Answers
Answer:
30 ft
Step-by-step explanation:
Hi!
So according to the Pythagorean theorem, a^2 + b^2 = c^2
Ok, so let's just plug those numbers in:
18^2 + 24 ^ 2 = c^2
324 + 576 = c^2
900 = c^2
\(\sqrt{900}\) = c
\(\sqrt{900}\) = 30
x = 30
You could also use Pythagorean triples, and there are Pythagorean triples for this which is 3:4:5; and since it's a ratio, we can write it as 3x:4x:5x. Then, according to a and b, x would equal 6, so then we plug in x:
3(6):4(6):5(6)
and you get:
18:24:30
Let me know if you have any questions.
Related Questions
What would the height need to be for this curve to be a density curve?
1/5
1/4
1/2
1
Answers
For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.
Let's see how the height would need to be for this curve to be a density curve.A density curve is a statistical representation of the distribution of a dataset or population. Density curves are used to describe the distribution of continuous data and provide a visual representation of the likelihood of an event occurring within a specific range of values. It helps to determine the proportion of data that falls within a given range of values. A density curve is used to provide a graphical representation of data without showing the individual data points.To be a density curve, a curve must have the following properties:The curve should be non-negative.The area under the curve should be equal to 1.The curve should be smooth and continuous.There should be no values outside the range of the data.From the above properties, we can conclude that the height required for a curve to be a density curve depends on the data that the curve represents. As long as the curve meets the above conditions, it can be considered a density curve. So, there is no specific height required for a curve to be a density curve. The height of the curve can vary depending on the range of the data and the distribution of the data.For such more question on properties
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Solving Systems of Linear Equations
Performance Assessment
You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.
Part 1 Choosing a Band
Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.
Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.
Part 2: Choosing a Caterer
A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.
Part 3: Analyzing cost
Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.
Part 4: Choosing Flowers
You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.
Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.
Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.
Answers
1.Band A: Cost = $500
Band B: Cost $350 + $1.50x
2. The caterer's fixed cost is $150 and the rate per student served is $6.
3.Cost per ticket $12.50
4.we can buy at most 3 bouquets of roses.
What are linear equations?
The first-degree equations are linear equations. The straight line's equation can be found here. ax+by+c=0 is the most common form of a linear equation, where a and b are zeros.
Part 1:
Let x be the number of students.
Band A: Cost = $500
Band B: Cost $350 +$1.50x
The system of equations representing the cost of the two bands is:
CostA = 500
CostB = 350+ 1.5x
Part 2:
Let F be the fixed cost and R be the rate per student served.
From the given information, we can write two equations:
50R + F = 450
150R + F = 1050
Subtracting the first equation from the second, we
get:
100R = 600
Therefore, R = 6.
Substituting R in the first equation, we get:
50(6)+F450
Therefore, F = 150.
So, the caterer's fixed cost is $150 and the rate per student served is $6.
Part 3:
For 100 students:
CostA 500
CostB = 350+ 1.5(100) 500
Both bands have the same cost, but Band A has a lower variable cost.
So, we should choose Band A.
Total cost for 100 students = 500 + 150+ 6(100) =
$1250
Cost per ticket = Total cost / Number of students = 1250/100 = $12.50
For 200 students:
CostA = 500
CostB = 350+ 1.5(200) = 650
Band A still has a lower cost, so we should choose Band A.
Total cost for 200 students 500+ 150 + 6(200) = $1850
Cost per ticket = Total cost / Number of students =
1850/200 $9.25
Part 4:
Let D be the number of bouquets of daisies and R be the number of bouquets of roses.
The cost of daisies is $25 per bouquet and the cost of roses is $35 per bouquet. We want to spend no more than $500, so we can write:
25D +35R < 500
If we buy 15 bouquets of daisies, then we can spend at most $425 on roses:
25(15) + 35Rs 500
375 +35R ≤ 500
35R ≤ 125
If we buy 15 bouquets of daisies, then we can.
Mathematics College spend at most $425 on roses:
25(15)+35R ≤ 500
375 +35R≤ 500
35R ≤ 125
R≤ 3.57
So, we can buy at most 3 bouquets of roses.
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Jerry's brought 4 DVD's for 25.20 . What was the unit rate?
Answers
Answer:
1 DVD cost $6.30
Step-by-step explanation:
Simply divide 25.20 by 4
25.20/4=6.3
1 DVD cost$ 6.30
Hope this helps : )
OK for real this is a hard only verified experts can do this!!!!
Answers
The numeric value of the exponential expression in this problem is given by the following option:
A. 2^12.
How to obtain the numeric value of the exponential expression?The exponential expression for this problem is defined as follows:
8^x/2^y.
8 is the third power of 2, hence:
8 = 2^3.
When a term is elevated to two of it's powers, the powers are multiplied, hence:
(2^3)^x = 2^(3x).
Meaning that the exponential expression is then written as follows:
8^x/2^y = 2^(3x)/2^y.
When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:
2^(3x)/2^y = 2^(3x - y).
As stated in the problem, the numeric value of the expression 3x - y is given as follows:
3x - y = 12.
Hence the entire expression is simplified as follows:
2^(3x - y) = 2^12.
Meaning that the correct option is given by option A.
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Answer:A. 2^12.
Step-by-step explanation:i did it and got it right
What is this? Please answer if u know what you are doing thank you
Answers
Answer:
y= 8
Step-by-step explanation:
y= k/x
-8= k/4
k= -8×4= -32
y= k/x
y= -32/-4
y= 8
hope it helps!
Answer:
the answer is 8 if y= -8 when x is 4 amd
please help, screenshot is here:
Answers
\(Answer:\ cos(\theta_1)=\boxed{-\frac{40}{41} }\)
Step-by-step explanation:
\(\displaystyle\\sin(\theta_1)=\frac{9}{41}\ \ \ \ \ \ 90^0 < \theta_1 < 180^0\ \ \ \ \ \ \ cos(\theta_1)=?\\\\sin^2(\theta_1)+cos^2(\theta_1)=1\\\\cos^2(\theta_1)=1-sin^2(\theta_1)\\\\cos^2(\theta_1)=1-(\frac{9}{41})^2\\\\cos^2(\theta_1)=1-\frac{81}{1681} \\\\cos^2(\theta_1)=\frac{1(1681)-81}{1681} \\\\cos^2(\theta_1)=\frac{1600}{1681} \\\\\)
Extract the square root of both parts of the equation:
\(\displaystyle\\\cos(\theta_1)=б\sqrt{\frac{1600}{1681} } \\\\\cos(\theta_1)=б\sqrt{\frac{40^2}{41^2} } \\\\\cos(\theta_1)=б\sqrt{(\frac{40}{41})^2 } \\\\\cos(\theta_1)=б\frac{40}{41}\)
\(\displaystyle\\Since\ 90^0 < \theta_1 < 180^0, \\\\ therefore\ cos(\theta_1)=-\frac{40}{41}\)
4/√8+3
please this little guy wants to disturb me,help, thanks.
Answers
Answer:
\( \sqrt{2} + 3\)
Step-by-step explanation:
SIMPLIFY the radical expression...
SO IT'S
\( \frac{4}{2 \sqrt{2} } + 3\)
Reduce the fraction with 2
Now it's
\( \frac{2}{ \sqrt{2} } + 3\)
Rationalize the denominator...
SO IT WILL BE
\( \sqrt{2} + 3\)
EASY EXPLANATION...
GAVE ME THE BRAINLIEST IF MY ANSWER WAS HELPFUL...
Sᴋ᭄Sᴀᴍɪʀᴮᴼˢˢ
What is the measure of angle R?
Enter your answer as a decimal in the
box. Round only your final answer to
the nearest hundredth.
Answers
Answer:
45??? or 30 I'm not very good with angles
help
I need an answer
Answers
The correct option that indicates the quadrant that contains the translation of the shaded figure is the option B
B. III
What is a translation transformation?A translation is a transformation in which the size, relative position of the points on the pre-image, are preserved but the location of the pre-image changes to obtain the image.
The shape of the shaded figure is an L-shape
The geometric figure in quadrant II and IV are a reflection of the shaded figure, across the y-axis and across the x-axis, respectively which is not a translation transformation.
The geometric figure in quadrant III can be obtained from the shaded figure by a translation 4 units to the left and 5 units downwards, which can be expressed as <-4, -5>, which is a translation transformation, therefore;
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Find the area of the parallelogram
Answers
Answer:
1191 cm²
Step-by-step explanation:
Area of parallelogram = base X vertical height.
Call the vertical line h.
h/ sin 80 = 7/ sin 10
h = (7 sin 80) / sin 10
= 39.7.
Area of parallelogram = 30 X 39.7
= 1191 cm²
The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.
Given:
Side length = 30 cm
Using Trigonometry
tan 80 = P / Base
5.6712 = P / 7
P = 39.6984 cm
Using the formula for Area of parallelogram
= Base x height
= 30 x 39.6984
= 1,190.952 square cm.
Therefore, the area is 1,190.952 square cm.
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Some factors need to be controlled to keep this test fair. name two of them….
Answers
Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.
What are the control variables?The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.
For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.
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Approximate the root by using a linearization centered at an approximate nearby number
√101
Answers
Linearization is the idea in calculus where if you zoom in really close onto a section of the graph, the curve and the tangent line will be extremely similar to each other.
We can use this idea and approximate nearby values to the tangent line.
The parent graph of a square root function is \(f(x)=\sqrt{x}\).
There are two methods in which we can calculate the approximate value of \(\sqrt{101}\) by using linearization techniques.
Method 1:Write equation of tangent line.Find the value of y at x = 101.Let's use the nearest perfect square to \(\sqrt{101}\), which is \(\sqrt{100}\). When drawing the graph of the square root function, we use the point (100, 10) because where x = 100, y = 10 on a square root function.
Now, we have a point that the tangent line passes through, and we want to find the slope.
We can do so by taking the derivative of \(f(x) =\sqrt{x}\).
\(f'(x)=x^\frac{1}{2}\) \(f'(x)=\frac{1}{2} x^-^\frac{1}{2}\) \(f'(x)=\frac{1}{2x^\frac{1}{2} }\) \(}f'(x)=\frac{1}{2\sqrt{x} }\)Plug in x = 100 to find the slope of the tangent line here.
\(f'(100)=\frac{1}{2\sqrt{100} }\) \(f'(100)=\frac{1}{2(10)}=\frac{1}{20}\)The slope of the tangent line at x = 100 is 1/20. Now, we can use the point and the slope of the tangent line to determine the equation for the tangent line.
(100, 10), m = 1/20
Point-slope equation:
\(y-y_1=m(x-x_1)\) \(y-(10)=\frac{1}{20}(x-(100))\) \(y=\frac{1}{20}x-5+10\) \(y=\frac{1}{20}x+5\)To find the value of y at x = 101, plug this into the tangent line equation.
\(y=\frac{1}{20}(101)+5\) \(y=\frac{101}{20}+5\) \(y=\frac{101}{20} +\frac{100}{20} = \frac{201}{20}\)201/20 is equal to 10.05. Let's estimate the error of this calculation to the actual value of \(\sqrt{101}\), inputted into a calculator.
We get \(\sqrt{101}=10.04987562\), which is extremely close to 10.05. Our estimate using linearization only has an error of 0.00012.
Method 2:You may have noticed that the first method uses little calculus, apart from taking the derivative of f(x).
The more "calculus-y" method involves finding the change in y in terms of the change of x.
We know that dy/dx is the the change in y due to a change in x, so we can use this to find the change in y when x = 101.
\(\frac{dy}{dx} =\frac{1}{2\sqrt{x} }\)Solve for dy by mutliplying dx to both sides of the equation.
\(dy=\frac{1}{2\sqrt{x} } \cdot dx\)The change in x is 1, because 101 - 100 = 1.
We want to find the change in y when x = 100, and has a change of 1. Therefore, we have:
\(dx=1\) \(x=100\)Plug these values into the equation \(dy=\frac{1}{2\sqrt{x} } \cdot dx\) and solve for dy.
\(dy=\frac{1}{2\sqrt{200} } \cdot 1\) \(dy=\frac{1}{2(10)}\) \(dy=\frac{1}{20}\)The change in y when x = 100 with a change of 1 is 1/20. We know when x = 100 the y-value is 10. Therefore, when x = 101, the change in y is 1/20, so y = \(10\frac{1}{20} = \frac{201}{20} = 10.05\).
You can see that we get the same answer with either method.
Add the equations 4x−4y =-2 and −9x4y=-3
Answers
Answer:-5x-8y=-5
Step-by-step explanation:
add right sides of equation and even them with result of adding right sides of equation
4x-4y-9x-4y=-2-3
-5x-8y=-5
graph y+2=2(x+3). What is the x intercept?
x intercept :
Answers
The given equation is y + 2 = 2(x + 3) and the x-intercept is -2.
To find the x-intercept of the equation y + 2 = 2(x + 3), we need to set y equal to zero and solve for x. The x-intercept occurs when the value of y is zero, meaning the graph crosses the x-axis.
Let's substitute y with 0 in the equation:
0 + 2 = 2(x + 3)
Simplifying the equation:
2 = 2(x + 3)
Dividing both sides by 2:
1 = x + 3
Subtracting 3 from both sides:
-2 = x
The x-intercept is -2. This means that the graph of the equation y + 2 = 2(x + 3) crosses the x-axis at the point (-2, 0).
The x-intercept represents the value of x where the graph intersects or crosses the x-axis. In this case, it occurs when x is equal to -2, and the y-value is zero.
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someone can help me please
Answers
Step-by-step explanation:
64 crayons school order 25 for the art class there are 5 art class they should be share evenly
A hotel charges its guests a 4% tax. The cost before tax for one guest's stay at the hotel is $375.
How much tax, in dollars, will the guest pay for the stay?
Answers
Answer:
I dont know the other homes but this one is $390 ( I think)
Step-by-step explanation:
4% of $375 is $15 so adding $15 on you would get $390.
I really hope this is right. And I hope this helped!
The guest will pay the amount of 15 dollars tax for the stay which is determined by the evaluation of 4% of $375.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that the 4% tax is charged to hotel guests. A single guest's stay at the hotel costs $375 before taxes.
We have to determine the evaluation of 4% of $375.
⇒ 4% of $375
4% is expressed as 4/100 in fractional form
⇒ (4/100)(375)
4/100 is expressed as 0.04 in decimal form
⇒ (0.04)(375)
Apply the multiplication operation, and we get
⇒ 15
Therefore, the guest will pay the amount of 15 dollars tax for the stay.
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I need help with this please
Answers
Answer:
D) 48
Step-by-step explanation:
area = length x width x height
8 x 2 x 3
16 x 3 = 48
Which of the points below correctly plots the point (−2,−5π/3)?
Select the correct answer below:
A
B
C
D
E
F
Answers
Answer: F
Step-by-step explanation:
Answer: correct answer is A
Step-by-step explanation:
Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.
4. Please complete the following math problem & show your work.
You are responsible for making sure that the club has a sufficient inventory of light bulbs. You need to have 20 light bulbs of each
size in storage. You need to check all of the storage closets to get a count. In the first storage closet, you find five boxes of 36" bulbs
with two in each box and four boxes of 24" bulbs with four in each box. In the second storage closet, you have three boxes of 36°
bulbs with four in each box. In addition, you know you need to replace four 36 bulbs. How many do you need to order in order to
keep twenty of each size in stock?
Answers
You need to order 2 36" bulbs and 4 24" bulbs in order to keep twenty of each size in stock.
What is the stock?The stock is a type of security that represents ownership in a company. It is a financial asset that can be traded, and the price of the stock is determined by the supply and demand of the market. When a company issues stock, the stockholders gain a share of the company’s ownership.
36" bulbs:
First storage closet: 5 boxes with 2 in each box = 10
Second storage closet: 3 boxes with 4 in each box = 12
Total = 10 + 12 = 22
Need to order = 20 - 22 = 2
24" bulbs:
First storage closet: 4 boxes with 4 in each box = 16
Total = 16
Need to order = 20 - 16 = 4
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Write a polynomial
f(x)
in general form that has the following characteristics.
• Degree 3
• Leading coefficient of 4
• One double root at
x = −6
• One root at
x = 5/2
Answers
The general form representation of the polynomial which is as described in the task content is; f(x) = 4x³ + 38x² + 24x - 360.
Polynomials in general form.It follows from the task content that the Polynomial in discuss has;
Degree 3.Leading coefficient of 4.One double root at, x = −6.One root at; x = 5/2.Therefore, the factored form of a polynomial can be written as follows;
P(x) = a (x - p) (x - q) (x - r) where p, q and r are the roots of the polynomial and a is the leading coefficient.
Since the factors of the polynomial f(x) are; (x + 6), (x + 6) and (x - 5/2).
Hence, the polynomial f(x) in discuss can be written as follows;
f(x) = 4 (x + 6) (x + 6) (x - 5/2)
f(x) = (x + 6) (x + 6) (4x - 10)
f(x) = 4x³ + 38x² + 24x - 360
Therefore, the required polynomial in standard form is; f(x) = 4x³ + 38x² + 24x - 360.
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0.001374 as a standard form.
What’s the answer to this? No spam links plz.
Answers
Step-by-step explanation:
0.001374
standard form means writing a value in shortened form, because sometimes values are too big or small to be written, so we use standard form.
in standard for the decimal always comes after the first digit
so,
\(1.374 \times {10 }^{ - 3} \)
the decimal moves 3 digits to the right so it becomes ten raised to the power minus 3.
6m+5n when m =6 and n=4
Answers
Answer:
Step-by-step explanation:First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:
5m +5n+6m−4n
Next, group like terms:
5m+6m+5n−4n
Now, combine like terms:
(5+6)m+(5−4)n
11m+1n
11m+n
Jason is buying wings and hot dogs for a party. One package of wings costs $7. Hot dogs cost $5 per package. He must spend no more than $40. Write and inequality to represent the cost of Jason’s food for the party. Jason knows that he will be buying at least 5 packages of hot dogs. Write an inequality to represent this situation. Graph both inequalities. Give two options for Jason when buying wings and hot dogs.
Answers
An inequality to represent the cost of Jason’s food for the party is
An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is
The two options for buying wings and hot dogs include the following:
One (1) package of wings and five (5) packages of hot dogs.Two (2) packages of wings and five (5) packages of hot dogs.How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of wings.Let the variable y represent the number of packages of hot dogs.Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;
7x + 5y ≤ 40
Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;
y ≥ 5
Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.
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Suppose that continuous random variables X and Y have a joint probability density function given by: f X,Y
(x,y)={ c⋅x 2 y,0,0≤x≤2;0≤y≤2 otherwise 1. Define the mode of a continuous random variable to be the point at which the density is maximized, if such a point exists. What is the mode of YY?
2. What value of cc makes this a valid probability density function?
3. What is the expected value of YY, E[Y]E[Y]?
4. What is the variance of YY, V[Y]V[Y]?
Answers
And , the Y's variance is \(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)To find the mode of Y, we need to find the value of y that maximizes the joint probability density function\(f_X, Y(x,y).\)
To do this, we can fix x to be a particular value and then find the value of y that maximizes \(f_X, Y(x,y).\)
For any fixed x between 0 and 2, the function\(f_X, Y(x,y)\) is maximized at y = 1, since this is the only value of y that depends on x and maximizes the function\(cx^2y.\) Therefore, the mode of Y is 1.
To find the value of c that makes this a valid probability density function, we need to ensure that the integral of \(f_X, Y(x,y)\)over the entire sky-plane is equal to 1. We can set up the integral as follows:
integral from 0 to 2 of (integral from 0 to 2 of cx^2y dy) dx
= integral from 0 to \(2 of [c*x^2/2 * y^2]\)evaluated from 0 to 2 dx
= integral from 0 to 2 of \(c*x^2 x2d\)
= [2c/3 * x^3] evaluated from 0 to 2
= (16c/3)
For this to equal 1, we must have c = 3/16. Therefore, the valid probability density function is:
f_X,Y(x,y) = { (3/16)x^2y, 0 <= x <= 2, 0 <= y <= 2; 0, otherwise }
To find the expected value of Y, we need to integrate Y times the joint probability density function f_X, Y(x,y) over the entire xy-plane:
E[Y] = integral from 0 to 2 of (integral from 0 to 2 of y*f_X, Y(x,y) dy) dx
= integral from 0 to 2 of \([(3/16)*x^2/2 * y^2]\) evaluated from 0 to 2 dx
= integral from 0 to 2 of (3/16)*x^2 dx
= [3/16 * x^3/3] evaluated from 0 to 2
= 1
Therefore, the expected value of Y is 1.
To find the variance of Y, we first need to find the second moment of Y by integrating Y^2 times the joint probability density function f_X, Y(x,y) over the entire xy-plane:
E[Y^2] = integral from 0 to 2 of (integral from 0 to 2 of y^2*f_X, Y(x, y) dy) dx
= integral from \(0 to 2 of [(3/16)*x^2/3 * y^3]\) evaluated from 0 to 2 dx
= integral from \(0 to 2 of (3/8)*x^2 dx\)
= \([3/8 * x^3/3]\) evaluated from 0 to 2
= 2
And , the Y's variance is
\(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)
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There are 17 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers
finish first through fifth?
Answers
This can be solved using permutations
What are permutations?
A permutation of a set in mathematics is a loosely defined organization of its members into a sequence or linear order, or, if the set is already sorted, a rearranging of its elements. The act or process of shifting the linear order of an ordered set is often referred to as "permutation." Permutations are distinct from combinations, which are random picks of certain members of a collection. For example, there are six permutations of the set 1, 2, 3 represented as tuples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 1, 2). (3, 2, 1). Permutations include anagrams of words with various letters.
No. of ways using permutation = ¹⁷P₅ = 742560
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Write 135 as a product of its prime factors. Write your answer in index form need answer quickly URGENT
Answers
135 as a product of its prime factors is written as 3 × 3 x 3 x 5
What are prime factors?The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.
In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.
From the information given, we have the value as;
135
The prime factors are 3 × 3 x 3 x 5
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is this a function. yes or no?
Answers
Answer:
no
Step-by-step explanation:
there are two 81 in the x values a function cannot have the same x value twice
A scientific calculator is 15% off. The sale price of the calculator is $13.99/ What tis the original cost of the clacultor?
Answers
14.14
Passes through (-1,-1), slope-2
Answers
1) Since we need a Linear function that passes through point (-1,-1) with a slope of -2
Let's use the slope-intercept formula y=mx+b an plug the slope and point (-1,-1)
to find the linear coefficient (b)
y =mx +b
-1=-2(-1) +b
-1=2+b
-1-2=b
b=-3
2) Therefore we can write our function as
y= -2x -3
Jayla says that the equation y=2x-3 matched the graph. Substitute the ordered pairs from part c into the equation to prove that jayla is correct. (3,3)(4,5)(5,7)
Answers
Given:
Jayla says that the equation \(y=2x-3\) matched the graph.
To prove:
Jayla is correct
Solution:
We have,
\(y=2x-3\) ...(i)
The ordered pairs are (3,3), (4,5), (5,7).
We need to substitute the ordered pairs into the equation to prove that Jayla is correct.
For point (3,3), put x=3 and y=3 in (i).
\(3=2(3)-3\)
\(3=6-3\)
\(3=3\)
\(LHS=RHS\)
So, point (3,3) lies on the line \(y=2x-3\).
For point (4,5), put x=4 and y=5 in (i).
\(5=2(4)-3\)
\(5=8-3\)
\(5=5\)
\(LHS=RHS\)
So, point (4,5) lies on the line \(y=2x-3\).
For point (5,7), put x=5 and y=7 in (i).
\(7=2(5)-3\)
\(7=10-3\)
\(7=7\)
\(LHS=RHS\)
So, point (5,7) lies on the line \(y=2x-3\).
All three point (3,3), (4,5), (5,7) satisfy the given equation.
Therefore, jayla is correct. Hence proved.