(x² - 4)/(x² - 7x + 10)
Use interval notation to indicate where ƒ(x) is continuous.

I got (-inf,2)U(5,inf) for my answer but it says there should be something else. What am I missing?

Note that the square feet of carpet that will be required for this area is:  42 Square Feet of Carpet.

This is solved using the knowledge of the area of rectangles and right-angled triangles.

A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees.

Note that the area  of a right-angled triangle is given as:
A = (½)×b×h square units

Where b is breath and h is height.

Note as well that the area of the rectangle is given as Lx B

To solve the above problem, we must create one more right-angled triangle beside the one already created, then solve for the areas of the respective shapes.

Now that the shape has been divided in to two Right-angled Triangles and one rectangle (See the attached) their respective dimensions are given as follows:

1) Right Angled triangled A

B = 2ft

H = 3ft

Area = 1/2 2 * 3 = 3ft

2) Right-Angled Triangle B

B = 4ft

H = 3ft

A = 1/2 * 4 * 3

A = 6ft

3) Rectangle - C

L = 11ft

B= 3ft

A = 11 * 3 = 33 Ft.

Thus total square feet of outdoor carpet required is:

3 + 6 + 33

= 42 Square Feet of Carpet.

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Answer:

10 cases

Step-by-step explanation:

We are given the equation: y = -0.25x + 85, where y is the # of cases, and x is the # of students who received the vaccine.

The question asks for the # of cases if 300 students received the vaccine. Since we know that 300 students received the vaccine, we can plug that in for x in the equation above, since x is that unit:

y = -0.25(300) + 85

Now, we can solve:

y = 10

Therefore, there will be 10 cases if 300 students received the vaccine.

Answer:

Step-by-step explanation:

The answer would look like (30n-44)/7

The value of EF , DC , AB are 40,14, 37 respectively.

What is trapezoid ?

Trapezoid can be defined as the 4-sided shape in which it has one of sides parallel to it .

ABCD is trapezoid with median EF

so,

DC+AB = 2EF

(2x+10) + (3x+20) = 2 * 4x

5x + 30 = 8x

8x-5x = 30

3x = 30

x = 30/3

x = 10

EF = 4x = 4*10 = 10

3x+10(x-2) = 2 (4x+10)

3x+10x-20 = 8x+20

5x = 40

x = 8

DC = 3x = 32

7(x-2) + (4x-6) = 2*3x

7x-14+4x-6 = 6x

5x = 20

x = 4

DC = (7*(4-2) ) = 14

(2x+3) + (8x+5) = 2*6x

8 = 2x

x = 4

AB = 8*4+5 = 37

Therefore, The value of EF , DC , AB are 40,14, 37 respectively.

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It took approximately 5.3 hours for the temperature inside the freezer to increase from -10°C to -2°C.

If the temperature inside the freezer increased by 1.5°C per hour, and it started at -10°C, then to reach -2°C the temperature inside the freezer would have had to increase by 8°C.

To find out how long it took for this to happen, we can use the formula:

Temperature increase/rate of increase = time

8°C / 1.5°C per hour = 5.3 hours (approx).

The temperature was exactly -10°C at the start and exactly -2°C at the end. It means that the temperature increased by 1.5°C per hour on average.

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Answer: I am not able to create images such as tree diagrams. But I can explain to you how it could be done.

A tree diagram is a visual representation of the possible outcomes and their probabilities.

The tree diagram to show the above information would have two branches: one representing the event that the bus is late and the other representing the event that the bus is not late.

The first branch, "Bus is Late", would have a probability of 0.1 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.8) and the other representing the event that Andrew is not late to school (with a probability of 0.2).

The second branch, "Bus is not Late", would have a probability of 0.9 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.05) and the other representing the event that Andrew is not late to school (with a probability of 0.95).

This tree diagram will help you to understand the relationship between the different events and their probabilities, as well as the overall probability of Andrew being late to school.

Step-by-step explanation:

The number of bean plants should she plant will be 60

t = tomato plants

b = beans

To Solve by using system of equations

Clear any fractional coefficients if there are any. Alternate the coefficients of a single variable. Select the variable you want to remove. Multiply one or both equations to make the variable's coefficients opposite.

Total plants = 100

t + b = 100     {equation 1}

20 more tomatoes than beans

t = b + 20       {equation 2}

b + 20 + b = 100

2b + 20 = 100

Finish solving for b to find a number of beans.

Then tomatoes will be b+20

Putting this in equation 1

b+20+b=100

2b+20=100

b=40

then t= b+20  {equation 2}

t=60

Hence the number of bean plants should she plant will be 60

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The table that has the correct values for A, B, and C will be:

D. Donuts 2 4 6 8

Cost 15.80 31.60 39.50 56.72

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since we know that 4 donut cost 31.60, the.vost for 2 donut will be:

= 31.60 / 4 × 2

= 15.80

Therefore, we can see that the correct table for this is D.

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Answer:

-5

Step-by-step explanation:

Our given equation is B-A, and we know that B = 2 and A = 7. Through what we know, we can plug in the variables' values and solve:

2 - 7 (from B-A)

= -5

Answer:

value for b-a is -5

if subsituition is only done b-a = 2-7

Step-by-step explanation:

if b=2

a=7,

b-a= 2-7

=-5

Answer:

The three side lengths given, 12 ft, 16 ft, and 20 ft can form a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 20^2 = 12^2 + 16^2, so the sides 12 ft, 16 ft and 20 ft can form a right triangle.

The vertex of the function is at - 2

The vertex of the function is at the point (a, 2), where the value of x, denoted as 'a', is the x-coordinate of the vertex.

To find the value of 'a', we can use the formula for the x-coordinate of the vertex, which is -b/2a, where b and a are the coefficients of the x-squared and x terms, respectively, in the standard form of the equation (y = ax^2 + bx + c).

Since the function is already in vertex form, we can directly read the value of 'a' from the equation which is -2.

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The translation rule (x + 7, y - 19) has the meaning given as follows:

The four translation rules are defined as follows:

The meaning of each translation in this problem is given as follows:

The problem asks for the meaning of the translation (x + 7, y - 19).

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The function that best represents the value of the computer in months is V(t) = 1,300(.61^(t/12)).Where t is the number of months since the computer was purchased

The given function V(t) = 1,300(.61), models the value of a computer in terms of the number of years since it was purchased. The value of the computer is represented by the function V(t) which is directly proportional to (0.61) raised to the power of t. Divide the t by 12, because there are 12 months in a year, to get the value in months.

As a consequence, the calculation V(t) = 1,300(.61(t/12)) displays the computer's value in terms of months from purchase. It demonstrates the decline in the value of the computer over time.

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Answer: slope = [tex]\frac{1}{4} x[/tex]

               point on the line= (0,-4.25)

Step-by-step explanation:

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

     [tex]y=\frac{1}{4} x-\frac{5}{4} -3\\\\y= \frac{1}{4}x -3\frac{5}{4} \\\\y=\frac{1}{4}x -\frac{17}{4}[/tex]

therefore the value with the x is the gradient so the gradient (slope) is [tex]\frac{1}{4} x[/tex]

since the y-intercept is [tex]-\frac{17}{4}\\[/tex] get the simplified version in decimals which is -4.25... so the point will be (0,-4.25)

We see the same three numbers in situations 10,34 and 144.

In the first situation, there is one shopping cart with a length of 34 and then an unknown number of carts with a length of 10. Similarly, an architect has 34 dollars saved and will save 10 each week for an unknown number of weeks. Both situations have one part of 34 and then equal parts of size 10 that add together to 144. The equation is: 34 + 10x = 144.

Since it takes 11 groups of 10 to get from 34 to 144, the value of x in these two equations is ( 144 -34) ÷ 10 = 11.

There will be 11 shopping carts in each row and it will take 11 weeks to raise the money.

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Answer:

area 202.93, perimeter  62.78

Step-by-step explanation:

the triangle:

18² +14² = 520

√520 = 22.8

the curve, without further info, we'll have to assume it's 1/2 circle.

so circumference = 2πr =2 π (14/2) = 14 π = 43.96, 1/2 of it is 21.98

so perimeter of the whole thing is 18+22.8 +21.98 = 62.78

area: 1/2 circle = 1/2 π r² = 1/2 * 3.14*7² = 76.93

triangle area + 1/2 *18*14 = 126

total 202.93

Area of semi circle

Area of Triangle

Total area

Perimeter

If two of the angles of an oblique triangle are equal, the Law of Sines can be used to fill in the remaining lengths or angle measurements.

In the accompanying diagram, two crossing lines are shown, with the angles 1 and 3 being vertical and congruent. In addition, the angles 2 and 4 are vertical and coincide. Vertical angles are two angles that are in opposition to one another, such as D and B in the illustration above.

The sum of the subsequent angles of a ||gm is A+B=180. To view an infinite number of solutions, download the app. Estimating ratios of a particular quantity is what it is. It is created by contrasting a given quantity with the reference unit. These are used to determine something's dimensions, including length, area, perimeter, volume, and amount. Measurement There are formulas for calculating length, area, surface area, volume, circumference, density, mass, etc.

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Complete question:

Which trigonometric law can be used if two of the angles of an oblique triangle are equal?

The graph of the linear inequality is shown below.

What is linear inequality?

A linear inequality is one that, if the equals relation were employed in place of the inequality, would result in a linear equation. The direction of the inequality is reversed when both sides are multiplied or divided by a negative integer to solve it. The solution set refers to all possible answers to an inequality.

We are given y < -x-4

In order to sketch the graph of the inequality, we need to have two points.

So, first let's put x = 0

So, we get y = -4

Now, let's put y = 0

So, we get x = -4

Thus, we get the points as (0,-4) and (-4,0)

From the points, the graph is sketched which is shown below.

Hence, the graph of the linear inequality is obtained.

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Since, there are multiple questions, so the question answered above is attached below

a. The function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]

b. To graph the function, f(x), you can use a graphing calculator or software such as Excel or a Python library like Matplotlib.

c. It will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.

The problem states that Oscar wants to own a bee colony and extract honey from the hive. He starts with a colony of 5,000 bees and the number of bees grows exponentially with a growth factor of 12% each month. To solve this problem, we can use the exponential growth formula to determine the number of bees in the colony based on the month.

The exponential growth formula is [tex]P(t) = P_0 * (1 + r)^t[/tex] where

In this case, [tex]P_0[/tex] = 5000, r = 0.12, and t = x (the number of months). So, the function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]

In order to get a decent amount of honey, Oscar feels that there should be at least 15,000 bees in the colony. To estimate how many months it will take Oscar until he has 15,000 bees, we can set f(x) = 15,000 and solve for x.

By doing this, we get x = log(15000/5000) / log(1.12) ≈ 7.9 months. This means it will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.

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The complete question is:

Oscar wants to own a bee colony so that he can extract honey from the hive. He starts a colony with 5,000 bees. The number of bees grows exponentially with a growth factor of 12% each month.

a. Write a function, f(x), for the bee population that can be used to determine the number of bees in the colony, based on the month, x.

b. Use technology to graph the function, f(x).

c. Oscar feels that in order to get a decent amount of honey, there should be at least 15,000 bees in the colony. Estimate how many months it will take Oscar until he has 15,000 bees.

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Answer: t = d/s

Step-by-step explanation:

Time = Distance/Speed
Substitute values in
E.g.
Jenny went for a drive in her new car. She drove for 8 miles at a speed of 4 miles per hour. For how many hours did she drive?

8/4 = 2 hours

The equation that is set up correctly using the Pythagorean Theorem for the triangle below is 9^2 + x^2 = 15^2.

The concept that will be used here is Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides:

According to theorem, the (adjacent)^2 + (opposite)^2 = (hypothenus)^2.

a^2+b^2=c^2

The 9^2 + x^2 = 15^2

Therefore, option C is correct.

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a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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Becca is not correct because her probability of 2/14 is not equal to the true experimental probability of 2/16.

We are given the tools in the box as;

Hammer = 2 nos

Pliers = 5 nos

Screw drivers = 6 nos

Wrench = 3 nos

Thus;

Total number of tools in the box = 2 + 5 + 6 + 3

= 16

Probability of selecting a hammer = 2/16

Now, Becca says that   for every 14 tools in a toolbox, there are 2 hammers. This means she is suggesting a probability of 2/14.

This is wrong because it is different from the experimental probability that we got.

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Answer: a = 2

Step-by-step explanation: 2.5 x 2 = 5 5 + 4.2 = 9.2

[tex]4.2+2.5a=9.2[/tex]

Rearrange:

[tex]2.5a+4.2=9.2[/tex]

Subtract 4.2 from both sides:

[tex]2.5a+4.2-4.2=9.2-4.2[/tex]

[tex]2.5a=5[/tex]

Divide both sides by 2.5:

[tex]\dfrac{2.5a}{2.5} =\dfrac{5}{2.5}[/tex]

[tex]\fbox{a = 2}[/tex]

The table is filled considering the numeric values of the function, as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The numeric value in this problem is found replacing the lone instance of x by it's value, hence the numeric value at x = -6 is given as follows:

y = 2(-6) - 3

y = -12 - 3

y = -15.

The same procedure is applied for x = -3, x = 0 and x = 3.

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It costs $0.208 more per hour to park in Lot A than in Lot B.

We know that the total parking hours = 48

Also, the cost of parking for Lot A= ($)19. 00/33. 00 and for Lot B = ($)20. 00/32. 00

To find out how many more dollars it costs per hour to park in Lot A than in Lot B, we will subtract the hourly rate of Lot B from the hourly rate of Lot A.

The hourly rate of Lot A is (33.00 - 19.00) / 48 = $0.541 (dollars and cents)

Similarly, the hourly rate of Lot B is (32.00 - 20.00) / 48 = $0.333 (dollars and cents)

So the difference in cost per hour is $0.541 - $0.333 = $0.208 (dollars and cents)

Therefore, it costs $0.208 more per hour to park in Lot A than in Lot B.

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Answer:

5x² + 2x = 14y

Step-by-step explanation:

2x - 5y + 6y + 5x² = 15y

the only terms we can combine are 5y and 6y; the others are not 'like'

2x + y + 5x² = 15y

5x² + 2x = 14y

The volume of water that are left in the tank is equal to 3.2 gallons.

Mathematically, the volume of a cuboid tank is a measure of its capacity and it can be calculated by using this following formula:

Volume of a tank = L × W × H

Where:

In order to determine the quantity (volume) of water that are left in the tank, we would use this mathematical expression:

Volume of water left = capacity of tank A - volume of water poured

Volume of water left = 9.5 gallons - 6 1/3 gallons

Volume of water left = 9.5 gallons - 6.3 gallons

Volume of water left = 3.2 gallons.

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The actual area of the garden without the scale factor is 6 square feet.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. Depending on the size and number of sides, different forms have varying areas.

Let the original area of the garden be x.

Given that the scale factor used is 1/3, thus we have:

x (1/3) = 2

x = (2)(3)

x = 6

Hence, the actual area of the garden without the scale factor is 6 square feet.

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