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3 years ago

10

A recipe calls for 3/5 gallon of milk. How much milk is needed to make half the recipe? If possible, write the answer in reduced

form.
3/10 gallon
2/3 gallon
6/5 gallons
1/2 gallon

1 answer:

Sloan [31]3 years ago

3 0

Answer:

3/10 gallon

Step-by-step explanation:

3/5 x 1/2 = 3/10

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The graph of y=tan(x) is vertically stretched by a factor of 7, shifted a distance of 12 units to the left, reflected across the

Mekhanik [1.2K]

Step-by-step explanation:

A transformation(s) of a parent function is

$f(x) = a(bx - c) + d$

where a is vertical compression/stretched or reflection

B is horinzotnal compression/stretch or reflection

C is horinzontal translation

D is vertical translation.

The parent function is

$y = \tan(x)$

First, we stretched this by 7

so we have

$y = 7 \tan(x)$

We need to shift this 12 units to the left so we have

$y = 7 \tan(x + 12)$

We need to reflect this across x axis so we get

$y = - 7 \tan(x + 12)$

We need to shift this downwards 15 so we get

$y = - 7 \tan(x + 12) - 15$

or because tan is a odd function you could say

$7 \tan( - (x + 12) ) - 15$

$7 \tan( - x - 12) - 15$

6 0

3 years ago

2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

2 years ago

Read 2 more answers

salantis [7]

Answer:

1. 424

2.471

3.512

Step-by-step explanation:

1. 10×12+8×10+8×13+8×15

=120+80+104+120

=424

2. 5×24+9×24+9×15+9×15

=120+216+135

=471

3. 24×16+2×24+2×20+2×20

=384+48+40+40

=512

3 0

3 years ago

Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour

Lera25 [3.4K]

The last one is correct because 60+35+35+35=165
55+55+55=165

8 0

3 years ago

2/5 times ( -10)=?<br> ?=

Rudiy27

$\frac{2}{5} \times ( - 10)$

$2 \times - 2$

$- 4$

6 0

3 years ago

Read 2 more answers