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2 years ago

-67 = 6x - 1

1 answer:

5 0

-66=6x
x=-11

-4e=28
e=-7

-40=-5q
q=8

-96=12t
t=-8

10k=250
k=25

-x=-72
X=72

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2. Graph the solution set to the following inequality:<br> 7-y<2x

nirvana33 [79]

Step-by-step explanation:

First solve for y,

7-y<2x

7-2x<y

y>-2x+7

your y intercept would be (0,7)

and your slope would be -2/1 so, you go down 2 and 1 to the right.

Since this is a greater than symbol, we have to shade above the line and the line would also be a dotted line.

7 0

2 years ago

(ASAPPP) The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the

prohojiy [21]

Answer:

The instantaneous velocity at $t = 2$ is $-6$ .

Step-by-step explanation:

We have the position as the function

$s(t) = -2 - 6t$

As we know that the velocity is the rate of change of position over time, so it is basically the derivative of the function.

so finding the derivate of $s(t) = -2 - 6t$

∴ $s'(t)=-6$

The instantaneous velocity at $t = 2$

$s'(2)=-6$

Therefore, the instantaneous velocity at $t = 2$ is $-6$ .

Please note that the negative value indicates the direction of movement, in this case, it would be backward.

7 0

2 years ago

A bowl of fruit punch is made by mixing 3 parts orange juice to 8 parts mango juice. How much mango juice needed to make 715 ml

Morgarella [4.7K]

Answer: 520 ml

Step-by-step explanation : Add 8+3. Then divide 11 into 715. Multiply 65 by 8.

3 0

3 years ago

In the given figure ABCD is a tripepizeum with AB||CD. If AO = x-1, CO = BO = x+1 and CD = x+4. Find the value of x.

Hitman42 [59]

$\longmapsto$ The value of "x" is 5.

$\large\underline{\sf{Solution-}}$

Given that,

A trapezium ABCD in which AB || CD such that

AO = x - 1

CO = BO = x + 1

OD = x + 4

Now,

$\rm In \: \triangle \: AOB \: and \: \triangle \: COD$

$\rm \: \angle \: AOB \: and \: \angle \: COD \: \: \{vertically \: opposite \: angles \}$

$\rm \: \angle \:ABO \: and \: \angle \: CDO \: \: \{alternate \: interior \: angles \}$

$\bf \: \triangle \: AOB \: \sim \: \triangle \: COD \: \: \: \{AA \: similarity \}$

$\bf\longmapsto\:\dfrac{AO}{CO} = \dfrac{BO}{DO}$

$\rm \longmapsto\:\dfrac{x - 1}{x + 1} = \dfrac{x + 1}{x + 4}$

$\rm \longmapsto\:(x - 1)(x + 4) = {(x + 1)}^{2}$

$\rm \longmapsto\: {x}^{2} - x + 4x - 4 = {x}^{2} + 1 + 2x$

$\rm \longmapsto\: 3x - 4 = 1 + 2x$

$\rm \longmapsto\: 3x - 2x= 1 +4$

$\bf\longmapsto \:x = 5$

7 0

2 years ago

Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

5 0

1 year ago