Answer:
Step-by-step explanation:
Step 1: Define
Point (2, 8)
Point (-6, -8)
Substitute in points [SF]: m= -8-8/-6-2
[Fraction] Subtract: m=-16/-8
[Fraction] Divide: m=2
The slope of the line joining points (2, 8) and (-6, -8) is 2.
A straight line is a line plotted on the Cartesian plane. The line is generally written in the form y = mx + c, where m is the slope and c is the intercept of the straight line. The slope of the line can be obtained by using many formulae but if two points are given then the following formula is used:
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex].
The given points are (2, 8) and (-6, -8).
So, [tex]x_1 = 2, y_1 = 8, x_2 = -6,[/tex] and [tex]y_2 = -8[/tex].
The formula to find the slope of the straight line is
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]= \dfrac{-8-8}{-6-2} \\= \dfrac{-16}{-8}\\= \dfrac{16}{8}\\= 2[/tex]
Therefore, the slope of the given line is 2.
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The complete question is as follows:
Use the formula m = [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex] to find the slope of the line joining points (2, 8) and (-6, -8).
lim_(g(x))
X-2
=
=
lim (2x - 1)
X-2
Use squeeze theorem
Answer:
привет как вы это t6767
Step-by-step explanation:
Algebra 2
Simplify h(f(x-3))
when
f(x)= 2x-4
h(x)= 5-x
Please use explanations with every step!!! Thank you in advance!!!!
The Algebra of Functions
Like terms, functions may be combined by addition, subtraction, multiplication or division.
Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2
+ 2x – 1 find ( f + g ) ( x ) and
( f + g ) ( 2 )
Solution
Step 1. Find ( f + g ) ( x )
Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;
( f + g ) ( x ) = ( 2x + 1 ) + (x2
+ 2x – 1 )
= 2x + 1 + x2
+ 2x – 1
= x
2
+ 4x
Step 2. Find ( f + g ) ( 2 )
To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.
Since ( f + g ) ( x ) = x2
+ 4x then;
( f + g ) ( 2 ) = 22
+ 4(2)
= 4 + 8
= 12
Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).
Solution
Step 1. Find ( f – g ) ( x ).
( f – g ) ( x ) = f ( x ) – g ( x )
= ( 2x – 5 ) – ( 1 – x )
= 2x – 5 – 1 + x
= 3x – 6
Step 2. Find ( f – g ) ( 2 ).
( f – g ) ( x ) = 3x – 6
( f – g ) ( 2 ) = 3 (2) – 6
= 6 – 6
= 0
Answer: 15-2x
Step-by-step explanation:
h(f(x)) means you have to write equation in f(x) to every x you see in h(x) which is,
h(f(x))=5-2x+4=9-2x
if we need h(f(x-3)) we will take x as x-3 so,
h(f(x))=15-2x
An insurance agent has a list of 7 prospects and decides to telephone 3 of the prospects today and the other 4 prospects tomorrow. In how many different ways can the agent telephone the prospects?
The number of different ways the agent can telephone the prospects = 1020
In this question, an insurance agent has a list of 7 prospects and decides to telephone 3 of the prospects today and the other 4 prospects tomorrow.
We need to find the number of different ways the agent can telephone the prospects.
We use the formula of permutation.
^n(P_r) = n! / (n - r)!
where n! = n × (n - 1) × (n - 2) × . . . × 1
For this question, n = 7
The number of different ways the agent can telephone the prospects today.
We use r = 3
^7n(P_3)
= 7! / (7 - 3)!
= 210
And the number of different ways the agent can telephone the prospects tomorrow.
We use r = 4
^7n(P_4)
= 7! / (7 - 4)!
= 810
so, the number of different ways the agent can telephone the prospects = 210 + 810
= 1020
Therefore, the number of different ways the agent can telephone the prospects = 1020
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If p-1 is a factor of p4+ p²+ p-k the value of k is
The value of k for the given equation is k = 3.
What is defined as the factor?A factor is a number which divides another number by itself and leaves no remainder.
In the other words, whenever multiplying two whole numbers yields a product, the numbers being multiplied are factors of a product because the product is divisible by them.Factors can be found using two methods: multiplication and division. Furthermore, rules of divisibility might well be applied.The factor of a number is always less than as well as equal to the number; it is never greater than the number.With the exception of 0 and 1, every integer has at least two factors: 1 and the amount itself.For the given equation;
p⁴ + p² + p - k has the factor of p -1.
It means, for p = 1, is the roots of the equation and thus, must satisfy it.
Put p = 1 in the equation and put equal to zero.
p⁴ + p² + p - k = 0
1⁴ + 1² + 1 - k = 0
3 - k = 0
k = 3
Thus, the value of the k is found as 3.
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its 3 because i know its 3
the table shows the maximum and minimum account balances for three college students for one month Giovanni claimed that he had the least variation from maximum to minimum in his account balance that month is he correct? write a mathematical argument to justify your solution
Yes, it should be that.Giovanni's account balance has the least variation from maximum to minimum that month.
How to illustrate the information?It should be noted that the formula for calculating the variation is;
Balance difference = Maximum balance - Minimum balance.
For Jordan;
Maximum balance = $145.
Minimum balance = $-25
Balance difference = 145 - (-25) = $170
For Giovanni;
Maximum balance = $168.
Minimum balance = $15.
Balance difference = 168 - 15 = $ 153.
For Elisa;
Maximum balance = $152.
Minimum balance = $-10
Balance difference = 152 -(-10) = $162.
Therefore, for the data it is clear that the minimum account variation is for Giovanni which is $153.
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Melissa Jackson, bookkeeper for Kinko Company, cannot prepare a bank reconciliation. The bank statement showed a $2,955.82 balance. Melissa’s checkbook showed a $3,301.82 balance. Melissa placed a $510.19 deposit in the bank’s night depository on June 30. The deposit did not appear on the bank statement. The bank included two DMs and one CM with the returned checks: $690.65 DM for NSF check, $8.50 DM for service charges, and $400.00 CM (less $10 collection fee) for collecting a $400.00 non-interest-bearing note. Check number 811 for $110.94 and check number 912 for $82.50, both written and recorded on June 28, were not with the returned checks. The bookkeeper had correctly written check number 884, $1,000, for a new cash register, but she recorded the check as $1,069. The May bank reconciliation showed check number 748 for $210.90 and check number 710 for $195.80 outstanding on April 30. The June bank statement included check number 710 but not check number 748.
Kinko's checkbook balance: $3,301.82 +Collection on notes receivable: $400,00 -Collection fee: $10.00 Notes-fee- $390.00 Error in recording: $69.00 Balance (Notes-fee)+Error= $3,760.82 -NSF Check: $690.65 -Service Charge: $8.50 Total in deduct: $699.15 Reconciled Balance: $3,061.67
Kinko's bank balance: $2,955.82
+Deposit in transit: $510.19 Balance+DIT= $3,466.01 -Outstanding checks (total): $404.34 Reconciled balance: $3,061.67
Brian ran 17 miles in 2.5 hours. What was brian’s rate in miles per hour .
PLEASE HELP ILL GIVE BRAINALIEST HURRY
The elevation of city A is 96 feet below sea level; the elevation of city C is 24 feet below sea level. The elevation of city D is 1 over 4 of the elevation of city C.
Part A: Write an expression to represent the elevation, in feet, of city D. (5 points)
Part B: Solve the expression and explain why the answer is negative or positive.
The elevation of city D is 1 over 4 of the elevation of city C.
D = (1/4)CPart BD = (1/4)*(-24) = - 6The answer is negative as it is the result of the product of positive and negative numbers.
Solve x+5>−3 and −2x−5≤1 and write the solution in interval notation. If there is no solution, type ∅.
Answer:
7/4≤x ≤-1
Step-by-step explanation:
Given the set of inequalities
−5x−3≥2 and 4x−2≥5
We are to write the solution in interval notation. We need to solve them individually first as shown;
For −5x−3≥2
add 3 to both sides
−5x−3+3≥2+3
-5x ≥5
divide both sides by -5 (note that dividing by a negative value will change the sense of the inequality sign)
-5x/-5 ≤5/-5
x ≤ -1
For the inequality 4x−2≥5;
add 2 to both sides
4x−2+2≥5+2
4x≥7
divide both sides by 4;
4x/4 ≥ 7/4
x≥7/4 or 7/4≤x
Combining 7/4≤x and x ≤ -1, the solution in interval notation is expressed as 7/4≤x ≤-1
The difference of the number of grades and the number of degrees of the same angle is 16. Find the number of degrees and grades of the angle.
Answer:
160 grades or 144 degrees================================
Relationship between grade and degree is:
100 grades is same as 90 degrees,or
100G = 90Dor
G = 90D/100G = 0.9DWe have angle x grades for which, the difference of grades and degrees is 16.
We can show this as:
x - 0.9x = 160.1x = 16x = 16/0.1x = 160The number of degrees is:
160 - 16 = 144I am simply not smart
T^T
Answer:
10^6
Step-by-step explanation:
Comment
1 second = 10^5computations
10 seconds would result in10*10^5 computations
10^1*10^5 = 10^(1 + 5) = 10^6
The length of a rectangle is 4 meters longer than the width. If the area is 40 square meters, find the rectangles dimentions. Round to the nearest tenth of a meter
Answer:
L = 32
W = 8
Step-by-step explanation:
Set it up algebraically:
A = L x W
A = 40 m^2
L = 4w
40 = 4w x w
40 = 5w
40/5 = 5w/5
W = 8
L = 4(8)
L = 32
Which three pairs of side lengths are possible measurements for the triangle?
Answer:
2 , 3 , and 6
Step-by-step explanation:
so basically , in 30 60 90 triangles , the long flat side ( GH ) is x square root 3 . the short flat side ( HI ) is x . and the hypotenuse ( opposite of the right angle aka the diagonal line GI ) is 2x . and thats the formula for it so yeah , the second 3rd and last work ! sorry for the wack explaination .
A pasta recipe calls for 3 cups of crushed
tomatoes, t, for every 1/4 of olive oil, v. What
equation can be used to represent this
relationship?
Answer: t=12v
Step-by-step explanation: 3t = 1/4v Find unit rate
1/3(3t) = 1t
1/3(1/4v) = 12v
Now let's check
if v = 1/4 then 12 x 1/4 =3
I explained it the best i could it prb doesn't help but i hope it does :D
dino has a pizza with a diameter of
Based on the given parameters, the square box is big enough to fit the pizza?
How to determine if the square box is big enough to fit the pizza?The given parameters are:
Diameter of pizza = ten and one third inchesLength of square box = 10.38 inchesRewrite the parameters properly as:
Diameter of pizza = 10 +1/3 inches
Length of square box = 10.38 inches
Express the diameter as a numeral.
So, we have:
Diameter of pizza = 10 + 1/3 inches
Evaluate the sum
Diameter of pizza = 10.33 inches
By comparison:
10.33 inches is less than 10.38 inches
This means that the square box is big enough to fit the pizza
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Complete question
Dion has a pizza with a diameter of ten and one third inches.is a square box of 10.38 inches big enough to fit the pizza?
A pilot flew a plane from an altitude of 6000 feet to an altitude of 18900 feet. What was the change in altitude?
Answer:
12,900
Step-by-step explanation:
18,900 - 6,000= 12,900
help
25:4 and 45:10 as a complex fraction
Complex fraction of 25 : 4 is 6 1/4.
Complex fraction of 45 : 10 is 4 5/10.
What is the Ratio?
A ratio is an ordered pair of numbers x and y, written x / y where b ≠ 0.
The ratios are given as;
25 : 4 and 45 : 10
Now, To write the ratios in complex fraction we use division method as;
25 : 4 = 25/4
_____
4 ) 25 ( 6
- 24
-----------
1
Hence, Complex fraction of 25 : 4 is 6 1/4.
And, For ratio 45 : 10;
45 : 10 = 45/10
10 ) 45 ( 4
- 40
---------
5
Hence, Complex fraction of 45 : 10 is 4 5/10.
Therefore, Complex fraction of 25 : 4 is 6 1/4.
Complex fraction of 45 : 10 is 4 5/10.
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What is the slope of the line represented by the equation y = 4/5x -3
• -3
• - 4/5
• 4/5
• 3
Answer:
The answer is 4/5
After his first month he had more than expected to have due to interest bank provided this that Rob come up with a better expression W squared over 25+45W +155 we’re W is the number of weeks how much will you have in one year
Rob will earn in one year $2603.16.
Given that,
After his first month, he had more than expected to have due to the interest the bank provided.
This let Rob come up with a better expression w²/25+45W +155 where W is the number of weeks how much will you have in one year is to be determined.
The equation is the relationship between variables and represented as y =ax +b is an example of a polynomial equation.
Here,
Given expression,
w² / 25 + 45w + 155
In i year w = 52
= 52²/25 + 45 * 52 + 155
= 2603.16
Thus, Rob will earn in one year $2603.16.
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What is the value of −163 − 18 − (−215)?
Answer:
34.
Step-by-step explanation:
-163 - 18 = -181
-181 - (-215) = 34.
Answer:
34
Step-by-step explanation:
-163-18-(-215)
-163-18+215
-181+215
34
(I tried my best, is this what your question was?)
Half of your baseball card collection got wet and was ruined. You bought 15 cards to replace some that were lost. How many did you begin with if you now have 55?
On solving the algebraic expression, the total cards present were 80.
An algebraic expression is what?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
the number of cards in the starting hand, let x
Total card = 55
(1/2)x + 15 = 55
By solving, we discover
x = 80 cards
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A project is budgeted for 2400 hours and will last 3 weeks. Technicians will cover 25% of the project for the first week and then 60% for the final two weeks. If each technician normally works 40 hours per week, how many technicians are there?*
Using the percentage and hours, the total number of technician that was there is 42.
How to find the number of technicians that are there?The project is budgeted for 2400 hours and will last 3 weeks.
This means the whole project will last for 2400 hours for 3 weeks.
Technicians will cover 25% of the project for the first week and then 60% for the final two weeks.
This simply implies 25% of the project will be completed in the first week. Then 60% of the remainder of the project will be completed the final two weeks.
Each technician normally works 40 hours per week.
Therefore,
Number of hours for the first week = 25 % of 2400
Number of hours for the first week = 25 / 100 × 2400
Number of hours for the first week = 600 hours
Therefore,
number of technicians for the first week = 600 / 40
number of technicians for the first week = 15 technicians
Therefore,
Number of hours for the final two week = 60 % of (2400 - 600)
Number of hours for the final two week = 60 / 100 × 1800
Number of hours for the final two week = 1080 hours
Hence,
number of technicians for the final two week = 1080 / 40
number of technicians for the final two week = 27 technicians
Therefore, the total number of technician that was there is 42.
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←−→ W X and ←→ Y Z intersect at point V. If m ∠ W V Y = ( 4 a + 58 ) ° and m ∠ X V Y = ( 2 b − 18 ) ° , find the values of a and b such that ←−→ W X is perpendicular to ←→ Y Z .
The values of a and b are 8 and 54 respectively
How to find the values of a and b such that WX is perpendicular to YZ?The given parameters are:
WVY= 4a + 58
XVY = 2b - 18
From the question, we understand that WX is perpendicular to YZ
This means that
WVY= 90
XVY = 90
So, we have
4a + 58 = 90
2b - 18 = 90
Solve for a in 4a + 58 = 90
4a = 90 - 58
Evaluate
4a = 32
Divide by 4
a = 8
Solve for b in 2b - 18 = 90
2b = 90 + 18
Evaluate
2b = 108
Divide by 2
b = 54
Hence, the values of a and b are 8 and 54 respectively
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Which of the following is true for the relation f(x)=1/3x+5
The true statement about the relation is both the relation and the inverse are functions
How to determine the true statement?The equation of the relation is given as
f(x) = 1/3x + 5
The above equation is a linear relation
A linear relation is a function.
Also, the inverse of the linear relation is a function.
Hence, the true statement about the relation is both the relation and the inverse are functions
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what is 11.273.26 in word form
Answer:one million one hundred and twenty-seven thousand three hundred and twenty-six
Step-by-step explanation:
Use the function to evaluate the indicated expressions and simplify.
f(x) = 4x² + 3
f(x + 2) =
f(x) + f(2)=
The function to evaluate the expression is f(x)+f (2) =4x^2+22.
The function simplify () attempts to "simplify" the input expression by using clever heuristics.
⇒ f(x)=4x^2+3
⇒ f(x+2)=4(x+2)^2+3
by using algebra formula
⇒ f(x+2)=4(x^2+4+4x)+3
⇒ f(x+2)=4x^2+16x+19
by adding f(x)+f (2)
⇒ f(x)+f(2)=4x^2+3+(4×(2)^2 )+3
⇒ f(x)+f(2)=4x^2+3+(4×4)+3
⇒ f(x)+f(2)=4x^2+3+16+3
⇒ f(x)+f(2)=4x^2+22
There is a general function called simplify () that seeks to reduce an expression to its most basic form. Simplify in simply, this function is defined. reduce module.
Hence, the function to evaluate the indicated expressions and simplify f(x)=4x^2+3, f(x+2)=4(x+2)^2+3 and f(x)+f(2)=4x^2+22.
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Hi can someone please help me with these!
Answer:
64=18
Step-by-step explanation:
Marcus dives from the surface of the ocean to a reef 18 meters below sea level .what integer represents Marcus location relative to the surface?How far does Marcus have to go to return to the surface
The integer that represents Marcus location relative to the surface is -18 and Marcus has to go 18 meters to return to the surface
What integer represents Marcus location relative to the surface?The depth is given as
Depth = 18 meters below sea level
Below sea level is represented as negative
So, we have
Depth = -18
Hence, the integer that represents Marcus location relative to the surface is -18
How far does Marcus have to go to return to the surfaceThe distance to return to the surface is
Distance = |Depth|
This gives
Distance = |-18|
Evaluate
Distance = 18
Hence, Marcus has to go 18 meters to return to the surface
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> Read and try to solve the problem below.
Mei is building a raised bed in her garden to grow lettuce.
She wants the base of the bed to be a square with an area of
2 square meters. Find an approximate side length of the base
of the bed. Plot the value on the number line.
When Mei is building a raised bed in her garden to grow lettuce, it should be noted that the approximate length will be 1.4m.
How to illustrate the information?It should be noted that from the information, Mei is building a raised bed in her garden to grow lettuce and she wants the base of the bed to be a square with an area of 2 square meters.
Therefore, an approximate side length of the base will be the square root of the value will be:
= ✓2
= 1.41 m
Therefore, based on the information, the approximate length will be 1.4m.
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The normal price of a laptop’s is 899€.In a sale, it’s price is reduced to 599.95€.How many percent is the discount?
Work Shown:
A = original price
B = final price
C = difference in price
C = A - B
C = 899 - 599.95
C = 299.05 <--- this is the amount you save
D = C/A
D = (299.05)/(899)
D = 0.3326
D = 33.26% approximately
