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4 years ago

Are the equations sometimes, always, or never true?

1 answer:

4 0

15 + 2x - 4 = 9x + 11 - 7x
2x + 11 = 2x + 11
always true

2x + 3(4x - 1) = 2(5x + 3) + 4x
2x + 12x - 3 = 10x + 6 + 4x
14x - 3 = 14x + 6
never true

You might be interested in

By how much does a a^3-2a exceed a^2 + a -6

olganol [36]

Answer:

a³ - a² - 3a+ 6

Step-by-step explanation:

we are asked by how much does (a³-2a) exceed (a²+a-6)

in other words, we are being asked to find the difference between the 2 terms above.

Mathematically we are asked to find:

(a³-2a) - (a²+a-6) (expand parentheses by distribution property)

=(a³-2a - a²- a + 6)

= a³ - a² - 3a+ 6 (answer)

8 0

3 years ago

Write the equation of the parabola that has the vertex at point (− 1/2 ,2.3) and passes through the point (5,2 3/4 ).

Alex73 [517]

Answer:

The equation of parabola in vertex form is $y=0.015(x+0.5)^2+2.3$

Step-by-step explanation:

Given coordinate of vertex is $(-\frac{1}{2},2.3)$ and the parabola passes through the point $(5,2\frac{3}{4})$

So, the equation of parabola in vertex form is

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

Where $(h,k)$ is the coordinate of the vertex.

$(h,k)=(-\frac{1}{2},2.3)=(-0.5,2.3).\\\\So,\ h=-0.5\ and\ k=2.3$

Plugging these value in equation we get,

$y=a(x-(-0.5))^2+2.3\\\\y=a(x+0.5)^2+2.3$

Now, we will find the value of $a$

Plug the coordinate $(5,2\frac{3}{4})$

$(x,y)= (5,2\frac{3}{4})\\\\(x,y)=(5,\frac{11}{4})\\\\(x,y)=(5,2.75)$

$2.75=a(5-(-0.5))^2+2.3\\\\2.75=a(5+(0.5))^2+2.3\\\\2.75=a(5.5)^2+2.3\\\\2.75=a\times30.25+2.3\\\\2.75-2.3=a\times30.25\\\\0.45=a\times30.25\\\\\frac{0.45}{30.25}=a\\ \\a=0.0149$

Plug the value of $a$ in the equation $y=a(x+0.5)^2+2.3$

So, the equation of parabola with vertex $(-\frac{1}{2},2.3)$ and passes through the point $(5,2\frac{3}{4})$ is

$y=0.0149(x+0.5)^2+2.3$ ≅ $y=0.015(x+0.5)^2+2.3$

5 0

3 years ago

A beach ball has a diameter of 18 inches. What is the approximate volume of the beach ball?

balu736 [363]

1. To solve this problem, you must aplpy the formula for calculate the volume of a sphere, which is:

V=4/3(πr)

V is the volume of the sphere.
r is the radius of the sphere.

2. You must calculate the radiius. You have that the beach ball has a diameter of 18 inches, then:

r=diametert/2
r=18 inches/2
r=9 inches

3. When you substitute r= 9 inches into the formula, you obtain:

V=4/3(πr)
V=3053.62 inches³

4 0

3 years ago

Seventy percent of light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircra

alukav5142 [94]

Answer:

Figure out the various probabilities first, that will make the rest of the questions easier:

P(discovered) = .7

P(not discovered) = 1 - .7 = .3

P(locator|discovered) = .6

P(no locator|discovered) = 1 - .6 = .4

P(locator|not discovered) = 1 - .9 = .1

P(no locator|not discovered) = .9

P(discovered and locator) = .7 * .6 = .42

P(discovered and no locator) = .7 * .4 = .28

P(not discovered and locator) = .3 * .1 = .03

P(not discovered and no locator) = .3 * .9 = .27

a) The total probability that an aircraft has a locator is .42 + .03 = .45. So the probability it will not be discovered, given it has a locator, is .03/.45 = .067

b) The total probability that an aircraft does not have a locator is .28 + .27 = .55. So the probability it will be discovered, given it does not have a locator, is .28/.55 = .509

c) Probability that 7 are discovered = C(10,7) * P(discovered|locator)^7 * P(not discovered|locator)^3

We already figured out P(not discovered|locator) = .067, so P(discovered|locator) = 1-.067 = .933. C(10,7) = 10*9*8, so we can compute total probability: 10*9*8 * .933^7 * .067^3 = .133

Step-by-step explanation:

3 0

4 years ago

i left home going to the movies. i had $90 when i left the house. i spent 31/45 on tickets, and out of the remaining cash i spen

ad-work [718]

First you can find $\frac{31}{45}$ of 90.

90 x $\frac{31}{45}$ = 62

Next, you have $62 left and spent $\frac{1}{7}$ of it. Meaning you have $\frac{6}{7}$ of 62 left.

62 x $\frac{6}{7}$ = about 53.14285

As your answer is not a whole number, you could round according to whatever guidelines your homework has given you (for example - rounding to the 2nd decimal place $53.14)

8 0

3 years ago