The equation in function form is f(x)=-4x+80.
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
We can find the equation in function form as shown below:
We have given two points (5,60) and (10,40)
Slope of line
m = (40-60)/ (10-5)
m=-20/5
m=-4
Equation in slope intercept form
(y-y1) =m(x-x1)
(y-60) =-4(x-5)
y-60=-4x+20
y=-4x+20+60
y=-4x+80
y=f(x)
f(x)=-4x+80
Hence, the equation in function form is f(x)=-4x+80.
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WILL MAKE BRAINLIEST!!Determine if the two triangles are congruent if they are state the postulate or theorem that provides they are congruent
Answer:
Yes they are congruent by SSS criterionStep-by-step explanation:
AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion.
Which number(s) satisfy a ∩ c? 16, 81 1, 16, 81 1, 4, 9, 16, 25, 36, 49, 81, 100 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer:
Step-by-step explanation:
B: 1, 16, 81
WHY?
Set A is perfect squares from A to 100:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
Set A = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Set C is perfect fourths
1^4 = 1
2^4 = 16
3^4 = 81
4^4 = 254 (This is greater than 100)
Set C = 1, 16, 81
Hope this helps :)
Find the indicated term of the geometric sequence.
10th term of 0.6, 0.06, 0.006,...
Answer:
0.0000000006
Step-by-step explanation:
0.6 * (0.1)^9 = 0.0000000006
What does the following expression mean? x <= y
As per inequality, it means that the value of x can be less than or equal to y.
Inequality in Mathematics
The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >, <, ≤, or ≥ are used to denote an inequality, when the two expressions aren't always equal.
Type of Inequality
The given expression, x <= y denotes the type of inequality where the possible values of x are either less than y or equal to less. The value of x cannot be greater than y in any case.
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The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is 10.4 inches and the length of each side is 12 inches.
The are of the triangle is mathematically given as
a=62.4in^2. This is further explained below.
What is the area of the triangle?Generally, the equation for the area is mathematically given as
a= 0.5(base X height)
Therefore
a= 0.5 (10.4 x 12)
a=62.4in^2
In conclusion, The area of the triangle is
a=62.4in^2
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Find the measure of each numbered angle.
Step-by-step explanation:
18z+10z+40z+5+1=360
68z+6=360
68z=360-6
68z=364
z≈5.353
solve -9 2/7 - (-10 3/7)
Find the indefinite integral by making a change of variables. (hint: let u be the denominator of the integrand. remember to use absolute values where appropriate. use c for the constant of integration.) 1 9 2x dx
The value of the indefinite integral is
Given:- The integration of is given whose lower limit is and upper limit is .
To Find:- We have to find the value of the integration of is given whose lower limit is and upper limit is .
By using the concept of indefinite integral it will be solved.
According to the problem,
Therefore, the value of the indefinite integral is .
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Who am I ?
- My thousands digit is 4
- My hundreds digit is 4 less than the digit in the thousands place
- The sum of my tens digit and ones digit is 7
- My tens digit is 3 more than my ones digit
- The digits in the thousands period have a sum of 10
- My first digit is half the digit that immediately follows it.
I am the number_______________
I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )
Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he prepared 20 cupcakes in 30 minutes.
A) Does the scenario represent a direct variation?
B) If yes, explain the meaning of the constant of proportionality in the scenario.
take your time if you want :)
a) As the constants are equal, the situation represents a proportional relationship.
b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the constants for each situation are:
k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.
Since the constants are equal, the situation represents a proportional relationship.
The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
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Members of a softball team raised $1353 to go to a tournament. They rented a bus for
$943.50 and budgeted $31.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Equation:
Answer: x =
Submit Answer
attempt 1 out of 2
The equation which can be used to determine x, the number of players the team can bring to the
tournament is 1353 = 943.50 + 31.50x and x = 13 players
EquationTotal amount raised = $1353Cost of renting a bus = $943.50Cost of each player's meal = $31.50Number of players in the team = x1353 = 943.50 + 31.50x
1353 - 943.50 = 31.50x
409.50 = 31.50x
x = 409.50 / 31.50
x = 13 players
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Which of the following is an arithmetic sequence where a₁ = 9 and d= 7?
A) 9, 16, 23, 30, 37, ...
B) 0, 9, 18, 27, 36,...
C) 7, 16, 25, 34, 43,...
D) 0, 7, 14, 21, 28, ...
Answer:
Option A
Step-by-step explanation:
Arithmetic sequence:In a arithmetic sequence, difference between any two consecutive term is constant.
a₁ = 9 & d = 7
t₁ = 9
t₂ = a₁ + d
= 9 + 7
= 16
t₃ = t₂ + d = 16+ 7
= 23
t₄ = t₃ + d
= 23 + 7
= 30
t₅ = t₄ + d
= 30 + 7
= 37
9,16,23,30,37,.......
What is the solution to the system of equations? (7, 4) (7, startfraction 13 over 3 endfraction) (8, startfraction 14 over 3 endfraction) (9, 7)
The points are (7, 13/3).
Lets simplify the equation,
The equation of first line: y = 1/3 x + 2
the equation of second line: y= 4/3x - 5
Solve the system of equations by elimination,
Multiply equation A by -4 both sides
-4y = -4(1/3x +2)
-4y = -4/3x-8
After eliminating the equation we get,
y = 13/3
So now have to find x
13/3 = 1/3x + 2
Lets multiply above by 3
x = 13-6
x = 7.
Hence the points are (7, 13/3)
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Answer:
B
Step-by-step explanation:
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
At a charity fundraiser, each female attendant donated $1,200 and each male attendant donated $800. If the average donation at the fundraiser was $900, what was the ratio of the number of female attendants to the number of male attendants.
Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem:
There were f + m donations.The sum was of 1200f + 800m.The average was of 900.Hence:
[tex]\frac{1200f + 800m}{f + m} = 900[/tex]
1200f + 800m = 900f + 900m
100m = 300f
[tex]\frac{f}{m} = 3[/tex]
Hence the ratio was of 3.
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You estimate that there are 40 marbles in a jar. the actual amount is 34 marbles. find the percent error. round to the nearest tenth of a percent if necessary.
The percentage error of the given estimation is 17.7%.
The percentage error of any estimation is calculated as:
Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.
In the question,
The estimated value is given to be 40 marbles.
The actual value is given to be 34 marbles.
We are asked to find the percentage error of this estimation.
We know that:
Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.
Substituting the values, we get:
Percentage error = {(|34 - 40|)/34}*100%,
or, Percentage error = 6/34*100%,
or, Percentage error = 17.6470 % = 17.7% (Rounding to the nearest tenth, that is, up to one decimal place).
Thus, the percentage error of the given estimation is 17.7%.
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how to simplify cos(6x) + 1
What is the nth term of the sequence below?
2, 6, 12, 20, . . .
A. [tex]n {}^{2} \: + \: 1[/tex]
B. [tex]3n[/tex]
C. [tex]n(n \: + \: 1)[/tex]
D. [tex] {n}^{2} \: - \: 1[/tex]
Answer:
Option C
Kindly award branliest
Step-by-step explanation:
Tn = n(n + 1)
T1 = 1(1 +1) = 1(2) = 2
T2 = 2(2+1) = 2(3) =6
T3 = 3(3 + 1) = 3(4) = 12
T4 = 4(4 + 1) = 4(5) = 20
... It obeys
A polynomial function has a root of 0 with multiplicity 1, and a root of 2 with multiplicity 4. If the function
has a negative leading coefficient, and is of odd degree, which of the following are true?
The function is positive on (-∞, 0).
The function is negative on (0, 2).
The function is negative on (2, ∞).
The function is positive on (0,0).
Using the Factor Theorem to find the function, the correct statement is:
The function is positive on (0,∞).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
The described roots means that:
[tex]x_1 = 0, x_2 = x_3 = x_4 = x_5 = 2[/tex]
Hence the function is:
f(x) = x(x - 2)^4
(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:
The function is positive on (0,∞).
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Help solve these (find the slope of each line) 8 problems don’t just give the answer show your work please
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
A zoologist researched the feeding habits of lemurs. she collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. what kind of statistical study did the zoologist conduct?
The kind of statistical study the zoologist conducted was D. observational study.
What is observational study in research?An observational study serves as a study whereby the researcher simply observes the subjects without interfering with it.
This is different from carrying out experiment on them or just a theoretical approach.
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CHECK THE COMPLETE QUESTION BELOW:
A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study
[tex]4(x+y)^{2} -20(x+y)^{2} +25z^{2}[/tex]
Answer:
I am pretty sure that it is 625.
Answer:
Step-by-step explanation:
please make sure you indicate whether to factorize , simplify, fatorize by grouping , evaluate, or finding the derivative
the product of two numbers is 8933. If each of the two numbers is doubled the product of these larger numbers is?
The product of two numbers when doubled, the product of these larger numbers is 35,732
Productlet
The two unknown number = x and yproduct of x and y = 8933
x × y = 8933
If each of the two numbers is doubled2x × 2y = 8933
4xy = 4(8933)
4xy = 35,732
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Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".
What is Multiplicative rule?The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.
If A and B are dependent events, then the probability of both events occurring simultaneously is given by:
[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]
The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:
[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]
Multiplication Theorem of Probability:
The multiplication guidelines that we use in probability have already been taught to us, including;
[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]
Therefore, the relationship between two events is explained by the probability multiplication rule.
Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.
Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.
Using the characteristics of conditional probability, the likelihood of event AB is calculated.
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HELP PLEASE ASAP:<
Consider the expressions given below.
A. 2x³ - x² - 6x
B. 2x³ + 8x + 4
C. 3x^4+ x² + x - 7
D. 3x^4 - 3x^2 + 5x - 7
For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x³ 4 + 7x) - (2x³ 8)is equivalent to expression
(-3x² + x¹ + x) + (2x¹ - 7+ 4x)is equivalent to expression
(²2x) (2x + 3)is equivalent to expression
3x² + 5x - 7
Which expresses the correct factorization
of….? look at pic
Answer:
Option 1
Step-by-step explanation:
Find 2 numbers that multiply to give 16 and sum to give +8 :
These numbers are 4 and 4
Now split +8x into +4x and +4x and factor each part :
x²+4x+4x+16 = 0
x(x+4)+4(x+4) = 0
Keep 1 bracket and the terms outside the brackets make their own :
(x+4)(x+4) = 0
(x+4)² = 0
Therefore answer will be Option 1
Hope this helped and have a good day
Multiplica: (5 ft 6 in) x 4.
Answer: 22 ft
Step-by-step explanation:
Let theta be an angle in quadrant iv such as sin theta = -5/8. find the exact value of sec theta and cot theta
Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:
[tex]\sec{\theta} = \frac{8\sqrt{39}}{39}[/tex][tex]\cot{\theta} = -\frac{\sqrt{39}}{5}[/tex]Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used, considering an angle [tex]\theta[/tex].
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem we are given the sine, then the cosine can be found as follows:
[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]
[tex]\cos^2{\theta} = \frac{39}{64}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]
In the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].
What is the secant of an angle?The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:
[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]
What is the cotangent of an angle?The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:
[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]
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There are seven roads that lead to the top of a hill. How many different ways are there to reach the top and come back ( you dont have to go on the same road there and back)?
Answer:
49 different ways
Step-by-step explanation:
If there are seven roads that lead to the top, you have seven possible choices to go to the top of the hill.
Then, to come back to the start, you also have seven possible choices (seven roads), and you can pick any road.
So, if you have seven ways to go up and seven ways to go down, the number of different ways of going to the top and coming back is the product of these numbers of possible choices.
N(total) = N(up) * N(down)
N(total) = 7 * 7
N(total) = 49 different ways
Brainliest pls and tysm!
Help with this word problem!
Answer:
2.0 km
Step-by-step explanation:
The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.
SetupThe law of cosines tells us ...
c² = a² +b² -2ab·cos(C)
Using the given values, we have ...
c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)
SolutionSimplifying the equation, we get ...
c² = 37.89 -37.8cos(26°) ≈ 3.91559
c ≈ 1.979 . . . . km
The width of the strait is about 2.0 km.
Solve:
-5/2 a + 5 = 25
a =
Answer:
A = -8
You're welcome! :)
Answer: a = -8
Step-by-step explanation:
Combine multiplied terms into a single fraction
then find a Find common denominator for the fraction
then Combine fractions with common denominator,
Multiply the numbers, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator,
Multiply the numbers making your equation like this -5a+10=50
subtract 10 by both sides and then you will need to simplify making it
-5a + 40 then you divide them both by the same factor which is -5 then you simplify again making the answer to your question -8