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3 years ago

PLEASE HELP ASAP WILL GIVE BRAINLIEST 5 STAR RATING THANKS AND BRAINLIEST!

Mathematics

1 answer:

PolarNik [594]3 years ago

5 0

Answer:

Step-by-step explanation:

If ABCD is a rectangle, then diagonals are congruent: AC = BD.

We have

AC = 5y - 2

BD = 4y + 1

Substitute:

5y - 2 = 4y + 1 <em>add 2 to both sides</em>

5y - 2 + 2 = 4y + 1 + 2

5y = 4y + 3 <em>subtract 4y from both sides</em>

5y - 4y = 4y - 4y + 3

y = 3

In a parallelogram opposite angles are congruent. Therefore m∠D = m∠B.

We have m∠D = 125° → m∠B = 125°

In the rhombus, the diagonals are bisectors of the rhombus angles.

Therefore ∠SPR and ∠QPR are congruent.

We have

m∠SPR = (2x +15)°

m∠QPR = (3x - 5)°

The equation:

2x + 15 = 3x - 5 <em>subtract 15 from both sides</em>

2x + 15 - 15 = 3x - 5 - 15

2x = 3x - 20 <em>subtract 3x from both sides</em>

2x - 3x = 3x - 3x - 20

-x = -20 <em>change the signs</em>

x = 20

Substitute it to the expression m∠SPR = (2x + 15)°:

m∠SPR = (2(20) + 15)° = (40 + 15)° = 55°

m∠SPR = m∠QPR → m∠QPR = 55°

∠SPQ = ∠SPR + ∠QPR → m∠SPQ = 2(55°) = 110°

In the parallelogram, the sum of the angle measures on one side is 180°.

Therefore we have the equation:

(2x + 15) + x = 180 <em>combine like terms</em>

(2x + x) + 15 = 180 <em>subtract 15 from both sides</em>

3x + 15 - 15 = 180 - 15

3x = 165 <em>divide both sides by 3</em>

3x/3 = 165/3

x = 55

In a parallelogram opposite angles are congruent.

Therefore z = y and x = 2z + 9 → x = 2y + 9 (*)

In the parallelogram, the sum of the angle measures on one side is 180°.

Therefore x + y = 180 (**)

Substitute (*) to (**)

(2y + 9) + y = 180 <em>combine like terms</em>

(2y + y) + 9 = 180 <em>subtract 9 from both sides</em>

3y + 9 - 9 = 180 - 9

3y = 171 <em>divide both sides by 3</em>

y = 57

Put it to (*):

x = 2(57) + 9

x = 114 + 9

x = 123

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3 years ago

A band consists of 3 woodwinds for every 7 members of the band. The independent quantity represents the total members of the ban

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Answer: $k=\frac{3}{7}$

Step-by-step explanation:

For this exercise it is important to remember the following:

The constant of proportionality, which is represented as "k", describe the constant ratio of two quantities that are proportional (the independent and dependent variables).

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3 years ago

What is the solution to -3a-4

Aleksandr-060686 [28]

Answer:

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Step-by-step explanation:

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3 years ago

Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.

Gennadij [26K]

The statement about the line that passes through (-2, 0) and (2, -4) that are true are:

Option B:The line intersects the y-axis at (0, −2).

Option C: The equation of the line is y = −x − 2.

Option D: The line intersects the x-axis at (−2, 0).

<u>Solution:</u>

Given, two points are (-2, 0) and (2, -4)

We have to select the options that states true about line that passes through given two points.

Now, let us find the line equation that passes through given two points using point slope form.

$\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right) \text { where } \mathrm{m} \text { is slope and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { is a point on the line. }$

Now slope "m" is given as:

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0-(-4)}{-2-2}=\frac{4}{-4}=-1$

Then, line equation = y – 0 = -1(x – (-2))

y = -1(x + 2)

y = -x – 2 --- equation 1

Now let us check options.

<u>Option a)</u> slope of line is 1

We know that slope of our line is -1 so this option is wrong.

<u>Option b)</u> line intersects y – axis at (0, -2)

When line meets y – axis x becomes 0 ⇒ 0 + y + 2 = 0 ⇒ y = -2 so point is (0, -2).

This option is right.

<u>Option c) </u>equation of line is y = -x – 2

The given equation is x + y + 2 = 0 ⇒ y = -x – 2 . so this option is correct.

<u>Option d) </u>line intersects at (-2, 0)

When line meets x – axis y becomes 0 ⇒ x + 0 + 2 = 0 ⇒ x = -2. So point is (-2, 0).

This option is right.

Hence, options b, c, d are correct.

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4 years ago

You dive 21 feet from the surface of a lake in 7 seconds. What is the mean change in your position in feet per second?

Alexxandr [17]

Answer:

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21 feet + 15 feet =36 feet

You are 36 feet from the surface.

Step-by-step explanation:

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3 years ago