MATHEMATICS HIGH SCHOOL

Find an equation of a line through √3,1 / 2) parallel to the line:a. x = −9
b. y = −√7
c. What can you conclude about your answer in parts (a) and (b)?

Answers

Answer 1
Answer:

Answer:

(a) x=√(3)

(b) y=(1)/(2)

(c) Answer of part a is equation of line x=√(3) which is parallel to y axis and in part by equation of line is y=(1)/(2) which is parallel to x axis

Step-by-step explanation:

We have given points are (√(3),(1)/(2))

(a) Equation of line is given x = -9

We have to find the equation of line parallel to x= -9 and passing through (√(3),(1)/(2))

x = -9 line is parallel to y axis and so slope will be infinite

Equation of line is given by y-y_1=m(x-x_1)

So y-(1)/(2)=(1)/(0)(x-√(3))

x=√(3)

(b) Equation of line is given y=-√(7)

This line is parallel to x axis so slope will be zero

So equation of line will be y-(1)/(2)=0(x-√(3))

y=(1)/(2)

(c) Answer of part a is equation of line x=√(3) which is parallel to y axis and in part by equation of line is y=(1)/(2) which is parallel to x axis

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Find the value(s) of k for which the expression is a perfect square trinomial.
49x^2-84x+k

Answers

Step-by-step explanation:

step 1. the perfect square will look like this: (7x + a)(7x + a) = (7x + a)^2.

step 2. by performing FOIL you will get 49x^2 + 14xa + a^2.

step 3. 14a = 84. a = 6

step 4. a^2 = 36.

step 5. k = 36.

Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of the summer. He withdraws $28 each week for food. Which inequality represents w, the number of weeks Manuel can withdraw money while not dropping below a $300 balance?28-600w < 300

28-600w > 300

600-28w < 300

600-28w > 300

Answers

The answer to this question is 600-28w > 300. This inequality can be described as $600 (money in the savings account) subtracted by $28w (withdrawal of $28 a week for food) should be greater than $300. It proves that the money will not drop below $300.

it would be the 3rd one i just took the test

Which inequality represents all the values of x for which the product below is defined?x

A: x≥-1
B: x≥4
C:x≤4
D:x≥0

Answers

Answer:

x≥0 is correct inequality.

D is correct.

Step-by-step explanation:

We are given a function f(x)=x√(x)-4√(x)+1

We need to find x where function is defined.

As we know negative inside the root not defined.

Inside the root value must be greater than equal to 0.

Here we have inside the root is x.

Therefore, x must be greater than equal to 0.

Inequality:  x≥0

Please see attached graph for more clarification.

Hence, x≥0 is correct inequality.

Answer:

x is greater than or equal to 4 (x>_4)

Step-by-step explanation: a p e x

Find x! I have no idea what it is

Answers

102+28=130 180-130=50, answer is 50°
the answer would be x=50°

A spherical ballon with a radius r inches has volume V(r)=4/3 pir^3. Find a function that represents the amount of air required to inflate the balloon from a radius inches to a radius of r+1 inches.

Answers

Answer:

The function that represents the amount of air is \Delta V =\cfrac 43 \pi (3r^3+3r+1)

Step-by-step explanation:

The amount of air here represents the difference between V(r) and V(r+1), so we can start working by finding an expression for the volume at r+1, and then subtract the original volume V(r).

Volume of balloon of radius r+1 inches.

We can replace r with r+1 on the formula and we get:

V(r+1)=\cfrac43 \pi (r+1)^3

We can expand (r+1)^3 since we will use it to simplify it later on.

So we will have first

(r+1)^2 = (r+1)(r+1)\n(r+1)^2 =r^2+r+r+1\n(r+1)^2 = r^2+2r+1

We can multiply that result by (r+1) to get (r+1)^3

(r+1)^3= (r+1)^2 (r+1)\n(r+1)^3=(r^2+2r+1)(r+1)\n(r+1)^3= r^3+2r^2+r+r^2+2r+1\n(r+1)^3 =r^3+3r^2+3r+1

Thus the volume equation at r+1 will be

V(r+1)=\cfrac 43 \pi (r^3+3r^2+3r+1)

Finding the amount of air required to inflate from r to r+1

The amount required to inflate is the difference of volumes, so we have

V(r+1)-V(r)=\cfrac 43 \pi (r^3+3r^2+3r+1)  \cfrac 43 \pi r^3

Combinging both into one term by factor \cfrac 43 \pi give us

V(r+1)-V(r)=\cfrac 43 \pi (r^3+3r^2+3r+1-r^3)

Simplifying

V(r+1)-V(r)=\cfrac 43 \pi (3r^2+3r+1)

And that function represents the amount required to inflate the balloon from r  to r+1 inches.

Find the measure of VYX.

Answers

Step-by-step explanation:

follow the above attachment, hope this helps you.
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