Answers
a.
i. In standard form y = 5x² - 20x + 27ii. The y intercept is (0, 27)iii. Find the graph in the attachmentb.
i. In standard form is y = 3x² + 6x + 15ii. The y-intercept is (0, 15)iii. Find the graph in the attachmentWhat is a quadratic function?A quadratic function is a function of the form y = ax² + bx + c
a. i. How to write the quadratic function y = 5(x - 2)² + 7 in standard form?To write y = 5(x - 2)² + 7, we expand the bracket and simplify.
So, y = 5(x - 2)² + 7
y = 5(x² - 4x + 4) + 7
y = 5x² - 20x + 20 + 7
y = 5x² - 20x + 27
So, the quadratic function y = 5(x - 2)² + 7 in standard form is y = 5x² - 20x + 27
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 5x² - 20x + 27
y(0) = 5(0)² - 20(0) + 27
y(0) = 0 - 0 + 27
y(0) = 27
The y intercept is (0, 27)
iii. The graph of y = 5(x - 2)² + 7Find the graph in the attachment
b. i. How to write the quadratic function y = 3(x + 1)² + 12 in standard form?To write y = 3(x + 1)² + 12, we expand the bracket and simplify.
So, y = 3(x + 1)² + 12
y = 3(x² + 2x + 1) + 12
y = 3x² + 6x + 3 + 12
y = 3x² + 6x + 15
So, the quadratic function y = 3(x + 1)² + 12 in standard form is y = 3x² + 6x + 15
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 3x² + 6x + 15
y(0) = 3(0)² - 6(0) + 15
y(0) = 0 - 0 + 15
y(0) = 15
The y-intercept is (0, 15)
iii. The graph of y = 3(x + 1)² + 12Find the graph in the attachment
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Related Questions
HELP PLEASE!!!!!!
Parallel lines r and s are cut by two transversals, parallel lines t and u.
How many angles are alternate exterior angles with angle 5?
Picture below:
Answers
The number of angles that are alternate exterior with angle 5 is one, which is angle 11.
What are Alternate Exterior Angles?Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.
The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.
Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.
Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.
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How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as many times as you want?
Answers
Answer: 4
Step-by-step explanation:
yeh
what is the domain of f(x)=√11-x?
Answers
The domain of the function f(x) is:
11 ≥ x
What is the domain of the function f(x)?
Here we have the function:
[tex]f(x) = \sqrt{11 - x}[/tex]
Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:
11 - x ≥ 0
Then, solving this for x, we get:
11 ≥ x
Concluding, the domain of the function f(x) is:
11 ≥ x
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Two ways to measure the relationship between the returns of two securities are ______ and blank______.
a. standard deviation
b. variance
c. covariance
d. correlation
Answers
Two ways to measure the relationship between the returns of two securities are correlation and covariance. That is options C and D.
What is Correlation?Correlation can be defined as the measure of the difference between two variables in a statistical analysis.
Covariance can be defined as the measure of the relationship between two variables in statistical analysis.
Therefore, Two ways to measure the relationship between the returns of two securities are correlation and covariance.
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ordenada al origen 6 = paralela a la recta 2x+3y+4=0
Answers
La ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
¿Cómo determinar la ecuación de una recta?
En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:
2 · 0 + 3 · 6 + k = 0
18 + k = 0
k = - 18
Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
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A hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what conclusion should be drawn
Answers
3.60
t = r√n − 2/1 − √r2
= 0.6√25 − 2/√1 − 0.62
= 3.5969 t or about 3.60 rounded to two decimal places.
Hypothesis Testing:
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.
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Consider dealing a hand of 8 cards from a well shuffled standard deck of playing cards. The expected value of the number of face cards in the hand is (Q
Answers
Answer:
2 face cards
Step-by-step explanation:
By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards. Aces are not considered face cards (no face on the card).
The ratio of face cards in a full deck is (12/52) or slightly over 23%.
The likelihood of a face card in a hand of 8 cards is:
(8 cards)*(12 face cards/52 cards) = 1.85 cards. We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.
if three pies require 2 dozen apples, then four bird require ? dozen apples?
Answers
Step by step
we know 2 dozen apples is 24 apples
We know 24 apples per 3 pies
To get the rate per pie, divide 24 apples per 3 pies
24/3 = 8 apples per pie
Now multiply 8 apples x 4 pies = 32 apples
Now we need to answer in how many dozen apples. Divide 32 by 12 (1 dozen)
Answer is 2.66 dozen apples or 2-2/3 dozen apples
HELP!!!!!!!!!!!!!!!!!!!! I WELL GIVE BRAINLIST AND 100 point if answered in less the 20 mins
If I have 419 assignments to do and i have pleated completed 79 how much work will I need to do every day to finish in one week
Answers
Answer:
10
Step-by-step explanation:
Answer:
You have to complete around 49 assignments everyday to finish in one week.
Step-by-step explanation:
• First, we have to calculate the number of assignments left to do:
Assignments remaining = 419 - 79
= 340
• There are 7 days in a week, which means 340 assignments need to be completed in 7 days.
7 days ⇒ 340 assignments
1 day ⇒ 340 ÷ 7
= 48.6
≅ 49 assignments
∴ You have to complete around 49 assignments everyday to finish in one week.
Consider the polynomial function of g(x)= -2x^8 +5x^6 -3x^5+50
Answers
Answer:
C) as x –> ∞, q(x) –> –∞, and as x –> -∞, q(x) –> –∞
Step-by-step explanation:
use the end behavior chart to figure out the end directions of the graph. remember these
E O
+|↑↑|↓↑
–|↓↓|↑↓
all you need to do is look at the first number of the equation and ask yourself:
1. Is the first number even or odd?
2. is the first number positive or negative?
find where the answers to both meet on the chart.
so, in this question, the first number is even and negative. when using the chart we see that they meet at the ↓↓ which means that the end behavior on both sides is going towards negative infinity.
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 20 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 6 and width of 2 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 10) 12 a = (x 20)(x 10) − 12 a = (x 26)(x 12) a = (x 14)(x 8)
Answers
The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.
What is a Rectangle?A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).
What is the Area of a Rectangle?The area of a rectangle = (length of rectangle)(width of rectangle).
Given the following parameters for the patio and the bench:
Length of rectangular patio = x + 20Width of rectangular patio = x + 10Length of rectangular bench = 6Width of rectangular bench = 2Area to be painted = area of rectangular patio - area of rectangular bench
Area of rectangular patio = (x + 20)(x + 10)
Area of rectangular bench = (6)(2) = 12
Area to be painted = (x + 20)(x + 10) - 12
The answer is: B. A = (x + 20)(x + 10) - 12.
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help please a.-5 b.-1/5 c1/5 d.5
Answers
Answer:
-5
Step-by-step explanation:
Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
Answers
As a rule of thumb, when each component is selected independently from the same population, the sampling distribution of the sample percentage may be estimated by a regular probability distribution.
Why is it crucial to use the thumb rule?One of our primary, simple-to-learn ways to handle complexity is the rule of thumb. Real thumb rules take into account operating, security, and financial constraints. They inform us of the likely location of a practical solution. Additionally, they reveal which tactics are most prone to failure.What is sampling distribution?A statistic that is obtained by sampled data from a bigger population is known as a sampling distribution. It depicts an array of potential results that may result from a statistic, such as the mean or mode of a certain parameter because there is really a population.Therefore the main solution is- from the identical group, each component is individually chosen.
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The diameter of the earth
at the equator is about
8.000 mi.
Based on this figure, how
far is it around the earth?
Answers
Answer:
25,132.74 miles
Step-by-step explanation:
Hello!
We are basically asked to find the circumference of the Earth's cross-section.
Circumference: [tex]C = 2\pi r[/tex]
We can replace 2r with the diameter, because the diameter is 2 times the radius.
Multiply the Diameter by pi:
[tex]C = \pi D[/tex][tex]C = 8000\pi[/tex][tex]C = 25,132.7412287183 \approx 25,132.74[/tex]It is around 25,132.74 miles around.
A rectangle's area is given by the expression 6–² -- − n +9. The width of the rectangle is 3n². w = 3n² A = 6n² − n +9
Answers
The length of the rectangle = 2 - (1/3n) +(3/n²).
How to estimate the length of a rectangle?
The formula for the area (taking this exists as a rectangle)
Area = length ⋅ width
where A exists the area of the rectangle
l exists the length of the rectangle and w exists the width of the rectangle.
If Area of the rectangle = length ⋅ width
then length of the rectangle = area/ width
Area = 6n² − n +9
width = 3n²
Area = length [tex]*[/tex] width
length = area/ width
= (6n² − n +9)/3n²
= 2 - (1/3n) +(3/n²).
The length of the rectangle = 2 - (1/3n) +(3/n²).
Therefore, the correct answer is option A. 2 - (1/3n) +(3/n²).
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The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what is the wavelength for radio waves with frequency 3 × 109?
Answers
The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.
What's the relation between frequency and wavelength of electromagnetic waves?For electromagnetic waves travelling in vaccum, the product of frequency and wavelength is the speed of light in vaccum.Mathematically, frequency × wavelength = 3×10⁸ m/s (which is speed of light)So, wavelength= 3×10⁸/ frequencyWhat's the wavelength of radio wave with frequency 3×10⁹ Hz ?Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m
Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.
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Write the standard equation of a circle that passes through(-4,0) with center (-1,-4)
Answers
The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).
According to the question,
The circle with center at (-1,-4) that passes through the point (-4,0).
To find the radius of the circle:
Radius r = √[(-4 - (-1))² + (0- (-4))²]
=√(-4+1)² + (4)²
=√9+16
=√25
=5.
In order to find the standard equation of the circle is
(x - (-4))² + (y - (0))² = (5)²
(x + 4)² + (y )² = 25
x² + 8x + 16 + y² = 25
x² + y² + 8x + 16 = 25
x² + y² + 8x = 25 - 16
x² + y² + 8x = 9
x² + y² + 8x - 9 = 0
Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.
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The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
[tex]G(x) = x^{3} -1[/tex]
Step-by-step explanation:
The red graph is the blue graph translated 1 unit down, so the answer is A.
y square plus 5y equals to 0
Answers
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5What are the solutions of the equation6x^2-x-1=0
Answers
Answer:
1/2
1/3
Step-by-step explanation:
x=1/2
x=-1/3
Answer:
[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]6x^{2} -x-1=0[/tex]
Factoring the equation:
[tex](3x+1)(2x-1)=0[/tex]
Extract the roots:
First factor
[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]
Second factor
[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]
Hope this helps
Katie has 100 apples, and she plans on eating 2 of them every day.
True or false...the number of apples Katie has left is proportional to the number of days that pass.
Answers
What is the minimum point on the graph of the equation y=f(x)+5 ?
Answers
Answer:
Step-by-step explanation:
This function will have a minimum point only if f(x) has one.
Examples:
y = x + 5: straight line with no minimum
y = x^2 + 5: parabola that opens up and has vertex at (0, 5); thus, the minimum is (0, 5)
What f(x) did you have in mind? Please share it.
What equation shows that 9 is a factor of 72?
Answers
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
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Alejandro wants to determine the average shoe size of all of the male students in his school. Which sample is likely to yield the most biased results?.
Answers
The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team
How to identify a bias in sampling?The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team.
The reason option B is the most biased is because members of a basketball team are typically taller than other people. We know that taller people generally have larger feet, and larger shoe sizes, than shorter people. Thus, choosing only people from this area would lead to a biased sample.
The missing options are;
A) every tenth boy on the school’s phone list
B) every member of the boys’ basketball team
C) every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class
D) every fifth boy who walks through the front doors of the school in the morning
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Answer:
B)
Step-by-step explanation:
Help me:-
Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y) =
Answers
Answer:
20 + 4y
Step-by-step explanation:
The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).
Lola has collected 935 buttons. what is the number of buttons rounded to the nearest ten?
Answers
Answer:
940
Step-by-step explanation:
Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940
Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained
Answers
Answer:
7
Step-by-step explanation:
we have 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now 1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 7
Answer:
1. 7
2. square root is 84.
Step-by-step explanation:
First find the prime factors:
1008 =2*2*2*2*3*3*7
There's an even number of 2's and 3's but only one 7, so we multiply by 7
Smallest number = 7.
The square number is 1008 * 7
= 7056.
Its square root is 2*2*3*7 = 84.
Which polynomial is a quintic trinomial?
A. -x^4-5x^2
B. x^3+2x^2−8x+16
C. x² + 4
D. 3x^5+7x^2−9x^4
Answers
Answer:
D
Step-by-step explanation:
a quintic polynomial is a polynomial of degree 5
A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )
B is a polynomial of degree 3 (x³ term )
C is a polynomial of degree 2 ( x² term )
D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )
Solution
We can start with the pythagorean theorem:
(leg 1)2 + (leg 2)² = (hypotenuse)²
Solve for x.
Substitute the values we know.
18² + x² = 27²
x=0√O
Answers
Step-by-step explanation:
324+x²=729
x²=405===> x=√405===> 9√5
The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.
The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.
To solve the equation x² = 72, to take the square root of both sides to find the value of x:
√(x²) = √(72)
Since the square root of x² is x (the absolute value of x), the equation simplifies to:
x = √(72)
Now, let's find the approximate value of √(72):
√(72) ≈ 8.49
So, the equation becomes:
x≈ 8.49
Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:
x= 8.49 → x = 8.49
x = -8.49 → x = -8.49
Rounded to the nearest tenth, the solutions are:
x ≈ 8.5 and x ≈ -8.5
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If the value of the sample standard deviation increases, what happens to the confidence interval?
Answers
If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.
What is Confidence interval?This term is used in statistics and refers to the probability that a population parameter will fall between two set values.
it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.
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The options are :
a. It becomes wider
b. It becomes more precise
c. It does not change
d. It narrows