Fourth, find the angles associated to roots by inverse trigonometric functions:
u₁ = - 2 / 3
θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°
u₂ = - 1 / 2
θ₂₁ ≈ 120°, θ₂₂ ≈ 240°
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How many times and how many ounces should I feed my goat if it is 7 pounds and I feed it 3 times a day
Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.
What is feeding?The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.
Define Ounces and Pounding.In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.
Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.
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Solve for x: -24 = 6x
Answer:
x = -4
Step-by-step explanation:
Solve for x: -24 = 6x
-24 = 6x
x = -24 : 6
x = -4
---------------------
check
-24 = 6(-4)
-24 = -24
the answer is goodTyrese works each day and earns more money per hour the longer he works. Write a function to represent a starting pay of $20 with an increase each hour by 3%. Determine the range of the amount Tyrese makes each hour if he can only work a total of 8 hours.
The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80
What is a range?The range is the space between the highest and lowest numbers.
Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.
To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.
The beginning wage is $20.
Suppose x hours are in a day.
A $20 salary is offered, with a 3% hourly raise.
e.g., increment = (3/100)*20*x = (3/5)x
A function's maximum possible earnings are
y = 20 + (3/5)x
He is only allowed to work a total of 8 hours, per our instructions.
Therefore, the most money she can make in 8 hours is
y = 20 + (3/5)*8
y = 20 + 4.8
y = 24*8
$20 is the first sum.
As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .
Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.
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What’s the formula to find principal please tell me please
Answer:
Step-by-step explanation:
(100xInterest)(RatexTime)
hope this helps
Step-by-step explanation:
The formula for calculating Principal amount would be P = 100I / (RT) where Interest is Interest Amount, R is Rate of Interest and T is Time Period.
Which triangles are congruent by ASA?
ABC and TUV
VTU and ABC
VTU and HGF
none of the above
Shade the points in the plane whose x-coordinates are greater than their y-coordinates. Write the inequality that describes these points.
The inequality that describes these points is y ≤ -1/2(x) -3. The graph is given the attachment.
How to graph an inequality?To graph a linear inequality in two variables (say, x and y), start with y on one side. Consider the related equation obtained by changing the inequality sign to an equality sign. This equation's graph is a straight line.
If the inequality is strict (< or >), draw a dashed line. If the inequality is not strict (≤ or ≥), draw a solid line.
Finally, choose one point that is not on either line ((0,0) is usually the easiest) and determine whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.
Graph each of the system's inequalities in a similar way.
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How to graph 4x-6y=36
What’s the x intercept
What’s the y intercept
Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).
Clarify the equationA depiction of two equal variables, one on either side of a "equals" sign, is what constitutes an equation in mathematics. To solve common issues, one can use equations. We frequently look for help with pre algebra to overcome obstacles in real life. Basic mathematical concepts are covered in pre-algebra lessons.
Here,
the x-intercepts,
In order to determine the x-intercept(s), put in for y and calculate 4x6y=36.
Make the equation work.
x=9 point form x-intercepts.
x-intercept(s): \s(9,0) (9,0)
the y-intercepts, please.
In order to determine the y-intercept(s), replace with and solve for y=.4(0-)6y=36.
Make the equation work.
To continue, tap.
Point shape y=6 y-intercept(s).
The y-intercept is (0, 6).
Write down the junctions.
x-intercept(s): (9,0)
The y-intercept is (0, 6).
Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).
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Alana and Petra go to a ued book ale , where every book i the ame price. Alana buy 4 book and Petra buy 2 book. They run into their friend angu, who really love to read, and dicover that he ha bought 16 book. Angu received a $15 dicount, but he till pent $5 more than Alana and Petra combined. How much doe one book cot?
A book cost $2.00.
What are variables in maths?In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
What are the 2 basic types of variables?Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.
Given the no of books purchased by
Alana =4
Petra =2
Angus = 16
So, the total price of 4 books of Alana =$4
Total price for Petra = $2
Total price of Alana and Petra =4x+2x
=6x
Total price for Angus = 16x
But given Angus received a discount of $15
So price post discount = 16x- 15
According to the question
16x-15 = 6x +5
Adding 15 both sides
16x +15-15 = 6x + 5+15
16x= 6x+20
Subtracting 6x both sides
16x - 6x = 6x - 6x + 20
10x = 20
i.e x=2
Cost of one book = $2
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what's 1/2r+3<6 two step inequalities
Answer:
r < 6
Step-by-step explanation:
[tex] \implies \dfrac{1}{2}r + 3 < 6[/tex]
[tex] \implies \dfrac{r}{2} < 6 - 3[/tex]
[tex] \implies \dfrac{r}{2} < 3[/tex]
[tex] \implies r < 3 \: \cdot \: 2[/tex]
[tex] \implies \underline{ r < 6}[/tex]
The sum of three segments measures 82 cm. The first is 4/9 of the second and the third exceeds the second by 16cm. Calculate the size of each segment.
Please help it’s for tmr
Answer:
12 cm27 cm43 cmStep-by-step explanation:
You have three segments totaling 82 cm, with the first being 4/9 of the second, and the third being 16 cm more than the second.
EquationsWe can describe the relationship by the equations ...
a + b + c = 82
a = 4/9b
c = b +16
SolutionThe equations give each segment in terms of the second one, so we can substitute those relations into the sum:
(4/9b) +b +(b +16) = 82
22/9b = 66
b = 66(9/22) = 27
a = (4/9)(27) = 12
c = 27 +16 = 43
The first segment is 12 cm; the second is 27 cm; and the third is 43 cm.
__
Additional comment
We used an ad hoc solution based on the observation that segments 'a' and 'c' were defined in terms of 'b'. We could write the equations as a system of 3 linear equations in 3 unknowns, and solve using matrix methods:
a +b +c = 829a -4b = 0-b +c = 16The solution is shown in the attachment: a=12, b=27, c=43.
What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal
There is a 0.0001 percent chance that the average amount of cereal in these boxes is less than 9.65 ounces.
What is meant by probability?The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. We can only forecast how likely an event is to occur using it, or how likely it is to occur.The probability is a metric for determining how likely an event is to occur. It gauges the event's degree of certainty. The probability formula is presented as follows: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.Given that,
Mean µ = 9.70
Sample size = n = 5
standard deviation = σ = 0.03
Its distribution is normal, therefore
σx = σ/
σx = 0.03
σx = 0.0134
We must now determine the z value in order to use the table.
z = (x - µ) ÷ σ
z = (9.65 - 9,70) ÷ 0.0134
z = -3.73
Now
From the probability index tables
So P (z ≤ - 3.73) = 0.0001
Hence, the correct option is e) 0.0001
The complete question is:
A company’s cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounce. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?
a. 0.4525
b. 0.9522
c. 0.9999
d. 0.0478
e. 0.0001
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I want to know how to get the GCF and LCM of 8,24,48
Answer:
GCF = 8
LCM = 48
Step-by-step explanation:
convert 11.011 to a base 10 number
Multiply each digit by its corresponding place value and add the results: 11 + 0.011
11.011 = 11 + 0.011 = 11.011
How to covert binary number to decimal number?Once the bits of the binary number have been multiplied by the corresponding positional weights, the binary number can then be converted into its corresponding decimal number by adding the resulting products.
To convert a number in base 2 (binary), base 8 (octal) or base 16 (hexadecimal) to a base 10 (decimal) number, you can use the following method:
Write the number in base 2, 8, or 16 and the corresponding base 10 place values.
Multiply each digit by its corresponding place value and add the results.
For example, to convert the base 10 number 11.011 to a base 10 number:
Write the number and the corresponding base 10 place values: 11.011
Multiply each digit by its corresponding place value and add the results: 11 + 0.011
11.011 = 11 + 0.011 = 11.011
As the number is already in base 10, it does not need to be converted. The value is 11.011
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Mario has 3/4 cups of chocolate chips needs 1/3 cup to make a batch of cookies how many batches can Mario make if he uses all of his chocolate chips
In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.
How to find the given equation?First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).
[tex]3/4 cups * 1 = 3/4 cups\\[/tex]
Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:
[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]
Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:
[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]
Mario can make 2.25 batches of cookies using all of his chocolate chips.
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Explain how the quotient was determined.