what value of c makes x^2 + 6x + c a perfect square trinomial ?

Answer:

8 hours

Step-by-step explanation:

10 x 8 x 5 = 400. 400 / 50 = 8. So it will take 8 hours to fill a pool with 400ft3

Answer:

5 nights

Step-by-step explanation:

Let x represent the number of nights.  She can spend up to and including 500; this gives us the inequality

60x+150 ≤ 500

Subtract 150 from each side:

60x+150-150 ≤ 500-150

60x ≤ 350

Divide both sides by 60:

60x/60 ≤ 350/60

x ≤ 5.83

Since she cannot stay just a portion of a night, she can stay up to 5 nights.

Jennifer can afford to stay in the hotel for up to 10 nights.

To determine the number of nights Jennifer can afford in the hotel, we need to subtract the cost of the flights from her budget and divide the remaining amount by the cost per night.

First, convert Jennifer's budget from pounds to dollars. Assuming an exchange rate of 1 pound = 1.5 dollars, £500 is equal to $750.

Next, subtract the cost of the flights from Jennifer's budget to find her remaining budget for the hotel. $750 - $150 = $600

Finally, divide the remaining budget by the cost per night to find the number of nights she can afford. $600 / $60 = 10 nights.

Therefore, Jennifer can afford to stay in the hotel for up to 10 nights.

Final answer:

To find the volume of a sphere with a diameter of 6 cm, first determine the radius, which is 3 cm, and then use the formula V = (4/3)πr³ to calculate the volume, resulting in approximately 113.097 cm³.

Explanation:

The volume of a sphere is calculated using the formula V = (4/3)πr³, where V represents the volume and r is the radius of the sphere. When the diameter of the sphere is given as 6 cm, the radius is half of that, which is 3 cm. Therefore, substituting the radius into the formula yields:

V = (4/3)π(3 cm)³ = (4/3)π(27 cm³) = 36π cm³

This results in a volume of approximately 113.097 cm³ (since π is approximately 3.14159).

Answer:

he's right tried to answer first

Step-by-step explanation:ut 85%

The equation 5x − 14y = 16, when rewritten in slope-intercept form, is[tex]y = (5/14)x - 8/7.[/tex]

To rewrite the given equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we'll isolate y. Starting with the equation 5x − 14y = 16:

1. Subtract 5x from both sides to move the x term to the other side:

  -14y = -5x + 16

2. Divide every term by -14 to solve for y:

  y = (5/14)x - 8/7

In this form, the coefficient of x represents the slope (m), which is 5/14, and the constant term is the y-intercept (b), which is -8/7. The slope indicates the rate of change of y concerning x, and the y-intercept represents the point where the line intersects the y-axis.

By following these steps, we've successfully transformed the given equation into slope-intercept form, making it easier to interpret and work within the context of linear relationships.

To convert the equation 5x - 14y = 16 to slope-intercept form, solve for y to yield y = (5/14)x - 8/7, where the slope is 5/14 and the y-intercept is -8/7.

To rewrite the equation 5x − 14y = 16 in slope-intercept form, we need to solve for y to get the equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

In simplified form, the slope-intercept form of the equation is y = (5/14)x − 8/7. Here, the slope (m) is 5/14 and the y-intercept (b) is −8/7.

Answer:

the solution is the point [tex](2,4)[/tex]

Step-by-step explanation:

we have

[tex]13x-6y=2[/tex] ------> equation A

[tex]3x-4y=-10[/tex] ------> equation B

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

The intersection point is the point [tex](2,4)[/tex]

see the attached figure

therefore

the solution is the point [tex](2,4)[/tex]

the answer is (2,4) the expert is right i put it and got it right

Answer:

Step-by-step explanation:

2*37=6000

Answer:

125 ≤ c

Step-by-step explanation:

The dot's average speed was 384 units per hour

To find the distance the dot covered, we can subtract the initial position from the final position:

Distance = Final position - Initial position

[tex]\[ \text{Distance} = (-66) - (-34) \]\[ \text{Distance} = -66 + 34 \]\[ \text{Distance} = -32 \][/tex]

However, distance is a scalar quantity, so the negative sign indicates the direction. To find the magnitude of the distance, we take the absolute value:

[tex]\[ |\text{Distance}| = |-32| \][/tex]

[tex]\[ |\text{Distance}| = 32 \text{ units} \][/tex]

So, the dot covered a distance of 32 units.

To find the average speed, we use the formula:

[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]

Given that the run took the dot 5 minutes, we need to convert the time to hours for the speed to be in units of distance per hour:

[tex]\[ \text{Time} = 5 \text{ minutes} = \frac{5}{60} \text{ hours} = \frac{1}{12} \text{ hours} \][/tex]

Now, plug the distance and time into the formula:

[tex]\[ \text{Average speed} = \frac{32 \text{ units}}{\frac{1}{12} \text{ hours}} \]\[ \text{Average speed} = 32 \times 12 \]\[ \text{Average speed} = 384 \text{ units/hour} \][/tex]

So, the dot's average speed was 384 units per hour.

Answer:

Area of circle is 1145.50 cm²

Step-by-step explanation:

Given : Circumference of circle = 120 cm

We have to find the area of the given circle.

Consider the given circle

We know circumference of circle = [tex]2\pi r[/tex]

Thus,  [tex]120=2\pi r[/tex]

Put π = 3.14

We have,

[tex]120 =2\times 3.14\times r[/tex]

Divide both sides by 6.28, we have,

r = 19.1 cm

Now, area of circle = [tex]\pi r^2[/tex]

Put r = 19.1

We have

Area of circle  = 1145.50 cm²

Thus, Area of circle is 1145.50 cm²

Answer is a - b + c - d + e - f + g

Answer:

After Simplifying we get a - b + c - d + e - f + g

Step-by-step explanation:

We are given : a - { b - [ c - ( d - e ) - f ] - g }

We have to simplify it.

Step 1: First open the parenthesis mean ( ) brackets  

we get ,  a - { b - [ c -  d + e  - f ] - g }

Step 2: Now we open Square brackets .i.e.,  [ ]

we get,  a - { b - c + d - e + f - g }

Step 3: In last we open curly brackets .i.e, { }

we get, a - b + c - d + e - f + g

Therefore, After Simplifying we get a - b + c - d + e - f + g