The distance between the point P(1, 4) and Q(4, 0) is ____.
Answer:
5
Step-by-step explanation:
The distance between any two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
(x₁, y₁) = (1, 4) and (x₂, y₂) = (4, 0)
So distance is
[tex]d = \sqrt {(4 - 1)^2 + (0 - 4)^2}\\\\d = \sqrt {(3)^2 + (-4)^2}\\\\d = \sqrt {(3)^2 + (-4)^2}\\\\d = \sqrt {25}\\\\d = 5[/tex]
Determine f(x+a)−f(x) for the following function.
f(x)=x−9‾‾‾‾‾√+6
The value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)
How to evaluate the function value?The function definition is given as
f(x) = √(x - 9) + 6
We start by calculating the function f(x + a)
So, we have
f(x + a) = √(x + a - 9) + 6
The function definition f(x + a) - f(x) is calculated as
f(x + a) - f(x) = √(x + a - 9) + 6 - (√(x - 9) + 6)
Open the bracket
So, we have
f(x + a) - f(x) = √(x + a - 9) + 6 - √(x - 9) - 6
Evaluate the difference
So, we have
f(x + a) - f(x) = √(x + a - 9) - √(x - 9)
Hence, the value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)
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find the measure of EF
Answer:
EF = 32
Step-by-step explanation:
since the base angles D and F are congruent then the triangle is isosceles with both legs congruent , that is
EF = DE = 32
Answer:
32 units
Step-by-step explanation:
It is an isosceles triangle so two sides will be the same length opposite the equal angles EF = 32
help
Use Structure Marika goes to dinner with some friends. She spends $x on dinner and leaves an 18% tip. Which expression can Marika use to find the total cost of the dinner, including the tip? Select all that apply.
Multiple select question.
cross out
A)
0.82x, because this gives the cost of the dinner without the tip.
cross out
B)
18x – 0.18x, because this gives how much Marika pays for the dinner.
cross out
C)
1.18x, because this gives the cost of the dinner and then 18% of that cost.
cross out
D)
x – 0.18x, because this multiplies the cost of the dinner and the tip by 18%.
cross out
E)
x + 0.18x, because this multiplies the cost by 100% and then by the tip percentage to give the total cost.
The expressions which Marika can use to find the total cost of the dinner, including the tip are:
1.18x, because this gives the cost of the dinner and then 18% of that cost.x + 0.18x, because this multiplies the cost by 100% and then by the tip percentage to give the total cost.What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to write and solve this word problem, we would assign a variable (x) to the cost and then evaluate the resulting algebraic expression. Therefore, let x represent the cost.
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umm I'm having difficulty in this question
its a indices question
Step-by-step explanation:
1. divide 10 with 5
2. using law indices, simplify the rest of the equation
3. you're done!
Answer: 5m³n³
Step-by-step explanation:
[tex]\frac{10m^5n^4}{2m^2n}[/tex] = [tex]\frac{5m^5n^4}{m^2n}[/tex]
= [tex]\frac{5m^3n^4}{n}[/tex]
= 5m³n³
or
[tex]10m^{5} n^{4}[/tex] ÷[tex]2m^{2}n[/tex] = [tex]5m^{5-2} n^{4-1}[/tex]
= [tex]5m^{3} n^{3}[/tex]
Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first
quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary.
The population density in country A is 113 people per square mile while in country B, it is 605 people per square mile.
Select one:
O a. Absolute difference: -492 people per square mile
Relative difference: -81.3%
O b. Absolute difference: 492 people per square mile
Relative difference: 435.4%
O c. Absolute difference: -492 people per square mile
Relative difference: -435.4%
O d. Absolute difference: -492 people per square mile
Relative difference: -8.1%
Answer: c
Step-by-step explanation:
The absolute difference is 492 people per square mile and Relative difference: 435.4%.
Thus, option (B) is correct.
To find the absolute difference between the two population densities, subtract the population density of country A from the population density of country B:
Absolute difference = Population density of country B - Population density of country A
= 605 people per square mile - 113 people per square mile
= 492 people per square mile
Now, the relative difference as a percentage, we use the formula:
Relative difference = (|Absolute difference| / Population density of country A) * 100
= (|492| / 113) * 100
= (492 / 113) * 100
= 4.35398230088 * 100
= 435.4%
Therefore, the absolute difference is 492 people per square mile
Relative difference: 435.4%
Thus, option (B) is correct.
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Which expression is equivalent to 8x3 − 64 when factored completely?
a
(2x − 4)(4x2 + 8x + 16)
b
(2x − 4)(4x2 − 8x + 16)
c
(2x + 4)(4x2 + 8x + 16)
d
(2x + 4)(4x2 + 8x − 16)
Answer:
A (2x − 4)(4x2 + 8x + 16)
Step-by-step explanation:
A
(2x − 4)(4x2 + 8x + 16) =
8x3 + 16x2 + 32x - 16x2 - 32x - 64 =
8x3 - 64
B
(2x − 4)(4x2 − 8x + 16)
8x3 - 16x2 + 32x - 16x2 + 32x - 64
8x3 - 32x2 - 64
c
(2x + 4)(4x2 + 8x + 16)
8x3 + 16x2 + 32x + 16x2 + 32x + 64
8x3 + 32x2 + 64x + 64
D
(2x + 4)(4x2 + 8x − 16)
8x3 + 16x2 - 32x + 16x2 + 32x - 64
8x3 + 32x - 64
The shadow of a building is 30m long when the angle of elevation of the sun is 56°. Calculate the:
(a) height of the building
(b) length of shadow when the sun is at an angle of 32°.
Answer:
(a) height: 44.5 m
(b) shadow: 71.2 m
Step-by-step explanation:
You want building height and shadow length for angles of elevation 56° and 32°, given the shadow is 30 m when elevation is 56°.
Trig relationThe building height and shadow length are the sides opposite and adjacent (respectively) to the elevation angle in the right triangle that models the geometry. The trig function that relates these sides to the angle is the tangent function:
Tangent = Opposite/Adjacent
Application(a) building height
Using the tangent relation, we have ...
tan(56°) = (height)/(30 m)
height = (30 m)(tan(56°)) ≈ 44.4768 m
The height of the building is about 44.5 meters.
(b) shadow length
Using the same relation with the building height known, we have ...
tan(32°) = (44.4768 m)/(shadow)
shadow = (44.4768 m)/tan(32°) ≈ 71.1778 m
The length of the shadow at an angle of 32° is about 71.2 m.
what is
x-6=2x-10 in the question
Answer:
x = 4
Step-by-step explanation:
x - 6 = 2x - 10
-2x -2x
-x - 6 = -10
+6 +6
----------------
-x = -4
÷-1 ÷-1
------------
x = 4
I hope this helps!
At BEST BUY a television
is marked down 40% and the original cost of
the television is 800 dollars. What is the new price of that television.
Answer:
$320
Step-by-step explanation:
This answer is relieved by turning 40% into .4 and multiplying 800 by .4
please help me im begging you im really stuck on this one
Answer:
[tex]\frac{1}{2} - \frac{1}{6} = \frac{3}{6} - \frac{1}{6} = \frac{2}{6}[/tex]
Step-by-step explanation:
It does not say to simplify so 2/6 would be your answer.
Which of the following is a factor of 2x4 + 20x3 + 50x2?
2x3
x4
x + 4
x + 5
D. (x + 5)
We have to find the factor of this expression which matches to the options.
13. For Tom's birthday, he AND 5 friends went to the aquarium. If Tom uses his mom's credit
card and pays $11 for each ticket, what integer represents the amount of money Tom spent on
his mom's credit card.
A. - $66
B. $55
C. - $55
D. $66
Answer:
66
Step-by-step explanation:
he will pay 66 dollars
Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. (Round your answer to the nearest cent.)
The monthly finance charge for the credit card transaction is $51.70.
We need to calculate the monthly finance charge for the given credit card transaction.
What is a credit card transaction?Credit card transaction means the purchase of goods or obtaining of services or cash against the use of the Credit Card, the Card number or in any manner authorised by the Cardholder for debit to the Credit Card Account or utilising of any services made available to the Cardholder by the Bank from time to time in respect.
Given that, $3,000 balance, 21% rate, 150 payments, average daily method
The particular month in question is 30 days long.
Your balance at the start of the month is $3,000.
Annual interest rate = 21%.
Payment = $150.00
When the payment is made in the month, it reflects on the tax amount you pay on both the average daily balance.
The average daily balance is $3000 from day 1 until day 10 (10 days)
The average daily balance is $2850 from day 11 until day 30 (20 days)
Average daily balance for the month = 10 × 3000 + 20 × 2850
= 87000 / 30
= $2900
Interest charge for the month = (0.21 × 2900× 30) / 365
The interest charge for the month = $50.05 rounded to the nearest penny
The average daily balance is $3000 from day 1 until day 29 (29 days)
The average daily balance is $2850 from day 30 until day 30 (1 day)
Average daily balance for the month = 3000 × 29 + 1 × 2850
= 89850 / 30
= $2995
Interest charge for the month = (0.21 × 2995 × 30) / 365
=51.6945≈$51.70
Therefore, the monthly finance charge for the credit card transaction is $51.70.
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A restaurant chef made 1 1/8 pints of mushroom soup. Each bowl of soup holds 1/8 of a pint. How many bowls of soup will the chef be able to fill?
Write your answer as a fraction or as a whole or mixed number.
Answer:
9
Step-by-step explanation:
We can determine the number of bowls that can be made by dividing the size of the bowl by the amount of soup. 1 1/8 can be expressed as 8/8 + 1/8, or 9/8. (9/8)/(1/8) = 9. The chef can fill 9 bowls of soup.
Mushroom soup sounds pretty good right now ngl
Elise says, “if you subtract 11 from my number and multiply the difference by -4, the result is -48” What is Elise’s number?
At a clothing store Kayla finds to sweaters she likes she wants to know if she has enough for both sweaters since $34.95 is about 35 she add $20.75 and 35 mentally and gets $55.75. How should Kayla compensate to go the exact sum of the two prices
In order to be able to compensate to get the exact sum of the two prices, Kayla should subtract $0.05 from $55.75.
How to get the exact sum?In order to be able to get the price of $55.75, Kayla rounded $34.95 up to $35 and then added $20.75.
To compensate for the rounding up and then get the exact sum of the prices of the sweaters, Kayla should subtract the difference between the $35 and the $34.95.
That difference is:
= 35 - 34.95
= $0.05
In conclusion, Kayla should subtract $0.05 from $55.75 to get $55.70.
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“If the side of the square is increased by 2 feet, the area is increase by 12 sq. ft.”?
In mathematical expression the given expression is written as;
⇒ S + 12 = x² + 2x + 4
Where, S is area of square with side x.
What is Area of square?
A square is a two dimension figure in which all the sides are equal. Since all the sides are equal, the area would be two times the side of a square.
Let a side of square is x feet.
Then, Area of a square (S) = x²
When, The side of the square is increased by 2 feet. Then area is increase by 12 sq. ft.
Then, Side of a square = (x + 2)
Hence, Area of a square = (x + 2)²
s + 12 = x² + 2 * x * 1 + 2²
s + 12 = x² + 2x + 4
So, In mathematical expression the given expression is written as;
⇒ S + 12 = x² + 2x + 4
Where, S is area of square with side x.
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Last year, Singer A performed one more than five times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 73. How many concert shows did each perform?
Singer A
Singer B
The number of concert shows that singer A and singer B attended will be 41 and 18 shows respectively.
How to illustrate the information?Based on the information, the equation for last year will be:
A = 2B + 5
The number will be illustrated as:
A = B + 23
Therefore, it should be noted that we will equate the expression. This will be:
2B + 5 = B + 23.
Collect like terms
2B - B = 23 - 5
B = 18.
A = 23 + B = 23 + 18 = 41
Therefore, the number of concert shows that singer A and singer B attended will be 41 and 18 shows respectively.
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Last year, Singer A performed two times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 23. How many concert shows did each perform?
True or false. The three interior angles of a triangle have a sum of 180 degrees. If you know two or three angles are complementary, then the triangle is a right triangle
Answer:
true took the test on edge
In a class of 23 learners, the girls were 7 more than the boys. How many boys were in the class
Answer:
8 boys.
Step-by-step explanation:
Lets say b is the number of boys and g is the number of girls.
We know that:
23 = b + g
g = b + 7
So then lets solve for b:
23 = b + g
23 = b + ( b + 7)
Simplify.
23 = 2b + 7
Subtract 7 from both sides to isolate the b.
16 = 2b
Divide both sides by 2.
8 = b
So there are 8 boys in the class.
We can check our work by substituting the value of b into our equation.
23 = b + ( b + 7)
23 = 8 + ( 8 + 7 )
23 = 8 + 15
23 = 23
So therefore our answer is correct.
An airplane's altitude changed -378 feet over 6 minutes. What was the mean change of altitude in feet per minute?
Given the change in altitude and time, the mean change of altitude of the airplane is -63 ft/min.
What was the mean change of altitude in feet per minute?The mean change of altitude is simply know as the average rate of change.
The average rate of change is the sum total of the change in altitude divided by the sum total of the change in time.
It is expressed as;
r = Δa/Δt
Where r is rate of change, Δa is total change in altitude and Δt is the total change in time.
Given the data in the question;
Change in altitude Δa = -378ftChange in time Δt = 6minrate of change r = ?Plug the given values into the above formula and solve for r.
r = Δa/Δt
r = -378ft / 6min
r = -63 ft/min
Given the change in altitude and time, the mean change of altitude of the airplane is -63 ft/min.
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PLEASE HELP BEEN STUCK ON THIS FORVER! AND ITS DUE SOON!
FIND THE 100TH LINE SEGMENT
CUBE #1 HAS 4 LINES
CUBE #2 HAS 12
CUBE #3 HAS 24
WHATS THE 100TH LINE SEGMENT USING NTH TERM.
PICTURE BELOW!
The 100th line segment by using the nth term of a sequence is equal to 20200.
What is a sequence?A sequence can be defined as a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.
Next, we would determine the differences between the terms in this sequence until all the differences are the same:
12 - 4 = 8
24 - 12 = 12
40 - 24 = 16
12 - 8 = 4
16 - 12 = 4
Since the differences are the same, the sequence is a quadratic function and it contains an n² term. Also, the coefficient of n² is one-half of the equal difference. This ultimately implies that, the coefficient of n² is equal to 2.
In order to determine the nth term of this sequence, we would develop a table to model increment:
n 1 2 3 4
2n² 2 8 18 32
Operation +2 +4 +6 +8
Sequence 4 12 24 40
By critically observing the table above, we can logically deduce that the nth term of this sequence is given by:
aₙ = 2n² + 2n
a₁₀₀ = 2(100)² + 2(100)
a₁₀₀ = 2(10000) + 2(100)
a₁₀₀ = 20000 + 200
a₁₀₀ = 20200.
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Annalea wants to know which school has higher athletic achievements relative to budget per student
The ways to know know which school has higher athletic achievements relative to budget per student are:
% of students in sports club divided by SAT averagethe number of sports medals won divided by SAT averageHow to illustrate the information?Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
% of students in sports club divided by SAT average
the number of sports medals won divided by SAT average
To determine which school has higher athletic achievements relative to the SAT average, according to the two definitions will be that Did you get the same result for both definitions?
No. The definitions have opposite results.
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Analia wants to know which school has higher athletic achievements relative to the SAT average. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A % of students in sports club divided by SAT average (Choice B) B Graduation rate divided by SAT average (Choice C) C Number of sports medals won (Choice D) D Number of sports medals won divided by SAT average 2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions? Choose 1 answer: Choose 1 answer: (Choice A) A Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average. (Choice B) B Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average. (Choice C) C No. The definitions have opposite results.
There are 6 yellow balls and 9 green balls in a bag. If 3 balls are chosen one by one randomly from the bag without replacement, find the probabilities of the following events.
(a) The first ball chosen is yellow and the last two balls chosen are green.
(b) Only the first two balls chosen are of the same colour.
Answer:
The answer will be A.
MATHHHHHHHHHHHHHHHHHHHHHH
Answer:
n= -35 .................................
Please help me asap!!! I need 3,5,7,9,10 first correct answer gets a crown and max points!!!
Answer:
3. 7
5. 8
7. 15
9. 6
10. 1
Step-by-step explanation:
Assuming a linear relationship, find the missing value in the table below.
Answer:
16
Step-by-step explanation:
4n -4 (pattern rule)
4x2 = 8-4 = 4
Find the y-coordinate of the midpoint for a line segment with endpoints at A (3 , -22) and B (8 , 4).
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{-22})\qquad B(\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 8 +3}{2}~~~ ,~~~ \cfrac{ 4 -22}{2} \right) \implies \left(\cfrac{ 11 }{2}~~~ ,~~~ \cfrac{ -18 }{2} \right) \implies (5.5~~,~~\stackrel{\stackrel{y}{\downarrow }}{-9})[/tex]
What is the degree of the polynomial? 10x4-11x2 +6
Answer:
is it is 10^4 - 11^2 + 6 then the answer will be 4
Step-by-step explanation: