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3 years ago

If x is a positive number greater than 10, what is always true about the solution to the problem to -3 + x ?

Mathematics

1 answer:

alexandr402 [8]3 years ago

3 0

Answer:

The equation answer will always be positive

Step-by-step explanation:

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Last month, a factory produced 800 television sets. This month, the same factory produced 1,064 television sets. The increase in

Harlamova29_29 [7]

Your answer is 264
1,064 - 800= 264

5 0

4 years ago

The area of a rectangle is 70 m², and the length of the rectangle is 11 m less than three times the width. Find the dimensions o

11111nata11111 [884]

Step-by-step explanation:

the area of a rectangle is

length × width

in our case

length × width = 70 m²

length = 3×width - 11

we can use this second equation in the first and get

(3×width - 11) × width = 70

3×width² - 11×width - 70 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 3

b = -11

c = -70

x = (11 ± sqrt((-11)² - 4×3×-70))/(2×3) =

= (11 ± sqrt(121 + 840))/6 =

= (11 ± sqrt(961))/6

x1 = (11 + 31)/6 = 42/6 = 7

x2 = (11 - 31)/6 = -20/6 = -10/3

the negative solution is not applicable for a length in an object.

so, only x1 = 7 m is our solution.

the width of the rectangle is 7 m.

the length = 3×width - 11 = 3×7 - 11 = 21-11 = 10 m

7 0

2 years ago

If f(x) = 2x+7 and g(x) = -3x+5, what is f(g(1))?

Murrr4er [49]

Answer:

$f(g(1))=11$

Step-by-step explanation:

So we have the two functions:

$f(x)=2x+7\text{ and } g(x)=-3x+5$

And we want to find f(g(1)).

So, let's find g(1) first:

$g(x)=-3x+5$

Substitute 1 for x:

$g(1)=-3(1)+5$

Simplify:

$g(1)=-3+5$

Add:

$g(1)=2$

So:

$f(g(1))=f(2)$

Now, substitute 2 for x in f(x):

$f(x)=2x+7\\f(2)=2(2)+7$

Multiply:

$f(2)=4+7$

Add:

$f(2)=11$

So:

$f(g(1))=11$

8 0

3 years ago

The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form

azamat

Answer:

$\large \boxed{y = (x - 5)^{2} + 2 }$

Step-by-step explanation:

y = x² - 10x + 27

y = ax² + bx + c

This is the general form of the equation for a parabola.

We must convert it to the vertex form

y = (x - h)² + k, where (h,k) are the coordinates of the vertex.

We can do this by completing the square.

$\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}$ The figure below shows that your parabola has its vertex at (5,2).

4 0

4 years ago

WHAT ARE THESE TWO ILL GIVE BRAINLESS AND SHOW UR WORK

belka [17]

N= 66°
k= 29°

All triangles add up to 180 so that’s how i got those

4 0

3 years ago

If x is a positive number greater than 10, what is always true about the solution to the problem to -3 + x ?​

If x is a positive number greater than 10, what is always true about the solution to the problem to -3 + x ?