The original Volkswagen Beetle follows
a quadratic curve, write an equation if
the height is 5 feet long and the length
is 14 feet long. Show your work in the
sketchpads below.
Answers
Answer:
[tex]y= -\frac{5}{49}x^{2}+5[/tex]
Step-by-step explanation:
In order to solve this, we need to start by drawing a sketch of what the problem looks like (see attached picture).
From the picture, we can see that the graph of the equation should be a parabola with a vertex located at the point (0,5) and x-intercepts located at (-7,0) and (7,0) respectively.
So, there are two ways in which we can build a quadratic equation:
Standard form:
[tex]y=ax^{2}+bx+c[/tex]
or
Vertex form:
[tex]y=a(x-h)^{2}+k[/tex]
Since we already have the vertex and two points on the equation, we can directly use the vertex form. Where vertex is located at the coordinates (h,k)
So in this case: h=0 and k=5, which simplifies our equation a lot:
[tex]y=a(x-0)^{2}+5[/tex]
[tex]y= ax^{2}+5[/tex]
So we only need to find the value of a for our equation to be complete. We can use either x-intercept to find this. Let's use the point (7,0) so we get:
[tex]0=a(7)^2+5[/tex]
and now we can solve for a:
[tex]-5=49a[/tex]
[tex]a=-\frac{5}{49}[/tex]
so this completes our equation:
[tex]y= -\frac{5}{49}x^{2}+5[/tex]
whose graph looks like the one in the attached picture.
Related Questions
The vertices of a triangle are P(-2, -4), Q(2, -5), and R(-1,-8). Name the vértices of the triangle after reflecting over the x-axis
Answers
Answer:
P(-2,4)
Q(2,5)
R(-1,8)
Step-by-step explanation:
The rule for reflecting points across the x-axis is to keep the x-value the same but "negate" the y-value. So, the points above are your answers.
log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)
Answers
I assume you're referring to the product,
[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]
Recall the change-of-base identity:
[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
where c > 0 and c ≠ 1. This means the product is equivalent to
[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]
and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to
[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]
Nineteen and four hundred fifteen thousand in word form
Answers
Answer: 19,415,000
I think
Step-by-step explanation:
Hope this helps!! :)
Answer:
If I understand what your trying to do, id think it would be 19,415? (IF IT IS IN THE MILLIONS, IT MAYBE 19,415,000 ALSO!)
I may be wrong, but I hope I helped!
What is the recursive formula for this sequence? 12, 16, 20, 24, 28, ...
Answers
Answer:
A
Step-by-step explanation:
first term is 12, and following terms are obtained adding 4 to previous term.
A computer manufacturer has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by where x is the number of days since the start of the job. Find the expenditure if the job takes 8 days.
Answers
Answer:
The expenditure would be $ 8600
Step-by-step explanation:
If the cost is given by the function
C(x)= 10x + 6 where x is the number of days
The cost for 1 day would be
C(1)= 16 *100 = 1600 $ ( the expenses are in hundreds of dollars)
Then Putting x= 8 in the given equation we get
C(8)= 10(8) + 6
= 86
Multiplying 86 by 100 because expenditure rate per day is in hundreds of dollars
The expenditure would be $ 8600
hey ms or mr could you help me out with this problem please?
Answers
Answer:
3
Step-by-step explanation:
We can approximate that triangle B is half the size of triangle A. We know this because the base for triangle A is six, meanwhile, for trinagle B it's 3. With this info we can then assume that in triangle A it's 10 for one side so, for triangle B it must be 5. However, there is n+2 instead. We can use the algebretic equation: 5=n+2. Once this equation is solved the answer is 3. Thus, n = 3.
Calculate the paychecks of the following people. Select the total hours and paycheck.
Answers
Answer:
If the numbers under the days of the week are the hours worked then the answers are Sue-40,$6.75,$270 Jerry-30,$5.15,154.5 Sam-38.75,$8.75,339 Step-by-step explanation:
Just add up the number of hours worked and multiply by the rate.
Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased
Answers
Answer: B
Step-by-step explanation:
It is $29.35 for each of the tickets that they buy for adults, so to figure out how much it is for all the adult tickets, it would be $29.35 times x. Same for the children tickets except it is times y and the amount of money is different.
An employer's accountant has announced that
the budget for the next year must be cut by 1/3 How much must be cut from the
budget if last year's budget was
$166,245?
A. $11,830
B. $55,415
C. $166,245
D. $498,735
Answers
What is the slope of a line parallel to the line whose equation is 2x+y=6.
Answers
Answer:
-2 is the slope...
So Basically -2/1
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
First, you solve for y by subtracting 2x from both sides of the equation and so now we have a y= -2x+6. The slope is going to be the number that is with x.
Doe has 2 3/8 pounds of hamburger meat. He is making 1/4 pound hamburgers .Does doe have enough meat to make 10 hamburgers
Answers
A factory employs over 3000 workers, of whom 30% are women. If the 15 members of the union executive committee were chosen from among the workers without regard to gender
Answers
Answer:
I think 4000 worker and I will be there at some point today and I
Theresa finds a shirt on sale at the store. The regular price of the shirt is $32.00. But there is a 20% off sale today. Theresa remembered that there is 8.1% tax on the sale price of the shirt. What is her final cost?
Question 10 options:
$28.92
$27.67
$29.31
$31.00
Answers
Answer:
Step-by-step explanation:
Given tgat:
Regular price = $32
Discount = 20%
Sale tax = 8.1%
chose the correct one quality to match the real-world situation. Gabe will spend no more than $100.
the answer choices are
a.x ≥100
b.x≤100
c.x>100
Answers
Answer:
B
Step-by-step explanation:
the other too are stating that Gabe will spend more than or more than/equal to $100
Find the volume and surface area of each prism 3cm by 3cm by 3cm
Answers
Answer:
3 x 3 x 3= 18 so 18cm squared
Step-by-step explanation
Answer:
Volume =27cm³
Total surface area=54cm²
Step-by-step explanation:
Formula for finding volume of an object is Volume =length×breadth×height
so V=3cm×3cm×3cm=9cm²×3cm=27cm³ because the cm is three so it will become cube.
Formula for finding the total subject of an object is T.S.A meaning total surface area=2((length ×breadth)+(length×height)+(breadth ×height))
so it will be 2((3cm ×3cm)+(3cm ×3cm)+(3cm ×3cm)) calculate and if you any problem let me know.
How do solve this problem?
find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form. line 2x + 5y= -10 point (10, 4)
Answers
Answer:
y=-2/5x+8
Step-by-step explanation:
Step 1: Begin by changing the equation into slope-intercept form. Subtract 2x to both sides to get 5y=-10-2x. Divide 5 to both sides to isolate the variable, y. You should get y=-2/5x-2.
Step 2: Because we are looking for a line parallel to the given line, the slope should be the same, but the y-intercept should be different. Remove -2 to replace it with b, so it's unknown. The equation should be y=-2/5x+b. Plug in the ordered pair, (10, 4), into the equation to get 4=-2/5(10)+b. Multiply -2/5 and 10 to get -4. Add -4 to both sides and b=8. Plug in 8 and your final equation should be y=-2/5x+8.
A car travels around a circular track of radius 1.5 miles. It traversed35of a complete revolution. Howfar did it travel?
Answers
Answer:
The total distance traveled by the car is 330 miles.
Step-by-step explanation:
The circular track is the circumference of circle with radius 1.5 miles.
Circumference of a circle = 2[tex]\pi[/tex]r
Thus,
Circumference of the track = 2 x [tex]\frac{22}{7}[/tex] x 1.5
= 9.4286571429
Circumference of the track = 9.4286571429 miles
But, one complete revolution by the car is the circumference of the track.
i.e One complete revolution round the track = 9.4286571429 miles
Therefore,
35 complete revolutions round the track = 35 x 9.4286571429 miles
= 330 miles
The total distance traveled by the car is 330 miles.
compare:
-5/6 is greater than or less than or equal to 2/3
Answers
Answer:
less than
Step-by-step explanation:
Answer:
-5/6 is less than to 2/3
Using the function h(x) = 2x – 3, what would the input need to be for an output of 7?
Answers
Therefore, the input needed for an output of 7 using the function h(x) = 2x - 3 is x = 5.
What is function?In mathematics, a function is a rule that assigns a unique output or value to each input of a given set. In other words, a function is a relationship between two sets, called the domain and the range, such that for each input value in the domain, there is exactly one output value in the range. A function can be represented by a mathematical expression or formula, a graph, a table, or a set of ordered pairs. Functions are used to model various phenomena and solve problems in many fields, including science, engineering, economics, and finance.
Here,
To find the input (x) that corresponds to an output of 7, we can set h(x) equal to 7 and solve for x as follows:
h(x) = 2x - 3
Setting h(x) = 7, we get:
7 = 2x - 3
Adding 3 to both sides, we get:
10 = 2x
Dividing both sides by 2, we get:
x = 5
To know more about function,
https://brainly.com/question/28193994
#SPJ1
Mrs. 1 ran 10 meters in 3.8 seconds. Mrs. 2 ran 10 meters in 3.2 seconds.
Who ran faster?
Answers
Answer:
Mrs. 2
Step-by-step explanation:
3.2 seconds is shorter than 3.8 seconds
Answer:
Mrs 2 ran 10 meters in 3.2seconds
A sphere has a radius of 4 in. Which equation finds the volune of the sphere?
Answers above on the picture^ thank you:)
Answers
Answer:
The first answer
Step-by-step explanation:
1. Given: y = -2x2
Domain
Range
Opening of the
parabola
Vertex
Axis of Symmetry
X - intercept
y - intercept
Answers
Domain: (-∞,∞) or -∞ < x < ∞ or all real numbers
Range: (-∞,0] or -∞ < y ≤ 0
Opens: Downwards since a is negative
Vertex: ( 0 , 0 )
Axis of Symmetry: x=0
x-intercept: ( 0 , 0 )
y-intercept: ( 0 , 0 )
Find the equation of the line that passes through (4,4) and is parallel to y = 2x + 4.
Leave your answer in the form y= mx + c
Answers
Answer:
x,y(0,12)
Step-by-step explanation:
Y=mx+c
4=2X+4
4=2x+4
2x=0
X=0
Y=mx+c
Y=2(4)+4
Y=8+4
Y=12
Please help me out quickly
Answers
Answer:
I dont see the stuff I think my internet is slow but I will help you when its up again im using hotspot just remind me
Step-by-step explanation:
Find the value of y,please help
Answers
Answer:
4.5255
Step-by-step explanation:
Use the Pythagorean theorem (a²+b²=c²) where A and B are equal to 3.2
What is the point-slope form of the equation of the line that passes through the point (-3,-4) and has a slope
of 2?
Answers
Answer:
y=2x+6
Step-by-step explanation:
Answer:
y=2x+2
Step-by-step explanation:
To find the point-slope form of the equation we need to get the slope-intercept form of (-3,-4) and 2
(Slope intercept form formula is y=mx+b) (m is slope) (b is y-intercept)
So we know that the slope of this equation is 2 so we can replace m with 2 since the slope is 2 and m is slope.
Equation will look like this:
y=2x+b
Now we need to find the b or y-intercept of the equation to do this the (-3,-4) come into play: replace x with -3 and replace y with -4
(x,y) -3 is x since it is the same spot in (-3,-4) and -4 is y since it is in the same spot in (-3,-4)
Replace:
-4=2(-3)+b
Multiply 2 and -3:
-4=-6+b
Move 6 to the other side by adding 6 on both side:
6-4=-6+6+b
Simplify
2=b
Now the equation looks like this: (If you replace b with 2 in y=2x+b)
y=2x+2
Answer: y=2x+2 (Point-slope form is the same thing as slope-intercept form)
look at picture and answer ASAP
Answers
Answer:
its B and A
Step-by-step explanation:
Answer:
its in between the fist and second one cuusing what is given thats what i figured out
Step-by-step explanation:
3 x 36= 108 / 3 x 15 = 45
9 x 12 = 108 / 9 x 5 = 45
6 x 18 = 108 / 6 x 7 = 42
i hope this helps :)
Please help! I will give brainliest!!!!!!
Answers
Answer:
3,10 please give me brainliest i need one more for 5 please please please
Step-by-step explanation:
Convert 51.7% to a fraction in simplest form and a decimal.
Answers
what is the equation for (4, 9.4) and (-3, -9.5)
Answers
Answer: I got an eqaution I hope it is basic
Step-by-step explanation:
4 times 9
9 - (-3 ) times -9 + 5