Question 6 of 10
The slope of the line below is -3. Which of the following is the point-slope
form of the line?
5
(2,-2)
O A. y-2 = 3(x+2)
O B. y + 2 = -3(x - 2)
O C. y2 = -3(x+2)
O D. y + 2 = 3(x-2)
Answers
The point-slope form of the line is y + 2 = -3(x - 2). The correct option is B. y + 2 = -3(x - 2)
Point-slope form of an equation of a lineFrom the question, we are to determine the point-slope form of the given line
The point-slope form of an equation of a straight line is written as
[tex]y-y_{1}=m(x-x_{1})[/tex]
Where m is the slope and [tex](x_{1},\ y_{1})[/tex] is a point on the line
From the given information,
m = -3
And in the diagram,
One of the points on the line is (2, -2)
Therefore, we can write that
x₁ = 2 and y₁ = -2
Substituting into the point-slope form of an equation of a line,
We get
y - (-2) = -3(x - 2)
This becomes
y + 2 = -3(x - 2)
Hence, the pointslope form of the line is y + 2 = -3(x - 2). The correct option is B. y + 2 = -3(x - 2)
Learn more on Point slope form of an equation of a straight line here: https://brainly.com/question/8386231
The diagram for the question is attached below.
Related Questions
In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day. Determine the mass of the radioactive sample at the beginning of the 13th day of the experiment. Round to the nearest tenth (if necessary).
Answers
Using an exponential function, it is found that the mass of the radioactive sample at the beginning of the 13th day of the experiment was of 169.1 mg.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day, hence A(0) = 500, r = 0.08, and the equation is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 500(1 - 0.08)^t[/tex]
[tex]A(t) = 500(0.92)^t[/tex]
At the 13th day, the mass is given by:
[tex]A(13) = 500(0.92)^{13} = 169.1[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
Find the 9th partial sum of the geometric sequence an=43n–1.
Answers
Answer:
39364.
Step-by-step explanation:
I guess its an = 4*(3)^(n-1)
r = 3, a1 = 4 and n = 9
Sum of n terms = a1 * (r^n - 1) / (r - 1)
so S9 = 4 *(3^9 - 1) / (3 - 1)
= 4 * (19683 - 1) / 2
= 78728/2
= 39364.
A child runs 200 meters in 40 seconds. Calculate the average speed of the child in m/s
Answers
If a circle has a circumference of 36pie cm, what is the area?
Answers
Answer:324pie cm^2
Step-by-step explanation:
What is the volume of this container? (image below)
Answers
Answer:
480 in³
Explanation:
Volume of Rectangular Prism = Length * Height * Width
Front Volume:
4 * 4 * 580 in³Behind Volume:
5 * 8 * 10400 in³Total volume:
400 in³ + 80 in³480 in³Both are cuboids
#1
L=8B=10C=5Volume:-
LBH8(10)(5)400in³#2
L=4B=4H=5Volume:-
4(4)(5)80in³Total:-
400+80=480in³
Kate has a coin collection. She keeps 7 in a box, which is only 5% of her entire collection. What is the total number of coins in Kate’s coin collection?
Answers
Answer:
140
Step-by-step explanation:
5%/100 = 7/?
7 times 100 = 700
700 divided by 5 = 140 coins
Which object will have more inertia? Object A that has a mass of 250 grams, Object B, that has a mass of 25,000 grams, or Object C that has a mass of 1,250,000 grams.
1.object a
2.b
3.c
4.all have the same
Answers
Answer:
3. Object C.
Step-by-step explanation:
The inertia of an object is the measure of the force required to set it in motion. For two objects to have the same motion, the one with the greater mass will require a proportionately greater force to achieve the same motion.
Object C, with a mass of 1,250,000 grams (1,250 kg) will have the greatest inertia.
Which of the following measurements results in the largest circle?
A.
radius = 8 in.
B.
diameter = 8 in.
C.
area = 30 sq. in.
D.
circumference = 30 in.
Answers
Answer:
A
Step-by-step explanation:
A) r = 8
B) r = 4
C) r = [tex]\sqrt{\frac{30}{\pi } }[/tex] ~ 3.09
D) r = [tex]\frac{30}{2\pi} = \frac{15}{\pi } ~ 4.77[/tex]
Circle A has the largest radius, and thus is the largest circle
If an investment has a 5% annual interest rate and it is compounded
monthly, how many years will it take to double in value?
Answers
Answer:
2 years
Step-by-step explanation:
If it is annunal I think it would be 2 years
5 x annual year (year) =2
(6.1D; 6.1F)
-
1. Which expression is equivalent to 32?
A 23 + (4) – 4 x 2
B 3x3 + (42) - 4
C 42 – 7x0
+
-
D 4x 5 + 2 – 4 + 2
Answers
Hey there!
Option A.
23 + (4) - 4 * 2
= 23 + 4 - 4 * 2
= 27 - 4(2)
= 27 - 8
= 19
19 ≠ 32
Option B.
3 * 3 + (42) - 4
= 3 * 3 + 42 - 4
= 9 + 42 - 4
= 51 - 4
= 47
47 ≠ 32
Option C.
42 - 7 * 0
= 42 - 0
= 42
42 ≠ 32
Option D.
4 * 5 + 2 - 4 + 2
= 20 + 2 - 4 + 2
= 22 - 4 + 2
= 18 + 2
= 20
20 ≠ 32
None of them are equivalent to 32
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Tell whether the triangle with the given side lengths is a right triangle.
24 m, 45 m, 51 m
Yes or No
GIVING TONS OF BRAINLIEST IF YOUR ANSWER IS CORRECT!!
Answers
Easy geometry need help tho.......25pts
Answers
Answer:
22 in.
Step-by-step explanation:
total volume= big thingy + long thingy
=>x=2.2.3+5.2=12+10=22
The relationship between women's whole
number shoe sizes and foot length forms an
arithmetic sequence, where is the foot
length in inches that corresponds to a shoe
size of n. A women's size 3 lits a foot 8 inches
long and women's size 7 lits a fool
9
inches long
What is the common difference of the arithmetic
sequence?
Answers
Using arithmetic sequence concepts, it is found that the common difference is of 0.25.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, we have that:
[tex]a_3 = 8, a_7 = 9[/tex]
Hence:
[tex]a_7 = a_3 + (7 - 3)d[/tex]
9 = 8 + 4d
4d = 1.
d = 0.25.
The common difference is of 0.25.
More can be learned about arithmetic sequence concepts at https://brainly.com/question/6561461
four friends each took different path walking from the lunchroom to the gymnasium
Answers
finish the question..............
Answer:
Part 1- Lydia
Step-by-step explanation:
The full question should be
Four friends each took a different path walking from the lunchroom to the gymnasium. The table shows the distance that each of them walked. Who walked the farthest?
is f=9/5c+32 a linear function
Answers
Answer:
"a linear function has the form y = mx + b. "
A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? Assume g represents the number of goals and a represents the number of assists.
g + a = 24. g + 2 a = 42.
g + a = 24. 2 g + a = 42.
g + a = 42. g + 2 a = 24.
g + a = 42. 2 g + a = 24.
Answers
Answer:
g + a = 24. 2 g + a = 42.
Step-by-step explanation:
Each goal gets 2 points and each assist gets 1 point
If # of goals = g , and you get 2 points for each goal, then points acquired by goals can be represented by 2g
If # of assists = a, and you get 1 point for each assist, then points acquired by assists can be represented by a
The total # of points the player had was 42. This means that 2g + a = 42 (this is the first equation)
We are also told the player scored a total of 24 goals and assists. If g = # of goals and a = of assists, then g + a = 24 (this is the second equations)
So the two equations are g + a = 24. 2 g + a = 42.
Answer:
g + a = 24. 2 g + a = 42.
Step-by-step explanation
trust
[tex]x-5=y, xy+4=0,[/tex] then what is [tex]4x^{2} +4y^{2}[/tex]
Answers
Answer:
68
Given:
x - 5 = y ........ eq 1xy + 4 = 0 ...... eq 2Substitute equation 1 into 2
x(x - 5) + 4 = 0x² - 5x + 4 = 0x² - 4x - x + 4 = 0x(x-4) -1(x-4) = 0(x-4)(x-1) = 0x = 1, 4Find y:
y = x - 5
y = 1 - 5 (when x is 1)
y = -4
========
y = x - 5
y = 4 - 5 (when x is 4)
y = -1
Then 4x² + 4y²:
4(1)² + 4(-4)²4 + 6468Answer:
68
Step-by-step explanation:
[tex]\textsf{Equation 1}:\:x-5=y[/tex]
[tex]\textsf{Equation 2}:\:xy+4=0[/tex]
Substitute Equation 1 into Equation 2:
[tex]\implies x(x-5)+4=0[/tex]
[tex]\implies x^2-5x+4=0[/tex]
Factorize:
[tex]\implies (x-1)(x-4)=0[/tex]
Therefore:
[tex]x=1, x=4[/tex]
Substitute found values of [tex]x[/tex] into Equation 1 and solve for [tex]y[/tex]:
[tex]x=1\implies 1-5=-4[/tex]
[tex]x=4\implies 4-5=-1[/tex]
Substitute found values into [tex]4x^2+4y^2[/tex] and solve:
[tex]\textsf{For}\:(1,-4)\implies 4(1)^2+4(-4)^2=68[/tex]
[tex]\textsf{For}\:(4,-1)\implies 4(4)^2+4(-1)^2=68[/tex]
Note: As [tex]4x^2+4y^2[/tex], the values of x and y can be interchanged, so no need to input both sets of ordered pairs into the equation to solve.
Calculate the constant difference
1,2,3
Answers
1
Step-by-step explanation:
Seeing its an arithmetic sequence
T1=1......T2=2.....T3=3
To get your constant difference
T2=T1 is also equals to T3=T2
so 3-2=1 and 2-1=1
therefore the constant difference is 1
Fill in the table using this function rule
y=4x-12
Answers
Second from top is 12
Third from top is 20
Fourth from top is 28
Find the perimeter of the cabin below.
Answers
the image is formed of a rectangle and a square
perimeter of the cabin = perimeter of rectangle + perimeter of square
= 2(l+b) + 4×side
= 2(7+5) + 4×5
= 24 + 20
perimeter of the cabin = 44 cm
A circle is drawn inside a square.
20 cm
The square has a height of 20 cm.
Work out the shaded area.
Give your answer in terms of T.
Answers
So basically first you have to find the area of both the square and the circle which is 400 cm^2 and 100pi cm^2 respectively.
Then we subtract the area of circle from the square
So that becomes 400 - 100pi
Taking 100 common, 100(4 - pi)
Now this is for the 4 remaining corners
To get the area of the shaded region, divide the remaining area by 4
Now we get 25(4 - pi)
That’s your answer
Does the scenario describe an observational study or an experiment?
Answers
You are given the following system of equations: y:
- 13x + 85 and y = 15 + 4x . It is
known that this system of equations has two solutions. If the variable k represents the product of the two
×-values that satisfy the system, what is the value of k?
Answers
Answer:
70.
Step-by-step explanation:
1) to calculate the values of the 'x':
4x+15=x²-13x+85; ⇔ x²-17x+70=0; ⇔
x₁=7; x₂=10;
2) to calculate the required k:
k=x₁*x₂; k=7*10=70.
Please help me with this!
Answers
Answer: Solve this problem using the angle bisector theorem. This theorem states that when given a triangle with an angle bisector (line that cuts one of the angles in half, into two of the same angles), that angle bisector divides the opposite side into two segment proportional to the sides of the triangle
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and
2 plastic containers contain 6p quarts of water in all
how much water can the plastic container hold? give your answer is terms of p.
Answers
Answer:
12
Step-by-step explanation:
collect the like terms and divide
(p+6)2×2=64p+24=6p1) Water in a plastic container, p'= 10 - 3 p
2) Water in a glass container = 27 quarts
Water in a plastic container = 1 quarts
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
Now,
Let j represents water in one glass jag while p' represents the water in one plastic container,
Hence, According to the question,
⇒ j - p' = 6p+8 --------(1)
And, 2j+2p'=56p --------(2)
2 × equation (1)
⇒ 2 j - 2 p' = 12p + 16 ---------(3)
Equation (2) + equation (3)
We get, 4 j = 12 p + 72
⇒ j = 3 p + 18
Putting this value in equation (1),
We get, 3p+18-p'=6p+8
p' = -3p + 10 = 10 - 3p
Thus, water in a plastic container, p'= 10 - 3 p
b) If p=3
Water in a glass container = 3 × 3 + 18 = 27 quarts
Water in a plastic container = 10 - 3 × 3 = 1 quarts
Learn more about the mathematical expression visit:
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#SPJ2
E 18 - 3x D F 150° B с 3.1.1 Show that: BE = AB cos 0 sin (a - 6) - 3.x2 3.1.2 Show that the area of A BCE = x 2 4
Answers
Answer:
find the ratio of 15 min and 1hiyr
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answers
Answer:
6.3 :)
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
Now lets solve!!!
3^2 + b^2 = 7^2
9 + b^2 = 49
Now we subtract!!
49 - 9 = b^2
40 = b^2
Now we need to find the square root!!
[tex]\sqrt{40}[/tex] = 6.3
Have an amazing day!!
Please rate and mark brainliest!!!
To solve the equation x ^2 - 2x = 3 by the technique of completing the square, you would add 4 to each side of the equation as one of the steps to reaching the solution.
Answers
Answer:
x = -1
x = 3
Step-by-step explanation:
[tex]\sf x^2 - 2x = 3[/tex]
Add 1 to both sides:
[tex]\sf \implies x^2 - 2x+1 = 3+1[/tex]
Factor the left side:
[tex]\sf \implies (x-1)^2 = 4[/tex]
Square root both sides:
[tex]\sf \implies x-1 = \pm2[/tex]
Therefore:
[tex]\sf \implies x-1=-2 \implies x=-1[/tex]
[tex]\sf \implies x-1=2 \implies x=3[/tex]
–2} -(-5) = 0
-
Can someone please help me
Answers
(-2)-(-5)=0
bit 2 minuses= + so:
-2+5=0
3=0
expand and simplify (x+1)(x+9)
Answers
Expansion : [tex](x+1)(x+9) = x(x+9) + 1(x+9) = x^{2} +9x + x + 9[/tex]
Simplify : [tex]x^{2} +10x + 9[/tex]
Answer:
[tex]\huge\boxed{ \bf\:x^{2} + 10x + 9}[/tex]
Step-by-step explanation:
[tex](x + 1)(x+9)[/tex]
Let's expand it at first.
[tex](x + 1)(x + 9)\\= x (x + 9) + 1 (x + 9)\\= x^{2} + 9x + x + 9[/tex]
Now, simplify it.
[tex]x^{2} + x + x + 9\\= \boxed{ x^{2} + 10x + 9}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
