The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.
what is a square root ?A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.
given
Use the average rate of change formula to substitute.
(√1)−(√−4) / (1)−(−4)
Condense the phrase.
1/5−2i/5
The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.
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what are the integers from -2 to 3 in ascending order?
Answer:
-2, -1, 0, 1, 2, 3
Step-by-step explanation:
Integers are whole numbers that can be either positive or negative. Integers cannot be decimals or fractions.
Ascending order is from least to great so we would start with the smaller number and end with the larger number. So there are 6 integers between -2 and 3.
How do you calculate seed multiplication ratio?
The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.
What is Seed?A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.
Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.
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What is the graph of the linear equation 2x +3y 6 that cuts the Y-axis at the point?
The graph of the linear equation 2x + 3y = 6 is a straight line that cuts the Y-axis at the point (0,2).
A linear equation is an equation in which the highest power of the variable is 1.
The general form of a linear equation is:ax + by = c where a, b and c are constants and x and y are variables. This equation represents a straight line when plotted on a graph.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept
To find the points at which the line will intersect y-axis,
take x=0 and substitute in the linear equation 2x+3y=6
2(0) + 3y = 6
3y = 6
y = 2
So the point where the line cuts the Y-axis is (0,2)
The straight line of the linear equation 2x+3y=6 intersects the y-axis at (0,2).
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The points (p, 6) and (4, 7) fall on a line with a slope of 1/9. What is the value of p?
Please find the missing coordinate using slope.
Step-by-step explanation:
(7 - 6)/(4 - p)= 1/9
4 - p = 9
-p= 5
p = -5
A person places $51200 in an investment account earning an annual rate of 5. 4%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 6 years
The amount of money in the account after 6 years is $68,847.56
To solve this problem, you can use the formula for compound interest,
V = Pe^(rt)where V is the final value of the account, P is the initial principal, r is the annual interest rate (expressed as a decimal), and t is the number of years the money is invested.
The formula for compound interest, V = Pe^(rt) is used to calculate the future value of an investment. It takes into account the effect of compounding, which means that interest is earned not only on the initial investment but also on the accumulated interest over time.
Plugging in the given values, we have
V = 51200e^(0.0546) = 51200e^0.324. e^0.324 is approximately 1.38, so the final value of the account is 512001.38 = $68,847.56
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A triangle has 2 sides of length 2 and 18 what compound inequality describes the possible lengths for the third side length
I'm pretty sure the answer is 72 :))
PLEASE HELP ME I DONT UNDERSTAND :(( GIVIN 100 POINTS
Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year
) Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
(e) y - 15= 3/4(x-15)
Is this equation okay to use for the height of the trees in this problem?
There is one equation that is incorrect.... determine which one? why is it incorrectly?
Creat two new equations written in point slope form
The equation in option e) is not correct because it would not give correct height of the trees in this problem
How to write equation in slope-point form?Since the Magnolia trees are 3 feet tall and grow at an average of 3/4 foot per year.
If x is the number of years and y is the height. we can write:
y = 3/4(x) + 3
The slope-point equation of a line is given as:
y-y1 = m(x−x1)
y = 3/4(x) + 3 in slope-point form is:
y = 3/4(x) + 3
y-3 = 3/4(x-0)
This means option a) is correct
Yes, this equation is okay to use for the height of the trees in this problem
b) y - 6 = 3/4(x-4)
y - 6 = 3/4(x-4)
y - 6 = 3/4(x)- 3
y - 6 + 3 = 3/4(x)
y - 3 = 3/4(x)
This is correct
c) y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x)- 1.5
y - 4.5 + 1.5 = 3/4(x)
y - 3 = 3/4(x)
This is correct
d) y - 12 = 3/4(x-12)
y - 12 = 3/4(x-12)
y - 12 = 3/4(x) - 9
y - 12 + 9 = 3/4(x)
y - 3 = 3/4(x)
This is correct
(e) y - 15= 3/4(x-15)
y - 15= 3/4(x-15)
y - 15= 3/4(x)-11.25
y - 15 + 11.25= 3/4(x)
y - 3.75 = 3/4(x)
This is not correct because it does not reflect the given information
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At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: 1/2 cups of flour 2 eggs, 3 tablespoons butter, 3/4 cups sugar 1 package of chocolate drops They will make only full recipes, no partial recipes. They learn that a big concert is scheduled for the same night and attendance will be down 25%. How many recipes of cookies should they make for their smaller party? (Some eggs and some cookies may be left over. )
(A) 1.
(B) 2.
(C) 5.
(D) 7.
(E) 15
The correct option is option (E) 15
To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.
=108 students * 0.75 = 81 students.
To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.
Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.
Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.
As 11 is not a given option, we consider the option which is greater than 11, which is 15.
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The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45
Customers older than 45 years are 11 in number. This can be solved using stem-and-leaf plot.
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
The stem and leaf plot represents the age of store patrons. The leaf represents the unit digit, while the stem stands for the tens digit. 45 is not taken into account because the question asks us to determine the percentage of consumers who are over 45.
Customers older than 45 years old include: 48, 50, 50, 51, 55, 56, 62, 64, 65, 65, 73.
So, there are a total of 11 clients.
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The complete question is as follows:
The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45
: Find the pherical coordinate of the point whoe rectangular coordinate are
(-2, 2√3,4)
The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
What is a peripheral coordinate?
A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.
To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:
[tex]r=\sqrt{(x^2 + y^2 + z^2)} = \sqrt{((-2)^2 + (2\sqrt3)^2 + 4^2)} = \sqrt{(4 + 12 + 16)} = \sqrt32 = 4\sqrt2[/tex]
θ = [tex]tan^{-1}(y/x) = tan^{-1}(2\sqrt3/(-2)) = tan^{-1}((-\sqrt3)/1) = -60^o[/tex]
φ = [tex]cos^{-1}(z/r) = cos^{-1}(4/4\sqrt2) = cos^{-1}(1/\sqrt2) = \degree 45 ^o[/tex]
So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
What is a peripheral coordinate?
A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.
To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:
[tex]r=\sqrt{x^2+y^2+z^2} = \sqrt{(-2)^2+(2\sqrt{3})^2+4^2}=4\sqrt{2}[/tex]
θ = [tex]tan^{-1}(y/x)=tan^{-1}(2\sqrt{3}/(-2))=60^o[/tex]
φ = [tex]cos^{-1}(z/r)=tan^{-1}(4/4\sqrt{4})=45^o[/tex]
So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
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Write the ratio. Explain what the ratio means.
butterflies : caterpillars
For every _
butterfly/butterflies, there is/are _
caterpillar(s).
The ratio is 1:4, which means for every 1 butterfly, there are 4 caterpillars.
This ratio represents the relationship between the number of butterflies and the number of caterpillars. In this case, the ratio is saying that for every 1 butterfly, there are 4 caterpillars. This could mean that for every butterfly that is observed, there are 4 caterpillars that are also present or for every butterfly that is caught, there are 4 caterpillars that are also caught.
This ratio may also indicate that for every butterfly that is born, 4 caterpillars are also born. It could also indicate the population ratio of butterflies to caterpillars in a specific habitat.
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I need help with this please
Answer in explanation:
*change the problem to [tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]
(change 3 into a fraction by putting 1 in the place of a denominator)
next cross multiply
5 x /1
/2 1
3 can go into 6- 1 time
since anything multiplied by 1 is 1, the answer is [tex]\frac{5}{2}[/tex]
Hope this helps ya!
*(disclaimer lol: alternatively, you could cross multiply without changing 3 to a fraction and get the same answer-- however, I wanted to explain as clearly as possible, and figured it was less confusing this way!)
The population of Smallville in the year 1890 was 6250. Assume the population increased at a rate of 2.75% each year. a) Estimate the population in 1915 and 1940. b) Predict when the population reached 50,000
If the population grew 2.75% each year then each year the population was multiplied by 1+2.75%=1+0.0275=1.0275
What is the population of Smallville in 1890 was 6250?Population in the year 1890 = 6250. Population increased at the rate of 2.75% per year or increased by 11400 , which will become 411400 after the increaseif you were to do it a step at a time it would mean multiplying 6250 by 0.0275(2.75%), and adding the result to 6250, then repeating the operation with the new number for each year until you reached the amount of years required (25 and 50 years).Now an easier way to do that first step would be multiplying by 1.0275, which already takes care of adding the original number. Now just do that for each of the intervals (25 and 50) required.
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Select all the inequalities that have the same graph as x<4
The inequalities that have the same graph as x<4 are:
x+6 < 105x < 20 x-2 > 2Hence, option(B) , (C) and (D) are correct.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
x +6 < 10 ⇒ x < 10-6 ⇒ x < 4
5x < 20 ⇒ x< 20/5 ⇒ x < 4.
x-2 > 2 ⇒ x < 2 + 2 ⇒ x < 4.
Hence, option(B) , (C) and (D) are correct.
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Your question is incomplete but most probably the question was:
Select all the inequalities that have the same graph as x <4.
A. x < 2.
B. x+6 < 10
C. 5x < 20
D. x-2 > 2
E. x <8
Mr. Hurd buys a trampoline for his kids. The cost of the trampoline is $699.99. He gets the items for $429.99. What is the percent of discount? Round to the nearest percent.
Answer:
Mr. Hurd received a discount of 57% on the trampoline. The cost of the trampoline was $699.99 and he got it for $429.99, resulting in a discount of 57% when rounded to the nearest percent.
Step-by-step explanation:
p = -log(2.1x10^12)
what is p?
The value of p for the given logarithmic function -log(2.1x10^12) is, -8.678
What is a logarithmic function ?The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function [tex]x = a^y[/tex].
Formulae for logarithmic function are,
LogAB = LogA + LogB .................(i)
Logₐaᵇ = b ................(ii)
Given expression,
p = -log(2.1x10^12)
p = -log2.1 + log10^12 (by applying formula i )
p = -log2.1 + 12 (by applying formula ii )
p = -(-3.322) + 12 (log2.1 = -3.322)
p = -8.678
Hence, the value of p is equal to -8.678
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Write the equation in standard form with integer coefficients. 0.5x - 2y - 0.75 = 0, y = - 3 x - 5
Answer:
50x - 200y = 75
3x + y = -5
Step-by-step explanation:
Standard form of a line
Ax + By = C
0.5x +-2y -0.75 Multiply through by 100
50x - 200 - 75 = 0 Add 75 to both sides
50x - 200y = 75
y = -3x - 5 Add 3x to both sides
3x + y = -5
solve for x: 2 < x + 4 < 4
Answer: −2<x<0
Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0
Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
The workers in shift B earns the bonus.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Mean is found by adding all the data values and then dividing with number of values in the set.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Number of data in shift A = 12
Mean = (77 + 91 + 82 + 68 + 75 + 72 + 85 + 65 + 70 + 79 + 94 + 86) / 12
= 944 / 12
= 78.67
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Number of data in shift B = 12
Mean = (68 + 93 + 53 + 100 + 77 + 86 + 91 + 88 + 72 + 74 + 66 + 82) / 12
= 950 / 12
= 79.17
The workers in the shift with the highest mean will earn a bonus. It is shift B.
Hence the workers in shift B earn the bonus.
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The full question is as follows :
The following are daily outputs from shift A and shift B at a factory.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
PLEASE HELP ME :((((
Jaya has a points card for a movie theater.
• She receives 85 rewards points just for signing up.
• She earns 8. 5 points for each visit to the movie theater.
• She needs 153 points for a free movie ticket.
Equation :
Answer v=
The number of visits Jaya can make to earn his first free movie ticket is 8
Total reward points received for signing up by Jaya = 85 rewards point
Total reward points received for each visit to the theatre by Jaya = 8.5 rewards point
Total reward points needed to Jaya for getting a free movie ticket = 153 rewards point
Let x represents the number of visits to the movie theatre
According to the question,
We can write it as:
85 + 8.5x ≥ 153 ------(i)
Now subtract 85 from both the side of equations,
We will get it as follows:
85 + 8.5x - 85 ≥ 153 - 85
8.5x ≥ 68
Further solving we will get it as:
x ≥ (68/8.5) ≥ 8
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what is the x and y of this equation 5x+7=6x+4
The value of x will be; x = 3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the equation 5x+7=6x+4
Here, we need to solve for x;
5x+7=6x+4
combine the like terms;
5x - 6x = -7 +4
-x= - 3
x = 3
Therefore, the solution will be as;
x = 3
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Find the area under the graph
Therefore , the solution of the given problem of function comes out to be 4 log2 + 3/4 is the are required.
What is meant by the word function?A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.
Here,
Given :
=> f(x) = x.2ˣ
=>A = [tex]\int\limits^2_{-1} x.2^{x}[/tex]dx
=> A = [tex]2^{x} \int\limits^2_{-1} x. + x\int\limits^2_{-1} 2^{x}[/tex]
=> [ xlog2 + x²/2 + x²log2 ]₋₁²
=> log2 + 3/4 + 3log2
=> 4 log2 + 3/4
Therefore , the solution of the given problem of function comes out to be 4 log2 + 3/4 is the are required.
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what is 8 1/4 divided by d=2/11
When 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement -
"8[tex]\frac{1}{4}[/tex] divided by 2/11"
We can write it as -
x = {8[tex]\frac{1}{4}[/tex]} ÷ {2/11}
x = 33/4 x 11/2
x = 363/8
x = 45[tex]\frac{3}{8}[/tex]
Therefore, when 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
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What is the value of 5 by 2?
The value of 5 divided by 2 is 2.5.
Therefore the answer is 2.5.
When dividing 5 by 2, we are trying to find out how many times 2 can fit into 5. The answer is 2 with a remainder of 1, this is why it can also be written as 2 and 1/2.
When dividing 5 by 2, we can also write the result as a fraction, in this case, it is 2 and 1/2 or 2.5 in decimal form. It is the exact same thing as 2.5, just represented in a different way.
It's important to note that, in general, dividing integers will give a decimal number. If you want the result to be a fraction, you will have to express it as such.
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Write the expression. Then, check all that apply. twice the difference of a number and six A 2-column table with 4 rows. Column 1 is labeled Key Words with entries twice, the difference of, a number, six. Column 2 is labeled Replace with entries 2 times, (minus), n, 6. Replace “a number” with the variable, n. The two operations are multiplication and addition. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6). The expression is written as 2 × 6 – n.
PLS HELP ME!
The expression for the sentence that is twice the difference of a number and six is given as follows:
2(n - 6).
How to write the expression?The sentence for this problem is defined as follows:
"Twice the difference of a number and six."
The number is unknown, hence the variable that represents the number is given as follows:
n.
The difference between the number and six is given by the subtraction of n by 6, as follows:
n - 6.
(the - symbol represents the subtraction).
The expression twice is equivalent to a multiplication of the expression n - 6 by 2, as follows:
2(n - 6).
(the multiplication symbol is implicit before the parenthesis, meaning that the distributive property is applied).
Which is the expression that represents the sentence given at the beginning of the answer.
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Using expanded forms, explain why the following problems with unlike bases do not follow the multiplication and division rules of exponents
Pls hurry and thank you!!!!
113.778=one hundred thirteen million seven hundred seventy-eight thousand, and 11,664=eleven thousand six hundred sixty-four is the enlarged form.
What do you meant by expanded form ?1.Comprehensive Notation Form:
[tex]$$\begin{aligned}& 11,664= \\& 10,000 \\& +1,000 \\& +600 \\& +\quad 60 \\& +4 \\&\end{aligned}$$[/tex]
Increased Factors Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10,000 \\& +1 \times 1,000 \\& +6 \times 100 \\& +6 x \quad 10 \\& +4 \times \quad 1 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10^4 \\& +1 \times 10^3 \\& +6 \times 10^2 \\& +6 \times 10^1 \\& +4 \times 10^0 \\&\end{aligned}$$[/tex]
Text Format:
11,664=eleven thousand six hundred sixty-four
2. Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 100 \\& +10 \\& +3 \\& +\quad 0.7 \\& +\quad 0.07 \\& +\quad 0.008 \\&\end{aligned}$$[/tex]
Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 100 \\& +1 \times \quad 10 \\& +3 \times \quad 1 \\& +7 \times \quad 0.1 \\& +7 \times \quad 0.01 \\& +8 \times \quad 0.001 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 10^2 \\+ & 1 \times 10^1 \\+ & 3 \times 10^0 \\+ & 7 \times 10^{-1} \\+ & 7 \times 10^{-2} \\+ & 8 \times 10^{-3}\end{aligned}$$[/tex]
Text Form:
113.778=one hundred thirteen million seven hundred seventy-eight thousand,
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Tran is making fasnachts (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 8 pounds of butter and her recipe calls for
1/4 cup of butter per 2 dozen
fasnachts. If 1 pound of butter is 2 cups,
then how many individual fasnacht doughnuts will Tran be able to
make?
Answer:
1,536
Step-by-step explanation:
1 pound equals 2 cups, so 8 pounds will be 16 cups.
[tex]\frac{16}{\frac{1}{4} }[/tex] = 16 x 4 = 64
She can make 64 2 dozen fasnachts. There are 24 fasnachts in 2 dozen.
64 x 24 = 1536 individual fasnachts doughnuts.
Write the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.
○ y = − 1/x + 2/1/2
O y = 2x + 4
○ y = 1/x + 1/2/2
○ y = 1/x + 1/2
The equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].
What is slope intercept form of the line?
Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.
Given:
The line passes through the points (7, 6) and (- 1, 2).
We have to find the equation of the line that passes through (7, 6) and (-- 1, 2) in slope-intercept form.
First to find the slope of the line using the formula,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1)= (7, 6), (x_2,y_2)=(-1, 2)[/tex]
Plug the values in the above formula.
[tex]m = \frac{2-6}{-1-7} = \frac{-4}{-8}=\frac{1}{2}[/tex]
Now consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)\\y-6=\frac{1}{2}(x-7) \\y-6=\frac{1}{2}x-\frac{7}{2}\\ y=\frac{1}{2}x -\frac{7}{2}+6 \\y=\frac{1}{2}x+\frac{5}{2}[/tex]
Hence, the equation of the line that passes through (7, 6) and (-1, 2) in slope-intercept form is, [tex]y=\frac{1}{2}x + \frac{5}{2}[/tex].
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Type the correct answer in each box.
Compete the statement about these similar cylinders.
The circumference of the base of figure 2 is____ pi inches, and the area of the base of figure 2 is____ pi square inches
(Hint: The circumference of a circle = 2nt and the area of a circle = 12, where r is the radius)
The circumference of the base of figure 2 is 5π inches, and the area of the base of figure 2 is 6.25π square inches
You can presume that the cylinders are proportionate because they are comparable.
9/5 = 4.5/x would be the equation to be used for the calculation.
The radius of 2.5 is obtained by dividing and multiplying by crosses.
Figure 1's circumference will be:
Circumference = 2 * 2.5 = 5π
The area for figure 2 is as follows:
Area = (2.5)² = 2.5 * 2.5 = 6.25π
As a result, the base of figure 1 has a 5π inches circumference.
The base of figure 2 has a 6.25π square inch area.
The base of figure 1 has a 5π inch circumference.
The base of figure 2 has a 6.25π square inch area.
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How do you check if an inverse is a function?
If a value of y relates only to one value of x, then the function does have an inverse function.
Define the term function and its inverse?A relation between such a collection of inputs and outputs is known as a function.
A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is just the input.If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f does have an inverse (passing from the vertical line test).Thus, if a value of y relates only to one value of x, then the function does have an inverse function.
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