The answers will be :
a. The length of the line segment will be equal to 8.24 units.
b. The midpoint of the line segment will be ( -2 , -2 ).
c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0
What is slope of a line segment ?
The ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.
It is given that a line segment has endpoints of Y(2,-3) and Z(-6,-1).
Let's solve the given parts based on the above data.
a.
The length of the line segment will be given by :
YZ = [tex]\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}[/tex]
YZ = √ [( -6 -(2)]^2 + [ -1 - (-3)]^2}
YZ = √ (-8)² + 2²)
YZ = √68
YZ = 8.24 units
b.
The midpoint (say M) of the line segment will be given by :
M = ( [tex]\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2}[/tex])
M = [(2-6)/2 , (-3-1)/2]
M = ( -2 , -2 )
c.
And the equation of line passing through points Y and Z will be :
[tex]y_{2} - y_{1}[/tex] = m ( [tex]x_{2} - x_{1}[/tex] )
Let's calculate value of slope (m) firstly which will be :
m =([tex]y_{2} - y_{1}[/tex]) / ( [tex]x_{2} - x_{1}[/tex] )
m = ( -1 + 3 ) / (-6 - 2)
m = 2 / -8
m = -1 / 4
or
m = -0.25
Using the value of slope (m) : we get the equation of line as :
[tex]y - y_{1}[/tex] = - 0.25 ( [tex]x - x_{1}[/tex] )
or
(y + 3) = - 0.25 ( x - 2)
y + 3 = -0.25 x + 0.50
or
y + 0.25 x - 2.5 = 0
If we multiply by 4 throughout the equation ; then the equation of line can also be written as :
4y + x - 10 = 0
Therefore the answers will be :
a. The length of the line segment will be equal to 8.24 units.
b. The midpoint of the line segment will be ( -2 , -2 ).
c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0
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Write each expression as a single logarithm.
log 7 +log 2
The expression log 7 +log 2 can be written as log 14 in a single logarithm form.
Given that the expression is log 7 +log 2.
We are required to write the expression is a single logarithm.
The Power Property basically states that if an exponent is being raised to another exponent, we can multiply the exponents.
The expression is log 7 +log 2.
We know that log mn= log m +log n.So,
log 7 +log 2=log (7*2)
=log 14
Hence the expression log 7 +log 2 can be written as log 14 in a single logarithm form.
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A Man rode His personal transporter 3/10 mi to the library, then 3/4 mi to class, and then 7/2 mi to his part-time job. How far did he ride his personal transporter?
If a man rode his personal transporter 3/10 mi to the library, then 3/4 mi to class, and then 7/2 mi to his part-time job, then he rode his personal transporter for 4.55 miles.
To determine how far the man rode his personal transporter we use addition.
total miles the man rode = miles to the library + miles to the class + miles to the part-time job
total miles = 3/10 + 3/4 + 7/2
As these fractions have an unlike denominator, we find a common denominator by determining the least common multiple.
As the least common multiple is equal to 20
Therefore,
total miles = 3(2)/10(2) + 3(5)/4(5) +7(10)/2(10)
total miles = 6/20 + 15/20 +70/20
total miles = 6+15+70/20
total miles = 91/20
total miles = 4.55
Hence, the man rode his personal transporter for 4.55 miles.
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The lunch bill for Eugene and Maggie totaled $20.20. Tax
on the meal was 5% and they wanted to leave a 15% tip.
How much was the meal including tax and tip?
O $24.39
O $21.21
O $22.20
O $3.03
Correct answer is A. The cost of meal in the caffeteria is 24.39.
What percentage is it?A percentage is a figure or ratio that represents a portion of 100. In addition to the percent symbol "%," the abbreviations "pct," "pct," and occasionally "pc" are also used to denote it. A% does not have any dimensions or a corresponding unit of measurement.
Your $20.20 bill is made up of the full amount (100%) plus the 15% tip, for a total of 115%. Decimal equivalent is 1.15.
Simply divide the entire charge by 1.15 to determine the price before the tip.
20.20/1.15 = 17.56
Consequently, the final amount due before the 15% tip was $17,56.
The total cost after tax and tip = 24.39
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A bicycle costs $175. salvadore has $55 and plans to save $18 each month. describe the number of months he needs to save to buy the bicycle. 1. choose the correct inequality to represent this situation. 2. choose the correct solution set.
Answer:
Step-by-step explanation:
55+18x=175
-55+18x=-55
18x= 120
Divide by 18
X=6,666666
So it will take 7 months
Eva bought 20 chicken wings for $20.00. If Eva spent $18.00, how many chicken wings did she buy?
Eva bought 18 chicken wings with $18
How to calculate the number of chicken wings that Eva bought ?Eva bought 20 chicken wings for $20
The first step is to calculate the cost of one chicken wing
= 20/20
= 1
1 chicken wings cost $1, if Eva spent $18 then the number of chicken wings bought can be calculated as follows
= 18 × 1
= 18
Hence Eva bought 18 chicken wings with $18
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Which is the best estimate for the value of r in the scatter plot? NEED HELP ASAP
A 0.7
B 0
C -0.5
D 1
Answer:
The anwser is A
Step-by-step explanation:
A is the best anwser choice given
What is an equation for the translation of y=2/x that has asymptotes at x=3 and y=-5 ?
(A) y=2/x-3 -5 (B) y=2/x+3+5 (C) y=2/x+5-3 (D) y=2/x-5+3
Correct option is A. Equation for the translation of y=2/x that has asymptotes at x=3 and y=-5 is y=2/x-3 -5.
Why do we use asymptotes?A curve's asymptote is the point at which the curve converges. In other words, despite being endlessly near, the curve and its asymptote never collide. Asymptotes are utilized in big O notation, are straightforward approximations to complicated equations, and are helpful for charting rational equations, among other uses.
Typically, the limit of a value when the function is not specified can be used to determine the asymptote(s) of a curve. Examples of such points include and as well as the location where the numerator of a rational function equals zero.
Given,
y = 2/x
asymptotes at x=3 and y=-5
⇒ denominator is (x-3)
⇒ y = -5 is highest degree of the equation.
⇒ The equation will be y=2/x-3 -5.
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Which of the choices will NOT correctly find the distance between the two points: (3, −4) and (−2, 5)?
The distance between two given points (3, −4) and (−2, 5) is √106 units.
Given that, two points are (3, −4) and (−2, 5).
What is the distance formula between two points?Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.
The formula for the distance, d, between two points whose coordinates are d=√(x2-x1)²+(y2-y1)²
Now, put two points (3, −4) and (−2, 5) in the distance formula and simplify.
That is, distance = √[(-2-3)²+(5-(-4))²]
=√(25+81)
=√106 units
Therefore, the distance between two given points (3, −4) and (−2, 5) is √106 units.
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Mr Adi types up a short story.
It takes him 9 minutes to finish typing up the story at an average of 40
words per minute.
Mr Blade also types up the same story.
He takes 12 minutes to type it.
Work out Mr Blade's average number of words per minute.
...... words per minute
The average rate at which Mr. Blade types is 30 words per minute.
Average or mean is a measure of central tendency where it defines the central number of a data set.
Average is calculated by dividing the total sum of the values of the dat set divided by the frequency or the number of data in the set.
Mr. Adi takes 9 minutes.
The average rate of Mr. Adi is 40 words per minute.
So in 9 minutes he writes 40 × 9 = 360 words in total.
Mr. Blade typed the same number of words.
he took 12 minutes to type it.
So average rate = total words typed ÷ time taken (in minutes)
Average rate= 360 ÷ 12 =30 words per minute.
Hence Mr. Blade writes at the average rate of 30 words per minute.
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linda is riding her bike to the restaurant. she rides at a constant speed of 32 feet per second. the restaurant is 6271 feet from her house. let t represent the number of seconds since linda left her house and let d represent linda’s distance from the restaurant.
Solving the distance-time problem here, the taken time to reach the restaurant is 196 seconds (approx.)
This is a distance-time problem.
To solve this problem the required formula is, d/t = v or, d/v = t,
where d is the represented distance and t denotes the required time, and v is denoted as the velocity or speed.
Here v, velocity is 32 feet/second, and d, distance is 6271 feet.
So, the taken time to reach the restaurant is 6271/32 = 196 seconds (approx.)
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Should I take Pre-Calculus 12 or Foundation of Math 12? PLEASE HELP ME Tell me the difference which one Is better when I graduate please help me
Answer:
honestly i say foundation of math12 ithink it will come more in handy in life
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
whoever gets it right gets marked branliest!!
pls pls help!!
The equivalent expression of the statement is as follows:
[tex](\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}[/tex]
How to find which expression is equivalent to the given expression?The expression is as follows:
Quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power
The equivalent expression of the statement is as follows:
[tex](\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}[/tex]
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Write the function that models each variation. Find z when x=4 and y=9 . z varies directly with x and inversely with y . When x=6 and y=2, z=15 .
The function that models each variation is : [tex]z = \frac{5 x}{y}[/tex]
value of z = 20/9
What is inversely and directly variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between them . Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. whereas, The direct variation state that the both values will show same pattern i.e. if one value will increase then another will also increase with the same amount or if one decrease another will also decrease.
In the question given,
First of all find the value of K in the model by putting in the values of x, y, and z so that to find the function model.
z = k (x) / (y)
put value of x=6, y=2 and z=15
15 = k (6) /2
k= 5
Thus we can write the equation as,
z=5x / y
put x=4, y=9
z = 20 / 9
Thus, z = 20/9
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I Will Give Brainly Crown Please Help I am so stressed its A Math Question (Geometry)
[tex]sum \: of \: interior \: angles = (5 - 2)180 = 540 \\ each \: angle = \frac{540}{5} = 108 \\ x + bcd = 180 \\ x + 108 = 180 \\ x = 180 - 108 = 72[/tex]
Answer: 72State which property or properties need to be used to write each expression as a single logarithm.
a. log₄5+log₄5
Product rule of logarithms is used in the single logarithm.
A single logarithm can be expanded into many logarithms or compressed into many logarithms by using the features of log. Just another approach to write exponents is with a logarithm. As a result, the characteristics of exponents are used to infer the characteristics of logarithms.
There are 7 properties of logarithms: Product Rule, Quotient Rule, Power Rule, Zero Rule, Identity Rule, Inverse Property of Logarithm, Inverse Property of Exponent, Change of base formula.
In the equation here, only the product rule is applied.
Product rule of logarithms states that the log of a product is equal to the sum of the logs of its factors. Example: logₐ (xy) = logₐ x + logₐ y
Therefore, in this question,log₄5 + log₄5 = log₄ 25
Therefore, in the equation log₄5 + log₄5, the property of the product rule of logarithms is used.
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What is the probability that client F, the 53-year-old you’re considering for a 20-year policy, lives to be 73 years old? Remember that client F is a Hispanic female.
Step-by-step explanation:
In this question , the 20 year policy is just for fun the probability is 53 / 73
Given f(x)=2x² evaluate f(-6)
A. 72
B. 78
C. -72
D. 441
E. -441
The value of f(-6) is 72, that is, option A.
In mathematics, a function from a given set X to a given set Y allots to each element of X one and only one element of Y. The set Y is called the range of the function and the set X is called the domain of the function.
Here, we are given a function f(x) = 2x²
f(-6) means that x = -6
Substituting x = -6 in the function, we get-
f(-6) = 2(-6)²
= 2 × -6 × -6
= 2 × 36
= 72
Thus, the value of f(-6) is 72.
From the given options, hence, option A becomes the correct answer.
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Complete the table given the following function:
y = 3x + 1
x y Ordered Pair
1
(1, 4)
2
(2,__)
3
(___,___),(____,____)
-1
(-1,___)
Considering the numeric values of the function, the points and ordered pairs are given as follows:
x = 2, y = 7, ordered pair (2,7).x = 3, y = 10, ordered pair (3,10).x = -1, y = -2, ordered pair (-1,-2).How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
An ordered pair is given by:
(x, f(x)).
In which f(x) is the numeric value.
For this problem, the function is given by the following rule:
y = 3x + 1.
When x = 2, the numeric value is given by:
y = 3 x 2 + 1 = 6 + 1 = 7.
Hence the ordered pair is (2,7).
When x = 3, the numeric value is given by:
y = 3 x 3 + 1 = 9 + 1 = 10.
Hence the ordered pair is (3,10).
When x = -1, the numeric value is given by:
y = 3 x -1 + 1 = -3 + 1 = -2.
Hence the ordered pair is (-1,2).
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What does 4.3 round to
Answer:
4
Step-by-step explanation:
Which system of linear inequalities is graphed?
S x < -2
ly≤-x+2
O
J x ≤-2
y≤-x-3
S. x < -2
y≤ x 2
-
{
√ x < −3
С
According to the question, to graph the linear inequality expressions then the given expressions should be equal to the respective number.
In the first equation that is: x<-2 or x = -2
The given expression can be drawn in the second quadrant when the value of the x-axis is negative and it is a straight line which tends to infinity.
In the second equation that is: y ≤ x+2 or y = x+2
The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive and it is a straight line which tends to infinity.
Similarly, in the third equation that is: y ≤ x-3 or y = x-3
The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive and it is a straight line which tends to infinity.
What is linear inequality?
Linear inequalities are those expressions in which comparison between the variables is performed. And the comparison can be done between two values or between the two expressions. It uses the symbols of the inequality like greater than, equal to, etc.
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Help please with question
Answer:
a. 62
b. 8.8
c. 2.8
Step-by-step explanation:
can you mark as brainiest if correct please?
what is the greatest common factor for 28 and 32
Answer:
4.
Step-by-step explanation:
28 = 2*2*7
32 = 2*2*2*2*2
Picking out the common factors:
GCF = 2 * 2 = 4.
Answer:28
Step-by-step explanation:
ask random person the explanation, sorry, I don't know how to explain
What is the coordinate of G' if triangle E'F'G' is created by dilating EFG with a factor of 4 about the origin?
The coordinate of G' if triangle E'F'G' is created by dilating EFG with a scale factor of 4 about the origin is (8, -8).
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is dilation?Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Since the dilatation was centered around the origin, then we would multiply the coordinate of G by a scale factor of 4 as follows:
G = (2, -2) → G'[(4 × 2), (4 × -2)]
G = (2, -2) → G'(8, -8)
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Please explain how.....
100 points
woah this looks hard
Isabel drove 335 miles in 5 hours.
At the same rate, how long would it take her to drive 536 miles?
Answer:
8
Step-by-step explanation:
distance/time=speed
335/5=67
536/t=67
t=8
Solve each equation. ln (x-7)=2
After the solving equation ln (x-7)=2, the value of x is equal to [tex]e^{2}[/tex] + 7
We have been asked to find x in ln (x-7)=2
⇒ ln (x-7)=2
⇒ x - 7 = [tex]e^{2}[/tex]
⇒ x = [tex]e^{2}[/tex] + 7
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Maria made a bunch of muffins for a bake sale. She made 5 corn, 6 banana, 2 blueberry, and 10 chocolate chip. What is the ratio of bananas to total?
Add. Write your answer in scientific notation.
(1.568×10^5)+(4.79×10^5)
The sum in scientific notation is 6.358 * 10^5
How to evaluate the sum in scientific notation?The summation expression is given as
(1.568 × 10^5) + (4.79 × 10^5)
Factor out 10^5 in the above expression
So, we have
10^5 * (1.568 + 4.79)
Evaluate the sum
10^5 * 6.358
Rewrite the expression as
6.358 * 10^5
Hence, the sum in scientific notation is 6.358 * 10^5
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Are they similar? Yes or no
Answer: Yes
Step-by-step explanation:
one is just bigger than the other if you blow the little one up than you can see they are the same!
Four years ago, Jennifer opened a saving account that earns 5% simple interest every year. She started the account with $650 and has not been touched the account since.
Answer:
$780
Step-by-step explanation:
Simple Interest Formula
[tex]\boxed{\sf A = P(1 + rt)}[/tex]
where:
A = Final amount.P = Principal amount invested.r = Interest rate (in decimal form).t = Time (in years).Given:
P = $650r = 5% = 0.05t = 4 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=650(1+0.05(4))[/tex]
[tex]\implies \sf A=650(1+0.2)[/tex]
[tex]\implies \sf A=650(1.2)[/tex]
[tex]\implies \sf A=780[/tex]
Therefore, the amount in the account now is $780.
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