The value of k is 1/4.
According to the statement
we have given
The equation of parabola is y=k−x2
And tangent to the line of equation is y = x
and we have to find the value of K.
So, let y=k−x2 -(1)
and let y = x -(2)
(2) is the tangent to the (1) then
therefore they cut at
y=k−x2 -(1)
y = x -(2)
so, put (2) in the (1) then
x = k- (x)^2
(x)^2 + x = k
The above written equation has one real number then for this D =0
so, (x)^2 + x - k = 0
-1 -1*4*k = 0
-1 - 4k = 0
-4k = 1
The value of k is -1/4.
So, The value of k is 1/4.
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Which of the following triplets are Pythagorean? (I)(8, 15,17) (ii) (18, 80,82) (iii)(14,48,51) (iv) (10,24,26) (v)(16,63,65) (vi) (12,35,38)
Only (i), (ii), (iv) and (v) are Pythagorean triplets. A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.
Pythagoras, Gauss, Edison, Hawking. The following are the most noted discoveries of each.
Pythagoras, 500 B.C. School Of Mathematics and Pythagorean theorem.Edison, Year 1879 - Invention of incandescent light bulb.Gauss, Year 1801 - Therom of Alegbraic Solution. Stephen Hawking Year1980 - Studies in cosmology particularly contributing to the context of black holes.
you can check by taking largest side square
and adding square of rest two sides
17^2= 15^2+ 8^2
82^2= 18^2+80^2
26^2= 24^2+10^2
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4. Susan is a plumber and charges a fee for any job that she does plus an hourly
rate for the time it takes her to complete the job. When she works 8 hours, she
gets paid $320. When she works 12 hours, she gets paid $440.
a. Explain what the independent and dependent variables are for this situation
and create two data points.
Answer:
Here are two data points that can be used to represent this relationship:
(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.
(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.
Step-by-step explanation:
In this situation, the independent variable is the number of hours that Susan works, and the dependent variable is the amount of money that she gets paid.
Here are two data points that can be used to represent this relationship:
(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.
(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.
We can use these two data points to represent the relationship between the number of hours that Susan works and the amount of money that she gets paid. It shows that, As her work hours increase, her pay increases as well.
If a "2" is rolled on a fair 6-
sided die, what event is most
likely to occur next?
A. a roll lower than 2
B. a roll higher than 2
C. another 2
D. all of these events are equally
likely
The event with the largest probability is rolling a number higher than 2, so the correct option is B.
Which event is most likely to occur next?First, the fact that a 2 was rolled before does not affect the next rolls of the dice, so that information is extra.
Now we just need to see which option has the largest probability.
A) There are only one number lower than 2, then the probability of this event is p = 1/6
B) There are 3 numbers higher than 2, then the probability is p = 3/6 = 1/2
C) The probability of get another 2 is 1/6
We can see that the event with the largest probability is B, so that one is the most likely to occur.
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Four gallon of paint are ued to paint 25 chair. If each chair ued the ame amount of paint, how many gallon are ued to paint each?
There are 0.16 gallon is used to paint each chair.
What is gallon?
A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters.
as given, Four gallon of paint are used to paint 25 chair.
i.e. 4 gallon ⇒ 25 chairs
and If each chair used the same amount of paint then how many gallon are used to paint each?
i.e. how many gallons ? ⇒ 1 chair
∴ 4 gallon ⇒ 25 chairs
∴ 25 chairs ⇒ 4 gallon
∴ 1 chairs ⇒ 4 / 25 gallon
∴ 1 chairs ⇒ 0.16 gallon
Therefore, there are 0.16 gallon is used to paint each chair.
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Mr. Remy Osta took earned leave for 50 days from February 10, 2008 onwards. When did he resume his duty?
The date Mr. Remy Osta will resume duty after his 50 days leave which lasted from February 10, 2008 is March 31, 2008
How to check the calendar?2008 is a leap yearA leap year is a year which has 366 days, that is, the days in February are 29 days.
So,
From February 10, 2008
The days remaining in February is 19 more days
The days of march is 31 days
Hence,
19 days + 31 days
= 50 days
Therefore, Mr. Remy Osta will resume duty on March 31, 2008
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Can please tell the answer
Answer:
24
Step-by-step explanation:
120 x 0.20 = 24
MATH
Eric ran 3 km in 20 minutes Taylor ran 2550 m and 17 minutes. What is one person running faster than the other or were they running at the same rate
Answer:
Taylor
Step-by-step explanation:
2.5km in 17 mins time 2=5km in 34mins 3km in 20 mins times 2=6km in 40 mins
23. Use Patterns and Structure An artist uses
colored tape to divide sections of a mural. She
needs to cut a piece of paper to cover triangle EFC
while she works on other sections. What are
the angle measures of triangle EFC?
As per the following diagram, the angle measures of triangle EFC is 118°
The term angle in math is known as a figure which is formed by two rays or lines that shares a common endpoint.
Here we have given that an artist uses colored tape to divide sections of a mural and she needs to cut a piece of paper to cover triangle EFC while she works on other sections.
According to the diagram, here we know that the value of
=> DE = EF
And the value of
=> EB = FB
Here we know that the value of the angles,
=> ∠EDB = ∠EFB = 90°
Thus implies that the angles,
=> ∠DFB = ∠FEB = 31°
Then the value of the angle is calculated as,
=> ∠EDB =∠EFB = 90° - 31°
=> ∠EDB = ∠EFB = 59°
Then the value of the angle ABC is calculated by sum the values of the angles, then we get,
=> ∠ABC = ∠EDB + ∠EFB = 59 + 59 = 118°
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I have to use a bar diagram or a scale factor how do I do it
In order to respond to the query ,of bar graph we must first comprehend what a compound Tim received 4 emails on Thursday and 8 SMS on Monday, making up 0.52 of all communications.
What exactly is a bar graph?A blended bar chart is used to display the rates of two connected sets of data. In this investigation, two forms of data—emails and emails used, but they are both grouped together under the term "messages" and are shown as vertical bars in the graph.
Here,
14+16+14+15+14=73 messages in total.
A total of 38 emails were sent: 6 + 10 + 10 + 4 + 8
Email to message ratio is 38/73, or 0.52.
Emails therefore made up 0.52 of the messages.
Tim received 4 emails on Thursday, 8 texts on Monday, and 0.52 of the messages were emails, as shown by an examination of the composite bar chart that we used to come up with the answers to the three questions.
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Solve the following system of equations graphically on the set of axes below
The solution is the point where the two lines intersect i.e. (-1,-7). The graph for the given system of equations is attached below wherein the blue line represents y=2x-5 and the green line represents y=-x-8.
What is system of equation?
A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.
For solving the equations graphically, we need to find points for plotting
So, for y = 2x-5,
The y-intercept is -5, so we need to place a point on the graph at (0,-5). For the another point, put x=1, we get y= -3. So we need to place another point at (1,-3).
Similarly for y = -x-8,
The y-intercept is -8, so we need to place a point on the graph at (0,-8). For the another point, put x=1, we get y= -9. So we need to place another point at (1,-9).
The solution is the point where the two lines intersect.
When the two lines intersect,
2x-5=-x-8
3x=-3
x=-1
So, y=-7
Hence, the two lines intersect at (-1,-7).
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Eight more than a number is 20. Find the number.
Answer:
12
Step-by-step explanation:
How can u add 3/10 and 2/5 explain
Answer:
7/10
Step-by-step explanation:
How do you add a fraction?
First you have to check if they have common denominator. If so, add the numerators and keep the denominator. If Not, you have to find common denominator before added. After that, check if your fraction need to be simplify.
Solve:
Least common multiplier of 10 and 5 is 10
[tex]\frac{3}{10}+\frac{2}{5}[/tex]
Since [tex]\frac{3}{10}[/tex] already have a denominator of 10 we keep it.
[tex]\frac{2}{5}=[/tex] [tex]\frac{2\times2}{5\times2}[/tex] [tex]=\frac{4}{10}[/tex]
Now we have;
[tex]\frac{3}{10}+\frac{4}{10}[/tex]
Apply fraction Rule which is; [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]
[tex]=\frac{3+4}{10}[/tex]
3 + 4 = 7
[tex]=\frac{7}{10}[/tex]
Hence, [tex]\frac{3}{10}+\frac{2}{5}=\frac{7}{10}[/tex]
RevyBreeze
Find the 6th term in the expansion of (4x + 1)^8 in simplest form.
on solving 6th term in the binomial expansion of (4x + 1)^8 in simplest form is 3584.
What is binomial Expanssion ?A binomial is an algebraic expression with two terms. For example, a + b, x - y, etc are binomials. We have a set of algebraic identities to find the expansion when a binomial is raised to exponents 2 and 3.
A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.
we know ,
So the 6th term in the equation
is ,8c5 -4x^8-5 = 8c34x^3 is , = 3584
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-2x+3y=14 x+2y=7 substitute
The values of x and y are -1 and 4 respectively.
What is substitution method?The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Given are two equations, -2x+3y=14 and x+2y=7
Solving equations by using substitution method,
-2x+3y=14..........(i)
x+2y=7
x = 7-2y.......(ii)
Using eq(ii) in eq(i)
-2(7-2y) + 3y = 14
-14+4y+3y = 14
7y = 28
y = 4
Put y = 4 in eq(ii)
x = 7-2(4)
x = -1
Hence, the values of x and y are -1 and 4 respectively.
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How many concepts are there in geometry?
Three fundamental ideas provide the foundation for all basic geometry notions. The three are the plane, line, and point.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
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Three basic ideas form the basis of all basic geometry concepts. The three are planes, lines, and points.
Who Named Geometry?Euclid, the father of geometry, was a brilliant mathematician. Learn about the history of Euclid and some of the mathematical ideas we use today, and see how important they have become. The terms ``ge'' and ``metria'', meaning ``measure,'' are of geometric origin. For over 2000 years, the Greek approach to geometry has served as the foundation of geometry.
Geometry is the study of various mathematical or actual forms, figures, and sizes. In geometry, you will discover the concepts of points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles, and area.
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PLEASE I NEED HELP ASAP‼️‼️
Answer:
a^m + a^n = a^m+n
Step-by-step explanation:
This is true for any value of a and n except 0.
If 16,000 divided by n=4
Answer: If you're asking for the answer if 16,000 divided by 4, it would be 4000, don't know for sure if that's what you were asking for! Hope I helped!
Mark the points A and B in your book 4 cm apart. Construct and shade the region that is closer to B than to A and within 3 cm of B. You must show all of your construction lines. A• B.
What is the value of x in the equation: 2^(3^x) = 10^(6^x) ?
____________________
False answer will be REPORTED immediately. Do not waste your time if you do not have sufficient knowledge.
Answer:
[tex]log\ (log\ 2)/\ log\ 2[/tex] or ≈ - 1.73------------------------------
Solve in below steps, using log and exponent rules:
[tex]2^{3^x}=10^{6^x}[/tex] Given[tex]log\ 2^{3^x}=log\ 10^{6^x}[/tex] Log both sides[tex]3^x\ log\ 2=6^x\ log\ 10[/tex] Log of power rule[tex]3^x\ log\ 2=6^x[/tex] log 10 = 1[tex]3^x\ log\ 2=(3*2)^x[/tex] Power of the product rule[tex]3^x\ log\ 2=3^x*2^x[/tex] Cancel 3ˣ on both sides[tex]log\ 2=2^x[/tex] Log both sides[tex]log\ (log\ 2)=x\ log\ 2[/tex] Divide both sides by log 2[tex]x=log\ (log\ 2)/\ log\ 2[/tex] AnswerAn art museum installed a large triangular sculpture. One of the sculpture’s exterior angles creates a 158 angle with the ground.
If the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, what is the measure of the interior non-adjacent angle?
The measure of the interior non-adjacent angle as required in the task content is; 95°.
What is the measure of the interior non-adjacent angle?Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.
On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;
x + x - 32.
where, x is the measure of the interior non-adjacent angle.
Hence, x + x - 32 = 158
2x = 158 + 32
2x = 190
x = 95°.
Ultimately, the measure of the interior non-adjacent angle is; 95°.
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Evaluate the following expressions if a=2 , b=6, and c=4 : 7a+b over b+c
Answer:
2 over 1
Step-by-step explanation:
I'm not really sure what you mean in the question but I've substituted the values in
4.1 is greater or less than 4.100
Help with this you will get points if you answer really need help asap
A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°).
What is a rectangle?Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.
A rectangle has four vertices since it has four sides, four angles, and four corners. The intersection of two sides forms the "vertices" of a polygon. They are corners, to put it another way.
Rectangles' basic characteristics include:
Four-sided shapes include rectangles.
Parallel and equal to each other are the opposing sides.At 90 degrees, every internal angle is equal.360 degrees is equal to the total of all internal angles.Crossing each other on diagonals.Equal lengths can be found for both diagonals.To learn more about rectangle refer to:
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Ian wants to ride his bicycle 36.5 miles this week he has already written 8 miles if he rides for five more days which equation could be used to determine M the average number of miles he would have to ride to meet his goal?
Answer:
M = (36.5-8)/5
[M = 5.7 miles/day]
Step-by-step explanation:
The goal is 36.5 miles. The remaining miles needed to achieve this goal is reduced by the miles already ridden, 8 miles.
(36.5 - 8) = 28.5 miles remaining.
We are asked to find a value for M, which is the average number of miles Ian would have to ride to reach his goal. By average, we can assume it is the average miles/days remaining. The days remaining are 5, so we have:
(28.5 miles remaining)/5 days = 5.7 miles/day
An equation for M using these steps would be:
M = (36.5-8)/5
What is the area of the right triangle with base 5 cm and altitude 4cm?
The area of the said triangle is 10 cm²
Here we have been given the right-angled triangle with base 5 cm and altitude 4 cm.
To find the area of a triangle we can either use Heron's formula or the other formula where area of a triangle = 1/2 X base X height
Since we have been given the base and the height we need to use the latter.
Hence area of the said triangle will be
1/2 X 5 X 4 cm²
= 10 cm²
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You (or your parents) are debating about whether to buy a new car for $19,072.00 or a used car for $15,635.00. Sales tax is 4.5%. You (or your parents) plan to make a down payment of $1,200.00 and your credit rating is fair. Use the table below to determine the difference in interest accrued by the end of the first month.
Secured Unsecured
Credit APR (%) APR (%)
Excellent 5.4 5.65
Good 5.95 6.35
Average 6.30 6.90
Fair 7.55 7.60
Poor 9.80 10.0
Answer: $20.95
Due to credit rating being fair:
Secured APR = 7.00%
Loan amount = sale price + tax - down payment
New car = [tex]19027 + (19072 x 0.045) - 1200 = 18730.24[/tex]
Used car = [tex]15635 + (15635 x 0.045) - 1200 = 15138.575[/tex]
---------------------------------------------------------------------------
Monthly interest = loan amount [tex]x 0.07 x 1/12[/tex]
New car = [tex]18730.24 x 0.07 x 1/12 = 109.26[/tex]
Used car = [tex]15138.575 x 0.07 x 1/12 = 88.31[/tex]
Thus, the difference is [tex]109.26 - 88.31 = $20.95[/tex]
Joyce has $13 in savings and saves an additional $6 each week. At the same time, Enrique has $80 in savings and spends $5 each week to go swimming at the community pool. Is there a week when Joyce and Enrique will have the same amount of money? Explain why or why not.
Answer: Yes, after 7 weeks, they will have the same amount of money
Step-by-step explanation: So let’s say Joyce will be equation 1, so it would be - T = 13 + 6x, where T represents the total money, and x represents the number of weeks. And let’s say Enrique will be equation 2, which will be - T = 80 - 5x, where once again, T represents the total money, and x represents the number of weeks.
So, let’s start going off numbers, we will start at 5 weeks, when we put that in, Joyce will have $43 and Enrique will have $65, so we know it will be more than 5 weeks, so let’s try 8 weeks, Joyce will have $61 and Enrique will have $40, so it’s below 8, so how about we try 7, at 7 weeks, Joyce will have $55, and Enrique will have $55 too. So this means, after 7 weeks, Joyce and Enrique will have the same amount of money
Refer to the figure. Name the intersection of lines m and t.
Point B
Point C
Point D
Point H
Answer:
Point C
Step-by-step explanation:
Lines m and t are on the same plane
We can see that they intersect at Point C
Which graph correctly represents 3x + y > 7?
NEED HELP!!
The graph of the inequality: 3x + y > 7
Can be seen in the image below.
Which graph correctly represents the inequality?We want to see which graph represents the inequality:
3x + y > 7
We can rewrite the inequality in slope-intercept form as:
y > -3x + 7
So we just need to graph the line:
y = -3x + 7
With a dashed line, and then shade all the region above the line.
To graph the line, you need to find two points that lie on the line.
if we evaluate the line in x = 0 we wll get:
y = -3*0 + 7
y = 7
if x = 1
y = -3*1 + 7
y = -4
Then we have the points (0, -7) and (1, -4), now we can graph these two points and connect them with a dashed line, then shade the region above.
The graph of the inequality is the one below.
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How do you tell if a table represents a linear function?
If the rate of the change in the input to the change in the output is the same for every point in the table, then the table represents a linear function.
If a table of values shows a constant rate of change, it is linear.
A non-vertical graph that is a straight line is linear. An equation that can be written in the form y=mx+b is linear. If a table of values shows a constant rate of change, it is linear.
Linear relationships can be modeled using the slope-intercept form y=mx+b, As x increases, y increases by a proportional amount.
A linear function is a linear relationship that obeys the rules of a function and has a graph that forms a straight line. Function notation is used to express a linear relationship when there are clearly defined inputs and outputs.
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