Answers
Step-by-step explanation:
a.
1) if A(2;9) and B(6;17), then it is possible to make up the equation of the required line according
2) the rule:
[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};[/tex]
3) if to substitute the coordinates of A&B into the rule, then:
[tex]\frac{x-2}{6-2}=\frac{y-9}{17-9}; \ => \ \frac{x-2}{4}=\frac{y-9}{8}; \ => \ \frac{x-2}{1}=\frac{y-9}{2};[/tex]
or 2x-y+5=0 or y=2x+5 (slope-interception form).
P.S. note, the suggested solution is not the shortest one. This task can be solved if to make up the system of two equations in slope-interception form.
b. see the attached picture (the required line is red colour);
c. f(4)=13. Short explanation: if to substitute the coordinate x=4 into the equation y=2x+5, then y=2*4+5=13;
d. the domain is (-∞;+∞), the range is (-∞;+∞).
Related Questions
Please help (picture is linked)
Answers
Answer:
[tex]\LARGE\mathsf{slope\:=\:\frac{9}{5}}[/tex]
y-intercept: (0, 32), b = 32
[tex]\LARGE\mathsf{y\:=\:\frac{9}{5}x\:+\:32}[/tex]
Step-by-step explanation:
Given (0, 32) as the freezing point of water in Celsius and Farenheit, and (100, 212) as the boiling point of water in Celsius and Farenheit.
SlopeUse these points to solve for the slope of their line.
Let (x₁, y₁) = (0, 32)
(x₂, y₂) = (100, 212)
Substitute these points into the following formula for the slope:
[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]
[tex]\LARGE\mathsf{m = \frac {(212\: -\: 32)}{(100\: -\: 0)}\:= \frac {180}{100}}[/tex]
[tex]\LARGE\mathsf{m\:=\:\frac{9}{5}}[/tex]
Therefore, the slope of the line is [tex]\LARGE\mathsf{m\:=\:\frac{9}{5}}[/tex].
Y-intercept:Next, the given problem asks for the value of the y-intercept. The y-intercept is the point on the graph where it crosses the y-axis, with its coordinates occurring at point, (0, b ). Thus, the y-intercept provides the value of y when its corresponding x-coordinate is 0.
To solve for the y-intercept, b, we must choose one of the given points, (100, 212), and the slope, [tex]\LARGE\mathsf{m\:=\:\frac{9}{5}}[/tex], and substitute these values into the slope-intercept form, y = mx + b:
y = mx + b
[tex]\LARGE\mathsf{212\:=\:\frac{9}{5}(100)\:+\+b}[/tex]
212 = 180 + b
Subtract 180 from both sides to isolate b:
212 - 180 = 180 - 180 + b
32 = b
The y-intercept is (0, 32), where b = 32.
Slope-intercept form:Given the slope, [tex]\LARGE\mathsf{m\:=\:\frac{9}{5}}[/tex], and the y-intercept, b = 32:
The linear equation in slope-intercept form is: [tex]\LARGE\mathsf{y\:=\:\frac{9}{5}x\:+\:32}[/tex]
Simplify the following expression. (0.5x – 3)(0.5x + 3)
Answers
Answer:
0.25x^2-9
Step-by-step explanation:
Difference of squares converse:
0.25x^2-9
Answer:
0.25x^2-9
Step-by-step explanation:
multiply 0.5x with 0.5x which is 0.25x^2. then multiply 0.5x with 3 which is 1.5x. then multiply -3 with 0.5x which is -1.5x. then multiply -3 with 3 which is 9. so you will have 0.25x^2+1.5x-1.5x-9.
1.5x and -1.5x is 0. so you are left with 0.25x^2-9
Factories often add filler when making meatballs sold by the bag. One factory obtained 72 kg of beef from overseas. They want to add 1.2 oz of filler for each
pound of beef, How many ounces of filler will the factory need in order to make meatbälls out of this shipment of beef? Help
Answers
Answer:
158.732829
rounded up: 159
Step-by-step explanation:
trust the calculator
Which angle is the smallest?
12
10
D
Answers
Answer:
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answers
Answer:
x2 + (y – 3)2 = 36
x2 + (y + 8)2 = 36
Step-by-step explanation:
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,
⇒ x² + (y - 3)² = 36
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Since, The standard form for finding the equation of a circle is expressed as;
⇒ (x - a)² + (y - b)² = r²
where;
(a, b) is the center of the circle
And, r is the radius of the circle
Given that;
Diameter = 12 units
And, Radius = 12/2 = 6 units
If the center lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have;
⇒ (x - 0)² + (y - 3)² = 6²
⇒ x² + (y - 3)² = 36
Thus, The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is,
⇒ x² + (y - 3)² = 36
Learn more about the circle visit:
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Given: △ABC, m∠A=60°,
m∠C=45°, AB=9
Find: Perimeter of △ABC,
Area of △ABC
Pleas be sure to answer BOTH PARTS ... thank you!
Answers
Answer:
p = 32.317
A = 47.911
Step-by-step explanation:
given ∠A = 60
∠C = 45
AB = 9
From sum of all angles in triangle is 180
∠A + ∠B + ∠C = 180
60 + ∠B + 45 = 180
∠B = 180 - 105 = 75
∠B = 75
from sine rule in ΔABC
AB / sin C = BC / sin A
=> 9 / sin 45 = BC / sin 60
=> 9 / 1/[tex]\sqrt{2}[/tex] = BC / [tex]\sqrt{3} / 2[/tex]
=> [tex]9\sqrt{2} = BC * 2 / \sqrt{3}[/tex]
BC = [tex]9\sqrt{2} * \sqrt{3} / 2\\[/tex]
BC = 11.023
length of AC is
AC / sin B = AB / sin C
AC / sin 75 = 9 / sin 45
AC = 9 / 1/[tex]\sqrt{2} * sin 75[/tex]
= [tex]9\sqrt{2} * sin 75\\12.294[/tex]
perimeter of ΔABC
AB + BC + CA
= 9 + 11.023 + 12.294
= 32.317
Area of ΔABC is
= 1/2 * AB * AC * sin A
= 1/2 * 9 * 12.294 * sin 60
= 1/2 * 9 * 12.294 * √3/2
= 47.911
432 women attended a conference. Women made up 72% of the total conference attendees.
Men made up the other 28% of attendees.
How many men attended the conference?
Answers
Answer:
168
Step-by-step explanation:
If entire number of attendees = y
then number of women = y* (72/100)
since y* (72/100) = 432 ( given)
y =( 432*100)/72
so, y = 600
since men made up the remaining 28% of attendees ,
number of men = y * (28/100) = 600* (28/100)
number of men = 168
Joe was looking through a numeric puzzle
book and found the following puzzle. The
sum of two numbers is two. The difference
of the two numbers is also two. What are
the two numbers?
Answers
0 and 2
Step-by-step explanation:
If you subtract 2 by 0 then it will equal 2 and if you add 2 to 0, you also have 2.
Choose the graph that matches the inequality –x + y ≥ 2
Answers
Answer:
D
Step-by-step explanation:
-x + y >= 2
first of all, it means it includes the line (the "=" part).
that eliminates B and C.
then just look at the line function itself :
-x + y = 2
y = x + 2
and now
y >= x + 2
so, everything above the line (and again including the line), as every y value greater than or equal to the result of the line function is valid.
The required graph has been attached below which represents the given inequality –x + y ≥ 2. which is the correct answer that would be an option (D).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question below as
–x + y ≥ 2
First and foremost, it signifies that it includes the line (the "=" element).
This rules out B and C.
Then evaluate the line function itself:
-x + y = 2
y = x + 2
and now
y ≥ x + 2
As a consequence, anything above the line (and including the line) is legitimate, as is any y value larger than or equal to the result of the line function.
Thus, the required graph has been attached below which represents the given inequality –x + y ≥ 2.
Hence, the correct answer would be an option (D).
Learn more about the inequalities here:
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Fill in the blank.
The
is the intersection of the three medians in a triangle.
O centroid
O incenter
O orthocenter
O circumcenter
Answers
O centroid
Step-by-step explanation:
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
A square has a side length of 36 feet. This square is dilated by a scale factor of 23
2
3
to create a new square. What is the side length of the new square?
Answers
Answer:
24
Step-by-step explanation:
I answerd it on ttm and got it right
u=xk , for x
please help me
Answers
Answer:
x=u/k
Step-by-step explanation:
To get x, you would divide by k. Because its x times k. The oppisite is division. This gets you u/k=x
x is equal to u divided by k.
x=u/k
multiples of 7 between 30 and 50
Answers
Answer:
It is 35, 42, 49
7x5=35
7×6=42
7²=49
=
35
42
49
Hope this helps!!
Question down below, Please answer if you know :)
Answers
Answer:
A
Step-by-step explanation:
Step-by-step explanation:
A garden table and a bench cost $783 combined. The garden table costs $83 more than the bench. What is the cost of the bench?
Answers
Answer:
$557.5
Step-by-step explanation:
783/2
391.5 + 83 (more) =
557.5
In the mystery number problem below, Rosa identified the missing number as 4. Is she correct? How can you check her answer?
(pls help) (pls no link i need to know its real and not a scam)
Answers
Answer:
Step-by-step explanation:
she is wrong the right answer is 15.98
What numbers can be used instead to x for this equation to remain the same -x>2
Answers
Answer:
2x + 1 = 11.
2x + 1 - 1 = 11 - 1 (subtracting both sides by the same number)
2x = 10.
2x/2 = 10/2 (dividing both sides of the equation by the same number)
x = 5.
Step-by-step explanation:
hope it helps
what is the solution to this system of equations?
5x-y=40
y=2x-4
A) 20, 12
B) -20, 12
C) 12, -20
D) 12, 20
Answers
5x - (2x - 4) = 40
Solve for x
5x - 2x + 4 = 40
3x = 36
x = 12
Plug in x for either equation
y = 2(12) - 4
y = 24 - 4
y = 20
X = 12 and Y = 20, so D
{ solve simultaneously }
rearrange equation to make y the subject
5x-y=40
y=5x-40
Sub y=5x-40 into the second equation given ( y=2x-4 )
5x-40 = 2x-4
Solve normally to find x
x = 12
Sub x=12 into y=5x-40
Solve normally to find y
y = 20
Therefore, answer is D) 12, 20
Find x if the line through the points (6, x) and (1,-5) has a slope of 2.
Answers
Answer:
Step-by-step explanation:
Use the slope formula
m = (y2 - y1)/(x2 - x1)
y2 = x
y1 = -5
x2 = 6
x1 = 1
m = 2
Solution
2 = (x - - 5)/(6 - 1)
2 = (x + 5)/ 5 Multiply both sides of the equation by 5
5*2 = 5(x + 5)/5 Simplify
10 = x + 5 Subtract 5 from both sides
10-5 = x
x = 5
PLEASSEE HELP:Dits for khan
What is the constant of proportionality in the equation
y
=
1
2
x
y=
2
1
xy, equals, start fraction, 1, divided by, 2, end fraction, x?
Answers
The constant of proportionality in the equation y=1/2x
is 1/2
The direct proportionality between x and y is established by :
y α x
α = proportionality symbol
y = kx - - - (1)
Where;
y and x are the variables
k = proportionality constant
Comparing (1) with the equation given : y=1/2x y=kx
The value of k aligns with 1/2 in the given equation.
Therefore, the constant of proportionality, k in the equation is 1/2
Answer:
yo yo yo! here to help :) answer is 1/2
Use the formula for the perimeter of a rectangle, P = 2 l + 2 w, where P is the perimeter, l is the length, and w is the width.
Answers
Answer:
The perimeter of the tabletop is 152 inches
Step-by-step explanation:
So if P = 2L + 2W we have to do
(2*48) + (2*28)
So
96 + 56 = 152
Which is a solution for 7 (x plus 2) equals 35?
Answers
x = 5
Hurry please
Answer ASAP
Answers
Susan made $117 for hours 9 of work.
At the same rate, how much would she make for 7 hours of work?
Answers
117/9 = 13 dollars per hour
Then find out how much she makes in 7 hours
13 • 7 = 91 dollars
$91 in 7 hours
The fuel capacity of a popular hybrid car is 11.9 gallons. The function for this situation is f(x) = -0.02x + 11.9, where x represents miles and f(x) represents the amount of fuel remaining. What is the rate of change for this scenario?
Answers
Answer:
-0.02 gallons per mile
Step-by-step explanation:
You're in luck. The fuel consumption of the car is linear, and the slope - ie, the coefficent of the x term gives you the rate of change. In this case, it's -0.02 gallons per mile.
(21x)-(-16+7x) Subtract.
Answers
Answer:
=14x+16
Step-by-step explanation:
21x−(−16+7x)
=21x+−1(−16+7x)
=21x+(−1)(−16)+−1(7x)
=21x+16+−7x
=21x+16+−7x
=(21x+−7x)+(16)
=14x+16
Answer:
14x+16
Step-by-step explanation:
(21x)-(-16+7x)
Distribute the minus sign
21x+16-7x
Combine like terms
14x+16
True or false
1: 4h and 4g are like terms: True or false?
2: 4x and 4xy are like terms. True or false?
3: the coefficient is the number by its self. True or false?
4: in the expression x-4+(-5x), the constant is 4. True or false?
5: in the expression x-4+(-5x), the constant is -4. True or false?
6: in the expression x-4+(-5x), the coefficient -5 is . True or false?
You dont need to explain the steps, if you like you may
Answers
Answer:
1 is true
2 is true
3 is true
4 is false
5 is true
6 is true
A farmer is measuring the average height y of her tomato plants x weeks after planting sprouts. What is the equation and slope.
Answers
The equation is y = 0.5x and the slope is 0.5.
A function is said to be linear if it is a straight line graph and it can be represented by the equation:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the height of the tomato after x weeks. Let us assume that the points are (0, 0) and (6, 3), hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{3-0}{6-0} (x-0)\\\\y=0.5x[/tex]
Therefore the equation is y = 0.5x and the slope is 0.5.
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The equation for the scenario "A farmer is measuring the average height y of her tomato plants x weeks after planting sprouts" is y = mx + c
The slope = m
The duration after which the farmer measures the average height of her tomato = x weeks
The average height of the tomato plant after x weeks = y
For the slope to be required, it means the relationship between the average height of the her tomato (y) and the number of weeks (x) is linear
This means that the average height of the tomato will be represented by a linear equation as shown below
y = mx + c
The slope of the equation is m
Learn more here: https://brainly.com/question/25759076
what is 4 1/2 - 1
8/10= in Fractions
Answers
[tex]4\frac{1}{2} - 1\frac{8}{10} = \frac{9}{2}- \frac{9}{5} = \frac{27}{10}[/tex]
ok done. Thank to me :>
Answer:
4 1/2= 9/2
1 8/10= 18/10= 9/5
9/2-9/5=
(45-18) /10=
27/10 or 2 7/10
Step-by-step explanation:
Simplify this expression:
[tex]7xy - x^{2}t+4xy+5x^{2}t[/tex]
Answers
Answer:
[tex]11xy+4x^{2} t[/tex]
Step-by-step explanation:
1. Collect Like Terms
[tex](7xy+4xy)+(-x^{2} t+5x^{2} t)\\[/tex]
2. Simplify.
[tex]11xy+4x^{2} t[/tex]