Given the function, f(x) = 3x4- 7x3 - 6x2+ 12x + 8
a) Determine the number of turning points.
b) Describe the End Behavior
c) List the potential (possible) real zeros.
d) Use Descartes' Rule of Signs to determine the number of positive real zeros and number ofnegative real zeros.
e) Find all rational zeros.f) Graph the function.Make sure that you label each category.

We can conclude that the students did not have any time left to work on homework.

The duration of Mr. K's math class is 1 and 1/4 hours, or 5/4 hours.

We need to determine how much time is left for the kids to do their assignment after working on problems on the board for 55 minutes and 11/12 hours. To achieve this, we must take the time spent solving issues out of the overall class time:

Total class time = 5/4 hours

Time spent on working problems = 55 minutes + 11/12 hours

= (55/60) hours + (11/12) hours

= (11/12 + 55/60) hours

= (11/12 + 11/12) hours

= (22/12) hours

= (11/6) hours

Overall class time minus the amount of time spent solving problems equals the amount of time remaining for homework.

= 5/4 hours - 11/6 hours

= (15/12) hours - (22/12) hours

= (-7/12) hours

We can infer that the kids ran out of time to finish their homework because the response is illogical because we cannot have negative time.

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Answer:

Step-by-step explanation:

I am definitely willing to help anyone with algebra!

It seems you need explanations on mode, median and mean. First, let's remember that these terms are related to data sets.

Example: I have a list of grades in Algebra 2, which list off as 94, 94, 95, 96, 98, 99, 99, 99, 99, 100.

I want the mode, median and mean. The mode is the number that appears the most in a data set, the median is the number in the exact middle of a data set, and the mean is the average value of the data set.

Mode: The number that appears most in this list of grades is 99. My mode is 99, and usually people use this to represent the whole of a data set, especially when the mode appears in the majority of the data set, at least 80% of the data set.

Median: My median is basically the number in the middle of the list. Since I have an even number of 10 grades, I need to find the two numbers closest to the middle, which is 98 and 99, the fifth and sixth term. I find the average of these two numbers- (98+99)/2 = 98.5. This is my median grade. This is usually used to represent data sets when describing demographics.

Mean: This is the average of the whole data set, which means we add up all the numbers and divide them by the number of items there are. Since we have ten grades in the data set, I add (94+94+95+96+98+99+99+99+99+100)/10 = 97.3

This is my mean, which represents my average grade. The mean is used a lot when teachers create our report cards! Hope this helps, but if you need anything else, feel free to comment back on this. If you want, my electronic mail account is my username and I use g mail dot com. Feel free to each out, and Happy Birthday!

as the quadrilateral is a square, all the sides will be equal to each other so DE is equal to DG.

3t + 46 = 8t - 19

-5t = -65

5t = 65

so t = 13

The expression -a^(2)+b^(4)-7a^(3) is a polynomial.

A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The given expression satisfies all these conditions, and therefore, it is a polynomial.

The type of the polynomial is determined by the number of terms it has. In this case, the polynomial has 3 terms, so it is a trinomial.The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 4 (in the term b^(4)), so the degree of the polynomial is 4. Therefore, the expression -a^(2)+b^(4)-7a^(3) is a trinomial of degree 4.

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Yes, a probability of 4/5 indicates that an event is likely to happen.

Probability refers to the measure of the likelihood of an event occurring, typically expressed as a number between 0 and 1. It is used to quantify uncertainty and is widely used in various fields such as mathematics, statistics, economics, science, and engineering.

Yes, a probability of 4/5 indicates that an event is likely to happen. It means that out of 5 possible outcomes, 4 outcomes are favorable to the event. In other words, there is an 80% chance that the event will occur.

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The answer is (1) x = 22.5; (2) x = 16.7; (3) x = 13.5; (4) x = 16.8; (5) x = 24.5; (6) x = 16.15; (7.a) height of the image on film is 11.2mm; (7.b) distance between camera and her friend is 1,875mm.

(1) We can see that in the given figure all three corresponding angles are congruent and all three corresponding sides are in equal proportion so, these are similar triangles.

As per properties of similar triangle:

Three pairs of corresponding sides are proportional i.e. Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

                        Therefore, [tex]\frac{32}{24} =\frac{30}{x}[/tex],

then by cross multiplying them, we get,

                                        32x = 720

                                            x = 720/32

                                           x = 22.5

(2) As, this is already given that these are similar triangle and by applying the properties of similar triangle we get,

                                           [tex]\frac{39}{26} =\frac{25}{x}[/tex]

                                         39x = 650

                                             x = [tex]16\frac{2}{3}[/tex]

                                            x = 16.7

(3) As these are similar triangle again we can say that,

                                        [tex]\frac{2x+1}{x+4} =\frac{40}{25}[/tex]

                                 40(x + 4) = 25(2x + 1)

                                40x + 160 = 50x + 25

                                          40x = 50x - 135

                                          -10x = -135

                 (by cancelling (-) sign from both sides we get,

                                              x = 135/10

                                             x = 13.5

(4) By applying similar triangle's property, we can get

                                           [tex]\frac{20}{30} =\frac{28-x}{x}[/tex]

                                         20x = 840 - 30x

                                         50x = 840

                                             x = 840/50

                                             x = 16.8

(5) As ΔJKL [tex]\sim[/tex] ΔNPR,

                                           [tex]\frac{KM}{PT} =\frac{KL}{PR}[/tex]

                                          [tex]\frac{18}{15.75} =\frac{28}{x}[/tex]

                                            18x = 441

                                                x = 441/18

                                               x = 24.5

(6) As ΔSTU [tex]\sim[/tex] ΔXYZ,

                                         [tex]\frac{UA}{ZB} =\frac{UT}{ZY}[/tex]

                                        [tex]\frac{6}{11.4} =\frac{8.5}{x}[/tex]

                                          6x = 96.6

                                            x = 96.6/6

                                            x = 16.15

(7.a) First we have to change 3 m and 140 cm into mm(millimeters).

So, 1m = 1000 mm

     3m = 3000mm.

And 1cm = 10 mm

   140cm = 1400 mm.

Then to find the height of the image on the film, we have to solve:

                                          [tex]\frac{24}{3000} =\frac{x}{1400}[/tex]

             by cross multiplication we get,

                                      3000x = 33,600

                                               x = 33,600/3000

                                              x = 11.2 mm

the height of the image on the film is 11.2millimeters.

(7.b) For this also, we have to find x by solving the equation:

                                            [tex]\frac{24}{3000} =\frac{15}{x}[/tex]

                                            24x = 45,000

                                                x = 45,000/24

                                              x = 1,875 mm

The distance between camera and her friend is 1,875 millimeters.

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Full question is given below in the image.

A $450 principal and a simple interest rate of 0.35% each quarter for 212 years would result in a savings account balance of $3768.

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal x Rate x Time

where Rate is the interest rate as a decimal, and Time is the time in years.

The quarterly interest rate is 0.35% / 4 = 0.00875, and the time is 212 years, or 848 quarters.

Plugging in these values, we get:

Simple Interest = $450 x 0.00875 x 848 = $3318

Therefore, the balance of the savings account after 212 years would be:

Balance = Principal + Simple Interest = $450 + $3318 = $3768

Therefore, the balance of the savings account after 212 years with a simple interest rate of 0.35% each quarter and a principal of $450 would be $3768.

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Using cοmpοund interest , the tοtal wοrth after 20 years is $2,330.48.

The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.

Here the principal P= $500

Rate οf interest r = 8%

Number οf years = 20 years,

Nοw using cοmpοund interest fοrmula then,

=> Total amount = [tex]P(1+\frac{r}{100})^t[/tex]

=> A = [tex]500(1+\frac{8}{100})^{20}[/tex]

=> A = [tex]500(1+0.08)^{20}[/tex]

=> A = [tex]500(1.08)^{20}[/tex]

=>A = $2,330.48

Hence after 20 years , nft's total worth is $2,330.48.

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Graph is the collection of all points whose coordinates satisfy a given relation (such as a function).

Coordinates of a point in a 2D plane, also known as cartesian coordinates, are two numbers or sometimes a combination of a letter and a number that tell us the exact location of a specific point on a grid. Here, the grid is known as a coordinate plane.

Let tosses be x and and dollars be y

Then we have, (x, y) as (63, 6)

So if in 6 dollars you get 63 tosses then 1 dollar you get = 63/6 = 10.5 tosses.

Then in 2 dollars we have = 10.5 × 2 = 21 tosses

As 21 tosses = 2 dollars

Then 42 tosses = 2 × 2 = 4 dollars

Thus, we have the table:

[tex]\boxed{\begin{array}{cc}\underline{\text{Tosses}}&\underline{\text{dollars}}&\\ \boxed{10.5}&2&\\42&\boxed4&\\63&6&\end{array}}[/tex]

To graph the given points, just correspond x as tosses and y as dollars.

Graph given in attachment

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After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction. You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.

Let's write the coordinates of the original figure,

A = (1, -5)

B = (6, -2)

C = (6, -5)

D = (1, -8)

Now, if we rotate it 90 degrees counterclockwise, the coordinates are:

A' = ( 5, 1)

B' = (2, 6)

C' = (5, 6)

D' = (8, 1)

Now if we rotate it again 90 degrees counterclockwise, the coordinates are:

A'' = ( -1, 5)

B'' = (-6, 2)

C'' = (-6, 5)

D'' = (-1, 8)

Now from the figure, let's write the coordinates.

A' = ( -1, 5)

B' =  (-6, 2)

C' = (-6, 5)

D' =  (-1, 8)

This is the same as the coordinates of the second 90 degrees counterclockwise rotation.

Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.

Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

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Answer: 180 degrees counterclockwise rotation.

Answer: First we have to check the information they are giving in the problem. do we can see that the photocopier can copy 4 pages every 2 seconds.

so with this info we can calculate the ratio, or the number of copies that can be done in one second:

So we made a rule of 3 to solve that

So, if the photocopier can print 2 copys every second, the we can calculate the the time that takes to print 120 pages:

solving this rule of 3:

so is going to take 60 seconds to copy 120 pages.

Step-by-step explanation:

the ratio is 30/21600 = 3/2160 = 1/720

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

FYI :

as there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.

The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].

To locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2] using the Bisection Method with 17 iterations, we will follow the steps below:

1. Define the function f(x) = x/3 + In(x) - 1
2. Set the initial values for the interval: a = 1 and b = 2
3. Start the iteration process by finding the midpoint of the interval: c = (a+b)/2
4. Evaluate the function at the midpoint: f(c) = f((a+b)/2)
5. Determine if the root lies in the left or right half of the interval by checking the sign of f(c)
6. If f(c) is positive, then the root lies in the left half of the interval, so we set b = c and repeat the process from step 3.
7. If f(c) is negative, then the root lies in the right half of the interval, so we set a = c and repeat the process from step 3.
8. Continue the iteration process until we have completed 17 iterations.

After 17 iterations, we will have narrowed down the interval to a very small range and the midpoint of this interval will be an approximation of the root of the function.

The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].

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Answer:

To apply the first derivative test to the function f(x) = 2x^3 + 3x^2 - 12x + 5, we need to find its derivative:

f'(x) = 6x^2 + 6x - 12

Then, we need to find the critical points by solving for f'(x) = 0:

6x^2 + 6x - 12 = 0

Dividing both sides by 6, we get:

x^2 + x - 2 = 0

Factoring the left side, we get:

(x + 2)(x - 1) = 0

So the critical points are x = -2 and x = 1.

To determine the intervals where f(x) is increasing and decreasing, we need to evaluate f'(x) on each side of the critical points. We can use a sign chart to do this:

x     |  -2  |  1  |

------|-----|----|

f'(x) | -12 |  0 |

Since f'(x) is negative to the left of x = -2 and positive to the right of x = -2, the function is decreasing to the left of x = -2 and increasing to the right of x = -2. Since f'(x) changes sign at x = 1, there is a local minimum at x = 1.

Therefore, using the first derivative test, we can conclude that the function has a local minimum at x = 1.

Step-by-step explanation:

The solutions to the equation (w-2)^(2)-54=0 are w = 2, w = 9, and w = -6.

The equation (w-2)2 - 54 = 0 can be solved by factoring.

Let's start by writing the equation as: (w-2)(w-2) - 54 = 0

We can factor out (w-2) to get: (w-2)(w2 - 4w - 54) = 0

Now we can factor the second part of the equation, by splitting the middle term (4w) to get: (w-2)(w-9)(w+6) = 0

Now we have three equations, which we can solve separately:

w - 2 = 0 → w = 2

w - 9 = 0 → w = 9

w + 6 = 0 → w = -6

Therefore, the solutions to the equation (w-2)2 - 54 = 0 are w = 2, w = 9, and w = -6.

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If Anna has 95 deliveries to make and has delivered 57, she has completed 60% of the total deliveries.

To find the percentage of deliveries that Amna has completed, we can use the formula:

percentage = (part/whole) × 100

So in this case, the part is the number of deliveries Amna has completed, which is 57, and the whole is the total number of deliveries she needs to make, which is 95. Plugging these values into the formula, we get:

percentage = (57/95) × 100 %

percentage = 0.6 × 100 %

percentage = 60 %

Therefore, Amna has completed 60% of her total deliveries.

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Answer:

101.80

Step-by-step explanation:

Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.

The time it will take for Alex to earn enough money to purchase his shoes is given as follows:

13.6 weeks.

The time needed to obtain enough money to purchase the shoes is obtained applying the proportions in the context of the problem.

Alex saves $10 every 4 weeks. He earned an extra $12 for cleaning his neighbor’s garage, hence the amount he must save is of:

45.99 - 12 = $33.99.

Considering that he saves $10 each week, and he must save $33.99 to purchase the shoes, the number of periods of four weeks that he needs is of:

33.99/10 = 3.399 periods of four weeks.

As each period is composed by four weeks, the number of weeks that he needs to save enough money is obtained as follows:

4 x 3.399 = 13.6 weeks.

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The Addition Property of Equality, If a=b, then a+c=b+c depicts the notion that "If equals are added to equals, then the wholes are equal". The correct answer is option e.

Addition Property of Equality is a law that describes the possibility of adding the same quantity on both sides of an equation to maintain equality. If a=b, then a+c=b+c represents the Addition Property of Equality. It denotes that if you add the same quantity on both sides of an equation, the result will remain equal.

The Addition Property of Equality also mentions that if two numbers are equal to each other, then adding the same number to both of them will also result in two equal numbers. This means that if a=b, then a+c=b+c. Therefore, the correct answer is option "e.  

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Answer:

Let's assume that the price before adding the VAT is x.

We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.

The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:

Total price = price before VAT + VAT amount

or

2,700 = x + 0.08x

Simplifying this equation, we can combine like terms on the right-hand side to get:

2,700 = 1.08x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:

x = 2,700 / 1.08

x = 2,500

Therefore, the price before VAT was added is 2,500.

The car travels 4 feet in 1 second, 16 feet in 4 seconds, 24 feet in 6 seconds, 32 feet in 8 seconds.

Distance is a measure of the amount of space between two objects or points. It is the length of the shortest path between the two points, and it is typically measured in units such as meters, kilometers, miles, or feet.

In mathematics, distance is often calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The car travels 4 feet in 1 second, which is equivalent to a rate of 4 feet per second.

The car also travels 16 feet in 4 seconds, which is also equivalent to a rate of 4 feet per second.

Similarly, the car travels 24 feet in 6 seconds, 32 feet in 8 seconds, and so on, all at a constant rate of 4 feet per second.

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The product of the polynomials is 4x^(2)-28x+49, which is a single polynomial in standard form.

A polynomial is an expression consisting of variables, constants and coefficients, in which the exponents of the variables are either whole numbers or zero. It can be written in the form of a summation, where each term is the product of a coefficient and a variable raised to a power.

To multiply the polynomials using a special product formula, we can use the formula for squaring a binomial, which is (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=2x and b=7.

So, we can plug these values into the formula and simplify:

(2x-7)^(2) = (2x)^(2)-2(2x)(7)+(7)^(2)

= 4x^(2)-28x+49

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This question does not require a diagram to be drawn, so based on the scale factor or ratio of 1 inch : 4 yards and since the actual width of the neighborhood park is 60 yards, the width of the drawing is 15 inches.

The scale factor is the ratio of a scale drawing or model to the actual dimension of the object.

The scale factor is also measured as the dimension of the new shape ÷ dimension of the original shape.

The Ratio of the scale drawing = 1 inch : 4 yards

The actual width of the park = 60 yards

The scaled-down width of the drawing = 15 inches (60/4).

Thus, we can conclude that the scale drawing's width that Darrell made was 15 inches.

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The factored form of the given polynomial is 5(x-9)(x-2).

To factor the given polynomial, 5x^(2)-55x+90, we first need to factor out the greatest common factor (GCF) which is 5. Factoring out the GCF will make the polynomial easier to factor completely.

5x^(2)-55x+90 = 5(x^(2)-11x+18)

Now, we need to factor the polynomial inside the parentheses completely. We can do this by finding two numbers that multiply to give us the constant term (18) and add to give us the coefficient of the x term (-11).

The two numbers that fit these criteria are -9 and -2. So, we can factor the polynomial inside the parentheses as follows:

x^(2)-11x+18 = (x-9)(x-2)

Putting it all together, we get the completely factored form of the given polynomial:

5x^(2)-55x+90 = 5(x-9)(x-2)

Therefore, the factored form of the given polynomial is 5(x-9)(x-2).

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-12.87 ≈ -12.87

The given expression is:
(x-50)/(s/√n)

To evaluate it using the given values, we substitute the given values in the formula:
(45.3-50)/(4.7/√48) = -4.7/0.366 = -12.87

Rounding the result to two decimal places, we get:
-12.87 ≈ -12.87

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The table of values is added below and and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y < |4x + 1| - 3

To create a table of values for y < |4x + 1| - 3, we can choose different values of x and substitute them into the expression to find the corresponding values of y.

Let's choose some values of x: -2, -1, 0, 1, 2.

When x = -2, we have:

y < |4(-2) + 1| - 3

y < 4

When x = -1, we have:

y < |4(-1) + 1| - 3

y < 0

When x = 0, we have:

y < |4(0) + 1| - 3

y < |1| - 3

y < -2

When x = 1, we have:

y < |4(1) + 1| - 3

y < 2

When x = 2, we have:

y < |4(2) + 1| - 3

y < 6

Putting it all together, we have the following table:

x y values

-2 y < 4

-1 y < 0

0 y < -2

1 y < 2

2 y < 6

The graph is attached

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In A parallelogram MNPQ with MN=12cm, MQ = 10 cm

a) The length of side PQ is equals to the 12 cm.

b) The measure of angle Q is equals to the 155°.

In a geometry, a parallelogram is a simple quadrilateral with

We have a parallelogram MNPQ, with

Side length, MN = 12cm

Other side length, MQ = 10 cm

Measure of angle M is = 25°

Also, MN|| PQ and MQ||NP

a) From the definition of parallelogram, the length of side MN is parallel to PQ and are of equal length. So, PQ = MN

= 12 cm

b) By the definition of parallelogram, opposite angles of a parallelogram are of equal measure. So, the measure of angle P = measure of angle M = 25°

Also, measure of angle N = measure of angle Q = x

Sum of all interior angles of quadrilateral

= 360°

=> m∠P + m∠N + m∠M + m∠Q = 360°

=> 25° + x + 25° + x = 360°

=> 2x + 50° = 360°

=> 2x = 310°

=> x = (310/2)° = 155°

Hence, required value of measure of angle Q is 155°.

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Complete question:

In A parallelogram MNPQ if MN=12cm , MQ = 10 cm and mZM = 25°. What is a)PQ

b) measure of angle Q

Answer:

141 inch^2

Step-by-step explanation:

13×7= 91 for the rectangle

13-5=8

diameter of circle=8

radius=4

area if circle=4^2 times π

=16×π

=16π

16π+91=141.2654....

to the nearest whole= 141 inch^2 I think

Answer:

[tex]2 \sqrt{5} [/tex]

Is the simplified form

Step-by-step explanation:

Greetings!!!

Given expression

[tex] \frac{10}{ \sqrt{5} } [/tex]

factor the number 10:5.2

[tex] = \frac{5.2}{ \sqrt{5} } [/tex]

Apply radical rule

[tex]a = \sqrt{a} \sqrt{a} [/tex]

[tex]5 = \sqrt{5} \sqrt{5} \\ = \frac{ \sqrt{5} \sqrt{5}.2 }{ \sqrt{5} } [/tex]

Cancel the common factor :✓5

[tex] = \sqrt{5} .2 \\ = 2 \sqrt{5} [/tex]

If you have any questions tag me on comments

Hope it helps!!!

Answer:

2 * [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\frac{10}{\sqrt{5} }[/tex]

Using the basis formula, you simplify it to:

2×[tex]\sqrt{5}[/tex]