The main cable of a suspension bridge forms a parabola, described by the equation y = a(x - h)2 + k, where y is the height in feet of the cable above the roadway, x is the horizontal distance in feet from the left bridge support, a is a constant, and (h, k) is the vertex of the parabola. At a horizontal distance of 30 ft, the cable is 15 ft above the roadway. The lowest point of the cable is 6ft above the roadway and is a horizontal distance of 90 ft from the left bridge support. Which quadratic equation models the situation correctly? y = -0.0025(x - 90)² + 6y = -0.0025(x - 30)² + 15✔ y = 0.0025(x - 90)² + 6y = 0.0025(x - 30)² + 15
The main cable attaches to the left bridge support at a height of 26.25 ft.The main cable attaches to the right bridge support at the same height as it attaches to the left bridge support. What is the distance between the supports?Answer:
The equation that models this situation correctly is C. y = 0.0025(x-90)² + 6.
Step-by-step explanation:
To find the quadratic equation that best models this equation, the only piece of information we need is "The lowest point of the cable is 6ft above the roadway and is a horizontal distance of 90 ft from the left bridge support."
The keyword lowest tells us the value is a minimum. Therefore, the parabola must be a positive one, because negative parabolas have maximum values. This disqualifies answer choices A and B because they have negative a values.
We also know the vertex occurs at (90, 6) because this is where the lowest point is. Therefore, the equation should be y = 0.0025(x-90)² + 6. (Note: the information about point (30, 15) is not relevant to the problem.)
(-8x) divided by (-2)
Giving away brainliest (assuming there is more than one person answering, of course)
Basic Cookie Recipe:
1/2 cup shortening. 1/2 teaspoon baking soda
1/2 cup butter 2 cups chocolate chips
2 1/2 cups flour. 1/3 cup cocoa
1 cup brown sugar. 1 teaspoon vanilla
1/4 cup granulated sugar
To enrich Choco flavor, you want to add more cocoa to the recipe. Because cocoa is bitter, you need to increase the amount of GRANULATED sugar in the recipe. Write an equation to describe how the amount of GRANULATED sugar, s, in the recipe relates to the amount of cocoa, c. If the amount of cocoa is tripled, how much more granulated sugar should you add? Explain reasoning (or not, but please).
At 5 a.m., the temperature at an airport was −9.4°F . Six hours later, the temperature was 2.8°F . Which expression represents the total temperature change over the six hours?
I need help with this now!
Answer:
(-9.8 + x) = 2.8
Step-by-step explanation:
The temperature at an airport at 5:00 am was -9.4° F.
Six hours later the temperature was 2.8° F.
Let temperature change in the 6 hours is = x° F
Then the temperature after six hours from -9.8° F will be = (-9.8 + x)° F
And the expression representing the change will be
(-9.8 + x) = 2.8
Which of the following represents two lines that are coplanar and do not intersect?
A. Perpendicular
B. Skew
C. Parallel
D. Intersecting
Two lines that are coplanar and do not intersect are called parallel lines. This means they exist within the same plane and while they never meet, they continue indefinitely in the same direction.
Explanation:Of the given options: Perpendicular, Skew, Parallel, and Intersecting, the term that represents two lines that are coplanar (existing in the same plane) and do not intersect is Parallel. A brief explanation of each option: A. Perpendicular lines are coplanar and do intersect at a right angle. B. Skew lines are not coplanar, hence they do not intersect nor are they parallel. C. Parallel lines are coplanar and do not intersect at any point. D. Intersecting lines are coplanar and do cross at some point.
Learn more about Parallel lines here:https://brainly.com/question/29762825
#SPJ6
Rachel flips a coin 150 times and finds that the probability of the coin landing heads up is Rachel wants to flip the same coin 15 more times. On the first 14 flips, the coin lands heads up. Which statement best describes the probability of the coin landing heads up on the 15th flip?
a.The probability of the coin landing heads up is
b.The probability of the coin landing heads up is 1.
c.The probability of the coin landing heads up is
d.The probability of the coin landing heads up is
every coin flip, it has a 1/2 probability of landing on heads.
it doesn't matter what the flips were before it.
Probability is 1/2
What is 0.000000783 written in scientific notation?
Enter your answer in the box.
=7.83 × 10-7
Step-by-step explanation:
What is 50= 28.10 + 0.15m
...anybody know this one
Twice a number (x) is less then 10
In a video game, a character is healed at a constant rate as long they are standing in a certain circle. Complete the table
Jeff's dog weighs 76 pounds what is the
Dog's weight rounded to the nearest ten pounds
The dog's weight rounded to the nearest ten pounds is 80 pounds.
The dog's weight, 76 pounds, can be rounded to the nearest ten pounds.
To round to the nearest ten pounds, we look at the digit in the ones place. If the digit is 0, 1, 2, 3, or 4, we round down to the nearest ten. If the digit is 5, 6, 7, 8, or 9, we round up to the nearest ten.
In this case, the digit in the ones place is 6. Since 6 is greater than 5, we round up to the nearest ten.
So, the dog's weight rounded to the nearest ten pounds is 80 pounds.
Since 1970, the # (in thousands) of males M and females F attending institutes of higher education can be modeled by: M=0.091t^3-4.8t^2+110+5,000 and F=0.19t^3-12t^2=350t+3,600 where t is the number of yrs since 1970. Write a model for the total # of people attending institutes of higher education.
The total number of people attending higher education institutions is modeled by T = 0.281t^3 - 16.8t^2 + 460t + 8,600, representing the sum of the models for males and females attending colleges.
Explanation:To answer the student's query regarding the total number of people attending institutes of higher education, we need to create a model that includes both the number of males and females attending as described by their respective equations. The model for the number of males attending college is given by M = 0.091t^3 - 4.8t^2 + 110t + 5,000, and the model for the number of females is F = 0.19t^3 - 12t^2 + 350t + 3,600. To find the total number of students, T, we simply add the two models together: T = M + F.
Therefore, the model for the total number of people attending institutes of higher education is:
T = (0.091t^3 - 4.8t^2 + 110t + 5,000) + (0.19t^3 - 12t^2 + 350t + 3,600)
Combining like terms, we get:
T = (0.091t^3 + 0.19t^3) - (4.8t^2 + 12t^2) + (110t + 350t) + (5,000 + 3,600)
Which simplifies to:
T = 0.281t^3 - 16.8t^2 + 460t + 8,600
This equation represents the total number of students, in thousands, attending institutes of higher education t years since 1970.
-3p-(-8+4p) combining like terms & distributive property
7.3579 E8 in standard form
For this case we have the following exponential expression:
[tex] 7.3579 E8
[/tex]
We can rewrite the exponential expression in scientific notation as follows:
[tex] 7.3579 E8 = 7.3579 * 10 ^ 8
[/tex]
Then, to write the number in its standard form, we move the decimal point 8 spaces to the right. This is because the exponent is positive.
We have then:
[tex] 7.3579 * 10 ^ 8 = 735790000
[/tex]
Answer:
7.3579 E8 in standard form is:
[tex] 735790000 [/tex]
Which statement best defines a universal law
A. It is in fact some of the time
B. It is in effect at all times
C. It changes over time
D. It operates only under specific times
dave has 30% off coupon for pair of jeans priced at $78.95. he will also have to pay a 6% sales tax and a 1% local option tax at the register. how much will he have to pay for the jeans?(p.s. please work it out in detail, so I can get a better understanding instead of just putting the answer. )
Answer:
$59.13355 ≈ $59.14
Step-by-step explanation:
Marked Price = $78.95
Discount @ 30% = 0.30 x $78.95
= $23.685
Selling Price = Marked Price - Discount
= $78.95-$23.685
= $55.265
Sales tax @ 6% = 0.06 x $55.265
= $3.3159
Local Option Tax @ 1% = 0.01 x $55.265
= 0.5526
Hence Billing amount = Selling Price +Sales tax + Local Option Tax
= $55.265 + $3.3159+$0.5526
= $59.13355
≈ $59.14
two minor league baseball players got a total of 378 hits. washington had 4 more hits than sanchez. find the number of hits for each player.
In the number 12.057,which digit has the greater value,the 5 or 7?explain
Give an example of addition problem in which you would and would not group the addends differently to add
Answer:
The numbers which have unit digit Zero for a two digit number, and for three digit number ones and tens place should be equipped with zero,So on..... does not require addends to group together.
For example, addition problem in which you would not regroup addends
→ 10+20+30
→ 30 +40 +50
→ 100+200+300
And Addition Problems in which you will regroup addends
→ 17 +5 +3=(17+3)+5=20+5=25
→ 4+9+6=(4+6)+9=10+9=19
→ 13+19+17=(13+17)+19=30+19=49
For what value of x do the functions f(x)=−52x+4 and g(x)=−12x−4 have the same output?
Answer:
-52x+4
Step-by-step explanation:
I took the test .
7,000 is ten times as much as what number?
Help!! 12am = 4, solve for a!! (literal equations)
are irrational numbers always/sometimes/never rational numbers
a
[1] Angle Addition Postulate[2] Subtraction Property of Equality
b
[1] Substitution Property of Equality [2] Transitive Property of Equality
c
[1] Segment Addition Postulate [2] Definition of Congruent Segments
d
[1] Segment Addition Postulate[2] Substitution Property of Equality
Answer:
d:(1)Segment addition Postulate
(2).Substitution Property of equality.
Step-by-step explanation:
We are given that
EG=FH
We have to write a justification for each step.
1.EG=FH
Given information
2.EG=EF+FG
Segment addition Postulate
3.FH=FG+GH
Segment addition postulate
4.EF+FG=FG+GH
Substitute property of equality
[tex]EF=GH[/tex]
Subtraction property of equality
Answer:d:(1)Segment addition Postulate
(2).Substitution Property of equality.
What is 4,785 rounded to the nearest thousand?
HOW DO I SOLVE THIS 1/5(6+3+1)2
How many people must attend the third show so that the average attendance per show is 3000 write an equation too
The third show must be attended by 3500 people.
To find the number of people that must attend the third show so that the average attendance per show is 3000, we can use the concept of averages.
The average attendance per show is the sum of the attendances divided by the number of shows.
In this case, we have attended 1 show by 2580 people, 2 shows by 2920 people, and the attendance for the third show is x people. So, the equation to represent the average attendance per show of 3000 is:
(2580 + 2920 + x) / 3 = 3000
To solve this equation, we can multiply both sides by 3 to eliminate the denominator and get:
2580 + 2920 + x = 9000
Then, we combine like terms:
5500 + x = 9000
Finally, we subtract 5500 from both sides to isolate x:
x = 3500
Therefore, for the average attendance per show to be 3000, the third show must be attended by 3500 people.
The probable question may be:
How many people must attend the third show so that the average attendance per show is 3000 write an equation too
1 show is attend by 2580 people,
2 show is attend by 2920 people,
3 show is attend by x people.
correct answer is x=3500
One movie club charges a $100 membership fee and $10 for each movie. Another club charges no membership fee but movies cost $15 each. Write and solve an equation to find the number of movies you need to buy for the cost of each movie club to be the same.
HELP!!!
solve -3.2=2.5+1.2m