The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
What is the equation of a perpendicular line?The equation of the line is given below.
2x - y = 4
Then the slope of the perpendicular line will be
y = 2x - 4
m = 2
Then the equation of the line will be
y = -(1/2)x + d
Then the line is passing through (4, 1), then we have
1 = -(1/2)4 + d
3 = d
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
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There is one bus driver, two coaches, and three teams, each with four dancers going to a competition. Nia writes the expression 1 + 2 + 3 ∙ 4 to represent everyone that will be on the bus and solves it using the following steps:
1 + 2 + 3 ∙ 4
= 3 + 3 ∙ 4
= 6 ∙ 4
=24
A. Nia concludes that 24 people will be on the bus going to the competition. Describe the mistake Nia made when solving her expression. Then write an explanation and draw a picture to help Nia understand how to solve her expression correctly.
B. How would you write this expression if n represents the number of teams?
C. How would this expression be different if there were two coaches for each team? Write an expression and draw a picture to support your expression.
A. The mistake that Nia made when solving her expression is that she added all the numbers before multiplying by 4.
B. The expression, if n represents the number of teams, will be 3 + 4n.
C. The expression be different if there were two coaches for each team will be 1 + 6n 4.
How to illustrate the information?It should be noted that the mistake that Nia made when solving her expression is that she added all the numbers before multiplying by 4.
Therefore, the correct answer will be:
= 1 + 2 + 3 × 4
= 1 + 2 + (3 × 4)
= 3 + 12
= 15
B When the number of teams is n, with four dancers in each, then the expression is:
1 + 2 + 4n = 3 + 4n
C When the number of teams is n and each team consists of two coaches and 4 dancers then the expression is:
1 + (2 + 4)n = 1 + 6n
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Correct way of calculation, using PEMDAS
1 + 2 + 3 · 4 = Multiply first1 + 2 + 12 = Add all together15 Correct answerThe mistake was incorrect order of operations. Addition (A) comes after multiplication (M) or division (D) if no parenthesis (P) or exponents (E) present.
Part BIf the number of teams is n, with four dancers in each, then the expression is:
1 + 2 + 4n or3 + 4nHere 4n is the number of dancers in n teams.
Part CIf the number of teams is n and each team consists of two coaches and 4 dancers then the expression is:
1 + (2 + 4)n or1 + 6nHere 6n is the number of coaches and dancers in n teams.
The Atlanta Falcons scored 13 more points than twice the number of points that the Miami Dolphins scored. Altogether, the teams scored 43 points. How many points did the Dolphins score? Is 21 a viable solution to this problem?
Yes, because 21 points is less than the total number of points scored
No, because 2(21) + 13 ≠ 43
Yes, because 21 points is less than the number of points Atlanta scored
No, because 2(21) ≠ 43
Answer:
No, because 2(21) + 13 is not equal to 43.
The Dolphins scored 10 points.
Step-by-step explanation:
A = 13 + 2D
43 = 13 + A + D
43 = 13 + 3D
43 - 13 = 30
30 = 3D
30/3 = 10
D = 10
A = 13 + 2(10)
A = 33
D + A = 43
33 + 10 = 43
Therefore, the Atlanta Falcons scored 33 points which is 13 points more than twice what the Dolphins scored.
Laci and Leon are saving money to go to an amusement park. Laci has $1 more than 4 times the amount of money Leon has. Together, they have $76. Write an equation to determine how much money they have together
Answer:
Step-by-step explanation:
x+4x+1=76 is the answer
(x−4)(x−6)
Cómo lo hago?
Ayuda!! me confunden mucho los signos!! :((
Choose the vocabulary term that correctly completes each sentence.
If an infinite geometric series ______ then it must have a sum.
If an infinite geometric series is a convergent series then it must have a sum.
What is a convergent series?
If a series' partial sum sequence tends to a limit, it is said to be convergent (or to be convergent)This indicates that as partial sums are added in the order indicated by the indices, they approach closer and closer to a certain number. When a series becomes closer to a particular value as it gets closer to infinity, it is said to be convergent. A series in mathematics is the total of all the terms in an infinite series of numbers.Two forces must be moving in concert for there to be convergence. If a finite real number L serves as the limit of a sequence of real numbers, the sequence is said to be convergent.To learn more about convergent series, refer:
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The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is not important is called the rule for?.
Combination is the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects, where order of selection is not important.
The formula for combination is given by:
C = N! / n!(N - n)!
where N is the set of objects
and n is the number of objects to be selected from N
example: If the order doesn't matter, how many ways can 3 girls be selected from a group of 5 girls?
C = N! / n!(N - n)!
where N = 5 and n = 3
C = 5! / 3!(5 - 3)!
C = 120/(6)(2)
C = 10
Hence, there are 10 ways to select 3 girls from a group of 5 girls.
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Identify a pattern and find the next three numbers in the pattern.
6,12,18,24, . . .
The answer is 6, 12, 18, 24, 30, 36, 42.
The pattern is in increasing order i.e., +6.
How to find the pattern in the numbers?Given,
6,12,18,24, . . .
Solution:
Note the difference in the given number series 6,12,18,24, . . .
12 - 6 = 6
18 - 12 = 6
24 - 18 = 6
The difference is common and is 6.
The sequence is in increasing order.
So, add 6 to 24 and the consecutive numbers to get the answer.
24 +6 = 30
30 +6 = 36
36 + 6 = 42
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Find the slope of the line that contains the points (4,3) and (-2,-5).
The slope of the line that contains the points (4,3) and (-2,-5) is 4/3
In this question,
we need to find the slope of the line that contains the points (4,3) and (-2,-5).
We know that the slope of the line passing though points (x1, y1), (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (4, 3),
(x2, y2) = (-2, -5)
Using the formula of the slope,
m = (y2 - y1) / (x2 - x1)
m = (-5 - 3) / (-2 - 4)
m = -8 / (-6)
m = 4/3
Therefore, the slope of the line that contains the points (4,3) and (-2,-5) is 4/3
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Solve each inequality. Check your solution. 3n < -4(2+n)
The inequality given by 3n < -4(2 + n) has the solution n < -8/7 or (-∞ , -8/7).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality 3n < -4(2 + n), expand the right term by distributing -4 inside the parenthesis.
3n < -4(2 + n)
3n < -8 - 4n
Add 4n to both sides.
3n + 4n < -8 - 4n + 4n
7n < -8
Divide both sides by 7
7n < -8
n < -8/7
To check, let n = -9/7
n = -9/7 < -8/7
Substitute this value to the inequality.
3n < -4(2 + n)
3(-9/7) < -4(2 + -9/7)
-27/7 < -20/7
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In this problem, you will investigate expected value.
b. Use the random number generator on a calculator to generate, 20 pairs of integers between 1 and 6 . Record the sum of each pair.
The 20 randomly generated pairs for the numbers 1 to 6 is (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6) and the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.
Sum of the number:
When we add two or more numbers, the result or the answer we get can be defined as the SUM. The numbers that are added are called addends.
For example if we add the numbers 2 and 7 then we get the um as 9.
Given,
Here we need to generate the 20 pairs of integers between 1 and 6 . And also we have to record the sum of each pair.
The 20 pairs by using the number 1 to 6 are,
Listed as,
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6).
Now the sum of these 20 pairs are,
(1,1) = 1 + 1 = 2
(1,2) = 1 + 2 = 3
(1,3) = 1 + 3 = 4
(1,4) = 1 + 4 = 5
(1,5) = 1 + 5 = 6
(1,6) = 1 + 6 = 7
(2,2) = 2 + 2 = 4
(2,3) = 2 + 3 = 5
(2,4) = 2 + 4 = 6
(2,5) = 2 + 5 = 7
(2,6) = 2 + 6 = 8
(3,3) = 3 + 3 = 6
(3,4) = 3 + 4 = 7
(3,5) = 3 + 5 = 8
(3,6) = 3 + 6 = 9
(4,4) = 4 + 4 = 8
(4,5) = 4 + 5 = 9
(4,6) = 4 + 6 = 10
(5,5) = 5 + 5 = 10
(5,6) = 5 + 6 = 11
Therefore, the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.
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Under a microscope, a single celled organism 200 microns in length appears to be 50 millimeters long. If 1 millimeter =1000 microns, what magnification setting (scale factor) was used? Explain your reasoning.
The length of the organism in millimeters is 200 ч 1000 or 0.2 mm.
What is a microscope?A microscope is a laboratory tool used to examine objects that are too small to see with the eye. Microscopy is the science of using a microscope to examine small objects and structures. Microscopic means invisible to the eye unless magnified.There are numerous types of microscopes, and they can be classified in various ways. One method is to describe the method a device uses to interact with a sample and produce images, such as sending a beam of light or electrons through a sample in its optical path, detecting photon emissions from a sample, or scanning across a short distance from a sample.In the given situation, the organism's length in millimeters is 200 ч 1000 or 0.2 mm.
Therefore, the length of the organism in millimeters is 200 ч 1000 or 0.2 mm.
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Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.
Answer:
Her age is 15.
Step-by-step explanation:
13 + 14 + 15 = 42
Julia is the oldest and 15 is the greatest of the 3 numbers
therefore Julia is 15
hj2 ÷ 5; use h = 5, and j = 5
The hj and the 2 after it is supposed to be squared so it’s 2 squared.
Answer:
25
Step-by-step explanation:
Work shown in the attached screenshot!! Please let me know if you have any questions! :)
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=x-2(x+5)
The given function y = x- 2(x+5), is a linear function.
It has no quadratic termIts linear term is -xIts constant term is -10What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree.
We rewrite the function and reduce it to its minimum expression:
y = x- 2(x+5)
y = x + (-2x - 10)
y = x - 2x - 10
y = -x - 10 , linear function.
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Find the missing term(s) of each geometric sequence. -20 ~, □,□,□,-1.25, l . . . l . . .
Missing terms of the geometric sequence = -10, -5, -2.5
For the geometric sequence to the nth term, the formula is
[tex]t_{n}[/tex] = a [tex]r^{n-1}[/tex]
Here the sequence is -20, __ , __, __, -1.25...
So we have to find the 2nd, 3rd and 4th terms of the sequence.
We know the 5th term of the series by which we can find out the common ratio.
[tex]t_{5}[/tex] = -20 [tex]r^{5-1}[/tex]
-1.25 = -20 [tex]r^{4}[/tex]
[tex]r^{4}[/tex] = 1.25/20
= 1/16
r = 1/2
The common ratio is 1/2
[tex]t_{2}[/tex] = -20 [tex](\frac{1}{2})[/tex]
= -10
[tex]t_{3}[/tex] = -20 [tex](\frac{1}{2} )^{2}[/tex]
= -20 [tex]\frac{1}{4}[/tex]
= -5
[tex]t_{4}[/tex] = -20 [tex](\frac{1}{2} )^{3}[/tex]
= -20[tex]\frac{1}{8}[/tex]
= -2.5
Therefore the missing terms are -10, -5 and -2.5.
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Select the reason that best supports Statement 6 in the given proof.
URGENTTTT!!!
Answer:
B) distributive propertyStep-by-step explanation:
The statements 6 covers the operation:
3(x + 7) = 3x + 21This is the reflection of the distributive property of multiplication.
The matching answer choice is B.
Solve each equation. Check your answer. 43-3 d=d+9
d= 17/2 is the solution of the given equation 43-3 d=d+9.
According to the given question.
We have a linear equation in one variable 43 -3d = d + 9.
Since, we have to solve the above linear equation in one varible 43 -3d = d + 9, which means we have to solve the above equation for d.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofore, the solution of the given linear equation in one variable 43 -3d = d + 9 is given by
43 -3d = d + 9
⇒ 43 - 9 -3d = d (subtracting 9 from both the sides)
⇒ 34 = d + 3d (adding 3d both the sides)
⇒ 34 = 4d
⇒ d = 34/4
⇒ d = 17/2
Now, we will check whether d = 17/2 is the solution of the given equation or not.
Thereofore,
LHS
= 43 - 3(17/2)
= 43 - 51/2
= 86 - 51/2
= 35/2
RHS
= 17/2 + 9
= 17 + 18/2
=35/2
Here, LHS = RHS for d = 17/2
Hence, d= 17/2 is the solution of the given equation 43-3 d=d+9.
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Expand, x³(3x - 5).
3x^4-5x³
Step-by-step explanation:
What are multiples of 5/4?
For example; Kendal is doing math problems to study for an exam, and she has completed 5/4of the number of assigned problems. What multiple of the number of assigned problems has Kendal completed?
I need help
Also, I'm in 6th grade and its a lot harder whenever you are in SEARCH/GT(Smart people classes basically)
pls I'm failing my class and I need to do this grade and get them all right to get my grade up
The multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.
How to illustrate the information?It should be noted that multiples simply mean the answer that one gets when the number of multiplied by any whole number.
Therefore, the multiples will be:
= 5/4 × 2 = 2 1/2
= 5/4 × 3 = 3 3/4
= 5/4 × 4 = 5
Therefore, the multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.
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The “communication revolution” has given us prepaid phone calling cards. These cards are used to make long distance phone calls from any phone. In a recent year the industry posted sales of $500.000. Three years later the sales figure had risen to $200,000,000. What is the increase in sales over the three-year period
The sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.
We have sales record of communication industry.
We have to determine the increase in sales over the three-year period.
What is the advantages of prepaid phone plans?The advantage of using prepaid phone plans is you only pay for the data you use, and you're not tied into a lengthy service contract.
According to the question -
Initial Sales - $500,000
Sales after 3 years - $200,000,000
Therefore, the rate at which the sales increased is -
r = [tex]$\frac{2\times 10^{8}- 5\times 10^{5} }{3}[/tex] = $6,65,00,000
Hence, the sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.
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help me pls pls pls pls pls pls pls pls
Answer:
15, 10, 6
Step-by-step explanation:
Gavin: 2.52 + 6.25 + 6.25 =15.02 = 15
Jason: 6.25 = 6
Evan: 6.25 + 3.72 = 9.97 = 10
i hope this helped if did pls mark brainliest
Compare and contrast inscribed angles and central angles of a circle. If they intercept the same arc, how are they related?
If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.
What is the relation between the central and inscribed angle on the same arc?According to the inscribed angle theorem, an angle inscribed in a circle is half the central angle 2 that subtends the same arc on the circle.
The central angle has the same length as the intercepted arc. As can be seen, if a central angle and an inscribed angle intersect the same arc, the central angle is twice as large as the inscribed angles. Similarly, the inscribed angle equals half of the central angle.
An inscribed angle is one that has its vertex on a circle and its sides are chords. The intercepted arc is the arc that is contained within the inscribed angle and has its endpoints on the angle.
If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.
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Find the value of x2 for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution.
The value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344
Chi-square Distribution:
The chi-square distribution is a continuous probability distribution. It is skewed to the right or positively skewed for low degrees of freedom but shifts towards the symmetric distribution as the degrees of freedom are increased.
Given,
Degree of freedom = 8
Area of the left = 0.05
Here we need to find the value X² of the chi-square distribution.
The value of X² of the chi-square distribution is calculated through the formula,
X² = X²₍₁ ₋ₓ₎,y
Where
x represents the area of the given tails
y represents the degree of freedom
Apply the values on the formula,
=> X² = X²₍₁ ₋₀.₀₅₎,8
=> X² = X²₍₀.₉₉₅₎,8
Now, based on the Chi square distribution table,
The value of
=> X² = 1.344
Therefore, the value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344
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The mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by
y = 3.50x + 6.00
Explain how you can use this linear function to find out how many games you can bowl for $34.
Pls don't send links or wrong answers I WILL REPORT YOU
The number of games that will be played will be 8 games.
How to illustrate the information?It should be noted that the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by
y = 3.50x + 6.00.
The games that you can bowl for $34 will be:
y = 3.50x + 6.00.
34 = 3.50x + 6.00.
Collect like terms
3.50x = 34 - 6
3.50x = 28
Divide
x = 28 / 3.50
x = 8
Therefore, the number of games will be 8 games.
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We have 6 books on mathematics, 3 on physics, and 1 on chemistry, and you must choose 1 book. in how many ways can you do that? (also think why the an
The number of ways that a book can be chosen from all the books can be determined by using combination.
Combination is a method of choosing items from a set in a way that order of selection does not matter. It refers to the combination of n items taken k at a time without repetition. From example, selection of food, menu, subjects, etc.
A combination is the selection of r items from a set of n items without replacement and where order is unimportant.
nCr=n!/r!(n-r)!
Where n! = 1*2*3*….*n
In the given situation, r = 1(number of books to be chosen) and n=10(total number of books)
10C1=10!/1!(10-1)!
10C1=10!/1!(9)!
10C1=(10*9!)/1!(9)!
10C1=10
The number of ways to choose a book from the ten books is 10.
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f(x)= -x-5 g(x)=x^2-6x+13 find f(g(x))
Answer:
f(g(x)) = x² - 6x + 8
Step-by-step explanation:
to evaluate f(g(x)) , substitute x = g(x) into f(x)
f(x² - 6x + 13)
= x² - 6x + 13 - 5 ← collect like terms
= x² - 6x + 8
points A(-1.5) and b(6) are marked on a number line. find the coordinate of point m if it is know that AM:md = 1:2
The coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
How to find the coordinates of point m?The given parameters are
A = (-1, 5)
B = (6, 5)
Ratio, m : n = 1 : 2
The coordinates of point m are calculated using
M = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
M = 1/(1 + 2) * (1 * 6 + 2 * -1, 1 * 5 + 2 * 5)
Evaluate the sum of products
So, we have
M = 1/3 * (4, 15)
Evaluate the product
M = (4/3, 5)
Hence, the coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
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What are the next three terms in the sequence, 500, 100, 20?
Answer: –1, 9, 19, 29, … (1 point)
38, 37, 32
40, 51, 62
39, 49, 59
38, 47, 56.
Step-by-step explanation: tried
What is the expected number of times Clarence will roll doubles with two number cubes in 90 trials? (Doubles occur when both number cubes show the same number in a trial.)
F. 6
G. 9
H. 10
J. 15
For 90 trials , expected no. of times of rolling doubles will be 15 times.
It is given that Clarence roll doubles with two cubes.
We have to find out the expected number of times of rolling doubles in 90 trials.
What do you mean by probability ?
Probability is the ratio of the number of favorable outcomes to the total number of outcomes of an event.
As per the question ;
Clarence roll doubles in 90 trials with two cubes.
We know that ;
There are 36 outcomes for a pair of dice.
So ;
In a pair , there are 6 possible doubles.
i.e.,
1-1 , 2-2 , 3-3 , 4-4 , 5-5 and 6-6
So ;
Probability will be ;
= 6 / 36
or
= 1 / 6
And
For 90 trials , expected no. of times of rolling doubles will be ;
= [tex]\frac{1}{6}[/tex] × 90
= 15 times
Thus , for 90 trials , expected no. of times of rolling doubles will be 15 times.
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what is the inverse of h(x)=7x^2+8 with the domain restriction x greater than or equal to 0
The inverse of the function is f-1(x) = √1/7(x - 8)
How to determine the inverse of the function?The function is given as
h(x) = 7x^2 + 8
Express h(x) as y
So, we have
y = 7x^2 + 8
Swap the positions of x and y
So, we have
x = 7y^2 + 8
Rewrite as
7y^2 = x - 8
Divide by 7
y^2 = 1/7(x - 8)
Take the square roots
y = √1/7(x - 8)
Hence, the inverse of the function is f-1(x) = √1/7(x - 8)
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