Find the greatest common factor of 10, 30, and 45.

Answer:

A linear relation can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

And if a line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Now let's look at our lines.

The left one passes through the points (0, -3) and (-2, 0)

Then the slope of this line is:

a = (0 - (-3))/(-2 - 0) = 3/-2 = -(3/2)

Then the line will be something like:

y = -(3/2)*x + b

Knowing that this line passes through the point (0, -3), we know that when x = 0, we must have y = -3

Then:

-3 = (-3/2)*0 + b

-3 = b

So the first linear equation is:

y = -(3/2)*x - 3

Now let's look at the second line, this one passes through the points (0, 2) and (1, 0)

Then the slope of this line is:

a = (0 - 2)/(1 - 0) = -2

And we can write the line as:

y = -2*x + b

Knowing that this line passes through the point (0, 2), we know that when x = 0 we must have y = 0, replacing that we get:

2 = -2*0 + b

2 = b

Then the equation of this line is:

y = -2*x + 2

Now that we know both equations we can write our system as:

y = (-3/2)*x - 3

y = -2*x + 2

To solve it, we need to remember that y = y

then:

(-3/2)*x - 3 = y = -2*x + 2

(-3/2)*x - 3  = -2*x + 2

We can solve this for x.

2*x - (3/2)*x = 2 + 3

(1/2)*x = 5

x = 5((1/2) = 5*2 = 10

And to find the y-value, we need to input this x-value in one of the equations:

y = -2*10 + 2 = -20 + 2 = -18

Then the solution of the system is the point (10, -18)

Answer:

Blank = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

blank = x

[tex]x-\frac{1}{2} =\frac{1}{6} \\\\x=\frac{1}{6} +\frac{1}{2} \\\\x=\frac{1}{6} +\frac{3}{6} \\\\x=\frac{4}{6} \\\\x=\frac{2}{3}[/tex]

Answer:

6x^2-x-1

Step-by-step explanation:

Use the FOIL method.

Answer:

One Point I believe

Step-by-step explanation:

Answer:

$315,840.00

Step-by-step explanation:

$564,000 x 0.56 = $315,840.00

Answer:

$315,840

Step-by-step explanation:

56% of 564,000 is this

Answer:

Infinitely many solutions.

Step-by-step explanation:

The given system of equations are :

3x+y=-5 ...(1)

3y+15=-9x

y+5 = -3x

or

3x+y = -5 ....(2)

Here, [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]

It means, two lines are coincident. It means they have infinitely many solutions.

I hope this helps you

Hi there!

[tex]\large\boxed{100^{o}}[/tex]

∠C = 40° and triangle ABC is isosceles, therefore:

∠C = ∠A = 40°

Angles in a triangle sum up to 180°, so:

180 = 40 + 40 + ∠A

180 = 80 + ∠A

100 = ∠A

Thus, arc CB has a measure of 100°.

9514 1404 393

Answer:

  90 m²

Step-by-step explanation:

The given linear dimensions have the ratio ...

  red/blue = (6 m)/(4 m) = 3/2

The ratio of areas is the square of the ratio of the linear dimensions:

  (red area)/(blue area) = (3/2)²

  S = (blue area)(9/4) = (40 m²)(9/4)

  S = 90 m²

Answer:

B is True

A, C. D are false

Step-by-step explanation:

Given :

Sample size, n = 120

Mean diameter, m = 10

Standard deviation, s = 0.24

Confidence level, Zcritical ; Z0.05/2 = Z0.025 = 1.96

The confidence interval represents how the true mean value compares to a set of values around the mean computed from a set of sample drawn from the population.

The population here is N = 10000

To obtain

Confidence interval (C. I) :

Mean ± margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 1.96 * 0.24/sqrt(120)

Confidence interval for the 10,000 ball bearing :

10 ± 1.96 * (0.24) / sqrt(120)

Hence. The confidence interval defined as :

10 ± 1.96 * (0.24) / sqrt(120) is the 95% confidence interval for the mean diameter of the 10,000 bearings in the box.

Answer:

she can buy 13

please brainliest or hear

Answer:

She can order 7 DVDS

Step-by-step explanation:

8.49 x 7 = 59.43

59.43 + 5 = 64.43.

Answer:

Step-by-step explanation:

it is C forty-three and six hundredths.

Answer:dddddd

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

30 ÷ 5 = 6

Answer:

6

Step-by-step explanation:

it is 6

Answer:

$450

Explanation:

after 15 weeks, stacy would have deposited a total of $25 × (15 - 1) = $350. (remember to subtract 1 from the 15 weeks since she did not deposit $25 during the week she opened the account, but only after that.)

now, we need to add this to the original deposit: $100 + $350 = $450.

therefore, after 15 weeks, there would be $450 in her account.

i hope this helps! :D

Answer:

60m

Step-by-step explanation:

To find the area of the triangle you multiply the base by height and divide by two, but we don’t know the base of the triangle!

Luckily, the bottom of the triangle is a rectangle. Rectangles are symmetrical, and the other side of the rectangle is 8.

So, the base of the triangle is 8.

Now let’s find the area of the triangle:

8 x 5 = 40

40/2 = 20

20 is the area of the triangle

Now, we must find the area of the rectangle!

The formula for rectangle area is just width x length:

8 x 5 = 40

Add them together:

40 + 20 = 60

Therefore, the area is 60m.

Answer: C and for the bottom is 3*3/8=9/8=1 1/8

Step-by-step explanation: hoped this helped :)

Answer:

y=-6

Step-by-step explanation:

just look at the bottom and yahhhh

Answer:

we need more info

Step-by-step explanation:

Answer:

Step-by-step explanation:

First you must understand that in geometry, the alternate interior angles are equal

Hence if ∠3 and ∠6 are alternate interior angles, then <3 = <6

Given that m<3 = 75 degrees

m<6 will also be 75 degrees since both angles are equal

Answer: the amount of money after the purchase depends on the amount of money before the purchase

Step-by-step explanation:

Answer:

252

Step-by-step explanation:

60+61+11

9514 1404 393

Answer:

  108 ft²

Step-by-step explanation:

When x=6, the length is 6+6 = 12 ft, and the width is 6+3 = 9 ft. The area is given by ...

  A = LW

  A = (12 ft)(9 ft) = 108 ft²

The area of Cameron's garden is 108 ft².

Answer:

1350

Step-by-step explanation:

multiply

Answer:

x = 12

Step-by-step explanation:

[tex]x - 9 = 3 \\ x = 3 + 9 \\ [/tex]

[tex]\boxed{Answer:{\boxed{\green{x = 12}}}}[/tex]

Answer:

[tex] I = \dfrac{1}{3}sin(3x) - 3cos(x) + C[/tex]

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

[tex]\implies\displaystyle I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]

[tex]\implies\displaystyle I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \boxed{\boxed{\displaystyle I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}[/tex]