Equation,
[tex]y - y1 = m(x - x1)[/tex]
Plugging in our values,
[tex]x1 = - 2, \: y1 = 4, \: m = 3[/tex]
[tex]y - 4 = 3(x - ( - 2))[/tex]
[tex]y - 4 = 3(x + 2)[/tex]
So the equation is,
[tex]y - 4 = 3(x + 2)[/tex]
Assuming the population is normally distributed, find the probability P(x>4.5) given the mean is 6 and the standard deviation is 0.7
Answer:
[tex]P(x > 4.5)= 0.983943[/tex]
Step-by-step explanation:
Given
[tex]\mu = 6[/tex]
[tex]\sigma = 0.7[/tex]
Required
[tex]P(x > 4.5)[/tex]
Start by calculating the z score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So:
[tex]z = \frac{4.5 - 6}{0.7}[/tex]
[tex]z = \frac{-1.5}{0.7}[/tex]
[tex]z = -2.143[/tex]
So, we have:
[tex]P(x > 4.5)= 1 - P(x < 4.5)[/tex]
This gives:
[tex]P(x > 4.5)= 1 - P(x < z)[/tex]
[tex]P(x > 4.5)= 1 - P(x < -2.143)[/tex]
Using the z score probability table, we have:
[tex]P(x > 4.5)= 1 - 0.016057[/tex]
[tex]P(x > 4.5)= 0.983943[/tex]
What is the value of
(4.1 x 103) (2.0 x 103)
expressed in scientific notation?
Option A is the answer of this question.
Can anybody help me out on this? Thanks.
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Given
[tex]y = -2x^2 + 12x +7[/tex]
Required
The x coordinate of the vertex
Using the general form:
[tex]y = ax^2 +bx +c[/tex]
The x coordinate is:
[tex]x = -\frac{b}{2a}[/tex]
In [tex]y = -2x^2 + 12x +7[/tex]
[tex]a = -2[/tex]
[tex]b = 12[/tex]
[tex]c = 7[/tex]
So, we have:
[tex]x = -\frac{b}{2a}[/tex]
[tex]x = -\frac{12}{2*-2}[/tex]
[tex]x = -\frac{12}{-4}[/tex]
[tex]x = \frac{12}{4}[/tex]
[tex]x = 3[/tex]
Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
(one-half, seven-quarters)
(one-half, three-halves)
(1, 1)
(1, 3)
Answer:
[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2 - x +2[/tex]
Required
The vertex
We have:
[tex]f(x) = x^2 - x +2[/tex]
First, we express the equation as:
[tex]f(x) = a(x - h)^2 +k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
So, we have:
[tex]f(x) = x^2 - x +2[/tex]
--------------------------------------------
Take the coefficient of x: -1
Divide by 2: (-1/2)
Square: (-1/2)^2
Add and subtract this to the equation
--------------------------------------------
[tex]f(x) = x^2 - x +2[/tex]
[tex]f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2[/tex]
[tex]f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}[/tex]
Expand
[tex]f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}[/tex]
Factorize
[tex]f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]
Factor out x - 1/2
[tex]f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}[/tex]
[tex]f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}[/tex]
Compare to: [tex]f(x) = a(x - h)^2 +k[/tex]
[tex]h = \frac{1}{2}[/tex]
[tex]k = \frac{7}{4}[/tex]
Hence:
[tex]Vertex = (\frac{1}{2},\frac{7}{4})[/tex]
Question: Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
Answer: A or 1/2 , 7/4
Step-by-step explanation:
did it on an assignment on EDGE
Que sucede cuando dividimos un numero entre si mismo
Answer:
no pasa nada
Step-by-step explanation:
espero que eso te ayude:)
Answer:
Cualquier número dividido entre si mismo da como resultado 1
please hurry need done asap
Answer:
[tex] y=0.46591x+7.71591[/tex]
Step-by-step explanation:
Labelled points are [tex] (21,\: 17.5)=(x_1,\:y_1) \: \&\:(43,\: 27.75)=(x_2,\:y_2) [/tex]
Slope of line (m) [tex] =\frac{27.75-17.5}{43-21} =\frac{10.25}{22} =\frac{41}{88} [/tex]
Equation of line in point - slope form is given as:
[tex] y-y_1 = m(x-x_1) [/tex]
[tex] \therefore y-17.5= \frac{41}{88} (x-21) [/tex]
[tex] \therefore y= \frac{41}{88} x-\frac{861}{88}+17.5[/tex]
[tex] \therefore y= \frac{41}{88} x+17.5-\frac{861}{88}[/tex]
[tex] \therefore y= \frac{41}{88} x+\frac{1,540-861}{88}[/tex]
[tex] \therefore y= \frac{41}{88} x+\frac{679}{88}[/tex]
[tex] \therefore y=0.465909091x+7.71590909[/tex]
[tex] \therefore y=0.46591x+7.71591[/tex]
Evaluate each expression for n= -5.
5. n-6
6.-15-n
7. n-(-12)
8. 1-n
Answer:
Hello!
5: -11
6: -10
7: 7
8: 6
Hope that helps!
Which sequence of transformations would create an image that is incongruent to the original pre-image? O A translation 4 units to the left followed by a dilation by 2 O A rotation of 90- followed by a translation of 2 units to the right O A reflection across the y-axis followed by a rotation of 180- O A rotation of 270 followed by a reflection across the x-axis.
Answer: Choice A
A translation 4 units to the left followed by a dilation by 2
=============================================================
Explanation:
The following transformations will make the pre-image and image congruent to one another:
ReflectionRotationTranslationIf you apply any of those transformations mentioned above, then the image is an identical copy of the pre-image. Nothing about the figure has changed other than it has been shifted, rotated, or reflected in some way. The figure retains its original size and shape. These transformations are called isometries.
A dilation on the other hand does not preserve the size. "Dilation by 2" means the scale factor is 2, so the image will be twice as large compared to the pre-image, in terms of linear dimension. This means there is no way the image is congruent to the pre-image if a dilation has occurred.
Based on all this, choice A is the answer. Choices B, C, and D only involve the three isometries mentioned earlier and no dilation at all, so they can be ruled out.
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
16 yd
Step-by-step explanation:
If a is missing, then use the square root of c^2-b^2. In this case that means you find the square root of 20^2-12^2. 20^2 is 400, and 12^2 is 144. When you subtract 144 from 400 you get 256. The square root of 256 is 16. I hope this helps :)
Answer:
16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
Leg a = a
Leg b = 12
Hypotenuse c = 20
Step 2: Solve for a
Substitute in variables [Pythagorean Theorem]: a² + 12² = 20²Evaluate exponents: a² + 144 = 400[Subtraction Property of Equality] Isolate a term: a² = 256[Equality Property] Square root both sides: a = 16Name the three labeled segments that are parallel to EF
Answer:
Answer D
Step-by-step explanation:
The answer here is D since all of the other ones have at least one option that is perpendicular to segment EF.
Zion collected leaves for a class
project. She collected 34 pinnate leaves
and 23 more palmate leaves than
pinnate leaves. How many leaves did
Zion collect in all?
Which of the following equations have the same solution as 3x - 5 = 5x + 11
Answer:
x = -8 Hope that helps bye!
Step-by-step explanation:
1. Subtract 3x from both side -5=5x+11-3x
2. Simplify 5x+11-3x= 2x+11
3. Subtract 11 from both sides -5-11=2x
4. Simplify -5-11= -16=2x
5. Divide both sides by 2 -16/2=x
4. Simplify 16/2 = -8 = x
5. Switch sides x= -8 would be your answer and if you want to check it just do 3x-5=5x+11 let x=-8 1. 3×-8-5=5×-8+11
2. 3×-8= -24 do -24-5=5×-8+11
3. Simplify 5×-8= -40 do -24-5=-40+11
4. Simplify -24-5= -29 do -29= -40+11=-29
-29=-29 this shows that x= -8 is your answer if you want to see if I'm right.
PLssssssssssssssssssssss help.
plz help 5th grade work
Answer:
I don't see where the question is...
Step-by-step explanation:
love yall again thx for the help
Answer :
Cost of running shoes = $92
Cost of total expenditure = $122
It is given that the four pairs of socks cost the same so if we let the cost of one pair of socks as s then 4 pairs of socks will cost us $ 4s
Thus the equation formed will be ,
4s + 92 = 122Option D is the correct answer
Find the circumference of a circle with a radius of 13.5 mm.
Answer:
84.82
Step-by-step explanation:
Answer: 84.82
Step-by-step explanation:
What is the product?
StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction
StartFraction x (x minus 4) (x minus 1) Over 2 (x + 4) EndFraction
StartFraction x (x minus 1) Over 2 EndFraction
StartFraction (x + 4) (x minus 4) Over 2 x (x minus 1) EndFraction
StartFraction (x minus 4) (x minus 1) Over 2 x (x + 4) EndFraction
Answer:
A
Step-by-step explanation:
The product of the expression [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
What is an expression?An expression is an algebraic term used for a mathematical statement that include variables and mathematical operations
Below is how to calculate the product
The product expression is given as:
[tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Express x^2 - 16 as a difference of two squares
[tex]\frac{(x - 4)(x + 4)}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Divide the expression
[tex]\frac{x - 4}{2} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Factorize the other fraction
[tex]\frac{x - 4}{2} * \frac{x(x^2 - 2x + 1)}{(x -1)(x + 4)}[/tex]
Further factorize
[tex]\frac{x - 4}{2} * \frac{x(x- 1)(x - 1)}{(x -1)(x + 4)}[/tex]
Divide
[tex]\frac{x - 4}{2} * \frac{x(x- 1)}{x + 4}[/tex]
Multiply the fractions
[tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Hence, the product of [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Read more about algebraic expressions at:
https://brainly.com/question/4344214
Find the area of the circle use 3.14 for pie
Answer:
50.24 cm²
Step-by-step explanation:
a = πr^2
r = d/2 = 8/2 = 4
a = 3.14(4²)
a = 3.14 * 16
a = 50.24 cm²
What is the slope of the graph shown below?
A. -2
B. 2
C. -5
D. 5
Rectangle A’B’C’D is the imagine if rectangle ABCD after a dilation. The center of dilation is the orgin. What is the scale factor of the dilation?
Answer:
D. 3
Step-by-step explanation:
Look at rectangle ABCD. It's dimensions are 1 by 2 (1 unit high and 2 units long). Now look at rectangle A'B'C'D', the image. It's a rectangle that is 3 by 6.
The dimensions of the original rectangle have been multiplied by 3.
Kadence took a random sample of students at her school and asked them how much they typically slept on a school night versus a weekend night. She noticed a positive linear relationship between the times. Here is computer output from a least-squares regression analysis on her sample:
Regression: weekend vs school night
Predictor Coef SE Coef
Constant 3.182 2.319
School night 0.789 0.237
S= 1.75 R-Sq= 20.9%
Required:
What is an appropriate test statistic for testing the null hypothesis that the population slope in this setting is 000?
Answer:
The answer is "3.329".
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\text{test statistic t} = \frac{slope}{standard \ error}[/tex]
[tex]=\frac{0.789}{0.237}\\\\=3.329[/tex]
Write the expression 53.7124 x 10 x 3 as a single number.
Answer:
The aswer is buy a rabbit
Step-by-step explanation:
Answer:
1611.372
Step-by-step explanation:
Solve the equation for x, and enter your answer in the box below.
4x = 40
Answer:
10
Step-by-step explanation:
4x=40
40/4= 10
Plssss help I’ll mark u brainliest!!!
Answer:
The answer to the question is C
HELP PLEASE
The gift shop at a science museum sells lollipops that are made to look like the planets. Each lollipop is shaped like a sphere and has a radius of 121212 mm.
What is the volume of each lollipop?
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Answer:
[tex]V=7.45\times 10^{15}\ mm^3[/tex]
Step-by-step explanation:
The radius of each lollipop is 121212 mm
We need to find the volume of each lollipop. The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Put all the values,
[tex]V=\dfrac{4}{3}\times 3.14\times (121212 )^3\\\\V=7.45\times 10^{15}\ mm^3[/tex]
So, the volume of each lollipop is equal to [tex]7.45\times 10^{15}\ mm^3[/tex].
For the following indicate whether a confidence interval for a proportion or mean should be constructed to estimate the variable of interest.
A researcher with a golf association obtained a random sample of 25 rounds of golf on a Saturday morning and recorded the time it took to complete the round. The goal of the research was to estimate the amount of time it typically takes to complete a round of golf on Saturday morning.
The confidence interval for a population____should be constructed because the variable of interest is____which is a____variable.
Answer: mean; time to complete round; quantitative
Step-by-step explanation:
Based on the information given in the question, the time to complete the round will be the variable of interest.
The confidence interval for a population (mean) should be constructed because the variable of interest is (time to complete round) which is a (quantitative) variable.
A bag contains 5 red marbles, 6 blue marbles and 9 yellow marbles.
What is the probability of picking out a red marble, putting in back in the bag, and then picking out a yellow marble?
What is the probability of picking out a blue marble, putting it in your pocket, and picking out another blue marble?
Answer:
Step-by-step explanation:
The total number of marbles is 20
Question A
P(Red) = 4/20 = 1/5
P(yellow) = 9/20
P(Red then Yellow) = 1/5 * 9/20 = 9 / 100
Question B
P(B) = 6/20
P(B again) = 5/19 because you have 1 less total plus 1 less blue.
P(B and B) = 6/20 * 5/19
P(B and B) = 30/ 380 = 3/38
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
According to hypotenuse
39²+b²=65²
b²=65²-39²
b²=4225-1521
b=√2,704
b=52 km
A triangle has sides of lengths 24, 143, and 145. Is it a right triangle? Explain.
Answer:
Yes, the given triangle is right angled
Step-by-step explanation:
To confirm if the given triangle is right angled, we have to apply pythagoras theorem. It states, if a triangle is right angled then
Hypotenuse² = Base² + Perpendicular²
We know that the longest side is hypotenuse.
ie; (145)² = (143)² + (24)²
(145)² = 20449 + 576
21025 = 21025
As LHS = RHS, it is clear that the given triangle with sides 24, 143 and 145 units is right angled
Find the surface area of the rectangular prism