Determine the equation of the line that passes through the points (0,−10) and (−8,1).
Answers
Solution:
Given the points below;
[tex]\left(0,−10\right)\text{ }and\text{ }(−8,1)[/tex]To find the equation of the line that passes through the points, we will apply the formula below
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(0,-10) \\ (x_2,y_2)=(-8,1) \end{gathered}[/tex]Substitute the values of the coordinates into the formula above
[tex]\begin{gathered} \frac{y-(-10)}{x-0}=\frac{1-(-10)}{-8-0} \\ \frac{y+10}{x}=\frac{1+10}{-8} \\ \frac{y+10}{x}=-\frac{11}{8} \\ Crossmultiply \\ 8(y+10)=-11(x) \\ 8y+80=-11x \\ 11x+8y+80=0 \end{gathered}[/tex]Hence, the equation of the line is
[tex]11x+8y+80=0[/tex]The graph is shown below with the points indicated using a graphing tool
Related Questions
Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 318 with 57% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
Answers
A population proportion's 95% confidence interval is 0.45416 ≤ P ≤ 0.66584.
Given sample size n is 318, the probability of success,
p = x ÷ n = 181 ÷ 318 = 0.56
A population proportion's 95% confidence interval is calculated as follows:
(p - [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n) , p + [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n)
(0.56 - 1.96 √ ((0.56(1 - 0.56) ÷ 318) , 0.56 + 1.96 √ ((0.56(1 - 0.56) ÷ 318))
(0.56 - 1.96 × 0.054) , (0.56 + 1.96 × 0.054)
(0.45416 , 0.66584)
95% confidence interval for a population proportion of 0.45416 ≤ P ≤ 0.66584.
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This year for Spring break you are taking a solo trip to an exotic destination. You are deciding between two destinations: Bali, Indonesia, and Paris, France. You want to choose the destination that will give you the best value for your money.The table below shows the cost to travel to each destination Flight Hotel (pernight)Bali $967 $58Paris $534 $2551. Create an equation for each destination to represent cost, C to travel to that location based on n Number of nights.
Answers
Let n represent the number of nights
Cost to travel to Bali:
[tex]C\text{ = 967 + 58n}[/tex]The cost of flight is constant so we simply add it to the cost of hostel per night times the number of nights
Cost to travel to Paris:
[tex]C\text{ = 534 + 255n}[/tex]It costs $35 per hour to rent a boat at the lake.
You also need to a pay a $25 fee for safety equipment.
You have $200.
How long can you rent the boat?
Answers
Answer:
7 hours
Step-by-step explanation:
25x + 25 = 200.
25x = 175
175/25 = 7.
Answer:
25 + 35h = 200
and
h = 5
(5 hours)
Step-by-step explanation:
you have 200.
costs:
35 per hour
and
25 fee
h will represent the total hours spent renting a boat
25 + 35h = 200
now we will do inverse operations
subtract 25 from both sides
35h = 175
now divide both sides by 35
h = 5
a) The perimeter is ____. Include units.b) The area is ___. include units.Another question is: Fully Simplify the following equation: (3x + 7) (5x^2 + 4x +9)
Answers
The perimeter is 54 inches
The area is 108 square inches
Explanation:The perimeter of the triangle is:
15 in + 15 in + 24 in
= 54 in
The area is:
(1/2)(24)(9)
= 108 sq. in
HELP ME OUT PLEASE!!!!!!!
What is the solution to the system?
Answers
Answer:
(-7, 5) is correct.
Step-by-step explanation:
[tex]2x + 3y = 1[/tex]
[tex] - 2x - y = 9[/tex]
Add these two equations, and then solve for y.
[tex]2y = 10[/tex]
[tex]y = 5[/tex]
Substitute this value of y into 2x + 3y = 1, and solve for x.
[tex]2x + 3(5) = 1[/tex]
[tex]2x + 15 = 1[/tex]
[tex]2x = - 14[/tex]
[tex]x = - 7[/tex]
So (-7, 5) is the correct solution.
Suppose you have $2750 in your savings account at the end of a certain period of time. You invested $2000 at a 4.36% simple annual interest rate. How long, in years, was your money invested ? (State your results to the nearest hundredth of a year.)
Answers
The money was invested for 8.60 years
Explanation:Given:
Amount in the savings account = $2750
Amount invested = $2000
rate = 4.36% = 0.0436
To find:
the time it took to invest the money to obtain the amount in the account
The investment was done using simple interest. So to get the time, we will apply simple interest formula
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest} \\ R\text{ = rate} \\ T\text{ = time} \end{gathered}[/tex][tex]\begin{gathered} Interest\text{ = amount in the account - amount } \\ \\ Interest\text{ = 2750 - 2000} \\ \\ Interest\text{ = \$750} \end{gathered}[/tex][tex]\begin{gathered} The\text{ simple interest formula becomes:} \\ 750\text{ = 2000}\times0.0436\text{ }\times\text{ T} \\ \\ 750\text{ = 87.2T} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by 87.2:} \\ T\text{ = }\frac{750}{87.2} \\ \\ T\text{ = 8.60 year} \end{gathered}[/tex]hello can you help me solve this plane trigonometry question
Answers
Problem
Solution
For this case we can find the remain angle with this operation:
180 -39-90= 51º
And then we can use the sines law and we can do this:
[tex]\frac{x}{\sin(39)}=\frac{14}{\sin (90)}[/tex]And solving for x we got:
x= 14*sin(39)/sin (90) = 14*sin 39= 8.81
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answers
Answer:
She worked for 4 hours and made 16 shirts (work below)
Step-by-step explanation:
let h = number of hours worked
and s = number of shirts made :]
28h+2s = 144
4h = s
28h+8h=144
h=4, s=16
:]
Atoms can’t ever be _ or _ in a chemical reaction. the atoms must always be _ each side of the equation
Answers
In a chemical reaction, atoms are neither CREATED nor DESTRUCTED. According to science, each side of the equation must contain the SAME amount of atoms.
You must place COEFFICIENTS in front of the chemical formulas in the equation in order to make it equal.
What does a chemical reaction always involve?
Only atoms from the reactants can end up in the products of a chemical reaction. No atoms are destroyed or made into new ones. When reactants come into touch with one another, the bonds between their atoms are broken, and the atoms then reorganize and form new bonds to create the products.
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Find the midpoint M of the line segment joining the points
Answers
Given,
The coordinates of the points is,
[tex](-4,5)\text{ and \lparen2,-1\rparen}[/tex]The coordinates of the mid point is:
[tex]\begin{gathered} Consider,\text{ x and y are the coordinates of the midpoint} \\ x=\frac{-4+2}{2}=-\frac{2}{2}=-1 \\ y=\frac{5-1}{2}=\frac{4}{2}=2 \\ \end{gathered}[/tex]Hence, the mid point of the line segment is (-1,2).
A hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour. what is the minimum and the maximum number of hours Jose can park his car at the carage if he can spend between 12.25$ and 19.25
Answers
Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour.
The modelled equation representing the above scenerio is -
y = 3.5 + 1.75x
where (x) represents the number of hours for which the car is parked.
Maximum amount with Jose = $19.25
Therefore -
3.5 + 1.75x ≤ 19.25
1.75x ≤ 15.75
x ≤ 9 hours [Maximum time]
Minimum amount with Jose = $12.25
3.5 + 1.75x ≥ 12.25
1.75x ≥ 8.75
x ≥ 5 hours [Minimum time]
Therefore, Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.
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define the domain of the following:
Answers
By identifying the first values of each point in the graph, we saw that the domain of the relationship is:
D: {-3, -1, 1, 3, 6}
How to get the domain?A relation can be defined by a set of points (x, y), where the values of x are the values in the domain and the values of y are the values in the range.
Here we have the graph of a relation, and we can see the points:
(-3, 3)(-1, -1)(1, 2)(3, 0)(6, -2)
The domain of the graphed relationship will be the set of the first values of each of these points, then we can see that the domain is:
D: {-3, -1, 1, 3, 6}
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what is zero divided by zero
Answers
Answer:
indetermination
Step-by-step explanation:
Hope this helps
A quiz consists of seven multiple choicequestions. Each question has four choices.A student who forgot to study guessesrandomly on every question. What is theprobability that the student answersexactly five questions correctly?
Answers
Solution
- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,
[tex]\begin{gathered} P(correct)=\frac{1}{4} \\ \\ P(incorrect)=1-P(correct) \\ P(incorrect)=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]- Since here are questions, it implies that there are multiplye trials the student has.
Ann is a software salesperson. Her base salary is $1900 and she makes $90 more for every copy of History is Fun she sells. Her total pay, P (in dollars), after
selling e copies is given by the following.
P=1900+90c
Answer the following questions.
(a) What is Ann's total pay if she sells 24 copies?
(b) If Ann's total pay is $4780, how many copies did she sell?
copies
Answers
Answer:
A - $4060
B - 32 copies
Step-by-step explanation:
A -
P = 1900 + 90c
P = 1900 + 90(24)
P = 1900 + 2160
P = 4060
Total if Ann sold 24 copies: $4060
B -
1900 + 90c = 4780
90c = 4780 - 1900
90c = 2880
c = 32
Total copies: 32
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12y-2x=12
Answers
Answer:
y = 1/6x + 1
Step-by-step explanation:
Add 2x to both sides of the equation.
12y = 12 + 2x
Divide each term in 12y = 12 + 2x by 12 and simplify.
y = 1 + x/6
Write in y=mx+b form.
y = 1/6x + 1
Translate the following equation into a verbal sentence. 5(x + 4) = x - y
Answers
Answer:
Five times the quantity x plus four equals x minus y.
Step-by-step explanation:
Probably the most confusing part is that parenthesis are pronounced "the quantity"
Find the critical value (tα/2) for a 95% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
Answers
The critical value (tα/2) for a 95% confidence interval for the sample size 15 is 2.009.
We have to find the critical value tα/2 for 95% confidence interval, we are given the sample size.
First we will find the alpha value to get the critical value.
=100%-95%
=1-0.95
=0.05
α=0.05
α/2=0.05/2
α/2=0.025
degrees of freedom(df)= n-1=15-1=14
We will use degrees of freedom and α/2 values to find the critical value that is tα/2.
By using the t table we get the critical value of tα/2=2.009.
Therefore, the critical value for 95% confidence interval with sample size of 15 is 2.009.
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2) In reply to an inquiry about the animals on his farm, the farmer says: "I
only ever keep sheep, goats, and horses. In fact, at the moment they are
all sheep bar three, all goats bar four, and all horses bar five." How many
does he have of each animal?
Answers
The number of horse is 1, goat is 2 and sheep is 3 a man has.
The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.
Now w consider x to be the number of sheep, y to be the number of goats, and z to be the number of horses the man owns.
the actual equation for the total number of animals he owns is :
x+ y+ z
according to the first condition:
that all sheep bar three, means
y+ z=3
similarly, for the other condition, it will be
x+ z=4 and x+ y=5
Now we adding the three equations:
y + z +x +z +x +y=5+4 +3
2(x+y+z)=12
x+y+z=6........equation(1)
As x + y = 5
Put this in equation in (1), we get
x+y+z = 6
5 + z = 6
z = 1
x + z = 4
x + y + z = 6
y + 4 = 6
y = 2
Now we know
x + y + z = 6
x + 1 + 1 = 6
x = 4
So simplifying the other equation we get, that the number of horse is 1, goat is 2, and sheep is 4.
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1. Which statement is true? (1 point)
29 20
35
18
34
14
A
A
30
16
32
17
>
21 24
20 28
15
23
Answers
Fraction - A,C,D is the incorrect option that means 18 >17 is the correct option B
What does compare mean in fractions?Equivalent fractions with the same denominator should be used to compare fractions with different denominators. Comparing fractions: If the denominators are the same, the numerators can be compared. The greater fraction is the one with a larger numerator.
Now, comparing the fraction,
first of all write the fraction in simplest form then cross multiplication.
1. [tex]\frac{29}{35} < \frac{20}{30}[/tex]
[tex]\frac{29}{35} < \frac{2}{3}[/tex]
87 < 70
This option is wrong.
2. [tex]\frac{18}{34} > \frac{16}{32}[/tex]
[tex]\frac{9}{17} > \frac{1}{2}[/tex]
18 >17
This option is correct.
3. [tex]\frac{14}{21} > \frac{17}{24}[/tex]
[tex]\frac{2}{3} > \frac{17}{24}[/tex]
48 > 51
This option is wrong.
4. [tex]\frac{20}{15} < \frac{28}{23}[/tex]
[tex]\frac{4}{3} < \frac{28}{23}[/tex]
92 < 84
This option is wrong.
Hence, option b is correct.
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Identify the translation of the vertices P (-4, -5), L (1, -7), and K (-9, 8), along the vector , <-6 , 3 >.
Answers
Given:
The vertices are P (-4, -5), L (1, -7), and K (-9, 8).
The vector is < -6,3 >.
Aim:
We need to find the image of the vertices when translating given vertices along the vector.
Explanation:
The translation vector <-6,3> means each point is being moved 6 units to the left and 3 units up.
For each vertex, we subtract 6 from each x value and add 3 to each y value.
[tex]P^{\prime}(-4-6,-5+3)=P^{\prime}(-10,-2)[/tex][tex]L^{\prime}(1-6,-7+3)=L^{\prime}(-5,-4)[/tex][tex]K^{\prime}(-9-6,8+3)=K^{\prime}(-15,11)[/tex]Final answer:
[tex]P^{\prime}(-10,-2)[/tex][tex]L^{\prime}(-5,-4)[/tex][tex]K^{\prime}(-15,11)[/tex]
JohanVanDeVaseYesterdayMathematicsHigh SchoolTARIFF SYSTEMSQUESTION 1 [13 marks]A shopping mall in Bloemfontein has several parking garages, each with its own tariff system. The table below shows the tariffs on garage A and garage B.(Please show calculation)Parking TariffsNumber of hours (h)0 < h < 11 < h < 22 < h < 44 < h < 66 < h < 7h > 7Garage AFreeR5,50R15,50R30,50R50,50R75,50Garage BR5,00R7,00R11,00R26,00R41,00R61,00Question 1.1 [4 marks]Sellwane works at the shopping mall. She arrives at 7:30 and leaves at 17:00 each day. Which parking garage is cheaper for her to use?Question 1.2 [3 marks]Isaac was having coffee with his friends at a restaurant at the shopping mall. They arrived at the mall at 8:23 and left at 10:53, how much would he pay if he used garage B?Question 1.3 [2 marks]On Monday morning Karabo parked her car in one of the parking garages and paid R26,00. In which garage did she park and for how long?
Answers
Step 1:
Question 1.1
Arrive time = 7:30
Departure time = 17:00
[tex]\text{Total time spent = 17:00 - 7:30 = }9\colon30[/tex]h (9:30) > 7
Garage B is cheaper
Question 1.2
Arrive time = 8:23
Departure time = 10:53
[tex]\text{Total time spent = 10:53 - 8:23 = 2: 30}[/tex]The time spent by issac and his friends is between 2 < h < 4
Since h = 2:30
Answer R11.00
Question 1.3
Karabo uses Garage B
Time spent is 4 < h < 6
What is the logarithm of
6.5
Answers
The logarithm of the number 6.5 is log(6.5) = 0.8129
What is the logarithm of numbers?This is the number that represents the power by which a fixed number known as the base must be raised to result in another number.
How to evaluate the logarithm of the number?The number is given as
6.5
The logarithm of the number is then represented as
log(6.5)
There are several ways to calculate the logarithm of the number
Some of which are:
By logarithm tableBy calculatorIn this case, the only way is by using a calculator
Using a calculator, we have
log(6.5) = 0.8129
Hence, the logarithm of 6.5 is 0.8129
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Need help fast. Please explain how to do it set by step. Thanks.
Answers
A sequence is a series that follows the sum general rule. The sum of the given sequence ∑(n=1 to 4) [tex]u_{n}[/tex] is {u₁ + u₂ + u₃ + u₄ + u₅}.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
As per the given series, ∑(n=1 to 4) [tex]u_{n}[/tex]
The sign ∑ is used to sum the terms of the series in the given interval.
Given that n = 1 to 4
Substiute n = 1 into [tex]u_{n}[/tex] ⇒ u₁
Substiute n = 2 into [tex]u_{n}[/tex] ⇒ u₂
Substiute n = 3 into [tex]u_{n}[/tex] ⇒ u₃
Substiute n = 4 into [tex]u_{n}[/tex] ⇒ u₄
So, the sum is {u₁ + u₂ + u₃ + u₄ + u₅}.
Hence "A sequence is a series that follows the sum general rule. The sum of the given sequence ∑(n=1 to 4)".
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find the surface area of the figure in square inches.
Answers
The surface area of a cone is given by the sum of the areas of the lateral surface and the area of the circular base.
The area of the circular base is given by:
[tex]\pi\cdot r^2[/tex]Where r is the radius of the base.
The area of the lateral surface is given by:
[tex]\pi rs[/tex]Where s is the length of the slant.
Since s=17 in and the radius is half the diameter, r=8 in, the area of the cone is:
[tex]\begin{gathered} A=\pi rs+\pi r^2 \\ =\pi(8)(17)+\pi(8)^2 \\ =136\pi+64\pi \\ =200\pi \\ =628.3185307\ldots \end{gathered}[/tex]To the nearest hundredth, the area of the cone in square inches, is:
[tex]628.32[/tex]500/675x9876=? what is the answer ???????????
Answers
Answer:
7315.55
Step-by-step explanation:
just dont be lazy solve it.
hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it..writing and. evacuating expressions
Answers
The price will increase if number of students increase
By multiplying the number of students with cost
Number of students varies in this example
The expression shown for trip amount is c = 10+13x.
The cost for 10 students is 140
The cost for 17 students is 231
What is the definition of evaluate an expression?Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
1). The price will increase if number of students increase.
2). By multiplying the number of students with cost.
3). Number of students varies in this example.
4). Let the number of students
Then total amount(c) of the trip is given by
c = 10+13x ------ equation (1)
5). Put x = 10 in equation (1)
c = 10+13(10)
c = 140
6). Put x = 17 in equation (1)
c = 10+13(17)
c = 231
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at what point does the like given by the following equation cross the y axis? y=(-5/7)x+5A.(0,-5/7)B.(5,0)C.(0,5)D.(0.-25/7)
Answers
Given:
Given the equation
[tex]y=-\frac{5}{7}x+5[/tex]Required: Point at which the equation crosses the y axis.
Explanation:
At y -axis, the value of x is zero. Substitute 0 for x in the equation of y.
[tex]\begin{gathered} y=-\frac{5}{7}\cdot0+5 \\ =0+5 \\ =5 \end{gathered}[/tex]So, the point at which the equation cross the y-axis is (0, 5).
Final Answer: The point at which the equation cross the y-axis is (0, 5).
Find the surface area of the net.Enter the correct answer in the box.
Answers
We can divide the given figure into different rectangular faces:
Faces 1 and 3 have the same measure, also 2 and 4, and faces 5 and 6.
Faces 1 and 3 have the following dimensions: L=100cm W=50cm.
Faces 2 and 4 have the following dimensions: L=100cm W=35cm.
Faces 5 and 6 have the following dimensions: L=50cm W=35cm.
The surface area of a rectangular face is given by:
[tex]SA=L*W[/tex]Thus, the surface areas of the given faces are:
[tex]\begin{gathered} SA_1=100cm*50cm=5000cm^2 \\ SA_3=100cm*50cm=5000cm^2 \\ SA_2=100cm*35cm=3500cm^2 \\ SA_4=100cm*35cm=3500cm^2 \\ SA_5=50cm*35cm=1750cm^2 \\ SA_6=50cm*35cm=1750cm^2 \end{gathered}[/tex]The surface area of the net is the addition of all of these surface areas:
[tex]\begin{gathered} SA_{net}=(5000+5000+3500+3500+1750+1750)cm^2 \\ SA_{net}=20500cm^2 \end{gathered}[/tex]Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find the probability distribution given the probability p = 0.82 of success on a single trial.
Answers
Answers in bold
[tex]\begin{array}{|c|c|} \cline{1-2}k & P(X = k)\\\cline{1-2}0 & \boldsymbol{0}\\\cline{1-2}1 & \boldsymbol{0}\\\cline{1-2}2 & \boldsymbol{0.04}\\\cline{1-2}3 & \boldsymbol{0.18}\\\cline{1-2}4 & \boldsymbol{0.41}\\\cline{1-2}5 & \boldsymbol{0.37}\\\cline{1-2}\end{array}[/tex]
Note: The P(x) values for k = 0 and k = 1 are not actually zero, but they are small enough that they round to 0 when rounding to two decimal places.
=======================================================
Explanation:
I used a spreadsheet to compute the values in bold.
The specific command is called BINOMDIST
The template is BINOMDIST(k,n,p,0)
k = value from the tablen = 5p = 0.82The 0 at the end tells us to use a binomial PDF and not CDFLet me know if you have any questions about how to use that function in a spreadsheet.
Also, I used the function called ROUND to round each value to 2 decimal places.
Example calculation
=ROUND(BINOMDIST(4,5,0.82,0),2)
This calculates the result of 0.41 and it corresponds to the value k = 4
Don't forget about the equal sign up front when computing these commands in the spreadsheet. Otherwise, it'll stay as text form.
-------------------
If you want to use a TI83 or TI84 calculator, then press the button labeled "2nd". Then press the button labeled "VARS". Scroll down until you reach "binompdf".
The template is binompdf(n,p,k)
So for example, type in binompdf(5,0.82,4) to get the P(X) value for k = 4
If you aren't able to access a spreadsheet or a TI83/84 calculator, then search out "binomial distribution calculator" and there are plenty of free ones to pick from.
In my opinion, a spreadsheet is the best option since the given data is already in tabular form. Also, many real world situations and careers use spreadsheets everyday.