Answer:
y = -1/2 x + 1
Step-by-step explanation:
Lines that are perpendicular to each other have slopes that are negative reciprocals. You get the negative reciprocal of a number by flipping the fraction for the slope, then changing the positive/negative.
The lines are written in slope-intercept form, y = mx + b.
"x" and "y" are points on the line.
"m" is the slope.
"b" is the y-intercept.
In y = 2x + 8, the slope is 2. Find its negative reciprocal.
Write the slope as a fraction.
[tex]m=2=\frac{2}{1}[/tex]
Flip the fraction.
[tex]m=\frac{1}{2}[/tex]
Change the negative/positive.
[tex]m=-\frac{1}{2}[/tex] This is the slope of the perpendicular line.
Now we need to find the y-intercept, "b", for our line. We know m = -1/2, and we know a random point (6, -2). Points are written (x, y), which mean x = 6 and y = -2. Substitute the values of the point and the slope into y = mx + b.
[tex]y = mx + b[/tex]
[tex]-2 = -\frac{1}{2}*6 + b[/tex] Multiply (-1/2)(6) by combining into the numerator
[tex]-2 = -\frac{6*1}{2} + b[/tex] Simplify numerator
[tex]-2 = -\frac{6}{2} + b[/tex] Reduce fraction
[tex]-2 = -3 + b[/tex] Isolate "b" now
[tex]-2 + 3 = -3 + b + 3[/tex] Add 3 to both sides
[tex]1 = b[/tex] Solved for "b"
[tex]b=1[/tex] Write the variable on the left side for standard formatting
b = 1 and m = -1/2
Substitute them into slope-intercept form for the final answer.
y = -1/2 x + 1
To find the equation of a line perpendicular to a given line and passing through a specific point, use the negative reciprocal of the original line's slope. Applying this to the point-slope form of the line equation gives y = -(1/2)x + 1, which is the correct answer as per the given options.
Explanation:The subject of the question is about writing the equation of a line that is perpendicular to another line, specifically y = 2x + 8, and passes through a specific point (6, -2). The concept involved here is the slope of the lines. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Since the slope of our given line is 2, the slope of the line that is perpendicular to this would be -1/2.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes, we can substitute m = -1/2 and (x1, y1) = (6, -2). Therefore, the equation of the line is y = -(1/2)x + 1.
The correct answer from the given options is (D) y = -(1/2)x + 1.
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A polygon plotted on a coordinate plane has 6 vertices. What is the name of the polygon?
Answer: the polygones name is a hexagon i believe
Step-by-step explanation:
hex means six in greek and has an internal angle of 120 so the correct ansewer is a hexagon.
A polygon with six vertices is called a hexagon.
It is a two-dimensional figure with six sides and six angles. Hexagons are common in various real-life patterns and have properties like area and perimeter.
A polygon plotted on a coordinate plane with six vertices is known as a hexagon. A hexagon is a two-dimensional geometric figure with six angles and six sides.
Polygons are closed figures made up of straight line segments. When the polygon has six sides, it has interior regions and exterior regions that divide the plane it lies on. Each vertex connects two sides of the hexagon, forming angles at each vertex.
A circle has an area of 324π cm2. What is the radius? a. 18 cm c. 18π cm b. 36π cm d. 36 cm
Answer:
a. 18 cm
Step-by-step explanation:
We are given that a circle has an area of 324π cm2. We are required to determine its radius. The formula for the area of a circle with radius r units is;
[tex]A=pi*r*r[/tex]
We plug in the area given and solve for r;
[tex]324pi=pi*r^{2}\\\\r^{2}=324\\\\r=18[/tex]
The radius of the circle is 18 cm
Answer:
a. 18 cm
Step-by-step explanation:
Area of a circle is given by: A=πr²
where r is the radius and A the area.
therefore we substitute A with the value for the area in the question.
324π=πr²
cancelling the factor π on both sides gives: 324=r²
√324=r
r=18cm
Connie has to solve the following problem.
5 boxes of cereal costs $12.50. How much will 18 boxes cost.
Choose EVERY proportion Connie could use to solve this problem.
= 12.50
12.50
13,5 = 18
Answer:
Step-by-step explanation:
= 12.50
12.50
13,5 = 18
To solve the problem, Connie can use the concept of proportion by setting up an equation with the given ratios.
By cross-multiplying and solving for x, the cost of 18 boxes of cereal can be determined.
Explanation:To solve this problem, Connie can use the concept of proportion.
A proportion is an equation that states that two ratios are equal.
In this case, the ratio of the cost of 5 boxes of cereal to the number of boxes is equal to the ratio of the cost of 18 boxes of cereal to the number of boxes.
Let's set up the proportion:
5 boxes / $12.50 = 18 boxes / x
To solve for x, we can cross-multiply:
5x = 18 * $12.50
Now, divide both sides by 5 to isolate x:
x = (18 * $12.50) / 5
Calculate the value of x to find the cost of 18 boxes of cereal.
PLEASE HELPPPPPPPP! THANK YOU!
The formula for area of a circle is:
A = [tex]\pi r^{2}[/tex]
In this case the radius is 7.4 cm so...
pi * 7.4^2
pi * 54.76
172.0033
so...
172.0 cm^2
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEASE HELP ME WITH THIS QUESTION.
Answer:
The ball hits the ground after 7.6 sec.
Step-by-step explanation:
Realize that h = 0 when the rocket hits the ground. Thus, we set h(t) = y = to 0 and solve for time (t):
y = 0 = h(t) = -16t^2 + 113t + 65.
Application of the quadratic formula is the easiest approach here. Note that a = -16, b = 113 and c = 65.
The discriminant is b^2-4ac, or, in this case, 113^2 - 4(-16)(65) = 16929.
Because the discriminant is positive, we confirm that this equation has two real, unequal roots.
The time values are as follows:
-113 ± √16929
t = --------------------- = -17.11/ (-32) sec, which we must reject
-32
because time in
this situation may not be (-).
The other root is:
-113 ± √16929
t = --------------------- = 7.6 sec
-32
The ball hits the ground after 7.6 sec.
Which of the following expressions are equivalent to 48? Select all that apply.
4(-3 +15)
4(4 + 2 + 5)
4(7 + 2 + 3)
4(8 + 6-2)
4-2-4 + 16)
Answer:
see below
Step-by-step explanation:
4(-3 +15) = 48
4(4 + 2 + 5) = 44
4(7 + 2 + 3) = 48
4(8 + 6-2) = 48
4(-2-4 + 16) = 40
We are required to select all expressions equivalent to 48
All expressions are equivalent to 48 except 4(4 + 2 + 5) and 4(-2-4 + 16)
Check all options:
4(-3 +15)= 4(12)
= 48
4(4 + 2 + 5)= 4(11)
= 44
4(7 + 2 + 3)= 4(12)
= 48
4(8 + 6-2)= 4(12)
= 48
4(-2-4 + 16)= 4(10)
= 40
Therefore, all expressions are equivalent to 48 except 4(4 + 2 + 5) and 4(-2-4 + 16)
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Help~~~~~~~~~~~~~~~~~~~~~~~~~
Answer:
28.25 square units
Step-by-step explanation:
A circumference of the circle is
[tex]C=2\pi r,[/tex]
where r is the radius of the circle.
So,
[tex]18.84=2\pi r\\ \\r=\dfrac{18.84}{2\pi}=\dfrac{9.42}{\pi}\ cm[/tex]
The area of the circle is
[tex]A=\pi r^2[/tex]
Substitute the value of the radius:
[tex]A=\pi \cdot \left(\dfrac{9.42}{\pi}\right)^2=\dfrac{9.42^2}{\pi}\approx 28.25\ un^2[/tex]
Answer:
Step-by-step explanation:
18.84=2\pi r\\ \\r=\dfrac{18.84}{2\pi}=\dfrac{9.42}{\pi}\ cm
The area of the circle is
find the slope of the line that passes through the points (-4,2) and (2,6)
Answer:
[tex]\large\boxed{\text{The slope}\ m=\dfrac{2}{3}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-4, 2) and (2, 6). Substitute:
[tex]m=\dfrac{6-2}{2-(-4)}=\dfrac{4}{6}=\dfrac{4:2}{6:2}=\dfrac{2}{3}[/tex]
The total cost of renting a movie for different numbers of days is shown in the table.
Which equation was used to create this table?
look at this table
The equation that fits this pattern is: [tex]\[ \text{Total Cost} = 3 \times (\text{Number of Days}) + 2 \][/tex]
The table depicts a linear relationship between the number of days a movie is rented and its total cost.
To identify the equation used to create this table, we can observe that each additional day increases the total cost by a constant amount.
Considering the initial cost and the rate of increase, we can formulate the equation. In this case, the initial cost appears to be $2, and for each additional day beyond the first, the cost increases by $3.
Therefore, the equation that fits this pattern is:
[tex]\[ \text{Total Cost} = 3 \times (\text{Number of Days}) + 2 \][/tex]
This equation represents a constant rate of increase of $3 per day, plus the initial cost of $2.
Thus, it accurately models the relationship between the number of days and the total cost.
The probable question may be:
The total cost of renting a movie for different numbers of days is shown in the table.
Which equation was used to create this table?
| Number of Days | Total Cost |
|----------------|------------|
| 1 | $5 |
| 2 | $8 |
| 3 | $11 |
| 4 | $14 |
| 5 | $17 |
The equation ac=5 represent a(n) ___ variation
Answer:
Direct Variation
Step-by-step explanation:
The relationship between two variables such that y = kx if k is a nonzero number. Also, as one quantity increases, the second quantity increases or as one quantity decreases, the second quantity decreases. Therefore ac=5 is a direct variation
Anton is drawing a flag of Switzerland, which has a square shape, for a school project. If he wants the flag to have sides that are 16 inches long, what will be the area of the completed flag?
Answer:
64 in2
hope it helps (:
Answer:
A
Step-by-step explanation:
it is what it is; you either know it or you don't.
When converting from inches to feet, the measurement in inches, m, of an object varies directly with
What the object adds up to
Write each expression using a single exponent. x to the ninth over x squared
Answer:
x^7
Step-by-step explanation:
The expression is written as a single exponent in x⁷
How to simply the expressionIndex forms are forms used to represent numbers or variables that are too large or small in more convenient forms.
From the information given, we have that the expression is;
x to the ninth over x squared
This is represented as;
x⁹/x²
Since the forms are of like bases, subtract the exponents, we get;
x⁹⁻²
Subtract the exponents, we get;
x⁷
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NNEED HELP!! GEETSS BRAINLIEST**
Answer:
D. [tex]y=3\cos \left(\dfrac{4}{3}x-2\pi\right)+2[/tex]
Step-by-step explanation:
The period of the functions [tex]y=\cos x,\ y=\sin x[/tex] is [tex]2\pi.[/tex]
The period of the function [tex]y=a\cos (kx+b),\ y=a\sin(kx+b)[/tex] is ALWAYS [tex]\dfrac{2\pi}{k}[/tex]
In your case, you have function [tex]y=-3\sin \left(\dfrac{2}{3}x-2\pi \right)+2[/tex] and this function has the period
[tex]\dfrac{2\pi}{\dfrac{2}{3}}=3\pi.[/tex]
You need to find the function that will have the period that is half of [tex]3\pi,[/tex] so
[tex]\dfrac{3\pi}{2}=\dfrac{2\pi}{k}\\ \\3k=4\\ \\k=\dfrac{4}{3}.[/tex]
So, correct choice is
[tex]y=3\cos \left(\dfrac{4}{3}x-2\pi\right)+2[/tex]
Answer:
The answer is y = 3 cos(4/3 x - 2π) + 2 ⇒ last answer
Step-by-step explanation:
* Lets revise the sine function
- If we have a sine function of the form f(x) = Asin(Bx + C) + D, where
A, B , C and D are constant, then
# Amplitude is A
- The Amplitude is the height from the center line to the peak .
Or we can measure the height from highest to lowest points and
divide that by 2
# Period is 2π/B
- The period goes from one peak to the next
# phase shift is C (positive is to the left)
- The Phase Shift is how far the function is shifted horizontally
from the usual position.
# vertical shift is D
- The Vertical Shift is how far the function is shifted vertically from
the usual position.
* Now lets solve the problem
∵ y = -3sin(2/3 x - 2π) + 2
- the period is 2π ÷ 2/3 = 2π × 3/2 = 3π
∴ The period of the function is 3π
- We look for a function has one-half (3π), means 3π/2
* Lets look to the answer to find the right one
- All of them have the same value of B except the last one, lets
check it
∵ y = 3cos(4/3 x - 2π) + 2
∵ B = 4/3
∴ The period = 2π ÷ 4/3 = 2π × 3/4 = 6π/4 = 3π/2
∵ 3π/2 is half 3π
∴ The last answer is right
How many edges, vertices, and faces does the figure shown have?
A.12 edges, 6 vertices, and 8 faces
B.12 edges, 8 vertices, and 6 facesC.
8 edges, 12 vertices, and 6 faces
D.12 edges, 8 vertices, and 8 faces
Answer:
A. 12 edges. 6 vertices, and 8 faces.
Step-by-step explanation:
The edges are the places where the faces meet. They can be easily identified as the lines that form the shape. There are 12 edges.
The vertices are the places where the edges meet. They are more commonly known as the corners of the figure. There are 6 vertices.
The faces are the flat sides/surfaces of the figure. In this case, the faces are the triangles. There are 8 faces.
Hope this helps!
The given figure has 12 edges, 6 vertices, and 8 faces. This can be obtained by understanding what edges, vertices and faces are and counting them.
What are edges, vertices and faces?Edge: A line segment on the boundary and is known as side of a polygon.Vertex (plural: vertices): A point where two line segments meet forming an angle.Face: A flat surface of a solid.For example, a cube has 12 edges, 8 vertices and 6 faces.In the given figure we can count the edges, vertices and faces.
It is observed that there are 12 edges, 6 vertices, and 8 faces.
Hence the given figure has 12 edges, 6 vertices, and 8 faces. The correct answer is A.
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PLEASE HELP! WHAT'S X??? URGENT!
Answer:
4
Step-by-step explanation:
The first thing you need to do is find the geometric mean between 2 and 6.
That is the ratio that they hypotenuse of the largest triangle is divided into.
altitude^2 = 2* 6
altitude^2 = 12
altitude = sqrt(12)
altitude = 2 sqrt(3)
Now use Pythagorus to find x
x^2 = 2^2 + altitude^2
x^2 = 2^2 + 12
x^2 = 4 + 12
x^2 = 16
x = 4
how many 4 letter words can you make from a list of 12 letters, if you use each letter only once in each word?
Answer:
it would be 3 because if you list words then just divide 12 by 4 and you get 3
The number of the 4 letter words that can be made from a list of 12 letters will be 495.
What is a combination?Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Then the number of the 4 letter words can be made from a list of 12 letters will be
¹²C₄ = 12! / [(12 - 4)! x 4!]
¹²C₄ = 12 x 11 x 10 x 9 x 8! / 8! x 4 x 3 x 2 x 1
¹²C₄ = 11 x 5 x 9
¹²C₄ = 495
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In triangle DEF, FE = 12 and angle D=62. Find DE to the nearest tenth.
Answer:
about 13.6
Step-by-step explanation:
Assuming DEF is a right triangle, you use trig functions to solve this problem. Out on sin, cos, and tan, sin would work for this problem. You plug in the numbers and put it into a calculator. This gives you the answer after you round to the nearest tenth. See work for more.
Answer: 6.4
Step-by-step explanation: trust
A board is made up of 9 squares. A certain number of pennies is placed in each
square, following a geometric sequence. The first square has 1 penny, the second
has 2 pennies, the third has 4 pennies, etc. When every square is filled, how many
pennies will be used in total?
A
512
B
511
256
D
81
Answer:
B) 511
Step-by-step explanation:
1. How many pennies are in the last square:
Sequence: # of pennies = 2^(box # - 1)
Plug in: # = 2⁸
Solve: # of pennies in box 9 = 256
2. Process of elimination:
Not C or D, since the total must be greater than 256.
So the answer is B, not A, since 2⁰ + 2¹ ... 2⁷ = 2⁸ + 1.
Final answer:
Using the formula for the sum of a geometric sequence, we find that a total of 511 pennies will be placed on the board after the 9 squares are filled, following the sequence where each square has double the pennies of the previous one.
Explanation:
The student is asked to calculate the total number of pennies used when they are placed in each of the 9 squares of a board following a geometric sequence, starting with 1 penny and doubling the amount in each subsequent square. To find the total, we use the formula for the sum of the first n terms of a geometric sequence, which is Sn = a1(1 - [tex]r^{n}[/tex])/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a1 = 1 (first square), r = 2 (doubling each time), and n = 9 (nine squares). Therefore, the sum is:
[tex]S_{9}[/tex] = 1(1 - [tex]2^{9}[/tex])/(1 - 2) = 1(1 - 512)/(-1) = 511 pennies.The correct answer is B: 511 pennies will be used in total when every square is filled.
What’s the square root of 36?
Answer:
6
Step-by-step explanation:
the square root is basically exponents 6*6 is 6^2 which is 36.
Suppose Jawan works 6 days. Using a rule that relates the hours worked to the amount earned if he work 36 hours
Answer:
huh
Step-by-step explanation:
Covington, Georgia has a total area of 13.9 square miles and a population of 11,547 people. What is the population density of the city?
Answer: 830.7 per square mile.
Step-by-step explanation:
The formula for population density is Number of people divided by total area.
11,547 divided by 13.9 is 830.7.
Hope this helps!
The population density of Covington, Georgia is calculated by dividing the total population (11,547 people) by the total area (13.9 square miles). The result is approximately 830.79 people per square mile.
Explanation:The population density of a place is calculated by dividing the total population by the total area. In this case, Covington, Georgia, has a total population of 11,547 people and a total area of 13.9 square miles. Thus, to determine the population density, we will use the following formula: Population Density = Total Population / Total area.
By substituting our given numbers into this formula, we would get: Population Density = 11,547 / 13.9. This calculation results in a population density of approximately 830.79 people per square mile for Covington, Georgia.
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what is the adverage of the numbers 12 13 13?
Answer:12.66667
Step-by-step explanation:
Answer:
Average = (sum of numbers) ÷ (the amount of numbers)
a = (12 + 13 + 13) ÷ 3
a = 38/3 = 12.6...
41,692.58
What place is the 6 in, in the number above?
A) hundreds
B) ones
C) tens
D) thousands
The correct answer is A. Hundreds. I hope this helps : )
A is the correct answer
4 people divide 10 scoops of lentils equally.
How many scoops of lentils does each person get?
Answer:
Step-by-step explanation:
0.25
Answer:
Between 2 and 3 scoops
and 10 divided by 4
Step-by-step explanation:
The ratio of the volumes of the similar solids is _____ 25:1 5:1 125:1
The ratio of the surface areas of the similar solids is _____ 125:1 5:1 25:1
The ratio of the heights of the similar solids_____ 125:1 5:1 25:1
Two spheres with different radii measurements are_____ similar (always, never sometimes)
The length of the diameter of a sphere is 8 inches. The volume of the sphere is____ the surface area of the sphere. (less than, greater than, equal to)
Answer:
Part 1)
a) The ratio of the heights of the similar solids is 5/1
b) The ratio of the surface areas of the similar solids is (5/1)²=25/1
c) The ratio of the volumes of the similar solids is (5/1)³=125/1
Part 2) Two spheres with different radii measurements are always similar
Part 3) The volume of the sphere is greater than the surface area of the sphere
Step-by-step explanation:
Part 1) we know that
The ratio of the corresponding heights of the similar solids is equal to the scale factor
The ratio of the surface areas of the similar solids is equal to the scale factor squared
The ratio of the volumes of the similar solids is equal to the scale factor elevated to the cube
In this problem
The scale factor is 5/1
therefore
a) The ratio of the heights of the similar solids is 5/1
b) The ratio of the surface areas of the similar solids is (5/1)²=25/1
c) The ratio of the volumes of the similar solids is (5/1)³=125/1
Part 2)
we know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
In this problem to prove that two spheres are similar, a translation and a scale factor (from a dilation) will be found to map one sphere onto another.
therefore
Two spheres with different radii measurements are always similar
Part 3) The length of the diameter of a sphere is 8 inches
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=8/2=4\ in[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (4)^{3}[/tex]
[tex]V=85.33\pi\ in^{3}[/tex]
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute
[tex]SA=4\pi (4)^{2}[/tex]
[tex]SA=64\pi\ in^{2}[/tex]
therefore
The volume of the sphere is greater than the surface area of the sphere
the graph shows 2 sides and 3 vertices of a parallelogram.
which point best represents the 4th vertex of the parallelogram
A. (6,4)
B. (7,4)
C. (7,5)
D. (8,5)
The fourth point would need to be at the top and in line horizontally with The point at (3,4) so the Y value needs to be 4.
The first top red dot is 2 units to the right of the lower dot, so the 4th dot needs to be 2 units to the right on the other lower dot.
The 4th point needs to be at (7,4)
The answer is B.
Answer:
b 7,4
Step-by-step explanation:
Should i wear a yellow shirt or a purple shirt
Answer:
Yellow of course but it depends on how you look in the colors
Step-by-step explanation:
Answer:
If your day is not feeling good then I would recommend a yellow to brighten it up. If your day is already good but feeling not good where a purple to stand out. Good Luck I hope your day is doing well!!
Step-by-step explanation:
Let f(x) = Square root of 6x and g(x) = x - 3. What's
the smallest number that is in the domain of
fºg?
For this case we have the following equations:
[tex]f (x) = \sqrt {6x}\\g (x) = x-3[/tex]
We must find [tex](f_ {o} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {o} g) (x) = \sqrt {6 (x-3)}[/tex]
We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined. That is to say:
[tex]6 (x-3) \geq0\\(x-3) \geq0\\x \geq3[/tex]
Then, the domain is given by [3, ∞)
Answer:
The smallest number that is the domain of the composite function is 3
Answer: on Plato I got it wrong for the answer 3
Step-by-step explanation:
What is the rule for the reflection
Answer:
hey user!
your answer is here...
laws ( rules ) of reflection are :-
• angle of incidence is equal to angle of reflection.
• the incident ray, Normal ray and reflected ray all lie in same plane.
cheers!!
Step-by-step explanation: