A line has a slope of –3 and a y-intercept of 3.

What is the x-intercept of the line?

A: –9
B: –1
C: 1
D: 9

Answer:

D). 1,808.64 in2

Step-by-step explanation:

Diameter - 48 in.

Therefore, the radius is half of 48. 48/2 = 24.

Area = 3.14(24) 24 = 1,808.64in2

Hope this helps

In Timra's math class, the ratio of boys to girls is 12:15, which can be simplified to 4:5. This means for every 4 boys, there are 5 girls.

In Timra's math class, there are 12 boys and 15 girls. The ratio of boys to girls in this case would be represented by the number of boys followed by the number of girls, separated by a colon. Therefore, the ratio of boys to girls is 12:15. You can also simplify this ratio by dividing both numbers by their greatest common divisor which is 3. After doing so, you will get a simplified ratio of 4:5. This means that for every 4 boys in the class, there are 5 girls.

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The equation y + 7 = 9/10(x + 3) is converted into standard form by distributing, isolating y, eliminating fractions, and rearranging terms, resulting in the standard form 9x - 10y = 43.

The equation y + 7 = 9/10(x + 3) needs to be converted into standard form. The standard form of a linear equation is Ax + By = C where A, B, and C are integers, and A should be non-negative.

To put the given equation into standard form, we need to distribute the 9/10 across the (x + 3) and then isolate y on one side:

y + 7 = (9/10)x + (9/10)x3

Step 1: Multiply 9/10 by each term in the parentheses.

y + 7 = (9/10)x + 27/10

Step 2: Subtract 7 from both sides to isolate the y term.

y = (9/10)x + 27/10 - 70/10

y = (9/10)x - 43/10

Step 3: To get rid of the fraction, multiply the entire equation by 10.

10y = 9x - 43

Step 4: Finally, to put this into standard form, we need to move the x term to the left side of the equation.

-9x + 10y = -43

Here, our standard form would be 9x - 10y = 43, as we usually do not want a negative A term in standard form.

Answer:

d 8 1/3

Step-by-step explanation:

Final answer:

Point Z is located at 2 on the number line, found by adding the distance YZ=11 to the location of Y at -9.

Explanation:

If Y and Z are points on the number line, YZ=11, and Y lies on -9, to find where Z would be located, you simply add the distance between Y and Z to the point Y. Since the distance YZ=11, and Y is at -9 on the number line, you add 11 to -9 to find Z.

Therefore, the location of point Z will be:

-9 + 11 = 2

So, point Z is located at 2 on the number line.

Answer:

Option A- 60°            

Step-by-step explanation:

Given : Function - [tex]4cos^2x-1=0[/tex]

To solve the function

Step 1 - Write the function

[tex]4cos^2x-1=0[/tex]

Step 2- Add 1 both side

[tex]4cos^2x=1[/tex]

Step 3- Divide 4 both side

[tex]cos^2x=\frac{1}{4}[/tex]

Step 4 - Taking root both side

[tex]cosx=\sqrt{\frac{1}{4}}[/tex]

Step 5 - solve

[tex]cosx=\pm{\frac{1}{2}}[/tex]

Either [tex]cosx={\frac{1}{2}}[/tex] or [tex]cosx=-{\frac{1}{2}}[/tex]

When [tex]cosx={\frac{1}{2}}[/tex]

            [tex]\rightarrow cosx={cos\frac{\pi}{3}}[/tex]

            [tex]\rightarrow x={\frac{\pi}{3}} or 60^{\circ}[/tex]

or when  [tex]cosx=-{\frac{1}{2}}[/tex]

               [tex]\rightarrow cosx={cos(\pi-\frac{\pi}{3})}[/tex]

            [tex]\rightarrow x={\frac{2\pi}{3}} or 120^{\circ}[/tex]

Therefore, Option A is correct solution of function is at 60°.

The solution of the given trigonometric ratio for the expression 4cos²x - 1 = 0 is equal to 60°

To find the solutions to the equation 4cos²x - 1 = 0, we first need to isolate the cosine term and then solve for x.

Let's go through the steps,

Add 1 to both sides of the equation:

4cos²x = 1

Divide both sides by 4:

cos²x = 1/4

Take the square root of both sides:

cosx = ±√(1/4)

Now, we have two cases to consider: positive and negative square roots.

Case 1,

cosx = √(1/4)

The cosine of an angle can never be negative when expressed in degrees, so we ignore the negative square root.

cosx = √(1/4) = 1/2

To find the angles for which the cosine is 1/2, we look at the unit circle or use a calculator to find the inverse cosine (arccos) values:

x = arccos(1/2)

The principal angle that satisfies this is x = 60°.

Case 2,

cosx = -√(1/4)

Again, we ignore the negative square root as the cosine is not negative in degrees.

Therefore, the only solution to the equation is:

x = 60°

Therefore, among the given options, the solution to 4cos²x - 1 = 0 is 60°.

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To find the number of albums Floyd sold last month, we calculate it using the linear equation $644 = $200 + ($12 \u00d7 a), where $644 is the total earnings, $200 is the base rate, and $12 is the amount earned per album. Floyd sold 37 albums last month.

To determine the number of albums Floyd sold last month, we can set up a linear equation based on the information provided. Floyd is paid a base rate of $200 per month, and he earns an additional $12 for every album sold. The total amount Floyd earned last month was $644.

Let's let a represent the number of albums sold. The equation that represents the total earnings for the month would be:

Total Earnings = Base Rate + (Number of Albums Sold × Price per Album)

Based on what has been given, we can express this as:

$644 = $200 + ($12 × a)

To find the number of albums sold, we subtract the base rate from the total earnings, then divide by the additional amount earned per album:

$644 - $200 = $12 × a

$444 = $12 × a

a = $444 / $12

a = 37

So, Floyd sold 37 albums last month.

Answer:

Because it is a rectangle, the area is expressed as A = xy, or length times width.

Step-by-step explanation:

Because it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

7500 = x + 2y        solve for x

x = 7500 - 2y         substitute into the area equation

A = (7500 - 2y)y     distribute

A = -2y2 +7500y

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

x = 7500 - 2(1875) = 3750

A = 3750(1875)  = 7,031,250 m2

If Farmer Ed has 3,500 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, Then 7,031,250  is the largest area that can be​ enclosed.

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.

As it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

7500 = x + 2y        

solve for x

x = 7500 - 2y        

substitute into the area equation

A = (7500 - 2y)y    

Distribute

A = -2y2 +7500y

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

x = 7500 - 2(1875) = 3750

A = 3750(1875)  = 7,031,250 m².

Hence 7031250  is the largest area that can be​ enclosed.

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