Answers
We have to match the functions with the corresponding ordered pair.
The easiest way is to pick an ordered pair and replace (x,y) in the function to verify if the equality stands or not. If it does stand, then the ordered pair is part of the function.
Then, we start with (-8,9) and function y = 6x+9. Replacing x and y, we get:
[tex]\begin{gathered} (x,y)=(-8,9) \\ y=6x+9 \\ 9=6\cdot(-8)+9 \\ 9=-48+9 \\ 0=-48\longrightarrow\text{False} \end{gathered}[/tex]As this equation does not verify for (-8,9), this ordered pair does not belong to the function.
We repeat the same process with the next function, y = -9x-1:
[tex]\begin{gathered} (x,y)=(-8,9) \\ y=-9x-1 \\ 9=-9(-8)-1 \\ 9=72-1 \\ 9=71\longrightarrow\text{False} \end{gathered}[/tex]As with the previous function, the equation does not verify.
The next function is y = -1x+1:
[tex]undefined[/tex]Related Questions
A math book is 2.5 cm thick.
How many of these books can
be stored on a shelf that is
one meter long?
Answers
The number of books that can be stored on one meter-long shelf is (forty) = 40.
Given
a book is 2.5 cm thick
number of books required are
Convert meters into centimeters first 1m = 100 cm now, divide them:
= 100 cm ÷ 2.5 cm to remove the decimal point divide 2.5 by 10 = 2.5/10
= [tex]100 * \frac{10}{25}[/tex]
= 40
thus the total number of books that can be stored on a one-meter bookshelf is 40 books.
learn more about simplification at
brainly.com/question/28716423
Herb Garrett has an 80% methyl alcohol solution. He wishes to make a gallon of windshield washer solution by mixing his methyl alcohol solution with water. If 128 ounces or a gallon of windshield washer fluid contain 6% methyl alcohol, how much of the 80% methyl alcohol solution and how much water must be mixed? Express your answer in ounces.
Answers
First, calculate the total volume of alcohol in the gallon of windshield washer solution by calculating what is 6% of a gallon equal to. Since a gallon is equal to 128 ounces, then:
[tex]undefined[/tex]helppppppppppppppppppp
Answers
TRIGONOMETRY Find the length of the longer diagonal of this parallelogram round to the nearest tenth
Answers
Given the parallelogram ABCD
As shown: AB = 4 ft
m∠BAC = 30
m∠BDC = 104
We will find the length of the longer diagonal which will be AC
See the following figure:
The point of intersection of the diagonals = O
The opposite sides are parallel
AB || CD
m∠ABD = m∠BDC because the alternate angles are congruent
So, in the triangle AOB, the sum of the angles = 180
m∠AOB = 180 - (30+104) = 46
We will find the length of OA using the sine rule as follows:
[tex]\begin{gathered} \frac{OA}{\sin104}=\frac{AB}{\sin 46} \\ \\ OA=AB\cdot\frac{\sin104}{\sin46}=4\cdot\frac{\sin104}{\sin46}\approx5.3955 \end{gathered}[/tex]The diagonals bisect each other
So,
[tex]AC=2\cdot OA=10.79[/tex]The longer diagonal is AC
Rounding to the nearest tenth
So, the answer will be AC = 10.8 ft
students at a local school were asked about how many hours do you spend on homework each week? the table shows the results of the survey classify the statement below as a true or false more students study for 3 to 4 hours than for 5 to 6 hours the statement is (true or false) because.... students study for 3 to 4 hours and..... students study for 5 to 6 hours.
Answers
The total of students that study for 3 to 4 h is 147
The total of students that study for 5 to 6 h is 107
Then, the statement: "more students study for 3 to 4 hours than for 5 to 6 hours" is true because 147 students study for 3 to 4 hours and 107 students study for 5 to 6 hours.
What is the solution to the equation below ? 0.5x = 6 A . 3 B . 12 C . 60
Answers
Given the equation:
[tex]0.5x=6[/tex]Multiplying both sides by 2
[tex]\begin{gathered} 2\cdot0.5x=2\cdot6 \\ x=12 \end{gathered}[/tex]So, the answer will be option B) 12
you’re making desert, but your recipe needs adjustment. your oatmeal cookie recipe makes 2 dozen cookies, but you need 3 cookies. If the recipe requires 1 and 1/3 cups of sugar, 3/4 teaspoon of salt, and 1 and 1/4 cups of raisins, how much of each of these ingredients are for 3 dozen cookies? simply your answer
Answers
we know that
For 2 dozen cookies
we need
1 1/3 cups of sugar
3/4 teaspoon of salt
1 1/4 cups of raisins
To convert 2 dozens to 3 dozens------> multiply by 3/2
but first convert mixed number to improper fractions
1 1/3=1+1/3=4/3 ----> multiply by 3/2
(4/3)*(3/2)=2 cups of sugar
3/4*(3/2)=9/8 ----> convert to mixed number
9/8=8/8+1/8=1 1/8 teaspoon of salt
1 1/4=1+1/4=5/4
5/4*(3/2)=15/8
15/8=8/8+7/8=1 7/8 cups of raisins
2.3x + 8 = - 1.7x - 8 solve for x
Answers
The value of x after solving (2.3x + 8) = (-1.7x-8) is -4.
According to the question,
We have the following expression:
(2.3x + 8) = (-1.7x-8)
Now, moving -1.7x from the right hand side to the left hand side will result in the change of its sign from minus to plus:
2.3x+1.7x +8 = -8
4x+8 = -8
Now, moving 8 from the left hand side to the right hand side will also result in the change of the sign from plus to minus:
4x = -8-8
4x = -16
x = -16/4 (4 was in multiplication on the left hand side. So, it is in division on the right hand side.)
x = -4
Hence, the value of x is -4.
To know more about solving here
https://brainly.com/question/315182
#SPJ1
Owners of a recreation area are adding water to a pond. The graph below shows the amount of water in the pond (in liters) versus the amount of time that water is added (in hours).Use the graph to answer the questions.(a)How much does the amount of water increase for each hour that water is added?liters=(b)What is the slope of the line?
Answers
GIVEN:
We are given a graph showing the increase in the amount of water pumped into a pond for every passing hour.
Required;
To determine the amount of increase in the water level for each hour that water is added.
Also, to determine the slope of the line as shown in the graph.
Step-by-step solution;
(a) Notice that the graph shows an increase in the water level for every passing hour. Notice also the following relationship;
[tex]\begin{gathered} (hours,liter) \\ \\ (0,100) \\ \\ (1,400) \\ \\ (2,700) \\ \\ (3,1000) \end{gathered}[/tex]We can see that the rate of change for every hour is 300 liters increment.
Therefore, for each hour that water is added, there is an increase of 300 liters.
(b) To calculate the slope of the line shown in the graph, we shall take the change in liters and divide by the corresponding change in the hours.
We now have the following;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(0,100) \\ \\ (x_2,y_2)=(1,400) \end{gathered}[/tex]We now have the slope as follows;
[tex]\begin{gathered} m=\frac{400-100}{1-0} \\ \\ m=\frac{300}{1}=300 \end{gathered}[/tex]The slope therefore is 300.
ANSWER:
[tex]\begin{gathered} (a)\text{ }Liters=300 \\ \\ (b)\text{ }slope=300 \end{gathered}[/tex]To the right is the graph of f(x) = x^2. The second graph, to the left of f(x) = x^2 is a new function made by stretching f(x) vertically by a factor of 2 and then translating it three units to the left and one unit down. Write the equation of the new function.
Answers
This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;
[tex]y=ax^2+b[/tex]For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).
Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.
To summarize the steps that we must do in order to find the equation of the RED line we will list them as,
1. Sample two(2) points in the graph to be used as reference points.
2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".
3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.
Let's start.
1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points
to determine)
Let us use the points (-3, -1) and (-2, 1) as shown in the picture.
2. Use the points (-3, -1) and (-2, 1) in our standard equation.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-3, -1)} \\ -1=a(-3)^2+b_{} \\ 9a+b=-1 \end{gathered}[/tex]
for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-2, 1)} \\ 1=a(-2)^2+b_{}_{} \\ 1=4a+b \\ 4a+b=1 \end{gathered}[/tex]and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.
[tex]\begin{gathered} 9a+b=-1\text{ and} \\ 4a+b=1 \end{gathered}[/tex]transforming eqatuin number 1 to
[tex]9a+b=-1\text{ is just the same as b = -1 -9a}[/tex]
then substitue b = -1 -9a to the 2nd equation we have.
[tex]\begin{gathered} 4a+b=1\text{ , where b = -1-9a} \\ 4a+(-1-9a)=1 \\ 4a-1-9a=1 \\ -5a=2 \\ a=-\frac{2}{5} \end{gathered}[/tex]
since a = -2/5, we can find b using,
[tex]\begin{gathered} 4a+b=1\text{ , where a=-}\frac{2}{5} \\ 4(-\frac{2}{5})+b=1 \\ b=1+\frac{8}{5} \\ b=\frac{5}{5}+\frac{8}{5} \\ b=\frac{13}{5} \end{gathered}[/tex]therefore our a and b are;
[tex]a=-\frac{2}{5}\text{ and b = }\frac{13}{5}[/tex]3. We can now proceed in substituting it in our standard equation;
[tex]\begin{gathered} y=ax^2+b\text{ , where a = -}\frac{2}{5}\text{ and b = }\frac{13}{5} \\ y=(-\frac{2}{5})x^2+(\frac{13}{5}) \\ y=-\frac{2}{5}x^2+\frac{13}{5} \end{gathered}[/tex]you can also simplify the final equation by multiplying all sides by 5,
[tex]\begin{gathered} 5y=(5)\lbrack-\frac{2}{5}x^2+\frac{13}{5}\rbrack \\ 5y=-2x^2+13 \end{gathered}[/tex]therefore our final answer can be,
[tex]\begin{gathered} f(x)=-\frac{2}{5}x^2+\frac{13}{5} \\ or \\ 5y=-2x^2+13 \end{gathered}[/tex]
A container of orange juice cost $3.29 for 59 ounces. What is the unit rate to the nearest penny?
Answers
Answer:
6 cents
find 2 numbers if their ratio is 9:11 and their difference is 6 the numbers can be _, _ or _, _ HELP ASAP
Answers
Answer:
27: 33
you could also do -27 and -33 ig
Step-by-step explanation:
That's the only one possible.
Answer:
The only two numbers that your ratio is 9:11 and their differences is 6 are:
33 and 27
Step-by-step explanation:
9a = 11b Eq. 1
a - b = 6 Eq. 2
From Eq. 2:
a = 6 + b Eq. 3
Replacing Eq. 3 in Eq. 1:
9(6+b) = 11b
9*6 + 9*b = 11b
54 + 9b = 11b
54 = 11b - 9b
54 = 2b
54/2 = b
27 = b
From Eq. 3:
a = 6 + 27
a = 33
Check:
From Eq. 1:
9*33 = 11*27 = 297
5x+y=4x-y=2GRAPHINGI need The Two slopes and The Two y- intercepts pleaseeeee
Answers
Given the equations:
5x + y = 4
x - y = 2
Convert the standard from to the slope intercept from
The slope intercept form is : y = mx + c
Where m is the slope and c is y-intercept
So, for the equation 5x + y = 4
the slope intercept form will be:
[tex]y=-5x+4[/tex]so, the slope = m = -5
and y-intercept = c = 4
The graph of the line will be as following:
For the second equation: x - y = 2
The slope intercept form is :
[tex]y=x-2[/tex]The slope of the line = 1
and the y-intercept = -2
The graph of the line will be as following :
Do you see my messages ?
a
Kui Software tinite Algebra 2 Compound Inequalities Solve each compound inequality and graph its solution. Name Samanthace ballos Date valgan 1) n+15-3 or-in- Perut k 2) ohs- n2-3-1
Answers
n<4 or n>8
10) Let's solve that compound inequality:
12 + 4n> 44 or 10 -12n> -38
2) Solving each one separately
12 + 4n > 44 Subtracting 12 from both sides
4n > 44 -12
4n > 32 Divide both sides by 4
n> 8
10 -12n> -38 Subtracting 10 from both sides
-12n > -38 -10
-12n > -48 Divide both sides by -1 and flipping the sign
n < 4
3) Graphing the solution, we have:
Notice that for that, we'll use open dots since 4 and 8 are not included.
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
Answers
NEED HELP FAST!!
For ΔABC, m∠A = 41.3° and m∠B = 103.4°. Determine m∠C.
144.7°
72.35°
54.7°
35.3°
Answers
Answer: The answer is D. 35.3
Step-by-step explanation: Because the triangle has to add up to 180 and 41.3 + 103.4 = 144.7. Then you could either do 180-144.7 = 35.3 or you could add 144.7 + 35.3. Hope this helps
The value of angle C based on the information is A. 35.3°
How to calculate the angle?It's important to know that the total sum of angles in a triangle is 180°.
In this case, the following can be deduced:
Angle A = 41.3°
Angle B = 103.4°
Therefore, Angie C will be:
= Total angle - {Angle A + Angle B}
= 180° - (41.3° + 103.4°)
= 180° - 144.7°
= 35.3°
Therefore, the correct option is D.
Learn more about triangles on:
brainly.com/question/17335144
#SPJ1
(1.2 x 10^7)(2.2 x 10^-3)
Answers
The value of the expression is:
2.64 x 10² or 26400
Step - by - Step Explanation
From the question;
(1.2 x 10⁷ )(2.2 x 10⁻³)
To sim plify the expression above, we will multiply the decimal part and then apply indices to the exponent.
That is;
[tex]1.2\times2.2\times10^{7-3}[/tex][tex]=2.64\times10^2[/tex]Or
=26400
Remmy establishes a loan for an $8000 vacation package to Transylvania. The vacation company charges 5.5% simple interest rate. Remy plans to pay back the loan over 1.5 years.How much interest will Remmy pay?
Answers
Remmy will pay $660 interest.
Step - by - Step Explanation
What to find? The amount of interest to be paid.
Given Parameters:
• Principal (P) = $8000
,• Rate of interest(R) = 5.5
,• Time(t in years) = 1.5
The formula for calculating simple interest is given below:
[tex]S.I=\frac{P\times R\times T}{100}[/tex]Where P is the principal.
R represents the rate.
T is the time given in years.
S.I is the simple interest.
Substitute the values into the formula and simplify.
[tex]S.I=\frac{8000\times5.5\times1.5}{100}[/tex][tex]S.I=\frac{80\cancel{00}\times5.5\times1.5}{1\cancel{00}}[/tex][tex]=80\times5.5\times1.5[/tex]= 660
Hen
In 2001, Rodney Hampton earned $75,200 as a self-employed worker. He also earned $41,350 as an employee. How much FICA tax did he pay for both earnings? Note:Self-employed tax rate is 15.3% and the employee tax rate is 7.65%.$14,668.88$14,577.25$14,324.09$14,225.50None of these choices are correct.
Answers
Step 1: Rodney Hampton earned $75,200 as a self-employed worker
% tax rate for self employed = 15.3%
[tex]\begin{gathered} =15.3\text{ \% of \$75200} \\ =\frac{15.3}{100}\text{ x \$75200} \\ =11505.6 \\ =\text{ \$11505.6} \end{gathered}[/tex]Step 2: Rodney Hampton earned $41,350 as a employee worker
%tax rate for employee = 7.65%
[tex]\begin{gathered} =\text{ 7.65\% of \$41350} \\ =\text{ }\frac{7.65}{100}\text{ x \$41350} \\ =\text{ 3163.3} \\ =\text{ \$3163.3} \end{gathered}[/tex]Step 3: FICA tax paid for both earnings = $11505.6 + $3163.3
= $14668.875
=$14668.88
Hence FICA tax paid for both earnings = $14668.88
Use the slope and y-intercept to graph the line whose equation is given. 2 y = -x + 5x+1
Answers
ok
y = -2/5 + 1
This is the graph
Use four rectangles to estimate the area between the graph of the function f(x) = Ty and the taxis on the interval 12, 6) using the left endpointsof the subintervals as the sample points. Write the exact answer, Do not round,
Answers
To find the area using four rectangles, we will use the following equation:
[tex]Area\approx A_1_{}+A_2+A_3+A_4[/tex][tex]Area\approx f(x_1)\Delta x+f(x_2)\Delta x+f(x_3)\Delta x+f(x_4)\Delta x[/tex][tex]Area\approx f(3)\Delta x+f(4)\Delta x+f(5)\Delta x+f(6)\Delta x[/tex][tex]Area\approx(\frac{6}{7(3)})(1)+(\frac{6}{7(4)})(1)+(\frac{6}{7(5)})(1)+(\frac{6}{7(6)})(1)[/tex][tex]Area\approx\frac{57}{70}[/tex]The initial directions are in the pic below. I’m sending 2 pics now. And the other 2 soon. For a total of 4.
Answers
Recall that the rule of transformation of a point reflected over the y-axis is as follows:
[tex](x,y)\rightarrow(-x,y).[/tex]Therefore, the transformed coordinates of the vertices of the triangle are:
[tex]\begin{gathered} N(4,6)\rightarrow N^{\prime}(-4,6), \\ P(1,6)\rightarrow P^{\prime}(-1,6), \\ Q(3,4)\rightarrow Q^{\prime}(-3,4)\text{.} \end{gathered}[/tex]Therefore, the image of the triangle is the triangle with the above vertices.
Answer:
Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.
Answers
Explanation
To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.
We will need to find
[tex]P\left(x>z\right)=0.05[/tex]Therefore; using a z score calculator, this gives;
[tex]z=1.645[/tex]We can then find the cutoff amount z using the formula below;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}[/tex]Therefore, we will have
[tex]\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}[/tex]Answer: 395410
Which ratio table shows equlvalent ratios? O First Quantity 63 Second Quantity 8 5 o First Quantity Second Quantity 15 4 22 First Quantity Second Quantity 6 3 First Quantity 2.1 Second Quantity 4 2
Answers
we are asked to determine which ratios are equivalent. For ratios to be equivalent the quotient of the ratios must be the same. For the ratios:
[tex]\frac{2}{4},\frac{1}{2}[/tex]If we take 2/4 and divide the numerator and denominator by 2 we get:
[tex]\frac{\frac{2}{2}}{\frac{4}{2}}=\frac{1}{2}[/tex]Since we got the same fraction that means that the ratios are equivalent.
13 divided by 10 5/6
Answers
Answer:
the answer is 1 1/5
Are they inverses?f(x) = 6x - 6, g(x) = 1/6x + 1
Answers
Given function,
f(x) = 6x - 6
or
y = 6x -6
The inverse of a function is calculated by replacing the values of x and y
therefore
Inverse (y = 6x - 6)
x = 6y - 6
x + 6 = 6y
6y = x + 6
y = x/6 + 6/6
y = 1/6*x + 1
or
g(x) = 1/6*x + 1
Hence, both are inverse of each other.
What two variables can you define to write an equation to match this scenario?x = number of minutes for fruit cans and y = number of minutes for vegetable cansx = total number of minutes and y = total number of cansx = number of minutes for fruit and y = total number of cansx = total number of minutes and y = number of minutes for vegetables
Answers
An equation to correctly match this scenario would have to include both separate products. The current order which is 384 cans of food, includes both fruits and vegetables, and therefore any expression that does not include them both would give a wrong answer and the order would not be properly met.
The correct scenario is;
[tex]\begin{gathered} x=Number\text{ of minutes for fruit cans} \\ y=\text{Number of minutes for vegetable cans} \end{gathered}[/tex]This way you can produce both at a maximum without overproducing one and underproducing the other.
2. The length of one side of the square is the square root ofits area. Use the table tofind the approximate length of one side of the square. Explain how you used thetable to find this information
Answers
we know that
the area of a square is equal to
A=b^2
where
b is the length side
Apply square root both sides of the formula we have
[tex]\sqrt{A}=b[/tex]Which is the best interpretation of the averagerate of change of this function?
Answers
We can calculate the rate of change as the slope between two points, like (1,2) and (2,4).
The slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{2-1}=\frac{2}{1}=2[/tex]If this is a linear function, this slope m has to be constant.
We will calculate the slope between other points, like (3,8) and (4,16):
[tex]m=\frac{y_4-y_3}{x_4-x_3}=\frac{16-8}{4-3}=\frac{8}{1}=8[/tex]The slope is not constant, so this function is not a linear function.
If we look at how f(x) increases, we can prove that f(x) is:
[tex]f(x)=2^x[/tex]and this function is an exponential function.
Answer: Option B (exponential function).
Find the value of k so that x-1 is a factor of x^2 - 2x^2 + 3x + k
Answers
The value of k so that x - 1 is a factor of the polynomial, x² - 2x² + 3x + k is -2.
How to find the factor of a polynomial?The polynomial given is x² - 2x² + 3x + k.
Let's find the value of k so that x - 1 is a factor of the polynomial x² - 2x² + 3x + k.
Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore, the value of k that will make x - 1 a factor is when the polynomial is equals to zero when we input the root of x - 1 in the polynomial.
Hence,
x - 1 = 0
x = 1
let's substitute the value of x in the polynomial. The polynomial must be equals to 0 for x - 1 to be a factor of the polynomial.
0 = x² - 2x² + 3x + k
0 = (1)² - 2(1)² + 3(1) + k
0 = 1 - 2 + 3 + k
0 = - 1 + 3 + k
0 = 2 + k
k = - 2
Therefore, the value of k is -2.
learn more on factors here: https://brainly.com/question/13587979
#SPJ1
