The yearly membership cost plus the cost per visit was set equal to the non-member cost per visit, and solving the equation gave us the result.
We need to find the number of visits it would take for the total cost of a member and a non-member to be the same if they both use the waterpark at each visit. Let's denote the number of visits as x.
The yearly membership cost is $275, and each visit to the waterpark costs an additional $5 for a member. So, for x visits, the total cost for a member is:
Member cost = $275 + $5x
Non-members pay $6 for parking, $15 for admission to the park, and $9 for the waterpark per visit. Therefore, the total cost for a non-member is:
Non-member cost = ($6 + $15 + $9)x = $30x
Setting both costs equal to find the number of visits where the costs are the same:
$275 + $5x = $30x
Now we solve for x:
$275 = $30x - $5x
$275 = $25x
x = $275/$25
x = 11
Therefore, it would take 11 visits for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.
Please help. Question in photo
3/5 = blue shirts
5/8 of 3/5 = on sale blue shirts
1/3 of 5/8 of 3/5 = medium on sale blue shirts
‘Of’ can be replaced by multipication symbols.
1/3 • 5/8 • 3/5
1/3 • 3/5 = 3/15 (or 1/5)
3/15 • 3/5 = 9/75 (or 3/25)
9/75 of the shirts are medium, on sale, and blue. If you wanted to simplify this it would just be 3/25 of the shirts.
What is the slope of the line that passes through the points (−4,0) and (2, 0)? Write your answer in simplest form.
since both points have a y- coordinate of zero, this is a horizontal line parallel to the x- axis
hence slope = 0
We want to find the slope of a line given that we know two points on the line.
We will see that the slope of the line is 0.
Generally, if we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we know that the line passes through (-4, 0) and (2, 0) then the slope will be:
[tex]a = \frac{0 - 0}{2 - (-4)} = 0[/tex]
The slope is equal to zero, meaning that this is a horizontal line (as you can see in the points, the y-component does not change).
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In training for a swim meet, Logan swam 750 meters in 1/3 of an hour. His swimming partner Mila, swam 2/3 of Logan's distance in 1/4 of an hour. What is Logan's average swimming speed?
The relationship between speed, distance, and time is easily remembered when you consider that speed is written in terms of units of distance per units of time. (miles per hour, or kilometers per hour, for example) Of course "per" means "divided by".
speed = distance/time
speed = (750 m)/(1/3 h) = 2250 m/h = 2.25 km/h
Logan's average speed is 2.25 kilometers per hour.
What values of x must be excluded from the domain of
f(x) = x + 7
_____
x^2 - 5x -6
A ) x =1 and x =-6
B ) x = -1 and x=6
C ) x= -7
D ) x = 2 and x = 3
E ) x = -6 and x = -7
Answer:
B) x = -1 and x = 6
Step-by-step explanation:
The values that must be excluded from the domain are the values for which f(x) is undefined. Those values are the ones that make the denominator be zero.
We can find the zeros of the denominator by factoring.
... x² -5x -6 = (x +1)(x -6)
The product is zero when either factor is zero, so when x=-1 or x=6.
Answer:
c
Step-by-step explanation:
-2 & 6
The look-out point of a lighthouse is 50 feet above sea level. A woman observes a boat in the water from the look-out point. The angle of depression to the boat in the water is 20°.
What is the distance from the base of the light house to the boat in the water?
Answer:
137.4 feet
Step-by-step explanation:
Consider the attached diagram. The given angle of depression from the lighthouse to the boat is the same as the angle of elevation from the boat to the lighthouse. The trig relationship for tangent tells you ...
... tan(20°) = opposite/adjacent = AL/AB = 50'/AB
Solving for AB, we get
... AB = 50'/tan(20°) ≈ 50'/0.36397
... AB ≈ 137.4'
Answer:
137.373871
Rounded to the 10th place
137.4
Rounded to the whole number
137
Step-by-step explanation:
There are a few methods for solving this type of problem. Please view the images I have provided. I gave two methods for solving this problem.
11 and 1/6 as a decimal
Assuming that you meant "11 plus 1/6" written as the equivalent decimal expression, then it'd be 11.16666.... Here the 6 repeats indefinitely.
what is 1 and 1/4% of 200?
The equation of a line is 6x-2y=12. Find the x-intercept and the y-intercept.
a.x = -2 , y= 6
b.x = 2 , y= -6
c.x = -2 , y= -6
a.x = 2 , y= 6
Which shows the line 3x -2y = -18 in slope-intercept form?
y=3/2x+9
y=2/3x+9
y=-3/2x-9
y=2/3x-9
A line passes through the point (-1,3) and has a slope of -2. What is the equation of the line in slope-intercept form?
y=2x+5
y=-2x+5
y=2x+1
y=-2x+1
A line passes through the points (1,7) and (-4,-3). What is the equation of the line in standard form?
4x-2y=10
4x+2y=10
4x-2y=-10
4x+2y=-10
Which points are a solution to the inequality <−3+4? (Choose all that apply)
(Select all that apply.)
(0,4)
(-2,7)
(3,-4)
(-1,-5)
First four is BBBC，The last one doesnt make sense to me，you probably didnt write it right
Answer:s
Step-by-step explanation:
Please answer and give an explanation!! 22 Points!!
Filling in 16 for a, we have ...
... lower limit ≤ heart rate ≤ upper limit . . . . . . . this is the meaning of upper and lower limits
... 0.5×(220 -16) ≤ heart rate ≤ 0.9×(220 -16) . . . . . substitute given expressions
... 0.5×204 ≤ heart rate ≤ 0.9×204 . . . . . . . . . . . . . begin expression evaluation
... 102 ≤ heart rate ≤ 183.6
what is the square root √−100=__+___i
the answer is:
√100 = 0 + 10 i
hope this helps! :o)
Figure ABCD is a parallelogram with point C (3, −2). Figure ABCD is rotated 90° counterclockwise to form figure A′B′C′D′. What coordinate would be the output for point C'?
C' (2, −3)
C' (−2, 3)
C' (2, 3)
C'(2, 3 )
under a counterclockwise rotation about the origin
a point (x, y ) → (- y, x ) hence
C(3, - 2 ) → C'(2, 3 )
Answer:
C' (2, 3)
Step-by-step explanation:
Remember that when you are rotating something 90 degrees and counter clockwise you just need to interchange the X and Y values, and change the value of the new X to a negative position because it woul be located in the second quarter:
(x,y) rotated 90º counter clockwise= (-y,x)
(3,-2)=(-(y),x)=(-(-2),(3)=(2,3)
So the answer would be C' (2, 3)
Since it's Wednesday, Buy for Less gives a 5% discount for purchases. The items in Rhonda's cart total $53.75. She needs to know the cost of the items with the discount. So, she multiplies 5% times $53.75 and subtracts the amount from $53.75. Which expression would give Rhonda the same result in one step? A) .90(53.75) B) .95(53.75) C) 1.05(53.75) D) 53.75 - .05(53.75)
she needs to count how much 90% is so
85.00 times 90%
or 8500 times 0.9
Answer:
B) .95(53.75)
Step-by-step explanation:
5% is equal to 0.05. So the following expressions are equivalent.
5% × 53.75 = 0.05 × 53.75
To find the final price, she first takes the 5% and then subtracts the amount from 53.75. That is,
53.75 - 5% × 53.75 = 53.75 - 0.05 × 53.75
We can take out the common factor 53.75
53.75 . (1 - 0.05) = 53.75 . 0.95 = 0.95 . 53.75 = 0.95 (53.75)
At a bargain store.Tanya bought 5 items that each cost the same amount. Tony bought 6 items that each cost the same amount, but each was $1.75 less than the items that tanya bought. both tanya and Tony paid the same amount of money. what was the individual cost of each person's items?
(A) write an equation. let x represent the cost of one of tanya's items.
(B) solve the equation. show your work
(C) check your solution. show your work
(D) state the solution in complete sentences.
(A) For x representing the cost of one of Tanya's items, her total purchase cost 5x. The cost of one of Tony's items is then (x-1.75) and the total of Tony's purchase is 6(x-1.75). The problem statement tells us these are equal values. Your equation is ...
... 5x = 6(x -1.75)
(B) Subtract 5x, simplify and add the opposite of the constant.
... 5x -5x = 6x -6·1.75 -5x
... 0 = x -10.50
... 10.50 = x
(C) 5x = 5·10.50 = 52.50
... 6(x -1.75) = 6·8.75 = 52.50 . . . . . the two purchases are the same value
(D) The individual cost of Tanya's iterms was $10.50. The individual cost of Tony's items was $8.75.
On the packaging for a triangular sail, the edge measurements for the sail are listed as 7ft x 15ft x 17ft without unfurling the sail, you want to determine if the sail forms a right triangle, an acute triangle or an obtuse triangle
The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...
... c² = a² + b² -2ab·cos(C)
Then
... cos(C) = (a² +b² -c²)/(2ab)
We don't actually need the angle. We only need to know the sign of the cosine.
... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°
The sail has the shape of an obtuse triangle.
_____
A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.
The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...
... c² = a² + b² -2ab·cos(C)
Then
... cos(C) = (a² +b² -c²)/(2ab)
We don't actually need the angle. We only need to know the sign of the cosine.
... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°
The sail has the shape of an obtuse triangle.
_____
A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.
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Which dimensions can create only one unique triangle?
three angles measuring 25, 65, and 90
three angles measuring 50, 50, and 50
three sides measuring 5 in., 12 in., and 14 in.
three sides measuring 4 ft, 8 ft, and 14 ft
When only angles are specified, the sides can be any length, so the triangle is not unique. In any event, the sum of angles must be 180°, so three angles measuring 50° cannot be closed to form a triangle.
Three sides measuring 4, 8, and 14 ft cannot be closed, either, as the long dimension exceeds the sum of the other two. The ends can't meet.
The appropriate choice is the 3rd one ...
... three sides measuring 5 in, 12 in, and 14 in.
Answer:
B three sides measuring 5 in, 12 in, and 14 in
Step-by-step explanation:
the three angles measuring 25, 65, and 90 is 180 and can make more triangle.
the three angles measuring 50, 50, and 50, doesn't even add up to 180 degrees.
the three sides measuring 4 ft, 8 ft, and 14 ft can make more triangles.
I got this right in my test and I got it right.I hope this helps you
Locating Zeros of Polynomial Function:
Determine the number of complex zeros
In a previous question about this function, you determined that there were two (2) real zeros, near -1.4 and +3.4. (q: question/11280846)
Since this is a 4th degree polynomial, there are 4 zeros total, so two complex zeros.
_____
The factorization is
... f(x) = (x² -2x -5)(x² -x +1)
The latter factor has zeros at 0.5±i·0.5√3.
EASY BRAINLIEST!
Which are perfect squares? Check all that apply.
9
24
16
200
169
625
The correct answers are;
A. [tex]3x^{2} =9[/tex]
C. [tex]4x^{2} =16[/tex]
E. [tex]13x^{2} =169[/tex]
F. [tex]25x^{2} =625[/tex]
Hope this helps!!!!
The numbers that are perfect squares include 9, 16, 169, and 625.
Perfect squares mean a number that's generated when two equal integers are multiplied together by each other.In this case, numbers that are perfect squares include 9, 16, 169, and 625. They're the squares of 3, 4, 13, and 25 respectively.In conclusion, the numbers that are perfect squares include 9, 16, 169, and 625.
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Find the average rate of change of f ( x ) = -2x^2 + 4x + 2 as X varies from 1.2 to 3.8
Here we need to find the average rate of change of [tex]f(x)[/tex].
Now,
[tex]f(x)=-2x^2+4x+2[/tex]
Let us find out the value of [tex]f(x)[/tex] at the point [tex]x=1.2[/tex].
Plugging [tex]x=1.2[/tex] in the equation we get:
[tex]f(1.2)=-2(1.2)^2+4(1.2)+2=-2\times 1.44+4.8+2=-2.88+4.8+2=3.92[/tex]
So,
[tex]f(1.2)=3.92[/tex]
Now calculating the value of [tex]f(x)[/tex] at [tex]x=3.8[/tex].
[tex]f(3.8)=-2(3.8)^2+4(3.8)+2=-2(14.44)+15.2+2=-28.88+15.2+2=-11.68[/tex]
So,
[tex]f(3.8)=-11.68[/tex]
Now that we have the values of the function at two distinct points, we can find the average by using the formula given below:
[tex]Avg= \frac{sum}{n}[/tex], where 'n' represents the number of values and that is two in our case and sum represents the sum of the values of the function.
Therefore,
[tex]Avg= \frac{3.92+(-11.68)}{2} =\frac{-7.76}{2} =-3.88[/tex]
So, the average rate of change of the function [tex]f(x)[/tex] from 1.2 to 3.8 is [tex]-3.88[/tex].
PLZ HELP ME GEOMETRY
AM I CORRECT?
Yes, the S. A. S. postulate is correct, because his proof stated two sides and the angle between those sides are congruent.
You're right. There is nothing in the text about a third side or a second angle, and doesn't say anything about the hypotenuse.
3. The equation y = 12x describes the amount of money Louis earns, where x is the number of hours he works and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl’s Earnings
Time: 3 5 8 10
Money Earned: 45 75 120 150
(a) How much money does Carl earn per hour? Show your work. Write your answer in a complete sentence.
(b) Who earns more per hour? Justify your answer. Write your answer in a complete sentence.
(c) Draw a graph that represents Carl’s earnings over time in hours. Remember to put a title, label the axes and use an appropriate scale. Use a ruler or straightedge to draw your lines.
Answer:
15 per hour
Carl earns more
Step-by-step explanation:
Carl's earnings = earnings/no ofhours
We select any hour and corresponding earnings say 150 and 10
Earning per hour of Carl = 150/10 = 15 per hour.
b) Carl earns more as 15 >12 hourly rate of other person
c)
Use the identity (x2+y2)2=(x2−y2)2+(2xy)2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6.
let a,b be the two numbers. we know that a2-b2=5 and a*b=6
using the formula we are given
[tex](a^2+b^2)^2 = 5^2 + 12^2 = 169[/tex] we get the solution [tex]\sqrt{169} = 13[/tex]
Answer:
13
Step-by-step explanation:
Let x and y are two numbers. The difference of the squares if the two numbers is 5 and the product of the numbers is 6 such that,
[tex](x^2-y^2)=5[/tex]......................(1)
[tex]xy=6[/tex]..........(2)
We need to find the sum of the squares of two numbers. By using following identities it can be calculated as :
[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]
Using equation (1) and (2) in above equation, we get :
[tex](x^2+y^2)^2=5^2+(2\times 6)^2[/tex]
[tex]x^2+y^2=\sqrt{5^2+12^2}[/tex]
[tex]x^2+y^2=13[/tex]
So, the sum of squares of two numbers is 13. Hence, this is the required solution.
If the greatest possible error of a measurement is 1/32 inches, what is the actual precision of this measurement?
Answer:
1/16 in
Step-by-step explanation:
The largest possible error in representing a number is half the unit of precision. Here, the error is said to be 1/32 in. That is half of 1/16 in. So, the unit of precision must be 1/16 in.
I really need help with this!
Since all triangles in these questions are similar, we use that the ratios of corresponding sides are equal
(1)
[tex]\frac{y}{6}[/tex] = [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex]
solving [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex] ( cross-multiply )
5x = 36 ( divide both sides by 5 )
x = [tex]\frac{36}{5}[/tex]
solving [tex]\frac{y}{6}[/tex] = [tex]\frac{5}{4}[/tex]
4y = 30 ⇒ y = [tex]\frac{15}{2}[/tex]
(2)
let h be the height of the flagpole, then
[tex]\frac{h}{5.5}[/tex] = [tex]\frac{50}{4}[/tex]
4h = 275 ⇒ h = 68.75 feet
(3)
[tex]\frac{x}{6}[/tex] = [tex]\frac{93.5}{12.75}[/tex]
12.75x = 561 ⇒ x = 44 feet
ASAP PLZ HELP GEOMETRY BELOW
Answer:
i think is d
Step-by-step explanation:
I thought of a number, added 4 5/7 to it, and got the number equal to the original one times 12. What was the original number?
Answer:
[tex]\frac{3}{7}[/tex]
Step-by-step explanation:
The number you thought of and original number = x
The number you thought of and added [tex]4\frac{5}{7}[/tex] and got the number equal to the original on times 12
[tex]x +4\frac{5}{7} = 12x[/tex]
Convert [tex]4\frac{5}{7}[/tex] to an improper fraction so it will be easier to work with.
[tex]x +\frac{33}{7} = 12x[/tex]
[tex]\frac{33}{7} = 12x - x[/tex]
[tex]\frac{33}{7} = 11x [/tex]
[tex]\frac{\frac{33}{7}}{11} = \frac{11x}{11} [/tex]
[tex]\frac{33}{7} * \frac{1}{11} = x [/tex]
[tex]\frac{3}{7} = x [/tex]
[tex]x = \frac{3}{7}[/tex]
The original number that the student thought of in the problem can be found by solving the algebraic equation x + 4 5/7 = 12x. After converting the mixed fraction to an improper fraction and simplifying, the original number is 33/77.
Explanation:The original question is a kind of algebra problem. Let's denote the original number as x, according to the student's description, it follows this formula: x + 4 5/7 = 12x. To solve this equation, you need to collect terms involving x on one side. This gives you 11x = 4 5/7.
Next, convert 4 5/7 to an improper fraction. That gives you 33/7. So, your equation now is 11x = 33/7. Finally, solve for x by dividing both sides of the equation by 11, x = 33/77. This is your original number.
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0.2(6x+1)/3.6 = 0.5x/9
The numbers are a bit ugly, but the equation can be solved as is.
... 1.2x/3.6 + (0.2/3.6) = 0.5x/9 . . . . use the distributive property on the left
... x(1/3 -1/18) + 1/18 = 0 . . . . . subtract the right side, simplify fractions
... x(6/18 -1/18) = -1/18 . . . . . . . use 18 for common denominator
... 5x = -1 . . . . . . . . . . . . . . . . . multiply by 18
... x = -1/5 . . . . . . . . . . . . . . . . divide by 5
_____
You can eliminate decimals and fractions by multiplying the given equation by 18.
... 6x +1 = x
... 5x +1 = 0
... 5x = -1
... x = -1/5
_____
The fraction simplification can work like this:
... 0.2/3.6 = 2/36 = 1/18
... 0.5/9 = (1/2)/9 = 1/(2·9) = 1/18 . . . . or . . . . (0.5)/9 × (2/2) = (0.5·2)/(9·2) = 1/18
Answer:
x=-0.2
Step-by-step explanation:
The given equation is
[tex]\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}[/tex]
We need to solve the given equation for x.
On cross multiplication we get
[tex]9[0.2(6x+1)]=3.6(0.5x)[/tex]
[tex]1.8(6x+1)=1.8x[/tex]
Using distribution property, we get
[tex]1.8(6x)+1.8(1)=1.8x[/tex]
[tex]10.8x+1.8=1.8x[/tex]
Subtract 1.8x and 1.8 from both sides.
[tex]10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8[/tex]
[tex]10.8x-1.8x=-1.8[/tex]
[tex]9x=-1.8[/tex]
Divide both sides by 9.
[tex]x=-\frac{1.8}{9}[/tex]
[tex]x=-0.2[/tex]
Therefore, the value of x is -0.2.
Write the equation of line in slope-intercept form. Line parallel to y=−2x+3 that passes through the point (−100,−100)
Remark
The line you want is parallel to y = - 2x + 3
That means it has the same slope as the given line. The given line has a slope of -2
y = -2x + b is what you have so far. Now you have to use the point to get b
y = - 100
x = - 100
Solve for b
-100 = -2(-100) + b
-100 = 200 + b Notice the sign change. Two minus's make a plus. Subtract 200 from both sides.
- 100 - 200 = b
- 300 = b
Answer
y = - 2x - 100
The line with equation y = -2x + 3 has a slope of -2
The line parallel to line with equation y = -2x + 3 has a slope of -2
This is because parallel lines have the same slope
Taking a point (x,y) along the parallel line passing through (-100,-100)
Slope = change in y-axis divide by change in x-axis
-2 = (y - -100) ÷ (x - -100)
-2(x + 100) = y + 100
y = -2x - 300
Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.
Solve the given expression for the sum of the two numbers:
[tex] x+y = \dfrac{x^3+y^3}{x^2-xy+y^2} [/tex]
which you can rewrite as
[tex] x+y = \dfrac{x^3+y^3}{x^2+y^2-xy} [/tex]
Now, we are given the product of the numbers (i.e. xy) to be 10, the sum of the squares of the numbers (i.e. [tex] x^2+y^2 [/tex]) to be 29, and the sum of the cubes of the numbers (i.e. [tex] x^3+y^3 [/tex]) to be 133.
If we plug these values in the formula written above, we have
[tex] x+y = \dfrac{133}{29-10} = \dfrac{133}{19} = 7 [/tex]
Each student needs 35 craft sricks for an art project. The art teacher has 7,140 craft sticks. How many students can get craft stick from teacher?
What number can i use to estimate the quotient?
Explain how to check the answer to a division problem.
Solution.
Answer:
204 students
just do 7140/35= 204
Step-by-step explanation:
Number of students who can get craft sticks are 204 .
To determine how many students can get craft sticks from the teacher, we need to divide the total number of craft sticks by the number of craft sticks each student needs.
Step-by-Step Solution
The total number of craft sticks is 7,140.
Each student needs 35 craft sticks.
To find out how many students can get the craft sticks, divide the total number of craft sticks by the number of craft sticks each student needs:
7,140 ÷ 35 = 204
Therefore, 204 students can get craft sticks from the teacher.
Estimation and Checking
To estimate the quotient, you can round the numbers to make the division easier. For example, round 7,140 to 7,000 and 35 to 30:
7,000 ÷ 30 ≈ 233.33
This estimation tells us that our division answer is reasonable, falling close to this rounded solution.
To check the division, multiply the quotient by the divisor and see if you get the original dividend:
204 × 35 = 7,140
Since the result matches the original number of craft sticks, the answer is verified as correct.
PLZ HELP ASAP GEOMETRY
Josh is building an enclosure with recycled cardboard for his collection of model cars. His design is as shown below:
What is the length of side BC in inches?
a. 14
b. 42
c. 49
d. 63
the correct answer is 63 because they are multiplying the length of each side by 7.
Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given two figures:
John's design is similar to Josh's project.
ML = 8 inches
CD = 56 inches
KL = 9 inches
We need to find value of 'BC'.
So, there ratio would be :
[tex]\dfrac{ML}{CD}=\dfrac{KL}{BC}\\\\\dfrac{8}{56}=\dfrac{9}{BC}\\\\\dfrac{1}{7}=\dfrac{9}{BC}\\\\BC=9\times 7\\\\BC=63\ inches[/tex]
Hence, Option 'd' is correct.