The table is a linear function and the equation is y = -3(x - 1) + 4
How to determine if the table represents a linear equation?From the question, we have the pairs to be
First pair = (-3, 16)Second pair.= (-1, 10)Third pair = (1, 4)Fourth pair = (3, -2)Fifth pair = (5, -8)From the above representations, we can see that:
As the values of x increase by +2, the values of y constantly increase by -6
This means that the table has a constant rate
By the definition of a linear function, the table represents a linear function
The linear equation of the functionIn (a), we have
x = +2
y = -6
The slope is calculated as
Slope = y/x
So, we have
Slope = -6/2
Evaluate
Slope = -3
The equation is then calculated as
Y = Slope * (X - x) + y
Where
(x, y) = (1, 4)
So, we have
y = -3(x - 1) + 4
Hence, the linear function is y = -3(x - 1) + 4
Read more about linear equations at
https://brainly.com/question/13738662
#SPJ1
Use integers or fractions for any numbers in the expression.
Solution:
Consider the following injective function:
[tex]f(x)=\frac{3x+6}{x-5}[/tex]this is equivalent to:
[tex]y=\frac{3x+6}{x-5}[/tex]by cross-multiplication, this is equivalent to:
[tex](x-5)y\text{ = 3x+6}[/tex]now, applying the distributive law, we get:
[tex]xy-5y\text{ = 3x+6}[/tex]this is equivalent to:
[tex]xy\text{ -5y -3x = 6}[/tex]Applying the common factor, we get:
[tex]x(y-3)\text{ -5y = 6}[/tex]this is equivalent to:
[tex]x\text{ (y-3)}=\text{ 6+5y}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{6+5y}{y-3}[/tex]so that, we can conclude that the correct answer is:
[tex]f^{-1}(x)=\frac{6+5x}{x-3}[/tex]Hi can somebody help me with this?
Answer:
Step-by-step explanation:
Which of the following is equivalent to 3/8 A) 0.3 B) 0.45 C) 0.6 D) 0.375
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given fraction
[tex]\frac{3}{8}[/tex]STEP 2: Convert to decimal
[tex]\frac{3}{8}=0.375[/tex]Hence, the equivalent is 0.375
Help, I don’t get this
The total earnings for the week for the same wage per hour is $501.6.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
For 5 of working earnings is $76
Hourly rate = 76 / 5 = $15.2 per hour
Now for 33 hours of working in a week,
Earning = 15.2 * 33 = $501.6
Thus, the total earnings for the week for the same wage per hour is $501.6.
Learn more about arithmetic here:
https://brainly.com/question/11559160
#SPJ1
Xavier has a bag of 20 marbles. 8 are blue, 7 are red, and 5 are green. Xavier pulls out a marble, records what color it is, and puts it back. He then selects another marble and records its color What is the probability of pulling out a blue marble and then a green marble?
Help please
Answer:
.1
We have 20 marbles.
Probability of blue marble = 8/20 = .4
Since the blue marble is put back, we still have 20 marbles.
Probability of green marble = 5/20 = .25
Multiplying these probabilities:
.4 × .25 = .1
jessica jogs on a path that is 25 meters long to get a park that is south of her location.it takes her 2.5hrs. what is her velocity
Answer:
10 meters per hour
Step-by-step explanation:
Velocity = Distance / Time
Consider the function f(x)= -2x-8.What is the value of f(-5) ?
substitute the -5 in the place of x in the expression -2x-8 and simplify
[tex] = - 2( - 5) - 8 \\ = 10 - 8 \\ = 2[/tex]
[tex]f( - 5) = 2[/tex]
ATTACHED IS THE SOLUTION
find the measures of the copleentary angles that satisfy each case angles have equal measure
Answer:
The measures of this complementary angles is:
45°
Step-by-step explanation:
Complementary angles sum 90°
∡A + ∡B= 90°
∡A = ∡B
Then:
∡A + ∡A = 90°
2∡A = 90°
∡A = 90/2
∡A = 45°
∡B = 45°
Five less than a number is at least eight
What.
is it 13?
.......................
Stella needed to get her computer fixed. She took it to the repair store. The technician
at the store worked on the computer for 4 hours and charged her $59 for parts. The
total was $359. Which tape diagram could be used to represent the context if z
represents the cost of labor per hour?
Answer: 75 per hour
Step-by-step explanation:
Here are 5 lines on a coordinate grid: Write equations for lines a,b,c,d and e a: b: c: d: e:
The equations of each of the given lines are:
Line a is: x = -4
Line b is: x = 4
Line c is: y = 4
Line d is: y = -2
Line e is: y = -¾x + 1
How to Write the Equation of a Line?If we determine the slope value, m, and the y-intercept value, b, the equation of a line can be written as y = mx + b in slope-intercept form by plugging in the values of the determined variables.
For a vertical line, the equation is expressed as x = b, where b is the x-intercept of the line.
For a horizontal line, the equation would be y = b, where b is the line's y-intercept value.
Equation of line a (vertical line):
The x-intercept is -4. This means that, the equation of line a is: x = -4
Equation of line b (vertical line):
The line's x-intercept is 4. To write the equation of the line, substitute the value of the x-intercept into x = b.
Therefore, the equation of line b is: x = 4
Equation of line c (horizontal line):
The y-intercept (b) = 4. Substitute the b = 4 into y = b.
The equation of line c is: y = 4
Equation of line d (horizontal line):
y-intercept (b) = -2. Substitute b = -2 into y = b.
Equation of line d is: y = -2
Equation of line e:
Slope (m) = rise/run = -3/4
y-intercept (b) = 1
To write the equation of the line, substitute m = -¾, and b = 1 in the equation y = mx + b
y = -¾x + 1
Learn more about equation of a line on:
https://brainly.com/question/18831322
#SPJ1
If P(x) = 5x and R(x) = 3x - 7, find P(x) • R(x).
P(x)•R(x)=___
According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0.Finding the polynomials' n roots and factoring them are two of their principal applications.
Calculate p(x(*r(x)?
The factorization of 62 + 17x + 5 by dividing the middle word can be used as an illustration of the factor theorem.In this example, two numbers, "p" and "q," can be discovered in such a way that p + q = 17 and pq = 6 x 5 = 30.One can then obtain the factors after that. A factor of | A | is (x - a) if each member of matrix A is a polynomial in x and | A | vanishes for x = a.When p(x) is divided by xc, the result is p if p(x) is a polynomial of degree 1 or higher and c is a real number (c).For some polynomial q, p(x)=(xc)q(x) if xc is a factor of polynomial p.Consequently, p(c)=(cc)q(c)=0, indicating that c is a polynomial zero.
I This theorem comes in very handy when we need to determine the determinant's value in "factors" form.
p(x) =5x
r(x) = 3x - 7
p(x)×r(x) =
=5x(3x-7)
5x² - 7
2×15x²-1
= 30x
p(x)*r(x) = 30x
To learn more about factor theory refer
https://brainly.com/question/24380382
#SPJ13
For the equation, complete the given ordered pairs.Need help solving the last order pair.
Hello!
First, let's remember:
In an ordered pair, we will have two variables represented as (x, y).
In the first two ordered pairs, the exercise informed the value of x. In the third ordered pair, it informs the value of y. We will solve it in a similar way, look:
[tex]\begin{gathered} 4x-y=7 \\ 4x-7=7 \\ 4x=7+7 \\ 4x=14 \\ x=\frac{14}{4}=\frac{7}{2} \end{gathered}[/tex]Answer:x = 7/2 or also x = 3.5.
What is the exchange rate? Show your work.
1 US dollar = _________ euro.
The current exchange rate is 1 US dollar = 1 euro.
What is an exchange rate?The exchange rate of a currency is the worth of one currency in respect to another, or the rate at which one currency will be exchanged for another.
The foreign exchange market, commonly known as Forex or FX, is a global decentralized market for currency trading that determines the exchange rates of such currencies.
A currency exchange rate is the rate at which one currency can be exchanged for another. In other words, the exchange rate is the price of one currency in terms of another.
Learn more about exchange rate on
https://brainly.com/question/2202418
#SPJ1
Cassie baked 24 cookies with 4 scoops of flour. How many scoops of flour does Cassie need in order to bake 42 cookies?
Answer:
7
Step-by-step explanation:
24 with four scoops is 6 with one scoop and 6 times 7 is 42 so 1 times 7 is 7 so the answer is 7 scoops
The shaded portion in each glass represents an amount of grape drink Martin's glass of grape drink has a weaker tasting grape flavor than Tia's glass of grape drink.
The stronger flavor of grape is in Tia's glass.
Given,
Martin's glass of grape drink has weaker tasting grape flavor
Tia's glass of grape drink has stronger tasting grape flavor
3 ounces of water is added to Martin's glass
One table spoon of grape mix is added to Tia's glass
We have to find the glass which contain the stronger grape flavor
Already in Martin's glass flavor is low. When we add water again to his glass, the flavor will again dissolves with water.
In Tia's glass grape flavor is stronger. By adding one tablespoon of grape mix the flavor will become more stronger.
That is,
The stronger flavor of grape is in Tia's glass.
Learn more about grape juice here;
https://brainly.com/question/28505250
#SPJ1
A teacher kept track of what students consumed at a school picnic. For three grades, the ratios of the amount of water consumed to the amount of fruit juice consumed were equivalent. Complete the table.
Based on the ratios of water consumed to the fruit juice consumed, the missing figures in the completed table would be:
24 water : 28 gallons of fruit juice 18 water : 21 gallons of fruit juice How to find the ratios?The ratio of water gallons consumed to fruit juice gallons is equivalent which means that at their simplest, they will always have the ratio of 6 : 7 as is the case in the 5th grade.
The missing ratio for Juice in 6th grade is:
= (Water gallons x Juice gallons in 5th grade) / water gallons in 5th grade
= (24 x 7) / 6
= 28 gallons of fruit juice
The missing ratio for water in 6th grade is:
= (18 x 7) / 6
= 21 gallons of fruit juice
Find out more on ratios at https://brainly.com/question/21491826
#SPJ1
Give two examples of each type of number: real, natural, integers, rational and irrational.
The following examples are shown below:
Natural numbers: 2, 9Integers: - 3, 0Rational numbers: 5 / 7, - 13 / 8Irrational numbers: √5, πReal numbers: 0, √6What kind of real numbers does exist?In this problem we have to present five types of real numbers, which are defined and shown below:
Natural numbers - Smallest subset of real numbers: N = {1, 2, 3, 4, ...}. Examples: 2, 7, 9Integers - Combination of the subset of real numbers and another subset N' = {0, - 1, - 2, - 3, - 4, ...}. Examples: - 5, - 3, 0, 5, 8Rational numbers - Subset of all real numbers of the form m / n, where m and n are integers and n is a non-zero integer. Natural numbers and integers are also rational numbers. Examples: 5 / 7, - 9 / 11, 19 / 3, - 10 / 7Irrational numbers - Subset of all real numbers that are not rational. This subset is the complement of the subset of rational numbers. Examples: √2, - e, πReal numbers - Set of all rational and irrational numbers. Examples: - 5, 0, 2, 19 / 3, √3To learn more on real numbers: https://brainly.com/question/551408
#SPJ1
Please help me asapppppp
Whileat the fruit stand, ramon bought 3 punds of apples that cost $0.89 per pound and 4 cantaloupes that each cost $1.09. about how much money did he spend, not including tax?
The total money spent on fruits is $7.03
While at the fruit stand, Ramon bought the following fruits,
3 pounds of apples that cost $0.89 per pound
4 cantaloupes that each cost $1.09
So, the total amount he spent on the materials he bought without including taxes is,
Total money spent = 3 x ( 0.89 ) + 4 x ( 1.09 )
= 2.67 + 4.36
= 7.03
The total money spent on fruits is $7.03
To learn more about Taxes click here:
brainly.com/question/16423331
#SPJ4
Using the information in the diagram determine the height of the tree
Given
To find the height of the tree.
Explanation:
It is given that,
From the figure, it is clear that ΔABC and ΔADE.
That implies,
[tex]\begin{gathered} \frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC} \\ \frac{x}{2x}=\frac{y}{2y}=\frac{DE}{200} \\ \frac{1}{2}=\frac{DE}{200} \\ DE=\frac{200}{2} \\ DE=100 \end{gathered}[/tex]Hence, the height of the tree is 100ft.
Austin makes a
commission of 20% on
his sales each week.
Last week, his sales
were $520. How much
was Austin’s
commission?
Answer:
His commission is 104$.
Step-by-step explanation:
1. Find 20% of 520$, which is 104$.
That's the answer! Please mark me as the brainliest!
any given season, a soccer team plays 65 % of their games at home.
When the team plays at home, they win 83 % of their games.
When they play away from home, they win 26 % of their games.
find the probability the team wins with explanation
Based on the percentage of games played at home by the team, and the percentage win rate, the probability that the team wins is 63.05%
How to find the probability the team wins?First, find the probability that the team wins playing at home:
= Percentage win rate at home x Percentage played at home
= 83% x 65%
= 53.95%
Then find the probability of winning away:
= Percentage win rate away x Percentage played away
= 26% x (1 - 65%)
= 9.1%
The probability the team wins is:
= 53.95 + 9.1
= 63.05%
In conclusion, the probability of the team winning at home and the probability of them winning away, can be summed up to find the probability of the team winning which is 63.05%.
Find out more on probability at https://brainly.com/question/23999063
#SPJ1
YAbisects ZXYZ. Which statement is false?A. YXYZB. ZXYA and ZZYA each measure 63º.C. ZXYA: ZZYAD. The total measure of ZXYA and ZZYA is 126º.
Given that
[tex]\vec{YA}\text{ bisesects}\angle XYZ[/tex]Then,
[tex]\begin{gathered} \angle XYA\text{ and }\angle ZYA\text{ each measure 63degr}ees \\ \angle XYA\cong\angle ZYA \\ \text{ The total measure of }\angle XYA\text{ and }\angle ZYA\text{ }is\text{ }63+63=126^{\text{0}} \end{gathered}[/tex]Therefore, the statement
[tex]\begin{gathered} \bar{YX}\cong\bar{YZ}\text{ is false} \\ The\text{ answer is Option A} \end{gathered}[/tex]A scientist needs 60 milliliters of buffer solution for each of 15 experiments. She has a bottle that contains 730 milliliters of buffer solution. Is there enough buffer solution in the bottle for all 15 experiments?
Represent the following sentence as an algebraic expression, where “a number” is the letter x. You do not need to simplify 3 is multiplied by the difference of seven and a number
The given statement can be written algebraically as follow:
3(7 - x)
3 means '3 is multipled by' and the factor (7-x) means 'the difference of seven and a number'
Solve for y:
2x+4y=32
Answer:
Step-by-step explanation:
2x+4y=32
Get Y on one side of equation by itself
(subtract 2x on both sides)
leaves 4y = 32 - 2x
Divide by 4 to get Y alone (without coefficient)
4y = 32 - 2x
4
y = 8 - 1/2x
help me plssssssssssssss
Answer:)0.3 I Think
Step-by-step explanation:
1.8/6
The answer is:
10.8 cm
Explanation:
6 × 1.8 = 10.8
- firstly, remove the decimal point
- Secondly, multiply regularly 6 by 18
- You'll get 108 as an answer
- Take back the decimal point one to the left because you took it one to the right before, so you will have to do the inverse of the previous action
Good luck
the angle of depression of the light to the nearest minute is
Answer
θ = 37° 30'
Explanation:
The angle of depression has the same measure as the angle of elevation, so a trigonometric function that related the sides of the triangle and the angle of elevation θ is tangent. Then:
[tex]\text{tan }\theta\text{ =}\frac{39.57}{51.56}[/tex]Therefore, the value of θ is:
[tex]\begin{gathered} \tan \text{ }\theta\text{ = 0.7674} \\ \theta=\tan ^{-1}(0.7674) \\ \theta=37.50 \end{gathered}[/tex]So, in grades and minutes, we get:
θ = 37.50 = 37° 30'
Therefore, the angle of depression is 37° 30'
Suppose Juan places $6000 in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.(b) Find the amount in the account at the end of 2 years.su
1) Since this investment has been in an account with 12% compound interest per year, then we can write out the following:
a) Note that there was no withdrawal during this first year.
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=6000(1+\frac{0.12}{1})^{1\cdot1} \\ F=6000(1.12)^1 \\ F=6720 \end{gathered}[/tex]b) To find out the amount of money over a course of this time 2 years, then we can write out the following:
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=6000(1+\frac{0.12}{1})^{1\cdot2} \\ F=7526.4 \end{gathered}[/tex]In this case, it is also compounded per year. Just the period (t) is greater than the other one.
So, we can tell the following about the earnings of this investment:
[tex]a)\$6720,b)\$7526.40[/tex]