The equations that passes through the points, (–4, –16) and (5, 2), are:
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
How to Find the Equations that Pass through a Point?To find the equation that passes through the points (–4, –16) and (5, 2), substitute each of the values of the points into the equations and see if it makes it true.
(–4, –16) = (x, y) into y + 4 = 2(x – 16):
-16 + 4 = 2(-4 – 16)
-12 = -40 [not true]
The equation does not passes through the point.
(–4, –16) = (x, y) into y – 2 = 2(x – 5):
-16 – 2 = 2(-4 – 5)
-18 = -18 [true]
The equation passes through the point.
(–4, –16) = (x, y) into y = 2x – 8:
-16 = 2(-4) - 8
-16 = -16 [true]
(–4, –16) = (x, y) into y + 16 = 2(x + 4):
-16 + 16 = 2(-4 + 4)
0 = 0 [true]
Therefore, the answers are:
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
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I NEED HELP!!!! Use the graph of the polynomial equation y=x^4-10x² + 16 to describe its concavity. How many points of inflection does this curve have?
Points of inflection does this curve have is:
Concave Up: [tex]$\left(-\infty,-\sqrt{\frac{5}{3}}\right),\left(\sqrt{\frac{5}{3}}, \infty\right)$[/tex]
Concave Down: [tex]$\left(-\sqrt{\frac{5}{3}}, \sqrt{\frac{5}{3}}\right)$[/tex]
Points of Inflection: [tex]$(-1.2910,2.1111),(1.2910,2.1111)$[/tex]
To find the concavity of a function?
We need to take the second derivative.
y' = 4x^3 - 20x
y'' = 12x^2 - 20
Finding the points of inflection involves setting the second derivative equal to 0. Add 20 over, divide by 12, and take the square root. The positive and negative square roots of 5/3 are the potential points of inflection.
Setting up a number line can help to determine concavity. Let's plug in -2 into the second derivative. From this, we have found that from negative infinity to the negative square root of 5/3, the graph is concave up, as f''(-2) > 0. f''(0) < 0, so from the negative square root of 5/3 to the positive square root of 5/3, the graph is concave down. f''(2) is also > 0, and therefore from the positive square root of 5/3 to infinity, the graph is concave up.
Since the graph shifted direction at both potential points of inflection, they are both actually points of inflection. To find the y-values for each point of inflection, plug the x-value back into the original polynomial equation.
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What is the breadth of perimeter=50 ft and Length=15ft
Answer:
Breadth = 10 ft
Step-by-step explanation:
Given information,
→ Perimeter (P) = 50 ft
→ Length (L) = 15 ft
→ Breadth (B) = ??
Now we have to,
→ find the required value of Breadth.
Formula we use,
→ P = 2(L + B)
Then the required Breadth will be,
→ P = 2(L + B)
→ 50 = 2(15 + B)
→ 30 + 2B = 50
→ 2B = 50 - 30
→ B = 20/2
→ [ B = 10 ft ]
Hence, required Breadth is 10 ft.
PLEASE HELP!
P(x)=x^3 - 4x^2 - 1
Where P is in hundreds of dollars and x is the number of years elapsed since the start up year
Answer:
Yes, the company will break even at some point in time
Step-by-step explanation:
I am not sure what methodology your teacher has been using. I am going to provide a simple methodology
The polynomial function for profit isTherefore the company will break-even at some point
Other Notes
You can also solve for the roots of the polynomial and see how many real roots are there. In this case there is one real root at [tex]x\approx \:4.0606[/tex]. But that is a lot of workAnother way to approach this problem is to simply graph the function and see if it crosses the x axis. I have provided the graph of this function and you can see that it does cross the x-axis at [tex]x = 4.06[/tex]I hope that helps you
Find the area of sector FIJ. Round to
the nearest tenth.
The area of sector FIJ is 233.4cm².
What is the area of the sector?
The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle.
Here, we have
Given: FI = 13cm and angle = 160°
The area of a sector is given as
= (θ/360)×π×r²
= (160/360)×π×13²
= 0.44×3.14×13²
= 233.4cm²
Hence, the area of sector FIJ is 233.4cm².
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how to simpify 2,400/100
Answer:
24/1
Step-by-step explanation:
[tex] \frac{2400}{ \\ 100} [/tex]
and u get 24/1
In the first week of July a record 1,120 people went to the local swimming pool in the second week 125 fewer people went to the pool than in the first week in the third week 130 more people went to the pool than in the second week in the fourth week 229 fewer people went to the pool than in the third week what is the percent decrease in the number of people who went to the pool over these four weeks
There is 20% decrease in the number of people who went to the pool over these four weeks.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.
Attendance of pool in first week of July = 1120
In second week, 125 fewer people joined.
Thus, attendance in second week is = 1120-125 = 995
In third week, 130 more people joined.
Thus, attendance in third week is = 995+130 = 1125
In fourth week, 229 fewer people joined.
Thus, attendance in fourth week is = 1125-229 = 896
Difference of attendance in first and fourth week = 1120-896 = 224
Percentage decrease = (Decrease number/Initial number)×100%
= (224/1120)×100%
= 0.20×100%
= 20%
Thus, there has been a 20% decrease over the four weeks.
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Please reply urgent I need it now
step by step
Answer:
x ≥ 5
Step-by-step explanation:
5 + 2 (2x - 3) ≥ 3x + 4
5 + 4x - 6 ≥ 3x + 4
-1 + 4x ≥ 3x + 4
4x ≥ 3x + 5
x ≥ 5
Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 5 comma 3, negative 5 comma negative 2, and 7 comma negative 2
5 units
13 units
26 units
30 units
The perimeter of the right triangle shown is given by the following option:
39 units.
How to obtain the perimeter of a figure?The perimeter of a figure is composed by the sum of the lengths of the outer edges of the figure.
The sides of the right triangle in this problem are given as follows:
5, vertical side, as 3 - (-2) = 5.12, horizontal side, as 12 - (-5) = 17.Then, applying the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:
h² = 5² + 17²
h = square root(5² + 17²)
h = 17.7.
The hypotenuse is the third side length of the triangle, hence it's perimeter is calculated as follows:
5 + 17 + 17 = 39 units.
(I suppose there was a typing mistake on the options).
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Answer:
its D
Step-by-step explanation:
30
Determine the intercepts for the graph of the linear equation.
\displaystyle -4 x+y=16−4x+y=16
Enter the xx-intercept as an ordered pair.
Preview
Enter the yy-intercept as an ordered pair.
The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).
What is meant by linear equation?In an alternative method, a linear polynomial over a field from which the coefficients are extracted is equalized to zero to produce a linear equation. The values that, when used as placeholders for the unknowns, result in the equality being true are the solutions to this kind of equation.
In this specific situation, where the variable is appropriately referred to as the unknown, the term "linear equation" frequently applies indirectly.
The Cartesian coordinates of a point on the Euclidean plane can be read as each solution in the case of two variables.
Given equation is:
-4x+y=16
For x-intercept, y=0
-4x+0=16
-4x=16
x= -4
The x-intercept has an ordered pair (-4, 0)
For y-intercept, x=0
-4(0)+y=16
y=16
The y-intercept has an ordered pair(0,16)
Therefore, The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).
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A number, d, is increased by 73% to give
4152.
Work out the original value of d.
Answer:
2400
Step-by-step explanation:4152 is just 173% of d.
We create an equation d = 4152/1.73
after solving you get 2400.
Determine whether AB¯¯¯¯¯¯¯¯ A B ¯ is congruent to CD¯¯¯¯¯¯¯¯ C D ¯ . Justify your answer. A(1, 5) A ( 1 , 5 ) , B(6, 1) B ( 6 , 1 ) C(−2, 8) C ( − 2 , 8 ) , D(−6, 3) D ( − 6 , 3 ) Which of the following best solves the problem? Show Hints
AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved)
What is the distance formula of coordinate geometry?In coordinate geometry, we use the distance formula to find the distance between two coordinates in a straight line. It represented D.
Let's consider two points on a coordinate plane given as A and B (x₂, y₂).
D = [tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]
Given:
The coordinates of the given quadrilateral are,
A(1, 5), B(6, 1), C(−2, 8), D(−6, 3).
According to the question we need to determine AB = CD.
By using the distance formula of coordinate geometry.
[tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]
Distance between A and B,
[tex]AB =\sqrt{(6 - 1)^2 + (5-1)^2 } \\AB = \sqrt{5^2 + 4^2} \\AB = \sqrt{25 + 16} \\AB = \sqrt{41} units[/tex] .......(1)
Distance between C and D,
[tex]CD =\sqrt{(-6 -(-2))^2 + (3-8)^2 } \\CD = \sqrt{(-4)^2 + (-5)^2} \\CD = \sqrt{16 + 25} \\CD = \sqrt{41} units[/tex].......(2)
From equation (1) and (2) we find that
AB = CD =[tex]\sqrt{14} units[/tex]
Hence, AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved).
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What is the true solution to 2 ln e superscript ln 5 x baseline = 2 ln 15?
x = 3 is the true solution to 2 ln e superscript ln 5 x baseline = 2 ln 15, using the concept of simplification.
What is simplification?Make something simpler by simplifying it. In mathematics, reducing an expression, fraction, or issue to a simpler form is referred to as simplification. With calculations and solutions, the problem is made simple.
In order to achieve consistency in efforts, costs, and time, procedures must be simplified. It gets rid of variation and variety that is superfluous, harmful, and unproductive. It is termed simplification to use and interpret the function in order to make it simpler or easier to grasp.
The equation can be simplified by using the fact,
ln(eˣ) = x
This gives,
2 ln(5x) = 2·ln(15)
Comparing arguments, we see that,
5x = 15
x = 3
Check if it is true or not:
2 ln(e^(ln(5·3))) = 2·ln(15)
2 ln(e^2.70805) = 2·2.70805
2 ln(15) = 5.41610
and,
2·2.70805 = 5.41610
So, it is true.
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Solve 9(2x−8)−2(4x−19)=26 .
3y= -6x+1. Find the value of y.
[tex]3y= -6x+1[/tex] for y
Divide both sides by 3:
[tex]\dfrac{3y}{3} =\dfrac{-6x+1}{3}[/tex]
[tex]\fbox{y = $-2x+\dfrac{1}{3} $}[/tex]
of the guests at a charity fundraiser, 180 own both a house in the hamptons and a house in palm beach. if not every guest at the fundraiser owns a house in either the hamptons or palm beach, what is the ratio of the number of people who own a house in palm beach but not in the hamptons to the number of people who own a house in the hamptons but not in palm beach? (1) one-half of the guests own a house in palm beach. (2) two-thirds of the guests own a house in the hamptons.
"NOT EVERYONE who attended ratio the fundraiser owned a home in the Hamptons or Palm Beach."
What is statement type questions?
In research, a statement of the problem is used as a claim that outlines the problem addressed by a study. The problem statement answers the question briefly: What is the problem that the research will address? What are the objectives of a problem statement?
Consider the following diagram in the attachment (12) for both statement
H = the number of people who owned a home in the Hamptons but did not own a home in Palm Beach.
P = the number of people who owned a home in Palm Beach but did not own a home in the Hamptons.
N = the number of people who did not own a home in Palm Beach or the Hamptons.
Union = H+P+180 Universal = H+P+180 + N P/H =??
Statement 1: (P+180) / (H + P + 180 + N) = 1/2 Inadequate
Statement 2: (H+180) / (H + P + 180 + N) = 2/3 Inadequate
1 and 2 statements
Solve for H and P to find P/H; however, N cannot be eliminated.
This is insufficient.
We should find the ratio of red boxes, however with the information provided, this is impossible.
"NOT EVERYONE who attended the fundraiser owned a house in the Hamptons or Palm Beach.".
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When it comes to creditors and
debtors, which of the following
occurs?
A. Creditors and debtors receive loans from
consumers as capital.
B. Every debtor is guaranteed a loan.
C. Debtors receive loans as capital from creditors.
D. All creditors have the same interest rates for
debtors.
The only true given statement about debtors and creditors is; C. Debtors receive loans as capital from creditors.
How to identify creditors and debtors?Debtors are defined as the party from whom we have to receive the payment in the form of cash or any negotiable instrument.This means an asset for the firm.
Meanwhile, the creditors are defined as the party to which we will pay in the future agreed date in the form of cash or any negotiable instrument. This means liability for a firm.
A) This is not true because creditors don't receive loans from consumers as capital. This is the role of debtors.
B) This is not correct because it is not true that every debtor is guaranteed a loan.
C) This is true as defined earlier on the role of debtors and creditors.
D) This is not true because different creditors have different lending rates as the case may be.
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What is life? Ok answer me that I'm okay just answer the question
The required life is any living thing that has the property to be born, grow and end of the life cycle is life.
What are living beings?Any object that has characteristics of life is called living a being.
Here,
Life can be defined as the ability for growth, response to encouragements, metabolism, energy vitality and reproduction are characteristics that set life apart from matter that lacks biological activities, such as signaling and self-sustaining processes.
Thus, the required life is any living thing that has the property to be born, grow and end the life cycle is life.
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Your team wins 66 of 82 games. Is this proportional to 99 wins in 125 games?
If you think about this, we can figure out that 66 is 2/3 of 99. To find out what 2/3 of 125 is, we can divide 125 by 3.
So, no. This is not proportional.
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them.
The formula for a proportional equation is y = kx. The letters y and x are the variables in the equation. The letter k represents the constant of proportionality, which remains the same.
What is a proportional relationship example?
Now, we're going to consider an example of proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.
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Let f(d)=-6d+54 represents the amount of firewood purchased and each night you burn six pieces of firewood. D = number of days and F = pieces of firewood. when will there be 36 pieces of firewood left?
Answers: a. end of first day B. End of second day C. end of third day D. End of fourth day
Answer: C. End of third day
Step-by-step explanation:
The question is asking when there will be 36 pieces left, so you start with the equation:
-6d + 54 = 36
Then, solve this equation:
-6d + 54 = 36
-6d = -18 (subtract 54 from both sides)
d = 3 (divide both sides by -6)
It will take 3 days until there are 36 pieces left, which is the end of the third day.
Proportions
Lily planted 8 zucchini plants and got 50
zucchinis. Next year she intends on planting
20 zucchini plants. How big will her harvest
be?
29
A 125
B 145
C 75
D 95
Answer:
a) 125
Step-by-step explanation:
[tex]\frac{8}{50}[/tex] = [tex]\frac{20}{x}[/tex] Cross multiply and solve for x
8x = 1000 Divide both sides by 8
[tex]\frac{8x}{8}[/tex] = [tex]\frac{1000}{8}[/tex]
x = 125
scientific notation is used to keep track of very small and vary large numbers during mathematical calculations. truefalse
It is true that very small and very large and small numbers can be expressed in terms of scientific notation.
What is Scientific Notation ?Scientific notation is a method of expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.
The general for of scientific notation is
In scientific notation, all numbers are written in the general form as
N × [tex]10^{m}[/tex]
N times ten raised to the power of m, where the exponent m is an integer, and the coefficient N is any real number. The integer m is called the order of magnitude and the real number N is called the significand.
The digit term in the scientific notation indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example,
4660000 = 4.66 x 106
This number only has 3 significant figures. The zeros are not important, they are just placeholders. As another example,
0.00053 = 5.3 x 10-4
This number has 2 significant figures. The zeros are only placeholders.
Scientific Notation Rules:
While writing the numbers in the scientific notation we have to follow certain rules they are as follows:
The scientific notations are written in two parts one is the just the digits, with the decimal point placed after the first digit, followed by multiplication with 10 to a power number of decimal point that puts the decimal point where it should be.
If the given number is greater than 1 and multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive
Example: Scientific notation for 8000 will be 8 × 103.
If the given number is smaller than 1 means in the form of decimal numbers, then the decimal point has to move to the right, and the power of 10 will be negative.
Example: Scientific notation for 0.008 will be 8 × 0.001 or 8 × 10-3.
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Given ab, and c is not parallel to a or b, which statements
must be true?
Select each correct answer.
O
□m/4=m/8
m/8=m/9
m/2=m/7
m/7=m/10
a
C
1/2
3/4
5/6
7/8
9/10
11/12
Use the formula y = mx + b and use point slope form to write an equation for a line given with the given information.
Either the slope intercept form or the point-slope form can be used to express the equation of a line-, the line's equation is - 3x - 5.
What is Slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two distinct points on a line can be used to calculate the slope of any line.
The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.
According to our question-
the points are given as
(x1,y1)=0,-5
(x2,y2)=-3,4
m = y2-y2/x2-x2
Hence, the line's equation is - 3x - 5.
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n divided by 6 equals 42 please explain
The value of n when is divided by 6 and it gives 42 is 252
What is division?Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division and 12 divided by 4 gives 3 in each group. This means that 3 and 4 are factors of 12
When dividing a number by another number that is not it's factor, there will be remainder for example 12 divided by 5 . It will give 2 remainder 2. This is because 5 is not a factor of 12.
Similarly, n divided by 6 to give 42. This means that 42 and 6 are factors of n
Therefore to find n we multiply 42 and 6.
n = 42×6
n = 252
therefore the value of n is 252
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Usually Cassandra tap dances 1 7/8 hours a day. Today she reduced this time by half. For how long did she tap dance today?
Answer: 15/16 hour
Step-by-step explanation:
7
a-4
a - 4
||
|
14
6
Are these 2 equivalent.
The equations a + 4 = 14 and a = 6 - 4 are not equivalent.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, a - 4 = 14
Therefore a = 14 + 4
a = 18.
a + 4 = 6
a = 6 - 4.
a = 2
They are not equivalent.
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a - 4 = 14
a + 4 = 6
Are these 2 equivalent.
Ron refills the oil in his car using a funnel. The upper rim of the funnel has a diameter of 8 inches. What is the rim's radius?
4 inches is the rim's radius
What is the rim's radius?The formula for finding the radius of a circle is r=d/2, where r is the radius and d is the diameter.The diameter of the funnel rim is 8 inches, so the radius is 8/2 = 4 inches. This can also be expressed as a mathematical equation as follows: r = 8/2 or r = 4. The radius of a circle is the distance from the center of the circle to its circumference.It is a measure of the size of the circle, and is used to calculate the area of a circle using the formula A = πr², where A is the area and r is the radius.The radius of the funnel rim is 4 inches, so the area can be calculated using the equation A = π(4)² = 16π. The radius is an important part of understanding the size and shape of a circle. When refilling oil in a car, a funnel with a larger radius can help to increase the flow of the oil.The radius of the funnel should be large enough to allow the oil to flow easily but not so large that it causes a mess. Refilling oil in a car using a funnel with a radius of 4 inches should provide ample flow of oil without.To learn more about the radius of a circle refer to:
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2(x+6)+3x+4=
what it equals
Answer:
5x + 16
Step-by-step explanation:
First you have to distribute the 2 into the parentheses
2 times x is 2x
2 times 6 is 12
so now the equation is
2x + 12 + 3x + 4
add the 2x and 3x and that is 5
so now the equation is...
5x + 12 + 4
add 12 + 4 and that is 16
so now the answer is
5x + 16
Can someone help this please and thank you
distributive property
Please match the formula and definition with the correct word. = W/t = F/d = (v₂-V₁)/t = m/v = d/t = ma 1. Speed 2. Acceleration 3. Force 4. Work 5. Power 6. Density plsss fast
Matching the formulas and their respective definitions are;
W/t = Power
F/d = Work
(v₂-V₁)/t = Acceleration
m/v = Density
d/t = Speed
ma = Force
How to identify mathematical formulas?A) W/t
This means work done divided by the time taken. This results in an expression called Power.
B) F/d
This means force divided by the distance. This results in an expression called Work.
C) (v₂-V₁)/t
This means change in velocity divided by time. This results in an expression known as acceleration.
D) m/v
This means mass divided by volume. This results in an expression known as density.
E) d/t
This means distance divided by time and this results in an expression called "speed"
F) ma
This means mass multiplied by the acceleration and this results in an expression called Force.
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