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3 years ago

Solve the system of equations using the substitution method.

Mathematics

2 answers:

Minchanka [31]3 years ago

4 0

Answer:

$y = - 2 \\ x = - 2$

Step-by-step explanation:

<h3>Question</h3>

$- 5x - 3y = 16 \: \: = > 1 \\ y = x = > 2$

Now you can write the 1st equation like this.

$- 5x - 3y = 16 \\ x = y \\ so \: \: you \: \: \: can \: \: write \\ - 5y - 3y = 16 \: \: \: = > 3$

Now simply Solve the 3rd equation

$- 5y - 3y = 16 \\ - 8y = 16 \\ \frac{ - 8y}{ - 8} = \frac{16}{ - 8} \\ y = - 2$

Now replace y as 2 in the 2nd equation like this

$y = x \\ - 2 = - 2$

Now let's check whether the answer correct or wrong

$- 5x - 3y = 16 \\ - 5 \times - 2 - 3 \times - 2 = 16 \\ 10 + 6 = 16 \\ 16 = 16$

Yes, the answer is correct

hope this helps you !!

Galina-37 [17]3 years ago

3 0

Answer:

x = y = -2

Step-by-step explanation:

Hope this helps

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Carly is buying deli meat for her lunches this week. Turkey is on sale for $5.80 per pound. If Carly buys 1.25 pounds of turkey,

alisha [4.7K]

Answer:

Carly will have to spend $7.25

Step-by-step explanation:

We know that:

1 pound of turkey = $5.80

To find how much 1.25 pounds of turkey will cost, multiply:

5.80 x 1.25 = 7.25

Therefore, 1.25 pounds of turkey will cost $7.25

I really hope this helps!

-SpaceMarsh

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3 years ago

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Can someone answer this question??

Andrews [41]

Answer:

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Step-by-step explanation:

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3 years ago

5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.

lesya692 [45]

9514 1404 393

Answer:

±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

|x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

A·cos(c) = 3 and A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

x = A·sin(θ +c) . . . . for some angle c

x = (√58)sin(θ +c)

This has the bounds ±√58.

3 0

3 years ago

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h

creativ13 [48]

It is given in the question that

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by

$V = x^2h cm^3$

And the edge length of the base is 12 cm, the edge length of the base is decreasing at a rate of 2 cm/min, the height of the box is 6 cm, and the height is increasing at a rate of 1 cm/min.

Here we differentiate V with respect to t, and we use product rule, that is

$V = 2xh(dx/dt)+ x^2(dh/dt)$

Substituting the given values , we will get

$[tex]dV/dt = 2(12)(6)(-2)+ 12^2(1)$ [/tex]

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So at that moment, the volume is decreasing at the rate of

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4 0

3 years ago

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On a single roll of a pair of dice, what are the odds against rolling a sum of 12?

o-na [289]

Answer:

$\frac{1}{35}$

Step-by-step explanation:

On a single roll of a pair of dice. When a pair of dice are rolled the possible outcomes are as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

The number of outcomes that gives us 12 are (6,6). There is only one outcome that gives us sum 12.

Total outcomes = 36

Odd against favor = $\frac{non \ favorable\ outcomes}{favorable \ outcomes}$

Number of outcomes of getting sum 12 is 1

Number of outcomes of not getting sum 12 is 36-1= 35

odds against rolling a sum of 12= $\frac{1}{35}$

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3 years ago