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Sveta_85 [38]
3 years ago
6

1. What is solution to 0.2(6x - 12) = 0.3(6 - 4x)

Mathematics
1 answer:
kompoz [17]3 years ago
5 0

Answer:

<h3><u>x = 1.75</u></h3>

Explanation:

0.2(6x - 12) = 0.3(6 - 4x)

  • <u>Simplify both sides of the equation</u>

0.2(6x − 12) = 0.3(6 − 4x)

(0.2)(6x) + (0.2)(−12) = (0.3)(6) + (0.3)(−4x) (Distribute)

1.2x + −2.4 = 1.8 + −1.2x

1.2x − 2.4 = −1.2x + 1.8

  • <u>Add 1.2x to both sides</u>

1.2x − 2.4 + 1.2x = −1.2x + 1.8 + 1.2x

2.4x − 2.4 = 1.8

  • <u>Add 2.4 to both sides</u>

2.4x − 2.4 + 2.4 = 1.8 + 2.4

2.4x = 4.2

  • <u>Divide both sides by 2.4</u>

2.4x / 2.4 = 4.2 / 2.4

  • x = 1.75
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Factor the trinomial. Factor out the GCF first.<br> 5x^2y - 30xy^2 - 35y^3
anzhelika [568]

Answer: 5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)

Step-by-step explanation:

GCF = Greatest common factor.

For example: 6 is the GCF of 12 and 18.

The given expression: 5x^2y - 30xy^2 - 35y^3

It can be written as

5x^2y - (5\times6)x( y\times y) - (5\times7)(y^2\times y)

Taking out common factor  5y , we get

5y(x^2-6xy-7y^2)\\\\ =5y(x^2+xy-7xy-7y^2)\  \ [\because-6xy=xy-7xy]\\\\=5y(x(x+y)-7y(x+y))\\\\= 5y((x+y)(x-7y))\\\\=5y(x+y)(x-7y)

Hence, 5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)

3 0
3 years ago
The perimeter of a rectangular campsite is 64 cm and its area is 207 cm. Find the length and the breadth of the rectangle.
AlladinOne [14]
Perimeter Formula:
2l + 2b = 64


Area Formula:
l \times b = 207
Set perimeter Formula equal to b:
2l + 2b = 64 \\ 2(l + b) = 64 \\  l+ b = 32 \\ b = 32 - l
Plug formula for be we just made above into the area Formula:
(32 - l) \times l = 207


Solve for L (you'll have to use quadratic formula) then plug that back into the area Equation and solve for b.

Here's a link to where the problem has been explained before (they go into more detail than me).

https://brainly.ph/question/468631

lmk if you need any more help
6 0
3 years ago
Read 2 more answers
Help ASAP show work please thanksss!!!!
Llana [10]

Answer:

\displaystyle log_\frac{1}{2}(64)=-6

Step-by-step explanation:

<u>Properties of Logarithms</u>

We'll recall below the basic properties of logarithms:

log_b(1) = 0

Logarithm of the base:

log_b(b) = 1

Product rule:

log_b(xy) = log_b(x) + log_b(y)

Division rule:

\displaystyle log_b(\frac{x}{y}) = log_b(x) - log_b(y)

Power rule:

log_b(x^n) = n\cdot log_b(x)

Change of base:

\displaystyle log_b(x) = \frac{ log_a(x)}{log_a(b)}

Simplifying logarithms often requires the application of one or more of the above properties.

Simplify

\displaystyle log_\frac{1}{2}(64)

Factoring 64=2^6.

\displaystyle log_\frac{1}{2}(64)=\displaystyle log_\frac{1}{2}(2^6)

Applying the power rule:

\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}(2)

Since

\displaystyle 2=(1/2)^{-1}

\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}((1/2)^{-1})

Applying the power rule:

\displaystyle log_\frac{1}{2}(64)=-6\cdot log_\frac{1}{2}(\frac{1}{2})

Applying the logarithm of the base:

\mathbf{\displaystyle log_\frac{1}{2}(64)=-6}

5 0
2 years ago
Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle is translated 4 units down and 3 units left. Which rule r
crimeas [40]

Option C: (x, y) \rightarrow(x-3, y-4) ; (5,-1) is the coordinates of C after translation.

Explanation:

The triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3).

Also, given that the triangle is translated 4 units down and 3 units left.

We need to determine the coordinates of the vertex C after translation.

The triangle is shifted 4 units down means subtracting 4 units from the y - coordinate of the graph.

Thus, it can be written as y-4

Also, the triangle is shifted 3 units left means subtracting 3 units from the x - coordinate of the graph.

Thus, it can be written as x-3

Thus, the translation is given by

(x, y) \rightarrow(x-3, y-4)

The vertices of C after translation can be determined by

(8, 3) \rightarrow(8-3, 3-4)\implies (5,-1)

Thus, (x, y) \rightarrow(x-3, y-4) ; (5,-1) is the coordinates of C after translation.

Hence, Option C is the correct answer.

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Nana76 [90]
Substitute 8 for x in the function.
y=50(8)=400
He would travel 400 miles
7 0
3 years ago
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