What is the solution set for the open sentence, using the given replacement set ? 6x?2=10 ; {1, 2, 3, 4} ?

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.

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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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.

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.

[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]

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: the correct answer is the third option

Answer:

60

Step-by-step explanation:

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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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.

[tex]\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}\\-------------------------\\\\\left(\dfrac{w^{15}}{w^5}\right)^4=\left(w^{15-5}\right)^4=\left(w^{10}\right)^4=w^{10\cdot4}=w^{40}\\\\Answer:\ \boxed{\left(\dfrac{w^{15}}{w^5}\right)^4=w^{40}}[/tex]

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.

The equation 4t = 70 can be solved by dividing both sides by 4, yielding t = 17.5. This is not a quadratic equation, so the quadratic formula is not required.

To solve the equation 4t = 70 and approximate the value of t to four decimal places, we will first perform a simple algebraic operation. Divide both sides of the equation by 4 to isolate t.

t = 70 / 4
t = 17.5

This is a straightforward equation, but we should be cautious not to mix it up with a quadratic equation, which would require the use of the quadratic formula. The quadratic formula is used for equations of the form at² + bt + c = 0 and would look like this:

-b ± √b² - 4ac over 2a.

Given that the original equation provided is not quadratic, we do not need this formula for our current problem. The correct solution for our equation is t = 17.5.

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)

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.

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:

B Twelve students answered Mr. Chiu’s question.

C Three people studied for two hours.

F Four people studied for four or more hours.

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

The information that can be missing from the dot plot is the scale and data points.

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.

Elias dot plot may not have a distinct scale on the axes, which makes it challenging to identify the precise values or quantities being displayed. This is based on the fundamental idea of a dot plot. A scale offers the required context for correctly analysing the data by, among other things, specifying the measurement intervals or units that were employed.

Furthermore, certain data points, such as the number of tropical fish in each tank or the exact values being displayed, may be absent from the dot plot. It would be difficult to evaluate the dot plot or make inferences from it without the actual data points. Overall, it is impossible to pinpoint exactly what information may be lacking without further detailed details concerning Elias' dot plot.

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complete question:

Elias made a dot plot that shows the number of tropical fish contained in the 14 aquariums at the pet store. What information is missing from Elias dot plot?

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.

Answer:

y=6+x

Step-by-step explanation:

2+6=8              6+6=12

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:

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.

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.

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

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.

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.