Catera has found that as she increases her price, p, the quantity she sells q decreases.
The following equations relates q, the quantity she sells, to p, the price she changes.
p = 284 - 4q
Catera's price is $232.
what is the quantity thats she sells? Show your work.
Answer:

Answer:

see the explanation

Step-by-step explanation:

step 1

Identify the equation of the given line

we know that

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

[tex]m=5\\b=-1[/tex]

substitute

[tex]y=5x-1[/tex]

step 2

Identify the coordinates of four points on the line

First point

The given y-intercept

point (0,-1)

Second point

The x-intercept

For y=0

[tex]0=5x-1[/tex]

[tex]x=\frac{1}{5}=0.20[/tex]

point (0.20,0)

Third point

For x=1

[tex]y=5(1)-1=4[/tex]

point (1,4)

Fourth point

For x=2

[tex]y=5(2)-1=9[/tex]

point (2,9)

Answer:

The 3rd one

Step-by-step explanation:

The steepest slope is basically the slope with the greatest absolute value. You can find slope by finding rise over run when given the graphs and finding change in y/change in x in the tables.

Function 1: -3

Function 2: (13-10)/(6-3) = 3/3 = 1

Function 3: 2

Function 4: (-4-(-12))/(2-4) = 8/-2 = -4

Function 4's slope has the greatest absolute value.

answer: the fourth one

Answer:

The total change in yardage of the team is by - 1 yards.

Step-by-step explanation:

Let us assume that the initial yardage of the team was x yards.

Now, the team gained 5 yards on their play of the game.

Hence, the team now has (x + 5) yards on their play of the game.

Next, the team lost 6 yards and finally, the team will have [(x + 5) - 6] = (x - 1) yards in total.

Therefore, the total change in yardage of the team is by - 1 yard. (Answer)

Answer:

The total change in yardage of the team is by - 1 yards.

Step-by-step explanation:

The total change in yardage of the team is by - 1 yards.

Answer:

The arc length, radius and the included angle are related as

r\theta=\widehat {XYZ}  where  \theta  is in radians.

The radius  r  is given by

r=\frac{\widehat {XYZ} }{\theta} \\ r=\frac{10.8}{1.8} \\ r=6\;units  

Correct choice is (B).

Step-by-step explanation:

A relation is a function if there is exactly one output for each input ⇒ b

Step-by-step explanation:

Let us revise the meaning of relation and function

Examples:

{(1 , 2) , (-2 , 3) , (1 , 5) , (2 , 4)}

∵ x is the input

∵ y is the output

∵ The input 1 has two output 2 and 5

∴ The set above is a relation

{(1 , 2) , (-2 , 3) , (-1 , 5) , (2 , 4)}

∵ x is the input

∵ y is the output

∵ Each input has only one output

∴ The set above is a function

A relation is a function if there is exactly one output for each input

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Answer:

  see attached

Step-by-step explanation:

The translation is 1 unit left and 5 units down. It is easy enough to count squares. It is just as easy to add (-1, -5) to each of the preimage coordinates.

x + (4 + x) = 20

2x + 4 = 20

2x = 16

x = 8

Proof

x + (4 + x) = 20

8 + 4 + 8 = 20

12 + 8 = 20

20 = 20

The numbers are 8 and 12.

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Answer:

14/15  

Step-by-step explanation:

find common denomerator 15

giving you -6/15 + 20/15

add

First find m<HGC.

m<HGC=14 degrees (through vertical angles)

So...

m<HGE=14+78=92 degrees (through adjacent angles)

Now we have two parallel line cut by a transversal. And so... <HGE and <CEG are same side interior angles which means they are supplements (sum to 180 degrees)

m<HGE+m<CEG=180

92+m<CEG=180

m<CEG=88 degrees

<CEG and <CEB make a linear pair and are thus are supplements as well.

So...

m<CEG+m<CEB=180

88+m<CEB=180

m<CEB=92 degrees

m<CEB=4x=92

x=92/4=23 degrees

answer: 23 degrees

Answer: 1

Step-by-step explanation:

It will be the smallest value for f(x).

The minimum of a sinusoidal function is the lowest point on the graph that is 1.

The minimum of a sinusoidal function is the lowest point on the graph. Looking at the image you provided, the minimum point is the lowest y-coordinate the curve reaches.

Since the graph is a sine wave, it oscillates between a maximum and a minimum value. For a standard sine function, which this graph appears to resemble, these extrema occur at points where the sine of the angle is either 1 or -1.

The minimum value of sine is -1, but the actual minimum value of the function on the graph will depend on any vertical shift and amplitude changes.

To find the exact minimum value from the graph, you'd look for the lowest point on the y-axis that the graph reaches. From the image, it's not perfectly clear, but it looks like the minimum value is around -2 on the y-axis.

This would be the case if the function has no vertical shift from the standard sine wave. If there's a vertical shift, the minimum would be the standard minimum value of sine (-1) plus the vertical shift.

Answer:

$6900

Step-by-step explanation:

Given:

Length = 45 yards

Width = 5 yards

thickness = 1/3 yard

Volume,

= Length x Width x Thickness

= 45 x 5 x (1/3)

= 75 yards³

Costs:

1 cubic yard = $92

75 cubic yards = $92 x 75 = $6900

Final answer:

To find how many text messages, x, Tim sent last month, use the equation: Total cost = fixed cost + variable cost. Given that Tim's phone bill was $30.58, the equation is $30.58 = $25.08 + $0.22x. Solving the equation gives x ≈ 25, so Tim sent approximately 25 text messages last month.

Explanation:

To find the number of text messages, x, Tim sent last month, we can use the equation:
Total cost = fixed cost + variable cost

Given that Tim's phone bill was $30.58, the fixed cost is $25.08. The variable cost is $0.22 per text message sent. Let's represent the number of text messages sent by x.

So, the equation becomes:
$30.58 = $25.08 + $0.22x

To solve for x, we need to isolate x. Subtract $25.08 from both sides of the equation:

$30.58 - $25.08 = $0.22x

Simplify:

$5.50 = $0.22x

Divide both sides of the equation by $0.22:

x = $5.50 / $0.22

x ≈ 25

Therefore, Tim sent approximately 25 text messages last month.

Answer:

3.728 cm²

90

Step-by-step explanation:

To built the envelope I am using a rectangular piece of material 28 m long and 12 m wide.  

Out of this material, I have to cut patches that are 1/12 the length and 2/15 the width of the whole material.

So, the length of the patches is [tex]28 \times \frac{1}{12} = 2.33[/tex] m and the width of the patches is [tex]12 \times \frac{2}{15} = 1.6[/tex] m.

Therefore, the area of the patches is (1.6 × 2.33) = 3.728 m² each. (Answer)

Now, the area of the rectangular piece of material is (28 × 12) = 336 m²

Hence, [tex]\frac{336}{3.728} = 90.37[/tex] ≈ 90 such patches can be made out of the whole material. (Answer)

Answer:

  7:00 pm

Step-by-step explanation:

You want to know Alexandra's arrival time if she started at the same time as Michael (8:00 am) and drove at 45 mph, while Michael drove at 55 mph and arrived at 5:00 pm.

Travel time is inversely proportional to speed, so the time it takes Alexandra to make the trip is 55/45 = 11/9 times what it take for Michael to make the trip.

Michael's travel time from 8 am to 5 pm is 9 hours, so Alexandra's travel time is ...

  (11/9)(9 h) = 11 h

She will arrive 2 hours after Michael does.

Alexandra arrives at 7:00 pm.

Final answer:

To find how many times more water the bucket can hold than the jar, divide the bucket's capacity by the jar's capacity.

Explanation:

The bucket holds b liters of water, and the jar holds 8 fewer liters than the bucket. To find out how many times more water the bucket can hold than the jar, we need to compare their capacities. \

The bucket's capacity is b liters, and the jar's capacity is b - 8 liters.

To find the ratio of the bucket's capacity to the jar's capacity, we divide the bucket's capacity by the jar's capacity:

This ratio represents how many times more water the bucket can hold than the jar.

Answer:

Step-by-step explanation:

3^-6 × (3^4 ÷ 3^0)^2 = 3^-6 × (3^4 ÷ 1 )^2           {any number raise to zero = 1}

     = 3^-6 × (3^4 )^2

   =  3^-6 × (3^8)             [ (a^m)^n = a^ m*n ]

     = 3^ -6 + 8 = 3^2 = 3 * 3 = 9

Answer:

$48.72

Step-by-step explanation:

5.6 liters x $8.70 per liter= $48.72 total cost

Final answer:

To determine the total cost of the olive oil, multiply the quantity of 5.6 liters by the price per liter, which is $8.70. The total cost for the restaurant owner is $48.72.

Explanation:

The question asks us to calculate the total cost for a restaurant owner who buys 5.6 liters of olive oil at a price of $8.70 per liter. To find the total cost, we multiply the quantity of olive oil by the price per liter.

Calculation: Total cost = Quantity x Price per liter

Total cost = 5.6 liters x $8.70 per liter

Total cost = $48.72

Therefore, the restaurant owner will pay $48.72 for 5.6 liters of olive oil.

The true statement is : D. The boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet. True statements are : A,D & E

Step-by-step explanation:

5.

The equation is given as : T(a)= -0.0018a +212 where T (a) is the boiling point of water measured in degrees at altitude a measured in feets.

From the equation , when the altitude is increased by 1000 feets, a=1000, the equation will be

T(1000) = -1.8 + 212, which means that the boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet

6.

The values given can be taken as coordinates and plotted on a graph tool as shown in the attached figure.

Finding the slope of the graph'

m=Δy/Δx

Taking points (14,73) and (9,51.75) the slope of the linear graph will be;

Δy=73-51.75 = 21.25

Δx=14-9 =5

m= 21.25/5 = 4.25

The equation of the linear graph taking m=4.25 and point (14,73)

m=Δy/Δx

4.25 = y-73/x-14

4.25(x-14) = y-73

4.25x - 59.5 =y-73

4.25x - 59.5 + 73 =y

y=4.25x+13.5

From the graph,

The price in 2005 will be $77.25

The predicted average change in ticket price per year is $4.25

The y -intercept is the price of ticket in 1990

True statements are : A,D & E

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Problem 1

The exterior angles sum to 360

9v+(19v-21)+45+(v+48)+7v = 360

36v+72 = 360

36v+72-72 = 360-72

36v = 288

36v/36 = 288/36

v = 8

===============================================

Problem 2

Why is this? because TW is perpendicular to VS (the right angle marker shows this). At the same time, TW cuts VS into two equal pieces, ie VW = WS. The tickmarks indicate the segments are the same length.

Answer:

D. $340.91

Step-by-step explanation:

420 trees

210 minutes in 3 1/2 hours

x2 per minute

=420 trees in 3 1/2 hours

There are 420 trees will be sold in three and a half hours.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Every minute, there are two Christmas trees sold at the tree farm.

Now,

Since, Every minute, there are two Christmas trees sold at the tree farm.

Hence, Number of sold Christmas tree in 1 hour = 2 × 60

                                                                          = 120

So, Number of sold Christmas tree in 3 1/2 hour = 120 × 3 1/2

                                                                          = 120 × 7/2

                                                                          = 420

Thus, There are 420 sold Christmas tree in 3 1/2 hour.

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Answer:

About the square root of 24 cubic centimeters

Answer: Its actually not. (maybe a typo)? The real bigger one is 5/8

Step-by-step explanation: So your question is "how much more is 1/8 than 5/8?" . The answer is its not. Lets do a example to help clarify. This is the butterfly method. this is by far the simplest way to compare fractions. Lets say your problem is " which is more, 5/8 or 3/4." the first thing you need to do is  line them up like so:

  5       3

  _       _

  8       4

The second thing to do is multiply the opposites.

  5       3

  _       _

  8       4

You would be multiplying 8*3 and 5*4 so like across or whatever.

put the answers on the equation like so,

20         24 <- Which ever in the top is bigger that would be 24. Which is 3/4

 5       3   ______________________________/

 _       _                                                                  

 8       4

3/4 is bigger in this problem.

Hope I helped!

:)

Surface area of cone is [tex]18 \pi[/tex] square units

Solution:

Given that cone with a slant height of 7 and a radius of 2

To find: surface area of cone

The surface area of a cone is equal to the curved surface area plus the area of the base

The surface area of cone is given by formula:

[tex]S. A=\pi r^{2}+\pi r l[/tex]

Where "r" is the radius and "l" is the slant height of cone

Substituting r = 2 and l = 7 in above formula,

[tex]\begin{array}{l}{S A=\pi\left(r^{2}+r l\right)=\pi\left(2^{2}+2(7)\right)} \\\\ {S A=\pi(4+14)=18 \pi}\end{array}[/tex]

Thus surface area of cone is [tex]18 \pi[/tex] square units

Answer:

For 1 is 1

For 4 is 1,2,4

Step-by-step explanation:

A fact family for 1, 4, and 4 can be created using addition and subtraction. The addition equations are 1 + 4 = 5 and 4 + 1 = 5. The subtraction equations are 4 - 1 = 3 and 4 - 3 = 1.

In mathematics, a fact family is a set of three numbers that can be used to create four different addition and subtraction equations. In this case, the numbers given are 1, 4, and 4. To create the fact family, we can use the numbers and their corresponding operations.

The addition equations would be: 1 + 4 = 5 and 4 + 1 = 5.

The subtraction equations would be: 4 - 1 = 3 and 4 - 3 = 1.

Therefore, the fact family for 1, 4, and 4 is: 1, 4, and 5 (addition) and 4, 1, and 3 (subtraction).

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The solution is Option A.

The measure of the equation A = -2xy is A = 12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -2xy   be equation (1)

Now , when x = -1 and y = 6

Substituting the values of x and y in the equation , we get

A = -2 ( -1 ) ( 6 )

On simplifying the equation , we get

A = 2 ( 6 )

A = 12

Therefore , the value of A is 12

Hence , the equation is A = 12

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Answer:

B. [tex]\frac{1}{x^2y^7}[/tex]

Step-by-step explanation:

Given:

[tex](x^3y^{-2}z)(x^{-5}y^{-5}z^{-1})[/tex]

Hence Solving the given expression we get;

By Law of Indices which states;

[tex](a^xb^yc^z)(a^pb^qc^r) = a^{x+p}b^{y+q}c^{z+r}[/tex]

Hence we get;

[tex]x^{3+(-5)}y^{(-2)+(-5)}z^{1+(-1)}\\\\x^{3-5}y^{-2-5}z^{1-1}\\\\x^{-2}y^{-7}[/tex]

Also We know that

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

So,

[tex]\frac{1}{x^2y^7}[/tex]

Answer:

97

Step-by-step explanation:

9+7*9=72

9+18+10=37

10+10+7=27

7+9*10=97

The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

Line L is mapped onto the line T by a dilation centered at the origin and  a scale factor of 3.

That means lint T is the image of line L after dilation

∵ The equation of line L is 2x - y = 7

∵ Line L is dilated by scale factor 3 and centered at origin

- That means multiply the equation of line L by 3 to find the

   equation of line t

∵ Line T is the image of line L after dilation

∴ The equation of line T is (3)(2x) - (3)(y) = (3)(7)

∴ The equation of line T is 6x - 3y = 21

Very important note:

The equation of line T is the same with equation of line L but multiplied by the scale factor 3 ⇒ L and T are coincide lines (same line)

That means the equation of lines T and L is 2x - y = 7

The equation of line T is 2x - y = 7 ⇒ (6x - 3y = 21)

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Answer:

-11

Step-by-step explanation:

Given

[tex]\log_bA=3\\ \\\log_bC=2\\ \\\log_bD=5[/tex]

Use properties:

[tex]\log_b(A\cdot C)=\log_bA+\log_bC\\ \\\log_b\dfrac{A}{C}=\log_bA-\log_bC\\ \\\log_bA^k=k\log_bA[/tex]

Thus,

[tex]\log_b\dfrac{A^5\cdot C^2}{D^6}\\ \\=\log_b(A^5\cdot C^2)-\log_bD^6\\ \\=\log_bA^5+\log_bC^2-\log_bD^6\\ \\=5\log_bA+2\log_bC-6\log_bD\\ \\=5\cdot 3+2\cdot 2-6\cdot 5\\ \\=15+4-30\\ \\=-11[/tex]

Answer:

(X-10y)(x+10y)

Step-by-step explanation:

Write in exponential form , calculate the product & factor !

Answer:

Step-by-step explanation:

x² - 100y² = x² -  (10y)²

                 =(x + 10y) (x - 10y)

Hint: a² - b² = (a + b) (a - b)