Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.

Answer:

DUOLINGOOOO

Step-by-step explanation:

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If each dimension was doubled, the volume of the prism would be: B. 896 cm³.

In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:

Scale factor of volume = (Scale factor of dimensions)³

Scale factor of volume = (2)³

Scale factor of volume = 8

Therefore, the new volume is given by;

New volume of prism = 112 × 8

New volume of prism = 896 cm³.

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Final answer:

To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.

Explanation:

When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.

Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.

Answer:

x = 6

Step-by-step explanation:

Given : Fiona decides to join a gym :

A joining fee of $100

A monthly fee of $38

x represents the number of months.

Fiona has allocated a maximum of $328 to spend on her gym        membership

Her total membership fee for that duration of time: 100 + 38x = C

Solution :

It is given that Fiona has allocated a maximum of $328 to spend

So, C = $328

Putting this value in equation 100 + 38x = C

⇒[tex]100+38x=328[/tex]

⇒[tex]38x=328-100[/tex]

⇒[tex]38x=228[/tex]

⇒[tex]x=\frac{228}{38}[/tex]

⇒[tex]x=6[/tex]

Thus, x = 6 is number line that shows the possible number of months that Fiona can be a member of the gym.

Through setting up and solving the equation 1/3 * x + 2 = 8, where x represents the number of Saturn's moons, it was determined that Saturn is known to have 18 moons.

The student's question pertains to a comparison of the moons of Neptune and Saturn, using mathematical operations to deduce the number of known moons of Saturn. First, we're told that Neptune has 8 known moons, which is said to be 2 more than 1/3 of the number of known moons on Saturn. We are seeking to solve for the number of moons that Saturn has.

To find out, we set up an equation where 1/3 of the number of moons of Saturn plus 2 equals the number of Neptune's moons: 1/3 * x + 2 = 8, where x represents the number of Saturn's moons. Solving for x, we subtract 2 from both sides to get 1/3 * x = 6. We then multiply both sides by 3 to isolate x and find that x = 18.

Therefore, Saturn is known to have 18 moons according to the given information.

To solve this problem, we make use of the formula:

y = a sqrt (b (x – h)) + k                  ---> 1

Since we are given the parent function:

y = sqrt (x)                                          ---> 2

Then this automatically means that:

a = 1       and        k = 0

So going back to equation 1 at a = 1 and k = 0:

y = 1 sqrt (b (x – h))

Since it is given that, b = 4            and        h = 1, therefore:

y = sqrt (4 (x – 1))

y = sqrt (4 x – 4)

Answer:

A. y = sqrt (4 x – 4)

Answer:

12

Step-by-step explanation:

because if you put it all together it will equal 12

Answer:

Step-by-step explanation:

tanα=height/distance

tanα=h/d

d=h/tanα  so

d1=h/tanα  and d2=h/tanß

Then the distance between them is:

d=h/tanß-h/tanα, we know that h=1300, α=(90°-71.9°=18,1°), and ß=90°-27.1°=62.9°) so

d=(3100*tan62.9)-(3100*tan18.1) meters

d≈2116 (to nearest meter)

The answer is C, or 113.04 cubic inches.

Answer:

A. 833

Step-by-step explanation:

Given:

The growth of a new strain of bacteria is represented by [tex]y = 79.31(1.48)^x[/tex], where "x" represents the number of days and "y" represents the number of bacteria.

We need to find the number of bacteria on day 6.

So, here x = 6, we need to plug in x = 6 in the given function and find the answer.

[tex]y = 79.31(1.48)^6[tex]

Simplify the above expression, we get

y = 833.49

The bacteria cannot be in decimal form, let's round off the answer to nearest whole number.

y = 833

Therefore, answer is A. 833

Let x = the number of pounds of Type A coffee.

We know that this month's blend used 3 times as many pounds of type B coffee as type A coffee.

Total pounds of coffee =  x + 3x

The total cost is:

(cost for Type A)(x) + (cost for Type B)(3x) = $603.45

$4.80x + $5.85(3x) = $603.45

$4.80x + $17.55x = $603.45

$22.35x = $603.45

x = 603.45/22.35 = 27 pounds

We can write 56% as a fraction to the simplest form as [tex]\mathbf{= \dfrac{14}{25} }[/tex]

A fraction is a numeric value divided into two parts, the upper part(numerator) and the lower part(denominator) which are separated by a division line.

From the given information:

56% can be written in fraction as [tex]\mathbf{\dfrac{56}{100}}[/tex]

Now, to its simplest form means to divide the numerator and the denominator to their lowest term. By doing so, we have:

[tex]\mathbf{\dfrac{56}{100}}[/tex]

Divided by (2)

[tex]\mathbf{= \dfrac{28}{50} }[/tex]

Divided by (2)

[tex]\mathbf{= \dfrac{14}{25} }[/tex]

Therefore, we can conclude that 56% as a fraction to the simplest form is [tex]\mathbf{= \dfrac{14}{25} }[/tex] since no other number can go in both the numerator and the denominator.

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To estimate 93 × 87 using mental math, round 87 to 90, multiply by 93 to get 8370, and subtract 3 × 93 (279) for an estimate of 8091.

To find 93 × 87 using mental math, we can employ a strategy that simplifies the multiplication process. One way is to round one of the numbers to the nearest multiple of ten, perform the multiplication, and then adjust the result accordingly. Here, we can round 87 up to 90 and multiply 93 by 90. This is easier because 90 is a multiple of 10.

93 × 90 = (93 × 9) × 10  = 837 × 10 = 8370

Since we rounded 87 to 90, we overestimated by 3 per unit of 93. Hence, we need to subtract 3 times 93 from 8370.

3 × 93 = 279

Thus, 8370 - 279 = 8091.

The graph 3 whose inverse is not a function.

The inverse function agrees with the resultant, operates and reaches back to the original function. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.

Horizontal Line Test :-

Let f be a function. If any horizontal line intersects the graph of f more than once, then f does not have an inverse. If no horizontal line intersects the graph of f more than once, then f does have an inverse.

So, according to the definition, the only graph which follows the rule of horizontal lines test is the graph 3.

Hence, the graph 3 whose inverse is not a function.

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By using the horizontal line test, a relation whose inverse is not a function is: D. relation D.

In Mathematics and Euclidean Geometry, the horizontal line test states that if the graph of a function (f) is intersected by any horizontal line more than once, then, the function (f) does not have an inverse.

Conversely, if the graph of a function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.

By critically observing the graph of the given relation shown in the image attached below, we can logically deduce that it does not have an inverse because it didn't pass the horizontal line test.

The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units

The square of the hypotenuse is equal to the sum of the square of the other two sides.

Mathematically;

l^2 = a^2 + b^2

Given

l = 8 units

a = 5 units

Substitute

8^2 = 5^2 + b^2

64 - 25 = b^2

b^2 = 6.2units

Hence the length in units of the other leg of the triangle is 6.2 units

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87.34-5 = 82.34

82.34/3.58 = 23

 she lives 23 miles away