when you multiply a function by -1, what is the effect on its graph?

a) the graph flips over the x-axis

b) the graph flips over the line y=x

c) the graph flips over the y-axis

Answer:

A is smaller.

Step-by-step explanation:

SAc of cylindrical container:

Diameter of base: 60 mm

Radius of base: 30 mm

Height of cylinder: 240 mm

SAc = lateral area + area of two bases

SAc = (pi)dh + 2(pi)r^2

SAc = (pi)(60 mm)(240 mm) + 2(pi)(30 mm)^2

SAc = 14,400(pi) mm^2 + 1,800(pi) mm^2

SAc = 16,200(pi) mm^2 which approximately equal to 50,868 mm^2

SAp of prism:

Rectangular prism with L = 120 mm, W = 120 mm, H = 0 mm

SAp = 2(LW + LH + WH)

SAp = 2(120 mm * 120 mm + 120 mm * 60 mm + 120 mm * 60 mm)

SAp = 2(14,400 mm^2 + 7,200 mm^2 + 7200 mm^2)

SAp = 2(28,800 mm^2)

SAp = 57,600 mm^2

The total surface are of the prism is greater than the total surface area of the cylinder.

Answer:

The point of change is the point (1,9)

Step-by-step explanation:

The first derivative of the function equated to zero will give you the point where the function changes.

Therefore, to solve this problem find the first derivative of f (x)

[tex]f '(x) = 3*3(x-1)^{3-1}\\\\f '(x) = 9(x-1)^2[/tex]

Now we equate the derivative to 0.

[tex]9 (x-1)^ 2 = 0\\\\x = 1[/tex]

Then the derivative of the function is equal to 0 when x = 1. This means that the concavity of the function changes in x = 1.

When [tex]x = 1, y = 3(1-1) ^ 3 +9\\\\x =1, y = 9.[/tex]

Then the point of change is the point (1,9)

Answer:

The point of inflection is (1,9)

Step-by-step explanation:

We have following  given function

[tex]f(x)=(x-1)^{3} +9[/tex]

The point at which the function changes its curvature is defined by the point of inflection.

To find point of inflection we set 2nd derivative to 0

[tex]f''(x)= 0[/tex]

The first derivative is given by

[tex]f'(x)= \frac{d}{dx} [(x-1)^{3} +9][/tex]

[tex]f'(x)= 3(x-1)^{2}[/tex]     ( using chain rule  and derivative of constant is 0)

now again we take 2nd derivative

[tex]f''(x)=3(2(x-1))[/tex]

[tex]f''(x)=6(x-1)[/tex]

now we equate 2nd derivative to 0

[tex]6(x-1)=0\\x-1=0\\x=1[/tex]

hence point of inflection is at x=1

now we find y coordinate of point of inflection by plugging x=1 in f(x)

[tex]y=f(1)=(1-1)^{3} +9 =9[/tex]

Hence the point of inflection is (1,9)

Answer:

It would cost $39.95 in a month when you use the internet for 14 hours.

Step-by-step explanation:

Suppose, the internet is used for [tex]x[/tex] hours and the monthly total cost is [tex]y[/tex] dollars.

The internet company charges $4.95 per month plus $2.50 for each hour of use.

That means, fixed cost is $4.95 per month and the cost for [tex]x[/tex] hours of use [tex]= \$2.50x[/tex]

So, the linear equation in slope intercept form to model the situation will be:  [tex]y=2.50x+4.95[/tex]

Now, if [tex]x= 14[/tex] hours, then [tex]y=2.50(14)+4.95=39.95[/tex]

So, it would cost $39.95 in a month when you use the internet for 14 hours.

Answer:The value of Zlatan's house has increased be 7%. His house is now valued at 749,000. Work out the value of the house before the increase.

Don't worry! I got you! just whip out a calculator and take 749,000 and tomes it by 0.07, which is 7%. That gives you 52,430, which means you take 749,000 and subtract 52430, which ultimately give you an ANSWER of (696,570) Hope that helps!

Step-by-step explanation:

Answer:

$ 700,000

Step-by-step explanation:

Let x be the original value of the Zlatan's house,

After increasing the value of the house by 7%,

New cost of his house = (100+7)% of x

= 107% of x

[tex]=\frac{107x}{100}[/tex]

= 1.07x

According to the question,

[tex]1.07x = 749,000[/tex]

[tex]x=\frac{749000}{1.07}=\$ 700000[/tex]

Hence, his house value would be $ 700000  before the increase.

Answer:

y = -2x + 25/2

Step-by-step explanation:

Slope intercept form is y = mx + b.

You must solve the equation for y.

4x + 2y = 25

Subtract 4x from both sides.

2y = -4x + 25

y = -2x + 25/2

Answer:

solution given:

4x+2y=25

we know that

slope intercept form is

y=mx+c

so

4x+2y=25

2y=-4x+25

y=-4/2 x+25/2

y=-2x+25/2 is a required answer.

The Kansas City Royals won approximately 78.57% of their playoff games in 2014.

To find the percentage of games won by the Kansas City Royals, we divide the number of games they won by the total number of games played and then multiply by 100. In this case, the Royals won 11 out of 14 playoff games in 2014. So the percentage of games they won is:

Percentage = (Number of games won / Total number of games) x 100

= (11 / 14) x 100 = 78.57%

Therefore, the Royals won approximately 78.57% of their playoff games in 2014.

[tex]\displaystyle\\(x-4)^2=49\\\\(x-4)^2-49=0\\\\(x-4)^2-7^2=0\\\\(x-4-7)(x-4+7)=0\\\\(x-11)(x+3)=0\\\\x-11 = 0~~~\text{or}~~~x+3=0\\\\x-11=0~~~\implies~~~\boxed{x_1=11}\\\\x+3=0~~~\implies~~~\boxed{x_2=-3}\\\\\boxed{\bf The~solutions~are:~~x =11~~\text{or}~~x =-3}[/tex]

The unit rate is another way of saying speed, so we divide the distance over the time. We can pick on any row

If we pick row 1, then, speed = distance/time = 90/2 = 45

Row 2 says the same thing: 135/3 = 45

So does row 3: 225/5 = 45

and so on

Because the speed is 45 mph, the unit rate is 45 miles in one hour. The term "unit" implies how much distance can be covered in one unit of time, in this case 1 hour.

You have the correct answer. Nice work.

The smallest possible whole number length for the third side of a triangle with sides of length 20 and 2, based on triangle inequalities, is 19.

The subject of your question revolves around triangle inequalities, a fundamental concept in geometry. Triangle inequalities state that the length of any one side of a triangle must be less than the sum of the lengths of other two sides. In this case, you have two sides of lengths 20 and 2. This means the third side must be less than 22 but more than 18 (since it also needs to be more than the difference of two sides).

However, your question asks for the smallest whole-number length possible for the third side. Hence, the smallest possible whole number length for the third side of the triangle is 19.

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The smallest possible whole-number length for the third side of the triangle is 18.

To determine the smallest whole-number length for the third side of a triangle with sides of length 20 and 2, one must consider the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.Let's denote the lengths of the sides as [tex]\( a \), \( b \), and \( c \)[/tex] , where [tex]\( a = 20 \) and \( b = 2 \)[/tex]  . We are looking for the smallest whole number [tex]\( c \)[/tex]  that satisfies the triangle inequality theorem:  

1. [tex]\( a + b > c \)2. \( a + c > b \)3. \( b + c > a \)[/tex] . Substituting the known values of [tex]\( a \) and \( b \), we get: 1. \( 20 + 2 > c \)[/tex]

2.[tex]\( 20 + c > 2 \)[/tex]

3. [tex]\( 2 + c > 20 \)[/tex] From inequality 1, we have: [tex]\( 22 > c \)[/tex] This means [tex]\( c \[/tex] must be less than 22.From inequality 2, we have:[tex]\( 20 + c > 2[/tex]  Since [tex]\( c \)[/tex]  is a positive number, this inequality will always hold true for any positive \( c \).From inequality 3, we have:[tex]\( 2 + c > 20 \)[/tex].  Solving for  [tex]\( c[/tex] , we get: [tex]\( c > 18[/tex]) .Since  [tex]\( c \)[/tex] must be a whole number and the smallest whole number greater than 18 is 19, one might initially think that the smallest possible length for [tex]\( c \)[/tex]  is 19. However, we must also consider that [tex]\( c \)[/tex]  must be less than the sum of the other two sides (inequality 1). The smallest whole number less than 22 is 21, but since [tex]\( c \)[/tex] cannot be equal to [tex]\( a \)[/tex]  or [tex]\( b[/tex]) (as this would not form a triangle), the next smallest whole number is 20, which is also not possible as it would make two sides equal and the triangle degenerate. Therefore, the next smallest whole number is 19. However, we must also consider that for a valid non-degenerate triangle, the difference between the lengths of any two sides must be less than the length of the third side. Since  [tex]\( a = 20 \) and \( b = 2 \)[/tex] , the difference between  [tex]\( a \). and \( b \)[/tex] is 18, which means [tex]\( c \)[/tex] must be greater than 18 to satisfy this condition.Thus, the smallest possible whole-number length for the third side [tex]\( c \)[/tex] is 19, but since we are looking for the smallest whole number greater than 18, the correct answer is actually 18, as it is the smallest whole number that satisfies all the conditions of the triangle inequality theorem and the condition that the difference between the lengths of any two sides must be less than the length of the third side.

Final answer:

The domain restrictions of the expression [tex]g^2[/tex] are the same as the domain restrictions for the variable g.

Explanation:

The domain restrictions of the expression [tex]g^2[/tex], can vary depending on the context in which it is used.

However, in general, the domain restrictions for this expression would be the same as the domain restrictions for the variable g.

This means that any values that make g undefined or result in a complex number would also be restrictions for [tex]g^2.[/tex]

For example, if g cannot be negative due to a square root operation, then the domain restrictions for [tex]g^2[/tex] would also exclude any negative values of g.

Answer:

The vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Step-by-step explanation:

Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2).

If a figure reflected over x-axis, then

[tex](x,y)\rightarrow (x,-y)[/tex]

Therefore the vertices of triangle ABC after reflection over x-axis are:

[tex]A(1,2)\rightarrow A'(1,-2)[/tex]

[tex]B(4,6)\rightarrow B'(4,-6)[/tex]

[tex]C(4,2)\rightarrow C'(4,-2)[/tex]

Rotation 180 degrees about the origin is defined as

[tex](x,y)\rightarrow (-x,-y)[/tex]

Therefore the vertices of triangle ABC after reflection over x-axis followed by rotated 180 degrees about the origin are:

[tex]A(1,-2)\rightarrow A'(-1,2)[/tex]

[tex]B(4,-6)\rightarrow B'(-4,6)[/tex]

[tex]C(4,-2)\rightarrow C'(-4,2)[/tex]

Therefore the vertices of A'B'C are  A'(-1,2), B'(-4,6) and C'(-4,2).

Answer:

C

Step-by-step explanation:

If ur not trying to look at all that but you should

Answer:

If we are to treat these as two ordered pairs, then the rate of change is 1.25.

Step-by-step explanation:

To find this, use the slope equation with the ordered pairs.

m(slope) = (y2 - y1)/(x2 - x1)

m = (11 9/16 - 9 1/16)/(12 - 10)

m = (2 8/16)/2

m = 2.5/2

m = 1.25

Now we know that this could be a function since we have a constant slope.

The rate of change between these two sets of measurements is 1 1/4 inch. Additionally, the relation is indeed a function because each x-value corresponds to exactly one y-value.

The rate of change in a relationship between two variables is a measure of how much one variable changes in relation to a change in the other variable. Here, we are dealing with pairs of measurements in inches. To find the rate of change, we subtract the y-values (the second number in each pair) and divide by the difference of the x-values (the first number in each pair).

We calculate as follows: (11 9/16 - 9 1/16) / (12 - 10), which simplifies to 2 1/2 / 2 or 1 1/4.

The relation is indeed a `function` because each input (x-value) corresponds to exactly one output (y-value). In other words, if you insert a particular measurement of the x-value into this relationship, you will always get the same corresponding y-value. In the context of mathematical functions, this is known as the vertical line test.

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x-2y=6

-2y=-x+6

2y=x-6

y=0.5x-3

Parallel=same slope

y=0.5x+5

Answer:

[tex]\frac{70+71+72+x}{4}\geq 73[/tex]        

[tex]x\geq 79[/tex]

Step-by-step explanation:    

Let x be the height of 4th plant purchased by Millie.

We have been given that Millie needs the average height of the plants she is buying to be at least 73 inches. She has selected three plants that are 70, 71 and 72 inches tall.

So the average of 4 plants purchased by Millie will be: [tex]\frac{70+71+72+x}{4}[/tex]

We can represent this information in an inequality as: [tex]\frac{70+71+72+x}{4}\geq 73[/tex]        

Therefore, our desired inequality will be [tex]\frac{70+71+72+x}{4}\geq 73[/tex].

Now let us solve our inequality by multiplying both sides of inequality by 4.

[tex]4*\frac{70+71+72+x}{4}\geq 4*73[/tex]  

[tex]70+71+72+x\geq 292[/tex]    

[tex]213+x\geq 292[/tex]

[tex]x\geq 292-213[/tex]    

[tex]x\geq 79[/tex]      

Therefore, the height of 4th plant purchased by Millie must be at least 79 inches.

Answer:

B. Rhombus

Step-by-step explanation:

A rombus has four congruent sides and has 2 equal pairs of angles, the rhombus has 4 equal sidesd that are conected by 4 suplemmentary angles between them, in the end the sum of the inner angles is 360 like in every polygon.

We are given that revenue of Tacos is given by the mathematical expression [tex]-7x^{2}+32x+240[/tex].

(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.

(B) Let us factor the given revenue expression.

[tex]-7x^{2}+32x+240=-7x^{2}+60x-28x+240\\-7x^{2}+32x+240=x(-7x+60)+4(-7x+60)\\-7x^{2}+32x+240=(-7x+60)(x+4)\\[/tex]

Therefore, correct option for part (B) is the third option.

(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.

(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.

(E) The table is attached.

Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.

Two equations for the purchase prices can be written. Let o and a represent the costs of an orange and an apple, respectively.

... 4o +5a = 3.56

... 3o +4a = 2.76

We can eliminate the o variable by subtracting 3 times the first equation from 4 times the second:

... 4(3o +4a) -3(4o +5a) = 4(2.76) -3(3.56)

... a = 0.36 . . . . simplify

This value can be substituted into either equation to find o. Let's use the first one.

... 4o +5·0.36 = 3.56

... 4o = 1.76 . . . . . . . . . subtract 1.80

... o = 0.44 . . . . . . . . . divide by 4

The cost of an orange is $0.44; the cost of an apple is $0.36.

_____

Comment on the solution

There are perhaps half a dozen different ways to solve a pair of linear equations in two variables. This method isn't necessarily the easiest, but it works. If you have a graphing calculator, quite often it includes matrix operations that will solve this quickly and easily.

Answer: the correct answer is the third option

Answer:

The vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5). The graph of image and preimage is shown below.

Step-by-step explanation:

From the given figure it is noticed that the vertices of  triangle ABC are A(0,0), B(1,5) and C(-4,5).

If a figure rotated at 180º about the origin, then

[tex]P(x,y)\rightarrow P'(-x,-y)[/tex]

The vertices of image are

[tex]A(0,0)\rightarrow A'(0,0)[/tex]

[tex]B(1,5)\rightarrow B'(-1,-5)[/tex]

[tex]C(-4,5)\rightarrow C'(4,-5)[/tex]

Therefore the vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5).

The graph of image and preimage is shown below.

We know that, Volume of a Rectangular Prism is given by :

✿  {Length × Width × Height}

Given : The Length of Rectangular Prism = 5.5

Given : The Width of Rectangular Prism = 6

Given : The Height of Rectangular Prism = 3

⇒ The Volume of given Rectangular Prism = {5.5 × 6 × 3}

⇒ The Volume of given Rectangular Prism = 99

Final answer:

The question is about estimating the number of ice cream cones sold at 106 degrees Fahrenheit based on a set of data correlating temperature with sales. An educated guess, without exact calculations, suggests that at least 649 cones might be sold, based on the pattern observed in the data provided.

Explanation:

The student's question touches on the relationship between temperature and the number of ice cream cones sold. Looking at the data provided, there seems to be a positive correlation: as temperature increases, so does the number of cones sold.

Based on the steady increase in the number of cones sold with each increase in temperature, it is reasonable to assume that if the temperature were to increase from 99 degrees (which correlated with 576 cones sold) to 106 degrees, the number of cones sold would increase by at least the same increment as previous temperature rises, if not more.

If we take the difference between 94 degrees and 99 degrees, which is an increase in 5 degrees and corresponds to an increase of 576 - 503 = 73 cones, we could estimate that at 106 degrees, the shop might sell at least 73 more cones than they did at 99 degrees.

This would yield an estimate of 576 + 73 = 649 cones as a conservative minimum estimate.

Answer:

y=6+x

Step-by-step explanation:

2+6=8              6+6=12

Using exterior angle formula, you get that ∠CAD=36+123=159°

Exterior angle formula says that the angles facing CAB (ACB and ABC) sum to CAD.

If Tonya bought 10 pears and spent a total of $10.00 in expression 0.50a+0.65p represents the total cost of a apples and p pears then Tonya bought 7 apples.

Let's use the information provided to set up an equation and solve for the number of apples (a) that Tonya bought.

Cost of pears (p) = $0.65 each

Cost of apples (a) = $0.50 each

Total cost = $10.00

We are told that Tonya bought 10 pears. So, the cost of 10 pears would be:

Cost of 10 pears = 10 * $0.65 = $6.50

Now, we can set up an equation to represent the total cost of apples and pears:

Total cost = 0.50a + 0.65p

We know that the total cost is $10.00 and the cost of 10 pears is $6.50:

$10.00 = 0.50a + $6.50

Now, let's solve for 'a' (the number of apples):

Subtract $6.50 from both sides:

$10.00 - $6.50 = 0.50a

$3.50 = 0.50a

Now, divide both sides by 0.50 to solve for 'a':

a = $3.50 / $0.50

a = 7

Tonya bought 7 apples.

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Answer:

The equation of this line would be y = -6

Step-by-step explanation:

In order to find this, we must first find the slope. For that we use the two points and the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-6 - -6)/(7 - 3)

m = 0/4

m = 0

Given that slope, we can use it along with a point in point slope form. From there we can solve for y and get the equation.

y - y1 = m(x - x1)

y + 6 = 0(x - 7)

y + 6 = 0

y = -6

Final answer:

To find the equation of a line passing through given points, calculate the slope, use the point-slope formula, and simplify to obtain the final equation. In this case, the line passing through (7,-6) and (3,-6) results in the equation y = -6.

Explanation:

To find the equation of the line passing through the points (7,-6) and (3,-6):

Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁)

Substitute one of the points and the slope into the point-slope formula: y - y₁ = m(x - x₁)

Simplify the equation to get the final answer: y = mx + b

The equation of the line passing through those two points is y = -6.

Answer:

tan C = 1/2

Step-by-step explanation:

The tan function in a right triangle is the opposite side over the adjacent side

tan C = 11/22

We can divide the top and bottom by 11

tan C = 1/2

Answer: Tan(C) = 1/2

Step-by-step explanation:

For a triangle rectangle, we have the relation, for an angle θ.

Tan(θ) = Opposite cathetus/Adjacent catethus.

Here, the opposite cathetus to C is equal to 11 units

The adjacent cathetus to C is 22 units.

Then we have Tan(C) = 11/22 = 1/2

and we can not simplify it anymore, so this is the answer.