The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
What is equilibrium?A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).
Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.
Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm
The amplitude decreases by 13/3 = 4.33 per second = 0.043%
The amplitude function can be then modelled as =
A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]
A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]
The spring oscillates 14 times each second, therefore,
T = 1/14
2π/B = 1/14
B = 28π
The graphical equation is;
D(t) = [tex]A_{cos}[/tex](Bt-C)+D
Horizontal shift = 0
Vertical shift = 0
Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
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Which inequality is represented by the graph
The inequality 4x - 2y < 12 is represented by the attached graph. which is the answer would be an option (B).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (B),
4x - 2y < 12
We can see that the x-intercept is (0, -6), and the y-intercept is (2.5, 0) in the given graph which is determined by substituting the value of x and y is equal to 0 in the equation 4x - 2y = 12.
The inequality 4x - 2y < 12 is represented by the attached graph.
Hence, the answer would be option (B).
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The graph shows the number of cups of coffee Sherwin consumed in one day and the number of hours he slept that same night:A scatter plot is shown. Data points are located at 1 and 9, 3 and 5, 5 and 6, 4 and 4, 2 and 7, and 6 and 4. A line of best fit crosses the y-axis at 10 and passes through the point 6 and 4.How many hours will Sherwin most likely sleep if he consumes 9 cups of coffee? (4 points)1, because y = −x + 102, because y = −x + 109, because y = −x + 1010, because y = −x + 10
Given:
The two endpoints (1, 9) and (6, 4).
To find the number of hours will Sherwin most likely sleep if he consumes 9 cups of coffee:
Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-9}{4-9}=\frac{x-1}{6-1} \\ \frac{y-9}{-5}=\frac{x-1}{5} \\ y-9=-x+1 \\ y=-x+10 \end{gathered}[/tex]Substitute x=9 we get,
[tex]\begin{gathered} y=-9+10 \\ y=1 \end{gathered}[/tex]Hence, the answer is,
[tex]1,because\text{ y=-x+10}[/tex]A book store sells used books. Paperback books cost $1.00. Hardback books sell for $5.00. The store sold 100 books and made $260 from the sale, How many paperback books did the store sell?
ANSWER
60 paperback books
EXPLANATION
We have that:
Paperback books sell for $1.00
Hardback books sell for $5.00
The store sold 100 books and made $260.
Let the number of paperback books be x
Let the number of hardback books be y.
This means that:
x + y = 100 _____(1)
and
1 * x + 5 * y = 260
=> x + 5y = 260 ____(2)
We have two simultaneous equations:
x + y = 100 ____(1)
x + 5y = 260 ___(2)
From (1):
x = 100 - y
Put that in (2):
100 - y + 5y = 260
=> 100 + 4y = 260
Collect like terms:
4y = 260 - 100
4y = 160
y = 160 / 4
y = 40 books
This means that:
x = 100 - 40
x = 60 books
Therefore, 60 paperback books were sold.
Question 7. Y=(5/2)^xSketch the graph of each of the exponential functions and label three points on each graph.
Given:
[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]To sketch the graph:
First find the three points.
Put x=-1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]Put x=0 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]Put x=1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).
The graph is,
4 The number of cars in 5 different parkinglots are listed below.35, 42, 63, 51, 74What is the mean absolute deviation ofthese listed numbers?
The number of cars in 5 different parking lots are given as data points as follows:
[tex]35\text{ , 42 , 63 , 51 , 74}[/tex]We are to determine the Mean Absolute Deviation ( MAD ). It is a statistical indicator which is used to quantify the variability of data points. We will apply the procedure of determining the ( MAD ) for the given set of data points.
Step 1: Determine the Mean of the data set
We will first determine the mean value of the data points given to us i.e the mean number of cars in a parking lot. The mean is determined by the following formula:
[tex]\mu\text{ = }\sum ^5_{i\mathop=1}\frac{x_i}{N}[/tex]Where,
[tex]\begin{gathered} \mu\colon\text{ Mean} \\ x_i\colon\text{ Number of cars in ith parking lot} \\ N\colon\text{ Total number of parking lots} \end{gathered}[/tex]We will use the above formulation to determine the mean value of the data set:
[tex]\begin{gathered} \mu\text{ = }\frac{35\text{ + 42 + 63 + 51 + 74}}{5} \\ \mu\text{ = }\frac{265}{5} \\ \textcolor{#FF7968}{\mu=}\text{\textcolor{#FF7968}{ 53}} \end{gathered}[/tex]Step 2: Determine the absolute deviation
The term absolute deviation is the difference of each point in the data set from the central tendency ( mean of the data ). We determined the mean in Step 1 for this purpose.
To determine the absolute deviation we will subtract each data point from the mean value calculated above.
[tex]AbsoluteDeviation=|x_i-\mu|[/tex]We will apply the above formulation for each data point as follows:
[tex]\begin{gathered} |\text{ 35 - 53 | , | 42 - 53 | , | 63 - 53 | , | 51 - 53 | , | 74 - 53 |} \\ |\text{ -18 | , | -11 | , | 10 | , | -2 | , | }21\text{ |} \\ \textcolor{#FF7968}{18}\text{\textcolor{#FF7968}{ , 11 , 10 , 2 , 21}} \end{gathered}[/tex]Step 3: Determine the mean of absolute deviation
The final step is determine the mean of absolute deviation of each data point calculated in step 2. Using the same formulation in Step 1 to determine mean we will determine the " Mean Absolute Deviation ( MAD ) " as follows:
[tex]\begin{gathered} \mu_{AD}\text{ = }\frac{18\text{ + 11 + 10 + 2 + 21}}{5} \\ \mu_{AD}\text{ = }\frac{62}{5} \\ \textcolor{#FF7968}{\mu_{AD}}\text{\textcolor{#FF7968}{ = 12.4}} \end{gathered}[/tex]Answer:
[tex]\textcolor{#FF7968}{MAD=12.4}\text{\textcolor{#FF7968}{ }}[/tex]find the mean the median the mode range and standard invitation of each data set that is obtained after adding the given content to each value (number 1)
Answers:
Mean = 43.7
Median = 44.5
Mode = doesn't exist
Standard deviation = 4.78
Explanation:
First, we need to add the constant to each value, so the new data is:
33 + 11 = 44
38 + 11 = 49
29 + 11 = 40
35 + 11 = 46
27 + 11 = 38
34 + 11 = 45
36 + 11 = 47
28 + 11 = 39
41 + 11 = 52
26 + 11 = 37
Now, we can organize the data from least to greatest as:
37 38 39 40 44 45 46 47 49 52
Then, the mean is the sum of all the numbers divided by 10, because there are 10 values in the data. So, the mean is:
[tex]\begin{gathered} \operatorname{mean}=\frac{37+38+39+40+44+45+46+47+49+52}{10} \\ \operatorname{mean}=43.7 \end{gathered}[/tex]The median is the value that is located in the middle position of the organized data. Since there are 10 values, the values in the middle are the numbers 44 and 45, so the median can be calculated as:
[tex]\operatorname{median}=\frac{44+45}{2}=44.5[/tex]The mode is the value that appears more times in the data. Since all the values appear just one time, the mode doesn't exist.
To calculate the standard deviation, we will calculate first the variance.
The variance is the sum of the squared difference between each value and the mean, and then we divided by the number of values. So, the variance is equal to:
[tex]\begin{gathered} (37-43.7)^2+(38-43.7)^2+(39-43.7)^2+(40-43.7)^2+ \\ (44-43.7)^2+(45-43.7)^2+(46-43.7)^2+(47-43.7)^2+ \\ (49-43.7)^2+(52-43.7)^2=228.1 \end{gathered}[/tex][tex]\text{Variance}=\frac{228.1}{10}=22.81[/tex]Finally, the standard deviation is the square root of the variance, so the standard deviation is:
[tex]\text{standard deviation =}\sqrt[]{22.81}=4.78[/tex]Find the value of x and y.
These 3 angles are equal value
5x + 1 = 6x - 10 = y
Then
5x + -6x = -10 - 1
-x = 11
x= 11
NOW find y value
y = 5x + 1
y= 6x - 10
y = 5•( 11) + 1= 56
y= 6•( 11) -10= 56
Answer is y= 56
Given the diagram shown, which of the following statements are true.
I,II
1) Since in this diagram we have two triangles, whose sides AI and LH are parallel to each other we can state the following:
2) And since similar triangles have congruent angles and proportional sides, we can state as true the following:
I.∠JHL ≅ ∠JIK Similar triangles have congruent angles
As they are similar triangles we can write out the following ratios:
[tex]\frac{JI}{JH}=\frac{JK}{JL}[/tex]These are true
And the third is not correct.
3) Hence, the answer is I,II
Challenge The vertices of ABC are , , and . ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A''B''C''. Graph and .
The graph shows triangle ABC with vertices as follows;
[tex]\begin{gathered} A=(-5,5) \\ B=(-2,4) \\ C=(-2,3) \end{gathered}[/tex]When translated 6 units to the right, and 7 units down, its becomes,
[tex]\begin{gathered} A^{\prime}=(1,-2) \\ B^{\prime}=(4,-3) \\ C^{\prime}=(4,-4) \end{gathered}[/tex]That means its reflected across the y-axis and the x-axis as follows;
[tex](x,y)\rightarrow(x+6,y-7)[/tex]After this the translation is complete.
5. Use the equation E =- my?my where E is kinetic energy, m is the mass of an object, and v is the object'svelocityLet E = 100, 000 J and v = 24 m/s. Find the object's mass.Show your work here:Choose the correct answer:173.6 kg86.8 kg8333.3 kg347.2 kg
In general, the kinetic energy is given by the formula below
[tex]E=\frac{1}{2}mv^2[/tex]Where m is the mass and v is the speed of the object.
Therefore, in our case,
[tex]\begin{gathered} E=100000,v=24 \\ \Rightarrow100000=\frac{1}{2}m(24)^2 \end{gathered}[/tex]Solve for m as shown below
[tex]\Rightarrow m=\frac{200000}{576}=347.2222\ldots[/tex]Thus, the answer is 347.2 kg, approximately.
What does the constant 1.6 reveal about the rate of change of the quantity?
The form of the exponential growth/decay function is
[tex]f(x)=a(1\pm r)^x[/tex]a is the initial amount
r is the rate of growth/decay per x years
We use + with growth and - with decay
Since the given function is
[tex]f(t)=2700(1.6)^{7t}[/tex]Where t is time per week
Compare the two functions
[tex]\begin{gathered} a=2700 \\ (1+r)=1.6 \\ x=7t \end{gathered}[/tex]Since 1.6 is greater than 1, then
The function is growth
Equate 1.6 by (1 + r) to find r
[tex]\begin{gathered} 1+r=1.6 \\ \\ 1-1+r=1.6-1 \\ \\ r=0.6 \end{gathered}[/tex]Change it to percent by multiplying it by 100%
[tex]\begin{gathered} r=0.6\times100\text{ \%} \\ \\ r=60\text{ \%} \end{gathered}[/tex]Since x = 7t then the time is every 7 weeks
The answer is
The function is growing exponentially at a rate of 60% every 7 weeks
Is (4,-3) a solution to the following system of equations?X - y = 42x + y = 5
No, (4, -3) is not a solution to the system of equations
Explanation:If (4, -3) is a solution to the given system of equations, then
for x = 4, and y = -3, both of the equations are satisfied.
x - y = 4 - (-3)
= 4 + 3
= 7
This is not 4, so the first equation is not satisfied
2x + y = 2(4) + (-3)
= 8 - 3
= 5
This equation is satisfied
It is sufficient to conclude that (4, -3) is not a solution to the system of equations since it doesn't satisfy the first equation
Find the value of the test statistic z using z =P-Ppan37) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics includen = 1158 subjects with 30% saying that they play a sport.Answer: - 13.6138) The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, andthe sample statistics include n = 647 drowning deaths of children with 30% of them attributable to beaches.Answer: 2.94
37. The given p-value is 0.5
Also the observed proportion is:
[tex]\hat{p}=30\%=0.3[/tex]And q is (1-p), so:
[tex]q=1-0.5=0.5[/tex]And the n-value is given 1158.
By replacing these values into the test statistic formula we obtain:
[tex]z=\frac{\hat{p}-p}{\sqrt[]{\frac{p\cdot q}{n}}}=\frac{0.3-0.5}{\sqrt[]{\frac{0.5\cdot0.5}{1158}}}=\frac{-0.2}{\sqrt[]{0.0002}}=\frac{-0.2}{0.015}=-13.61[/tex]The answer is -13.61
Write using an exponent: 1×7×7×7×7×7a. 1×7×5b.[tex]1 \times {7}^{5} [/tex]c. [tex]1 \times {5}^{7} [/tex]
In the expression, the number 7 is multiplied to itself 5 times or five 7's are multiplied with each other. So exponential expression for the equation is,
[tex]1\cdot7\cdot7\cdot7\cdot7\cdot7=1\cdot7^5[/tex]Option B is correct.
The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the sample variance for ATM fees for each city.City A1.25 1.00 1.50 1.25 1.50City B2.50 1.25 1.00 0.00 2.00The variance for city Ais $(Round to the nearest cent as needed.)
City A (n = 5)
1.25 1.00 1.50 1.25 1.50
City B
2.50 1.25 1.00 0.00 2.00
The variance formula is:
So, the mean A is:
(1.25 + 1.00 + 1.50 + 1.25 + 1.50)/5 = 1.30
The variance for city A is:
s²_A = 0.04
For city B:
Mean B = 1.35
The variance for city B is:
s²_B = 0.92
Draw the dilation of PQRS using center Q and scale factor 1/2. Label the dilation TUWX. 2. Draw the dilation of PQRS with center R and scale factor 2. Label the dilation ABCD. 3. Show that TUWX and ABCD are similar.
Based on the given image, you obtain the following figures:
Draw the dilation of PQRS using center Q and scale factor 1/2
Draw the dilation of PQRS with center R and scale factor 2. Label the dilation ABCD
You can notice that both figure TUWX and ABCD are similar because the quotient between sides TU and PQ, XW and RS, UW and BC, TX and AD are the same.
Hi! Can someone please check my work real quick? I’m not sure what I’m doing wrong. I’m trying fo find the remainder using synthetic division.
Given:
The polynomial is given as,
[tex]\begin{gathered} p(x)=2x^3+4x^2-5 \\ g(x)=x+3 \end{gathered}[/tex]The objective is to divide the polynomial by synthetic division.
Explanation:
The general equation of a polynomial with degree 3 is,
[tex]f(x)=ax^3+bx^2+cx+d[/tex]So, consider the given polynomial as,
[tex]p(x)=2x^3+4x^2+0x-5[/tex]The divisor can be converted as,
[tex]\begin{gathered} x+3=0 \\ x=-3 \end{gathered}[/tex]To find synthetic division:
Now, the synthetic division can be evaluated as,
Hence, the remainder of the division is -23.
find the range of the data set show in the table below
Remember that
the range is the spread of your data from the lowest to the highest
so
range=Maximum value-Minimum value
we have
Maximum value=170
Minimum value=27
Range=170-27=143
therefore
answer is
Range 143Given that sin A= -4 over 5 and angle A is in quadrant 3, what is the value of cos(2A)?
Solution:
Given;
[tex]\sin(A)=-\frac{4}{5}[/tex]Then, the value of cosine x is;
[tex]\cos(A)=-\frac{3}{5}[/tex]Because cosine and sine are negative on the third quadrant.
Then;
[tex]\begin{gathered} \cos(2A)=\cos^2(A)-\sin^2(A) \\ \\ \cos(2A)=(-\frac{3}{5})^2-(-\frac{4}{5})^2 \\ \\ \cos(2A)=\frac{9}{25}-\frac{16}{25} \\ \\ \cos(2A)=-\frac{7}{25} \end{gathered}[/tex]Choose the expression that is equal to 28.3A. 3³+27.2-6.8+2⁴-3.1B. 3³+27.2-(6.8+2⁴-3.1)C. [3³+(27.2-6.8)]+2⁴-3.1D. 3³+27.2-(6.8+2⁴)-3.1
solution
For this case we can solve each case and we have:
A) 27 +27.2 -6.8 +16 -3.1= 60.3
B) 27 +27.2 -(6.8 +16 -3.1)= 54.2- 19.7= 34.5
C) 27 + 20.4 +16 -3.1= 30.1
D) 27 +27.2 - 22-8 -3.1= 28.3
then the correct solution for this case would be:
D)
Suppose someone wants to accumulate $120,000 for retirement in 30 years. The person has two choices. Plan A is a single deposit into an account with annual compounding and an APR of 6%. Plan B is a single deposit into an account with continuous compounding and an APR of 5.8%. How much does the person need to deposit in each account in order to reach the goal?The person must deposit $______ into the account for Plan A to reach the goal of $.The person must deposit $______ into the account for Plan B to reach the goal of $.(Round to the nearest cent as needed.)
We want to calculate the amount needed as an initial investment to have 120000 after 30 years.
Recall that the formula of annual compounding is given by the formula
[tex]S\text{ =}P\text{ \lparen1+r\rparen}^t[/tex]where P is the principal, r is the interest rate and t is the time in years. When compounded continously the formula is
[tex]S=Pe^{rt}[/tex]where the variables have the same meaning. In both cases we want to find P sucht that
[tex]S=120000[/tex]when t=30 and r is the interest rate that we are given.
So we have the following equation in the first case
[tex]120000=P\text{ \lparen1+}\frac{6}{100})^{30}[/tex]so if we divide both sides by (1+6/100)^30 we get
[tex]P=\frac{120000}{(1+\frac{6}{100})^{30}}\approx20893.22[/tex]so for Plan A 20893.22 is needed to have 120000 after 30 years.
now, we want to do the same with the second plan. We have
[tex]120000=Pe^{\frac{5.8}{100}30}[/tex]so we divide both sides by exp(5.8*30/100). So we get
[tex]P=\frac{120000}{e^{\frac{5.8}{100}\cdot30}}\approx21062.45[/tex]so for Plan B 21062.45 is needed to have 120000 after 30 years
Which of the following represents the equation of a quadratic curve?y = 3x + 7y = 8 - 3x + 7x2y = 7(3)xy = 8 x 6
An equation will be a quadratic curve when the expression has the following definition
[tex]y=ax^2+bx+c[/tex]We can have b and c equal to 0, but never a, therefore we have few variations like
[tex]\begin{gathered} y=ax^2+bx \\ y=ax^2+c \\ y=ax^2 \end{gathered}[/tex]All they are quadratics. Looking at the options we can see that the only function that has that definition is
[tex]y=8-3x+7x^2[/tex]Therefore the correct answer is
[tex]y=8-3x+7x^{2}[/tex]For the function f(x) = x^2 + 3x,a) Find f(-2).b) Is this function linear or quadratic? Justify your answer.c) Will the graph of this function appear as a line or a parabola?
a) Evaluating the function at x= -2 we get:
[tex]f(-2)=(-2)^2+3(-2)=4-6=-2[/tex]b) Notice that the given function has the form:
[tex]y=ax^2+bx+c[/tex]Therefore f(x) is a quadratic function.
c) Since f(x) is a quadratic function its graph is a parabola.
[in the following write an expression in terms of the given variables that represents the indicated quantity.]the sum of three consecutive integers if the greatest integer is x.the expression for the sum of the three consecutive integers is _________
Answer
Sum of the three consecutive integers = 3x - 3
Explanation:
Find the sum of three consecutive integers
Condition given: Greatest integer should be x
Since, x is the greatest integer, therefore, the other integers should be less than x
The three consecutive integers are: x, x - 1, and x - 2
Sum of the three integers = x + x - 1 + x - 2
Sum = x + x - 1 + x - 2
Collect the like terms
= x + x + x - 1 - 2
Sum = 3x - 3
Therefore, the sum of the three consecutive integers is 3x - 3
Yoko, Austin, and Bob have a total of $57 in their wallets. Austin has $7 less than Yoko. Bob has 2 times what Yoko has. How much does each have?
Yoko has $16 money, Austin has $9 and Bob has $32.
According to the question,
We have the following information:
Yoko, Austin, and Bob have a total of $57 in their wallets. Austin has $7 less than Yoko. Bob has 2 times what Yoko has.
Now, let's take the money Yoko has to be $x.
So, we have the following expressions for the money Austin and Bob have:
Austin = $(x-7)
Bob = $(2x)
Now, we have the following expression by adding them:
x+x-7+2x = 57
4x-7 = 57
4x = 57+7
4x = 64
x = 64/4
x = $16
Now, the money Austin has:
16-7
$9
Money Bob has:
2*16
$32
Hence, Yoko has $16 money, Austin has $9 and Bob has $32.
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I need to solve each system by graphing. so pls help! This is Algebra 1
Given the system of inequalities:
2x + 3y < -6
-2x + 3y < 6
Let's solve the system by graphing.
To graph, rewrite the inequalities in slope-intercept form:
y = mx + b
Inequality 1:'
Subtract 2x from both sides:
2x - 2x + 3y < -2x - 6
3y < -2x - 6
Divide all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}<-\frac{2x}{3}-\frac{6}{3} \\ \\ y<-\frac{2}{3}x-2 \end{gathered}[/tex]Inequality 2:
Add 2x to both sides:
-2x + 2x + 3y < 2x + 6
3y < 2x + 6
Divde all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}<\frac{2x}{3}+\frac{6}{2} \\ \\ y<\frac{2}{3}x+2 \end{gathered}[/tex]Now, let's plot 3 points from each inequlality and connect using a straight edge.
Inequality 1:
When x = -3
Substitute -3 for x and solve for y:
[tex]\begin{gathered} y<-\frac{2}{3}(-3)-2 \\ \\ y<2-2 \\ \\ y<0 \end{gathered}[/tex]When x = 0:
[tex]\begin{gathered} y<-\frac{2}{3}(0)-2 \\ \\ y<-2 \end{gathered}[/tex]When x = 3:
[tex]\begin{gathered} y<-\frac{2}{3}(3)-2 \\ \\ y<-2-2 \\ \\ y<-4 \end{gathered}[/tex]From inequality 1, we have the points:
(x, y) ==> (-3, 0), (0, -2), (3, -4)
For inequlity 2:
When x = -3:
[tex]\begin{gathered} y<\frac{2}{3}(-3)+2 \\ \\ y<-2+2 \\ \\ y<0 \end{gathered}[/tex]When x = 0:
[tex]undefined[/tex]Ian is a salesperson who sells computers at an electronics store. He makes a base payof $80 each day and then is paid a $5 commission for every computer sale he makes.Make a table of values and then write an equation for P, in terms of x, representingIan's total pay on a day on which he sells x computers.
ANSWER
[tex]P=5x+80[/tex]EXPLANATION
Let the number of computers sold be x.
Let the total pay be P.
We have to find the equation that represents the total pay in terms of the number of computers sold.
The equation that represents the total pay is a linear equation and a linear equation has a general form of:
[tex]y=mx+b[/tex]where m = slope
b = y intercept
To find the slope, we have to apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are two sets of points from the table.
Let us pick (0, 80) and (3, 95)
Therefore, the slope, m, is:
[tex]\begin{gathered} m=\frac{95-80}{3-0} \\ m=\frac{15}{3} \\ m=5 \end{gathered}[/tex]Now, we apply the point-slope formula to find the equation:
[tex]P-P_1=m(x-x_1)[/tex]Note: P is used in place of y (the dependent variable)
Therefore, we have:
[tex]\begin{gathered} P-80=5(x-0) \\ P-80=5x \\ \Rightarrow P=5x+80 \end{gathered}[/tex]That is the equation that represents the total pay, P.
Solve 3x-9 = 6.A. x = 2B. x=-1C. x = 1D. x = 5
Step 1. The expression that we have is:
[tex]3x-9=6[/tex]And we need to solve for x.
If we are going to solve for x, we need to have the 'x' alone on one side of the equation.
For that, the first step is to add 9 to both sides:
[tex]3x-9+9=6+9[/tex]Step 2. On the left side, -9+9 cancel each other, and on the right side 6+9 is 15:
[tex]3x=15[/tex]Step 3. The next step is to divide both sides by 3:
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]In this way, 3/3 on the left side cancel each other and we are left only with x:
[tex]x=\frac{15}{3}[/tex]And on the right side, 15/3 is equal to 5:
[tex]\boxed{x=5}[/tex]This is shown in option D.
Answer:
D. x=5
How much work is done when a book weighting 2.0 new newtons is carried at a constant velocity from one classroom to another classroom 26 meters away.
Find the domain of the rational function.f(x)=(x−7)/(x+8)
Answer:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]Explanation:
Given the rational function:
[tex]f(x)=\frac{x-7}{x+8}[/tex]The domain of f(x) is the set of the values of x for which the function is defined.
A rational function is undefined when the denominator is 0.
Set the denominator of f(x) equal to 0 in order to find the value(s) of x at which f(x) is undefined.
[tex]\begin{gathered} x+8=0 \\ \implies x=-8 \end{gathered}[/tex]-8 is the excluded value of the domain.
Therefore, the domain of f(x) is:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]