Suzie drew the line of best fit on the scatter plot shown.
What is the approximate equation of this line of best fit in slope-intercept form?
y = 6 over 5x + 3
y = 3x + 6 over 5
y = 5 over 6x + 3
y = 3x + 5 over 6
Answers
Slope intercept form is defined as:
y = mx +b
In this form for lines, m is the slope, and b is the y intercept. Hence, slope intercept. That means that in order to write it in this form, we need to know both the slope and y intercept. We'll start with the former.
Slope is defined as ride over run, or up over right (you know it's negative when it goes left). In order to calculate this, we can take two points that lie directly on a coordinate and put them into a fraction as rise/run.
We have;
(0,3) and (5,9)
As we can see, the difference between the two points is that (5,9) is 5 more to the right, and is 6 higher. We get 6/5. We can even see that in the coordinates, because they're written as (x, y). Additionally, you can use the slope given two points formula:
y2-y1/x2-x1 =
9-3/5-0 = 6/5
Notice how we get the same thing, because in both methods you're finding the difference between the two coordinates based off of rise/run. That's why it's y2 minus y1.
Now that we have our slope, we need the y intercept. The y intercept is simply where the line crosses the y axis. As we can see, it crosses at (0,3) - so the intercept is 3. Now we can create our equation
Slope = 6/5
Y intercept = 3
y = mx + b --> y = 6/5x + 3
Your answer is A, the first option.
Hope this helps!
Related Questions
Evaluate the determinant for the following matrix:
-4 -4 -3
3 3 -5
-5 2 -5
A. –203 B. 75 C. –152 D. –263
Answers
Answer:
The determinant of matrix is -203
Step-by-step explanation:
Given the matrix of order 3 i.e
[tex]A=\begin{bmatrix}-4&-4&-3\\ 3&3&-5\\ -5&2&-5 \end{bmatrix}[/tex]
we have to find the determinant of matrix A
[tex]|A|=-4(-5(3)-(-5)(2))-3((-4)(-5)-(-3)(2))+(-5)((-5)(-4)-(-3)(3))\\\\|A|=-4(-15+10)-3(20+6)-5(20+9)\\\\|A|=-4(-5)-3(26)-5(29)\\\\|A|=20-78-145\\\\|A|=-203[/tex]
Hence, the determinant of matrix is -203
Option A is correct.
Which of the following statements describes a correct method for solving the equation below?
3x + 3 = 6x
A. Subtract 3x from both sides of the equation, and then divide both sides by 3.
B. Add 3x to both sides of the equation, and then divide both sides by 3.
C. Divide both sides of the equation by 6, and then subtract 3 from both sides.
D. Divide both sides of the equation by 6, and then add 3 to both sides.
Answers
_____
The other choices get you to a place where further work is necessary. They don't really contribute to solving the equation.
3x + 3 = 6x
3x-3x + 3 = 6x - 3x
(3x -3x cancel each other out, leaving you with 3)
3 = 3x
3/3 = 3x/3
1 = x
x = 1
Now Verify-
3x + 3 = 6x
3(1) + 3 = 6(1)
3 +3 = 6
6 = 6
Now can also use the guess and check way. But this is my way of solving it. I hope it helped.
Find the least common multiple of x² + x – 12 and x² + 2x – 15.
Answers
Solution:
we have been asked to find the Least Common multiple of the given polynomial x² + x – 12 and x² + 2x – 15.
To find the least common multiple. Lets first find the factors.
[tex] x^2+x-12=x^2+4x-3x-12\\
\\
x^2+x-12=x(x+4)-3(x+4)\\
\\
x^2+x-12=(x+4)(x-3)\\ [/tex]
[tex] x^2+2x-15=x^2+5x-3x-15\\
\\
x^2+2x-15=x(x+5)-3(x+5)\\
\\
x^2+2x-15=(x+5)(x-3)\\ [/tex]
Hence the LCM of the given set of Polynomials is (x+4)(x-3)(x+5).
The LCM is (x+4)*(x-3)*(x+5)
Three fourths of the students in class said they like word problems . If fewer than 30 students said they like word problems , how many students are there ?
Answers
To compute for the total number of students in the class, you have to divide the fraction of the students who said they like word problems with the number of students who said they like word problems.
30 students / ¾ of the students said they like word problems = 40 students are there in the class
Choose the BEST answer.
1. What is a Web page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
2. What is a home page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
3. What is the object of storyboarding? (1 point)
To help you visualize your Web site before writing any pages in HTML. To help prevent duplicati
Answers
2. A home page is the entry page of the Web site
3.The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.
Answer:
1)
A single page of a Web site that consists of an HTML document.
2)
The entry page of the Web site.
3)
The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.
Step-by-step explanation:
Web page:
A web page or webpage is a document commonly written in HTML (Hypertext Markup Language) that is accessible through the Internet or other networks using an Internet browser.
Hence, option: A is true.
Home page:
A home page also refers to the first page that appears upon opening a web browser, sometimes called the start page.
Hence, option: B is correct.
( The entry page of the Web site )
object of storyboarding:
The object of storyboarding is to help you visualize your Web site before writing any pages in HTML
You must be at least 48 inches tall to ride a certain roller coaster.iIan is 3 ft, 11 in. tall. Is ian tall enough to ride the roller coaster?
Answers
STEP 1
Multiply 3 feet by 12 inches per foot
= 3 feet * 12 inches per foot
= 36 inches
STEP 2
Add inches in 3 feet with the additional 11 inches
= 36 inches + 11 inches
= 47 inches
ANSWER: Ian is 47 inches tall so he is not tall enough to ride.
Hope this helps! :)
how many fluid ounces are in 3 quarts and 2 cups ?
Answers
1quart= 4 cups
I hope this helped you.
What is the answer plz help
Answers
Then y is given, and you have to write the x-value from the tile you used.
2 ---> -3
14 ---> 3
7 ----> 2
-1 ---> -2
Troy’s canoe is 18 feet long. Ariel’s canoe is 5/6 the length of Troy’s canoe.
What is the length of Ariel’s canoe?
Express your answer in simplest form
Answers
90/6 = 15
it is 15 feet
Miriam ahorró durante toda la semana $14.00.El sabado se gasto 1/7 de esa cantidad y el domingo 5/8, ¿Que cantidad gastó en total durante esos dos días?
Answers
Which of the following describes the transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x
Answers
Answer:
function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.
Step-by-step explanation:
Given : Transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x.
To find : Which of the following describes the transformations.
Solution : We have given
Parent function f(x) = 2x.
Transformed function g(x) = -(2)x+4-2.
By the transformation rule : (1) reflection across x - axis f(x) →→ -f(x) .
(2) f(x) →→ f(x) + k it mean function shifted up by k unit.
(3) f(x) →→ f(x) - k it mean function shifted down by k unit.
Then
f(x) = 2x →→→→-(2)x+4-2.
It mean function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.
Therefore, function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.
Please helplpppp solve each equation 9.4k + 3.5 + 4.8k =46.2
Answers
we subtract 3.5 from both sides
14.20 k=42.70 divide both sides by 14.20
k=3.007
help, please simplify.. thank you
Answers
[tex]\bf \cfrac{37(42)\times 10^{-13}}{25(4)\times 10^910^{-15}}\implies \cfrac{1554\times 10^{-13}}{100\times 10^{9-15}}\implies \cfrac{1554\times 10^{-13}}{1\times 10^2\times 10^{9-15}} \\\\\\ \cfrac{1554\times 10^{-13}}{10^{2+9-15}}\implies \cfrac{1554\times 10^{-13}}{10^{-4}}\implies 1554\times 10^{-13}\times 10^4 \\\\\\ 1554\times 10^{-13+4}\implies 1554\times 10^{-9}\implies \cfrac{1554}{10^9}\implies 0.000001554[/tex]
A trapezoid has an area of 150 square meters. If the bases are 14 meters and 16 meters, what us the height of the trapezoid?
Answers
[tex]a = \frac{1}{2} (b1 + b2) \times h[/tex]
In this formula a represents the area and b1 and b2 each represent a base of the trapezoid.
So, we have got the following information
[tex]a = 150[/tex]
[tex]b1 = 14[/tex]
[tex]b2 = 16[/tex]
Filling in the formula gives us:
[tex]150 = \frac{{1} }{2} \times (14 + 16) \times h[/tex]
[tex]150 = \frac{1}{2} \times 30 \times h[/tex]
[tex]150 = 15 \times h[/tex]
Finally we have to divide both sides by 15.
[tex]h = 150 \div 15 = 10[/tex]
Therefore, the height of the trapezoid is 10 meters.
helpppppppppppppppppppppppppp
Answers
We then have to evaluate:
y = -2sinx - 1
y = -2sin (0) - 1
y = -1
Then, the intersection with the y-axis is -1 and the amplitude is 2.
Answer:
y = -2sinx - 1
option 2
Seven pounds of birdseed is used to fill 4 identical bird feeders.
A.How many pounds of birdseed are used to fill each bird feeder?
Answers
Perform the following calculations.
To calculate the number of pounds of meat required to feed diners do the following: for poultry or meat with bones, divide the number to be served by 2.5; for meat with little or no bone, divide the number to be served by 3.5; and for fish fillets divide the number to be served by 3.5.
Guests = 100
Meat served = boneless chicken
How many pounds of chicken required?
30
40
250
350,
Answers
To feed 100 guests with boneless chicken, divide the number of guests by 3.5 to get 28.57 pounds, and round up to the closest whole number or choose the closest option given. Therefore, you would need 30 pounds of chicken.
The question involves a calculation related to catering and food preparation. To find out how many pounds of boneless chicken are needed to serve 100 guests, use the provided guideline: 'for meat with little or no bone, divide the number to be served by 3.5.' Therefore, we perform the calculation:
Number of guests ÷ Serving ratio = Required meat in pounds
100 ÷ 3.5 = 28.57 pounds
Since you cannot have a fraction of a pound of chicken when buying, you would need to round up to the closest whole number. Therefore, you would need 29 pounds of boneless chicken to serve 100 guests. However, to answer the multiple choice question provided, the closest option given is 30 pounds, which should be sufficient to feed 100 guests with slight leftovers.
complete the equation of the line whose y-intercept is (0,5) and slope is -9
Answers
to check--
when you create a line using the y-intercept and the slope. if you put the (x,y) coordinates that are on your line in your function/equation. both sides should equal each other
ex- 14=14✓
what's the numerator for the following rational expression?
2/f + 5/f = ?/f
Answers
A tent forms an equilateral triangular prism, with both triangular faces exposed. each side of the triangular face has a length of 196196196 centimeters (\text{cm})(cm)left parenthesis, c, m, right parenthesis, and the tent is 250\,\text{cm}250cm250, space, c, m long. what is the height, in centimeters, of the tent?
Answers
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long
I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.
I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.
a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm²
a = 169.74cm
The height of the tent is 169.74 centimeters.
I'm having a problem with probability. Please someone help ASAP.
A first grade class of nine girls and seven boys walks into a class in alphabetical order (by last name). What is the probability that three girls are the first to enter the room? Show your calculation.
(A) 0.15
(B) 0.20
(C) 0.35
(D) 0.45,
Answers
PLEASE HELP! ^^
A 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. What is the volume of 100 pages of the book?
A. 20 in^3
B. 60 in^3
C. 188 in^3
D. 6,000 in^3
I think it's 600 and I think they made a typo but, help please.,
Answers
Explanation:
Since the book is rectangular, we use the formula for the volume of a rectangular prism: V = l*w*h.
Using the measurements of the book we have
V = 10*8*(3/4) = 80*(3/4) = 240/4 = 60 in³.
However, 100 out of 300 pages means we want 100/300 = 1/3 of the book: 60(1/3) = 60/3 = 20 in³.
Answer:
A. [tex]20\text{ in}^3[/tex]
Step-by-step explanation:
We have been given that a 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. We are asked to find the volume of 100 pages of the book.
First of all, we will find the volume of whole book using volume of cuboid formula.
[tex]\text{Volume of cuboid}=l\cdot w\cdot h[/tex], where,
l = Length of cuboid,
w = Width of cuboid,
h = Height of cuboid.
Upon substituting our given values in volume formula we will get,
[tex]\text{Volume of entire book}=10\text{ in}\times 8\text{ in}\times \frac{3}{4}\text{ in}[/tex]
[tex]\text{Volume of entire book}=10\text{ in}\times 2\text{ in}\times 3\text{ in}[/tex]
[tex]\text{Volume of entire book}=60\text{ in}^3[/tex]
Since there are 300 pages in entire book and 100 is 1/3 of 300, so the volume of 100 pages will be the 1/3 of the volume of entire book.
[tex]\text{Volume of 100 pages}=\frac{60\text{ in}^3}{3}[/tex]
[tex]\text{Volume of 100 pages}=20\text{ in}^3[/tex]
Therefore, the volume of 100 pages will be 20 cubic inches and option A is the correct choice.
can anyone find an irrational number between 7.7 and 7.9??
Answers
Which of the following are continuous functions of time?
The quantity of gas in the tank of a car on a journey between New York and Boston (continuous or discontinuous)
The number of students enrolled in a class during a semester (continuous or discontinuous)
I want to verify my answers:
Discontinuous for the car
Continuous for the students,
Answers
The quantity of gas in a car's tank during a journey is continuous, whereas the number of students enrolled in a class is discontinuous due to discrete changes.
Explanation:Continuous functions of time imply that values can change smoothly without jumps or breaks. For the quantity of gas in the tank of a car on a journey between New York and Boston, this would be a continuous function because the gas level decreases gradually as the car is driven. However, for the number of students enrolled in a class during a semester, this is a discontinuous function, because the enrollment can only change through discrete additions or subtractions when students enroll or drop out of the class.
Medals and Fan!
Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2. Open the compass to the length of AB
Step 3: With the same compass setting, put the compass point on point C. Draw and arc that intersects the ray. Label the point of intersection D.
A. A perpendicular Bisector
B. A congruent segment
C. an angle bisector
D. a congruent angle,
Answers
Jennifer is 30 years old. She has $1200 in a checking account, $8000 in a savings account, $6000 in stock investments, $12,000 in a retirement account, and owns a car worth $8000. What is the total value of her liquid assets?
A. $20,000
B. $15,200
C. $23,200
D $25,200
APEX
Answers
Answer:
B.15,200
Step-by-step explanation:
A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in. What is the length of the actual wall?
A) 6.67 inches
B) 80 feet
C) 960 feet
D) 6.67 feet
Answers
Answer:
the length of the actual wall= 80 feet
Step-by-step explanation:
A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in.
Blueprint has a scale ratio of [tex]\frac{1}{10}[/tex]
As per the scale, the wall in the blue print is 1 in then the length of the actual wall is 10 feet
A wall in the blueprint is 8 inches, the length of the actual wall is [tex]10*8= 80[/tex] feet
the length of the actual wall= 80 feet
In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Find the values of x and y.
x = 5, y = 12
x = 5, y = 9
x = 4, y = 9
x = 9, y = 4
Answers
DH = HF
x + 3 = 3y
GH = HE
3x - 3 = 5y + 4
We then have the following system of equations:
x-3y = -3
3x-5y = 7
Resolving the system graphically we obtain the following values:
x = 9
y = 4
Note: see attached image.
Answer:
The values of x and y are:
x = 9, y = 4
Final answer:
In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Solving the equations yields x = 9, y = 4.
Explanation:
To find the values of x and y in parallelogram DEFG, we'll use the properties of parallelograms. In a parallelogram, opposite sides are equal in length.
Given that DH = x + 3 and HF = 3y, and that DH is opposite to HF, we have:
x + 3 = 3y ...(1)
Similarly, given GH = 3x - 3 and HE = 5y + 4, and that GH is opposite to HE, we have:
3x - 3 = 5y + 4 ...(2)
Now, we have a system of two equations (1) and (2) to solve for x and y.
From equation (1):
x = 3y - 3 ...(3)
Substitute equation (3) into equation (2):
3(3y - 3) - 3 = 5y + 4
9y - 9 - 3 = 5y + 4
9y - 12 = 5y + 4
4y = 16
y = 4
Now, substitute the value of y into equation (3):
x = 3(4) - 3
x = 12 - 3
x = 9
So, the values of x and y are x = 9 and y = 4. Thus, the correct answer is x = 9, y = 4.
How many of the first 200 positive integers are multiples of neither 6 nor 15
Answers
.. floor(200/6) = 33 multiples of 6
in the range 1 .. 200.
There are
.. floor(200/15) = 13 multiples of 15
in the range 1 .. 200, half of which are also multiples of 6.
So, there are 33 +13 -6 = 40 numbers in the range 1 .. 200 that are multiples of either 6 or 15 or both.
The remaining 200 -40 = 160 numbers are not multiples of either.
Last question thanks guys!! (only 1!)
Answers
_________________________________________________
Explanation:
_________________________________________________
Note: Working backward, "(± 4√2)" , squared, equals what value(s)?
_________________________________________________
Note: We are actually given 2 (TWO) solutions:
" +4√2" and "–4√2" ;
_______________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;
- √32 = -1 * √32 = - 4√2
_______________________________
or:
√32 = √16 √2 = 4√2 ;
-1 * √32 = - 4√2
______________________________________________________
However, BOTH these values, when "squared" (i.e. raised to the exponential power of "two"; will result in the same value— which is: "32" ;
_______________________________________________________
is equal to: "(4√2)² = (4)² *(√2)² = (4*4) (√2*√2) = 16*2 = " 32 " .
______________________________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;
- √32 = -1 * √32 = - 4√2
_______________________________
or:
√32 = √16 √2 = 4√2 ;
-1 * √32 = - 4√2
_________________________________________________
" (4√2)² = (4)² * (√2)² = (4 * 4) (√2*√2) = 16 * 2 = " 32 " .
" (-4√2)² = (-4)² * (√2)² = (-4 *-4) (2) = 16 * 2 = " 32 " .
_________________________________________________
The correct answer is: " 32 " ; which is: Answer choice: [D]: " x² = 32 " .
We know that the answer is: " " {" ± 8 "}; since we are dealing with equations that contain "x SQUARED"; that is, " x²"; and when we solve for the 'square root of all values of a [variable raised to an even positive integer] ;
we take the "plus or minus" square root values ; since the value, "x" could be plus or minus; since a "negative value" multiplied by a "negative value" is a "positive value" ;
______________________________________________
So, the correct answer is: Answer choice: [B]: " x² = ± 8 " .
______________________________________________
Let us check our answer:
√32 = √16*√2 = 4√2 ;
– √32 = – 4√2 ;
________________________________________________
Also, note:
________________________________________________
x² = 32 ; Solve for "x" ;
→ Take the square root of "each side" of the equation ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ √(x²) = √32 ;
→ | x | = √32 ;
→ x = ± √32 . Yes!
____________________________________________________