Answer:
See below.
Step-by-step explanation:
Hi there!
We want to find the equation of the line that has a slope (m) of 1 and that passes through the point (-10, -6)
There are 3 ways to write the equation of the line:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptPoint-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be equal to zero, and a cannot be negativeSince we are given both a point and a slope in this situation, it makes sense to write the equation in point-slope form.
Let's label the values of everything we were given to avoid confusion and mistakes:
m=1
[tex]x_1=-10\\y_1=-6[/tex]
Now substitute these values into the equation (note: we have NEGATIVE numbers, while the formula gives SUBTRACTION, which is why we're subtracting a negative)
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y--6=1(x--10)[/tex]
Simplify:
y+6=1(x+10)
The equation can be left as this, or it can be converted into slope-intercept form if you wish.
In that case, we would distribute 1 to each number on the right side.
y+6=x+10
Then, we'll isolate y on one side. Subtract 6 from both sides.
y=x+4
You can also convert it into standard form if you would prefer it that way. To do that, start with slope-intercept form, which we earlier found as y=x+4
In standard form, x and y are on the same side. So subtract x from both sides to move it
-x+y=4
Remember we don't want a (the coefficient in front of x) to be negative. In order to flip the sign, multiply both sides by -1
x-y=-4
Therefore, the answer can be written as y+6=1(x+10), y=x+4, or x-y=4.
Hope this 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
multiples of 7 between 30 and 50
Answer:
It is 35, 42, 49
7x5=35
7×6=42
7²=49
The last time it placed an order for ingredients, Sweet Treats Bakery ordered 7,160 kilograms of sugar. This time, the bakery is ordering 40% less sugar. How much sugar is that?
Answer:
4296 kg
Step-by-step explanation:
40/100 = x/7160
716 times 6 is 4296
Please help (picture is linked)
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]
(21x)-(-16+7x) Subtract.
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
What numbers can be used instead to x for this equation to remain the same -x>2
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
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)
Answer:
Step-by-step explanation:
she is wrong the right answer is 15.98
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?
Answer:
$557.5
Step-by-step explanation:
783/2
391.5 + 83 (more) =
557.5
what is 4 1/2 - 1
8/10= in Fractions
[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:
c) 2 x x 3 x y
Please help
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?
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.
Susan made $117 for hours 9 of work.
At the same rate, how much would she make for 7 hours of work?
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?
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
Choose the graph that matches the inequality –x + y ≥ 2
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:
brainly.com/question/20383699
#SPJ2
Which angle is the smallest?
12
10
D
Answer:
Step-by-step explanation:
Simplify this expression:
[tex]7xy - x^{2}t+4xy+5x^{2}t[/tex]
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]
Fill in the blank.
The
is the intersection of the three medians in a triangle.
O centroid
O incenter
O orthocenter
O circumcenter
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.
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.
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
u=xk , for x
please help me
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
4x+8=3
help asap
step by step please
[tex]4x +8 =3\\\\\implies 4x = - 5 \\\\\implies x = - \dfrac 54[/tex]
Answer:
x= -5/4
Step-by-step explanation:
4x+8=3
4x=3-8
4x=-5
x= -5/4
A farmer is measuring the average height y of her tomato plants x weeks after planting sprouts. What is the equation and slope.
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.
Find out more at: https://brainly.com/question/21835898
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
Which is a solution for 7 (x plus 2) equals 35?
Question down below, Please answer if you know :)
Answer:
A
Step-by-step explanation:
Step-by-step explanation:
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
Answer:
158.732829
rounded up: 159
Step-by-step explanation:
trust the calculator
I would appreciate if you answered!
Answer:
None of those options
Step-by-step explanation:
I just did the work myself and even ran it through a calculator but the correct answer isn't one of those options. Here's my work:
[tex]-\frac{5}{6} =z+\frac{1}{8}\\-\frac{5}{8}-\frac{1}{8}=z\\-\frac{40}{48}-\frac{6}{48}=z\\-\frac{46}{48}=z\\-\frac{23}{24}[/tex]
I'd contact you teacher about that...it might be an error in their system (it's happened to me a few times before where the correct answer is marked as incorrect or isn't even an option)
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!
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
Simplify the following expression. (0.5x – 3)(0.5x + 3)
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
Hurry please
Answer ASAP
WILL MARK BRAINLIEST
Solve 39.2 ÷ 7 = ________.
5.2
5.3
5.5
5.6
Answer:
5.6
Step-by-step explanation:
Answer:
5.6
Step-by-step explanation:
I just take each answer and multiply it by 7 until the answer matches 39.2.
5.6 * 7 = 39.2
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
Answer:
1 is true
2 is true
3 is true
4 is false
5 is true
6 is true