Middle school question.
The ground floor of the Ponce Inlet Lighthouse in Florida is circular with a diameter of 32 feet. What is the area of the ground floor?

Answer:

(2,0)

Step-by-step explanation:

Answer:  x2 + y2. − 4x + 5y − 8=0.

Step-by-step explanation:

Answer:

[tex]\dfrac{dy}{dx}=\dfrac{1}{2y}[/tex]

Step-by-step explanation:

Given equation:

[tex]y^2=x[/tex]

Differentiate:

[tex]\implies y^2\:\dfrac{d}{dx}=x\:\dfrac{d}{dx}[/tex]

[tex]\implies 2y\:\dfrac{dy}{dx}=1[/tex]

[tex]\implies \dfrac{dy}{dx}=\dfrac{1}{2y}[/tex]

Answer:

fire: risk  

Employee salaries: cost

theft: risk

health insurance for employees: cost

losing important data from computer: cost

taxes: cost

employee injury: cost

Answer:

Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).

Step-by-step explanation:

Simplified y-4 = 2(x + 1) ⇒ y = 2x + 6

Graphed function on desmos graphing calculator

Matched the through points of option #4, (-3, 0) and (0 ,6) to the graph.

Answer: D. "Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four)."

Step-by-step explanation:

We know that our graph passes through two given sets of points, therefore we can plug in those points to find the correct answer.

Let's test it with choice A. It gives us the points (0,-6) and (3,0). We can plug these into the equation to see if it is true. y-4 = 2(x+1) becomes
-6-4 = 2(3+1), or -10 = 8 which is not true, so we can eliminate it.

Choice B gives us (0,-4) and (1,0) -4-4 = 2(0+1) or -8 = 2, this one is wrong.

Choice C gives us (-1,0), so 0-4 = 2(-1+1) or -4 = 0, this one is also wrong.

Choice D gives us (-3,0) so 0-4 = 2(-3+1) or -4 = -4. This is the only option which has a correct solution, and therefore it is your answer.

Answer:

a. 7

b. 50

c. 11?

d. 8

Step-by-step explanation:

I think these are right

The quotient is 4x+2 and remainder is +6

In math, long division is a method used for dividing large numbers into groups or parts.

The long division helps in breaking the division problem into a sequence of easier steps.

Just like all division problems, a large number, which is the dividend, is divided by another number, which is called the divisor, to give a result called the quotient and sometimes a remainder.

The long division of

(4x²-2+4)÷(x+1), is attached below.

Hence, The quotient is 4x+2 and remainder is +6.

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Answer:

4) 34.1 ft²

6) 9.9 ft²

Step-by-step explanation:

The formula for the area of a triangle is A = 1/2 × b × h.
Plugging in the givn values, we have the equations: A = 1/2 × 11 × 6.2 and A = 1/2 × 6 × 3.3. Now we can solve.

--------------------------

4) A = 1/2 × 11 × 6.2

5.5 × 6.2 = 34.1 ft²

--------------------------

6) A = 1/2 × 6 × 3.3

3 × 3.3 = 9.9 ft²

hope this helps!

Answer:

  D)  3.8 cm

Step-by-step explanation:

There are several ways this problem can be solved. Maybe the easiest is to use the Law of Cosines to find angle BAC. Then trig functions can be used to find the length of the chord.

__

In triangle BAC, the Law of Cosines tells us ...

  a² = b² +c² -2bc·cos(A)

  A = arccos((b² +c² -a²)/(2bc)) = arccos((8² +6² -3²)/(2·8·6)) = arccos(91/96)

  A ≈ 18.573°

The measure of half the chord is AB times the sine of this angle:

  BD = 2(AB·sin(A)) ≈ 3.82222

The length of the common chord is about 3.8 cm.

_____

Additional comment

Another solution can be found using Heron's formula to find the area of triangle ABC. From that, its altitude can be found.

  Area ABC = √(s(s-a)(s-b)(s-c)) . . . . where s=(a+b+c)/2

  s=(3+8+6)/2 = 8.5

  A = √(8.5(8.5 -3)(8.5 -8)(8.5 -6)) = √54.4375 ≈ 7.64444

The altitude of triangle ABC to segment AC is given by ...

  A = 1/2bh

  h = 2A/b = 2(7.64444)/8 = 1.911111

BD = 2h = 3.822222

Answer:

  1/10

Step-by-step explanation:

You can convert a percentage to a fraction by dividing it by 100%.

__

  10% = 10%/100% = 10/100 = 1/10

The slope of the road is 1/10.

Answer:

640 = .8j

640 = 1.15c

Step-by-step explanation:

Let j = cost of Jocelyn's computer

c = cost of Corbin's computer

We know that Adrian's computer costs $640.

Since Adrian's computer costs 20% less than Jocelyn's computer, the cost of Adrian's computer is 80% of (.8 times)the cost of Jocelyn's computer, so 640 = .8j

Since Adrian's computer costs 15% more than Corbin's computer, the cost of Adrian's computer is 115% of (1.15 times) the cost of Corbin's computer, so 640 = 1.15c

Answer:

640 = .8j

640 = 1.15c

Step-by-step explanation:

Answer:

42 cm

Step-by-step explanation:

So, the dimensions of the square are 6*6, so we can find the area of that easily. 6*6 is 36. Now, we have to find the area of the triangle. Since 6 of the 8 cm across were used for the square, we only have 2 cm left to work with. The height of the triangle is 6. The formula to find the area of a triangle is 1/2(b)h. That would mean 1/2*2, which is 1, and then 1*6, which is 6. Finally, we add the areas of both shapes, which is 6 and 36, and we get 42.

Hope this helped!

Answer:

x = 12°

Welcome to concept of Inscribed Angle theorem

In the diagram shown above, the inscribed angle m∠SUT intercepts the diameter ST.

Then,

m∠SUT = 90°

In Δ SUT,

m∠S + m∠U + m∠T = 180°

Substitute.

m∠S + 90° + 43° = 180°

m∠S + 133° = 180°

Subtract 133° from each side.

m∠S = 47°

m∠UST = 47°

By Inscribed Angle Theorem,

m∠arc UT = 2 ⋅ m∠UST

Substitute.

(9x - 14)° = 2 ⋅ 47°

(9x - 14)° = 94°

9x - 14 = 94

Add 14 to each side.

9x = 108

Divide each side by 9

x = 12

Hence, we get as x = 12°

Answer:

its C 305

Step-by-step explanation:

ik this i got a 100 rofl

Based on the information in the table, it can be inferred that the values with two dots are 28 1/2 and 25 1/2.

A dot plot is a type of graph that is characterized by representing the frequency of an event by means of points on a line that has the values.

According to the information in the table, it can be inferred that two values have a frequency of 2, these values are:

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Step-by-step explanation:

when given similar terms sometimes its easier to work the problem out before sinplifying

The question is an illustration of Excel formulas, and the formula to enter in cell C2 is: =(B2/600)

To enter a formula in Microsoft Office Excel, we make use of the following syntax:

= (Formula)

From the question, the total score is 600.

So, the formula to enter in cell C2 is:

=(B2/600)

Next, drag the content of cell B2 through cell C12.

This is to ensure that all cells C2 to C12 have the appropriate formula.

Lastly, following the highlighted steps to show the result as percentage

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Answer:

(5-i)

(5-4i)

(-12i^2+2i+2)

(6i^2-2i)

Answer:

9.2 Minutes

Step-by-step explanation:

46 minutes divided by 5 miles is equal to 9.2 minutes per mile

Answer:

  9.2

Step-by-step explanation:

To find minutes per mile, divide minutes by miles:

  (46 min)/(5 mi) = 9.2 min/mi

On average, it takes 9.2 minutes for Christine to run a mile.

Answer:

-5(y - 3)/-2

Step-by-step explanation:

y² - 9/-2y × -5y/y + 3

Multiply Rewrite

Simplify the expression

(y - 3)×(y + 3)/2 × 5/y + 3

Simplify the expression

y - 3/2 × 5

Calculate

5(y - 3)/2

HOPE THIS HELPS :)

Answer:

[tex]\huge\boxed{\dfrac{-5(y-3)}{-2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{y^2-9}{-2y}\cdot\dfrac{-5y}{y+3}=\dfrac{y^2-3^2}{-2y}\cdot\dfrac{-5y}{y+3}[/tex]

use: a² - b² = (a - b)(a + b)

[tex]=\dfrac{(y-3)(y+3)}{-2y}\cdot\dfrac{-5y}{y+3}[/tex]

simplify fractions

(y + 3) and y

[tex]=\dfrac{y-3}{-2}\cdot\dfrac{-5}{1}=\dfrac{-5(y-3)}{-2\cdot1}=\dfrac{-5(y-3)}{-2}[/tex]

The Mean Absolute Deviation for the following data: 6, 1, 3, 8, 5, 11, 1, 5 is 2.5

The mean absolute deviation of a dataset is the average distance between each data point and the mean.

mean absolute deviation = [tex]\frac{summation|x-mean|}{n}[/tex]

where

Therefore, let's calculate the mean first.

Arrange the data in ascending order.

1, 1, 3, 5, 5, 6, 8, 11

mean = 1 + 1 + 3 + 5 + 5 + 6 + 8 + 11 / 8 = 40 / 8 = 5

Therefore, let's calculate the distance between each dat point and mean.

|1 - 5| + |1-5| + |3-5| + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|

4 + 4 + 2 + 0 + 0 + 1 + 3 + 6 = 20

Hence,

mean absolute deviation = 20 / 8 = 2.5

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Answer+Step-by-step explanation:

[tex]\frac{1}{5} \left( 4m+20\right) =\frac{4}{5}m + \frac{20}{5} = \frac{4}{5}m + 4[/tex]

[tex]9\left( \frac{5}{4} y-\frac{1}{3} \right) =\frac{9\times5}{9} y-\frac{9}{3} = 5y - 3[/tex]

Answer:

the red line is 300 meters further

Step-by-step explanation:

since you have 100 meters as the blue line you add 300 meters th get to the 400 meters red line

Answer:

300

Step-by-step explanation:

621 rounds to 600 because 21 is smaller than 50. 267 round to 300 since 67 is bigger than 50.

600-300=300

Answer:

14.44 (Letter D)

Step-by-step explanation:

The answer is 14.44

Hopefully its correct!!!

Answer:

B. x = 6

Explanation:

[tex]\rightarrow \sf x^2 = 36[/tex]

[tex]\rightarrow \sf x= \pm \sqrt{36}[/tex]

[tex]\rightarrow \sf x= \pm 6[/tex]

[tex]\rightarrow \sf x= +6, \ -6[/tex]

As asked for positive, (+)

[tex]\rightarrow \sf x = 6[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \sqrt{36} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \pm6[/tex]

but since we gave been asked to find positive solution, it's 6

So, correct choice is B. x = 6

Answer:

center = (-2, 6)

radius = 6

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Therefore, we need to rewrite the given equation into the standard form of an equation of a circle.

Given equation:

[tex]x^2+y^2+4x-12y+4=0[/tex]

Collect like terms and subtract 4 from both sides:

[tex]\implies x^2+4x+y^2-12y=-4[/tex]

Complete the square for both variables by adding the square of half of the coefficient of [tex]x[/tex] and [tex]y[/tex] to both sides:

[tex]\implies x^2+4x+\left(\dfrac{4}{2}\right)^2+y^2-12y+\left(\dfrac{-12}{2}\right)^2=-4+\left(\dfrac{4}{2}\right)^2+\left(\dfrac{-12}{2}\right)^2[/tex]

[tex]\implies x^2+4x+4+y^2-12y+36=-4+4+36[/tex]

Factor both variables:

[tex]\implies (x+2)^2+(y-6)^2=36[/tex]

Therefore:

Answer:

a) x = 9.

b) y = 61.

Step-by-step explanation:

As the 2  weighing scales balance:

4 + 4x = 31 + x

3x = 31 - 4 = 27

x = 9.

Also 4 + 4x + x + 31  = y + 2x + 1

Substituting  for x:

4 + 4(9) + 9 + 31 = y + 2(9) + 1

80 = y + 19

y = 80 - 19 = 61.

Answer:

x = 9

y = 61

Step-by-step explanation:

The main scales are balanced.

The left side of the main scales comprises another scale, which is also balanced.

From this and the values given, we can construct two equations.

Equation 1

Balancing the scales on the left of the main scales:

⇒ 4 + 4x = 31 + x

Solving this for x:

⇒ 4 + 4x - 4 = 31 + x - 4

⇒ 4x = 27 + x

⇒ 4x - x = 27 + x - x

⇒ 3x = 27

⇒ 3x ÷ 3 = 27 ÷ 3

⇒ x = 9

Equation 2

Balancing the main scales:

4 + 4x + 31 + x = y + 1 + 2x

Rearranging to make y the subject:

⇒ 5x + 35 = y + 1 + 2x

⇒ 5x + 35 - 1 = y + 1 + 2x - 1

⇒ 5x + 34 = y + 2x

⇒ 5x + 34 - 2x = y + 2x - 2x

⇒ 3x + 34 = y

Substituting the found value of x (from Equation 1) and solving for y:

⇒ y = 3(9) + 34

⇒ y = 27 + 34

⇒ y = 61

Therefore: