In a rectangle ABCD, A and B are the points (4,2) and (2,8) respectively l. Given that the equation of AC is y=x-2. Find the equation of BC

Answer:

c) -16 ≤ x < 5

Step-by-step explanation:

The given function is f(x) = -3x + 2 and domain is  -1 < x ≤ 6

The maximum value of the domain is 6 and the minimum value of the domain is -1.

To find the range, plugin the maximum and minimum value of the domain.

Plug in x = 6 in the given function, we get

f(6) = -3(6) + 2 = -18 +2 = -16

f(-1) = -3(-1) + 2 = 3 + 2 = 5

So the range is -16 ≤ x < 5

Answer:

[tex]A\approx 37.95^{\circ}[/tex]

Step-by-step explanation:

We have been given that [tex]\text{tan}(A)=0.78[/tex]. We are asked to find measure of angle A in degrees.

We will inverse tangent to find measure of angle A as:

[tex]A=\text{tan}^{-1}(0.78)[/tex]

[tex]A=37.954230875133^{\circ}[/tex]

Upon rounding our answer to nearest hundredth, we will get:

[tex]A\approx 37.95^{\circ}[/tex]

Therefore, the measure of angle A is approximately 37.95 degrees.

Answer:

The value of 25th percentile equals:

 lower quartile

Step-by-step explanation:

We have to find the value of the 25th percentile

25th percentile is equal to the lower quartile.

50th percentile is equal to the median.

and 75th percentile is equal to the upper quartile.

Hence, the value of 25th percentile equals:

 lower quartile

Prius can travel up to 4.23 × x kilometers on 16 liters of gasoline.

It is given that Prius runs on gasoline.

We have to find out that how many kilometers it can run if amount of gasoline is 16 liters.

What will be the value of 16 times of a number x ?

The value will be ; 16 × x .

No. of kilometers Prius travels depends on what is the model of Prius . Also quality of roads makes a difference.

∵ 1 liter = 0.264172 gallons

⇒ 16 liters = 16 × 0.264172 = 4.23 gallons

Let's say a Prius travels x kilometers per gallon.

So ; on 16 liters of gasoline , Prius will travel ;

x × 4.23 = 4.23 × x kilometers

Thus , Prius can travel up to 4.23 × x kilometers on 16 liters of gasoline.

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Answer: [tex]\text{Area}=9.8\ \text{square centimeter}[/tex]

Step-by-step explanation:

Given: The height of the triangle h= 3.0 cm

The base corresponding to the given height b= 6.5 cm

We know that the area of a triangle is given by :-

[tex]\text{Area}=\frac{1}{2}bh\\\\\Rightarrow\text{Area}=\frac{1}{2}(3)(6.5)\\\\\Rightarrow\text{Area}=\frac{19.5}{2}\\\\\Rightarrow\text{Area}=9.75\approx9.8\ \text{square centimeter}[/tex]

Answer:

34 inches.

Step-by-step explanation:

Answer:

1.3 miles

Step-by-step explanation:

Solution:-

- The surveyor stands at a platform that is B = 4 miles and at an elevation of θ = 18 ° away from the point on the mountain.

- We can construct a right triangle from surveyor to the point of observation. To determine the change in height/elevation (H) we will apply the trigonometric relation as follows:

                              tan ( θ ) = H / B

- Solve for the elevation (H):

                              H = B*tan ( θ )

                              H = 4*tan ( 18 )

                              H = 1.3 miles

- The change in elevation from surveyor to point of observation is H = 1.3 miles.

90-7 =83 degrees

height = 3 miles

divide 3 by the cos of 83 degrees

3/cos(83) = 24.6165

rounded to nearest mile = 25 miles

Answer:

The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]

Step-by-step explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

[tex]AC=BC[/tex] -----> is the radius of the circle  

[tex]m<CAB=m<CBA[/tex]

[tex]m<ACB=60\°[/tex] ----> given problem (central angle)

Initially the triangle ABC is an isosceles triangle

Remember that

the sum of the internal angles of triangle must be equal to [tex]180\°[/tex]

For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to [tex]60\°[/tex]

The equilateral triangle has three equal sides and tree equal angles

so

[tex]AC=BC=AB[/tex]

Hence

The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]

The number to write [tex]7.9\times 10^-6[/tex] in standard notation is 0.0000079.

Given that,

Based on the above information, the calculation is as follows:

[tex]= 7.9\times 10^-6 = 7.9 \times \frac{1}{1,000,000}[/tex]

= 0.0000079

Therefore we can conclude that the number to write [tex]7.9\times 10^-6[/tex] in standard notation is 0.0000079.

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Answer with explanation:

⇒Consider a Non Zero Rational Number = 2, 3, [tex]\frac{2}{3}[/tex], 53,....

The decimal Expansion of Rational number is Either terminating or  Non Teminating repeating.

⇒ Irrational Number = π, √2,√7,...

The decimal Expansion of Irrational number is Non terminating Non repeating.

⇒Product of a non-zero rational number and an irrational number

  =2 ×√2 or 3 × √2 or 3 π

are all Irrational number.

In terms of decimals:

                     (c)⇒a non-repeating, non-terminating decimal=(Irrational Number)

Option C

3x +4y =12

2x = y-6 Rewrite this as y = 2x+6

 now replace that for y in the first equation

3x + 4(2x+6) = 12

now do all the calculations:

3x + 8x +24 =12

11x + 24 = 12

11x = -12

x = -12/11 = -1 1/11

 now substitute -12/11 for x in the 2nd equation and solve

y = 2x+6

y = 2(-1 1/11) +6

y = 42/11 = 3 9/11

Answer:

Option B.[tex]\sqrt[6]{200}[/tex]

Step-by-step explanation:

The given expression is ∛5.√2 and we have to find the product.

In this question ∛5 can be written as [tex]5^{\frac{1}{3} }[/tex] and [tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]

We know to multiply these terms we should have the same powers of both the terms.

Now we will convert these terms to the terms having same powers.

first term [tex]5^{\frac{1}{3}}=5^{(\frac{1}{3}).(\frac{2}{2})}[/tex]

=[tex]5^{\frac{2}{6}}[/tex]

=[tex]25^{\frac{1}{6}}[/tex]

Second term √2 = [tex]2^{\frac{1}{2}}[/tex]

= [tex]2^{(\frac{1}{2}).(\frac{3}{3})}[/tex]

= [tex]2^{\frac{3}{6}}[/tex]

= [tex]8^{\frac{1}{6}}[/tex]

Now we multiply these terms

[tex]25^{\frac{1}{6}}.8^{\frac{1}{6}}[/tex]

= [tex]200^{\frac{1}{6} }[/tex]

Therefore option B is the answer.