[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{14}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +14}{2}~~~ ,~~~ \cfrac{ y +21}{2} \right) ~~ = ~~\stackrel{midpoint}{(41~~,~~50)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +14}{2}=41\implies x+14=82\implies \boxed{x=68} \\\\\\ \cfrac{ y +21}{2}=50\implies y+21=100\implies \boxed{y=79}[/tex]
Distance between (4,2) and (-3,4)
it is 22 units <3 your welcome
Find the average rate of change of g(2) = -4 + 4 between the points (-3,16) and (4,-12)
The average rate of change of the function between the points is -4/7
What are average rates of change?The constant average rates of change of a function is also regarded as the slope or the gradient of the function
How to determine the average rates of change?Here, we have the points to be
(-3, 16) and (4, 12)
The average rates of change between these points is calculated as
Average rate of change = [f(b) - f(a)]/[b - a]
So, we have
Average rate of change = [12 - 16]/[4 + 3]
Evaluate the sum and the difference
So, we have
Average rate of change = -4/7
Hence, the average rate of change between the points is -4/7
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Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
2 x+y=16
4 x-y=1
The solved logarithmic function is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: 2x + y = 16 and 4x - y = 1
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take the expression, 2x + y = 16
Applying log on both sides, we get,
log (2x + y) = log (16)
log (2x + y) = log (2⁴)
log (2x + y) = 4 log (2)
To Check Results,
Taking exponential on both sides,
e^[log (2x + y)] = e^(4 log 2)
2x + y = e^(log 2⁴)
2x + y = 2⁴
2x + y = 16
Thus, the answer is verified.
Take expression, 4x - y = 1
Applying log on both sides, we get,
log (4x - y) = log 1
log (4x - y) = 0
To Check Results,
Taking exponential on both sides,
e^[log (4x - y)] = e^0
4x - y = 1
Thus, the answer is verified.
Hence, the solved expression is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.
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Death valley is a desert in northern california with many place of interest. one such place is the badwater basin, the elevation is
-282 feet. at another location, salt creek trail, the elevation is-220 feet. write an inequality to compare the elevations and state
which elevation is closer to sea level.
The inequality comparing the elevations is -220 > -282 and -220 feet is closer to sea level.
The elevation of Bad Water Basin = -282 feet
The elevation of the Salt Creek = -220 feet
We are asked to compare the elevations and find which is greater than the other.
So we know that on a number line -220 is greater than -282.
This can be understood in the same sense that -1 > -2 on the number line.
So the inequality comparing the elevations is -220 > -282.
Now consider the sea level as 0 on the number line.
Then clearly -220 is closer to 0 on number line.
Hence the elevation closer to the sea level = -220 feet.
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ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Which graph best represents the solution set of y ≤ 3/4x − 4?
The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the graph of the inequality expression?The inequality expression is given as
y ≤ 3/4x − 4
The inequality symbol in the above inequality expression is
≤
This implies that the inequality expression is a less than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the bottom part is shaded
Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)
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How many minutes have passed, m, when Tank A contains the following amounts of water?
a. 151 liters
b. 191.5 liters
c. 270.25 liters
d. p liters
The minutes that have passed, m, when Tank A contains the following amounts of water will be:
151 liters = 3 minutes
191.5 liters = 7.5 minutes
270.25 liters = 16.25 minutes
p liters = (p-124) / 9 min
How to calculate the minutes?It should be noted that for 151 lit = (151 - 124)/9 = 3 min
Also, for 191.5 lit = (191.5-124) /9
= 67.5/9 = 7.5 min = 7 min 30 sec
It should be noted that for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 = 16 min 15 sec
For p lit = (p-124) / 9 min
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Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
How many minutes have passed, m, when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
p liters
Follow • 1
On a fantasy football team the Titans score is 11.15 points and a running back score is 11.75 points a wide receiver score is 1.05 points less than the run pack how many total points do three players scored
Answer: The total would be 33.6 points.
Step-by-step explanation:
Titans Score: 11.15
Running Back Score: 11.75
Wide Receiver: 1.05 less than Running Back (11.75 - 1.05), which would be 10.7 points.
11.15 + 11.75 + 10.7 = 33.6 total points
Answer: the problem was a little confusing but I'm assuming the answer is 10.7 making the final answer 32.97
Step-by-step explanation: if the titans scored (11.15) points and the running back scores (11.75) points and the wide receiver scores 1.05 points less then the running back it would be...
11.75 (the running backs points)
- minus
1.05
__________
=10.07(how many points the wide receiver had)
Then 10.07+ 11.15+ 11.75=32.97
Hope I got it right! <3
Which expression represents the model?
9*1/6
Step-by-step explanation:
1= 6/6 and there are 9 boxes so multiply 9*1/6
SOLVE THE FOLLOWING EQUATION FOR Y
Answer: 74
Step-by-step explanation: calculator
The two triangles displayed are scaled copies of one another. Find the scale factor.
Answer: 6
Step-by-step explanation:
Which is a benefit of being an employee paid commission?
You receive more paid time off than other types of pay.
Excellent job performance is rewarded with higher pay.
The work schedule is typically weekdays 9:00 a.m. to 5:00 p.m.
Commission is typically paid monthly making budgeting easier.
Answer:b
Step-by-step explanation:
b
factor the following
the equation is f(x) = x^3+27
The factored form of the cubic equation x³ + 27 is equal to (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2). The roots of the cubic equation are - 3, 3 / 2 + i 3√3 / 2 and 3 / 2 - i 3√3 / 2.
How to factor a cubic equation
In this problem we find a cubic equation of the form x³ + a³, whose factor form can be found by using algebra properties:
f(x) = x³ + 27
f(x) = (x + 3) · (x² - 3 · x + 9)
f(x) = (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2)
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11. Chris buys six guppies. Every month his guppy population doubles. [4]
a) How many guppies will there be after 1 month? 2 months? 3 months?
b) Create a formula that would express the statement above. In your formula let n
equal the number of months, and G equal the total population of guppies.
c) How many guppies will there be after 6.5 months?
d) Can the fish population continue to grow at this rate? Explain
Answer:
G = 6(2)^n
Step-by-step explanation:
a) At 1 month he will have 12 guppies, at 2 months he will have 24 guppies and at 3 months he will have 48 guppies.
b) G = 6(2)^n
This is following the exponential formula.
c) G = 6(2)^6.5 = 543 guppies
d) At this rate, there will be no room for the guppies to continue growing.
Four stores are having a sale on cans of Sprite. The sale prices are listed below:
Shop A: 6 cans for $5.10
Shop B: 6 cans for $5.70
Shop D: 12 cans for $10.80
Shop C: 12 cans for $9.60
Which store has the best buy?
Answer:
Shop C
Step-by-step explanation:
Without any calculations, you can eliminate stores B and D.
Shop A: $5.10/6 = $0.85/can
Shop C: $9.60/12 = $0.80/can
Answer:
It would be B
Step-by-step explanation:
Because A is 1.17 per can
B is 1.05 per can
D is 1.11 per can
and C is 1.25 per can
pls help me..................
Answer:
$142.60
Step-by-step explanation:
an increase of 15% on the original cost of 100% means
percentage increase = 100% + 15% = 115% , then
cost = 115% × $124 = [tex]\frac{115}{100}[/tex] × $124 = 1.15 × $124 = $142.60
What is the greatest common factor of 9 and 48?
Answer:
3 is the greatest common factor that can go into 9 and 48
The greatest common factor of 9 and 48 is 3.
What is the greatest common factor?The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of both (or all) of the given numbers.
For example, the GCF of 12 and 18 is 6, beca
To find the greatest common factor (GCF) of 9 and 48, we need to determine the largest number that both 9 and 48 can be divided by evenly.
We can start by listing the factors of each number:
9: 1, 3, 9
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then we can look for the greatest factor that appears in both lists. In this case, the greatest common factor of 9 and 48 is 3, since it is the largest number that appears in both lists of factors.
Therefore, the GCF of 9 and 48 is 3.
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What is the remainder when 316 is divided by 13?
Answer:
24 reminder 4
Step-by-step explanation:
Reminder is 4
316/13 = 24 R 4
Aisha buys 2 packets of bread rolls costing £1.20 for each packet 1 bottle of ketchup costing £2.10 3 packets of biscuits Aisha pays with a £10 note. She gets 70p change. Work out the cost of one packet of biscuits. You must show how you get your answer. Optional working Answer: £|
The cost of one packet of biscuit is £1.60.
What is the cost of one packet of biscuit?The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.
Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup
Total cost of bread rolls = cost per packet x number of packets bought
2 x £1.20 = £2.40
Total cost of ketchup = cost of one bottle x number of bottles bought
1 x £2.10 = £2.10
Total cost of biscuits = cost of one packet x number of packets bought
3 x b = 3b
Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b
Total amount paid by Aisha = note given - change received
£10 - 70p
£10 - £0.70 = £9.30
Total amount paid by Aisha = total cost
£9.30 = £4.50 + 3b
£9.30 - £4.50 = 3b
£4.80 = 3b
b = £4.80 / 3
b = £1.60
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Are ∠2 and ∠5 vertical angles? Explain your reasoning.
Answer:
no
Step-by-step explanation
an example of vertical angles would be 6 and 8
pls give brainliest :)
Determine which line the point (2,-1) lies on.
Answer:
the point will not lie on any line. it will come in the first coordinate
in science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution
When zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature, the change in temperature is 1/2 degree.
How to illustrate the information?It should be noted that from the information, science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 9/10 degrees as the. ending temperature.
Therefore,the change in temperature will be the subtraction of the temperature given. This will be illustrated as:
= 1/5 - (-3/10)
= 1/5 + 3/10
= 2/10 + 3/10
= 5/10
= 1/2
The change on temperature is 1/2 degree.
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In science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature. What was the change in temperature?
#1 You are in charge of ordering hats for a youth
baseball team. Each hat costs $22.50. There are at
least 10 but no more than 16 players on the
baseball team. The total cost of ordering hats can
be modeled by the function f(x)=22.50x,
where x represents the number of hats ordered. answer
The range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?The function is given as
f(x) = 2.250x
Where there are at least 10 but no more than 16 players on the baseball team
This means that the domain of the function is
10 <= x <= 16
Substitute the domain values in the given function
So, we have
f(x) = 2.250x
f(10) = 2.250 * 10
Evaluate
f(10) = 22.5
f(x) = 2.250x
f(16) = 2.250 * 16
Evaluate
f(16) = 36
The range of the function is then represented as
f(10) <= f(x) <= f(16)
So, we have
22.5 <= f(x) <= 36
Hence, the range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36
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Complete question
ou are in charge of ordering hats for a youth baseball team. Each hat costs $22.50. There are at least 10 but no more than 16 players on the baseball team. The total cost of ordering hats can be modeled by the function f(x)=22.50x, where x represents the number of hats ordered.
What is the range of the function?
Do you think that the measures of central tendency (mean, median, mode) tell you the entire picture of a data set? Why or why not?
Answer:
Step-by-step explanation:
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most
Megan is thinking of a number that is divisible by both 9and 7. What is the smallest possible number that Megan is thinking?
Answer:
Step-by-step explanation:
63
because 9x7=63
and 7x9=63
Need the answer for the function as stated in the photo
The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient
[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]
Over the interval [tex]3\le x\le5[/tex], we have
[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]
The area of a rectangle is 132.99 in2 and the length is 14.3 in. Find the width.
4.6 in.
12.9 in.
9.3 in.
18.7 in.
Answer:9.3
Step-by-step explanation:
Area= length times width
132.99= 14.3xw
Divide by 14.3
W= 9.3
Solve each equation.
3x⁺²=27²x
After solving the equation, x = 2/5 is the value of x in [tex]3^{X+2} = 27^{2x}[/tex]
⇒ [tex]3^{X+2} = 27^{2x}[/tex]
⇒ [tex]3^{X+2} = ((3)^3)^{2x}[/tex]
⇒ [tex]3^{X+2} = (3)^{6x}[/tex]
⇒ [tex]3^{X+2} = (3)^{6x}[/tex]
⇒ x+2 = 6x
⇒ 2 = 6x - x
⇒ 2 = 5x
⇒ x = 2/5
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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Let athe event of getting at least one defective calculator when four are randomly selected with replacement from a batch. Write a statement describing event
Answer: do you have a pic??
Step-by-step explanation:
Write the ratio that compares the championships won by Australia to the total number of championships. Then explain it's meaning
The ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.
According to the question we have been given that,
Total number of championship = 41
Total number of championship won by Australia = 6
Thus we need to find the ratio that compares the championship won by Australia to the total number of championship.
For this the ratio will be : [tex]\frac{number of championship won by Australia}{Total number of championship }[/tex]
= 6/41
Hence the ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.
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What is the multiples of 2/5
Answer:
Step-by-step explanation: 2x5=10
:) have a good day