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2 years ago

If Fred is x years old now, and his sister is half as old, how old will his sister be in 5 years?

Mathematics

1 answer:

Elanso [62]2 years ago

6 0

Answer: x/2+5 years old

Step-by-step explanation:

His sister would be x/2+5 years old. x/2 is his sisters age right now, and +5 is years later!

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706,421 rounded to the neares thousand

ella [17]

706,421 rounded to the nearest thousand is 706,000 because the 421 is less than 500 so the 6 would remain a 6.

3 0

3 years ago

The school purchased baseball equipment and uniforms for a total cost of $1836. the equipment cost $612 and the uniforms were $2

liraira [26]

Answer:

48 uniforms

Step-by-step explanation:

1836-612=1224.

1224/25.50=48.

Checked answer:

25.50 x 48= 1224

6 0

3 years ago

What are the slope and y-intercept of the linear function graphed?

vitfil [10]

Answer:

Its a

Step-by-step explanation:

7 0

2 years ago

What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

Vertex — Formula

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

Vertex — Calculus

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

7 0

2 years ago

Rewrite the expression 9(6 + 5) as the sum of 54 and another whole number.

lisabon 2012 [21]

Answer:

45 is the other whole number.

Step-by-step explanation:

Method I:

Given: 9(6 + 5)

Distribute 9 over 6 and 5. We get:

9 X 6 + 9 X 5 = 54 + 45

⇒ 45 should be added to 54 to arrive at the sum.

Method 2:

Given: 9(6 + 5)

⇒ 9 X 11 [Since, 6 + 5 = 11]

= 99

Therefore, 99 = 54 + a

⇒ a = 99 - 54

⇒ a = 45

Hence, the other number is 45.

6 0

2 years ago