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4 years ago

The sum of four consecutive integers os -18. what is the greatest of these integers?

1 answer:

5 0

Hello! The sum of four consecutive integers that equal -18 are -6, -5, -4, And -3. -3 is the greatest out of all of the integers and -6 is least out of all the integers. The further right on the number line, the greater it is. The further left on the number line, the lower it is.

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A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a

Komok [63]

Answer:

a) 64 feet

b) 3 seconds

Step-by-step explanation:

The maximum height of $h=h(t)$ can be bound by finding the y-coordinate of the vertex of $y=-16x^2+32x+48$ .

Compare this equation to $y=ax^2+bx+c$ to find the values of $a,b,\text{ and } c$ .

$a=-16$

$b=32$

$c=48$ .

The x-coordinate of the vertex can be found by evaluating:

$\frac{-b}{2a}=\frac{-32}{2(-16)$

$\frac{-b}{2a}=\frac{-32}{-32}$

$\frac{-b}{2a}=1$

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating $y=-16x^2+32x+48$ at $x=1$ :

$y=-16(1)^2+32(1)+48$

$y=-16+32+48$

$y=16+48$

$y=64$

So the maximum height of the rocket is 64 ft high.

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

$0=-16t^2+32t+48$

I'm going to divide both sides by -16:

$0=t^2-2t-3$

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

$0=(t-3)(t+1)$

This implies we have either $t-3=0$ or $t+1=0$

The first equation can be solved by adding 3 on both sides: $t=3$ .

The second equation can be solved by subtracting 1 on both sides: $t=-1$ .

So when $t=3$ seconds, is when the rocket has hit the ground.

5 0

3 years ago

Two patrol boats leave Cape May at the same time, the same speed, but on different bearings. One has bearing 41°45

VMariaS [17]

Based on the information given, the computation shows that the distance between them is 2.47 miles.

<h3>Solving the distance.</h3>

Since one has bearing 41°45', this will be: = 41° + (45/60) = 41° + 0.75 = 41.75°.

The other has bearing 59°13'. This will be:

= 59° + (13/60) = 59° + 0.22 = 59.22°.

The difference of the angles will be:

= 59.22° - 41.75°

= 17.47°

Let the distance between them be represented by c. Therefore, we'll use cosine law to solve the question. This will be:

c² = a² + b² - 2ab cos 17.47°

c² = 20² + 20² - (2 × 20 × 20 × 0.19)

c² = 6.07459

c = 2.47

Learn more about distance on:

brainly.com/question/2854969

8 0

2 years ago

What is the point-slope form given the following slope and a point on the line? m = 3/7 , (7, -4)

GarryVolchara [31]

Answer:

The equation is y = (3/7)x - 7.

Step-by-step explanation:

Given that the point slope form of an equation is y = mx + b where m represents the gradient and b is the y-intercept. Then, you have to substitute the following values into the equation :

$y = mx + b$

$let \: m = \frac{3}{7} ,x = 7,y = - 4$

$- 4 = \frac{3}{7} (7) + b$

$- 4 = 3 + b$

$- 4 - 3 = b$

$b = - 7$

7 0

3 years ago

Express -5 1/4 as a decimal

rewona [7]

I believe it would be -5.25

5 0

4 years ago

Read 2 more answers

Pamela and her friend Nicole are each baking apple pies and tarts for a bake sale, using the same recipes. Pamela baked 5 apple

valentina_108 [34]

Answer:

Each apple pie requires 8 apples, and each apple tart requires 4 apples.

Step-by-step explanation:

We see that both Pamela and Nicole bake the same amount of apple pies, but different amounts of apple tarts. Because of this, we can subtract the two to try to figure out the amount of apples for each apple tart. We subtract 68 from 76, giving us 8. Nicole baked 9 apple tarts, while Pamela baked 7, and 9-7=2. So we can bake two apple tarts with 8 apples, so one apple tart requires 4 apples (we divide by 2). Now that we know the amount of apples per each apple tart, we multiply 7 apple tarts that Pamela made by 4 apples, giving us 28. We subtract that from the total amount of apples Pamela used, which was 68, giving us 40. From this we can deduct that 5 apple pies need 40 apples, and we divide by 5, giving us 1 apple pie requires 8 apples.

3 0

3 years ago