Remember combine like terms :)

14 - k + 3k - 6 =

Answer:

The correct option is (a)

Answer:

Part A)

Approximately 318.1318 meters.

Part B)

Approximately 137.7551 meters.

Step-by-step explanation:

The path of a projectile is given by the equation:

[tex]\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}[/tex]

Part A)

The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.

Let y = 0 and solve for x:

[tex]\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}[/tex]

Factor:

[tex]\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)[/tex]

Zero Product Property:

[tex]\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0[/tex]

Solve for each case:

[tex]\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318[/tex]

Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.

Part B)

Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -49/9000 and b = √3.

Find the x-coordinate of the vertex:

[tex]\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}[/tex]

Then the maximum height will be:

[tex]\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}[/tex]

The maximum height reached by the projectile will be 137.7551 meters.

Step-by-step explanation:

3x²+1+8=27

3x²+9=2

3x²=27-9

3x²=19

x²=19/3

[tex]x = \frac{ \sqrt[]{19} }{ \sqrt{3} } [/tex]

Answer:

[tex]3^{2x} + 1 + 18 = 27\\ 3^{2x} = 18\\2x = log_{3} 18[/tex]

Step-by-step explanation:

Answer:

$38

Step-by-step explanation:

$14+24=38 Amy pays her mom 38 dollars. :)

Answer:

-175/31

Step-by-step explanation:

-301 = -3x = 7(4x – 18)

-301 = -3x = 28x - 126

-301 = 31x = -126

-175 = 31x

x = -175/31

Answer:

-3

Step-by-step explanation:

move the constant to the other side and get

X = 2 - 5

and X = -3

Step-by-step explanation:

Open the brackets

2t+1-t+9 = -52-8t

Collect the like terms

2t-t+8t = -52-1-9

9t= -62

Divide both sides by 9

t= -62/9

= -6.88

Approximately -6.9

Answer:

Umm, I believe your only correct answer for your equation above would be -1.

Step-by-step explanation:

Using the PEDMAS method:

-2 - 3= -5

= -5 - (-4)

-(-4) = 4

= -5 + 4

-5 + 4 = -1

So, your answer would be -1. Hope this helps!

Answer:

height is 4ft.

Step-by-step explanation:

I used pathagorus theorem .All explaination is in the pic below.

Answer: 36π

Step-by-step explanation:

Answer:

Option A is correct.

Step-by-step explanation:

Between B and C, the value of height (y) remains constant, as shown as a horizontal line on the graph.

Answer:

Yesterday 4/5 and by 5 more people

Step-by-step explanation:

Ok so 3/4 of 100 is just 100/4*3, which is 75. 4/5 of 100 is 100/5*4, therefore, equaling 80. So 80 > 75, and when you find by how much more you do 80-75, which is 5. I hope this helps and if you have any questions you can comment them on this answer

Answer:

The answer is 4/5

Step-by-step explanation:

well 3/4 of 100 is 75. 4/5 of 100 is 80.

one fourth is equal to 25. We know that because we divide 100/4 and since there's 3 out of 4 (25x3=75)

one fifth is equal to 20. (100/5 = 20) 4 times 20 equals 80

Answer:

x = 13, y = 24.

Step-by-step explanation:

5x - 8 + 63 + 7x - 31 = 180  (interior alternate angles are equal).

12x + 24 = 180

12x = 180 - 24 = 156

x = 156/12

x = 13.

4y + 27 =  63 + 7x - 31       (interior alternate angles are equal).

4y +27 = 32 +7(13)

4y = -27 +32 + 91

4y = `96

y = 96/4

y = 24.

Answer:

It equals 2900 decigrams

Step-by-step explanation:

29 dekagrams = 290 grams

290 grams = 2900 decigrams

Therefore, 29 dekagrams = 2900 decigrams

The equivalent weight in grams for a given weight in dekagrams is approximately 10 times the weight in dekagrams.

To find the equivalent weight in grams for a given weight in dekagrams, you can use the conversion factor that 1 dekagram (dag) is equal to 10 grams.

Given the information that 29 dekagrams equals 290 grams, you can set up a proportion:

[tex]\(\frac{29 \text{ dag}}{290 \text{ g}} = \frac{1 \text{ dag}}{x \text{ g}}\)[/tex]

Cross-multiplying:

[tex]\(29x = 290 \times 1\)[/tex]

Solving for x:

[tex]\(x = \frac{290}{29}\)\\\\\(x \approx 10\)[/tex]

Therefore, the equivalent weight in grams for a given weight in dekagrams is approximately 10 times the given weight in dekagrams.

To know more about weight, refer here:

https://brainly.com/question/32319871

#SPJ3

Complete Question:

If 29 dekagrams equals 290 grams, what is the equivalent weight in grams for a given weight in dekagrams?

Answer:

B. 1

Step-by-step explanation:

Answer:

Option B is correct

The number of real number solutions for the given equation is, 1.

Step-by-step explanation:

Given the equation:  

Since, this is a quadratic equation of the form of  

where a =1 , b = -10 and c =25.

The discriminant of a quadratic equation is,  

then;

Discriminant =  = (100-100) = 0

Since, a  discriminant of zero means there is only one real solution for x.

Substitute the given values.

Simplify:

x = 5

Therefore, the number of real solution for the given equation is, 1

Answer:

good night

sweet dreams

Answer: 240ft

Step-by-step explanation:

Width:

10(15) + 10

= 150 + 10

= 160

Length:

4(15) + 20

= 60 + 20

= 80

L x W

= 160 + 80

= 240

Answer:

1.06 m²

Step-by-step explanation:

To find the area of the two ends, you need to find the area of the inner circle, then subtract that from the area of the large circle.

As we know, A = πr²

The diameter of the larger circle is 1.8, so the radius is 0.9.

π(0.9)² = 2.54

The diameter of the smaller circle is 1.6, so the radius is 0.8

π(0.8)² = 2.01

2.54 - 2.01 = 0.53 m² (this is for one end)

0.53 x 2 = 1.06 m²

Answer:

Anything greater or equal to 750 will be rounded to 800

and anything less than 850 will be rounded to 800,

So the numbers are:-

767

788

810

Answer:

let Greg's age be X

therefore;

4X - 3 = 3X + 7

4X - 3X = 7 + 3

X = 10

Greg is 10 years old

hope it's helpful

Answer:

1, 2, 3, 6, 7, 14, 21, and 42 are the factors of 42

Step-by-step explanation:

Answer:

Factors of 42 are: 1, 2, 3, 6, 7, 14 and 21

Answer:

Here are the formulas

[tex]\boxed{\sf Volume_{(Cylinder)}=\pi r^2h}[/tex]

[tex]\boxed{\sf Volume_{(Cone)}=\dfrac{1}{3}\pi r^2h}[/tex]

[tex]\boxed{\sf Volume_{(Sphere)}=\dfrac{4}{3}\pi r^3}[/tex]

Answer:

The volume for a cylinder is πr2h, for a cone 1/3hπr², and for a sphere is 4/3πr³

Step-by-step explanation:

I hope this will help you

Answer:

46 cm

Step-by-step explanation:

To calculate the perimeter of a rectangle, you have to add the length with itself then add the width with itself. After that, you add both of the sums together to get the answer. For this particular question, this is what you have to do.

1.Add the length with itself 15+15=30

2.Add the width with itself 8+8=16

3. Add both sums 30+16=46

In conclusion, the perimeter of the rectangle is 46 centimeters.

Answer:

10in

Step-by-step explanation:

8-3=5

5+5=10

Answer:

10 inches.

Step-by-step explanation:

Assuming that before Monday, there was no snow.

On Monday, it snowed 8 inches, which is a net positive of 8:

0 + 8 = 8in total.

On Tuesday, it melted 3 inches, which is a net negative of 3:

8 - 3 = 5in total.

On Wednsday, it snowed another 5 inches, which is a net positive of 5:

5 + 5 = 10in total.

10 inches total of snow was on the ground on Wednesday.

~

F(-2)

is

x2 + 2x

f(0)

=

x2

+

2x

-

10

Answer:

saiufhiuaewriufidnskjnckj

Step-by-step explanation:

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Answer:

the answer is 500!!

Step-by-step explanation:

10 x 50=500

Answer:

500

Step-by-step explanation:

50*10=500

50 into 10 equals 500

Answer:

15/2

Step-by-step explanation:

3/4(x)=45

x = 45 x 4/3

x = 15 x 4

x = 60

1/8 of 60

=> 15/2

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