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2 years ago

Anyone know the answer? Also could you put down what equation I’m supposed to use?

Mathematics

1 answer:

goldenfox [79]2 years ago

5 0

Answer:

The bottom two are your answers.

Step-by-step explanation:

What you do is use the slope formula which is y_2-y_1/x_2-x_1.

So for PQ it will be 12(which is y_2)-6(which is y_1)/4(which is x_2)-5(which is x_1) which equals -6.

12-6/4-5=-6.

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Which could be the first step in simplifying this expression? Check all that apply. (x cubed x Superscript negative 6 Baseline)

PtichkaEL [24]

Answer:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

Step-by-step explanation:

$(x^{3} x^{-6} )^{2}$ is the expression given to be solved.

First of all let us have a look at 3 formulas:

$1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}$

Both the formula can be applied to the expression( $(x^{3} x^{-6} )^{2}$ ) during the first step while solving it.

Applying formula (1):

$(x^{3} x^{-6} )^{2}$

Comparing the terms of $(x^{3} x^{-6} )$ with $p^a \times p^b$

$p=x, a =3, b=-6$

$\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $(x^{-3} )^{2}$

Applying formula (2):

Comparing the terms of $(x^{3} x^{-6} )^{2}$ with $(p^a \times q^b)^c$

$p=q=x, a =3, b=-6, c=2$

$\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $x^6 x^{-12}$ .

So, the answers can be:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

8 0

2 years ago

Mr. Sawyer drove his car from his home to New York at the rate of 45 mph and returned over the same road at the rate of 40 mph.

AveGali [126]

Answer: Time taken by him in going = 8 hours

Time taken by him in returning = 9 hours

Step-by-step explanation:

Let the total distance from home to New York is x miles,

$\text{ Since, Time} = \frac{\text{Distance}}{\text{Speed}}$

Also, he drove his car from his home to New York at the rate of 45 mph,

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

And, returned over the same road at the rate of 40 mph.

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

According to the question,

Time taken by him in returning - Time taken by him in going = 30 minutes = 1/2 hours, ( 1 hours = 60 minutes )

⇒ $\frac{x}{40}-\frac{x}{45}=\frac{1}{2}$

⇒ $\frac{9x}{360}-\frac{8x}{360}=\frac{1}{2}$

⇒ $\frac{x}{360} = \farc{1}{2}$

⇒ $2x=720$

⇒ $x=360\text{ miles}$

Hence, the total distance from home to New York = x miles = 360 miles

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

$=\frac{360}{45}=8\text{ hours}$

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

$=\frac{360}{40}=9\text{ hours}$

3 0

3 years ago

A card player selects a playing card from a well-shuffled deck of standard playing cards and sees if the card is a red card or n

dmitriy555 [2]

Answer:

Step-by-step explanation:

there could be no red cards inside

8 0

3 years ago

Help me please I need it

7nadin3 [17]

Answer:

Step-by-step explanation:

The formula for a rectangular prism is length*width*height. Thus, the equation would be 6*4*16, which equals 384 cm^3.

6 0

2 years ago

Which pair of triangles is congruent?

stiv31 [10]

Answer:

The first pair.

Step-by-step explanation:

3 corresponding parts must be congruent for two triangles to be congruent. The first pair has 3 congruence markings; two angles and one side are congruent. Additionally, they are congruent by the ASA postulate because two angles and the included side are congruent.

7 0

2 years ago

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