Write the equation of the line that passes through the points (-6,5) and (3,−5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
[tex]\displaystyle y-5=-\frac{10}{9}(x+6)[/tex]
Or:
[tex]\displaystyle y+5=-\frac{10}{9}(x-3)[/tex]
Step-by-step explanation:
We want to write the equation of a line that passes through the points (-6, 5) and (3, -5) in point-slope form.
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Thus, first, we need to find the slope. We can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{(-5)-(5)}{(3)-(-6)}=\frac{-10}{9}=-\frac{10}{9}[/tex]
Next, we can use either of the two given points. I'll use (-6, 5). So, let (-6, 5) be (x₁, y₁). Substitute:
[tex]\displaystyle y-(5)=-\frac{10}{9}(x-(-6))[/tex]
Or, fully simplified:
[tex]\displaystyle y-5=\frac{-10}{9}(x+6)[/tex]
Using the other point, we will acquire:
[tex]\displaystyle y-(-5)=-\frac{10}{9}(x-(3))[/tex]
Or, simplified:
[tex]\displaystyle y+5=-\frac{10}{9}(x-3)[/tex]
20 Points!!!
A ping pong ball is released from a height of 60 centimeters (cm) and bounces to a height that is 3/4 the previous height. What function estimates the height, H, in cm of the ping pong ball after x bounces?
Enter a number in each empty box to correctly complete the function.
H = ____ (____)^x
Multiply the starting height (60) by the height of each bounce (3/4) raised to the number of bounces (x)
H = (60)(3/4)^x
The answer to the given expression is:
H = 60(3/4)^x
What do we mean by exponents?A number is raised by another number which is called the power/exponent which implies that the number is multiplied by itself for that many number of times.
How do we solve for H?After every release, it bounces 3/4th of the previously released height.
After 1st bounce H = 60(3/4)
After 2nd bounce, it will be 3/4th of the previous H,
∴ H = 60(3/4)(3/4) = 60(3/4)^2
Similarly, after the 3rd bounce, it will be 3/4th of the previous H,
∴ H = 60(3/4)^2 * (3/4) = 60(3/4)^3
So it goes on like this. After x bounces,
H = 60(3/4)^x
Learn more about the Exponents at
https://brainly.com/question/11464095
#SPJ2
Select the correct answer from each drop-down menu. Mallory goes to the farmers market every weekend. She buys six apples for $0.75 each and a bagful of oranges that are priced at $1.25 per orange. The total charge is $14.50. Write the equation representing this situation where n represents the number of oranges.
Answer:
a) The equation for the situation = 14.50 = 4.5 + 1.25n
b) The number of oranges she bought = 8 oranges
Step-by-step explanation:
Where n represents the number of oranges.
The equation is written as
Total charge = $0.75 × 6 + $1.25 × n
$14.50 = $0.75 × 6 + $1.25 × n
14.50 = 4.5 + 1.25n
1.25n = 14.5 - 4.5
1.25n = 10
n = 10 / 1.25
n = 8 oranges
someone help me answer these two
I will give BRAINLIEST to the correct answer
Find the measure of angle 3
Answer:
2X+100 =8X+208
8X-2X=100-208
6X=-108
X=-18
8X+208=(8×-18)+208
=-144+208
=64
ANGLE 3=180-64
=116
Answer: The measurement of angle #3 on the photo you provided it would be a 300 Degree angle if that is what you're asking
Step-by-step explanation: If you're asking what measure of an angle #3 is the correct measurement is 300 Degrees
What is the y-intercept for y = 5x^2 + 2x -2?
Answer: (0, -2) or -2
Step-by-step explanation:
Sub in 0 for x since at the y intercept x is 0
[tex]y=5(0)^2+2(0)-2\\y=5(0)+0-2\\y=0+0-2\\y=-2[/tex]
A ball is dropped from a height of 5m. After each bounce it rises to 35% of its previous height. After how many bounces does the ball reach a Height of less than 50cm?
Answer:
After the third bounce the ball reaches a height of less than 50cm.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient between consecutive terms is always the same, and it's called common ratio. The nth term of a geometric sequence is given by:
[tex]A_n = A_0(r)^{n}[/tex]
In which [tex]A_0[/tex] is the first term and r is the common ratio.
A ball is dropped from a height of 5m.
This means that [tex]A_0 = 5[/tex]
After each bounce it rises to 35% of its previous height.
This means that [tex]r = 0.35[/tex]
Thus
[tex]A_n = A_0(r)^{n}[/tex]
[tex]A_n = 5(0.35)^{n}[/tex]
After how many bounces does the ball reach a Height of less than 50cm?
50cm = 0.5m. This is n for which [tex]A_n = 0.5[/tex]. Thus
[tex]A_n = 5(0.35)^{n}[/tex]
[tex]0.5 = 5(0.35)^{n}[/tex]
[tex](0.35)^n = \frac{0.5}{5}[/tex]
[tex](0.35)^n = 0.1[/tex]
[tex]\log{(0.35)^n} = \log{0.1}[/tex]
[tex]n\log{0.35} = \log{0.1}[/tex]
[tex]n = \frac{\log{0.1}}{\log{0.35}}[/tex]
[tex]n = 2.19[/tex]
Rounding up:
After the third bounce the ball reaches a height of less than 50cm.
Hannah has a part-time job making holiday wreaths. This week, she made x medium wreaths, twice as many large wreaths as medium wreaths, and 12 as many small wreaths as medium wreaths. In terms of x, how many wreaths did Hannah make this week?
Answer:
Total number of wreaths = 3.5 wreaths
Step-by-step explanation:
Given:
Number of medium wreaths = x
Number of larger wreaths = 2[Number of medium wreaths]
Number of small wreaths = [1/2][Number of medium wreaths]
Find:
Total number of wreaths
Computation:
Total number of wreaths = Number of medium wreaths + Number of large wreaths + Number of small wreaths
Total number of wreaths = Number of medium wreaths + 2[Number of medium wreaths] + [1/2][Number of medium wreaths]
Total number of wreaths = x + 2x + 0.5x
Total number of wreaths = 3.5 wreaths
Simplify the expression ( a^3/2)^3
Answer:
(a^9/8)
Step-by-step explanation:
(a/b)^n = (a^n/b^n)
Please help I will award brainless to whoever helps please it’s urgent
Answer:
128 sq units :)
Step-by-step explanation:
hope this helps! have a great day :)
An icicle is 12 inches long and melts at a rate of 1/4 inch per hour
Answer:
It will take 48 hours for the entire icicle to melt.
Step-by-step explanation:
12 divided by 1/4 = 48
The linear equation to model the situation is f(x) = -1/4x + 12
Complete questionWrite a linear equation in slope-intercept form to model the situation. An icicle is 12 inches long and melts at a rate of 1/4 inch per hour.
How to determine the linear equation?The given parameters are:
Length = 12 inchesRate = 1/4 inch per hourThe above means that:
Y-intercept (c) = 12Slope (m) = -1/4A linear equation is represented as:
f(x) = mx + c
Where f(x) represents the function and x represents the number of hours.
So, we have:
f(x) = -1/4x + 12
Hence, the linear equation to model the scenario is f(x) = -1/4x + 12
Read more about rate at:
https://brainly.com/question/4931057
#SPJ6
is How many oranges did
Sally eat last month? a statistical question
Answer:
25
Step-by-step explanation:
Lets say it's a 30 day month. Sally really likes oranges so she eats them a lot.
Share $150 among John, Mary, and Sarah so that each of the two girls receives twice as much as John. Calculate the amount of money Jon received.
In a bag there are blue sweets and red sweets. The ratio of blue sweets to red sweets is 5:3 What fraction of the sweets are blue?
Answer:
5/8
Step-by-step explanation:
SUM OF RATIOS = 5 + 3 = 8
fraction of blue sweet = blue sweet ratio / sum of ratios = 5/8
20 POINTS PLEASE ANSWER!
Answer:
area = 15 units ^2
Step-by-step explanation:
you look at width times height (just count the blocks vertical and horizontal)
width = 3 units
height = 5 units
area = 15 units ^2
The basketball team did not record how many baskets each player made during the last game. Zulie remembers that she made three
times as many baskets as Aileen. Melody knows that she made four more baskets than Aileen. Zoe thinks that she made 3 fewer baskets than Aileen.
Abigail is sure that she made the same number of baskets as Zoe. Altogether the five players made 82 baskets. How many baskets did each player
make?
Answer:
There is a mistake in the question. x results in a decimal answer, which is not possible for number of hoops.
Step-by-step explanation:
Aileen: x
Zulie: 3x
Melody: 4 + x
Zoe: x - 3
Abigail: x - 3
82 = (x) + (3x) + (4+x) + (x-3) + (x-3)
Combine Like Terms
x + 3x + x + x + x = 7x
4 - 3 - 3 = -2
7x - 2 = 82
7x = 80
x results in a decimal answer, which is not possible for number of hoops.
On a math exam, Joel had a score of 90, which was exactly 2 standard deviations above the mean. The standard deviation for the test is 3.
Answer:
84
Step-by-step explanation:
Score = 90
Standard deviation = 3
Score = mean + 2(standard deviation)
90 = mean + 2(3)
90 = mean + 6
Mean = 90 - 6
Mean = 84
I need help asap pls pls pls...
Answer:
c)
Step-by-step explanation:
please don't trust ;-;
Kara and Karl love steak, fried chicken, hamburgers, mashed potatoes, and french fries. They like green beans and peas. How many different meals including a meat, potatoes and a green vegetable can they make from these choices? 8 meals 16 meals a. C. b. 12 meals d. 24 meals
Answer:
steak, chicken, and hamburger are meats. 3 meats.
The French fries and mashed potatoes are potatoes. 2 Potatoes.
And Green beans and peas are green vegetables. 2 Vegetables.
I think we just do 3 x 2 x 2 = 12 Meals.
hope that helps bby<3
Can anyone help me out?
Answer:
55° because 2and 6 are corresponding angles (they are equal)
6 and 8 are vertically opposite angles (they are equal)
Step-by-step explanation:
hope this is helpful
if x and 5x are supplementary angles, find them
Answer:345678098321
Step-by-step explanation: I think so lol
Answer:
x+5x=180( adj.suppl.ls)
6x=180
6x÷6=180÷6
x=30
What is the simplified expression for -3(2x-y)+2y+2(x+y)
Answers:
8x+y
y-4x
7y-4x
-4x-y
Answer:
7y - 4x
Step-by-step explanation:
Given
- 3(2x - y) + 2y + 2(x + y) ← distribute parenthesis
= - 6x + 3y + 2y + 2x + 2y ← collect like terms
= 7y - 4x
10 points!
If you are going to answer, actually answer!
Answer:
1/27
Explanation:-
(1/3)^3=(1x1x1)/(3x3x3)=1/27
Answer:
0.03703703703 or
²/27
sorry i am late but still hope I helped
Step-by-step explanation:
Please help me that is the volume???
Let us first find the hieght of the triangle:
= 16² = p² + 8²
= 256 = p² + 64
= 256 - 64 = p²
= √192 = p
= 13.85 = p
Area of equilateral trianglular prism:
= ⅓× l² × h
Here, l = length of side and h is height= ⅓ × 16² × 13.85
= 256 × 13.85 × ⅓
= 1181.86 cm³
= 1182 cm³ (approx)
Pls help I don’t know how to do this
The right answer is a i think i don't known step by step
Step-by-step explanation:
a
a
(pls help i’m suffering) 3.06a Finding Standard Form by Completing the Square
Classify each as Circle, Quadratic (parabola) or other
(x - 5)2 + (v - 2) = 16
= 100
22 - x = 25
(x - 2) - (y + 5)= 10
y = 2x + 5
Step-by-step explanation:
A circle equation is represented by
[tex]x {}^{2} + {y}^{2} = r {}^{2} [/tex]
A circle have both terms to the 2nd. degree
The 1st equation, 2nd equation, 4th equation are circles.
A quadratic is represented by
[tex] {x}^{2} + bx + c[/tex]
A quadratic equation only has one term that is second degree.( meaning if x and y are both to the 2nd degree, it will not be a quadratic, it will be a circle.
The 3rd equation is a quadratic.
The fifth equation has a leading coefficient at the degree of 1 so it is other(linear)
This language derives from the area of a square being its side length multiplied by itself. The word "quadratic" comes from quadratum, the Latin word for square.
What is a quadratic function?f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.
From the given table we can get the dy/dx which is the slope (m) ,
Therefore,
dy/dx = (7 - 10 ) / ( 4 - 3 )
dy/dx = -3
Now,
( y - y1 ) = m ( x - x1 )
Putting the value from the table,
( y - 10 ) = -3 ( x -5 )
=> y - 10 = -3x + 15
=> 3x + y = 25
To learn more about quadratic function refer
https://brainly.com/question/28870194
#SPJ2
Is 3:5 and 5:7 equivalent
Ratios
Answer:
no its not equal
Given the linear equation 5x+3y-9=0. Write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines
Answer:[tex]5x+3y+1=0[/tex]
Step-by-step explanation:
Given
The linear equation is [tex]5x+3y-9=0[/tex]
The other linear equation parallel to the given line can be represented by
[tex]5x+3y+c=0[/tex]
Here, c can take any value . for example c=1, line becomes
[tex]\Rightarrow 5x+3y+1=0[/tex]
Find the opposite of each polynomial.
Answer:
Step-by-step explanation:
The word "opposite" is indicated by the - sign out front. Mathematically, we multiply a -1 into the parenthesis which, not coincidentally, changes the signs of everything inside the parenthesis, making them "opposite". The opposite of this polynomial is
- a - b - c
A rectangle has an area of 117 cm^2 and width of 9 cm. Find its lenght
Answer:
13cm
Step-by-step explanation:
if the area is 117 then to find out the missing length, you divide 117 by 9 which gets you 13.
to check its correct, 13 x 9 = 117cm^2