Simplify the expression and write your answer as a complex number: 7√49 - √(-16).

Answers

Answer 1

Answer:

Answer:

$\Huge \boxed{ \boxed{\boxed{\bf{49 - 4i}}}}$

Step-by-step explanation:

We'll start with the first term: $\large \boxed{\tt{√(49)}}$ . The square root of 49 is 7, so this term simplifies to $\boxed{\tt{7 * 7}}$ , which is 49.

Now let's simplify the second term: $\large \boxed{\tt{√(-16)}}$ . The square root of a negative number is not defined in the real number system, so we need to express it as a complex number. The square root of -16 can be written as 4i, where 'i' represents the imaginary unit (√(-1)). Therefore, √(-16) = 4i.

Now we can rewrite the expression with the simplified terms:

$\Large \boxed{\boxed{\bf{49 - 4i}}}$

So, the simplified expression, written as a complex number, is 49 - 4i.

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Which choice gives the solution of this inequality? 3t+ < 28

Answers

Answer:

its 9.33 reapetting or just 9.33

Step-by-step explanation:

HELP ME PLS one bottle of shampoo costs 6 dollars for 8 Oz a second bottle costs 4 dollars for 5oz of shampoo wich has a lower unit rate and how much lower

Answers

Answer:

The 8 oz has lower unit rate, it's lower by .2.

Step-by-step explanation:

8 oz divided by $6 = $1.333 for 1 oz ---- (round to 1.3)

6 oz divided by $4 = $1.5 for 1 oz

Solve the following system of equations by using the substitution method.x – y = 3
2x + 2y = 2

(3, 4)

(-4, 5)

(2, -1)

Answers

Solution :

Given equations, $x-y=3\n2x+2y=2$

Applying Substitution method to solve the equation.

Solve the first equation $x-y=3$ for x,

$x-y=3\:\Rightarrow x=3+y$

Substitute the value of x in second equation,

$2x+2y=2\n\n\Rightarrow 2(3+y)+2y=2\n\n\Rightarrow 6+2y+2y=2\n\n\Rightarrow6+4y=2\n\n\Rightarrow4y=2-6\n\n\Rightarrow4y=-4\n\n\Rightarrow y=(-4)/(4) =-1\n\n\Rigtharrow y=-1$

To calculate the value of x substitute the value of y in first equation

$x-y=3\n\n\Rightarrow x-(-1)=3\n\n\Rightarrow x=3-1=2\n\n\Rightarrow x=2$

Hence, the solution of the equations $x-y=3\n2x+2y=2$ is (2,-1).

3,4 would be the answer

A 1500 kg hippo is completely submerged, standing on the bottom of a lake. What is the approximate value of the upward normal force on the hippo?

Answers

Answer:

About 428 N

Step-by-step explanation:

Weight = 1,500 * 9.8 = 14,700 N

Density = Mass ÷ Volume

1,030 = 1,500 ÷ V

V = 1,500 ÷ 1,030 = 1.46 m^3.

Buoyant force = Density * g * V

Buoyant force = 1,000 * 9.8 * (1,500 ÷ 1,030)

Buoyant force = 9,800 * (1,500 ÷ 1,030) = 14,272 N.

Net force = 14,700 – [(9,800 * (1,500 ÷ 1,030)]

Final answer:

The upward normal force on a 1500 kg submerged hippo is approximately equal to its weight, calculated as its mass times the acceleration due to gravity (1500 kg × 9.81 m/s²), resulting in a force of 14715 N.

Explanation:

The question is asking about the upward normal force on a submerged hippo in a lake. To find this force, we must understand that the upward normal force that the ground (or in this case, the lake bed) exerts on the hippo is equal to the weight of the hippo, which is the product of the hippo's mass (m) and the acceleration due to gravity (g).

In equation form: Normal Force = m × g. Plugging in the values, we have a 1500 kg hippo and the acceleration due to gravity is approximately 9.81 m/s². Therefore, the upward normal force is:

Normal Force = 1500 kg × 9.81 m/s² = 14715 N.

This is the approximate value of the upward normal force exerted on the hippo standing on the bottom of the lake.

Learn more about normal force here:

brainly.com/question/18799790

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Phil made 50 ounces of purple dye by mixing a solution consisting of 15% blue dye and 85% red dye. How many ounces of red dye did he use in the process?

Answers

In accordance with given data correct answer is

RD= 85% * 50 = 0.85 * 50 = 42.5 ounces of red dye.

Good luck!!!

Final answer:

Phil used 42.5 ounces of red dye in the process of making 50 ounces of purple dye, given that the mixture was 85% red dye.

Explanation:

The question is asking us to determine how many ounces of red dye was used in the mixing process to produce 50 ounces of purple dye. Phil used a solution of 15% blue dye and 85% red dye. Therefore, the amount of red dye used can be computed by taking 85% of the total amount of dye made, which is 50 ounces.

To do this, we multiply the total ounces of dye (50 ounces) by the percentage of red dye (85%) used in the mixture. Mathematically, this is represented by the equation: (85/100) * 50.

Therefore, Phil used 42.5 ounces of red dye in the mixing process to make the purple dye.

Learn more about Percentage Calculation here:

brainly.com/question/329987

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Could someone help me please :)