.8x-.3y=5<br> 1.4x-.9y=11

It takes a machine 15 hour to assemble a toy.

solniwko [45]

12 toys. Dividing 15 by 60 equals 4 so 4 tots in a hour. Then multiple the 4 toys an hour by 3 hours.

8 0

3 years ago

Solve for y: 5x-3y<75

Arada [10]

y<-5/3x+25 Is your answer. To get it you subtract the 5x to both sides and then you divide the 3 on both sides

answer : y < -5/3x +25

4 0

3 years ago

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

$f(x)=3x(x^2-5x+x-5)$

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0

3 years ago

Solve for n: n/3 > 66 2/3

Kitty [74]

Answer: The 2 answers are inequality form and interval notation: n>200, and (200, ∞).

Step-by-step explanation: To solve for n, you’ll need to simplify the both sides of the inequality, and then isolating the variable.

5 0

3 years ago

Adam divides 32/8032. In which place should he write the first digit of the quotient?

kow [346]

Answer:

We have a quotient between a 2 digit number and a 4 digit number.

The usual rule for this type of problems is:

If the denominator has n more digits than the numerator, then the first digit will be in the nth position at the right of the decimal point.

If also, the denominator is larger than the numerator times 10^n, then the decimal will be moved another place to the right.

For example, if we divide 10 by 100 we have:

10/100

The denominator has one more digit than the numerator, then n = 1.

this means that the first digit of the quotient, will be on the first place at the left of the decimal point.

We can solve the quotient to get:

10/100 = 0.1

And, as we predicted, the first decimal is in the first place.

Now, with our quotient we have:

32/8032

n = 2.

and:

32*10^n = 3200

The denominator is larger than this, then we will move the first decimal to another place to the right.

Then we should expect to have the first decimal in the third place after the decimal point.

We can solve the quotient to get:

32/8032 = 0.0039

As we expected.

3 0

3 years ago

.8x-.3y=5 1.4x-.9y=11