MATHEMATICS HIGH SCHOOL

Express the ratio 20:35 in simplest form.

Answers

Answer 1

Answer:

Answer:4:7

Step-by-step explanation:

20:35

/5 on both sides.

4:7

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Rewrite with only sin x and cos x.cos 2x - sin x
Select one:
a. cos2x - sin2x - sin x
b. cos2x - sin3x
c. cos2x + sin2x + sin x
d. cos2x - 3 sin x

Answers

The answer is a. cos2x - sin2x - sin x. Use the rule: cos2x = (cos^2)x - (sin^2)x. So, substitute cos2x in the expression: cos2x - sinx = ((cos^2)x - (sin^2)x) - sinx = (cos^2)x - (sin^2)x - sinx. Therefore, choice a. is correct choice.

$cos^2x - sin^2x - sin x$ is the solution of the given equation.

To rewrite the expression cos 2x - sin x using only sin x and cos x, we can apply trigonometric identities.

Using the identity $cos 2x = 1 - 2sin^2x$ , we can rewrite the expression as:

$1 - 2sin^2x - sin x$

Since,

$sin^2x +cos^2x = 1$

Therefore, the correct answer is:

a. $cos^2x - sin^2x - sin x$

Learn more about trigonometric functions here:

brainly.com/question/25618616

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4. Find the sum of the first eighteen terms of the arithmetic sequence whose nthterm is an = 15 + 8n.
a. 1438
b. 1638
c. 1836
d. 1783

Answers

Answer:

The sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

Step-by-step explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is: $S_n=(n)/(2)(a_1+a_n)$

Finding a₁ by putting n=1

$a_n=15+8n\na_(1)=15+8(1)\na_(1)=15+8\na_(1)=23$

We have $a_1=23$

Finding 18th term n=18

$a_n=15+8n\na_(18)=15+8(18)\na_(18)=15+144\na_(18)=159$

So, the sum of first eighteen terms of the arithmetic sequence is:

$S_n=(n)/(2)(a_1+a_n)\nS_(18)=(n)/(2)(a_1+a_(18))\nS_(18)=(18)/(2)( 23+159)\nS_(18)=9(182)\nS_(18)=1638$

So, the sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

Which term describes what a manufacturer spends for goods or services?cost
price
markup

Answers

It is the cost.
A markup is when something requires x dollars to produce but is sold for more than x.
A price is just how much money the item is worth
A cost is what amount of money is needed to make the product, in this case terms and services.
Hope this helps!

Cost is the correct answer.

Point (1,-5) 6. The slope is 5 , and the line passes through the (-1,-3).

Answers

Step-by-step explanation:

You have given a point (1, -5), a slope of 5, and the line passes through the point (-1, -3). You can use this information to find the equation of the line.

The equation of a line in point-slope form is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope.

Using the given point (1, -5) and the slope m = 5, you can plug these values into the equation:

y - (-5) = 5(x - 1)

Now, simplify:

y + 5 = 5(x - 1)

To put it in slope-intercept form (y = mx + b), expand and solve for y:

y + 5 = 5x - 5

Subtract 5 from both sides:

y = 5x - 5 - 5

y = 5x - 10

So, the equation of the line with a slope of 5 that passes through the point (1, -5) is:

y = 5x - 10

The perimeter(P 2l+2w)of a rectangle is 18 cm. If w is the width of the rectangle and L is the length, which graph below shows the relationship between the width and the length of the rectangle?

Answers

the question does not present the options, but thisdoes not interfere with the resolution

we know that

Perimeter of rectangle=2*[W+L]

where

L is the length of rectangle

W is the width of rectangle

Perimeter=18 cm

18=2*[W+L]-----> divide by 2------> 9=W+L

Let

x-------> L

y-------> W

then

x+y=9

using a graph tool

see the attached figure

the slope of the line is m=1

the x intercept is the point (9,0)

the y intercept is the point (0,9)

Final answer:

The relationship between the width and length of a rectangle given a constant perimeter is inverse; as the length increases, the width decreases proportionally. The graph representing this relationship would feature the length on the x-axis and width on the y-axis, and the line would represent all pairs of length and width that satisfy the equation

Explanation:

The problem in question asks to find the relationship between the width and length of a rectangle given its perimeter. In the given expression,

P = 2l + 2w

, where P is the perimeter, l is the length, and w is the width of the rectangle. Given that P = 18 cm, the relationship between the width and length can be represented by the equation

w = (P - 2l)/2

which implies that as the length increases the width decreases proportionally to maintain the constant perimeter. We must then create a graph where the x-axis represents the length and the y-axis represents the width, and a line representing possible solutions (l, w) that satisfy both the equation and the conditions given (length and width must be greater than 0).