Evaluate.



12⋅(4^−2/4^−4)



a) 14

b) 34

c) 16

d) 192

Answer:

x = 5

Step-by-step explanation:

We need to remember that vertical angles are opposite to each other when two lines cross. The vertical angles that result from two lines crossing have the same measure.

In this problem we have angle E which measures 8x + 8 and angle F which measure 2x + 38.

Since they are vertical angles, we know that they have the same measure and therefore we can equal them both and solve for x:

[tex]8x+8=2x+38\\8x-2x=38-8\\6x=30\\x=5[/tex]

Therefore, x = 5 (and ∠E = ∠F = 48)

The regular polygon with an interior angle of 140 degrees has 9 sides. This conclusion can be reached by using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides.

The number of sides in a regular polygon can be determined using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides. This formula comes from the fact that a polygon can be divided into (n-2) triangles, each of which has angles summing up to 180 degrees.

In this particular case, an interior angle of 140 degrees is given. So we will set up an equation: 140 = (n-2)*180/n. Solving for 'n', we get a value of 9.

Therefore, the regular polygon with an interior angle of 140 degrees has 9 sides.

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I used associative property  and the product of 20 x 9 x 5 is 900.

"The associative property states that when an expression has three terms, they can be grouped in any way to solve that expression. The grouping of numbers will never change the result of their operation. The associative property is true for the cases of addition and multiplication. Neither the sum nor the product of the expression changes."

For the given product of 20 x 9 x 5

I am using the associative property.

(20 x 9) x 5 = 900

First multiply 20 x 9, which gives 180

(180) x 5 = 900

Next multiply 180 x 5, which gives 900.

Hence, I used associative property  and the product of 20 x 9 x 5 is 900.

Learn more about associative property here

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The distance formula is simply a variation of the theorem. The method is the same with the Pythagorean however we are now dealing with 2 sets of points instead of 2 lengths. 

In the distance formula, the lengths are derived from the (x1,y1)->(x2,y2) coordinate points and the formula simplified. We still square the difference of x’s and difference of y’s to get our two squares then square root the sum to give our length. While the Pythagorean theorem is directly the sum of the square of the other two sides. 

Nevertheless, both formulas work on the same principle.

Answer:

Both formulas can be used to find the distance between two points on the coordinate plane. The vertical leg of the right triangle represents the difference in the y values of the two points. The horizontal leg of the right triangle represents the difference in the x values of the two points. The hypotenuse of the right triangle represents the distance between the two points.

Step-by-step explanation:

4 = 3/4m -6

 add 6 to both sides

10 = 3/4m

 divide both sides by 3/4

m = 10 / 3/4 =  10 *4 = 40 /3 = 13 1/3

The distance Margarita covers in [tex]\( \frac{s-5}{4} \)[/tex]hours is  [tex]\( \frac{1}{4} \)[/tex] miles.

Given that Margarita is driving at the speed of [tex]\( \frac{s-4}{s^2 - 9s + 20} \)[/tex] miles per hour, we can express the distance function as:

[tex]\[ d(s) = \text{speed} \times \text{time} = \left( \frac{s-4}{s^2 - 9s + 20} \right) \times s \][/tex]

[tex]\[ d\left(\frac{s-5}{4}\right) = \left( \frac{s-4}{s^2 - 9s + 20} \right) \times \frac{s-5}{4} \][/tex]

Let's simplify this expression:

[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{(s-4)(s-5)}{4(s^2 - 9s + 20)} \][/tex]

[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{s^2 - 9s + 20}{4(s^2 - 9s + 20)} \][/tex]

[tex]\[ d\left(\frac{s-5}{4}\right) = \frac{1}{4} \][/tex]

Answer:

the answer is 1

hpoe this helps

x = 3 weeks

Growth: 5(2)(3) = 30 flies in 3 weeks

eaten: 3(3) +2 = 9+2 =11 flies eaten in 3 weeks

30-11 = 19 flies ( population after 3 weeks)

Answer:

Find out the what percentage discount is seller offering you .

To prove

Formula

[tex]Discouunt\ percentage = \frac{Discount\times 100}{Marked\ price}[/tex]

Discount = Marked price - Selling price

As given

You are offered an item for $17.85. If the seller states he normally sells the same item for $19.95 .

Here

Marked price = $19.95

Selling price = $17.85

Discount = 19.95 - 17.85

               = $2.1

Put in the formula

[tex]Discouunt\ percentage = \frac{2.1\times 100}{19.95}[/tex]

[tex]Discouunt\ percentage = \frac{210}{19.95}[/tex]

Discount percentage = 10.5% (Approx)

Therefore the discount is seller offering you is 10.5 % .

To calculate the map distance between Austin and Dallas with a scale of 1 inch representing 20 miles, and an actual distance of 195 miles, set up a proportion and solve to find that Austin and Dallas would be 9.75 inches apart on the map.

To find out how many inches Austin is from Dallas on the map, we need to set up a proportion. The scale given on the map is 1 inch represents 20 miles. We know the actual distance between Austin and Dallas is 195 miles. To calculate the distance on the map, we use the proportion 1 inch / 20 miles = x inches / 195 miles.

Cross-multiply to solve for x:

(1 inch) * (195 miles) = (20 miles) * (x inches)

195 inch-miles = 20x inch-miles

Now, divide both sides by 20 miles to solve for x:

x = 195 inch-miles / 20 miles

x = 9.75 inches

So, on the map, Austin and Dallas would be 9.75 inches apart.