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2 years ago

Solve the system of equations. – 3y +51 = 26 – 2y - 51 = -16

Mathematics

2 answers:

Natalka [10]2 years ago

6 0

Answer:

-2

Step-by-step explanation:

add both equations up

-5y = 10 ➡ y = -2

marissa [1.9K]2 years ago

5 0

Answer:

y= -2

Step-by-step explanation:

ADDING BOTH EQUATIONS

-3y + 51 =26

-<u>2y -51 = -16</u>

-5y = 10

-5y/5 = 10/5

-y =2

y = -2

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Simplify the expression.<br> -5+i/2i

Lostsunrise [7]

Answer:

$\rm - \dfrac{11}{2}$

Step-by-step explanation:

$\rm Simplify \: the \: following: \\ \rm \longrightarrow - 5 + \dfrac{i}{2} i \\ \\ \rm Combine \: powers. \\ \rm \dfrac{i \times i}{2} = \dfrac{i^{1 + 1}}{2}: \\ \rm \longrightarrow - 5 + \dfrac{i^{1 + 1}}{2} \\ \\ \rm 1 + 1 = 2: \\ \rm \longrightarrow - 5 + \dfrac{i^2}{2} \\ \\ \rm i^2 = -1: \\ \rm \longrightarrow - 5 + \dfrac{( - 1)}{2} \\ \\ \rm \longrightarrow - 5 - \dfrac{1}{2} \\ \\ \rm Put \: - 5 - \dfrac{1}{2} \: over \: the \: common \: denominator \: 2. \\ \rm - 5 - \dfrac{1}{2} = \dfrac{2( - 5)}{2} - \dfrac{1}{2} : \\ \rm \longrightarrow \dfrac{ - 5 \times 2}{2} - \dfrac{1}{2} \\ \\ \rm 2 (-5) = -10: \\ \rm \longrightarrow \dfrac{ - 10}{2} - \dfrac{1}{2} \\ \\ \rm \dfrac{ - 10}{2} - \dfrac{1}{2} = \dfrac{ - 10 - 1}{2} : \\ \rm \longrightarrow \dfrac{ - 10 - 1}{2} \\ \\ \rm -10 - 1 = -11: \\ \rm \longrightarrow - \dfrac{11}{2}$

7 0

2 years ago

Which of the following is equivalent to tan2θcos(2θ) for all values of θ for which tan2θcos(2θ) is defined?

Aloiza [94]

Answer:

2sin²θ - tan²θ

Step-by-step explanation:

Given

tan²θcos(2θ)

Required

Simplify

We start by simplifying cos(2θ)

cos(2θ) = cos(θ+θ)

From Cosine formula

cos(A+A) = cosAcosA - sinAsinA

cos(A+A) = cos²A - sin²A

By comparison

cos(2θ) = cos(θ+θ)

cos(2θ) = cos²θ - sin²θ ----- equation 1

Recall that cos²θ + sin²θ = 1

Make sin²θ the subject of formula

sin²θ = 1 - cos²θ

Substitute sin²θ = 1 - cos²θ in equation 1

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 +cos²θ

cos(2θ) = cos²θ + cos²θ - 1

cos(2θ) = 2cos²θ - 1

Substitute 2cos²θ - 1 for cos(2θ) in the given question

tan²θcos(2θ) becomes

tan²θ(2cos²θ - 1)

Open brackets

2cos²θtan²θ - tan²θ

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

Simplify tan²θ

tan²θ = (tanθ)²

Recall that tanθ = sinθ/cosθ

So, we have

tan²θ = (sinθ/cosθ)²

tan²θ = sin²θ/cos²θ

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

Substitute sin²θ/cos²θ for tan²θ

2cos²θtan²θ - tan²θ becomes

2cos²θ(sin²θ/cos²θ) - tan²θ

Open bracket (cos²θ will cancel out cos²θ) to give

2(sin²θ) - tan²θ

2sin²θ - tan²θ

Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ

Option E is correct

7 0

2 years ago

04.01)Which unit rate is the lowest price per ounce? Choice A: 15 ounces of chocolate chips for $2.49 Choice B: 20 ounces of cho

riadik2000 [5.3K]

The unit rates are equal to one another.

6 0

2 years ago

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Find the diameter of the object.

Anni [7]

Answer:

1 $\frac{1}{5}$ centimeters

Step-by-step explanation:

The diameter is equal to the radius × 2. We know that the radius is equal to 3/5 centimeters.

To solve this you must do $\frac{3}{5}$ × 2.

This equals $\frac{6}{5}$ , or 1 $\frac{1}{5}$ cm.

5 0

2 years ago

8x2 - 6x + 3 – 2x – 10x?

Marina CMI [18]

Answer:

8 $x^{2}$ + 3 + -6x

Step-by-step explanation:

First we need to find the like terms so that we could add them. In this case the like terms are,

1. 6x , -2x , -10x

So, these are the only terms that we can add in this expression.

Hence,

=> 8 $x^{2}$ + 3 + (6x - 2x - 10x)

=> 8 $x^{2}$ + 3 + -6x

And this is as simple as this expression can go until we find the value of "x" which is not yet told.

Hope my answer helped.

4 0

2 years ago

Read 2 more answers