MATHEMATICS HIGH SCHOOL

Find a number that is between 8/11 and 0.85(repeating) .A.23/33


B.39/66


C.157/198


D.88/99

Answers

Answer 1
Answer: The answer is C. If you have any questions then leave a comment. Good luck!

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Dad is 7 times as old as his son. 10 years later, he will be three times as old as his son.find their ages?

Answers

so dad is represented by x
son is represented by y

so x is (x=) 7 times his son (7y)

our first sentence is x=7y

10 years later (x+10, y+10) he will be 3 times as old as his son (x+10=3(y+10))
or 10+x=3(y+10)

so our sentences are
x=7y
and
x+10=3(y+10)
first we subsitute x=7y for x in the second equation
(7y)+10=3(y+10)
7y+10=3(y+10)
we distribute
7y+10=3y+30
subtract 3y from both sides
4y+10=30
subtract 10 from both sides
4y=20
divide both sides by 4
y=5

the son is currently 5 years old
x=7y
subsitute y=5 for y in equation
x=7(5)
x=35
the dad is currently 35 years old
in 10 years
dad is 45 and son is 15



dad=35
son=5
these are the answers
son = 5
dad= 35

One-sixth of a number is 66

Answers

1/6n = 66
(1/6) × 6 = 66 × 6
n = 396 .

Find the first,fourth, and eighth terms of the sequence. A(n)=-5*2^n-1

Answers

Answer: A(1)=-5

A(4)=-40

A(8)=-640

Step-by-step explanation:

Given sequence :A(n)=-5*2^(n-1)

To find the first term, we need to put n=1 in the above sequence , we get

A(1)=-5*2^(1-1)=-5*2^0=-5

To find the fourth term, we need to put n=4, we get

A(4)=-5*2^(4-1)=-5*2^3=-5*8=-40

To find the eighth term, we need to put n=8, we get

A(8)=-5*2^(8-1)=-5*2^7=-5*128=-640

Answer:

A(1)=-5*2^1-1=-11

A(1)=-5*2^4-1=-81

A(1)=-5*2^8-1=-1281

Step-by-step explanation:

Given :     A(n)=-5*2^n-1


To find :   A(1), A(4), A(18)


Solution:

Put n=1, A(1)=-5*2^1-1

               A(1)=-10-1=-11


Put n=4, A(1)=-5*2^4-1

                A(1)=-80-1=-81

Put n=8, A(1)=-5*2^8-1=

               A(1)=-1280-1=-1281

A projectile is fired straight upward with an initial velocity of 400 feet per second. The height of the projectile, h(t), if represented by the function h(t)=-16t^2+400t, where t is the time in seconds. How long does it take the projectile to reach the maximum height?

Answers

Taking into account the definition of maximum, minimum and vertex of a quadratic function, it takes 12.5 seconds for the projectile to reach maximum height.

A quadratic function is defined in the form:

y= f (x) = ax² + bx + c

Every quadratic function has a maximum or a minimum, which is the vertex of the parabola. If the parabola has an upward concavity, the vertex corresponds to a minimum of the function; whereas if the parabola has concavity downwards, the vertex will be a maximum.

That is, if the coefficient a is positive the parabola is concave and the vertex will be a minimum of the function, while if a is negative the parabola will be convex and the vertex is a maximum.

The maximum or minimum is reached in xv=(-b)/(2a)  

The maximum or minimum value of y is obtained by evaluating the function at xv, this is, f (xv).

In this case, the function is:

h(t)= -16t² + 400t

where t is the time in seconds

Being a = -16 and b = 400, the value of a is negative, so the vertex will be the maximum.

You want to know the time it takes for the projectile to reach the maximum height, that is, the maximum in t. That is, you must calculate t using the expression: t=(-b)/(2a)

So: t=(-400)/(2x(-16))

Solving:

t=(-400)/(-32)

t= 12.5 seconds

It takes 12.5 seconds for the projectile to reach maximum height.

Learn more about cuadratic function with this examples:

Answer:

You can find the answer by using the formula x=-b/2a

Step-by-step explanation:

Remember the maximum height will be at the vertex. The x value of the vertex is your time, so use x=-b/2a. Then if it had also asked what the height was, you would plug that answer into your equation to find the y value of the vertex. Pretty sure your teacher is just asking you to find the x though:)

I need help with this please

Answers

The area of the first one would be the area of the rectangle minus the area of the circle, so 18*8 - (pi*3*3). That's equal to around 115.7257 inches squared.

The area of the second one would be the area of the triangle plus the area of the semicircle, so [(4*5)/2]*[(pi*2*2)/2]. That would be 20pi, or around 62.8319 ft squared

I'm not sure about the third one. Is it a trapezoid?

I have some white and black marbles in a box. There are 30 white marbles. There are 14 more white marbles than black marbles. How many black marbles do I have?

Answers

(30 white marbles) - (14 marbles) = 16 black marbles.
that makes 46 marbles in all
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