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Suppose that a spotlight is used for lighting objects at many different distances and that the area A of the light circle produced is related to the distance x to the lighted object by A=0.1x^2.

a. If the spotlight produces 250 lumens of light energy, what function gives the intensity of the light I, (in lumens per square foot) as a function of the distance x in feet from the spotlight to its target?

b. Write and solve equations that match these questions about the light intensity from the spotlight.

i. What is the intensity of light on an object that is 20 feet from the spotlight source?

ii. How far from the spotlight is an object that recieves 100 lumens of light per square foot?

Answer:

c

Step-by-step explanation:

Answer:

D. 0.007

Step-by-step Explanation:

0.07= 10 x

= 0.07/ 10

= 0.007

Answer:

.0000269 hectograms/ deciliter

2.69 * 10^e-5 hectograms/ deciliter

Step-by-step explanation:

micro grams to hectograms

10^8 micrograms = 1 hectogram

milliliters to deciliter

100 milliliters = 1 deciliter

Using conversion factors

26.9 microgram         1 hectogram           100 milliliters

----------------------- * ---------------------------  * ---------------------

milliliter                     10^8 micrograms           1 deciliter

2690 hectograms

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

10^8 deciliters

.0000269 hectograms/ deciliter

2.69 * 10^e-5 hectograms/ deciliter

Answer:

$14.16 for 6 gallons.

Step-by-step explanation:

35.40/15 = 2.36

2.36*6 = 14.16

Answer:

100π cubic units is left

Step-by-step explanation:

πr²h - 1/3πr²h

π(5)²(6) - 1/3π(5)²(6)

150π - 50π = 100π

The volume of the foam is 100π cubic units remaining in the cylinder.

Given,

Radius of cone (r) = 5

Height of cone (h) = 6

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

∵ The volume of the cone (V )= 1/3πhr²

To determine the volume of the foam remaining in the cylinder

Subtract the volume of the cone into the volume of the cylinder

⇒ πr²h - 1/3πr²h

Substitute the values of h and r,

⇒ π(5)²(6) - 1/3π(5)²(6)

⇒ 150π - 50π

⇒ 100π

Hence, The volume of the foam is 100π cubic units remaining in the cylinder.

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Answer:

-60%

-$50

Step-by-step explanation:

As the statement says that the price of the jacket was reduced by 40%, to determine the percent that the sale price represents from the original price, you have to subtract 40% from 100% that represents the original price:

100%-40%= 60%

This means that $30 represents 60% of the original price.

-To determine the original price of the jacket, you can use the rule of three:

$30 →  60%

 x    ←  100%

x=(100*30)/60= 50

According to this, the original price of a jacket was $50.

Answer:

See  below.

Step-by-step explanation:

Convert to decimal form

7 3/5 = 7.6

7 7/10 = 7.7

10 2/5 = 10.4

8 1/2 = 8.5

So the answer is

7 3/5 , 7 7/10, 8.3, 8.1/2, 10.2  10 2/5, 11.1.

Answer:

Please refer to the attached diagram for answer.

Step-by-step explanation:

Upper-left coordinates on a rectangle are (-1, 4)

Upper-right coordinates are (3, 4)

Perimeter of rectangle = 24 units

To find:

To draw the rectangle on the coordinate plane.

Solution:

Let the rectangle be ABCD.

So, sides AB  = CD and BC = DA

Let Point A has coordinates (-1, 4).

And upper right coordinates will be adjacent to A.

So, let Point B (3, 4).

Let us find the distance between A and B by distance formula:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where,

[tex]x_2 = 3\\x_1 = -1\\y_2 = 4\\y_1 = 4[/tex]

[tex]AB = \sqrt{(3-(-1))^2+(4-4)^2}\\\Rightarrow AB = \sqrt{(4)^2+(0)^2}\\\Rightarrow AB = 4[/tex]

AB = 4 = CD

Perimeter of rectangle = Sum of all four sides = 2 (AB+DA) = 24

[tex]2 \times 4 + 2DA = 24\\\Rightarrow 2DA=24-8\\\Rightarrow 2DA=16\\\Rightarrow DA =8\ units[/tex]

As it is a rectangle, its adjacent sides will be perpendicular to each other.

When we move from A to B only x coordinate is changing and it has changed by  4 (3- (-1) ) units. (Found by subtracting the x coordinates of the two points.)

Similarly, when we will move from D to A, only y coordinate will change by 8 units. (D is lower left coordinate so add 8 to y)

[tex]\Rightarrow y + 8 = 4 \Rightarrow y =-4[/tex]

[tex]x[/tex] coordinate will be same as that of A i.e. -1.

So, D will be (-1, -4)

Similarly, when we will move from C to B, only y coordinate will change by 8 units. (C is lower right coordinate so add 8 to y)

[tex]\Rightarrow y + 8 = 4 \Rightarrow y =-4[/tex]

[tex]x[/tex] coordinate will be same as that of B i.e. 3.

So, C will be (3, -4).

Now, let us draw

A(-1, 4)

B(3, 4)

C (3, -4)

D(-1, -4)

Please refer to the attached diagram for answer.

Answer:

A(-1, 4) B(3, 4)C (3, -4)D(-1, -4)

Step-by-step explanation: Brainliest plus-size

Answer:

x2 + x = 42

Step-by-step explanation:

x = nhmber

x² = its square

then:

The sum of a number and its square is 42 is:

x² + x = 42

Answer:

56 miles

Step-by-step explanation:

Answer:

-15.

Step-by-step explanation:

G(-5) = 2(-5) - 1

= -10 - 1

= -11

H(-11) = -11 - 4

= -15

Hope this helps!

Answer:

h(g(-5))= -15

Step-by-step explanation:

We are asked to find h(g(-5)).

First, we must find g(-5).

We know that g(x)=2x-1. Therefore, to find g(-5), we must plug -5 in for x.

g(x)= 2x-1

g(-5)= 2(-5) -1

Multiply 2 and -5.

g(-5)= -10 -1

Subtract 1 from -10.

g(-5)= -11

Now, we can substitute -11 in for g(-5).

h(g(-5)

g(-5)= -11

h(-11)

Now, we must find h(-11).

We know that h(x)= x-4. So, we can plug -11 in for x.

h(x)= x-4

h(-11)= -11-4

Subtract 4 from -11.

h(-11)= -15

h(g(-5)=  -15

Answer:

(x²)² + 2(9)x² + 9²

(x² + 9)²

Step-by-step explanation:

Given expression in the question is,

(x⁴ + 18x²+ 81)

We have to factorize this expression.

We know the formula of (a + b)² = a² + 2ab + b²

Comparing this formula with the given expression,

a = x²

b = 9²

By substituting these values in the given formula,

Therefore, (x⁴ + 18x²+ 81) = (x²)² + 2(9)x² + 9²

                                         = (x² + 9)²

Answer:

The correct option is;

D. x = -1.38 and 0.82

Please find attached the combined function chart

Step-by-step explanation:

The given equation is x³ + 3 = -x⁴ + 4

Plotting the equation using Excel, we have;

f(x) = x³ + 3, h(x) = -x⁴ + 4

x                                             f(x)                                       h(x)

-1.4                                         0.256                                   0.1584

-1.39                                       0.314381                              0.26699

-1.38                                       0.371928                             0.373261

-1.37                                       0.428647                             0.477246

-1.36                                       0.484544                             0.57898

Which shows an intersection at the point around -1.38

x                                          f(x)                                     h(x)

0.77                                    3.456533                         3.64847

0.78                                    3.474552                         3.629849

0.79                                    3.493039                          3.610499

0.8                                         3.512                                3.5904

0.81                                      3.531441                           3.569533

0.82                                       3.551368                          3.547878

0.83                                       3.571787                            3.525417

Which shows the intersection point around 0.82

Therefore, the correct option is x = -1.38 and 0.82

From the graphing calculator the intersection point is given as

x = -1.3802775691 and 0.81917251339.

c...................

Answer:

65

Step-by-step explanation:

Let c = number of correct answer.

Let i = number of incorrect answers.

There are 100 questions, so

c + i = 100

The correct answers are worth 0.5c.

The incorrect answers are worth -0.3i (a negative value because 30 cents is taken away for each incorrect answer)

The total worth of the answers is 0.5c - 0.3i. The total worth of the answers is $22.00, so the second equation is

0.5c - 0.3i = 22

We have a system of two equations in 2 unknowns:

c + i = 100

0.5c - 0.3i = 22

We'll use the substitution method to solve the system of equations.

Solve the firt equation for c:

c = 100 - i

Now substitute 100 - i for c in the second equation.

0.5(100 - i) - 0.3i = 22

50 - 0.5i - 0.3i = 22

-0.8i = -28

i = 35

c = 100 - i

c = 100 - 35

c = 65

Answer: 65 problems were solved correctly.

Answer:

≈ 83.9 cm²

Step-by-step explanation:

Given:

Then:

Area of  the triangle is found by using Herons formula:

where s = P/2 = 44/2 = 22 cm

Answer:

[tex]\huge \boxed{\mathrm{83.9 \ cm^2}}[/tex]

Step-by-step explanation:

Two sides of the triangle are given.

The perimeter is given.

We need to solve for the third side.

[tex]P=a+b+c[/tex]

[tex]P= \sf perimeter[/tex]

[tex]a,b,c= \sf side \ lengths[/tex]

[tex]44=18+12+c[/tex]

[tex]c=14[/tex]

The measure of the third side is 14 cm.

When three sides of the triangle are given, we can solve for the area using Heron’s formula.

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]s=\sf semi \ perimeter[/tex]

[tex]\displaystyle s=\frac{P}{2} =\frac{44}{2} =22[/tex]

Plugging in the values and evaluating.

[tex]A=\sqrt{22(22-18)(22-12)(22-14)}[/tex]

[tex]A = 83.904708...[/tex]

The area of the triangle is approximately 83.9 cm².

Answer: this is your answer

  10

_____

6-5x

Answer:

1.7-20x OR 10/6-5x

Step-by-step explanation:

40÷(24-4x(2+3))

first you add the last set of ()

40÷(24-4x(5))

then you multiply by 4x

40÷(24-20x)

since you can't subtract those two you do this

40÷24-20x

divide 40 and 24

you get 1.66666667 then you round up

1.7-20x

you put 40/24-20x

divide the top and the bottom by 4

(40÷4)/(24÷4) -(20x÷4)

and your answer will be

10/6-5x

Answer:2 hundred+1 tens+3 ones

Step-by-step explanation:

Answer:

Step-by-step explanation:

He ate 15, 19, 23, 27, 31, 35 pies for each day.

Addition in math is a process of combining two or more numbers.

Given that, Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days, each day, he ate 4 more pies than the day before. Homer ate 150 pies while in training.

Let he ate x pie for 1st day, then according to question,

1st day = x

2nd day = x+4

3rd day = x+8

4th day = x+12

5th day = x+16

6th day = x+20

He ate 150 pies for 6 days

Therefore, x+x+4+x+8+x+12+x+16+x+20 = 6x + 60 = 150

6x = 90

x = 15

Hence, he ate 15, 19, 23, 27, 31, 35 pies for each consecutive day.

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Answer:

-10x

Step-by-step explanation:

-2x-4=-6x

-4-6x = -10x

Answer:

x = -2

Step-by-step explanation:

To solve for x:

Therefore, x equals -2.

To simplify the equation:

Answer:

400 cubic yards

Step-by-step explanation:

There are three cubic feet in each cubic yard

Answer: (22)(39) = 858.

Step-by-step explanation:

Product of a number simply means that one has to multiply the numbers that are given. For example, if a student is told to find the product of 2 and 5, it simply means that 2 × 5 = 10.

Regarding the above question, the product of 22 and 39 is represented by: (22)(39) = 858. It should be noted that 22 × 39 = 858

Answer:

Read Exp:

Step-by-step explanation:

Area = 3.14 x r^2

I've Included a picture to tell you how to get the diameter as well as the circumference.

Answer:

formula is πr² ( pi x radius squared)

Step-by-step explanation:

the value of π is 3.142...

multiply this value with the squared radius of the circle and you'll get your answer.

For example:

we have a circle with diameter 5

so,  π x 5² = 3.142 x 25 = 78.5

Answer:

Caleb's actual height is 48 inches

Step-by-step explanation:

Alison's height in the photograph= 4 cm

Caleb's height in the photograph= 3.2 cm

Alison's actual height= 60 in

Caleb's actual height=x in

60 in= 152.4 cm

Alison's height in photograph : Her actual height = Caleb's height in photograph : his actual height

4cm : 152.4cm = 3.2cm : xcm

4 / 152.4 = 3.2 / x

Cross product

4 * x = 152.4 * 3.2

4x = 487.68

Divide both sides by 4

x= 121.92 cm

121.92 cm = 48 in

Caleb's actual height is 48 in

Answer:

A) 9

Step-by-step explanation:

Hello!

A constant is a fixed and defined number.

A constant is any number that does not have a variable next to it

The only number in the equation that follows this is 9

Hope this Helps!

The constant from the expression is 9. option A

Algebraic expressions are defined as expressions that are made up of variables, constants, factors and coefficients.

Also, these algebraic expressions are made up of arithmetic operations, such as;

From the information, we have that the expression is given as;

[tex]15x^2 + 2x + 9[/tex]

We have then that;

The terms are; 15x , 2x and 9

The coefficient of x is 2

The coefficient of x² is 15

The constant is 9

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answer

r = b²-4ac

= 81 + 36

= 117

Answer:

see below (I hope this helps!)

Step-by-step explanation:

C = 6h + 11f + 7p

Get all non-f terms on one side:

C - 6h - 7p = 11f

Divide by 11:

f = [tex]\frac{C - 6h - 7p}{11}[/tex]

Answer:

2. -6

4. 0

8. 2

Step-by-step explanation:

Order of Operations: BPEMDAS

2

Step 1: Write out expression

-(8 - 2)

Step 2: Parenthesis (Subtract)

-(6)

Step 3: Multiply

-6

4

Step 1: Write out expression

-(0 + 0)

Step 2: Parenthesis (Add)

-(0)

Step 3: Multiply

0

8

Step 1: Write out expression

3 - [-(-1)]

Step 2: Brackets (Multiply)

3 - 1

Step 3: Subtract

2