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3 years ago

Positive or negative exponents represesent very small numbers

Mathematics

1 answer:

Taya2010 [7]3 years ago

3 0

Answer:

<u>Negative</u> exponents represent very very small numbers ( ex. .0000000006)

Step-by-step explanation:

can i get brainly?

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(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

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

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

A machinist can produce 114 parts in 6 minutes. At this rate, how many parts can be produced in 15 minutes?

KonstantinChe [14]

285

just figure out how many is made then multiple that by 15

4 0

2 years ago

Read 2 more answers

if y is the midpoint of xz, y is located at (3,-1), and z is located at (11,-5), find the coordinates of x

svlad2 [7]

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{11}~,~\stackrel{y_2}{-5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{11+x}{2}~~,~~\cfrac{-5+y}{2} \right)=\stackrel{\stackrel{midpoint}{y}}{(3,-1)}\implies \begin{cases} \cfrac{11+x}{2}=3\\[1em] 11+x=6\\ \boxed{x=-5}\\ \cline{1-1} \cfrac{-5+y}{2}=-1\\[1em] -5+y=-2\\ \boxed{y=3} \end{cases}$

7 0

3 years ago

Read 2 more answers

there are 2.54 centimeters in 1 inch. how many centimeters are there in 1 foot? in 1 yard? explain your reasoning

AVprozaik [17]

Answer:

1 foot = 30.48 centimeters

1 yard = 91.44 centimeters

Step-by-step explanation:

If there are 2.54 centimeters in an inch, and 12 inches in a foot, then you need to multiply 2.54 by 12.

Their are 36 inches in a yard so you need to multiply 2.54 by 36

3 0

3 years ago

Juanita says that a scale of 1 in. : 0.4 ft is equivalent to the ratio 6 in. : 2.4 ft. Do you agree? Explain why or why not.

Umnica [9.8K]

Answer:
Agree

Explanation:
The given scale is:
1 in : 0.4 ft
We want to get the equivalent ft for 6 in, therefore all we have to do is cross multiplication as follows:
1 in : 0.4 ft
6 in : ??
equivalent ft = (6*0.4) / (1) = 2.4 ft
This means that:
6 in : 2.4 ft is equivalent to the given scale

7 0

3 years ago