Answer:
Step-by-step explanation:15(x+2) =25
15x+30=25
15x=5
3x=1
x=1/3
francine wants to join a health club and has narrowed it down to two choices. the sportshaus charges an initiation fee of $ 500 and $ 10 per month. fitness first has an initiation fee of $ 50 and charges $ 25 month.
The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is 50 + 25x .
In the question ,
it is given that ,
Francie wants to join the health Club .
For the Sports Haus the initiation fees = $500
per month charge = $10
let the number of months be= "x" ,
so , the equation to represent the total cost for Sports Haus Club for x months is 500 + 10x .
For the Fitness First the initiation fees = $50
per month charge = $25
so , the equation to represent the total cost for Fitness First Club for x months is 50 + 25x .
Therefore , The equation for the total cost for Sports Haus is 500 + 10x and the equation for Fitness First is 50 + 25x .
The given question is incomplete , the complete question is
Francine wants to join a health club and has narrowed it down to two choices. The Sports Haus charges an initiation fee of $ 500 and $ 10 per month. Fitness First has an initiation fee of $ 50 and charges $ 25 month . write an equation for the total cost of each health club for x months .
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The average annual rainfall for a town is 43.2 inches. What is the average monthly rainfall?
Answer: 3.6
Step-by-step explanation: Annual means yearly, therefore 43.2 divided by 12 is 3.6. So 3.6 inches monthly.
Giovanni can read 250 words per minute. If there are approximately 300 words on a page, about how many pages can he read in 2 hours?
The temperature in a town increased 18°F in 4 hours. The temperature decreased 40°F in the next 6 hours. Write the total change in temperature as a rate in the form of a quotient of integers.
The total change in temperature is 58°F.
What is temperature?It should be noted that temperature simply means the degree of hotness and coldness in a body.
In this situation, the temperature in a town increased 18°F in 4 hours and the temperature decreased 40°F in the next 6 hours.
The change in temperature will be:
= Old temperature - New temperature
= 18°F - (-40°F)
= 18°F + 40°F
= 58°F
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The value in dollar of a $3,000 invetment after n year i given by f(n) = 3,000(1. 05)n. Find the value of the invetment (in dollar) after 4 year. (Round your anwer to the nearet cent. )
The value of investment after 4 years would be $12600
What is investment?
Spending money on an item with the intention of seeing its value rise over time is known as investing. Sacrificing any current item, whether time, money, or effort, is necessary for investment. In the world of finance, investing is done in order to profit from the asset that is being put up for investment.
Main body:
f(n) = 3000(1.05)n
where n= no. of years invested
here n= 4
so total investment = 3000*1.05*4
= $12600
Hence the value of investment is $12600.
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how can i simplify this?
Answer:u dont
Step-by-step explanation:
alfred tried to solve the system of equations shown below. he concluded that the system has an infinite number of solutions. which is the best evaluation of alfred's conclusion? a. he is incorrect. for any positive value of , the corresponding value of is negative, which means the system has no solution. b. he is correct. both equations describe lines that have infinitely many solutions. c. he is incorrect. if the first equation is multiplied by 4 and added to the second equation, the result is , which leads to exactly one solution. d. he is correct. if the first equation is multiplied by 4 and subtracted from the second equation, the result is , which means the system has an infinite number of solutions.
The Correct option is D .
System of linear equations,gives us the result that given system has unique solution such that 13x= 6 or x = 6/13 and y = -40/13 .
If a, b, and c are real numbers, the graph of the equation ax + by = c
is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.
Unique Solution: A system of linear equations has a solution if the graphs intersect at a point.No Solution: If the graph is parallel, the system of linear equations has no solution.Infinitely Many Solutions: There are infinitely many solutions to a system of linear equations if the graph is exactly the same straight line.given system of equations is
2x - y = 4 --(1)
and 5x + 4y = -10 ---(2)
comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2
we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,
c2= -10
Now, the ratio are
a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5
=> a1/a2 not equal to b1/ b2
therefore the given system of equations has unique solution.
Now , we find the soltion of given system using Elimination method,
multipling equation (1) by 4 to making same cofficient of y in both equations of system we get
8x - 4y = 16 --(3) and 5x +4y = -10
adding equation (2) from (3) we get,
8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13
putting this value of x in (1)
2×6/13 - y = 4 => y = 12/13-4 = -40/13
Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.
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Complete Question:
Alfred tried to solve the system of equations shown below..
2x - y = 4 and 5x + 4y = -10
He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?
He is correct. Both equations describe lines that have infinitely many solutions.
He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.
He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.
He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.
-4|w-16|+9=39
solve for w
Answer:
There is no solution because after solving the absolute value, the number will be multiplied by -4 which would be getting positive 9 impossible.
Which statement best reflects the solutions of the equation X over X minus one minus one over X -2 equals 2X -5 over X squared minus 3X +2
The statement which best reflects the solutions of the equation; as given in the task content is; x = 3 is a valid solution and x = 2 is an extraneous solution.
What is the solution of the equation?It follows from the task content that the statement which represents the solution of the given equation be determined.
Since the given equation can be written algebraically as follows;
x/(x - 1) - 1/(x - 2) = (2x - 5) / (x² - 3x + 2)
By observation; (x - 1) (x - 2) = x² - 3x + 2.
Therefore, by multiplying through the equation by; x² - 3x + 2; we have;
x (x - 2) - 1 (x - 1) = 2x - 5
x² - 2x - x + 1 = 2x - 5
x² - 5x + 6 = 0.
Hence, the equation above can be solved quadratically so that we have;
(x - 3) (x - 2) = 0.
Therefore, the solution to the given equation is; x = -3 Or x = 2.
However, the solution x = 2 renders the equation undefined, hence, it is not a valid solution but an extraneous solution.
Therefore, the statement which reflects the solutions to the given equation is; x = 3.
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Function g can be thought of as a translated (shifted) version of f(x) = x^2
The new function's equation is g(x) = (x - 2)² + 6
Given,
The parent function, f(x) = x²
We have to determine the equation for the new function g(x)
Vertical shift:
The parent function is clearly pushed 6 units upward from the graph.
The general formula to increase the c units on the graph is f(x) + c
As a result, by using the rule, the new function g(x)of vertical shift is provided by g(x) = x² + 6
Horizontal shift:
It is clear from the graph that the parent function has been moved 2 units to the right.
To move the graph's c units to the right, follow this basic formula: f(x - c)
Consequently, the new function g(xhorizontal )'s shift is given by g(x) = (x - 2)²
The new function g( x ) is as follows:
The equation results in the new function being shifted 2 units to the right and 6 units upward.
g(x) = (x - 2)² + 6
Therefore, the new function's equation is g(x) = (x - 2)² + 6
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Bumper car A (281 kg) moving
+2.82 m/s makes an elastic
collision with bumper car B
(209 kg) moving +1.72 m/s.
What is the velocity of car A after
the collision?
(Unit = m/s)
Remember: right is +, left is -
Enter
After collision, Car A moves with a velocity of 4.1 m/s
Elastic CollisionAn elastic collision is a collision in which there is no net loss in kinetic energy in the system due to the collision. Both momentum and kinetic energy are conserved in an elastic collision. It can be either one-dimensional or two-dimensional. In the real world, perfectly elastic collision is impossible because there is bound to be some energy conversion, however small. However, though there is no change in the linear momentum of the whole system, there is a change in the individual momenta of the involved components, which are equal and opposite in magnitude and cancel each other out and the initial energy is conserved.
The formula of elastic collision is given as
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Assuming after collision, car B has a velocity of 0m/s
281(2.82) + 209(1.72) = 281 * v + 0
792.42 + 359.48 = 281v
1151.9 = 281v
v = 1151.9 / 281
v = 4.1 m/s
The velocity of car A after collision is 4.1 m/s
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Given that
4x:3=11:5
Calculate the value of x.
Answer:
THE ANSWER IS x= 33/20
hope it help
with the steps:
1) Multiply all terms by the same value to eliminate fraction denominators
2) Cancel multiplied terms that are in the denominator
3) Multiply the numbers
1) 4x//3==11/5 then 15 ✖️ 4x/3= 15 ✖️ 11/5
2) 5 ✖️ 4= 3 ✖️ 11
3) 5 ✖️ 4x=3 ✖️ 11
20x=3 ✖️ 11
solution : x= 33/20
Answer:
x = [tex]\frac{33}{20}[/tex]
Step-by-step explanation:
[tex]\frac{4x}{3}[/tex] = [tex]\frac{11}{5}[/tex] cross multiply and solve
20x = 33 divide both sides by 20
x = [tex]\frac{33}{20}[/tex]
You buy a basket of 24 strawberries. You eat them as you walk to the beach. It takes the same amount of time to walk each block. When you are halfway there, half of the berries are gone. After walking 3 more blocks, you still have 5 blocks to go. You reach the beach 28 minutes after you began. One-sixth of your strawberries are left.
You walked
blocks in 28 minutes. At this rate you walk 1 block in
minute(s)
second(s).
Addison and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $5 and a drink for $4.25. How much would it cost if they bought 8 bags
of popcorn and 4 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Really hope this helps you!
The figure shows the reflex angle BOD measures 3,5y and AOB measures y. Find the measure of the non-felex DOB in degrees.
The measure of the non-felex DOB in degrees is 140°.
How to calculate the angle?It is important to note that the value of the angles at a point is 360°.
Therefore, it should be noted that also vertically opposite angles are equal.
Therefore, the angles will be:
3.5y + 3.5y + y + y = 360°
9y = 360°
Divide
y = 360° / 9
y = 40°
Therefore, DOB will be:
= 3.5y.
= 3.5 × 40
= 140°
DOB is 140°.
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The graph of the function, f(x) = x2 - 5x - 7 opens
and has a
value.
The two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14).
What is a general equation of a quadratic equation?The general equation of a quadratic equation is -
y = ax² + bx + c
It has two possible roots. It has a degree of 2.
Given is the graph of the function, f(x) = x² - 5x - 7.
We have the following -
f(x) = x² - 5x - 7.
We will draw the graph of this function.
Now, the graph cuts the [x] axis at (-1.14) and (6.14).
Therefore, the two solutions of the quadratic equation are f(x) = x² - 5x - 7 are (-1.14) and (6.14). The graph opens upwards.
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On a scale drawing, a building has length 12.4 cm and width 9.4 cm. The real length of the building is 62 metres. Work out, in metres, the real width of the building.
The real width of the building is given by 47 meters.
Given that the actual length of the building is 62 meters.
In a scale drawing, the length of the building is 12.4 cm.
So, 12.4 cm = 62 meters
1 cm = 62/12.4 = 620/124 = 5 meters.
Also given that the width of building on scale drawing = 9.4 cm
Hence the real width of the building = 9.4 * 5 = 47 meters.
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A triangle has two sides of length 12 and 18. What is the smallest possible whole-number length for the third side?
Answer:
7
Step-by-step explanation:
You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.
Triangle inequalityThe triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...
x +12 > 18
x > 6 . . . . . . subtract 12
The smallest integer greater than 6 is 7.
The third side must be at least 7 units long.
__
Additional comment
Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.
i need help with this question i will give brainliest!!
Answer:
Question 1 is G.
Question 2 is B
Question 3 is D
Question 4 is A.
Step-by-step explanation:
Katherine drove home from college traveling an average speed of 65.1 mph and drove back to the college the following week at an average speed of 70.7 mph. If the total round trip took 7 hours, how much time did it take Katherine to drive from home back to college? Express the time in hours and minutes. Round to the nearest minute.
The number of time it take Katherine to drive from home back to college is: 3 hrs 21 min.
How to find the time?Going home:
Rate = 65.1 mph , distance = x miles ; time = distance /rate = x/ 65.1 hrs
Going to college:
Rate = 70.7 mph ; distance = x miles ; time = x/70.7 hrs
Equation:
x/70.7+ x/ 65.1= 11
70.7x + 65.1x = 7 × 65.1 × 70.7
Combine like terms
135.8x = 32,217.99
Divide both side by 135.8x
x = 32,217.99/ 135.8
x = 237.25 miles
Home back to college
= 237.25 /70.7
=3.35 hrs
= 3 hrs 21 min
Therefore it take Katherine 3 hrs 21 min.
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Laurie earns $7. 50 per hour at the fruit stand plus an extra $2. 00 per hour on sundays. One week in august, she worked on sunday, monday, and wednesday. She worked the same number of hours on monday and on wednesday. On sunday she worked 4 hours. If she earned a total of $83. 00 for the week, how many hours did laurie work on monday? enter and solve an equation.
If she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be 3.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given,
if she put in the same amount of time on Wednesday and Monday. She worked 4 hours on Sunday. The amount of hours Laurie will work on Monday if she earns a total of $83.00 for the week will be: 3.
$7.5= 1 hour various days
Sunday: $9.50 or ($7.50+$2.00) = 1 hour
Sunday = 4 + $9.50 = 38
Let Monday equal x $7.5 = 7.5x.
Let Wednesday equal x $7.5 equal x.
Let the total income be $83
Let x be the amount of hours.
Hence:
The first step is to create
Equation:
7.5x+7.5x+38=83
The next step is to determine the number of hours Laurie worked on Monday.
x =83-38÷ 7.5+7.5
x=83-38÷15
x=45÷15
3 hours = x
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writr equivalnt fractions for 2 2/3 and 2 1/4 using common denominator.
2 2/3 + 2 1/4= 2 ?/? + 2 ?/?
The value of the fraction 2 2/3 + 2 1/4 is 4 11/12.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the addition of the fraction will be:
= 2 2/3 + 2 1/4
= 2 8/12 + 2 3/12
= 4 11/12
The value is 4 11/12.
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I have two turtles. Today, the older turtle's age is $11$ times that of the younger turtle. In $24$ years, the older turtle's age will only be $7$ times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be $3$ times that of the younger turtle?
Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500
How to solve Algebra Word Problems?
Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;
(x/6) - (x/5) = 50
Multiply by 30 to get;
5x - 6x = 1500
-x = 1500
x = -1500
Let the older turtle be represented x and the younger one be y.
Todays age,
Older turtle = 11y years
Younger turtle = y years
Also the equation form as;
11y + 24 = 7(y + 24)
11y + 24 = 7y + 168
11y - 7y = 168 - 24
4y = 144
y = 144/4
y = 36
Thus;
Age of older turtle today = 396 years
Age of younger turtle today = 36 years
Therefore,
3(36 + t) = 396 + t
108 + 3t = 396 + t
2t = 292
t = 292/2
t = 146 years
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Step-by-step explanation:
Find the area of the triangle.
A=?in^2
Answer:
7.5 in²
Step-by-step explanation:
You want the area of a triangle shown as having a base of 6 inches and a height of 2.5 inches.
AreaThe formula for the area of a triangle is ...
A = 1/2bh
where b is the base length, and h is the height.
ApplicationThe figure shows the base of the triangle as 6 in, and the height as 2.5 in. This means the area is ...
A = 1/2(6 in)(2.5 in) = 7.5 in²
__
Additional comment
The attachments show the triangle to be overs-specified. If the side dimensions are correct, the area is actually about 7.48 square inches. If the base and height are correct, at least one side length is slightly off.
In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x)=log(x), to achieve the graph of g(x)=log(-3x+9) + 4
The graph g(x)=log(-3x + 9)+4 is the outcome of a transformation on the function, f (x) = log (x), which can be visualized as a reflection across the y-axis. Then you contract by a factor of 3 horizontally, 3 to the right, and 4 to the up.
What is a function?The connection between an independent variable and a dependent variable is established by a mathematical expression, rule, or law (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function:
Parent function: f(x) = log(x)
Transformation function: g(x) = log(-3x + 9) + 4
Step 1 - Shift 3 unit right, to achieve the function
y = log (x - 3) (x - 3)
Step 2 - Reduce the graph by thrice by multiplying x by three:
y = log 3(x - 3) (x - 3)
Step 3 - The formula y = log 3(x - 3) to line -3 = x is to be reflected to obtain: y = -3 (x - 3)
Step 4 - The function y = log 1 - 3(x - 3) should be translated by four units to reach
Therefore, the function can be transformed by reflection and translation.
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4.43 overweight baggage. suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. most airlines charge a fee for baggage that weigh in excess of 50 pounds. determine what percent of airline passengers incur this fee.
The percentage of airline passengers covered by this fee is 85.99%.
If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is
less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.
This is the p-value of Z for X = 50 minus 1 as a
ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%
So, 85.99% of the airline passengers pay this fee.
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Graph the line with y-intercept 3 and slope -4/3
The line graphed with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m=(y₂-y₁) / (x₂-x₁)
It is given that, the line is having the y-intercept 3 and slope -4/3.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
The equation with the y-intercept 3 and slope -4/3 is,
y=mx+c
y= -4/3x+3
3y= -4x+9
Thus, the line graph with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.
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HELP PLEASE!!!! I don't understand this.
Answer:
1 yes y does vary directly with x
2 to find slope apply the given formula,
y2-y1/m2-m1
2/3 is slope
then the equation should be
y=2/3x
good luck
the function h(x) is a transformation of the square root parent function
f(x)=[tex]\sqrt{x}[/tex]. what function is h(x)
The function h(x) is a translation of 4 units to the left, so the correct options is B.
h(x) = √(x + 4)
What is the rule for function h(x)?We know that h(x) is a transformation on the parent square root function:
f(x) = √x
If we look at the graphs, we can see h(x) is translated 4 units to the left.
Now, for a function f(x), we define a horizontal translation of N units as:
h(x) = f(x + N)
if N < 0, the translation is to the right.
if N > 0, the translation is to the left.
In this case we have a translation of 4 units to the left, then N = 4, so we can write:
h(x)= f(x + 4)
Replacing the function f(x) we get:
h(x) = √(x + 4)
So the correct option is B.
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Find the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above
the diagonal, and 0’s below the diagonal.
The determinant of nxn matrix A 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.
From the given information, the matrix will appear as follows
[tex]A= \left[\begin{array}{ccccc}2&1&......&1 &1\\0&2&......&1 &1\\0&0&2 ......&1 &1\\0&0&0 ......&2 &1\\0&0&0 ......&2 &1\\0&0&0 ......&0 &2\end{array}\right][/tex]
The matrix is nxn, there are n rows and n columns. As we can see, this matrix has an upper diagonal, and in terms of linear algebra, its determinant is the sum of all its principal diagonal members. As a result, the matrix's determinant is: 2^n
Therefore, the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.
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