Part (a)
The variable y is the dependent variable and the variable x is the independent variable.
Part (b)
The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:
[tex]0.75\times 18=13.5[/tex] dollars
Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.
Therefore, the price of the fair admission is: $33.50-$13.50=$20
If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be written as:
[tex]y=0.75x+20[/tex]......Equation 1
Part (c)
The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.
Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.
You are constructing a tangent line from a point outside a given circle to the circle is to draw a circle and a point outside the circle. You have drawn the circle, a point outside the circle and connected the center of the circle to the point outside the circle. You found the midpoint of the segment. Next you must use your compass. After you set it, where should you put the point?
Answer choices
A) The center of the circle
B) The point outside the circle
C) The midpoint of the segment
D) The intersection of the segment and the circle
Answer: Option C) The midpoint of the segment.
Then, you draw a circle with radius the half of the distance between the center of the circle and the point outside the circle.
The tangency points are the points where this circle cuts the given circle.
How do you solve this equation?
5-3z-18= z-1+ 8z
Thanks
The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario.
Answer:
B
Step-by-step explanation:
The wording in the problem statement is ...
... "less than 3 years"
... "at least 3. but less than 6 years"
so we expect the inequality symbols to look like ...
... 0 ≤ x < 3
... 3 ≤ x < 6
These match the second piecewise function.
Juan is participating in a 40 mile bike race. He will pedal at a steady rate of 11.5 miles per hour. He pedaled for 1 hour and 45 minutes with the wind and for 2 hours and 30 minutes against the wind and finished the race in 4 hours and 15 minutes. What was rate at which the wind was blowing in miles per hour?
To work this problem, you must assume that Juan's pedaling speed adds to the wind speed when going downwind, and that the wind speed subtracts from Juan's pedaling speed going upwind. (In other words, Juan's pedaling speed is relative to the air, not the ground.)
Let w represent the wind speed in miles per hour.
... distance = speed × time
Juan's total distance is 40 miles, so we have ...
... 40 = (11.5 +w)×1.75 + (11.5 -w)×2.50
... 40 = 48.875 - 0.75w . . . . . simplify
... -8.875/-0.75 = w . . . . . . . . subtract 48.875, divide by -0.75
... w = 11.833... = 11 5/6
The wind was blowing 11 5/6 miles per hour.
_____
Compared with real-life experience, and working through the details, this problem makes no sense whatever. Pedaling a bicycle is not like rowing a boat, where the current of the medium directly affects speed.
If you work through the segments of the problem, you find that Juan traveled 40.833 miles with the wind in the first 1.75 hours, so actually finished the race and then some. He spent the next 2.5 hours being blown backward by the wind, even though he was pedaling forward at 11.5 mph. (How much sense does that make?)
Tell what you would do to isolate the variable.
3z = 5
a.
multiply 5 on both sides
c.
multiply 3 on both sides
b.
divide 5 on both sides
d.
divide 3 on both s
3z = 5
To isolate the variable ( solve for z), you need to divide both sides by 3.
The answer is D.
In ΔPQR shown below, segment QS is an altitude:
Triangle PQR with segment SQ drawn from vertex Q and intersecting side RP.
Which of the following is a justification used while proving the similarity of triangles ΔPSQ and ΔQSR?
a. Transitive Property of Equality
b. Addition Property of Equality
c. Definition of an Altitude
d. Definition of Supplementary Angles
Answer:
c. Definition of altitude.
Step-by-step explanation:
We are given that segment QS is an altitude in ΔPQR and we are asked to find a justification used while proving the similarity of triangles ΔPSQ and ΔQSR.
Since we know that altitude meets opposite side at right angles. When QS will intersect line PR we will get two right triangles QSR and QSP right angled at S.
ΔPQR is similar to ΔPSQ as they both share angle P and right triangle. So their third angle should also be similar.
ΔPQR is similar to ΔQSR as they both share angle R and both have a right triangle at Q and S respectively. So they will have their third angle equal.
ΔPQR is similar to triangles ΔQSR and ΔPSQ. Therefore, ΔQSR is similar to ΔPSQ.
Therefore, by definition of altitude triangles ΔPSQ and ΔQSR are similar as ΔPSQ and ΔQSR are created from ΔPQR by altitude QS.
What does the equal? Keep getting it wrong
Answer:
A) -9/4
Step-by-step explanation:
The answer ends up becoming -2.25.
So if you do the math, that's -9/4. or add up 4 until you're at 9.
4, 8. Now we know we have 2 whole. What's left? 1/4.
So now we have, -2 1/4. or "-9/4".
WILL GIVE BRAINLIEST!
Which of the following are ways to express the same probability? Check all that apply.
30%
3/10
1/3
0.3
0.03
30%
3/10
0.3
I think these are the right answers if I am understanding you correctly. :)
30% ✔
3/10 ✔
1/3 ✖
0.3 ✔
0.03 ✖
Hope i Helped ❤
What will be the common denominator when the operation is completed?
7/3 - 8/12x-8
To solve the given operation firat we take LCM for both terms.
As denominator of first term is 3 and second term is [tex] 12x-8 [/tex]
Therefore, the Lcm is [tex]3(12x-8) [/tex]
Now solving and making same denominator for each term
[tex]\frac{7}{3} [/tex] [tex]\times [/tex] [tex] \frac{12x-8}{12x-8} [/tex]
On multiplying we get
[tex]\frac{7(12x-8)}{3(12x-8)} [/tex] [tex]=\frac{84x-56}{3(12x-8)} [/tex]
Now solving other term
[tex]\frac{8}{12x-8} [/tex] [tex]\times [/tex] [tex]\frac{3}{3} [/tex]
On multiplying we get
[tex]\frac{24}{3(12x-8)} [/tex]
Now solving the expression by putting the values
[tex]\frac{84x-56-24}{3(12x-8)} [/tex]
[tex]\frac{84x-80}{12(3x-2)} [/tex]
[tex]\frac{4(21x-20)}{12(3x-2)} [/tex]
On solving we get
[tex]\frac{21x-20}{3(3x-2)} [/tex]
There denominator of the expression is
[tex]9x-6 [/tex]
Hope this will help
The square root of 75 times the square root of 12.
A. the square root of 63
B. 3 times the square root of 7
C. 3 times the square root of 3
D. 8 times the square root of 3
option E) 30 is the answer for the square root of 75 times the square root of 12
We start by using the property of square roots that states the product of two square roots is the square root of the product of the numbers. This gives us:
[tex]\sqrt{75} \times \sqrt{12} = \sqrt {75 \times 12}[/tex]
Now we can simplify the expression by finding the product of 75 and 12. This gives us:
[tex]\sqrt {75 \times 12} = \sqrt{900} = 30[/tex]
Thus, the square root of 75 times the square root of 12 gives 30 as the answer. So, option E) 30 is the correct answer.
Correct question:
The square root of 75 times the square root of 12.
A. the square root of 63
B. 3 times the square root of 7
C. 3 times the square root of 3
D. 8 times the square root of 3
E. 30
These are two angles that are located outside two parallel lines on opposite sides of the transversal.
Answer:
The answer is the angels will be the equivalent.
Explanation:
Lines on a plane that never meet. They are dependably a similar separation separated. Here the red and blue line sections are parallel.In different words, the slants of parallel lines are equivalent. Note that two lines are parallel if their slants are equivalent and they have distinctive y-blocks. As it were, opposite inclines are negative reciprocals of one another. Here is a fast survey of the slant/capture type of a line.
Answer:
Alternate Exterior Angles
Step-by-step explanation:
what is the value of the 4 in 2.704
The value of 2.704 is .004 because it is 3 spaces to the right of the decimal point.
help me out please geometry
Try this option (see the attachment, the answers are marked by red colour), note, the value of the left angle in not visible (task no. 3) >> solution not given.
Will give brainliest!
In the diagram, which pair of angles are alternate interior angles?
2 and 5
1 and 7
5 and 3
7 and 4
"Alternate" angles are on opposite sides off the transversal.
"Interior" angles are between the lines the transversal is crossing.
The appropriate choice for alternate interior angles is ...
... 5 and 3
Answer:
The pair of angles the are alternate interior angles are 5 and 3. Or C.
Step-by-step explanation:
Two circles, called c1 and c2, are graphed below. The center of c1 is at the origin, and the center of c2 is the point in the first quadrant where the line y=x intersects c1. Suppose c1 has radius 2. C2 touches the x and y axes each in one point. What are the equations of the two circles?
Answer:
The equation of [tex]C_{1}[/tex] is: [tex]x^2+y^2=4[/tex]
and the equation of [tex]C_{2}[/tex] is: [tex]x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0[/tex]
Step-by-step explanation:
The standard form of circle equation: [tex](x-h)^2+(y-k)^2 = r^2[/tex] , where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius of the circle.
The center of the circle [tex]C_{1}[/tex] is at origin or at (0, 0) and has radius of 2.
So, the equation of the circle [tex]C_{1}[/tex] will be........
[tex](x-0)^2+(y-0)^2=(2)^2\\ \\ x^2+y^2=4 ..........................................(1)[/tex]
Now, the center of [tex]C_{2}[/tex] is the point in the first quadrant, where the line [tex]y=x[/tex] intersects [tex]C_{1}[/tex]
Solving the equations [tex]x^2+y^2=4[/tex] and [tex]y=x[/tex] , we will get......
[tex]x^2+x^2= 4[/tex] (Substituting [tex]y[/tex] as [tex]x[/tex])
[tex]2x^2= 4\\ \\ x^2=2\\ \\ x=\pm \sqrt{2}[/tex]
So, [tex]y=x = \pm \sqrt{2}[/tex]
Thus, the center of the circle [tex]C_{2}[/tex] will be at [tex](\sqrt{2},\sqrt{2})[/tex] (Negative value is ignored as the point is in first quadrant)
Now, the distance between the center of [tex]C_{2}[/tex] and the x-axis is [tex]\sqrt{2}[/tex] and the circle touches the x-axis only at one point.
That means, the radius of the circle [tex]C_{2}[/tex] will be also [tex]\sqrt{2}[/tex]
So, the equation of the circle [tex]C_{2}[/tex] will be......
[tex](x-\sqrt{2})^2+(y-\sqrt{2})^2= (\sqrt{2})^2\\ \\ x^2-2\sqrt{2}x+2+y^2-2\sqrt{2}y+2=2\\ \\ x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0[/tex]
Write an expression to match the description: 2 less than y
y - 2
Step-by-step explanation:You get 2 less than a value when you subtract 2 from that value.
6 + 10 - 2 = 11 +
how to find the missing number
The missing number can be shown as the variable x.
6 + 10 - 2 = 11 + x
So, you need to figure out what x is by getting it by itself. First, combine everything on the left side of the equation.
16 - 2 = 11 + x
14 = 11 + x
Now, what you do to one side of an equation, you have to do to the other. Subtract 11 from both sides
14 - 11 = 11 - 11 + x Cancel out the 11s and solve the left side.
3 = x
There's your answer! Now you can check your work by trying the 3 in your original problem.
6 + 10 - 2 = 11 + 3
14 = 14
Your missing number is 3.
which beest describes the triangle or triangles, if any, that can be formed with two sides that each measure 5 inches and an angle that measures 60 degrees?
A. one equilateral triangle
B. one isosceles triangle
C. no triangle
D. two different isosceles triangles.
Answer:
One isosceles triangle
Step-by-step explanation:
At an animal rehabilitation center the baby armadillos need to be fed every four hours and the baby bats need to be fed every three hours if the bats and armadillos are both fed at 7:00 AM when will they be fed again at the same time
Answer:
19:00 or 7:00 PM
Step-by-step explanation:
Baby armadillos need to be fed every four hours.
Baby bats need to be fed every three hours.
So we need to figure out when will they be fed again at the same time:
Basically, we need to find the LCM of two numbers i.e. 4 and 3. And the reason why are we finding the LCM is because that time difference will is the least common multiple of both the time differences, it is the smallest non-zero number that is the multiple of both 4 and 3.
The LCM of 4 and 3 is 12. So the time when they will be fed again at the same time will be 12 hours after 7:00 AM that is 19:00 hours or 7:00 PM.
Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the nearest tenth of a percent, what is the rate of interest on the account?
Invested amount (P) = $300.
Time in years (t) = 2 years.
Balance after 2 years (A) = $329.49.
Let us assume rate of interest = r % compounds annually.
We know, formula for compound interest
[tex]A=P(1+r)^t[/tex]
Plugging values in formula, we get
[tex]329.49=300(1+r)^2[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}300[/tex]
[tex]\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}[/tex]
[tex]\left(1+r\right)^2=1.0983[/tex]
Taking square root on both sides, we get
[tex]1+r=\sqrt{1.0983}[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]1+r-1=\sqrt{1.0983}-1[/tex]
[tex]r=\sqrt{1.0983}-1[/tex]
[tex]r=1.048-1[/tex]
r=0.048.
Converting it into percentage by multiplying by 100.
r=0.048 × 100
r = 4.8 %
Therefore, the rate of interest on the account is 4.8% compounds annually.
The excursion boat on the river takes 2 1/2 hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current? Which of the following equations can be used to solve for c, the rate of the current? (4c)(2.5) + (6c)(2.5) = 24 (4c)(12) + (6c)(12) = 2.5 [12/(4c)] + [12/(6c)] = 2.5
Answer:
[12/(4c)] + [12/(6c)] = 2.5
Step-by-step explanation:
time = distance/speed
You know the speeds upstream (5-1)c and downstream (5+1)c, the distance, and the total time for both trips. This information can be combined to give the equation above.
_____
The first equation assumes the trips upstream and down took 2.5 hours each.
The second equation is an incorrect combination of the numbers, as the units on the left are miles²/hour and are equated to hours on the right.
The third equation makes appropriate use of the relation between speed, distance, and time.
Answer:
Last option as
[tex][12/(4c)] + [12/(6c)] = 2.5[/tex]
Step-by-step explanation:
Time = distance/speed
Speed of boat = 5c (given)
Hence upstream speed = 5c+c =6c and
downstream speed = 5c-c =4c
Distance remains the same 12 miles for up and down
Total time = 2.5 hours
The first equation assumes total time as 5 hours when it is actually 2.5 hours.
The second equation is an incorrect because time x distance will not yield any result instead distance /time should have been done.
The third equation calculates time taken for upstream and downstream and add to equate to 2.5 hours.
So this is correct.
What number has the opposite value from 20.04? please show your work.
-20.04 because they are opposites
The opposite value of a number is a number that when added to the original number, results in zero. In this case, the opposite value of 20.04 is -20.04.
Explanation:The question is asking for the opposite value of 20.04. In mathematics, the opposite value, also known as the additive inverse, is a number which when added to the original number, results in zero. In other words, it's the number you would have to add to a specific number to get a sum of zero. Therefore, the opposite value of 20.04 is simply -20.04.
Learn more about Opposite Value here:https://brainly.com/question/780403
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What units would you use for each scenario that follows?
1. riding a bicycle
2.rainfall during a storm
3.water coming from a fire hydrant
4. watching caloric intake
Thanks
Answer:
m - Meter - Length.
s - Second - Time.
K - Kelvin - Temperature.
kg - Kilogram - Mass.
Units you might use in these scenarios include meters or kilometers for distance, meters per second or kilometers per hour for speed, millimeters or inches for rainfall, gallons or liters for volume, gallons per minute or liters per second for flow rate, and calories for caloric intake.
Explanation:In each of these scenarios, you would use different units to measure different things:
For riding a bicycle, you might use units like meters or kilometers to measure distance, or meters per second or kilometers per hour to measure speed.In the case of rainfall during a storm, the unit of measurement would generally be millimeters or inches to indicate the amount of rain that fell.If we're referring to water coming from a fire hydrant, you would measure the volume in gallons or liters, or the flow rate in gallons per minute or liters per second.When watching caloric intake, the unit you would use is calories.Learn more about units here:https://brainly.com/question/33241167
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What number needs to be added to both sides of the equation in order to complete the square? x ^2+16x=18 Enter your answers in the boxes.
Find the number needs to be added to both sides of the equation in order to complete the square
x ^2+16x=18
In completing the square , we take the coefficient of x and divide it by 2
Then square it and add it on both sides.
The coefficient of x is 16
Half of 16 is 8
Then we square it . [tex](8)^2 = 64[/tex]
Add 64 on both sides
[tex]x ^2+16x + 64=18+64[/tex]
Now we factor x^2 + 16x+64
[tex](x+8)(x+8)=18+64[/tex]
[tex](x+8)^2=82[/tex]
so 64 is added to both sides of the equation in order to complete the square.
30 Points! Please answer each question or just answer one!
Answer:
1. See below for the table
2a. Early Pay: y = 45
2b. Deposit Plus: y = 12 + 4x
2c. Daily Pay: y = 6x
3. See the second attachment for a graph.
Step-by-step explanation:
1. The deposit (Deposit Plus) and the flat rate (Early Pay) are paid whether or not any days are spent swimming. For Early Pay, there are no additional charges, so the total cost is the same regardless of the number of days spent swimming.
For Deposit Plus, the $4 per day cost will add $20 for each 5 swimming days.
For Daily Pay, the $6 per day cost will add $30 for each 5 swimming days.
2. As described above, the Early Pay and Deposit Plus have charges when the number of swimming days is zero. The Daily Pay does not. The Deposit is only paid once, not each day.
a. Early Pay: y = 45
b. Deposit Plus: y = 12 + 4x
c. Daily Pay: y = 6x
3. The above equations are graphed in the second attachment. You will note that the plan that results in a minimum charge depends on the number of swimming days.
Answer:
2a. Early Pay: y = 45
2b. Deposit Plus: y = 12 + 4x
2c. Daily Pay: y = 6x
Step-by-step explanation:
The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 2 pi cubic inches when the radius is 1 inch and the height is 6 inches, find the volume of a cone when the radius is 5 inches and the height is 3 inches. Please help!!!!!!! :(
The variation statement tells you that when the radius is multiplied by 5, the volume is multiplied by 5² = 25. When the height is multiplied by 1/2, the volume is multiplied by 1/2.
Both of these variations together will multiply the volume by 25·(1/2) = 25/2.
So, the revised volume is (2π in³)·25/2 = 25π in³.
The number of cubic feet of water in a curved container can be approximated by V = 0.95h2.9. Find the amount of water in the container when h = 8 feet. Round to the nearest tenth.
We are given
[tex]V=0.95h^2[/tex]
we can plug h=8
and then we can find volume
[tex]V=0.95(8)^2[/tex]
[tex]V=60.8ft^3[/tex]
so,
the amount of water in the container when h = 8 feet is 60.8 ft^3........Answer
Answer:
395.1
Step-by-step explanation:
Simplify
0.95 ( 8 ) ^2.9= v
395.07956558
2(1-k), k-1, k+8 are the first three terms of a geometrical sequence. Find the value of k.
If these are terms of a geometric sequence, they have a common ratio. That is, ...
... (k -1)/(2(1 -k)) = (k +8)/(k -1)
... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.
... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses
... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)
... 3(k +5)(k -1) = 0 . . . . . . . . . factor
Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)
The value of k is -5.
_____
The three terms are 12, -6, 3. The common ratio is -1/2.
what is an equation of the line with slope 3 that goes through point (-1/2, 5/2)?
a.) y=4x+3
b.) y=-3x+4
c.) y=4x-3
d.) y=3x+4
The only equation that has 3 as the coefficient of x (a slope of 3) is ...
... d.) y = 3x+4
_____
Happily, it also goes through the given point.
... 5/2 = 3(-1/2) +4
... 5/2 = -3/2 + 8/2 . . . . true
The equation of the line with a slope of 3 that passes through the point (-1/2, 5/2) is y = 3x + 4, which corresponds to answer option (d.) y = 3x + 4.
To find the equation of a line with a given slope and that passes through a specific point, we can use the point-slope form of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the given point. So, for a line with a slope of 3 that goes through the point (-1/2, 5/2), we can plug in the values to get the equation.
Substituting into the point-slope form, we get y - 5/2 = 3(x + 1/2). Simplifying and solving for y will give us the equation of the line in the form of y = mx + b. After distributing and rearranging, the equation will be y = 3x + 4.
Therefore, the correct answer is (d.) y = 3x + 4.
Need help one this one please answer quickly