Answer:
The only true statement is:
"The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution."
Step-by-step explanation:
First, some definitions.
A system of linear equations has infinite solutions if both equations define the same line, has no solutions if we have two parallel lines, has one solution in all the other cases.
Where two lines are parallel if we can write them as:
a*x + b*y = c
a*x + b*y = d
where c and d are different numbers.
Now we can analyze the given statements:
a)
6x - 5y = 8
12x - 10y = 16
has no solution?
If we divide both sides of the second equation by 2, we get:
(12x - 10y)/2 = 16/2
6x - 5y = 8
We get the first equation, then both equations define the same line, thus the system has infinite solutions, then the statement is false.
b)
7x + 2y = 6
14x + 4y = 16
has infinite solutions?
Let's divide the second equation by 2, then we get:
(14x + 4y)/2 = 16/2
7x + 2y = 8
If we rewrite our system of equations, we get:
7x + 2y = 6
7x + 2y = 8
These are parallel lines, thus, this system has no solutions.
So the statement is false.
c)
8x - 3y = 10
16x - 6y = 22
has no solution?
Again, let's divide the second equation by 2 to get:
(16x - 6y)/2 = 22/2
8x - 3y = 11
If we rewrite our system:
8x - 3y = 10
8x - 3y = 11
These are parallel lines, thus the system has no solutions, so this statement is correct.
d)
9x + 6y = 14
18x + 12y = 26
Has infinite solutions?
Dividing the second equation by 2 we get:
(18x + 12y)/2 = 26/2
9x + 6y = 13
So the equations are different (are parallel lines again) so this system has not infinite solutions.
Then the statement is false.
Answer:
The answer to your question is the third choice.
Step-by-step explanation:
a) 6x - 5y = 8
12x - 10y = 16
We observe that these lines are the same so they have infinite solutions.
b)
7x + 2y = 6
14x + 4y = 16
These lines are parallel because they have the same slope, so they do not cross, there is no solution.
c)
8x - 3y = 10
16x - 6y = 22
These lines are parallel because they have the same slope, so they do not cross, there is no solution.
d)
9x + 6y = 14
18x + 12y = 26
These lines are parallel because they have the same slope, so they do not cross, they do not have an infinite number of solutions.
The club with an occupancy of 100 will sell out at $25 per ticket. If the owner decides to increase the price by $5, then 2 less tickets will be sold. Determine the revenue function if x is the number of $5 increases.
Answer:
100 + (5X) = -2X
Step-by-step explanation:
Since the club with an occupancy of 100 will sell out at $ 25 per ticket, and if the owner decides to increase the price by $ 5, then 2 less tickets will be sold, to determine the revenue function if X is the number of $ 5 increases the following calculation must be performed:
100 + (5X) = -2X
So, for example, if the price were increased by $ 15, the equation would apply as follows:
15/5 = 3
100 + (5x3) = -2 x 3
100 + 15 = -6
115 = -6
0.36% as a fraction in simplest form
Answer: 9/2500
Step-by-step explanation:
We start with turning it into a fraction:
0.36/100
Then, we turn every number into a whole number by multiplying by whatever the last decimal place is called (hundreth= x100)
36/10000
Lastly, we simplify as much as we can by finding the least common denominator. In this case, the smallest whole number both 36 and 10000 can be divided by is 4:
(36/4)/(10000/4)
= 9/25000
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Which is the graph of g(x)
Answer:
the second one after first
Step-by-step explanation:
it strictly obeys the rules of boundary
Select the correct answer.
Which expression is equivalent to the glven expression?
(3m-4)^3(3m^5)
A. 81/m^2 B.27/m^7 C. 27/m^2 D.81/m^7
The correct expression which is equivalent to the given expression is,
⇒ 81 / m⁷
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (3m⁻⁴)³ (3m⁵)
Now, We can simplify as;
⇒ (3m⁻⁴)³ (3m⁵)
⇒ (3³m⁻¹²) (3m⁵)
⇒ (27m⁻¹²) (3m⁵)
⇒ 81 m⁻¹²⁺⁵
⇒ 81 m⁻⁷
⇒ 81 / m⁷
Thus, The correct expression which is equivalent to the given expression is,
⇒ 81 / m⁷
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Tell wether x and y show a proportional relationship.
x 1 2 3 4
y 4 8 12 16
Answer:
They do because y is always 4 times of x.
Step-by-step explanation:
A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours
Answer:
The Sample Size Need To be at least 114
Step-by-step explanation:
According to the Question,
Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.The Maximum Error(E) is given as 1.5 hours and the standard deviation(σ) is 6.2 hours.
Now, For 99% Confident the level of value α is 0.01.α/2 = 0.01/2 ⇒ 0.005
Thus, From The table, We get that the value of [tex]Z_{alpha/2}[/tex] is 2.58.Hence, the sample size n can be found as
n = {[tex]\frac{(Z_{alpha/2} * Standard Deviation)}{E}[/tex]}²
n = {2.58 × 6.2}² / 1.5²
n = 113.72 .
So, The Sample Size Need To be at least 114.
I would appreciate if someone could answer this
Answer:
x = 15
LN and MO both equal 43
Step-by-step explanation:
LN and MO are diagonals in rectangle
Diagonals of a rectangle are congruent Hence, 4x - 17 = 2x + 13
Now we solve for x
4x - 17 = 2x + 13
Add 17 to both sides
4x = 2x + 30
Subtract 2x from both sides
2x = 30
Divide both sides by 2
x = 15
Now we want to find the values of LN and MO
To do so we substitute 15 for x in it's given expression ( note: because LN = MO we only need to do this process once )
LN = 4x - 17
Substitute 15 for x
4(15) - 17
Multiply
60 - 17
Subtract
LN and MO = 43
Please, I'm desperate need of help I will mark Brainliest to the one who answers with the full process! Gold will Bless You!
Two angles of a triangle are 85° and 65°, and the longest side of the triangle is 34 cm. How long is the shortest side? Include a labelled diagram.
Add 65 and 85
65+85= 150
Next subtract 180-150
The answer is 30, so that is the missing angle is 30.
The side opposite to 30 is the shortest side
Here I added the picture!
Which equation represents the function y - 5 = –2(x+3) in slope-intercept form?
Oy= 2x + 1
Oy = 2x - 1
Oy= -2x - 1
Oy = -2x + 11
Oy = -23 - 11
Answer:
-2x-1
Step-by-step explanation:
when you graph the equation it gives you a decreasing slope with the y intercept of -1. the slope is 2 and since its decreasing it is -2. therefore its -2x-1
The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
given that,
the function y - 5 = –2(x+3)
now, we have to find in slope-intercept form.
now, we have,
function has a decreasing slope with the y intercept of -1. the slope is 2
and since its decreasing it is -2.
again, we have,
y - 5 = –2(x+3)
or, y = -2x - 6 + 5
or, y = -2x -1
here, slope = m = -2
and, y-intercept = c = -1
as, we know that,
slope-intercept form is: y = mx+ c
so, we get, y = -2x -1
Hence, The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .
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Use slopes and y-intercepts to determine if the lines y=−2/3x+2 and −3x+2y=−4 are parallel.
Answer:
the answer is no
Step-by-step explanation:
y = -2/3x+2
2y = 3y-4
y = 3/2y-2
but here's a comment: it is perpendicular because it is it's opposite reciprocol
plz it's do to day HELP PLZ
Answer:
9 units^3
Step-by-step explanation:
V = l*w*h
= 1 1/2 * 4 * 1 1/2
Change to improper fractions
= 3/2 * 4 * 3/2
= 36/4
= 9 units^3
Simplify (2 1/6 - 1 2/3) - 2 2/3
Answer:
[tex]- 2\frac{1}{6}[/tex]
Step-by-step explanation:
[tex](2\frac{1}{6} -1\frac{2}{3}) - 2 \frac{2}{3}[/tex]
[tex](\frac{13}{6} -\frac{5}{3}) - 2 \frac{2}{3}[/tex]
[tex](\frac{13}{6} -\frac{10}{6}) - 2 \frac{2}{3}[/tex]
[tex]\frac{3}{6} - 2 \frac{2}{3}[/tex]
[tex]\frac{3}{6} - \frac{8}{3}[/tex]
[tex]\frac{3}{6} - \frac{16}{6}[/tex]
[tex]- \frac{13}{6}[/tex]
[tex]- 2\frac{1}{6}[/tex]
Riley's cat has 8 kittens. Of those 8 kittens, 4 are brown, 1 is grey, and the rest are orange. Which of the following could be used to find the probability that the first kitten Riley picks up at random is NOT orange?
Answer:
5/8 or 62.5 percent
Step-by-step explanation:
Which of the following functions has a rate of change that stays the same?
A. y=-4+10
B. y=1/2x^2
C. y=3^x
D. y=x^2+2
Answer:
The answer is A because the rest are parabolas
Simplify the fraction to lowest terms.
56/
182
Which expression is equivalent to 5^15 x 5^5
Answer:
[tex]5^{15} * 5^{5}[/tex]
= [tex]25^{20\\}[/tex]
What is half of 3/4 in fraction?
Answer:
3/8
Step-by-step explanation:
1/2 times 3/4= 3/8
Find the equal measures of 1. 28 m = ________ km 2. 3899 ml = ______ l 3. 79 kg = _____ g Show the process of each
Answer:
1. 0.028 km
2. 3.899 L
3. 79,000 g
A grocery store chain uses loyalty cards that offer discounts on sale attheir store. The probability that a randomly chosen shopper has a loyaltycard is 0.8. A group of shoppers have been selected at random to completea customer satisfaction survey. Let Xi be a random variable that equals 1 when a customer has a loyalty card and 0 otherwise.
Required:
a. Construct a joint probability table for the random variables X, and X.
b. Define the event that the first four customers sampled have loyalty cards in terms of the random variables X, X2, X3, and Xd. Then compute the probability of this event.
Identify the x-intercept points of the parabola
Answer:
(3,0) and (-1,0)
Step-by-step explanation:
The X intercept are the point(s) where the line croses the X axis (the horizontal/leftright line). the points for this graphing system are always listed (x,y) so to find a certain point you find the X value then the Y value
11. f(x) = x + 3, g(x) = -x + 2. Find (f + g)(x)
Answer:
(f + g)(x) = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x + 3
g(x) = -x + 2
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in function values: (f + g)(x) = x + 3 - x + 2[Subtraction] Combine like terms (x): (f + g)(x) = 3 + 2Add: (f + g)(x) = 5If using the method of completing the square to solve the quadratic equation
x^2 + 8x – 4 = 0, which number would have to be added to "complete the square"?
Step-by-step explanation:
everything can be found in the picture
Please answer this, I am confused (5^2)(7^2)(3^2)
Given:
The expression is:
[tex](5^2)(7^2)(3^2)[/tex]
To find:
The value of the given expression.
Solution:
We have,
[tex](5^2)(7^2)(3^2)[/tex]
On simplification, we get
[tex](5^2)(7^2)(3^2)=(25)(49)(9)[/tex]
[tex](5^2)(7^2)(3^2)=11025[/tex]
Therefore, the value of the given expression is 11025.
In general, half of all the customers you speak to will ask about any upcoming pricing discounts or promotions. Of those who do ask, only 20% qualify for the discount. So that means if I speak to 300 customers, how many will qualify for the discount
Answer:60
Step-by-step explanation:
300 of 20% is 60
The number of qualified customers for the discount will be 60.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
It is given that half of all the customers you speak to will ask about any upcoming pricing discounts or promotions. Of those who do ask, only 20% qualify for the discount. So that means if I speak to 300 customers.
The number of qualified customers will be calculated as below:-
The qualified customers are 20% of 300.
Number = 300 x (20/100)
Number = 300 x 0.2
Multiply the number 330 with 0.2 to get the final value.
Number = 60
Therefore, the number of qualified customers for the discount will be 60.
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A student is taking a multiple-choice exam in which each question has four choices.
Assume that the student has no knowledge of the correct answers to any of the questions.
She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box.
She randomly selects one ball for each question and replaces the ball in the box.
The marking on the ball will determine her answer to the question.
There are five multiple choice questions on the exam.
What is the probability that she will get
a. Five questions correct?
b. At least four questions correct?
c. No questions correct?
d. No more than two questions correct?
Answer:
d no more than two questions correct
An aeroplane descended 1.4 miles to an elevation of 0.6 miles as shown by the equation below.
Solve the equation to find the elevation of the plane before its descent.
x-1.4 = 0.6
A 0.8
B 1.0
C 2.0
D 1.2
Quick
Answer:
C 2.0
Step-by-step explanation:
x-1.4 =0.6
add 1.4 to both sides
x=2.0
What is the value of y in the equation 3y - 8 = 22?
7.3
8
10
14
I would really appreciate if someone could answer this:)
Answer:
first you need to know that the the sum of the co-interior angle is 180 degree and the sum of the opposite side of parallelogram is always equal.
now x+140=180(being co - interior angle)
or, x= 180-140
therefore, x =40 degree
y= 140 degree because sum of the opposite side of parallelogram is always equal.
x= z=40 degree (sum of the opposite side of parallelogram is always equal.
when you are again confused go in this link
----> https://www.scholr.com/ncert-solutions/consider-the-following-parallelograms-fi/40087/
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I neeed the answer plssss
Answer:
300km
Step-by-step explanation:
if 1 hr=80
then take 80 and multiply it by 3.75
hope this helps!
please give brainiest if you want<3
Answer:
300km
Step-by-step explanation:
Triangle ABC IS dilated using the origin as the center of dllation to create triangle A'B'C'. What rule best represents the dilation applied to triangle ABC to
