Answers
The equation of the lines are:
5. y - 5 = -3(x - 1)
6. y - 3 = 2(x + 4)
7. y - 6 = -4/3(x - 1)
8. y - 8 = -12/9(x + 2)
9. y = -5x + 1
10. y + 1 = -2(x - 2)
11. y - 1 = 2/3(x - 3)
How to Write the Equation of a Line?For any given line, the equation that represents the line can be written as:
y = mx + b, in slope-intercept form, where m is the slope and b is the y-intercept of the line.y - b = m(x - a), in point-slope form, where m is the slope and (a, b) is a point on the line.5. Substitute m = -3, and (a, b) = (1, 5) into y - b = m(x - a):
y - 5 = -3(x - 1) [equation in point-slope form]
6. Substitute m = 2, and (a, b) = (-4, 3) into y - b = m(x - a):
y - 3 = 2(x - (-4))
y - 3 = 2(x + 4) [equation in point-slope form]
7. Given the points, (4, 2) and (1, 6)
Find the slope (m):
Slope (m) = change in y/change in x = (6 - 2)/(1 - 4)
Slope (m) = -4/3
Substitute m = -4/3, and (a, b) = (1, 6) into y - b = m(x - a):
y - 6 = -4/3(x - 1) [equation in point-slope form]
8. Given the points, (-2, 8) and (7, -4)
Find the slope (m):
Slope (m) = change in y/change in x = (-4 - 8)/(7 -(-2))
Slope (m) = -12/9
Substitute m = -12/9, and (a, b) = (-2, 8) into y - b = m(x - a):
y - 8 = -12/9(x - (-2))
y - 8 = -12/9(x + 2) [equation in point-slope form]
9. y - 6 = -5(x + 1)
y - 6 = -5x - 5
y - 6 + 6 = -5x - 5 + 6 [addition property of equality]
y = -5x + 1 [equation in slope-intercept form]
10. Find the slope (m):
Slope of the line (m) = rise/run = -2/1
Slope (m) = -2
Substitute m = -2, and (a, b) = (2, -1) into y - b = m(x - a):
y - (-1) = -2(x - 2)
y + 1 = -2(x - 2) [equation in point-slope form]
11. Find the slope (m):
Slope of the line (m) = rise/run = 2/3
Slope (m) = 2/3
Substitute m = 2/3, and (a, b) = (3, 1) into y - b = m(x - a):
y - 1 = 2/3(x - 3) [equation in point-slope form]
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Related Questions
Use the Distributive Property to simplify.
4(3+2)
Answers
With distributive property, you multiply both terms inside the parentheses with the term outside the parentheses.
So 4•3=12 and 4•2=8
12+8=20
Therefore the answer is 20
given function f(x)=-4x+11, evaluate when f(13)=
Answers
We can evaluate the function as follows:
[tex]f(x)=-4x+11\Rightarrow f(13)=-4\cdot(13)+11\Rightarrow f(13)=-52+11[/tex]Then, the function evaluated in f(13) is equal to -41, f(13) = -41.
Scientific Notation
CO
8
Directions: Select the correct answer from each drop-down menu.
In a particular year, the population of Dallas, TX, was approximately 1 x 106 people. If the population of Los Angeles, CA, was
approximately three times that of Dallas, there were about
people living in Los Angeles that year.
The population of Pittsburgh, PA, was approximately 3 x 105 people during the same year, which was about
that of Dallas.
Reset
Submit
times
Answers
Dallas, Texas, had a population of about 1 x 106 peoples in that specific year. There were above 3×10⁶ people in Los Angeles; The population of Pittsburgh was about 0.3 times of Dallas.
Given that,
Dallas, Texas, had a population of about 1 x 106 peoples in that specific year. If Los Angeles, California, had a population of
There were almost three times as many people there as in Dallas.
peoples who called Los Angeles home in that year.
In the same year, there were about 3 x 105 peoples living in Pittsburgh, Pennsylvania. one from Dallas.
In Dallas the population is P₁=1×10⁶
Then in Las Angeles the population is P₂=3P₁=3(1×10⁶)= 3×10⁶
In Pittsburgh the population is P₃=3×10⁵
P₃÷P₁=(3×10⁵)÷(1×10⁶)=0.3
Therefore, There were above 3×10⁶ people in Los Angeles; The population of Pittsburgh was about 0.3 times of Dallas.
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Suppose that country A and country B initially have the same per capita GDP. After that, country A grows at 3.5 percent per year and country B grows at 7 percent per year. According to the rule of 70, after 40 years what is the ratio of country B's GDP to country A's?
Answers
Using the Rule of 70, it is found that after 40 years, the ratio of country B's GDP to country A's is of 2.
What is the Rule of 70?The rule of 70 is a rule that is used to determine how long it takes for an amount to double, dividing 70 by the variable's growth rate, as a percentage.
Country A grows at 3.5 percent per year, hence the time it takes to double is:
70/3.5 = 20 years.
Hence in 40 years, it's GDP will be of:
4n, in which n is the current GDP, and 4 because it will have doubled twice.
Country B grows at 7 percent per year, hence the time it takes to double is:
70/7 = 10 years.
Hence in 40 years, it's GDP will be of:
8n, in which n is the current GDP, and 8 because it will have doubled three times.
Then the ratio of country B's GDP to country A's will be of:
8n/4n = 2.
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Answer please. Need help, 20 points
Answers
Using it's concept, there is a 0.3913 = 39.13% probability of picking a non poisonous animal or a spider.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
In the context of this problem, we have that:
There are 14 + 3 + 6 = 23 animals in total that can be picked, which is the denominator of the calculus of the probability.Of those, 3 are non poisonous snakes and 6 are poisonous spiders, hence the number of desired outcomes is of 9, which is the numerator of the calculus of the probability.Applying it's concept, of desired outcomes divided by total outcomes, the probability of picking a non poisonous animal or a spider is given as follows:
p = 9/23 = 0.3913 = 39.13%.
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Find the final price of each item television: $375.00 discount: 25% tax: 6%
PLEASE HELP MEEEEEEEE!!!
I really need to understand how to work out this problem and solve it!
Thank You!
Answers
The final price of the television is $299.53.
Discount is somewhat a reduction in the actual or usual price of the object or service. Whereas, tax is the money that we have to pay to the government.
Price of television before discount = $375.00 (given)
Discount given = 25% (given)
25% of $375 is,
$375* (25/100)= $93.75.
The cost of the television after sale off and before the sales tax is:
$375- $93.75= $281.25
The sales tax = 6% (given)
$281.25* (6.5/100)= $18.28
The price of the television including everything is,
$281.25+ $18.28= $299.53
Therefore, we can conclude the the final price of television is $299.53.
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If 539 is invested at 17%, how much money will be in the account after 21 months
Answers
Step-by-step explanation:
[tex]i = prt \div 100[/tex]
p=539
r=17%
t=21
I=?
[tex]i = 539 \times 17 \times 21 \div 100[/tex]
Rewrite the following in the form log (c) log(4) + log(3)
Answers
The required logarithm in the form log(c) is log(12).
What are logarithms?The inverse function to exponentiation in mathematics is called the logarithm. If aˣ = n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐ n.
Given:
log(4) + log(3)
Using the product property of logarithms, which states that a product's logarithm is equal to the sum of its logarithms.
log(ab) = log a + log b
Here, a = 4 and b = 3
So, log(12) = log(4) + log(3)
Therefore, the required logarithmic function in the form log(c) is log(12).
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Please answer with if the slope is positive or negative and what the slope is.
Answers
The slope of the line is 60 and speed of the bus is 60 miles per hour
The slope of the line is the measure of the steepness. In other words the slope of the line is the change in y coordinate with respect to the change in x coordinate.
Here the points are
(1,60) and (2,120)
The slope of the line m =[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the points
Substitute the values in the equation
The slope of the line m = [tex]\frac{120-60}{2-1}[/tex]
= 60
The speed = Distance / Time
Take one point (2,120)
The distance = 120 miles
Time = 2 hours
The speed = 120/2
= 60 miles per hour
Hence, the slope of the line is 60 and speed of the bus is 60 miles per hour.
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Use the exponential decay model, A=A o e^kt. The half-life of thorium-229 is 7310 years. How long will it take for a sample of this substance to decay to 20% of its original amount? Round six. decimal places
Answers
The time it will take for a sample of this substance to decay to 20% of its original amount
t=16973.294years
This is further explained below.
What is half-life?The amount of time needed for a quantity to decrease to half of its original value is referred to as its half-life.
In nuclear physics, this word is often used to define the rate at which unstable atoms undergo radioactive decay or the amount of time stable atoms are able to persist.
Additionally, the phrase may be used in a broader sense to define any form of exponential decline.
Generally,
A = A0e^{-kt}
Therefore
A(t) = A0e^{[ln(0.5) / 7310 t}, t in years
0.20 = e^{ln(0.5) / 7310 ]t}
Solve for t.
ln(0.20) = [ln(0.5) / 7310 ]t
t = 7310 [ln(0.20) / ln(0.5)]
t=16973.294years
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Identify the missing statement or reason
A. Definition of midpoint
B. Definition of angle bisector
C. Reflexive property
D. Alternate interior angles Theo
Answers
Answer:Definition of Midpoint-A
Step-by-step explanation:
A factory produce 11,650 gallon of lemonade 4,950,fewer gallons of ice tea than lemonade
Answers
Factories produce a total of 21550 gallons in a calendar year.
The gallon is used as a unit of volume in both imperial and US customary measurements.
Eight pints make up a gallon, which is a unit of measurement for liquids. It is equivalent to roughly 4.546 litres in Britain. It is roughly equivalent to 3.785 litres in America.
Lemonade, it has been stated, equals 11,650 gallons.
Lemonade = 4,950 fewer than ice tea.
Ice tea: 3,500 fewer than Root beer.
Using the formula Ice tea = 11,650 - 4,950
6700 gallons of iced tea
Root beer = 6700 - 3,500
3200 gallons equals root beer.
Total manufacturing output for a year is equal to 11,650 + 6700 + 3200
Thus, 21550 gallons are produced in total by factories each year.
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Here are three different recipes for Orangey-Pineapple Juice. Two of these mixtures taste the same and one tastes different.
Recipe 1: Mix 4 cups of orange juice with 6 cups of pineapple juice.
Recipe 2: Mix 6 cups of orange juice with 9 cups of pineapple juice.
Recipe 3: Mix 9 cups of orange juice with 12 cups of pineapple juice.
Which two recipes will taste the same, and which one will taste different? Explain or show your reasoning.
Answers
Using ratio we can conclude that Recipe 1 and recipe 2 tastes the same.
The multiplicity of two integers is shown by a ratio. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
An ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or the value represented by this fraction are all ways to conceptualize ratios. Rational numbers, and occasionally natural numbers as well, are ratios of counts stated in terms of (non-zero) natural numbers. When two numbers are compared using the same unit of measurement, which frequently occurs, their ratio is a dimensionless number. A rate is created by multiplying two amounts with different unit measurements.Let us consider the ratio of the orange juice top the pineapple juice for the 3 recipes.
Recipe 1 = 4 : 6 = 2 : 3
Recipe 2 = 6 : 9 = 2 : 3
Recipe 3 = 9 : 12 = 3 : 4
Hence from the above ratios we can conclude that Recipe 1 and recipe 2 tastes the same.
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Members of a soccer team raised $2143.50 to go to a tournament. They rented a bus
for $888.50 and budgeted $62.75 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Answers
Answer:
Step-by-step explanation:
$2143.5 = $62.75x - $888.5.
Mrs. Byers rents a water trampoline for her son's birthday party. The delivery fee for the trampoline is $75, plus a rental fee of $8 per hour. She wants to spend less than $125 on the trampoline. Find h, the number of hours Mrs. Byers could rent the trampoline?
Answers
Answer:
h= 6
Step-by-step explanation:
To find out the value of h, start by forming an equation for the cost of renting a trampoline:
Cost of renting= $(75 +8t), where t is the rental duration.
When the cost is $125,
75 +8t= 125
Subtract 75 from both sides:
8t= 125 -75
8t= 50
Divide both sides by 8:
t= 50 ÷8
t= 6.25
Since she wants to spend less than $125, let's round the value down to the nearest hour.
∴ h= 6
Thus, she could rent it for 6 hours.
Let's check!
Total cost of renting for 6 hours
= 6(8) +75
= $123
Total cost of renting for 7 hours
= 7(8) +75
= $131
Hence, 6 hours is indeed the maximum number of hours she can rent the trampoline for, such that the total cost is less than $125.
[tex]x^{2 + 5x+6[/tex]
Answers
The resulting factors on factorizing the expression is (x+2)(x+3).
Factorizing quadratic expressionQuadratic equations are equation that has a leading degree of 2.
Writing a number or other mathematical object as the sum of several factors typically smaller or simpler things of the same kind—is known as factorization or factoring.
Given the quadratic equation below:
x^2 + 5x + 6
Factorize to have:
x^2 + 2x + 3x + 6
Group
(x^2+2x)+(3x+6)
Factor out the common variable or value
x(x + 2) + 3(x + 2)
Find the factors
(x+3)(x+2)
Hence the factored form of the expression in its simplest form is (x+2)(x+3)
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Complete question
Factorize x^2 + 5x + 6
I need help with this pls
Answers
STEP - BY - STEP EXPLANATION
What to find?
Determine how much greater the average rate of change over the interval [ 7, 9] than the interval [4, 6].
Given:
Step 1
Calculate the average rate of change over the interval [ 7, 9] using the formula below:
[tex]Rate\text{ of change=}\frac{f(b)-f(a)}{b-a}[/tex]a= 7 f(a)=1852
b=9 f(b)=3878
Substitute the values into the formula and simplify.
[tex]Average\text{ rate of change=}\frac{3878-1852}{9-7}[/tex][tex]=\frac{2026}{2}=1013[/tex]Step 2
Calculate the average rate of change over the interval [4, 6] using the same formula in step 2.
a=4 f(a)=358
b=6 f(b)=1178
[tex]average\text{ rate of change=}\frac{1178-358}{6-4}[/tex][tex]=\frac{820}{2}=410[/tex]Step 3
Compare the average rate of change over the two intervals.
Clearly, the average rate of change over the the interval [7, 9] is greater than the average rate of change over the interval [4, 6].
ANSWER
T
A sub shop ordered 40 pounds of tomatoes. If the tomatoes are evenly distributed into 12 tubs, how many pounds will go into each tub?
Answers
Using unitary method we conclude that, 3.33 pounds of tomatoes will go into each tub.
In this question, we have been given a sub shop ordered 40 pounds of tomatoes.
The tomatoes are evenly distributed into 12 tubs.
We need to find the number of pounds of tomatoes will go into each tub.
Let x be the number of pounds of tomatoes will go into each tub.
By unitary method,
x = 40 / 12
x = 3.33 pounds
Therefore by using unitary method we conclude that, 3.33 pounds of tomatoes will go into each tub.
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y
=
−
2
x
+
8
x
-intercept:
Enter as a coordinate: such as
(
a
,
b
)
.
y
-intercept:
Enter as a coordinate: such as
(
a,
b
)
.
Answers
Answer:
234
Step-by-step explanation:
How do you answrt? I'm aknskwnwekene
pls help i dont get it
Answers
a.) A triangle is equal to 2 squares.
b.) For this triangle it is equal to 3 circles
c.) Each star is 1 circle
"Your name" solved this by for example question a, splitting the squares on right's into two sections of 2 and 2 which helped me understand that one triangle is equal to 2 squares
b) 3
c) 2
d) subtract the amount of what you need to find. So like for a) you would subtract 4 minus 2 because there are 4 squares on the right side and 2 on the left, so you would get 2 which means that 2 squares equal 1 triangle.
Solve the systems of equations
-8x + 2y = -4
x^2 + 2y = 5
Answers
x=1, y=2
Ms. Jacobs gave her class the number 45.692 to round. Three students rounded correctly. Which place did each student round to.
Answers
Olivia bought snacks for her team's practice. She bought a bag of chips for $2.25 and a 8-pack of juice bottles. The total cost before tax was $11.69. Which equation could be used to determine j, how much each bottle of juice costs?
Answers
you can swim 915 feet, tread water for 4 minutes, and swim 18 feet underwater without taking a breath. Do you satisfy the requirements of the course? explain.
Answers
The values of the swimmer is 305 yards which is less than 350 yards required, thus the course is not suitable for swimmer.
What is defined as the unit conversion?Unit conversion is a multi-step process that involves multiplying or dividing by a mathematical factor or, more particularly, a conversion factor.For the given question;
The data of the swimming is given as;
915 feet, Tread water for 4 minutes, 18 feet under water.The life guard requirement is -
Swim at least 350 yard.Tread water at least 2 minutes.Underwater swim 5 yards.To compare the requirements, convert the given values in feet to yard.
1 foot = 0.33 yards.
915 feet = 0.33×915 yards
915 feet = 305 yards
305 yards < 350 yards, not suitable.
18 feet under water.
18 feet = 0.33×18 yards
18 feet = 6 yards , suitable
Tread water at least 4 minutes > Tread water at least 2 minutes required, suitable.
As, the values of the swimmer is 305 yards which is less than 350 yards required, thus the course is not suitable for swimmer.
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Which of the following sets of rational numbers
is ordered from least to greatest?
|-35| 18 |0.58|
Answers
The most appropriate choice for modulus of a number and ascending order will be given by-
|0.58|, 18, |-35| is in ascending order.
What is Modulus of a number and ascending order?
Modulus of a number returns the absolute value of the number.
Modulus of positive number is positive and modulus of negative number is also positive.
If the numbers in a series are arranged in increasing order of their value, then the series is arranged in ascending order
Here,
|-35| = 35
18 = 18
|0.58| = 0.58
As, 0.58, 18, 35 is in ascending order,
So, |0.58|, 18, |-35| is in ascending order
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June has 72 gallons of punch for a party. June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Answers
If June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
The bigger cooler is five times as large as the smaller cooler
Consider the capacity of smaller cooler as x
The capacity of bigger cooler=5x
June has 72 gallons of punch for a party
Then the linear equation will be
x+5x=72
6x=72
x=12
Then the capacity of bigger cooler=5x
=5×12
=60
Hence, if June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
it is just a matter of definition that can be easily looked up.
the domain is the interval or set of all valid x values.
while the range is the interval or set of all valid y (function result) values.
so, the domain here is every value of x used in this function.
e.g. does x = -6 have a functional (y) value in the curve ?
no, it does not.
x = - 4 ? no.
x = -2 ? no.
x = -1 ? ah, yes, this is just the left-most point of the curve.
and then all x values further to the right of -1 are covered. as the arrows indicate : into all eternity ("to infinity and beyond !")
so, the domain is [-1, +infinity).
and you need to use B.
please note, the round bracket indicates that that ends of the interval is not included or undefined (after all, infinity is not a number we can work with, it is basically undefined and only represents a principle).
for the range this is tricky, as the graph does not really show us the limit. it could be y = -1 or 0 down to y = -9 or -10.
My dinner at San Felipe cost $15.20 before tax and $15.96 after tax. What was the sales tax?
Answers
Answer:
Step-by-step explanation:
Answer
I hope this is not the tip!
Total Cost of the meal 15.96
Menu Cost 15.20 Subtract
Tax .76
The tax on the meal is 76 cents or 0.76 dollars.
The tables show relationships between two quantities. Which table shows a proportional relationship? A INSERT_TEXT B INSERT_TEXT C INSERT_TEXT D INSERT_TEXT
Answers
The table that shows a proportional relationship between the variables a and b is Table B, which is the second table graphed.
What is a direct proportional relationship?In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
Hence, a data-set such as a table will represent a proportional relationship if the ratio between the output and the input is the same for all the terms of the relationship.
In this problem, we have that:
Table 1 does not show a proportional relationship between a and b, as the ratios are of 3, 3 and 4, respectively.Table 2 shows a proportional relationship between a and b, as the ratios are of 5/4, 5/4 and 5/4, respectively, that is, all the ratios are the same.Table 3 does not show a proportional relationship between a and b, as the ratios are of 3, 3 and 4, respectively.Table 4 does not show a proportional relationship between a and b, as the ratios are of 4/3, 3/2 and 4/3, respectively.What is the missing information?In the context of this problem, the tables are missing, and are given by the image at the end of the answer.
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Answer:
its D.
Step-by-step explanation:
i did the test.
What is the probability that a person who is alive at age 10 will not be alive at age 70 if the following is true? (Enter your probabilities as fractions.)
(a) The person is male.
b) The person is female.
Answers
The probability that a person who is alive at age 10 will not be alive at age 70 if the following is true for males and Female is
P(not alive at age 70 | male) =26999/99065P(not alive at age 70 | female) =17284/98983This is further explained below.
What is probability?Generally, A number that expresses the possibility or likelihood that a certain event will take place is referred to as its probability. Both proportions and percentages with values ranging from 0 to 1 may be used to indicate probabilities. Proportions can range from 0 to 1, while percentages can range from 0 to 100.
Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.
A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.
The characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.
In conclusion,
P(not alive at age 70 | male)
=(99065-72066)/99065
=0.273
As fraction
=26999/99065
P(not alive at age 70 | female)
=(99228-81944)/98983
0.17461
As fraction
17284/98983
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