Given:
The height of the swipe card in feet after t seconds is
[tex]h(t)=-3t^2+15t+18[/tex]
To find:
The maximum height of the swipe card and the time at which it reaches this height.
Solution:
We have,
[tex]h(t)=-3t^2+15t+18[/tex]
Here, leading coefficient is -3, which is negative. It means it is a downward parabola and the vertex of the downward parabola is the point of maximum.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex is
[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, we get
[tex]a=-3,b=15,c=18[/tex]
Now,
[tex]-\dfrac{b}{2a}=-\dfrac{15}{2(-3)}[/tex]
[tex]-\dfrac{b}{2a}=2.5[/tex]
Putting t=2.5 in the given function, we get
[tex]h(2.5)=-3(2.5)^2+15(2.5)+18[/tex]
[tex]h(2.5)=36.75[/tex]
So, the vertex of the given parabola is at (2.5,36.75).
Therefore, the maximum height of the swipe card is 36.75 feet and it reaches this height after 2.5 seconds.
Factor the polynomial
3x^2+3x-6
Answer:
3(x-1)(x+2)
Step-by-step explanation:
i dont know if this what u looking for but i think:
3(x-1)(x+2)
What is the area of a circle if the diameter is 9cm?
Round to the nearest hundredth (0.01cm2)
Answer: A≈63.62
Step-by-step explanation:
9/2= 4.5
A=πr2=π·4.52≈63.61725
Answer:
To find the area of a circle we have [tex]\pir^{2}[/tex] and the radius is half of the diameter so we have 4.5² which gives 16.25π
An entrepreneur sold a damage bedspread for $130.50, there by making a loss of 13% on the cost price. Determine the cost price of the bedspread.
Answer:
130.50 X 13% = $16.97
130.50 - 16.97 = 113.53
Answer 113.53
Step-by-step explanation:
Which fraction is equal to 36%?
Answer:
[tex] \frac{36}{100} = \frac{9}{25} [/tex]
Step-by-step explanation:
3600%/100% cancel them you will get 36% answer..
Which expression is not equivalent
to (x + 4)(x – 3)?
Answer:
A) x² + 7x - 12 is NOT equivalent to the expression.
Step-by-step explanation:
1) expand by distributing terms.
[tex] {x }^{2} - 3x + 4(x - 3)[/tex]
2) Expand by distributing terms.
[tex] {x}^{2} - 3x + 4x - 12[/tex]
3) Collect like terms.
[tex] {x}^{2} + ( - 3x + 4x) - 12[/tex]
4) Simplify.
[tex] {x}^{2} + x - 12[/tex]
The second equation are equivalent to the equation. but the first equation is not equivalent to the main equation.
what is the measure of x? someone actually help im confused
Answer:
angle x = 28 degrees
Step-by-step explanation:
Because of vertical angles, angle IAK and angle BAC are equal, and angle GCJ and angle ACB are also equal due to vertical angles
Since KL is perpendicular to FG, angle ABC is 90 degrees
ABC is a right triangle and acute angles in a right triangle are equal to 90 degrees
This means that angle BAC + angle ACB = 90 degrees
angle BAC = 62 degrees and angle ACB = x degrees
62 + x = 90
x = 28 degrees
Helpppp pleeasseee, will mark brainliest!
Answer:
a
Step-by-step explanation: I am 99% sure
Please help me with this I will make you brainlist if you respond with no links and fully! Do NOT steal points.
Answer: 6782.4 ft is your answer
Step-by-step explanation:
Answer: 6785.84
Step-by-step explanation:
Volume of a cylinder is [tex]\pi r^{2}h[/tex]
So solve both cylinders to get
20357.52
13571.68
Subtract to get the difference
6785.84
PLEASEE SOMEONE HELP ME ON THIS ITS TODAY IN A COUPLE HOURS!!!
Answer:
[tex]\displaystyle y = 2.90717[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA [Right Triangles Only] sinθ = opposite over hypotenuseStep-by-step explanation:
Step 1: Identify
Angle θ = 20°
Opposite Leg = y
Hypotenuse = 8.5
Step 2: Solve for y
Substitute in variables [sine]: [tex]\displaystyle sin20^\circ = \frac{y}{8.5}[/tex][Multiplication Property of Equality] Multiply 8.5 on both sides: [tex]\displaystyle 8.5sin20^\circ = y[/tex]Evaluate: [tex]\displaystyle 2.90717 = y[/tex]Rewrite: [tex]\displaystyle y = 2.90717[/tex]You invest $1,000 into a start up company at a 3% annual interest rate for 20 years. How much interest do you earn?
Answer:
600
Step-by-step explanation:
? = 1000 x .03 x 20
the 1000 is the original amount
the .03 is the percent/interest
the 20 is the time
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
Answer:
3+11+9+7
Step-by-step explanation:
You add all the numbers
a calculator is listed for $110 and is on clearance for 35% off. sales tax is 7%. what is the cost of the caculator
Answer:
76.5
Step-by-step explanation:
Write 51/7 in radical form
help please! i can't find the answer anywhere
Answer:
A
Step-by-step explanation:
-16t^2 + 24t= 0
-2t^2+3t =0
3t= 2t^2
3= 2t
t=1,5
Your friend uses 2 1/2 ounds of dried fruit and 1/2 pound of raisins to make trail mix.How many 1/2 pound packages can he make.
Answer:
he can make 6 because 2 and 1/2 plus 1/2 = 3 and 3 divided by 2 is 6
Step-by-step explanation:
Round 7.27 to the nearest whole number.
Answer:
Step-by-step explanation:
they right it is 7
eight more than the product of 16 and greg's height
3 2/3 x+3 1/4=6 whats the value of x
Answer:
x = 3/4
Step-by-step explanation:
Answer:
x = 3/4
Step-by-step explanation:
Find the LCD of the fractions. Multiplying the denominators 3 and 4 together, we get LCD = 12.
Rewriting the mixed numbers, we get
3 2/3 = 3 8/12 and 3 1/4 = 3 3/12
So the original equation becomes
(3 8/12)x + 3 3/12 = 6
We must now combine like terms: subtract 3 3/12 from both sides of this equation, obtaining:
(3 8/12)x = 6 - 3 3/12, or
(3 8/12)x = 2 9/12. Converting the mixed numbers into improper fractions, we get:
(44/12)x = 33/12. Multiplying both sides by 12 yields 44x = 33
and so x = 33/44 = 3/4
x = 3/4
Alternatively, convert the original mixed numbers into improper fractions right away. Then the original 3 2/3 x+3 1/4=6
becomes (11/3)x + 13/4 = 72/12, or
(44/12)x + 39/12 = 72/12
Multiplying all three terms by 12 yields:
44x + 39 = 72, which simplifies to 44x = 33, or x = 3/4
Helpppppp please look at the picture i added
Ten friends shared a bag of popcorn. Using p to represent the bag of popcorn, which expression represents the amount each friend received? *
1 point
p / 10
10 - p
10p
10 + p
A team can spend no more than $300 on shirts. The team has already spent $80. How many shirts for $15 each can they still buy?
Answer:
80 + 15x ≤ 300
Step-by-step explanation:
max amount = $300
already spent = $80
$300 - 80 = $220
shirts = $15 each
80 + 15x ≤ 300
$80 that is already spent + $15x ≤ $300 maximum
x = number of shirts
Can someone help me with this? I don't understand?
[tex] \sqrt[3]{1000 {}^{2} } [/tex]
How do you do the whole process? I need some explanation...
9514 1404 393
Answer:
100
Step-by-step explanation:
A root is equivalent to a fractional power. A square root is a 1/2 power. A cube root is a 1/3 power. The index of the root is the denominator of the fraction.
Of course the usual rules of exponents apply in evaluating an expression.
(a^b)^c = a^(bc)
__
Your expression can be simplified as follows.
[tex]\displaystyle\sqrt[3]{1000^2}=(1000^2)^{\frac{1}{3}}=1000^{\frac{2}{3}}=(10^3)^{\frac{2}{3}}=10^2=\boxed{100}[/tex]
It can also be simplified another way:
[tex]\displaystyle\sqrt[3]{1000^2}=\sqrt[3]{(10^3)^2}=\sqrt[3]{(10^2)^3}=10^2=100[/tex]
_____
Additional comments
A problem like this is simpler if you are familiar with the squares and cubes of small integers.
Divide f(x) by d(x), and write a summary statement in polynomial form and fraction form. F(x)=x^2-12x+43;\ d(x)=x-6
Answer:
Quotient: x^(2)-6
Reminder: 7
Step-by-step explanation:
See the attached image.
The Polynomial form of F(x) / d(x) is (x - 6) + 7 / (x - 6).
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
F(x) = x² - 12x +43
d(x) = x - 6
Then,
F(x) / d(x) = x² - 12x +43 / x - 6
Factorize the numerator,
F(x) / d(x) = [(x - 6) (x - 6) + 7] / (x - 6)
F(x) / d(x) = (x - 6) (x - 6) / (x - 6) + 7 / (x - 6)
F(x) / d(x) = (x - 6) + 7 / (x - 6),
Therefore, the Polynomial form of F(x) / d(x) is (x - 6) + 7 / (x - 6).
To know more about division:
https://brainly.com/question/27566440
#SPJ5
I am in fourth grade and I have no idea how to find whole numbers between a fraction can you show me?
Answer:
To find a a fraction of a whole number, you multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction
Solved example for finding a fraction of a whole number:
1)
Find 1/3 of 21.
To find 1/3 of 21, we multiply the numerator 1 by the given whole number 21 and then divide the product 21 by the denominator 3.
1/3 × 21 = 1 × 21/3 = 21/3 = 7
So, 1/3 of 21 = 7.
1/3 of 21 is 7
Answer:
For finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction.
Examples for finding a fraction of a whole number:
Find 1/3 of 21.
To find 1/3 of 21, we multiply the numerator 1 by the given whole number 21 and then divide the product 21 by the denominator 3.
1/3 × 21 = 1 × 21/3 = 21/3 = 7
So, 1/3 of 21 = 7.
Here are some more examples
Step-by-step explanation:
Find 2/5 of 15.
To find 2/5 of 15, we multiply the numerator 2 by the given whole number 15 and then divide the product 30 by the denominator 5.
2/5 × 15 = 2 × 15/5 = 30/5 = 6
So, 2/5 of 15 = 6.
Find 3/8 of 48.
To find 3/8 of 48, we multiply the numerator 3 by the given whole number 48 and then divide the product 144 by the denominator 8.
3/8 × 48 = 3 × 48/8 = 144/8 = 18
So, 3/8 of 48 = 18.
sovle the following inequalitiea for x. 3x - 5 ≥ 22
Answer:
x ≥ 9
Step-by-step explanation:
MULTIPLE CHOICE QUESTIONS
Choose the correct answer from the given four options (3 to 18):
3. a x a x a x b x b x b is equal to
Answer:
C due to distrubtive properties
ill mark brainlist plsshelp
PLS HURRY I NEED AN EXPLANATION!!!!
Can someone pls give me an example on how to solve hypotenuse
Answer:
c = √(a² + b²)
Step-by-step explanation:
c=√a2+b2
Answer: so if you have a right triangle and only know the horizontal and vertical lines you would which equal 13 and 12 you would find those squared which are, 169 and 144. Add those together. 313. Then get the square root of 313. Which is rounded 17.7. So the answer to the hypotenuse is 17.7
Step-by-step explanation:
Persevere Write the difference in factored form. (24x4 − 15x2 + 6x) − (10x4 + 5x2 − 4x)
Answer:
ur horrid
Step-by-step explanation:
A taxi hurries for 1 hour 54min with a constant speed of 93km and then for another 5 hours 15min with a constant speed of 72km. What distance did it go
Speed = 93km /h and 72km/h
Answer: The taxi went a distance of 554.7km
Step-by-step explanation:
Speed = Distance / Time
Distance covered in the first trip = Speed x Time
Time = 1 hour 54 min =1+0.9 hours =1.9hours
=93km / h x 1.9 hours =176.7km
Distance covered in the second trip = Speed x Time
Time = 5 hours 15min = 5+0.25hours =5.25hours
=72km / h x 5.25hours =378 km
Total distance =176.7km+378 km
=554.7km