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Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.

(x − 4)^2 = 3
(x − 3)^2 = 2
(x − 2)^2 = 1
(x − 1)^2 = 4

Answer:

The number of steps in a stairway is discrete.

Step-by-step explanation:

A discrete data is that, which can take only integer values like number of apples in a basket.

But the continuous data is that, which can take on any value like a decimal. For example, the weight of patients in a hospital.

So, the number of steps in a stairway will be a discrete data. As stairs are counted in whole numbers and not decimals.

Answer:

Option D is correct

Step-by-step explanation:

Given Equations of Circles:

Circle 1 - [tex](x+12)^2+(y+16)^2=(r_1)^2[/tex]

Circle 2 -  [tex](x-30)^2+(y-16)^2=(r_2)^2[/tex]

Both circles passes through origin.

To find: Values of [tex]r_1\:,\:r_2[/tex]

Coordinates of origin = ( 0 , 0 )

Circles passes through origin means x = 0 & y = 0 must satisfy the equation of circles.

So, Substituting x = 0 &  y = 0 in Eqn of Circle 1

we get

[tex](0+12)^2+(0+16)^2=(r_1)^2[/tex]

[tex](r_1)^2=12^2+16^2[/tex]

[tex](r_1)^2=144+256[/tex]

[tex](r_1)^2=400[/tex]

[tex]r_1=\sqrt{400}[/tex]

[tex]r_1=20[/tex]

Now, Substituting x = 0 &  y = 0 in Eqn of Circle 2

we get

[tex](0-30)^2+(0-16)^2=(r_2)^2[/tex]

[tex](r_2)^2=(-30)^2+(-16)^2[/tex]

[tex](r_2)^2=900+256[/tex]

[tex](r_2)^2=1156[/tex]

[tex]r_2=\sqrt{1156}[/tex]

[tex]r_2=34[/tex]

Therefore, Option D is correct .i.e., [tex]r_1=20\:\:,\:\:r_2=34[/tex]

Answer:

26

Step-by-step explanation:

3 x 8 = 24

50-24=26

She will get $26 dollars back

Easy Step by Step explanation

The length of the diagonal of a square with side lengths 7√2 is approximately 14.1 units.

The length of the diagonal of a square can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides. Since a square has all sides equal, the length of each side can be represented as 7√2. Substituting this value into the Pythagorean theorem, we get:

Diagonal² = (7√2)² + (7√2)²

Diagonal² = 98 + 98 = 196

Taking the square root of 196, we find the length of the diagonal to be approximately 14 units. Rounding to the nearest tenth gives us 14.1 units.

Answer: [tex]5\sqrt{2}\ in[/tex]

Step-by-step explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.

Let H be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 5 in.

Now applying Pythagoras theorem, we get

[tex]H^2=5^2+5^2=25+25\\\\\Rightarrow\ H^2=50\\\\\Rightarrow H=\sqrt{50}\\\\\Rightarrow H=5\sqrt{2}\ in[/tex]

Hence, the length of the hypotenuse = [tex]5\sqrt{2}\ in[/tex]

Answer:

circle 1 is a dilation of circle 2 with a scale factor of 2.5.

Step-by-step explanation:

The radius of circle 1 is 5x and the radius of circle 2 is 2x.

This means the scale factor of the dilation is 5x/2x = 2.5.

Circle 1 is a dilation of circle 2 with a scale factor of 0.4.

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Given that circle 1 has radius of 5x and circle 2 has radius of 2x, hence:

Circle 1 scale factor = 2x / 5x = 0.4

Hence:

Circle 1 is a dilation of circle 2 with a scale factor of 0.4.

Find out more on similar figures at: https://brainly.com/question/14285697

Answer is -2x^2+8-10 hope this helps!!!!

Answer:

The rocket is at a greater height when t = 3 than it is when t = 1.

Option B

Step-by-step explanation:

Just took the test

Answer:

B

Step-by-step explanation:

!

Final answer:

To find out how far the plane is from the closer end of the runway, we use the angles of depression and runway length to calculate the distance using trigonometric ratios. The distance is found to be approximately 26153 meters.

Explanation:

To determine the distance from the plane to the closer end of the runway, we use trigonometric ratios based on the angles of depression given. The angles of depression to the ends of the runway are 14° and 20°. Since the problem involves a horizontal surface (runway) and vertical angles (angles of depression), we can create two right triangles. One triangle has an angle of 14° between the plane's line of sight and the horizontal surface, and the other one has a 20° angle.

Let x be the distance from the plane to the point directly above the closer end of the runway and y be the distance from the plane to the point directly above the far end of the runway. We are looking for x, which can be found using the tangent of the 14° angle.

x = runway length / (tan(20°) - tan(14°))

Given the runway length as 3000 meters, we can calculate:

x = 3000 / (tan(20°) - tan(14°))

Crunching the numbers:

x ≈ 3000 / (0.3640 - 0.2493)

x ≈ 3000 / 0.1147

x ≈ 26153 meters (rounded to the nearest tenth)

Therefore, the distance from the plane to the closer end of the runway is approximately 26153 meters.

Answer:

c

Step-by-step explanation:

Answer:

360°

Step-by-step explanation:

I just took the test.

Answer:

The answer is 5.

Step-by-step explanation:

Answer:

Approximately 157.08 sq. cm.

Step-by-step explanation:

The Area of an Ellipse is given by the formula  [tex]A=\pi a b[/tex]

Here 2a = 10, so a = 5

Also, 2b = 20, b = 10

Substituting these into the area formula gives us:

[tex]A=\pi a b\\A=\pi (5)(10)\\A=50\pi\\A=157.08[/tex]

The Area is approximately 157.08 sq. cm.

The confirmed correct answer is -9%. Trust me.

Answer:

Option B = -9%

Step-by-step explanation:

Given : Given an exponential function for compounding interest, [tex]A(x) = P(.91)^x[/tex]

To find : What is the rate of change?  

Solution :

The general form of the exponential function is [tex]f(x)=a(1+r)^x[/tex]

Where,

r is the rate of change

if r> 1 then it is growth rate    

if r< 1 then it is decay rate.

Comparing given function with exponential function,

[tex]A(x) = P(.91)^x[/tex]

[tex]1+r=0.91[/tex]

[tex]r=0.91-1[/tex]

[tex]r=−0.09[/tex]

It is a decay rate.

Convert into percentage, multiply with 100

[tex]-0.09\times 100=-9\%[/tex]

Therefore, Option B is correct.

The rate of change is -9%.      

Solution for Q1:

Given is the height of ice-cream cone, h = 6 inches.

Given is the diameter of ice-cream cone, d = 2 inches. Then radius of cone would be half of diameter, r = d/2 = 1 inch.

The ice-cream without scoop would be in the shape of cone only. So we need to find the volume of cone.

We know the formula for volume of cone is given as follows :-

[tex] Volume = \frac{1}{3} \pi r^{2} h \\\\Volume = \frac{1}{3} \pi (1)^{2} (6) \\\\Volume = \frac{6\pi}{3} = 2\pi = 2(3.14) = 6.28 \;cubic \;inches. [/tex]

So the volume is 6.28 ≈ 6 in³.

Hence, option A is correct i.e. 6 cubic inches.

Solution for Q2:

A candy is in shape of sphere with diameter, d = 0.25 inches.

Then radius of sphere, r = d/2 = 0.250/2 = 0.125 inches.

The formula for volume of sphere is given as follows :-

[tex] Volume = \frac{4}{3} \pi r^{3} \\\\Volume = \frac{4}{3} \pi (0.125)^{3} \\\\Volume = 0.00818123 \;cubic \;inches. [/tex]

So, volume of one candy = 0.00818123 cubic inches.

There are total 120 candies in the machine.

Total volume of all 120 candies = 120 x 0.00818123 = 0.981748 cubic inches.

Hence, the total volume of all candies in the machine is about 0.982 in³.

Answer:

This should definitely help for question 1 :)

What is the volume of a ball if its diameter is 6 inches? Leave your answer in terms of π.

A)V = 12 π cubic inches

B)V = 36 π cubic inches

C)V = 288 π cubic inches

D)V = 27.75 π cubic inches

Explanation:The volume of the ball above is V = 36 π cubic inches. Use the formula V = 4/3π 3. Just remember to cut the diameter in half to get the radius.

Step-by-step explanation:

The area of the remaining wall after the mural has been painted is 46x^2+73x+15. Hence, he correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex]

To find the area of the remaining wall after the mural has been painted, we need to find the area of the entire wall and then subtract the area of the mural.

The area of the rectangular wall is given by the product of its dimensions:

[tex]\[ \text{Area of wall} = (6x+7)(8x+5) \][/tex]

Expanding this expression:

[tex]\[ \text{Area of wall} = 48x^2 + 30x + 56x + 35 \][/tex]

[tex]\[ \text{Area of wall} = 48x^2 + 86x + 35 \][/tex]

Now, the area of the mural is given by the product of its dimensions:

[tex]\[ \text{Area of mural} = (x+4)(2x+5) \][/tex]

Expanding this expression:

[tex]\[ \text{Area of mural} = 2x^2 + 5x + 8x + 20 \][/tex]

[tex]\[ \text{Area of mural} = 2x^2 + 13x + 20 \][/tex]

Now, to find the area of the remaining wall, we subtract the area of the mural from the area of the wall:

[tex]\[ \text{Area of remaining wall} = \text{Area of wall} - \text{Area of mural} \][/tex]

[tex]\[ \text{Area of remaining wall} = (48x^2 + 86x + 35) - (2x^2 + 13x + 20) \][/tex]

[tex]\[ \text{Area of remaining wall} = 48x^2 + 86x + 35 - 2x^2 - 13x - 20 \][/tex]

[tex]\[ \text{Area of remaining wall} = 46x^2 + 73x + 15 \][/tex]

So, the correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex].

The complete question is:

A group of art students are painting a mural on a wall. The rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?

A. 46x^2+73x+15

B. 48x^2+86x+35

C. 2x^2+13x+20

D. 50x^2+99x+55