Answer:
From 1846 to 1847 there was a 30% decrease and from 1847 to 1848 it increased by 51.4%
Step-by-step explanation:
How it decreased by 30%
V2-V1/V1x100
V2=3.5 V1=5
=(3.5−5)|5|×100
=−1.55×100
=−0.3×100
=−30%change
=30%decrease
How it increased by 51.4%
V2-V1/V1x100
V2=5.3 V1=3.5
=(5.3−3.5)|3.5|×100
=1.83.5×100
=0.514286×100
=51.4286%change
=51.4%increase
the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store?
For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.
Probability is a measure of the likelihood that an event will occur.
Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it.The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 505 and standard deviation of 115.
Then, we can say that,
Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P (250 <X< 450)
= P {(250-505)/155} < Z < {(450-505)/155}
= P (-1.64 <Z< -0.03)
Where, Z is the standard normal variate.
ρ = -1.64 <ρ< -0.03
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.00585
For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.
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write the equation of the line in slope-int form that is perpendicular to y=-x - 18 and passes through (-6,11)
Answer:
y = x + 17
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 18 ← is in slope- intercept form
with slope m = - 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1 , then
y = x + c ← is the partial equation of the perpendicular line
to find c substitute (- 6, 11 ) into the partial equation
11 = - 6 + c ⇒ c = 11 + 6 = 17
y = x + 17 ← equation of perpendicular line
given a function with one vector parameter scores. how should the parameter be defined if scores may be very large, and the function will modify the parameter? group of answer choices constant, and pass by value constant, and pass by reference not constant, and pass by reference not constant, and pass by value
Given a function with one vector parameter scores, if scores may be very large, and the function will modify the parameter, the parameter would be defined as pass by reference but not constant.
Pass-by-reference refers to passing the reference of an argument in the calling function to the corresponding formal parameter of the called function. The called function can modify the value of the argument by using its reference passed in. It refers to an alias or reference to the actual parameter that is passed to the method. Pass by reference makes the parameter modifiable, but constant prevents the parameter from being modified.
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Edwin wants to know the height of a water tower. If the water tower casts a shadow 12 yards
long and a nearby street sign that is 3 yards tall casts a shadow 4 yards long, then how tall is the water tower?
the manufacturer of allay pain reliever offered a free sample of the product to visitors who registered at its website. in this case, the communications objective of the website was to
The manufacturer of allay pain reliever offered a free sample of the product to visitors who registered at its website. in this case, the communications objective of the website was to increase awareness of Allay Pain Reliever and generate customer leads.
What are the goals of communications?Communication objectives are the aims and principles that guide how a person or company interacts with customers, staff, or other stakeholders. Workplaces can establish and uphold uniform standards for every contact by adopting communication strategies.
Why is it vital to have communication objectives?In order to achieve marketing goals with an increase in the rate of purchases or information requests, the communication objectives must first develop a good consumer attitude.
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Need help with this question, this is the unit about triangle mid segments
The length of the midsegment of the triangle DEF is 47 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the midsegment of a triangle is half of the length of the parallel side.
∴ GH = (1/2)DF.
3x - 4 = (1/2)(9x - 59).
6x - 8 = 9x - 59.
- 3x = - 51.
x = 17.
So, The length of GH is 3(17) - 4 = 51 - 4 = 47 units.
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. question 10 a data analyst wants to find out how much the predicted outcome and the actual outcome of their data model differ. what function can they use to quickly measure this? 1 point cor() bias() mean() sd()
A data analyst uses bias() to find out how much the predicted outcome and the actual outcome of their data model differ.
What does a bias meaning?The act of unfairly favoring or opposing a certain person or item due to allowing your judgment to be influenced by your opinions: The senator charged bias on the part of the media. Journalists must be unbiased and free from political bias.
What is the example of bias?There is a lack of objectivity in the way we view things. Both intentional and inadvertent biases are possible. When given an option, a person might prefer one shirt over two others if it also happens to be their favorite color.
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8010005 in international number system
Answer:
8,010,005
Step-by-step explanation:
eight million ten thousand and five
hope this helps
Is the product of √1024 and -3.4 rational or irrational? Explain your answer.
Answer:
The product is rational-------------------------------------------
The first number is:
[tex]\sqrt{1024} =\sqrt{32^2} =32[/tex]And the second number is -3.4.
Both numbers are rational, hence their product is rational.
Answer:
Rational as it is a terminating decimal.
Step-by-step explanation:
Given expression:
[tex]\sqrt{1024} \cdot -3.4[/tex]
Rewrite 1024 as 32²:
[tex]\implies \sqrt{32^2} \cdot -3.4[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies 32 \cdot -3.4[/tex]
Multiply the numbers:
[tex]\implies -108.8[/tex]
Therefore, the product is a terminating decimal.
A rational number is a number that can be expressed as the ratio of two integers (where the denominator does not equal zero).
A terminating decimal can be written as a rational number.
To convert a terminating decimal into a rational number, multiply the number by a multiple of 10 that eliminates the decimal, then divide by the same number:
[tex]\implies \dfrac{-108.8 \cdot 10}{10}[/tex]
[tex]\implies -\dfrac{1088}{10}[/tex]
Reduce the fraction to its simplest form by dividing the numerator and denominator by 2:
[tex]\implies -\dfrac{544}{5}[/tex]
Therefore, the product of √1024 and -3.4 is rational as it is a terminating decimal.
How do you convert 0.916 (6 repeating) to a fraction?
Step-by-step explanation:
0.91666666...
is the sum of
0.91 and 0.006666666...
0.66666666... = 2/3
0.0066666666... = 2/300
0.91 = 91/100
so,
0.91666666... = 91/100 + 2/300 =
= 91×3/300 + 2/300 =
= 273/300 + 2/300 = 275/300 =
= 11/12
if you fail to find a fraction at the beginning (like the 2/3 we did), remember the following basics
0.1111111111... = 1/9
0.2222222... = 2/9
0.33333333... = 3/9 = 1/3
0.44444444... = 4/9
0.55555555... = 5/9
0.66666666... = 6/9 = 2/3
0.777777777... = 7/9
0.88888888... = 8/9
0.99999999... = 9/9 = 1
if you want to repeat a pattern like
0.125 to
0.125125125125125...
remember this simple trick
0.125 = 125/1000
0.125125125125125... = 125/999
you must use as many 9s as you have digits in the basic pattern.
227/999 = 0.227227227227227...
6382/9999 = 0.63826382638263826382...
and so on.
Answer:
11/12
Step-by-step explanation:
1. Let x = 0.916 (6 repeating)
2. Identify the FIRST repeating digit's place value:
6 is in the 1000ths place
3. Multiply BOTH sides of x = ... by the value you got in step 2
x = 0.916 (6 repeating)
1000x = 916.6 (6 repeating)
4. Subtract the x = ... from the 1000x = ...:
1000x = 916.666...
x = 0.916...
999x = 915.75
5. Divide both sides by 999: [tex]x=\frac{915.75}{999}[/tex]
6. Rewrite as a corrected fraction: [tex]x=\frac{91575}{99900}[/tex]
7. Simplify as far as possible: [tex]x=\frac{91575}{99900}/\frac{8325}{8325}=\frac{11}{12}[/tex]
Find the difference. Enter your answer in the box below as a fraction, using the slash mark ( 1 ) for the fraction bar. 3/5 + 9/19
Therefore the solution to the difference of fraction comes out to be
12/95
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.
Here,
the given fractions are 3/5 and 9/19
and to find the difference
we take lcm of both denominators
=> 3/5-9/19
=> (3*19-9*5)/5*19
=> (57-45)/95
=> 12/95
Therefore the solution to the difference of fraction comes out to be
12/95
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HELP PLEASE I NEED THIS AS SOON AS POSSIBLE!!!
Sixteen-year-old Janet has earned money the last few years by babysitting and shoveling snow for neighbors, who pay her in cash which she mostly spends on clothes and snacks. This summer she is applying for her first formal job, and because she’ll be paid by check or direct deposit, her parents are allowing her to open a checking account. Janet is excited, until she does some quick Googling and finds out she can’t legally open an account until she’s 18. She finds these other options:
Joint accounts
Custodial accounts
Education
Prepaid Cards
Answer This:
Which of these four banking options is probably best for Janet? Why?
Now that Janet knows her parents will need to be somewhat involved in her bank account, what questions or concerns should she raise with them before they open an account?
The best option for Janet will be to open an educational account.
The basic structure of student bank accounts is frequently the same as that of the institution's standard offerings, with adjustments made for students' typically lower amounts.
These organisations may remove maintenance fees or minimum balance requirements, provide free ATM withdrawals, offer budgeting apps or programmes, or even waive fees altogether because students are still learning how to manage their finances and navigate their daily financial lives.
Some benefits of educational account is
Interactive spending and budgeting options, such as the ability to round up and deposit "spare change" from debit card purchasesAccount remains open following graduationOverdraft defenseTo learn more about bank
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according to the video, what percentage of your brain is dedicated to decoding images? group of answer choices 23% 18% 40% 30%
The movie claims that 40% of your brain is used for visual decoding.
Williams, the William G. Allyn Professor of Medical Optics, notes that processing visual information takes up more than 40% of the cortex, the surface of the brain.
Light and dark pixels in the eye are where our visual experience begins. These signals are sent to the V1 region in the rear of the brain, where they are changed to match to the borders of visual scenes.
The visual cortex processes information from the sensory periphery in accordance with a highly regulated hierarchy, according to experiments utilizing static stimuli, such as images. The information about visual sceneries is subsequently translated by deeper brain areas into more intricate forms, objects, and ideas.
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what is geometric sequence
Answer: A Geometric sequence is a type of sequence in which each subsequent term after the first term is determined by multiplying the previous term by a constant (not 1), which is referred to as the common ratio.
Step-by-step explanation: Hope this was helpful
Step-by-step explanation:
The sequence
a, ar, ar^2, .....ar^n-1,...
where a is the first term and any two consecutive numbers differ by a factor r, is called a Geometric progression (G.P.).
Geometric progression also known as Geometric sequence.
. consider the following situation: janet is examining triangles in her geometry class. all of the triangles janet examined were isosceles. janet concludes that all triangles are isosceles triangles. the type of reasoning janet used in this situation was
The type of reasoning janet used in this situation was
Inductive reasonings .
What is reasoning ?In mathematics, reasoning involves drawing logical conclusions based on evidence or stated assumptions. Sense making may be considered as developing understanding of a situation, context, or concept by connecting it with existing knowledge or previous experience.
Why is reasoning in maths important?
Reasoning in maths is the ability to make logical links and connections which help you tackle a new maths problem. The skill of reasoning equips students not only with the ability to say how they will attempt to work out an answer, but why and how they can be sure it will work.
Inductive reasoning is a type of reasoning that draws general conclusions from specific observations .
In this case Janet examines only isosceles traingle ( specific ) and concluded that all triangles are isosceles ( generalised ).
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which statement correctly describes the relationship between △def and △d′e′f′?
△DEF is congruent to △D'E'F' because you can map △DEF to △D'E'F' using a reflection across the x-axis, which is a rigid motion.
What does a math congruent mean?
Congruent refers to having precisely the same form and size. Even after the shapes have been flipped, turned, or rotated, the shape and size ought to remain constant.
1) Reflections, rotations and translations are rigid transformations, because they do not modify the lengths of the segments nor the angles, so the images and the preimages are congruents.
2) Let's see what transformation map △DEF is to △D'E'F' by analyzing the vertices of preimage and image:
Preimage Image
D (-3, -1) D' (-3, 1)
E (2, -4) E' (2, 4)
F (4, -4) F' (4, 4)
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one of the factors of g2 − 28g 196 is (1 point) g − 7 g − 14 g 14 g 7
( g - 14)² is factor of equation .
What is factor ?
A number that divides another number by itself with no residual is known as a factor.The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8.
In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Since the numbers we are multiplying are divisible by the product, they are factors of the product.
g2 − 28g + 196
= g² - 14g - 14g + 196
= g( g- 14 ) - 14( g - 14 )
= ( g - 14) ( g - 14)
= ( g - 14)²
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The complete question is -
One of the factors of g2 -28g + 196 is a. g-7 b. g-14 c. g+14 d. g+7
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 250 square feet is 30,300 pounds when the plane is going at 190 miles per hour. Find the lifting force if the speed is 180 miles per hour. Round your answer to the nearest integer if necessary.
F= k*a*v^2
a= 250
v=190
30300=k*250*{190^2}
k= 0.003357
F= 0.003357*250*180*180
F=27135
The lifting force is 27135
What is surface area and an illustration?The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.
How does one determine surface area?The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.
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What is an equation of the line that passes through the point ( − 2 , − 6 ) and is parallel to the line x + 2 y = 8 ?
The line parallel to the line x + 2y = 8 is y = -(1/2)x - 7 Or (1/2)x + 7 = - 7.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
The given line is x + 2y = 8 ⇒ 2y = - x + 8 ⇒ y = -(1/2)x + 8.
We know line parallel to each other have the same slope and it passing through (-2, - 6).
∴ - 6 = -(1/2)(-2) + b.
- 6 = 1 + b.
b = - 7.
So, The required line is y = -(1/2)x - 7.
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George walks around one quarter of a quarter of a circular garden. He walks a total of 30 meters. To the nearest tenth of a meter, what is the radius of the circular garden?
The radius of the circular garden is 14.3 meters
The radius of a circle:Any line connecting a circle's center and circumference is said to be the circle's radius. Within a circle, a diameter is equal to the sum of two radii. The area and circumference of a circle are determined using the radius of the circle.
The perimeter of a circle with a radius of r is given by
Perimeter = 2πrHere we have
George walks around one-quarter of a quarter of a circular garden.
He walks a total of 30 meters.
Let x be the Perimeter or circumference of the circular garden
Given that George walks around one-quarter of a quarter of a circular garden.
=> The length of the path that George walked = x/3
Given that He walks a total of 30 meters
=> x/3 = 30 meters
=> x = 90 meters
So we can conclude that circumference of the circular garden = 90 m
As we know Perimeter of the circle = 2πr
=> 2πr = 90
=> πr = 45
=> 22/7(r) = 45
=> 22(r) = 315
=> r = 14.318181818181 ≅ 14.3
Therefore,
The radius of the circular garden is 14.3 meters
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you have 3.35$ in quarters and nickels. If you have 31 coins how many each do you have?
a. Write a system for the problem
b. how many types of each coin do you have?
SOMEONE ANSWER PLSS IM DYING HERE
0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From given,
3.35$ in quarters and nickels. If you have 31 coins
0.25Q+0.05N=3.25..(1)
Q+N=31
Q=31-N
Now substitute Q value in (1)
0.25(31-N)+0.05N=3.25
7.75-0.25N+0.05N=3.25
7.75-0.2N=3.25
Subtract 7.75 on both sides
-0.2N=3.25-7.75
-0.2N=-4.5
Divide both sides by 0.2
N=22.5
and Q+22.5=31
Q=31-22.5
Q=8.5
Hence, 0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5
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A system of two linear equations in two variables has no solution. What statement is accurate about these two linear equations?
Responses
The two linear equations never intersect.
The two linear equations never intersect.
The two linear equations graph the same line.
The two linear equations graph the same line.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the y-axis.
The two linear equations do not cross the y-axis.
The two linear equations intersect at exactly one point.
The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.
How many types of solution are there for two linear equations ?
There are 2 types of solution :
Consistent :
A consistent system is said to be an independent system if it has a single solution.
A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.
Non-consistent :
Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.
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The two linear equations never intersect.
When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.
If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.
It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.
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Find the absolute value.
|-3 + 2i| = []
(Simplify your answer. Type an exact answer, using radicals as needed.)
√13 is the absolute value of |-3 + 2i| .
What is Complex Number?Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number.
For a complex number z = x + iy,
The absolute value |z| as being the distance from z to 0 in the complex plane C
Complex numbers are the numbers that are expressed in the form of a+ib
The complex number here is minus three plus two i.
|-3 + 2i|
Absolute value=√(-3)²+(2)²
=√9+4
=√13
Hence, √13 is the absolute value of |-3 + 2i| .
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Use Green's Theorem to calculate the circulation of G around the curve, oriented counterclockwise. G = 7yi + xyj around the circle of radius 6 centered at the origin. Close int C G. dr= [ ]
The circle's perimeter is determined by F = -9π, according to green's theorem.
What is Green's theorem?The simple formula for Green's theorem is the link between the total amount of microscopic circulation inside curve C and the macroscopic circulation revolving around it.
Remembering that we are talking about two dimensions, if C is a straightforward closed curve in the plane, it will enclose the region D (shown in red) in the plane.
So, knowing that this exercise should be solved using Green's theorem, then:
[tex]\begin{aligned}& \int 4 y d x+2 x y d y=\iint(d / d x)(2 x y)-(d / d y)(4 y) d A \\& =\iint 2 y-4 d A\end{aligned}[/tex]
You must convert in this manner to polar coordinates, and the result will be:
[tex]\begin{aligned}& \int_0^3 \int_0^{2 \pi}(2 r \sin (\theta)-4)(r) d \theta d r \\& =\int_0^3(-2 r \cos (\theta)-4 \theta)(-2 r \pi) d r \\& =-(\pi)\left(r^2\right)=-9 \pi\end{aligned}[/tex]
Therefore, the circle's perimeter is determined by F = -9π, according to green's theorem.
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Correct question;
Suppose F⃗ (x,y)=4yi⃗ +2xyj⃗ . Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of a circle C of radius 3 centered at the origin and oriented counter-clockwise.
a recent study of cardiovascular risk factors reported that 30% of adults met criteria for hypertension. if 15 adults are assessed, what is the probability that a. exactly 5 meet the criteria for hypertension? b. none meet the criteria for hypertension c. how many would you expect to meet the criteria for hypertension?
On solving the provided question, we got to know that - 40/155 adults will not have hypertension (70%),
How is probability calculated?The probability is calculated by dividing the total number of outcomes by the total number of possible ways an event may occur. Probability and odds are two different ideas. The chances are calculated by dividing the likelihood that a certain event will occur by the likelihood that it won't.
What is probability?Probabilities are mathematical explanations of the chance that an event will happen or that a proposition is true. The probability of an occurrence is a number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty.
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tell whether the orthocenter is inside, on, or outside the triangle. then find the coordinates of the orthocenter. x(-3,2)
Therefore , the solution of the given problem of triangle comes out to be
Orthocentre (0, - 5 ).
How do triangles function?Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides end to end at a single point. The triangle has three angles, and the sum of them is 180 degrees.
Here,
We need the lengths of the triangle's three sides in order to identify which of the aforementioned cases the triangle fits into.
Make the length calculations using the distance formula.
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
L(0, 5) and M(3, 1)
LM =d = [tex]\sqrt{(3-0)^{2}+(1-5)^{2}}[/tex] = 5
L(0, 5) and (N(8, 1)
LN = d = [tex]\sqrt{(8-0)^{2}+(1-5)^{2}}[/tex] = √80
M(3, 1) and (N(8, 1)
MN = [tex]\sqrt{(8-3)^{2}+(1-1)^{2}}[/tex] = 5
If a triangle has three sides, a, b, and c, and side c is the longest, then
• Right triangle formed by a2 + b2 = c2
• a2 + b2 c2 - acute triangle
Triangle with angles a2, b2, and c.
A, B, and C are equal to five in this instance.
a² + b² = 5² + 5² = 25 + 25 = 50
c² = (4 )² = 80
A triangle is obtuse and the orthocentre lies outside the triangle because a2 + b2 c2.
The place where the triangle's three altitudes converge is known as the orthocentre.
For the orthocentre's coordinates, we only need to simultaneously solve
the equations for two of the altitudes.
A line drawn at a right angle from a vertex to the other side is known as an altitude.
Altitude from M to LN
Calculate the slope of LN using the slope formula
m = (y2 - y1 )/ (x2- x1 ) = 1-5/8-0 ⇒ = 2
Equation of altitude
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1)
Altitude between M and LN
Utilize the slope formula to determine LN's slope.
m = (y2 - y1)/ (x2- x1) = 1-5/8-0 ⇒ = 2
formula for altitude
y - 1 = 2(x - 3) (x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1) (1)
Altitude between N and LM
m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4
formula for altitude
y - 1 = (x - 8) (x - 8)
y - 1 = x - 6
y = x - 5 → (2) (2)
Adding (1) to (2)
2x - 5 Equals x - 5 ( multiply through by 4 ) ( multiply through by 4 )
8x - 20 = 3x - 20
5x - 20 = - 20 ( add 20 on both sides ) ( add 20 to both sides )
5x = 0 ⇒ x = 0
Place x = 0 in place of (1)
y = 0 - 5 = - 5
It is the orthocentre (0, - 5 )
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A regular polygon is shown with one of its angle measures labeled a. 5 sided regular polygon with one angle labeled a If m∠a = (2z + 54)°, find the value of z.
The value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.
What is a polygon?A polygon can be defined as a flat or plane, two-dimensional closed object circumscribed with straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.
Given:
m ∠ a = (2z + 54)°
The number of sides = 5,
Calculate the value of the sum of the interior angle by the formula given below,
[tex]S = 180(n - 2)[/tex]
S = 180 (5-2)
S = 180 × 3
S = 540°
Calculate the value of a as shown below,
[tex]a = S/5[/tex]
a = 540 / 5
a = 108
108 = 2z + 54
2z = 108 - 54
z = 54 / 2 = 27
Therefore, the value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.
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b(x) = 6x², when x = 16
Answer:
Step-by-step explanation:
b(x)=6x^2
That is the same as b(x)=6*x*x
when x=16
b(16)=6*16*16=1536
Parallelogram MNOP with vertices M(1, 7),
N(8, 5), O(4, 2), and P(-3, 4): and it rotates 180° What will be the new coordinates
The new coordinates are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)
What is a 180 degrees rotation?A 180 degrees rotation denoted by R(180, 0) is a rotation that has the same effect as the 180 degrees counterclockwise of a figure.
And it has the algebraic rule of its rotation to be changed from (x, y) to (-x, -y) i.e (x, y) ⇒ (-x, -y)
How to determine the image of the rotation?The coordinates of the parallelogram are given as
M(1, 7), N(8, 5), O(4, 2), and P(-3, 4)
The rotation is given as 180° rotation
As mentioned above,
We have (x, y) ⇒ (-x, -y)
Substitute M(1, 7), N(8, 5), O(4, 2), and P(-3, 4) in (x, y) ⇒ (-x, -y)
So, we have
M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)
Hence, the coordinates of the image are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)
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HELP ASAP WITH SLOPE PLEASE
the options are:
1
undefined
0
-1
Answer: 0
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
Slope is a value that describes the steepness and direction of a line.
A line with a negative slope, said to be decreasing, runs downwards from left to right.
A line with a positive slops, said to be increasing, runs upwards from left to right.
A horizontal line has a slope of zero because y does not change. A vertical line has an undefined slope because you cannot divide by zero (x does not change).
I hope this helps to understand :)
