A function that models the profit for a new pet-monitoring system shows that there is no profit made until the price reaches
$95 per unit, a maximum profit at a price of $140 per unit, and no profit at a price over $185 per unit. Which graph models
the function?
Graphing

Answer:

The correct option is;

A. a shaded region below a solid boundary line

Step-by-step explanation:

The parameters given are;

The equation, y ≤ 2x - 1

We compare the above equation with the equation for a straight line, y = m·x + c to get

The slope m = 2

The y-intercept c = -1

Therefore, we have;

The graph of an inequality of a y value which is less than or equal to a function is represented by a solid line having the shaded region, which shows the area that satisfies the inequality, shaded below the line

Which gives the correct option as A. A shaded region below a solid boundary line.

Answer:

f(x) = (x + 5)² - 21.5

Step-by-step explanation:

Step 1: Subtract both sides by 7

2x² + 20x = -7

Step: GCF and divide

2(x² + 10x) = -7

x² + 10x = -7/2

Step 3: Complete the Square

x² + 10x + 25 = -7/2 + 25

(x +5)² = 43/2

Step 4: Subtract 43/2 to both sides

(x + 5)² - 43/2

And we have our equation!

Answer:

Step-by-step explanation:

From the figure attached,

Given : LM ≅ OP

            PQ ≅ MN

            NL ≅ QO

To Prove : ΔLMN ≅ ΔOPQ

In the triangles LMN and OPQ,

             Statements              Reasons

1). LM ≅ OP                       1). Given

2). PQ ≅ MN                     2). Given

3). NL ≅ QO                      3). Given

4). ΔLMN ≅ ΔOPQ            4). By SSS property of congruence

Answer: y = 1/2x - 6

Step-by-step explanation:

#4 We are going to use slope intercept form, (y = mx+b)

1. The line crossing the y-intercept at (0,-6)

2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)

3. Make the equation: y= 1/2x - 6

Answer: 3 . y = -1/3 + 4/3   4. y= 1/2x -6

Step-by-step explanation:

3.   In the first graph  they have the coordinates,  (-2,2)  and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.

To find the slope we have to find the change in the y values  and divide it by the difference in the x values.

2-0 = 2

-2 -4 = -6

2/-6 =  -1/3  Now we know that the slope is -1/3  so we need to  find the y-intercept.

2= -1/3(-2) +b   where be is the y intercept.

2= 2/3 + b

-2/3  -2/3

b= 4/3  

Now we could write the equation as  y= -1/3 + 4/3  

4. The same with number 4.  

We will find the slope and the y intercept by using some points on the number line.

(0,-6)  This already have the y-intercept graphed so we will need to just find the slope.

(0,-6)

(4,-4)  

-6 - (-4) = -2

0 - 4 =  -4

-2/-4 = 1/2

Equation: y = 1/2x  -6

Answer:

3, 12, 27 and 300

Step-by-step explanation:

Plug n as 1, 2, 3 and 10.

3(1)² = 3

3(2)² = 12

3(3)² = 27

3(10)² = 300

Answer:

36 toilet rolls

Step-by-step explanation:

1 pack consist of 4 rolls

So,

1 pack = 4 toilet rolls

Multiplying both sides by 9

=> 1×9 = 4×9

=> 9 packs = 36 toilet rolls

Answer:

believe its 2x cause 1 was wrong

Answer:

f(-7)=224

Step-by-step explanation:

[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]

Answer:

x = -1/8

Step-by-step explanation:

The greater than sign can be replaced with an equal sign to solve.

5x + 4 < 3 – 3x =>

5x + 4 = 3 - 3x =>

+3x  -4    +3x - 4

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

8x = -1

x = -1/8

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Hey there! :)

Answer:

D, e - 2b.

Step-by-step explanation:

Check each answer choice using the pattern given:

A. e - c = d because c + d = e. This is correct.

B. b + c = d. This is correct.

C. a + 2b = d because c = a + b. This is correct.

D. e - 2b ≠ d. This is incorrect.

E. f - e = d because d + e = f. This is correct.

Therefore, the only answer that does not equal "d" is D, e - 2b.

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0                        x² + x + b = 0

a*1² +a*1 + 2 = 0                        1² + 1 + b = 0

a +a + 2 = 0                                 1 + 1 + b = 0

2a + 2 = 0                                    2 + b = 0

2a = -  2                                         b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

Answer:

3.98 cm

Step-by-step explanation:

V= πr²h

V= 200 cm³, r= 4 cm, h=?

h= V/(πr²)= 200/(3.14*4²)= 3.98 cm

Answer:

Brainliest if correct!

Step-by-step explanation:

6561

9^4

the first one!!!

Answer:

0.100

Step-by-step explanation:

0.0995 has 4 decimal places

5>4 so round up

9 turns to 10, the 1 is "added on" to the number ahead

9 turns to 10 again, the 1 is "added on" to the number ahead

0 turns to 1

you are left with 0.100

Answer:

0.100

Step-by-step explanation:

Three decimal places: 0. 0 / 9 / 9 / 5

Rounding number: 0. 0 / 9 / 9 / 5

Since it is 5, add 1 to the second 9. This will result to 0 while adding 1 to the first 9. Again, this would result to 10 which will add 1 to the next number, 0.

0.1000

Since the question wants you to round three places, you were not told to remove the zeros in those decimal places. So only remove the last 0.

0.100 is the answer

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer:

Step-by-step explanation:

Parallel lines have same slope

19) y = x - 4

m = 1 ;   (2, 3 )

Equation: y - y₁ = m(x- x₁)

             y - 3 = 1(x - 2)

              y - 3 = x -2

                   y = x - 2 + 3

y = x + 1

20) 2x + 3y = 3

We have to write in y = mx + b  form

3y =  - 2x - 3

[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)

[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]

for perpendicular lines, m2 = -1/m1

21) y = 2x+ 5

m1 = 2

[tex]m_{2}=\frac{-1}{2}[/tex];     (-2,8)

[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]

22) x+ 4y = 8

           4y = -x + 8

             [tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]

m2 = 4;  (-2,-11)

y - [-11] = 4(x -[-2])

y + 11 = 4 (x + 2)

y + 11 = 4x + 8

      y = 4x + 8 - 11

      y = 4x - 3

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]

PART B

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

[tex]=\dfrac{15}{64}\\=0.234375[/tex]

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]

Answer:

Hope it will helpful.Follow for more answers.

Answer:

[tex]9\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{3} \div \frac{1}{4}[/tex]

[tex]\frac{7}{3} \div \frac{1}{4}[/tex]

[tex]\frac{7}{3} \times \frac{4}{1}[/tex]

[tex]\frac{7 \times 4}{3 \times 1}[/tex]

[tex]\frac{28}{3}[/tex]

[tex]9\frac{1}{3}[/tex]

[tex]9 \frac{1}{3} \\ solution \\ 2 \frac{1}{3} \div \frac{1}{4} \\ = \frac{7}{3} \times \frac{4}{1} \\ = \frac{7 \times 4}{3 \times 1} \\ = \frac{28}{3} \\ = 9 \frac{1}{3} [/tex]

Hope it helps...

Good luck on your assignment....

Explanation:

Label the slots A,B,C for first through third place.

There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values

8*7*6 = 336

There are 336 ways to select three people from a pool of eight overall.

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

If you want to use the permutation formula, then your steps might look like this

[tex]_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336\\\\[/tex]

Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.

Answer:

Height of building is 57.12 m.

Step-by-step explanation:

Let us try to understand the given dimensions as per the attached diagram.

Please refer to attached image (Right angled [tex]\triangle OBT[/tex])

with [tex]\angle B =90^\circ[/tex]

Let O be the point where the Surveyor is standing.

B be the point of the base of building.

T be the point of top of building.

As per question statement,

[tex]\angle O = 55^\circ[/tex]

Side OB = 40 m

To find: Side BT = ?

Using tangent trigonometric identity:

[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]

[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]

So, height of building is 57.12 m.

Answer:

Step-by-step explanation:

We will make a table with the values for both a 6% account and a 9% account.

The formula for this problem is Prt = I, where P is the amount invested in each account, r is the interest rate each carries in decimal form, t is the time in years, and I is the interest earned from the multiplication of the 3 previous values. We don't know how much is invested in either account, but we do know that no matter how much is invested in the 6% account, there is 6 times that in the 9% account. We know that the 6% account has a decimal rate of .06 and that the 9% account has a decimal rate of .09. "Annual" means 1 year, so the time is 1 year. Filling in the table, then:

                     P  *    r     *     t     =     I

Acct 6%         x     .06         1

Acct 9%       6x    .09          1

What we do with those number is multiply them straight across each row to get the amount of interest earned from each:

                    P     *     r     *     t     =     I

Acct 6%       x      *  .06    *    1      =   .06x

Acct 9%      6x     *  .09    *    1      =   .54x

The amount of Interest for both ADDS UP to 800; therefore:

.06x + .54x = 800 and

.6x = 800 so

x = 1333.33

That's how much was invested in the account that earned 6% interest annually.  

Answer:

[tex](C) \dfrac{x+3}{x}[/tex]

Step-by-step explanation:

We want to determine an  equivalent expression to:

[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]

Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.

[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]

Step 2: Change the division sign to multiplication

[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]

Step 3: Cancel out common terms and simplify

[tex]= \dfrac{x+3}{x}[/tex]

The correct option is C.

The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Given expression is,

                        [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]

Use factorization,   [tex]x^{2} -9=(x-3)(x+3)[/tex]

Now simplify the given expression.

                       [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]

Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

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Answer:

x = ±20

Step-by-step explanation:

x^2 -1=399

Add 1 to each side

x^2 = 399+1

x^2 = 400

Take the square root of each side

sqrt(x^2) = ±sqrt(400)

x = ±20

Answer:

That is already at its simplest form.

Step-by-step explanation:

(y + 1)(y + 1) or (y + 1)² is the factored form of y² + 2y + 1. You cannot break it down any further after you reached binomials after you factor unless you are solving for x.

Answer:

(i) 12.25

(ii) 12.25.

Step-by-step explanation:

(1) cot^2 O = (7/2)^2 = 49/4

= 12.25.

(2) (1 - sin O) ( 1 + sin O)         1 - sin^2 O          cos^2 O

     ----------------------------  =     -------------   =       --------------

    (1 - cos O)(1 + cos O)         1 - cos^2 O         1 - cos^2 O

As cot O = 2/7, tan O = 1 /2/7 = 7/2.

Hypotenuse of the right  triangle = √( 2^2 + 7^2)

= √53

So cos O = 7/√53

Therefore  the original function = cos^2 O / (1 - cos^2 O)

= (7/√53)^2 / (1 -  (7/√53)^2 )

= 49/53 / 4/53

= 49/4.

Answer:

x = 12:15=×5

36

060

Step-by-step explanation:

12:15=0

x=0

Answer:

4

Step-by-step explanation:

Divide the left side by 3

12:15

12/3 : 15/3

4:5

x would be 4

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

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