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3 years ago

Someone help please

Mathematics

1 answer:

Helen [10]3 years ago

7 0

Answer:

Step-by-step explanation:

If you look at the graph, you notice there is no data to determine the slope, but there (0,b) represents the y-intercept. So my guess is, they give you a clue what the slope is already, but if you notice the y-intercept lowers the linear line a few notches because (0,18) is lower than the (0,30). That is what I would choose as the answer

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One piece of pizza has been removed from a large pizza pie. The shaded area shown represents the piece that has been removed.

shusha [124]

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Step-by-step explanation:

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3 years ago

Solve the system of equations.

Alenkasestr [34]

Step-by-step explanation:

Step 1: Substitute x from the second equation into the second one

$2x - 9y = 14$

$2(-6y + 7) - 9y = 14$

$(2 * -6y) + (2 * 7) - 9y = 14$

$-12y + 14 - 9y = 14$

$-21y +14 - 14 = 14 - 14$

$-21y/-21 = 0 / -21$

$y = 0$

Step 2: Substitute y into the second equation

$x = -6y + 7$

$x = -6(0) + 7$

$x = 0 + 7$

$x = 7$

Answer: $x = 7, y = 0$

4 0

4 years ago

Read 2 more answers

A rectangle is 13 centimeters wide and 18 centimeters long. how long is its diagonal

Naddika [18.5K]

You have to use the Pythagorean theorem a squared plus b squared is c squared so 13 squared plus 18 squared equals c squared. 13x13=169 18x18=324 169+324=493 so c squared is 493 to get c you square root 493 which equals 22.2 so the diagonal, c, is 22.2 centimeters long

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3 years ago

What is the value of 324 + 435 + 546 when written in base 7?

Arada [10]

The sum of 324, 435, and 546 is 1305. If this number were to be expressed by the base of 7, we would need to figure out what value of exponent would satisfy the requirement. This can be done by setting up an equation where 7 to the power of x must equal 1305. Using logarithms, one can solve for x and find it to be 3.6866853. Thus the sum of the aforementioned numbers, expressed in by the base of 7, is 7^3.6866853.

6 0

3 years ago

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)

vichka [17]

Answers:

a = -6/37

b = -1/37

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Explanation:

Let's start things off by computing the derivatives we'll need

$y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\$

Apply substitution to get

$y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\$

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0

3 years ago