The functions that have a maximum and are transformed are:
q(x) = –5(x + 10)2 – 1t(x) = –2x2 – 4x – 3What is a function?This is the rule in mathematics that is used to show the relationship that is in existence between variables.
In order to check for the minimum and the maximum, we have to check on the coefficient of the x square. When it is negative, we have a maximum. When it is positive it is a minimum.
Read more on maximum and minimum here:
https://brainly.com/question/15903408
#SPJ1
Answer: b and e
Step-by-step explanation: algebra edge 2022 :)
QUESTION IS DOWN BELOW
Using proportions, the ratios are given as follows:
a) 9:196.
b) 27:2744.
c) 3:14.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the standard ratio of 3:14 units, we have that:
The area is given in units squared, hence the ratio will be of [tex]\left(\frac{3}{14}\right)^2 = \frac{9}{196}[/tex].The volume is given in cubic units, hence the ratio will be of [tex]\left(\frac{3}{14}\right)^3 = \frac{27}{2744}[/tex]. The width is also given in units, hence the ratio is also of 3:14.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
vase with a circular base exerts a force of 15 N on a table with a pressure of 700 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
radius =
cm
The radius of the base is 8.245 cm
Given, a vase with a circular base exerts
Pressure = 700 N/m²
Force = 15 N
Area = ?
∴ area = πr²
By finding out the area of the vase we can calculate the radius.
We know that Pressure = Force/Area
According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.
therefore apply the above the formula to find out the area and radius.
700 = 15/πr²
πr² = 15/700
πr² = 3/140
r² = 3/140 × 3.14
since π value is 3.14
r² = 0.0068
r = √0.0068
r = 0.0824 m
r = 0.0824 × 100
r = 8.245 cm
we get radius as 8.245 .
Hence we get the radius of the base of the vase as 8.245 cm.
Learn more about "Force pressure and area" here-
brainly.com/question/26369337
#SPJ10
Pls help! Geometry!
How long is the other side?
Answer: 18 feet
Step-by-step explanation:
The area of a rectangle is given by [tex]A=lw[/tex], which means that the length of the unknown side is [tex]\frac{216}{12}=18[/tex] feet.
Find the angle [OA] makes with the positive x-axis if the x-coordinate of the point A on the unit circle is 0.222
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
How to find an angle in an unit circle
Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:
[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]
tan θ ≈ 77.173°
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
To learn more on unit circles: https://brainly.com/question/12100731
#SPJ1
You are in charge of planning a reunion party for your high school alumni. The food will cost $12 per person. The rental fee for the room is $650. The entertainment fee is $730. Other miscellaneous expenses costs $1,000. If 120 alumni are expected to come then what will be the total cost? How much must each alumnus contribute to cover the cost of the reunion (round to the nearest whole number)?
Answer:
$3820 total, $32 per alumnus.
Step-by-step explanation:
The total cost will be [tex]12\times120+650+730+1000=3820[/tex]
Each alumnus pays [tex]\frac{3820}{120} =31\frac{5}{6}[/tex]
Rounding to nearest whole number = $32 per alumnus.
which number would be equivalent to the expression: 3 times 4 to the second power plus 6 divided by 2
The given expression is equivalent to the number 147.
We have given that,
[tex](3\times4)^2+\frac{6}{2}[/tex]
We have to determine the value of the given expression.
What is the expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
[tex]=(12)^2+\frac{6}{2} \\=144+3\\=147[/tex]
Therefore the given expression is equivalent to the number 147.
To learn more about the expression visit:
https://brainly.com/question/723406
#SPJ1
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
two to the seven eighths power, all over two to the one fourth power
The expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
What are Exponents?Exponents are the base raised to a power, It is written in the superscript of a number.
The expression given in the statement can be written as
[tex]\rm \dfrac{ 2^{7/8}}{2^{1/4}}[/tex]
By the Exponent rule,
[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]
So the expression can be written as
=[tex]\rm { 2^{7/8-1/4}[/tex]=[tex]\rm 2^{5/8}[/tex]
=[tex]\rm \sqrt[8]{2^5}[/tex]
Therefore, in radical form, the expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
The complete question is
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
2 to the 7 over 8 power, all over 2 to the 1 over 4 power
the eighth root of 2 to the fifth power
the fifth root of 2 to the eighth power
the square root of 2 to the 5 over 8 power
the fourth root of 2 to the sixth power
To know more about Exponents
https://brainly.com/question/5497425
#SPJ1
6x^2+18x=0 rounded the nearest 10th
By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.
How to solve a quadratic equation
In this question we must apply algebraic rules to find the roots of a quadratic equation, the roots are the values of the equation such that is equal to zero. Now we present the complete procedure:
6 · x² + 18 · x = 0
6 · x · (x + 3) = 0
x = 0 ∨ x = - 3
By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.
To learn more on quadratic equations: https://brainly.com/question/17177510
#SPJ1
Use the logarithm lays to simplify this expression
log2 8x^3/2 = log2 8x^3 - log2 2y
By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.
How to simplify a logarithmic expressions
Herein we must simplify an expression that uses logarithms by applying any of the following three laws:
[tex]\log_{a} (b \cdot c) = \log_{a} b + \log_{a} c[/tex] (1)
[tex]\log_{a} \left(\frac{b}{c} \right) = \log_{a} b - \log_{a} c[/tex] (2)
[tex]\log_{a}{b^{c}} = c \cdot \log_{a} b[/tex] (3)
Now we proceed to simplify the expression:
[tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex]
[tex]\log_{2} 2\cdot y = \log_{2} 8\cdot x^{3} - \log_{2} \frac{8\cdot x^{3}}{2}[/tex]
[tex]\log_{2} 2 \cdot y = \log_{2} \frac{\frac{8\cdot x^{3}}{1} }{\frac{8\cdot x^{3}}{2} }[/tex]
[tex]\log_{2} 2\cdot y = \log_{2} 2[/tex]
By the relationship between logarithms and powers of same base:
2 · y = 2
y = 1
By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.
To learn more on logarithms: https://brainly.com/question/20785664
#SPJ1
Two rules for creating a pattern are given below. Each rule begins with a number called the input and creates a number called the output.
Rule 1: Divide the input by 2 to get the output.
Rule 2: Subtract by 10 to get the output.
Which input and output table works for both rules?
The input and output table that works for both rules is input = 20 and output = 10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the output and x represent the input.
From the first rule:
y = x/2
From the second rule:
y = x - 10
To work for both rules:
x/2 = x - 10
x = 2x - 20
x = 20
y = 20 - 10 = 10
The input and output table that works for both rules is input = 20 and output = 10.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
The scale of a map says that 4 çm represents 5 km.
What distance on the map (in centimeters) represents an actual distance of 4
kilometers?
Answer:
Distance on the map (in centimeters) represents an actual distance of 4 kilometers is 3,2 cm.
Step-by-step explanation:
The scale of a map = 4 cm : 5 km
The scale of a map = 4 : 500.000
So, 0,000008 times the actual distance is the distance on the map.
0,000008 × 400.000 = 3,2 cm
Two trains leave a station at the same time. One train is heading south at a rate that is 1.5 times faster than the other train, which is heading north. After 5 hours, the trains are 750 miles apart.
1) At what speed, in mph, are the two trains getting farther away from each other?
2) What is the speed, in mph, of the faster train?
3) Suppose the trains simultaneously leave stations that are 450 miles apart and travel toward each other. In how many hours will the trains meet?
Answer:
1) 150 mph
2) 90 mph
3) 3 mph
Explanation:
1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150
2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.
3) We know that both trains combined travel 150 mph. 450/150=3.
Based on the data given, the speeds and time taken are as follows:
The combined speed of the two trains is 150 mphThe speed of faster train 150 x 3/5 = 90 mphThe time taken by the trains to cover 450 miles = 3 hoursWhat is speed?Speed is the ratio of distance covered and time taken.
Speed = distance/time1)The distance covered by the two trains in 5 hours = 750 miles.
The trains move at a constant speed and their combined speed will be:
Combined speed = 750/5
Combined speed = 150 mph
2) The train heading south has a speed 1.5 times faster than the other train heading north.
Ratio of speeds = 3 : 2
Speed of faster train 150 x 3/5 = 90 mph
3) The combined speed of the trains = 150 mph
Distance to be covered = 450 miles
Time taken = 450/150
Time taken = 3 hours
In conclusion, the speed of the two trains are determined from the distance travelled and time taken.
Learn more about speed at: https://brainly.com/question/6504879
#SPJ1
Fthis other one but this is cheesing hard
A is zero
B) D
C) x= - 1 & x= 4
Hope this helps!
A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 222 inches and a height of 666 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 444 inches.
What will the height of the new cones be?
Based on the given parameters about old cone, the height of the new cone is 12 inches
Equivalent ratioOld cone:
Radius, r = 2 inchesHeight, h = 6 inchesNew cone:
Radius, r = 4 inchesHeight, h = hequate ratio of radius to height in old and new cone
2 : 6 = 4 : h
2/6 = 4/h
cross product
2 × h = 6 × 4
2h = 24
h = 24/2
h = 12 inches
Learn more about ratio:
https://brainly.com/question/2328454
#SPJ1
Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.
The center of mass is mathematically given as
[tex]\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]
What is the center of mass.?Determine the center of mass in one dimension:
Represent the masses at the respective distances.
[tex]\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end[/tex]
We calculate the total mass of the system.
[tex]\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}[/tex]
Step 03: Calculate the moment of the system.
[tex]\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}[/tex]
we calculate the center of mass.
[tex]\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]
Read more about the center of mass.
https://brainly.com/question/27549055
#SPJ1
2x + 15 = 3x + 10 help BRAINLIEST
Answer:
5
Step-by-step explanation:
2x + 15 = 3x + 10
3x + 10 = 2x + 15
3x - 2x = 15 - 10
x = 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
[tex]2x + 15 = 3x + 10[/tex]
• Group like terms together:
• Subtract 5 from both sides:
[tex]2x = 3x - 5[/tex]
• Subtract 3x from both sides:
[tex]-x = -5[/tex]
• Multiply both sides by -1:
[tex]x = 5[/tex]
Factor completely.
Y^2-12y+32
A. (y+4)(y+8)
B. (y-4)(y-8)
C. (y+18)(y + 2)
D. (y-18)(y-2)
Answer:
B
Step-by-step explanation:
y² - 12y + 32
consider the product of factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)
the factors are - 4 and - 8 , since
- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then
y² - 12y + 32 = (y - 4)(y - 8)
Answer:
B. (y-4)(y-8)
Step-by-step explanation:
Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.
1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.
They are: -8 and -4.
2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.
y² - 8y - 4y +32
y(y - 8) - 4(y - 8)
(y - 4)(y -8)
A patient admitted to the hospital was prescribed a pain medication to be given every 4 hr and an antibiotic to be given every 5 hr. Bandages applied to the patient's external injuries needed changing every 12 hr. The nurse changed the bandages and gave the patient both medications at 6:00 A.M. Monday morning. A patient admitted to the hospital was prescribed a pain medication to be given every 4 hr and an antibiotic to be given every 5 hr . Bandages applied to the patient's external injuries needed changing every 12 hr . The nurse changed the bandages and gave the patient both medications at 6:00 A.M. Monday morning.
Answer:
First Question: 1. 60 hours 2. Wednesday 6:00 PM
Step-by-step explanation:
Sorry but I couldn't figure out the answer to the second question :(
Hope this helped :D
Find the distance between the two points.
(-8,-8) and (-14, -16)
Answer:
the distance between both points is 10
Step-by-step explanation:
Distance (d) = √(-14 - -8)2 + (-16 - -8)2
= √(-6)2 + (-8)2
= √100
= 10
The distance between the two points (-8, -8) and (-14, -16) is 10 units.
We have,
To find the distance between two points in a coordinate plane, you can use the distance formula:
Distance = [tex]\sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
In this case, the two points are (-8, -8) and (-14, -16).
Let's plug the values into the distance formula:
Distance = √[(-14 - (-8))² + (-16 - (-8))²]
Distance = √[(-14 + 8)² + (-16 + 8)²]
Distance = √[(-6)² + (-8)²]
Distance = √[36 + 64]
Distance = √100
Distance = 10
Thus,
The distance between the two points (-8, -8) and (-14, -16) is 10 units.
Learn more about the distance between two points here:
https://brainly.com/question/14645718
#SPJ7
A line with gradient of -3 passes through the points(3,k) and (k,8). Find the value of k and hence express the equation of the line in the form ax + by = c, where a,b and c are constants.
Answer:
3x + y = 9.5
Step-by-step explanation:
1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.
y = -3x + c
2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.
-3 = 8 - k / k - 3
-3(k - 3) = 8 - k
-3k + 9 = 8 - k
-3k + k = 8 - 9
-2k = -1
k = -1/-2
k = 1/2
3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.
y = -3x + c
1/2 = -3(3) + c
1/2 = -9 + c
1/2 + 9 = c
9.5 = c
Completed equation of the line: y = -3x + 9.5
4) Write it in the form of ax + by = c.
3x + y = 9.5
How many terms of the G.P 3 , 3/2,3/4 are needed to give the Sum 3069 /512
Answer: 10
Step-by-step explanation:
The first term is 3 and the common ratio is 1/2.
Using the sum of a geometric series formula,
[tex]\frac{3069}{512}=\frac{3(1-(1/2)^{n}}{1-(1/2)}\\\\\frac{3069}{1024}=3(1-(1/2)^{n})\\\\\frac{1023}{1024}=1-(1/2)^{n}\\\\-(1/2)^{n}=-\frac{1}{1024}\\\\(1/2)^n=\frac{1}[1024}\\\\2^{-n}=2^{-10}\\\\n=10[/tex]
The diagonal of the square is 10 cm. The length of the sides in cm is:
A. 5
B. 5sqrt2
C. 10sqrt2
D. 20
E. 100
*sqrt = square root I can't put the icon in
The length of a square with diagonal of 10 cm is 5√2 cm.
How to find the length of a square?Each angle in a square is 90 degrees.
Therefore, the diagonal form a right triangle with the length of the square.
The length of the square are equal.
Hence, using Pythagoras theorem,
let
x = length of square
x² + x² = 10²
2x² = 100
x² = 50
x = √50
x = 5√2
Therefore, the length of a square with diagonal of 10 cm is 5√2 cm.
learn more on square here: https://brainly.com/question/15065958
#SPJ1
Question
Find the x- and y-intercepts of the parabola y
=
=-3x²
-
10x 10.
-
Answer:
-100/3,0
Step-by-step explanation:
substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
if that makes sense Hope this helps pls brainliest have a nice day :>
Answer:
100- 3X
Step-by-step explanation:
SLAY
What additional information would allow you to prove the quadrilateral is a parallelogram?
The additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ
How to prove a Parallelogram?The six basic properties of parallelograms are primarily;
Both pairs of opposite sides are parallelBoth pairs of opposite sides are congruentBoth pairs of opposite angles are congruentDiagonals bisect each otherOne angle is supplementary to both consecutive angles (same-side interior)One pair of opposite sides are congruent AND parallel.Now, looking at the parallelogram properties above and comparing with the given image of the quadrilateral attached, we can say that the additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ
Read more about Parallelogram Proof at; https://brainly.com/question/24056495
#SPJ1
The radius of a circle is 17 inches. What is the circumference? Round your
answer to the nearest tenth.
OA. 106.8 inches
OB. 907.9 inches
OC. 53.4 inches
OD. 289 inches
Answer: A
Step-by-step explanation:
[tex]C=2\pi r=2(\pi)(17) \approx 106.8[/tex]
Can someone please help me
Answer:
Vertex form: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]
Standard Form: [tex]y=0.50x^2-2x-1[/tex]
Step-by-step explanation:
Well the vertex form of an equation is given in the form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you: [tex]y=a(x-2)^2-3[/tex]. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in
Plug in (0, -1) as (x, y)
[tex]-1 = a(0-2)^2-3[/tex]
calculate inside the parenthesis
[tex]-1 = a(-2)^2-3[/tex]
square the -2
[tex]-1 = 4a-3[/tex]
Add 3 to both 3 to both sides
[tex]2 = 4a[/tex]
divide both sides by 4
[tex]a=\frac{1}{2}[/tex]
This gives you the equation: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]
To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to: [tex](a+b)^2=a^2+2ab+b^2[/tex].
Original equation:
[tex]y=\frac{1}{2}(x-2)^2-3[/tex]
expand square binomial:
[tex]y=\frac{1}{2}(x^2-4x+4)^2-3[/tex]
Distribute the 1/2
[tex]y=0.50x^2-2x+2-3[/tex]
Combine like terms:
[tex]y=0.50x^2-2x-1[/tex]
(02.02 MC)
Given the function g(x) = 8x − 2, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values.
Group of answer choices
The value of g(−2) is larger than the value of g(4).
The value of g(−2) is the same as the value of g(4).
The value of g(−2) is smaller than the value of g(4).
The values of g(−2) and g(4) cannot be compared.
Answer:
The value of g(-2) and g(4) cannot be compared because they are two different functions with two completely different values.
Step-by-step explanation:
So, you plug in -2 in the function of the x in g(x) = 8x - 2
Then, you multiply 8 by -2 in g(-2) = 8x - 2
8 × -2 would be -16
Afterwards you subtract -16 by 2 in g(-2) = -16 - 2
The function of g(-2) is -14 in g (x) = -14
You plug in 4 in the function of x in g(4) = 8x - 2
g(4) = 8 (4) - 2
Then, You multiply 8 by 4 which will give you 32 in
g(4) = 32 - 2
Lastly, you subtract the 32 by 2 and the function of the answer would be 30 in g(x) = 30
Anil is a married teacher in a college. He has monthly salary of Rs 45,000
dearness allowance Rs 4,000. His life insurance premium paid by his college is
Rs 15,000. Dashain allowance is equals to one month's basic salary. Anil has contributed
in Employee Provident Fund 10% of basic salary. The college also contributed same amount.
Tax rate for first 450000 1% , next 100000 10% and 25% above that
The amount paid in tax based on the information is Rs 13500.
How to compute the tax?From the information given, the monthly salary is 45000. Therefore, the yearly salary will be:
= 45000 × 12
= 540000
Also, it's stated that the tax rate for first 450000 is 1% and next 100000 is 10%. Therefore, the amount that will be paid in tax will be:
= (450000 × 1%) + (90000 × 10%)
= 4500 + 9000
= 13500
Therefore, the amount paid in tax will be Rs 13500.
Learn more about tax on:
brainly.com/question/25783927
#SPJ1
Determine the slope of a line that is perpendicular to the equation 3x + 6y =18
Rewriting the equation of the given line in slope-intercept form,
[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]
This means the slope of the given line is -1/2.
As perpendicular lines have slopes that are negative reciprocals, the answer is 2.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Determine the slope of the line perpendicular to 3x+6y=18
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form
[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x
[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].
[tex]\cline{1-2}[/tex]
Now, perpendicular lines' slopes are opposite inverses of each other.
The opposite inverse of -1/2 is
= 2
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=2}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]
Work out the height of this
triangle with base, b = 4.9mm
and area, A = 108.29mm².
Answer: 44.2
Step-by-step explanation:
108.29*2/4.9=44.2