1st and 5th tables represent the same function
To find the two equal functions we will formulate their equations, using the formula [tex]\frac{y-y1}{x-x1} = \frac{y2-y1}{x2-x1}[/tex] where (x1,y1) and (x2,y2) are the endpoints of the equation.
Now finding the equation for each table we get:
Table 1:
(x1,y1) = (4,8) and (x2, y2) = (6,7)
Putting this in the formula we get:
= [tex]\frac{y-8}{x-4} = \frac{7-8}{6-4}[/tex]
So, the equation will be x + 2y = 20
Table 2:
(x1,y1) = (4,5) and (x2, y2) = (6,4)
Putting this in the formula we get:
= [tex]\frac{y-5}{x-4} = \frac{4-5}{6-4}[/tex]
So, the equation will be x + 2y = 14
Table 3:
(x1,y1) = (2,8) and (x2, y2) = (8,5)
Putting this in the formula we get:
= [tex]\frac{y-8}{x-2}=\frac{5-8}{8-2}[/tex]
So, the equation will be x+2y=18
Table 4:
(x1,y1) = (2,10) and (x2, y2) = (6,14)
Putting this in the formula we get:
= [tex]\frac{y-10}{x-2} =\frac{14-10}{6-2}[/tex]
So, the equation will be x-y=-8
Table 5:
(x1,y1) = (2,9) and (x2, y2) = (8,6)
Putting this in the formula we get:
= [tex]\frac{y-9}{x-2}=\frac{6-9}{8-2}[/tex]
So, the equation will be x+2y=20
Hence, table 1 and table 5 represent the same function
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Given f(x)=(x+3)^2 and g(x)=|x+1| , which value is a solution to the equation f(x)=g(x) ?
A. –5
B. 5
C. 4
D. -1
help asap pls
Answer:
A) [tex]x = -5[/tex]
Step-by-step explanation:
[tex](x + 3)^2 = | x + 1 |\\\to x^2 + 6x + 9 = | x + 1|[/tex]
Case 1: x + 1 is positive
[tex]x^2 + 6x + 9 = x + 1\\\to x^2 + 5x + 8 = 0\\\to \text{No solutions.}[/tex]
Case 2: x + 1 is negative
[tex]-x^2 - 6x - 9 = x + 1\\\to 0 = x^2 + 7x + 10\\\to 0 = (x + 5)( x + 2)\\\to x = -5 \text{ or } x = -2[/tex]
please answer asap. 100 points and marked brainliest!
Answer:5 per Gallone
Step-by-step explanation:
Answer:
Gas in India is $3.88 per gallon.
This is MORE expensive than $2.36 per gallon.
Step-by-step explanation:
Use the conversion factors given to change rupees to dollars and liters to gallons. See image.
(and btw, this question has very outdated information. Gas is $5.90 per gallon today in this poster's City, State, USA)
need help with # 6 asap
The equation that is parallel and perpendicular are y + 4 = 7/5(x-35) and y+4 = -5/7(x - 35) respectively.
Equation of a lineA line is defined as the shortest distance between two points. The formula for finding the equation of a line in point slope form is:
y - y₁ = m(x-x₁) (Parallel lines)
y - y₁ = -1/m(x-x₁) (Perpendicular lines)
Given the following parameters;
Point = (35, -4)
Given the equation 7x-5y = 0
5y = 7x
y = 7/5x
Slope = 7/5
Substitute the slope and point into the equation
y + 4 = 7/5(x-35) (Parallel lines)
y +4 = -1/(7/5)(x-35) (Perpendicular lines)
y+4 = -5/7(x - 35)(Perpendicular lines)
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Is the product of 3/6 x 5/4 equal to the product of 3/4 x 5/6? Explain.
The product of 3/6×5/4 is equal to the product of 3/4×5/6.
What is simplification?
A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statementMaking something simpler is making it less intricate or cluttered. When you describe a complex mathematical idea to a child in words they can easily understand, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.Here,
3/6×5/4 = 3 * 5 / 6* 4
= 15 / 24
3/4×5/6 = 3 * 5 / 4 * 6
= 15 / 24
Thus, The product of 3/6×5/4 is equal to the product of 3/4×5/6.
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Simplifying complex fractions: Where does the 3 in 21 and 15 come from? I understand how 14 and 21 became 2 & 3
(because both 14 & 21 are divisible by 7)
but I'm confused as to how the 1 came
about.
ACTIVITY SHEET: MATHEMATICS AS A LANGUAGE
Classify each of the following as a MATHEMATICAL EXPRESSION or a MATHEMATICAL
SENTENCE.
Use the given property to complete each mathematical equation.
1. Commutative:
(ab) (8)
=
2. Closure:
(3) (4)
3. Identity:
1(p) + 1(q)
4. Distributive:
5. Inverse:
1. A = {10, 100,
1000}
2. B = {(1, 2), (2, 1),
(3, 2), (4, 3), (4,4),
(5,4)}
Identify if the given is a SET, a RELATION, and/or a FUNCTION.
3. C = {(1, 30), (2,
31), (3, 30), (4, 29)}
1. a +9
2. x + y + 0 = x + y
_3.-—--
4. 0.25
5. b + c = c + b
4. D = {x/x is a real
number}
5. E identification
number of the
student to his or her
identity
=
=
[(3m)( 7p)](5p) =
0.25
SET
RELATION
FUNCTION
Answer: 1; talkative 2; an act of kindness 3; to make yourself public
4; buying a car for someone
Step-by-step explanation:
The coordinate 6 has a weight of 2, the coordinate 9
has a weight of 2, and the coordinate 15 has a weight
of 1. Find the weighted average.
The weight average of the coordinates is 9
Given,
The coordinate 6 has a weight of 2
The coordinate 9 has a weight of 2
The coordinate 15 has a weight of 1
We have to find the weight average:
The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
So, we have:
Weight average = ( (6 x 2) + (9 x 2) + (15 x 1) ) / (2 + 2 + 1)
= (12 + 18 + 15) / 5
= 45 / 5
= 9
Hence, the weight average of the coordinates is 9
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In an election, 313 votes are cast. How many votes are needed to have a majority of
the votes in this election?
Answer with a whole number of votes.
I need more help on other questions! Same assignment
Answer:
a. [tex]\frac{10}{3}[/tex]
b. [tex]\frac{4}{3}[/tex]
c.[tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
a.
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
[tex]3\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{7}{2}[/tex]
b.
reciprocal is technically the opposite
c.
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
[tex]=\frac{7}{2}\div \frac{3}{4}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=\frac{7}{2}\times \frac{4}{3}[/tex]
[tex]\mathrm{Cross-cancel\:common\:factor:}\:2[/tex]
[tex]=\frac{7}{1}\times \frac{2}{3}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]\frac{7\times \:2}{1\times \:3}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:7\times \:2=14[/tex]
[tex]=\frac{14}{1\times \:3}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:1\times \:3=3[/tex]
[tex]=\frac{14}{3}[/tex]
[tex]\mathrm{Convert\:improper\:fraction\:to\:mixed\:numbers}[/tex]
[tex]4\frac{2}{3}[/tex]
Estimate the probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws.
The probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws is 0.384
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.
Now it is given that,
The proportion of free throws the player makes, p = 80% = 0.8
The number of throws, n = 3
The throws the player makes, r = 2
Since the probability is given as,
P(r) = nCr x p^r x (1 - p)^(n-r)
So, the probability that an NBA player makes 2 of his next 3 free throws
Putting the values we get,
P(2) = ³C₂ x (0.8)^2 x (1 - 0.8)^(3-2)
Solving we get,
P(2) = 3 x 0.64 x (0.2)^(1)
Thus we get,
P(2) = 3 x 0.64 x 0.2
Multiplying we get,
P(2) = 0.384
this is the required probability that an NBA player makes 2 of his next 3 free throws.
Thus, the probability that an NBA player who makes 80% of his free throws makes 2 of his next 3 free throws is 0.384
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Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra. How old is Pamela now?
Pamela is 1 year old now.
How to solve problems on ages ?
If the present age of a person be X, thenAge after n years = X +n
Age n years ago = X - n
n times the present age = nX
If ages in the numerical are mentioned in the ratio A : B, then A : B will be AX and BX.
If the sum of ages is X and Y and the ratio of their ages is p : q respectively, then you can determine the age of Y by using the formula shown below:Age of Y = Ratio of Y / Sum of ratios x sum of ages
Age of Y = q/ (p +q) x A
In the given statement is:
Debra is 7 years younger than Pamela. In 6 years, Pamela will be twice as old as Debra.
To find the how old is Pamela now.
Now, Based on the given conditions,
Formulate:
Let x be the Pamela's age
6 + 7 + x = 2(6 + x)
13 + x = 12 + 2x
x - 2x = 12 - 13
-x = -1
x = 1
Hence, Pamela is 1 year old now.
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Amos says that the opposite and the absolute value of a number are always the same
Amos says that the opposite and the absolute value of a number are always the same. This is true.
How to express the information?It should be noted that from the information, Amos says that the opposite and the absolute value of a number are always the same.
For example, given the number 23, the opposite will be -23 and the absolute value is also -23. This implies that they are the same.
Therefore, Amos says that the opposite and the absolute value of a number are always the same. This is true.
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Amos says that the opposite and the absolute value of a number are always the same. True or false.
the sum of 8 and matts savings is 52
Answer:
8 + x = 52
Where x = Matt's savings
15 points!!
Please help.
The value the equation related to S and N is 25.
What is algebraic expression ?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 3x2 + 2xy + c.
N will be the function of S since the number of cookies made is dependent on the amount of sugar
N = 25S, S ≥ 0
This is the for the every cup of sugar we make 25 cookies. for the graph we can plot some points
S N
_________
0 0
1 25
1.5 37.5
2 50
This will be a line with slope of 25
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Will Give Brainliest!!!! Match each step with the correct justification.
Given: QM MR
a. Given
b. Subtraction Property of Equality
c. Addition Property of Equality
d. Substitution.
e. Division Property of Equality
Answer:
A D B C E
Step-by-step explanation:
That is the order of steps in the solution
The larger of two numbers is 10 less than the smaller number. The sum of the two numbers is 50 . Find the two numbers.
The value of the two numbers are 30 and 20.
According to the statement
We have to find that the value of the two numbers.
So, For this purpose, we know that the
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
From the given information:
The larger of two numbers is 10 less than the smaller number. The sum of the two numbers is 50.
Then
Let the first number be x and the second number y
Then
y = x -10
And
x+y = 50
Then
Substitute the value then
x+x-10 = 50
2x = 50+10
2x = 60
x =30
Then
y = x -10
y = 30 -10
y = 20
So, The value of the two numbers are 30 and 20.
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solve each system of inequalities and indicate any three solutions. x-0.8 <0, -5x<10
The three solutions of the inequalities are x < 0 , x < 0.8 , x< -2
What are inequalities?Inequalities are defined as mathematical expressions in which both sides are not made equal to each other.
Given the inequalities;
x-0.8 <0-5x<10Let's solve for the value of x
x - 0.8 < 0
Make 'x' the subject
x < 0 + 0. 8
x < 0. 8
-5x < 10
Make 'x' the subject by dividing both sides by - 5
-5x/ 5 < 10/ -5
x < -2
Thus, the three solutions of the inequalities are x < 0 , x < 0.8 , x< -2
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Athena's credit card has an APR of 32.99%. If her current monthly balance, before interest, is $2,719.83, what amount will she be charged for interest?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. Athena's will be charged $74.77 for interest.
What is Interest Rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Given,
Athena's credit card has an APR of 32.99%.
We need to convert the percentage to decimal.
32.99%=32.99/100
=0.3299
The amount will she be charged for interest is
=(2719.83*0.3299)/12
=897.27/12
=74.77
Therefore Athena's will be charged $74.77 for interest.
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how to turn y=3x+45 into ax+by=c form
The given equation y = 3x + 45 in form ax+by=c is 3x - y = - 45.
What are linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful. A linear equation has the slope-intercept form y = MX + b. Variables in the equation are x and y. When x is 0, the numbers m and b provide the line's slope (m) and the value of y(b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.So, y=3x+45 into ax+by=c form:
y = 3x + 45 ⇒ Bring y to the other side of the equation and bring 45 to the opposite side of the equation as: y = 3x + 45 ⇒ 3x - y = - 45Therefore, the given equation in form ax+by=c is 3x - y = - 45.
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x=3(x-15)
can you guys show work
Answer: x = 45/2
Step-by-step explanation:
x=3(x-15)
x=3x-45
-2x=-45
x=45/2
Keep it as a fraction to keep it simple or you can make it a decimal which is x = 22.5
WILL give branilist if correct!! Answer both questions correctly
Answer:
6. perfect squares 5 and 6
7. between integers 5 and 6
Step-by-step explanation:
[tex]\sqrt[3]{141} = 35.62\\[/tex]
Which statement is true about the function f(x) = 8x^3?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
The function is odd because f(–x) = –f(x).
The function f(x) = 8x³ satisfies the condition f(-x) = -f(x) and is odd. D.
To determine whether the function f(x) = 8x³ is even or odd, we need to analyze the symmetry of the function with respect to the y-axis and the origin.
Even function:
If a function is even, it satisfies the condition f(-x) = f(x), meaning that the function is symmetric with respect to the y-axis.
Odd function:
If a function is odd, it satisfies the condition f(-x) = -f(x), meaning that the function is symmetric with respect to the origin.
Now, let's analyze the given function, f(x) = 8x³:
Testing for evenness:
If we substitute -x for x in the function, we have f(-x) = 8(-x)³
= -8x³.
This is not equal to f(x) = 8x³.
The function f(x) = 8x³ is not even.
Testing for oddness:
If we substitute -x for x in the function, we have f(-x) = 8(-x)³
= -8x³.
This is equal to -f(x) = -8x³.
The function is odd because f(–x) = –f(x).
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An investment of $34,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third
9%. Total interest from the investments was $2700. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment.
The first part of the investment was $
Answer:7000
Step-by-step explanation:3400-2700=7000
O.N.L.Y., ONLY, OnLy answer if you are SURE I do not want " pretty sure" or "I think", NO! ONLY answer if you are 100% sure.
Answer:
0.11 because i did it before
Step-by-step explanation:
Answer:
The answer is D I've done it before
Solve the equation 5k^2−20k=15 . Present exact values of the solutions. If there are more than one solutions, separate them by a comma.
Two or more expressions with equal sign is equation, if the equation 5k^2−20k=15 then 1 and 3 are exact values of the solutions.
What is Equation?Two or more expressions with equal sign is called as Equation.
The given equation 5k^2−20k=15,
let us make it a QE by taking 15 to left.
5k^2−20k-15
a=5, b=-20, c=-15
k=-b±√b^2-4ac/2a
=20±√(-20)^2-4(5)(-15)/2(5)
=20±√400-300/10
=20±√100/10
=20±10/10
k=20+10/10 or k=20-10/10
k=3, or k=1
Therefore the solutions of equation 5k^2−20k=15 are 1 and 3.
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Mr. Jordan's class is having a pizza party with the $100 they earned in a competition. A cheese pizza costs $10, and a pepperoni pizza costs $15. They must order at
least 2 pepperoni pizzas. They also must order at least twice as many cheese pizzas as pepperoni pizzas.
What is the greatest total number of pizzas Mr. Jordan's class can order?
7
PLEASE HELP!
Solve for x: 1 < x + 3 < 4
4 > x > 7
4 < x < 7
−2 > x > 1
−2 < x < 1
Answer:
the last choice
Step-by-step explanation:
u will minus 3 from each side. that's the point
Which equation and number line show that a number and its opposite are additive inverses?
Which equation and number line show that a number and its opposite are additive inverses?
An equation and number line which shows that a number and its opposite are additive inverses is: 2 + (-2) = 0 in graph B.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is an additive inverse?An additive inverse can be defined as a number (n) which when added to another number (a) makes it equal to zero (0). This ultimately implies that, an additive inverse is the opposite of another number (a).
Mathematically, an additive inverse can be represented by the following expressions:
a + n = 0
a = -n
In this context, we can reasonably infer and logically deduce that an equation and number line which shows that a number and its opposite are additive inverses is 2 + (-2) = 0 in graph B (see attachment).
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Who invented and defined zero
Answer:
Brahmagupta in 628
Step-by-step explanation:
Answer:
Zero and its operation are first defined by Brahmagupta in 628. He developed a symbol for zero: a dot underneath numbers.
Does any one know the answer?
Answer:
C= right angle (90 degrees)
Step-by-step explanation:
a + b + c = 180
The triangle is perfectly 180 degrees, making it supplementary
I wasn't very sure what you were asking, but I hope this helped