Find the slope of the graph using two of the points marked in the slope formula?
Answers
Given:
There is a geaph given in the question
Required:
We need to find the slope of given graph
Explanation:
Take two points from graph
[tex]\begin{gathered} (x_1,y_1)=(0,40) \\ (x_2,y_2)=(10,60) \end{gathered}[/tex]formula to find the slope m is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substitute the values
[tex]m=\frac{60-40}{10-0}=\frac{20}{10}=2[/tex]Final answer:
Slope m of given graph is 2
Related Questions
Use the function below to find F(-4).Fx) = 2x
Answers
We are given a function f(x) = 2x
To find f(-4), we simply substitute the value of x with -4
This gives:
f(-4) = 2(-4)
f(-4) = 2 x -4 = -8
Therefore, f(-4) = -8
d. Wind speed - Wind wane Kimberly’s family invested in a Certificate of Deposit (CD) for her when she was born. The interest is compounded quarterly.a. What will be the difference after 15 years if the CD is compounded semiannually rather than quarterly?Enter your answer.b. What will be the difference after 15 years if the CD is compounded monthly rather than quarterly?Enter your answer.
Answers
Answer: The basic formula for determining the compound interest is as follows:
Write the compound statement "If I eat too much, then I'll exercise" in symbols. Then, construct a truth table for the symbolic statement.p = "I eat too much"q = "I'll exercise"
Answers
Both statements in the sentence have the following structure:
If I eat too much, then I'll exercise.
If p then q.
When we have this structure, we represent it symbolically as:
[tex]p\to q[/tex]For these cases, the only situation in which the statement is false is when the first part of the sentence is true, and the second false:
p q p->q
T T V
T F F
F T V
F F V
With this, option C is the correct answer.
Divide. Reduce your answers to lowest terms. -4/3 divide 5/9
Answers
Given
-4/3 Divide 5/9
Procedure
-4/3 ÷ 5/9
=-12/5
The answer is -12/5
A concession stand wants to determine, with 90% confidence, what proportion of people like lettuce on their hamburgers.They want to know the correct proportion to within 4%.A preliminary study showed that 36% of those surveyed like lettuce on hamburgers.What sample size is necessary to estimate the true proportion of people who like lettuce on their hamburgers?
Answers
To calculate the size of the sample we use the following formula:
[tex]n=\frac{Z^2P(1-P)}{d^2}[/tex]N is the size of the sample, P is the expected proportion of people liking lettuce (36% for this case) and d is the precision, 4% in this case. Z is the Z score for confidence. In this case, 90% of confidence will have a Z value of 1.645.
Then, applying the formula:
[tex]\begin{gathered} n=\frac{1.645^2\cdot0.36(1-0.36)}{0.04^2} \\ n=389.66 \end{gathered}[/tex]Rounding to the unit, the sample size should be 390.
To be able to buy a new computer, Keisha decides to save for 6 years. She opens a savings account with $600. The account pays simple interest at an annualrate of 3%. She doesn't make any more deposits.Answer the following questions. If necessary, refer to the list of financial formulas.x5?(a) How much total interest will Keisha earn?$0(b) What will the total amount in the account be including interest)?$Submit AssignmentContinue2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center Accessibility3:47 AMM68°F MOOED »)5/19/2022-*O PiType here to searchFONumWoonPausePrisc
Answers
Given:
[tex]\begin{gathered} P=600 \\ R=3\% \\ T=6year \end{gathered}[/tex]Required:
To find the total interest and the total amount in the account be including interest.
Explanation:
(a)
The total interest is
[tex]\begin{gathered} I=\frac{PTR}{100} \\ \\ =\frac{600\times6\times3}{100} \\ \\ =108 \end{gathered}[/tex](b)
The total amount in the account be including interest is
[tex]600+108=708[/tex]Final Answer:
(a) The total interest is $108.
(b) The total amount in the account be including interest is $708.
If f(x) varies directly with x and f(x)= 64 when x=29 , find the value of f(x) when x=8.Round you final answer to the nearest whole number.
Answers
18
Explanation
Direct variation describes a simple relationship between two variables, it can be defined by the expression
[tex]\begin{gathered} f(x)=kx \\ \text{where} \\ f(x)=\text{ y, } \\ \text{and k is a constant} \end{gathered}[/tex]Step 1
find the k value,
set the equation and solve for k
so
let
f(x)=64 when x=29
so
[tex]\begin{gathered} f(x)=kx \\ \text{replace} \\ 64=k\cdot29 \\ to\text{ solve for k, divide both sides by 29} \\ \frac{64}{29}=\frac{k\cdot29}{29} \\ \frac{64}{29}=k \end{gathered}[/tex]Step 2
now, set the equation:
with k=64/29 , the function would be
[tex]\begin{gathered} f(x)=kx \\ f(x)=\frac{64}{29}x \end{gathered}[/tex]finally, to check the f(x) when x= 8, just replace and calculate
[tex]\begin{gathered} f(x)=\frac{64}{29}x \\ f(8)=\frac{64}{29}\cdot8 \\ f(8)=\frac{512}{29} \\ f(8)=17.655 \\ \text{rounded} \\ f(8)=18 \end{gathered}[/tex]threfore, the answer is
18
I hope this helps you
what is perpendicular to y equal -1/3x - 1
Answers
The original line is:
[tex]y=-\frac{1}{3}x-1[/tex]So the perpendicular line would have a slope equal to the negative reciprocal of the first line so:
[tex]m=3[/tex]So a new line is:
[tex]y=3x[/tex]Angle a and b are supplementary,angle a is 32 What is angle b?
Answers
By definition, two angles are called supplementary when their measures add up to 180 degrees.
Given:
angle a and b are supplementary
a = 32
Using the definition above:
[tex]\begin{gathered} a\text{ + b = 180} \\ 32\text{ + b = 180} \\ \text{Collect like terms} \\ b\text{ = 180 -32} \\ b=148^0 \end{gathered}[/tex]Answer:
b = 148
Suppose the data below shows a linear relationship.What is the rate ofRate of Change =
Answers
A relation is a function only if any two first values in the pairs are the same. O True False
Answers
Answer:
False
Explanation:
A relation can become a function only if each of the element of the set X (input) is related to only one element one element of set Y (output). That means only one input is related to each output.
For the question;
A relation is a function only if any two first values in the pairs are the same. False.
A relation cannot become a function when two first value of distinct pair are the same.
Please answer the Unit 2 Essential Question below.How can you analyze, model, and solvemathematical situations using algebraicequations?
Answers
Explanation
We can use algebraic models to solve problems. By taking the information given in a problem, we can represent quantities using variables and then set up an equation using those variables. This equation is our algebraic model. We can then use that model to answer questions about the scenario by finding the unknow values.
I hope this helps you
7.) Explain how to use that additivity principle to determine the area of the dark glaciated triangle that is inside a rectangle in figure 12.35
Answers
In order to find the area of the dark triangle (let's call it 'x'), we need to calculate the area of the whole rectangle and the area of the three small triangles.
The area of the rectangle is:
[tex]\begin{gathered} A_R=\text{length}\cdot\text{width} \\ A_R=(5+2)\cdot(2+2) \\ A_R=7\cdot4=28\text{ u}^2 \end{gathered}[/tex]The area of each triangle is:
[tex]\begin{gathered} A=\frac{\text{base}\cdot\text{height}}{2} \\ \\ A_1=\frac{5\cdot2}{2}=5 \\ A_2=\frac{2\cdot(5+2)}{2}=7 \\ A_3=\frac{2\cdot(2+2)_{}}{2}=4 \end{gathered}[/tex]Now, using the additivity principle, we have that:
[tex]\begin{gathered} A_1+A_2+A_3+x=A_R \\ 5+7+4+x=28 \\ 16+x=28 \\ x=28-16 \\ x=12 \end{gathered}[/tex]So the area of the dark triangle is equal 12 square units.
2. A patient who transferred at 5 p.m. to unit A from unit B is counted in unit A's 12:01 a.m. census as oneadditional patient present. Would that patient still be included in unit B's 12:01 a.m. census? Explain youranswer.
Answers
The patient cannot be in two places at the same time. If both units are counting heads only once a day at midnight, the patient is counted as being present in unit A only. However, the patient is indicated in unit B's census as a transfer. The answer is no.
Given f(x)=3x-8,find the range for the domain {-4,2,7}pls show work
Answers
Answer:
{-20,-2,13}
Explanation:
Given f(x)=3x-8 for the domain {-4,2,7}.
When x=-4
[tex]\begin{gathered} f(-4)=3(-4)-8 \\ =-12-8 \\ =-20 \end{gathered}[/tex]When x=2
[tex]\begin{gathered} f(2)=3(2)-8 \\ =6-8 \\ =-2 \end{gathered}[/tex]When x=7
[tex]\begin{gathered} f(7)=3(7)-8 \\ =21-8 \\ =13 \end{gathered}[/tex]So, the range for the given domain is:
[tex]\{-20,-2,13\}[/tex]What values make the inequality v > -3 true (multiple choice) -11, -4, -3.001, -2.99, 0, -8, -3.1, -3, -2.9, 2, -6, -3.01, -2.999, -2, 5
Answers
For the inequality
[tex]v>-3[/tex]the values for v which are greater than -3 are:
[tex]-2.99,-2.9,2,-2.999\text{ and -2.5}[/tex]we can see this by means of the following picture:
given : g(x) = square root of x+3 and h(x) = x- 7
Answers
Given g(x) and h(x) below:
[tex]\begin{gathered} g(x)=\sqrt[]{x+3} \\ h(x)=x-7 \end{gathered}[/tex]To find the quotient (g/h)(x), divide g(x) by h(x):
[tex]\begin{gathered} (\frac{g}{h})(x)=\frac{g(x)}{h(x)} \\ =\frac{\sqrt[]{x+3}}{x-7} \end{gathered}[/tex]Thandi starts a new business baking pies that she sells to a local Spaza shop. She uses the family kitchen to bake her pies. Thandi used this formula to calculate her profit: Profit = money received for sales - cost of ingredients Her profits are shown in the table. Week Number of pies sold Profit 1 2 3 4 5 25 34 39 42 40 R75 R102 R117 R126 R120 a) Write Thandi's profit per pie as a rate. (1)
Answers
Answer:
Step-by-step explanation:ni
6) A cab company charges $0.20 per mile plus $8 for tolls. Melissa has at most $26 to spend on her cabfare. Write and solve an inequality to determine if she has enough money to go to the airport that is 45miles away, and requires 2 tolls.Let x =Inequality:
Answers
Let x = the number of miles.
Let y = the number of tolls.
Total charges per mile is $0.20 times x or 0.20x.
Total charges per toll is $8 times y or 8y.
Since Melissa's money is at most $26 only, the total charges per mile and per toll must not exceed $26 so that her money will be enough. With that, we can form the inequality:
[tex]0.20x+8y\leq26[/tex]To check if her money is not enough, let's plug in the number of miles x = 45 miles and the number of tolls y = 2 to the inequality above.
[tex]\begin{gathered} (0.20\times45)+(8\times2)\leq26 \\ 9+16\leq26 \\ 25\leq26 \end{gathered}[/tex]The total charge for 45 miles and 2 tolls is $25 only. Since $25 is less than $26, Melissa's money is enough for her to go to the airport.
The cylinder below has a radius 3 inches and a height of 8 inches. If two points are located on the surface of the cylinder, what is the maximum straight line distance they could be a part?
Answers
Consider the two situations below:
1) Two points are located on opposite sides of a diameter; as in the next diagram
The distance between the two points is equal to the diameter of the circle; in other words, 2 times the radius. Thus, the distance between the two orange points above is 6in.
2) Consider two points on opposite faces of the cylinder
The distance between the two points is equal to 8in, in this situation.
Mixing both diagrams so as to obtain the maximum distance between two points on the cylinder,
Thus, the maximum distance is given by the Pythagorean theorem, as shown below
[tex]d_{max}=\sqrt{6^2+8^2}=10[/tex]Hence, the answer is 10in
How do I solve the following system of equations by substitution. I have to show all steps
Answers
In order to solve this system by substitution, let's equate both functions, substitute the expressions for f(x) and g(x), and calculate the values of x:
[tex]\begin{gathered} f(x)=g(x)\\ \\ -x^2+2x+3=-2x+3\\ \\ -x^2+2x+2x+3-3=0\\ \\ -x^2+4x=0\\ \\ x^2=4x\\ \\ x=4\text{ or }x=0 \end{gathered}[/tex]Therefore the solutions are x = 0 and x = 4.
Using slope intercept for, write the equation of the line through each pair of points. (-4, 1) and (-2,-2)
Answers
Answer:
Explanation:
Given:
To find the slope intercept form, we use the formula:
y=mx+b
where:
m=slope
b= y intercept
First, we find the slope(m) using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We plug in what we know.
[tex]\begin{gathered} m=\frac{-2-1}{-2-(-4)} \\ m=-\frac{3}{2} \end{gathered}[/tex]Next, use any of the given points ( Ex. Let x= -4, y=1) and m=-3/2, and plug in into y=mx+b.
So,
y=mx+b
1=(-3/2)(-4) +b
Simplify and rearrange
1=6+b
b=1-6
b=-5
Then, plug in m= -3/2 and b= -5 into y=mx+b.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{3x}{2}-5 \end{gathered}[/tex]Therefore, the slope intercept form is:
[tex]y=-\frac{3x}{2}-5[/tex]Type the correct answer in box. Use numerals instead of words. THIS IS NOT A TEST.
Answers
The expression is,
[tex]|m^2+n^2|[/tex]Substitute -5 fo m and 3 for n in the expression.
[tex]\begin{gathered} |(-5)^2+(3)^2|=|25+9| \\ =|34| \\ =34 \end{gathered}[/tex]So answer is 34.
Let f(x)=−2sec^2(x^2). Find f′(x).
Answers
Given:
[tex]f(x)=2\sec ^2(x^2)[/tex]Differentiate with respect to x
[tex]\begin{gathered} f^{\prime}(x)=2\lbrack2\sec (x^2)\rbrack\lbrack\sec (x^2)\tan (x^2)\rbrack\lbrack2x\rbrack \\ f^{\prime}(x)=8x\sec ^2(x^2)\tan (x^2) \end{gathered}[/tex]I'll send a pic of the Homework
Answers
given the value of a and b in each set:
Set 1 :
[tex]\begin{gathered} a=-\frac{1}{2},b=6 \\ \\ \end{gathered}[/tex]We will find the value of the following :
[tex]\begin{gathered} -a=-1\cdot-\frac{1}{2}=\frac{1}{2} \\ \\ -4b=-4\cdot6=-24 \\ \\ -a+b=\frac{1}{2}+6=6\frac{1}{2} \\ \\ a\div-b=\frac{1}{2}\div-6=\frac{1}{2}\cdot-\frac{1}{6}=-\frac{1}{12} \\ \\ a^2=(-\frac{1}{2})^2=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4} \\ \\ b^3=6^3=216 \end{gathered}[/tex]The expression with the largest value = b^3 = 216
The expression with the smallest value = -4b = -24
the expression which is closest to zero = a ÷ -b
Find the domain of this without using the graphical method
Answers
By definition, the domain of a function is the complete set of possible values of the independent variable (x, usually).
We must find the domain of the following function:
[tex]f(x)=\sqrt[5]{x^2-7x+2}\text{.}[/tex]We see that the function is the odd root of a polynomial. Odd roots are defined for all real numbers, so this function is defined for all real numbers. The domain of the function is:
[tex]\text{Domain }=(-\infty,\infty).[/tex]Answer
[tex]\text{Domain }=(-\infty,\infty).[/tex]Writing an equation of an eclipse given the foci and major axis length
Answers
Answer:
The equation of the ellipse is:
[tex]\begin{equation*} \frac{(x-3)^2}{64}+\frac{(y+3)^2}{55}=1 \end{equation*}[/tex]Step-by-step explanation:
Remember that the general equation of an ellipse is:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where:
• (h,k), are the coordinates of the center
,• a, is the major axis lenght
,• b, is the minor axis lenght
We also have that the equation for the foci is:
[tex]F(h\pm c,k)[/tex]And we also have that:
[tex]c^2=a^2-b^2[/tex]Since we have two foci, we can find the values of h and c as following:
[tex]\begin{gathered} F(h\pm c,k) \\ \\ (6,-3)\rightarrow h+c=6 \\ (0,-3)\rightarrow h-c=0 \end{gathered}[/tex]We'll have the following system of equations:
[tex]\begin{cases}h+c=6 \\ h-c={\text{ }0}\end{cases}[/tex]Adding up both equations and solving for h,
[tex]\begin{cases}h+c=6 \\ h-c={\text{ }0}\end{cases}\rightarrow2h=6\rightarrow h=3[/tex]Using this h value in the first equation and solving for c,
[tex]h+c=6\rightarrow3+c=6\rightarrow c=3[/tex]We'll have that the solution to this particular system of equations is:
[tex]\begin{gathered} h=3 \\ c=3 \end{gathered}[/tex]Now we know the value of c we can calculate the value of b as following:
[tex]\begin{gathered} c^2=a^2-b^2 \\ \rightarrow b^=\sqrt{a^2-c^2} \\ \rightarrow b=\sqrt{8^2-3^2} \\ \\ \Rightarrow b=\sqrt{55} \end{gathered}[/tex]With all these calculations, we'll have all the values we need to put together the equation:
[tex]\begin{gathered} h=3 \\ k=-3 \\ a=8 \\ b=\sqrt{55} \end{gathered}[/tex]This way, we'll have that the equation of the ellipse is:
[tex]\begin{gathered} \frac{(x-3)^2}{8^2}+\frac{(y-(-3))^2}{(\sqrt{55})^2}=1 \\ \\ \Rightarrow\frac{(x-3)^2}{64}+\frac{(y+3)^2}{55}=1 \end{gathered}[/tex]What is the equation of the line that passes through the point (3, -5) and has aslope of 0?
Answers
If the line has a slope of 0, the value for y is a constant:
[tex]y=0\cdot x+b=b[/tex]If the point (3,-5) belongs to the line, and the slope is 0, the line is y=-5.
A movie theater gave away couponsfor small, medium, and large drinks.Customers could randomly pull a couponfrom a box that held 75 small drinkcoupons, 125 medium drink coupons,and 150 large drink coupons.What is the probability that the firstcustomer to pull a coupon from thebox got a medium drink coupon?A ſaBczD 214
Answers
EXPLANATION
Let's see the facts:
Number of small drinks ---> 75 coupons
Number of medium drinks --> 125 coupons
Number of large drinks --> 150 coupons
So, the probability that the first customer pull a coupon from the box got a medium drink coupon is:
[tex]P=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}[/tex]The total number of possible outcomes is 75+125+150=350 coupons
Medium drink favourable outcomes is equal to 125 coupons
[tex]P=\frac{125}{350}=\frac{5}{14}[/tex]The answer is 5/14
Help with math discussion precalculus Select any city in the world that interests you. Research the average high temperature of that city each month for two years. Next, plot that data. The x-axis should be months (1-24) and the y-axis should be temperature. Embed your graph and table into the discussion board by uploading the image.
Answers
SOLUTION
The Picture below is a table showing the average high temperature for Dallas for two years.
From the graph
[tex]\begin{gathered} x_1=\text{ represents the months for 24 months} \\ y_1=\text{ represents the average high temperature for each month } \end{gathered}[/tex]The graph for the data is shown below
We can see that the graph is a sinusoidal graph. That is it follows a sine wave form.