The polynomic function that contains the points (0, 6), (3, 15.8) and (9.5, 0) is a quadratic function, whose model is y = -0.600 · x² + 5.066 · x + 6.
How to derive a polynomic function from given points
To determine the coefficients of a polynomic function we must know a set of distinct points, whose number is the same number of coefficients. In this case, we can derive a quadratic function, as quadratic functions have three coefficients:
y = a · x² + b · x + c (1)
Now we substitute x and y in (1) and solve the resulting system of linear equations:
c = 6
9 · a + 3 · b + c = 15.8
90.25 · a + 9.5 · b + c = 0
Whose solution is a ≈ -0.600, b ≈ 5.066 and c = 6.
Remark
The statement is incomplete. The complete form is shown below:
There is a polynomial function. Find the function of (0, 6), (3, 15.8) and (9.5, 0).
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Identify coordinate point C.
(1, 5)
(6, 7)
(7, 3)
(0, 2)
Answer: (6,7)
Step-by-step explanation:
Answer:
(7,6)
Step-by-step explanation:
look above as your axis x it's 7, and then down is axis y is 6.
Mr. Rodrigo pours himself a glass of orange juice every morning. Yesterday he drank 5/6 of his glass. Today he drank 7/12 of his glass. On which day did drink more
From his eye, which stands 1.63 meters above the ground, Isaac measures the angle
of elevation to the top of a prominent skyscraper to be 17°. If he is standing at a
horizontal distance of 294 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest hundredth of a meter if
necessary.
The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of the skyscraper, hence:
tan(17) = h/294
h = 89.88 meter
Total height = 89.88 + 1.63 = 91.51 meter
The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter
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Use the digits 1-9 without repeating, to create two prisms with the same volume
Two prisms with the same volume are rectangular prisms of the dimensions 1 by 4 by 9 and 2 by 3 by 6
How to create the prisms?To do this, we start by determining the type of prism to create.
Assume that we want to create a rectangular prism.
The volume of a rectangular prism is:
Volume = Length * Width * Height
Using the digits 1 - 9, we have:
Prism 1
Length = 1
Width = 4
Height = 9
The volume is
Volume = 1 * 4 * 9 = 36
This means that the second prism must have a volume of 36.
Using the digits 1 - 9, we have:
Prism 2
Length = 2
Width = 3
Height = 6
The volume is
Volume = 2 * 3 * 6 = 36
Notice that the digits are not repeated.
Hence, two prisms with the same volume are rectangular prisms of the dimensions 1 by 4 by 9 and 2 by 3 by 6
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Given the circle has a radius of 9 and a center of (-6,4) what is the equation of the
circle?
Answer:
(x+6)2 + (y-4)2 = 81
Step-by-step explanation:
The equation of the circle is in the for (x-a)2 + (y-b)2 = c2
Two similar triangles are shown below
Which two sets of angles are corresponding angles?
Answer:
I cant help unfortunately
Step-by-step explanation:
can you help me in the comprehension of the story uncle Marcos ?
My exam is in 4 hours btw
Why won't anyone help me :(
The probability will include:
P(A and 1) = 1/24
P(C and 2) = 1/12.
P(B and 3) = 1/12.
P(A and 4) = 1/12
How to calculate the probability?The probability of P(A and 1) will be:
= 1/4 × 1/6
= 1/24
The probability of P(C and 2) will be:
= 1/4 × 2/6
= 1/12
The probability of P(B and 3) will be:
= 2/4 × 1/6
= 1/12
The probability of P(A and 4) will be:
= 1/4 × 2/6
= 1/12
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What is the equation of the line that passes through the point (-6, -7) and has a
slope of1/2?
Answer:
y = x/2 - 4
Step-by-step explanation:
What is the equation of a line through the points (0,9) and (3,0)?
Answer:
The image has the ans.
Step-by-step explanation:
The image will help.
(Refer to the attached image)
Answer:
missing side: 133 cm
Explanation:
Provided 2 length sides and one angle also need to find one missing side.
So, use cosine rule:
⇒ a² = b² + c² - 2bc cos(A)
Insert values
⇒ g² = 166² + 147² - 2(166)(147) cos(50)
⇒ g² = 17794.3935
⇒ g = √17794.3935
⇒ g = 133.3956
⇒ g = 133 (rounded to nearest whole number)
write an equation for a prabola with a vertex at the origin, passing through(5,6), and symmetric with respect to the x-axis
a parabola with symmetry or mirror image across the x-axis, will be a horizontal parabola, namely one that opens either to the right or left.
a horizontal parabola will be a parabola whose independent variable is the "y", so it'll be an x(y) type of equation.
[tex]~~~~~~\textit{horizontal parabola vertex form} \\\\ x=a(y- k)^2+ h\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\supset}\qquad \stackrel{"a"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies x=a(y-0)^2+0\qquad \textit{we also know that} \begin{cases} x=5\\ y=6 \end{cases} \\\\\\ 5=a(6-0)^2 +0\implies 5=36a\implies \cfrac{5}{36}=a~\hfill \boxed{x=\cfrac{5}{36}y^2}[/tex]
Find the 14 term of the following geometric sequence.
10, 20, 40, 80,
Answer:
81920
Step-by-step explanation:
Finding the common ratio (r) :
20/102Finding the 14th term :
a₁₄ = ar¹⁴⁻¹a₁₄ = ar¹³a₁₄ = (10)(2)¹³a₁₄ = (10)(8192)a₁₄ = 81920Answer:
the 14th term in the sequence would be 81920.
Step-by-step explanation:
because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.
If the diameter of a youth baseball is 2. 8 inches and the diameter of an adult softball is 3. 8 inches, what is the approximate difference in their volumes? use 3. 14 for pi. round to the nearest tenth. recall the formula sphere volume = four-thirds pi r cubed. 1. 0 cubic inch 17. 2 cubic inches 40. 2 cubic inches 137. 8 cubic inches.
The approximate difference in their volumes is 17.2 cubic inches
How to determine the difference in the volume?The given parameters are:
Diameter, d = 2.8
Diameter, D = 3.8
The radii are the half of the diameter.
So, we have:
r = 1.4
R = 1.9
The volume of the balls is then calculated using:
[tex]V = \frac{4}{3}\pi r^3[/tex]
The difference is then represented as:
[tex]D = \frac{4}{3}\pi (R^3 - r^3)[/tex]
Substitute known values
[tex]D = \frac{4}{3}* 3.14* (1.9^3 - 1.4^3)[/tex]
Evaluate
D = 17.2
Hence, the approximate difference in their volumes is 17.2 cubic inches
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Which function is increasing and has a domain of (1, )?
A. -log(x − 2) + 1 B. -log(x − 1) + 2 C. log(x − 1) + 2 D. log(x − 2) + 1
Answer:
B . it was right when I picked it
Find the volume of this rectangular pyramid.
length =5cm
width =6cm
hight =7cm
PLEASE HURRY
Sean counts by 2s from 15 to 35. which number does Sean count?
HELP ME ASAP!!!
The number that Sean counts is 27.
What number does Sean count?
When Sean counts by 2s from 15 to 35, he would be counting odd numbers. An odd number is a number that cannot be perfectly divided by 2. There would always be a remainder.
Here are the options:
13
27
16
22
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How many solutions are there for the system of nonlinear equations represented by this graph?
The total solution for the system of nonlinear equations represented by this graph is 2 solutions
Graphs and FunctionsQuadratic function have a leading degree of 2. The graph of a quadratic function is parabolic in nature.
Since the given graph consists of a parabola, hence the total solution for the system of nonlinear equations represented by this graph is 2 solutions
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opposite of expanded form
Answer:
factored form
Step-by-step explanation:
example
(x + 2)(x + 3) ← is an expression in factored form
= x² + 5x + 6 ← in expanded form
Answer:
factored formStep-by-step explanation:
Factored form is opposite of expanded form.
More info:-
Expanded form:
[tex]\sf{5(x+7)=5x+35}[/tex]Factored form:
[tex]\sf{5x+35=5(x+7)}[/tex]f(x) = x². What is g(x)?
Answer:
We want to get g(x) given that we know f(x) and the graphs for both functions. We will see ...
Step-by-step explanation:
A map shows that the vertices of a backyard are W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) . The coordinates are measured in feet. The line segment XZ separates the backyard into a lawn and a garden. The area of the lawn is greater than the area of the garden. How many times larger is the lawn than the garden?
The area of the lawn is 2.5 times greater than the area of the garden.
What is Heron's formula in math?Heron's formula for finding the area of a triangle in terms of the lengths of its sides.
In symbols, if a, b, and c are the lengths of the sides: Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given vertices W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) of a backyard,
We have to find distances WX, XY, YZ, ZW and XZ:
1. WX= √(-100+100)²+(0+70)²
=√0+4900
=70
2. XY= √(0+100)²+(0-0)²
=100 units.
3. YZ= √(-60-0)²+(-70-0)²
=√3600+4900
= √8500= 10√85
4. ZW= √(-60+100)²+(-70+70)²
=√40²+0
=40 units
5. XZ= √(-60+100)²+(-70+0)²
=√40²+70²
=√6500=10√65
Then:
1. the area of WXZ
[tex]\sqrt{(70+40+10\sqrt{65}) /2 * ({70+40+10\sqrt{65}) /2 -70* {(70+40+10\sqrt{65}) /2 -40[/tex]*[tex]\sqrt{(70+40+10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=1400 feet²
Area of XYZ= [tex]\sqrt{(100+10\sqrt{65}+10\sqrt{85}) /2 * (100+10\sqrt{65}+10\sqrt{85}) /2 -100* {(100+10\sqrt{85}+10\sqrt{65}) /2[/tex]-[tex]\sqrt{-10\sqrt{85}*(10+10\sqrt{85} +10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=3500 feet²
Then, ar(WXZ)/ ar (XYZ)= 3500/1400=2.5 times.
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A piece of card, 1200 cm² in area, will make a tube 13 cm long. How long is a similar
tube made from a similar piece of card with an area of 500 cm³?
The length of the similar tube will be 5041 cm.
What is the area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Given that:-
A piece of card, 1200 cm² in area, will make a tube 13 cm long. How long is a similar?Tube made from a similar piece of card with an area of 500square centimetres.The radius of the first tube will be calculated as:-
1200 = 2πr ( 13 )
r = 12 / 2π x 113
r = 14.7 cm
Now the length of the second tube will be:-
500 = 2π x 14.7 x L
L = 500 / 2π x 14.7
L = 5.41 cm.
Therefore the length of a similar tube will be 5041 cm.
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Hunter picked three quarts of blueberries. some of the blueberries are ripe and some are not ripe. If he takes one blueberry from the basket without looking, what are the outcomes
Answer:
Berries with any blush of red are not ripe, yet may ripen further once picked if kept at room temperature. That said though, you really want to ...
Which number line represents the solution set for the inequality –4(x 3) ≤ –2 – 2x?
The solution to the inequality expression is x ≥ - 5
Inequality expressionsInequality are expressions not separated by an equal sign. Given the inequality;
–4(x + 3) ≤ –2 – 2x
Expand
-4x - 12 ≤ -2 - 2x
Collect the like terms
-4x + 2x ≤ -2 + 12
-2x ≤ 10
Divide both sides by -2
-2x/-2 ≤ 10/-2
x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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Answer:
First line
Explanation: Edge2023
Select the correct answer for the blank: if everything else stays the same, the required sample size ____ as the confidence level decreases to reach the same margin of error. answer: question 1 options: increases decreases remains the same
The complete statement is "if everything else stays the same, the required sample size decreases as the confidence level decreases to reach the same margin of error." This is further explained below.
What is the margin of error?Generally, the margin of error is simply defined as a measure of how far your findings depart from the population average.
In conclusion, As confidence levels decline, the needed sample size reduces to provide the same margin of error, assuming all other variables remain constant.
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help me pls I need to get my grade up before July 11th so help ASAP
the hcf of 12x^2-4xy+15x-5y
Answer:
-1
Step-by-step explanation:
We have 2 letters, x and y. what letter is in all of them? none of them. that means the HCF can't contain a letter. let's take away the letters, we have 12, -4, 15, -5. Since -5 is a prime number. the answer is -1
Question 2
suppose there is a city where the mean cost per
month of a one-bedroom apartment is $1,500, with a
standard deviation of $250.
approximately what percentage of one-bedroom
apartments in the city cost between $750 and
$1,000?
Using the normal distribution, it is found that 2.15% of bedroom apartments in the city cost between $750 and $1,000.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 1500, \sigma = 250[/tex]
The proportion of apartments that cost between $750 and $1,000 is given by the p-value of Z when X = 1000 subtracted by the p-value of Z when X = 750, hence:
X = 1000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1000 - 1500}{250}[/tex]
Z = -2
Z = -2 has a p-value of 0.0228.
X = 750:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{750 - 1500}{250}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0228 - 0.0013 = 0.0215.
0.02215 = 2.15% of bedroom apartments in the city cost between $750 and $1,000.
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What is the volume of the rectangular prism?
A rectangular prism with dimensions 4 and 1 third feet by 3 and 1 third feet by 4 feet.
57 7/9ft3
11 2/3ft3
48 2/9ft3
28 2/3ft3
Answer:
A or 57 7/9ft3
Step-by-step explanation:
13/3x10/3x4/1 = 520/9=57 7/9
Answer:
The volume of the rectangle would be [tex]57\frac{7}{9}[/tex] ft^3. (The first answer).
Step-by-step explanation:
To solve you have to multiply [tex]4\frac{1}{3},3\frac{1}{2}, and, 4[/tex] to get an answer of [tex]57\frac{7}{9}[/tex].
I hope this helps! :)
[((a ^ 2 - 25b ^ 2) ^ 3 + (25b ^ 2 - 9c ^ 2) ^ 3 + (9c ^ 2 - a ^ 2) ^ 3)/((a - 5b) ^ 3 + (5b - 3c) ^ 3 + (3c - a) ^ 3)]
The factorization is [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
To answer the question, w e need to know what factorization is
What is factorization?Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.
So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have
[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Factorizing out the denominator, we have
= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]
Cancelling out the denominator, we have
= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
So, the factorization is [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³
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What is 12x³ – 9x² − 4x + 3 in factored form?
Pls hurry
Answer:
[tex]\bold{\green{(4x-3)(3x^{2}-1) }}[/tex]
Step-by-step explanation:
[tex]\sf{12x^{3}-9x^{2}-4x+3 }[/tex][tex]\sf{3x^{2}(4x-3)-1(4x-3) }[/tex][tex]\sf{(4x-3)(3x^{2}-1) }[/tex]Answer:
(3x^2 - 1)(4x - 3)
Step-by-step explanation:
We can use grouping to factor this
12x^3 – 9x^2 − 4x + 3
group into: (12x^3 – 9x^2)(− 4x + 3)
Solve one side at a time:
(12x^3 – 9x^2)
3x^2(4x - 3) factor out a 3x^2
(− 4x + 3)
- 1 (4x - 3) factor out a -1
put the two equations togeth
(3x^2 - 1)(4x + 3)