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3 years ago

Find the value of x. Round to the nearest degree.

Mathematics

2 answers:

Yuri [45]3 years ago

5 0

The answer will be 53!

dmitriy555 [2]3 years ago

4 0

Answer:

a. 53

Step-by-step explanation:

The side with length 15 is opposite the right angle, so it is the hypotenuse of the right triangle.

For angle x, the side measuring 12 is the opposite leg.

Our 3 items of interest are: angle, opposite leg, hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.

sin x = opp/hyp

sin x = 12/15

sin x = 0.8

Now we take the inverse sine of 0.8 to find the measure of the angle.

x = sin^(-1) 0.8 = 53 deg

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What is an equation of the line that passes through the point (-4,-6) and is perpendicular to the line 4x+5y=25

elixir [45]

Answer:

$y = \frac{5}{4} x - 1$

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.

First rewrite the equation of the given line in the form of y=mx +c.

4x+5y=25

5y= -4x +25

$y = - \frac{4}{5} x + 5$

The gradient of the given line is $- \frac{4}{5}$

The product of the gradient of perpendicular lines is -1.

$( - \frac{4}{5} )(gradient \: of \: line) = - 1 \\ gradient \: of \: line = - 1 \div ( - \frac{4}{5} ) \\ gradient \: of \: line = \frac{5}{4}$

Thus, m= $\frac{5}{4}$

$y = \frac{5}{4} x + c$

Substitute a coordinate to find c.

When x= -4, y= -6,

$- 6 = \frac{5}{4} ( - 4) + c \\ - 6 = - 5 + c \\ c = 5 - 6 \\ c = - 1$

Hence, the equation of the line is

$y = \frac{5}{4} x - 1$

7 0

3 years ago

Tìm một đoạn nghiệm của phương trình<br> 3/x+1 +4/(x+1)^2+5/(x+1)^3+6/(x+1)^4=10

SVETLANKA909090 [29]

Answer:

btfrt34598fc

Step-by-step explanation:

6 0

3 years ago

Which fraction is larger 8/10 or 73/100

goldenfox [79]

80/100 that is what it will be transferred to

7 0

4 years ago

Read 2 more answers

Select all expressions equivalent to 60

kvv77 [185]

The answer could be
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4 0

3 years ago

HURRYYY !!!! A bacteria population doubles in size every 5 hours. After 5 hours, the sample contains 2,000 bacteria. Which equat

Ainat [17]

Equation of y, the population size after x hours is y = 1000 (1.15)ˣ

<h3>Further explanation</h3>

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

<em />

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>r = common ratio between adjacent numbers</em>

Let us now tackle the problem!

Let :

Initial number of population = a

After 5 hours → Population = y = a × 2 = 2000

2a = 2000

a = 2000 ÷ 2

a = 1000

After 10 hours → Population = y = a × 2 × 2 = a × 2² = 1000 × 2²

After 15 hours → Population = y = a × 2 × 2 × 2 = a × 2³ = 1000 × 2³

After x hours ↓

Population = y = $1000 \times 2^{\frac{x}{5}}$

Population = y = $1000 \times (2^{\frac{1}{5}})^x$

Population = y = $\large{ \boxed {1000 \times (1.15)^x} }$

Let's prove the equation above :

After 5 hours :

Population = y = $1000 \times (1.15)^5$ = 2011 ≈ 2000 ✔

After 10 hours :

Population = y = $1000 \times (1.15)^{10}$ = 4046 ≈ 4000 ✔

After 15 hours :

Population = y = $1000 \times (1.15)^{15}$ = 8137 ≈ 8000 ✔

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

4 0

4 years ago

Read 2 more answers