The most appropriate choice for simultaneous linear equation will be given by -
x = 1, y = 1
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
y = −2x + 3
y = 5x - 4
So, -2x + 3 = 5x - 4
5x + 2x = 3 + 4
7x = 7
[tex]x = \frac{7}{7}\\x = 1[/tex]
Putting the value of x in the first equation'
y = [tex]- 2\times 1 +3[/tex]
y = 1
So, x = 1, y = 1
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If the standard deviation of the data values in a sample is 19, what is the variance of the data values?
When the standard deviation of a data set is 19 then the datasets variance will be :
361
What is the relation between standard deviation and variance? This same standard deviation of a set of numbers is the distance between them and the mean. The variance is a measure of how far each point deviates from the mean on average. Variance is the average of all data points within a group, whereas standard deviation is the square root of the variance.variance formula :
variance = σ2
We are given a data set with a standard deviation of 19 and are asked to calculate the variance of the data values.
standard deviation = 19
We know that the variance of a data set is equal to the square of the standard deviation of the data values, so if the standard deviation is 19, the variance will be 19².
variance = standard deviation²
variance = 19²
= 361
As a result, the variance of the data values is 361.
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write the equation of a parabola with stretch 4 and vertex (-5,0)
I need help with 15, 16, 17, and 18 please
Answer:
y = 2x + 2
Explanation:
We can use the following equation to write an equation in slope-intercept form.
[tex]y-y_1=m(x-x_1)[/tex]Where (x1, y1) is a point in the line and m is the slope. Additionally, the slope can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x2, y2) is another point in the line.
So, replacing (x1, y1) by (0, 2) and (x2, y2) by (3, 8), we get that the slope is equal to:
[tex]m=\frac{8-2}{3-0}=\frac{6}{3}=2[/tex]Finally, replacing m by 2 and (x1, y1) by (0, 2), we get:
[tex]\begin{gathered} y-2=2(x-0) \\ y-2=2x \\ y-2+2=2x+2 \\ y=2x+2 \end{gathered}[/tex]Therefore, the equation in slope-intercept form is:
y = 2x + 2
what is the equation of the line that passes through the point (6,1) and hs the slope of -1/2?
The equation of the line: y=-1/2x+4
Describe slope.A line's slope is the ratio of how much y increases as x increases by a specific amount. How steep a line is, or how much y climbs as x rises, is determined by its slope. The slope is constant anywhere along the line (the same).
The slope of the line and its passing point are given to us.
Using this information, we can write the equation in point-slope form as follows:
y-y1 = m(x-x1)
y-1 = -1/2(x-6)
y-1 = -1/2x+3
Move -1 to the right now by performing the reverse operation:
y = -1/2x+3+1
y = -1/2x+4
Hence, The equation of line is y = -1/2x+4
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a-2=3+6a/3 what is a
Answer:
a = -5
Step-by-step explanation:
Let's solve the problem,
→ a - 2 = 3 + (6a/3)
→ 2a - a = -2 - 3
→ [ a = -5 ]
Hence, the value is -5.
Light A flashes every 5 seconds.
Light B flashes every 6 seconds.
Light C flashes every 7 seconds.
All three lights flash at the same time.
How many times in one hour will the three lamps flash at the same time?
Answer: 210
Step-by-step explanation:
This question is about LCM.
We are finding the same time for all 3 light flashes.
Light A: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,205,210
Light B: 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150, 156,162,168,174,180,186,192,198,204,210
Light C: 7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126,133,140,147,154,161,168,175, 182,189,196,203,210
Light A: 42 Light B: 35 Light C: 30
I NEED HELP ASAP , no tutor was able to solve this.
given
Number of customers = 20
number of successes = 30% = 0.30
Find
a) Probability of exactly 15 customers will make a purchase.
b) Probability of atleast 15 customers will make a purchase.
c) Probability of atmost 4 customers will make a purchase.
Explanation
here we use binomial distribution.
n = 20
p = 0.30
q = 1 - 0.30 = 0.70
a) Probability of exactly 15 customers will make a purchase =
[tex]\begin{gathered} ^{20}C_{15}(0.30)^{15}(0.70)^5 \\ \frac{20!}{5!15!}(0.30)^{15}(0.70)^5 \\ \frac{20\times19\times18\times17\times16}{5\times4\times3\times2\times1}\times(0.30)^{15}(0.70)^5 \\ 0.00004 \\ \end{gathered}[/tex]b) Probability of atleast 15 customers will make a purchase =
[tex]\begin{gathered} P(X\ge15)=0.00005 \\ \end{gathered}[/tex]c) Probability of atmost 4 customers will make a purchase =
[tex]P(X\leq4)=0.23751[/tex]Final Answer
Hence
a) 0.00004
b) 0.00005
c) 0.2375
Subtract. 15/57−6/45
please help me if u can i need this really fast <33
The resulting value after the subtraction of 15/57 - 6/45 is 37/285
Subtraction:
Subtraction is an arithmetic operation that represents the operation of removing the particular objects from a collection.
It is signified by the minus sign, −.
Given,
Here we need to find the value of the subtraction of 15/57 - 6/45.
The fractions have unlike denominators.
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(57, 45) = 855
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD.
This is basically multiplying each fraction by 1.
[tex]\frac{15}{57}\times\frac{15}{15}-\frac{6}{45}\times\frac{19}{19}[/tex]
Complete the multiplication and the equation becomes
=> 225/855 - 114/855
Complete the multiplication and the equation becomes
=> 111/855
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 111 and 855 using
GCF(111,855) = 3
[tex]= > \frac{111 \div 3}{855 \div 3} = \frac{37}{285}[/tex]
Therefore, resulting value is 37/285.
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What value of m makes this equation true? m/4−3=9
Answer:
m = 48
Step-by-step explanation:
m/4-3 = 9
lets add 3 on both side
m/4 = 12
now lets multiply both sides by 4
m = 48
Answer: m=48
Step-by-step explanation:
48/4=12
12-3=9
9=9
Therefore m=48 as it makes the equation true.
What is the remainder when P (x) is divided by (x + 1)?
Answer:
4
Explanation:
From the graph, the roots of the polynomial are -2, 1, and 1.
Therefore, the polynomial P(x) is defined below:
[tex]P(x)=(x+2)(x-1)(x-1)[/tex]When P(x) is divided by x+1, the remainder will be the value of x when x+1=0
When x+1=0
[tex]x=-1[/tex]Therefore:
[tex]\begin{gathered} P(-1)=(-1+2)(-1-1)(-1-1) \\ =1\times-2\times-2 \\ =4 \end{gathered}[/tex]The remainder when P (x) is divided by (x + 1) is 4.
Which expressions are equivalent to the one below? Check all that apply.
log(105)
A. 5
B. 5.log 10
C. 1
D. 5.10
The given expression is equivalent to option (A)
What is an expression?
An expression, often referred as a mathematical expression, is a continuous collection of signs that are well-formed in accordance with context-dependent principles. Numbers (predictor variables), parameters, processes, functions, brackets, capitalization, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features. In algebra, a value may be designated by an expression; this value may rely on the values given to the variables that the expression contains. The semantics associated with the symbols in the expression determine this value. The expression's context determines which semantics to use. It is unclear if two lambda expressions are equivalent. The phrases used to represent real numbers are the same way.
The given expression is equivalent to option (A)
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Part 1 of 2 Question content area top Part 1 Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than $. The price of car A is $. a. Assuming that you do not know which model is more expensive, write an absolute value inequality that describes this situation. Use x for the price of car B. b. What are the possibilities for the price of car B?
Considering the given situation, it is found that:
a. The absolute value inequality is: |x - 131745| > 15000.
b. The possibilities for the price of car B are of x < $116,745 or x > x > $146,745.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.It gives the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
In this problem, the difference between the price of car B of x and the price of car A of $131,745 is greater than $15,000, hence the absolute value inequality that models this situation is:
|x - 131745| > 15000.
Hence the possibilities for the price of car B are:
x - 131745 < -15000 -> x < -15000 + 131745 -> x < $116,745.x - 131745 > 15000 -> x > 131745 + 15000 -> x > $146,745.What is the missing information?The complete problem is given by:
"Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than $15,000. The price of car A is $131,745. a. Assuming that you do not know which model is more expensive, write an absolute value inequality that describes this situation. Use x for the cost of car B. b. What are the possibilities for the price of car B?"
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QUICKLYY PLS I NEED NOW TY
Answer:
5.004 X 10^6
0.51 then 1.445 × 10³
0.071 then 0.884
Probability trees
.. inhale attached
The probability of the team winning exactly one of their first two games is 0.1382.
What is a probability tree diagram?Without utilizing sophisticated calculations, a probability tree diagram is used to show the probability that an event will occur. It shows each potential result of an action. A probability tree serves as a visual representation of all the outcomes of an event while also calculating the probability of each occurrence.Given is a probability tree diagram with the respective probabilities of winning and losing a game by the teams.
To find the probability of the team winning exactly one of their two games multiply their probabilities of winning in the first game and losing in the second game and vice versa and find the sum of the two cases.
From the probability tree diagram,
P = (0.83 × 0.06) + (0.17 × 0.52)
P = 0.0498 + 0.0884
P = 0.1382
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Find the rule for the line that passes through each of these pairs of points. Use : y - y1 = m(x - x1).
(4, -8) and (0,4)
(3,1) and (-3, -1)
The rule for the line that passes through the points (4, -8) and (0, 4) is 3x + y = 4
The rule for the line that passes through the points (3, 1) and (-3, -1) is x - 3y = 0
Equation of a line and rule for a lineFrom the question, we are to determine the rule for the line that passes through each of the given pairs of points
For (4, -8) and (0, 4)
First, we will determine the slope, m, of the line
Using the formula,
m = (y₂ - y₁)/(x₂ - x₁)
m = (4 - (-8))/(0 - 4)
m = (4 + 8)/-4
m = 12/-4
m = -3
Now, for the rule
Using the formula,
y - y₁ = m(x - x₁)
Then,
y - (-8) = -3(x - 4)
y + 8 = -3x + 12
3x + y = 12 - 8
3x + y = 4
The rule is 3x + y = 4
For (3, 1) and (-3, -1)
The slope, m is
m = (-1 - 1)/(-3 - 3)
m = -2/-6
m = 1/3
Now, for the rule
Using the formula, y - y₁ = m(x - x₁)
y - 1 = 1/3(x - 3)
3(y - 1) = x - 3
3y - 3 = x - 3
-3 + 3 = x - 3y
0 = x - 3y
x - 3y = 0
Hence, the rule is x - 3y = 0
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Ryan has a bank account balance of -$19.43. As soon as he realizes this, he deposits $36.40 in the account. What is Ryan's bank account balance after the deposit is made? $16.97 $ 55.83 - $16.97 - $55.83
The Answer is $16.97
explanation:
At first Ryan have balance of -$19.43 that is negative balance.
And after that he deposited $36.40.
so now we need to find how much money has he have in account :
For that add -$19.43 + $36.40 = $16.97 .
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whats the slope (m) and equation?
The slope of the line is: -3/4.
The equation of the line is: y = -3/4x + 4.
How to Find the Slope of a Line?The slope of a line is given as, m = change in y / change in x.
How to Write the Equation of a Line?
Using the slope (m) and the y-intercept of the line (b), substitute the values into y = mx + b to write the equation of the line in slope-intercept form.
Using two points on the line, (0, 4) and (4, 1):
Slope(m) = (4 - 1)/(0 - 4) = 3/-4
Slope (m) = -3/4.
The y-intercept (b) = 4.
Substitute m = -3/4 and b = 4 into y = mx + b:
y = -3/4x + 4.
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If polygon ABCD rotates 70° counterclockwise about point E to give polygon A'B'C'D', which relationship must be true?
A.
BB' = DD'
B.
m∠ABC > m∠A'B'C'
C.
A'E' = AE
D.
m∠ABC < m∠A'B'C'
Answer:
C. m∠ABC=m∠ABC
Step-by-step explanation:
A polygon stands as a two-dimensional geometric formation that contains a finite number of sides. It is shown that when polygon ABCD exists rotated by 70°in a counterclockwise order about point E to present polygon A'B'C'D'. so C. is your answer
hope this helps
5/2 convert to percentages
The answer is two hundred and fifty percent
f(x) =x^2-3x-18 vertex?
Answer:
(3/2, -81/4)Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex (h, k).
Answer:
[tex]\sf Vertex \left(\dfrac{3}{2}, \dfrac{-81}{4}\right)[/tex]
Step-by-step explanation:
Vertex of quadratic function: Write the equation in vertex form by using the method completing the square.y = x² - 3x - 18
Add 18 to both sides.
y + 18 = x² - 3x
Divide the co-efficient of x by 2 and square the result and then add it to both sides.
Co-efficient of x = 3. Divide 3 by 2and add (3/2)² to both sides
[tex]\sf y + 18 + \left(\dfrac{3}{2}\right)^2= x^2 - 3x + \left(\dfrac{3}{2}\right)^2\\\\\\y + 18+\dfrac{9}{4}=x^2 - 3x + \dfrac{9}{4}\\\\\\[/tex]
[tex]\sf y + \dfrac{18*4}{1*4}+\dfrac{9}{4}=\left(x - \dfrac{3}{2}\right)^2\\\\\\y + \dfrac{72}{4}+\dfrac{9}{4}=\left(x - \dfrac{3}{2}\right)^2\\\\\\y + \dfrac{81}{4}=\left(x-\dfrac{3}{2}\right)^2\\\\ y = \left(x-\dfrac{3}{2}\right)^2 -\dfrac{81}{4}\\\\[/tex]
Vertex form: f(x) = (x - h)² + k
where h and k are the vertex co-ordinates.
[tex]\sf \boxed{\bf Vertex \left(\dfrac{3}{2}, \dfrac{-81}{4}\right)}[/tex]
A ladder leans against an apartment building at an angle of 40 degrees . The laddies is 12ft. Tall. How far is the bottom of the ladder from the base of the house? Round to the nearest foot.
Given:
[tex]\begin{gathered} \cos \theta=\frac{BC}{AC} \\ \cos 40\degree=\frac{BC}{12} \\ 0.766=\frac{BC}{12} \\ BC=0.766\times12 \\ BC=9.192\text{ ft} \end{gathered}[/tex]The bottom of the ladder from the base of the house is 9 foot.
In 8x - 5 what are the monomials?
8x - 5 are the monomials
How Do You Identify Monomials ?A monomial in algebra is an expression with just one term. In other words, a polynomial with a single term is a monomial. Monomials typically consist of numbers, variables, multiplied numbers and variables, or multiplied numbers and multiple variables. A monomial, often known as a power product, is a product of variables, sometimes with repetitions, and powers of variables with nonnegative integer exponents. Monomials are negative numbers. A monomial is a product of any combination of real numbers, variables, and/or positive integer powers of those variables, according to the definition of a monomial.
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help please!!! it’s due soon!!!!!!
Answer:
-2
Step-by-step explanation:
The question tells you to find f (2). 2 is in the position where x is, so you can plug 2 into the function. According to the function, f(x)= -2 if x=2, so that makes f(2) equal -2 since x=2.
the original price of an item is p dollars. is the price of the item with an 18% markup the same as multiplying the originaal price by 1.18?if yes use two expressions to justify your answer.
Answer:
• Yes
,• p+0.18p
,• 1.18p
Explanation:
Let the original price of the item = p dollars.
If there is an 18% markup, the new price of the item will be:
[tex]\begin{gathered} \text{New Price}=p+(18\%\text{ of p)} \\ =p+(\frac{18}{100}\times p) \\ =p+0.18p \\ =1.18p \end{gathered}[/tex]Yes, the price of the item with an 18% markup is the same as multiplying the original price by 1.18.
Yes, the price of the item with an 18% markup is the same as multiplying the original price by 1.18.
Given that, the original price of an item is p dollars.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the original price of the item = p dollars.
If there is an 18% markup, the new price of the item will be
New price = p + 18% of p
= p + 0.18p
= 1.18p
Yes, the price of the item with an 18% markup is the same as multiplying the original price by 1.18.
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A bus arrives at the bus depot every half hour from 6:00am until 7:00pm every day. How many times in a week does a bus arrive at the depot?
Answer:
175
Step-by-step explanation:
0 = 6:00 am
1 = 6:30 am
2 = 7:00 am
3 = 7:30 am
4 = 8:00 am
5 = 8:30 am
6 = 9:00 am
7 = 9:30 am
8 = 10:00 am
9 = 10:30 am
10 = 11:00 am
11 = 11:30 am
12 = 12:00 pm
13 = 12:30 pm
14 = 1:30 pm
15 = 2:00 pm
16 = 2:30 pm
17 = 3:00 pm
18 = 3:30 pm
19 = 4:00 pm
20 = 4:30 pm
21 = 5:00 pm
22 = 5:30 pm
23 = 6:00 pm
24 = 6:30 pm
25 = 7:00pm
25 * 7(days a week) = 175
Whatttttttttttttt is x+2y+3z
all of those numbers are unlike terms, you can’t combine them, so there is no answer! :)
What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
Ø
{all reals}
{1/7}
The solution set of the equation is Ø.
8. Gerald's account balance is -$45.72. He writes a check for $32.80 and then deposits a $420.99 paycheck. What is his balance now?
Answer:
$342.47
Step-by-step explanation:
Gerald currently has -45.72 dollars.
If he gives writes a check to someone else, you lose money. Since he wrote a check for $32.80, subtract 32.8 from -45.72.
After writing the check, Gerald has -78.52 dollars. If you receive a paycheck and deposit it into your bank account, you add money. Add 420.99 to -78.52.
$342.47
Diego is buying shrimp and rice to make dinner. Shrimp costs $6.20 per pound and rice costs $1.25 per pound. Diego spent $10.55 buying shrimp and rice. The relationship between pounds of shrimp s, pounds of rice r. and the total cost is
represented by the equation 6.20s + 1.25 = 10.55.
Write an equation that makes it easy to find the number of pounds of rice if we know the number of pounds of shrimp purchased.
The act of expressing anything is the process of verbally, writtenly, or by another medium, your thoughts, feelings, etc. [noncount] Freedom of expression [=the ability to publicly express what one believes and feels]
Explain about the Expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
We change the number of pounds of rice, r, to be the subject of the given equation by applying the principle of subject of formula. The formula would therefore be r = (10.55 - 6.20s)/1.25.
Given the phrase:
6.20s + 1.25r = 10.55
Separate 1.25r
1.25r = 10.55 - 6.20s
To identify r, divide both sides by 1.25.
r = (10.55 - 6.20s)/1.25
Consequently, the necessary phrase would be
r = (10.55 - 6.20s)/1.25
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I need help with this question
10x i think is the correct answer
