Answer:
y=(-5/2)x-4
Step-by-step explanation:
Step 1: Define the equation of a line.
Equation of a line is written in the form y=ax+b where a is the slope and b is the y-intercept.
Step 2: Write the given parameters
(x1,y1)=(-2,1)
m=-5/2
Using the formula y-y1=m(x-x1)
y-1=-5/2(x-(-2))
y-1=-5/2(x+2)
y-1=(-5x-10)/2
By cross multiplication,
2(y-1)=-5x-10
2y-2=-5x-10
2y=-5x-10+2
2y=-5x-8
y=(-5x-8)/2
y=(-5/2)x-4
Someone please help me solve the problem
========================================================
Explanation:
Check out the diagram below.
We have the following points
A = center of both the circle and the squareB = point on the circle directly to the left of point AP,Q,R,S = corner points of the squareE = intersection of segments AB and PSF = point on the square directly to the right of point AC and D = intersection of segment PS and the circleLet x be the length of segments DE and EC. Note how segment AB bisects segment DC. Whenever the radius is perpendicular to the chord like this, the radius will bisect the chord.
We're told that the chord length CD is the same as the radius AD, since CD = CE+ED = x+x = 2x, this means AD = 2x as well.
At this point, you probably can recognize we have a 30-60-90 triangle. One useful property of such triangles is that the hypotenuse is double the length of the short leg. The long leg is [tex]x\sqrt{3}[/tex] which is the length of segment EA. You can use the pythagorean theorem to confirm this.
----------------------------------
To summarize that last section, we formed triangle DAE and this triangle is a 30-60-90 triangle as shown in the diagram below.
Notice how the segments EA and FA span the entire width of the square. That width being [tex]EA+FA = x\sqrt{3}+x\sqrt{3} = 2x\sqrt{3} = EF[/tex]
The square has side lengths of [tex]2x\sqrt{3}[/tex] while the circle has radius 2x.
Use these two facts to find the area of each in terms of x.
[tex]A_1 = \text{area of square} = (\text{side})^2 = (2x\sqrt{3})^2 = 12x^2[/tex]
[tex]A_2 = \text{area of circle} = \pi*r^2 = \pi*(2x)^2 = 4\pi x^2[/tex]
-----------------------------------
The last step is to divide the two results. The x^2 terms cancel out.
We'll be left with...
[tex]\frac{A_1}{A_2} = \frac{12x^2}{4\pi x^2} = \frac{12}{4\pi} = \frac{3}{\pi} \approx 0.9549[/tex]
There are many ways to express this ratio. One way we could write it is to say 3:pi to indicate that if the area of the square is 3, then the circle has area of pi (approximately 3.14). No matter what the square's area is, the circle is always slightly larger in area.
Find the measure of angle Y.
Answer:
Y = 62°
Step-by-step explanation:
The sum of angles in a triangle is 180°.
W + X + Y = 180°
(4n -9°) + (7n -16°) +(6n -16°) = 180°
17n -41° = 180° . . . . . . . . . . simplify
17n = 221° . . . . . . . . . . add 41°
n = 13° . . . . . . . . . . divide by 17
Then the measure of Y is ...
Y = 6n -16° = 6(13°) -16° = 78° -16°
Y = 62°
_____
The other angles are W = 43°, X = 75°.
Angles of a triangle adds to 180° .
===============================> W + X + Y = 180°
=> (4n-9°) + (7n-16°) + (6n-16°) = 180°
=> 17n-41° = 180°
=> 17n = 180° + 41°
=> 17n = 221°
=> n = 221/17
=> n = 13°
The measure of Y is,=> 6n-16° = 6(13°) -16° = 62°
Y = 62°
The doctor told her patient that every day he needs
to consume more than 1800 but less than 1900 calories.
Write an inequality representing the possible amount of
calories the patient could cconsume.
Select all the correct answers.
Which equations represent functions?
A class is made up 15 girls and 12 boys. If a group is made up 3 girls and 3 boys, then how many groups can be created?
Answer:
The answer would be 5 Girls and 4 Boys.
Step-by-step explanation:
15 Girls divided by 3 groups= 5 girl groups
12 boys divided by 3= 4 boy groups
Answer:
3+3=6
the answer is 6 many groups created
Given the point and the slope, write the function in point-slope form:
(2,−5);m=23
Group of answer choices
y−5=23(x−2)
y+5=23(x−2)
y−5=23(x+2)
y+5=23(x+2)
Answer:
2nd answer choice
Step-by-step explanation:
point slope form: y-y1=m(x-x1)
y-(-5)=23(x-2)
y+5=23(x-2)
Answer:
(b) y+5=23(x−2)
Step-by-step explanation:
The point-slope form for the equation of a line is ...
y -k = m(x -h) . . . . . . point (h, k), slope m
You have point (2, -5) and m=23, so the equation becomes ...
y -(-5) = 23(x -2)
y +5 = 23(x -2) . . . . . . simplify a bit
What is the radius of a circle whose equation is (x – 7)2 + (y – 10)2 = 4? 2 units 4 units 8 units 16 units
Answer:
A. 2 units
Step-by-step explanation:
took the test and got it right
The radius of the circle is r = 2 units
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the equation of the circle be represented as A
Now , the value of A is
( x - 7 )² + ( y - 10 )² = 4
The equation ( x - 7 )² + ( y - 10 )² = 4 represents a circle in standard form, where the center of the circle is located at the point (7, 10) and the radius is the square root of the number on the right side of the equation
Taking the square root of 4, we find that the radius of the circle is 2 units
Hence , the radius is r = 2 units
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Mathematic 14 dont undertsqnd
Subtract. (5d+6)–(2d+2)
Answer:
3d+4
Step-by-step explanation:
(5d+6)–(2d+2)
To find the opposite of 2d+2, find the opposite of each term.
5d+6−2d−2
Combine 5d and −2d to get 3d.
3d+6−2
Subtract 2 from 6 to get 4.
3d+4
Hope this helps! :)
A rhombus has a side length of 6 centimeters, and a height of 2
centimeters.
What is the area of the rhombus, in centimeters??
Answer:
12 cm^2
Step-by-step explanation:
The area of the rhombus is 12 cm².
Given that, a rhombus has a side length of 6 centimetres, and a height of 2 centimetres.
We need to find the area of the rhombus, in centimetres.
What is the area of the rhombus?The formula for the area of the rhombus when base and height are known.
The rhombus is a parallelogram. We know that the area of a parallelogram is given by multiplying base and height sq units. The same is applied to the rhombus as well. Area of a rhombus = Base × Height sq units.
Now, the area of a rhombus= 6×2=12 cm²
Therefore, the area of the rhombus is 12 cm².
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Two different floor plans are being offered in a new housing development. Several prospective buyers from three different age groups were surveyed about which plan they preferred. Find the probability that a randomly selected buyer preferred Plan A or was in the 40- to 49-year-old age group.
Answer:
0.677
Step-by-step explanation:Add up the values in the plan A column. There are 10+12+16 = 38 people who prefer plan A.
Add up the values in the "40-49" row to find that 16+8 = 24 people are ages 40 to 49.
We have 38+24-16 = 46 people who either prefer plan A, are aged 40-49, or fit both descriptions. I subtracted off 16 because those 16 people were counted twice when adding 38 and 24.
An alternative way to get this value of 46 is to add up everything that is in column1 or row 3 (or both). So that would get 10+12+16+8 = 46.
Now add up everything in the table to find out how many people were surveyed total. That would be 10+7+12+15+16+8 = 68 people overall.
The probability of someone liking plan A, or being age 40-49, or both is 46/68 = 0.6765 approximately. Rounding to 3 decimal places gives 0.677
Graph 7x+y=10x-4.
Show your work and explain the method used to determine the graph.
The graph must pass through the y-axis at y = -4 with a positive slope of 3
Given the expression
7x+y=10x-4.Write the given equation in standard form to have:
7x+y=10x-4.
y = 10x - 7x - 4
y = 3x - 4
From the equation, the slope is 3 and the y-intercept is -4
The graph must pass through the y-axis at y = -4 with a positive slope of 3.
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A train travels at a rate of 150 mph on a flat
plain. How long did it take the train to get from a
distance of 68 miles to 222 miles on its journey?
Answer:
61 minutes and 36 seconds
Step-by-step explanation:
150 mph is equal to 2.5 miles per minutes divide miles by 2.5
Simplify the following expressions using the laws of exponents.
Answer:
Salmat po sa lahat
Step-by-step explanation:
ako ay from pilipinas na padpad lng dito ^_^
4(n-16)=16 this is my question and what I need help on
Answer:
n = 20.Step-by-step explanation:
4(n - 16) = 16=> 4n - 64 = 16=> 4n = 16 + 64=> 4n = 80=> n = 20Conclusion:
Therefore, n = 20.
Hoped this helped.
[tex]GeniusUser[/tex]
Use each model to predict the life expectancy of residents of a country for which the average annual income is $80,000
The life expectancies of residents of a country for which the average annual income is $80,000 for the three models are 12309.9352, 172.2436 and 4828.1393
The life expectancies of the models are given as:
[tex]y =69.9352 + 0.1530\times (income)[/tex] --- model 1
[tex]y =4.2436 + 0.0021\times (income)[/tex] --- model 2
[tex]y =4.1393 + 0.0603\times (income)[/tex] --- model 3
Given that the average annual income is $80,000;
We simply substitute 80000 for income in the equations of the three models.
So, we have:
Model 1
[tex]y =69.9352 + 0.1530\times (income)[/tex]
[tex]y =69.9352 + 0.1530\times 80000[/tex]
[tex]y =12309.9352[/tex]
Model 2
[tex]y =4.2436 + 0.0021\times (income)[/tex]
[tex]y =4.2436 + 0.0021\times 80000[/tex]
[tex]y =172.2436[/tex]
Model 3
[tex]y =4.1393 + 0.0603\times (income)[/tex]
[tex]y =4.1393 + 0.0603\times 80000[/tex]
[tex]y =4828.1393[/tex]
Hence, the life expectancies are 12309.9352, 172.2436 and 4828.1393
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Mrs. Clark's plant is 4 3/4 inches tall. It is 1 7/8 inches taller than Jimmy's plant.
How tall is Jimmy's plant?
a) What is the domain?
b) What is the range?
c) Is this relation
a function?
Answer:
Step-by-step explanation:
A. x is negative infinite to positive infinite
b. Y=3
c. Yes
reasoning
a. It’s asking what can x equal Be used domain is like another name for x and of you look on thw graph the arrow is crossing all the x points
B. It’s asking for y since range is another name for y and you see on the y axis, y is only interacts with three and no other point so it’s just y=3
C. It’s a function because it passes the vertical line tes!
The function f(x)is graphed on the coordinate plane.
What is f(−2)?
Enter your answer in the box.
f(−2) =
Answer:
f(-2) = -2
Step-by-step explanation:
f(-2) means find the y value when x = -2
The y value when x = -2 is-2
f(-2) = -2
Question 1 (1 point)
Order the decimals from least to greatest.
10 3.06, 3.6, 3.066, 3.006
least
greatest
10) LEAST
GREATEST
Blank 1:
Answer:
3.006, 3.06, 3.066, 3.6, 10
Step-by-step explanation:
Numbers written in a place-value system are compared left-to-right. If the digits with the same place-value multiplier being compared are the same, then the next digits to the right need to be compared.
The number 10 is the greatest. (None of the others have a digit in the 10s place.)
The number 3.6 is the next greatest. (6 in the tenths place is the largest digit there.)
The number 3.066 follows that, then 3.06.
3.006 is the least.
In order from least to greatest, the numbers are ...
3.006, 3.06, 3.066, 3.6, 10
The perimeter of the triangle is 20.6 centimeters. What is the unknown side length?
Answer:
OK so a triangle has 3 sides and the perimeter around it is 20.6 cm to find the unknown for the length of a side it would be 20.6 ÷3 which is = to 6.86 to 2 decimal places
Step-by-step explanation:
20.6÷3
= 6.86 cm to 2 dp
Jane’s starting annual salary is $45,520. At the beginning of each new year, she receives a $1,580 raise. What will her salary be after 11 years?
Answer:
$62,900
Step-by-step explanation:
Write the standard form of a polynomial functions whose zeros/roots are
4-3i, 4+3i
and has a lead coefficient of 1
Answer:
In other words, x = r x = r is a root or zero of a polynomial if it is a solution to the equation P (x) =0 P ( x) = 0.
Step-by-step explanation:
please help me asap..
ty :)
Answer:
x-intercept = 3, 0
y-intercept = 0, -4
Step-by-step explanation:
A truck can be rented from Company A for $110 a day plus $0.20 per mile. Company B charges $80 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
130
Step-by-step explanation:
Step 1: write equations:
Company A: y = 0.20x + 110
Company B: y = 0.50x + 80
Step 2: graph your lines
Step 3: Find your intersect point
Step 4: find the points: (100,130)
The number of miles is y, so at 130 miles, both trucks are the same cost
Hope that helps
Which graph represents the function f(x) = −|x − 2| − 1?
Answer:
Graph C
Step-by-step explanation:
please help, i really beg
Answer:
Undefined
Step-by-step explanation: Because the pints are a line so there isnt a slope unless ther is a shape.
I'm saying positive. I don't think you need a shape to find the slope
need help with question 4
Step-by-step explanation:
it's option D (x³)
hope this helps you.
help please its timed
i have to write 20 characters so there is ur answer
The height y, in feet, of a football x seconds after it is thrown is modeled by the equation y = â€"16x2 24x 1. What information does the zero of the equation 6 = â€"16x2 24x 1 represent?.
The zero of the equation [tex]6 = -16x^2 + 24x + 1[/tex] represents the moment when the ball is 6 ft above the ground.
Given that,
The height y, in feet, of a football x seconds, after it is thrown is modeled by the equation,
[tex]\rm y = -16x^2 + 24x + 1.[/tex]
We have to determine,
What information does the zero of the equation [tex]6 = -16x^2 + 24x + 1[/tex] represent?
According to the question,
In the quadratic equation for the ball's height, it is found that the zero of the equation represents,
[tex]\rm 6 = -16x^2 + 24x + 1[/tex]
The instant of the time x is when the ball is 6 ft above the ground.
The height of the ball is y(x), after x seconds, is modeled by:
[tex]\rm y = -16x^2 + 24x + 1.[/tex]
The equation given is,
[tex]\rm 6 = -16x^2 + 24x + 1[/tex]
In which the height is 6 feet above the ground, and the zeroes are the instants of time when the ball is 6 ft above the ground.
Hence, These points represent the moment when the ball is 6 ft above the ground.
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