-2(3x+9)=24 ( find the x )

Answers

Answer 1

Answer: Hello!! Let's solve this!

-2(3x+9)= 24

Distribute the 2 using the distributive property, which states: a(b + c) = ab + ac

-2(3x+9)= 24

-2(3x) + (-2)(9) = 24

Simplify it

-6x - 18 = 24

Add 18 on both sides

-6x - 18 + 18 = 24 + 18

-6x = 42

Divide -6 on both sides

-6x/-6 = 42/-6

x = -7

Your answer is x = -7.

Hope I helped! If you have any other questions or would like further explanation just let me know!! :)

Answer 2

Answer: Distribute -2 into parentheses for -6x-18=24
add 18 for -6x=42 for -7 so your answer is x=-7

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What are the solutions to the equation x-7/x=6? a. x=-7 and x=1
b. x=-6 and x=-1
c. x=-1 and x=7
d. x=1 and x=6

Answers

$x - (7)/(x) = 6$
$(x^(2))/(x) - (7)/(x) = 6$
$(x^(2) - 7)/(x) = 6$
$x^(2) - 7 = 6x$
$x^(2) - 6x - 7 = 0$
$x^(2) - 7x + x - 7 = 0$
$x(x) - x(7) + 1(x) - 1(7) = 0$
$x(x - 7) + 1(x - 7) = 0$
$(x + 1)(x - 7) = 0$
$x + 1 = 0$ $or$ $x - 7 = 0$
$x = -1$ $or$ $x = 7$

Answer:

Step-by-step explanation:

The equation is $x-(7)/(x)=6$

LCM of the denominator on the left side gives us:

$(x^(2)-7)/(x)=6$

Cross multiplying and arranging gives us:

$x^(2)-7=6x\nx^(2)-6x-7=0$

This is a binomial, to factor this, we have to think of 2 numbers that multiplied gives us $-7$ [the constant term] and added gives us $-6$ [the coefficient of x].

The two numbers are: $-7$ and $1$ .

Now we can write:

$x^(2)-6x-7=0\n(x-7)(x+1)=0$

Hence, either $(x-7)=0$ OR $(x+1)=0$ . This gives us two solutions, $x=7$ and $x=-1$ . Answer choice C is correct.

Which property can be used to show that if 3a = 4b, then 4b = 3a?

Answers

Answer:

commutative property

Step-by-step explanation:

The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at the origin?

Answers

The image of the point (-6, -2) after dilation by a scalefactor of 4 centered at the origin is (-24, -8).

What is a scale factor?

A scalefactor is defined as the ratio between the scale of a given original object and a new object,

We have,

To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.

Substituting the values given in the problem, we get:

(x', y') = (4*(-6), 4*(-2))

Simplifying,

(x', y') = (-24, -8)

Therefore,

The image of the point (-6, -2) after dilation by a scalefactor of 4 centered at the origin is (-24, -8).

Learn more about scalefactors here:

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How do you solve this?

Answers

you X to the second power.. 4 to the second power is 16 and 16-16=0 so x=4

Add 16
x² - 16 = 0
+ 16 +16

x² = 16
Take square root

$√(x^2) = √(16)$

Remember when you take the square root of a perfect square you get two values. +ve and -ve

x = -4
x = 4

because (-4)² = 16
( 4)² = 16

Differentiate the following functions s=4e^3t-e^-2.5 w.r.t.t

Answers

Answer:

$\displaystyle (ds)/(dt) = 12e^(3t)$

General Formulas and Concepts:

Algebra I

Functions
Function Notation

Calculus

Derivatives

Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)$

eˣ Derivative: $\displaystyle (d)/(dx) [e^u]=e^u \cdot u'$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle s = 4e^(3t) - e^(-2.5)$

Step 2: Differentiate

eˣ Derivative: $\displaystyle (ds)/(dt) = 4e^(3t) \cdot (d)/(dt)[3t] - (d)/(dt)[e^(-2.5)]$
Basic Power Rule: $\displaystyle (ds)/(dt) = 4e^(3t) \cdot 3t^(1 - 1) - 0$
Simplify: $\displaystyle (ds)/(dt) = 12e^(3t)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

The local grocery store usually sells large bottles of water for $2.69 each. This week they have a promotion, 3 large bottles for $6.30. How much less is the cost of a large bottle this week with the promotion?

Answers

Answer:

$0.59

Step-by-step explanation:

We first find the unit rate of the large water bottles after the promotion. To do this we divide 6.3 by 3 to get 2.1. Then we want to subtract 2.69 by 2.1 to get our final answer, $0.59.

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