Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 6 inches.

You calculate this by first understanding that '28 tens' means 280, and then dividing 280 by 4. So, 28 tens divided by 4 equals 70.

The phrase '28 tens' refers to 28 multiplied by 10, 28 x 10 = 280.

To find the result of dividing this by 4, we calculate 280 ÷  4 = 70.

Therefore, 28 tens divided by 4 equals 70.

Final answer:

Deborah ran a total of 7 3/5 miles combined on Monday and Tuesday. This was determined by adding 3 2/5 miles and 4 1/5 miles together after converting them to improper fractions.

Explanation:

On Monday, Deborah ran 3 2/5 miles and on Tuesday she ran 4 1/5 miles. To find the total distance Deborah ran over these two days, we need to add the two distances together. When working with mixed numbers, it's often easiest to convert them to improper fractions before adding.

3 2/5 miles is the same as (3 × 5 + 2)/5 = 17/5 miles.
4 1/5 miles is the same as (4 × 5 + 1)/5 = 21/5 miles.

Adding these two fractions:

17/5 miles + 21/5 miles = (17 + 21)/5 miles

= 38/5 miles

= 7 3/5 miles

So, Deborah ran a total of 7 3/5 miles on Monday and Tuesday combined.

Refer to the image attached.

Given: [tex]\angle BAC[/tex] and [tex]\angle BCA[/tex] are congruent.

To Prove: [tex]\Delta ABC[/tex] is an isosceles triangle.

Construction: Construct a perpendicular bisector from point B to line segment AC.  Label the point of intersection between this perpendicular bisector and line segment AC as point D.

Proof:

Consider [tex]\Delta BDA, \Delta BDC[/tex]

[tex]\angle BDA = \angle BDC= 90^\circ[/tex]

(By the definition of perpendicular bisector)

[tex]AD=DC[/tex] (By the definition of perpendicular bisector)

So, Line segment AD is congruent to DC by the definition of perpendicular bisector.

[tex]\angle BAC[/tex] = [tex]\angle BCA[/tex] (given)

So,  [tex]\Delta BDA \cong \Delta BDC[/tex] by ASA congruence postulate.

∆BAD is congruent to ∆BCD by the ASA congruence Postulate.

Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).

So, Option C is the correct answer.

The total number of eggs in the carton is 12, as there are 2 rows with 6 eggs each, and you calculate the total by multiplying these two numbers.

Paco buys a carton with 2 rows of eggs and there are 6 eggs in each row.

To find the total number of eggs in the carton, you multiply the number of rows by the number of eggs in each row: 2 rows× 6 eggs per row equals a total of 12 eggs in the carton.

So, in this case, the number is 12, and the unit is eggs.

Answer:

[tex]tan^-1( v)  - \frac{1}{2} ln(1+{v}^2) +c[/tex] is the answer.

Step-by-step explanation:

∫[tex]\frac{1-v}{1+{v}^2} \\\frac{1}{1+{v}^2}- \frac{v}{1+{v}^2}}[/tex]

∫[tex]\frac{dv}{1+{v}^2}[/tex]-∫[tex]\frac{2v}{1+{v}^2}[/tex]dv

[tex]{tan}^{-1} (v)-\frac{1}{2} ln(1+{v}^2) +c[/tex]

The ratio that is not equivalent to 6:10 is 24/45, as it simplifies to 8/15 instead of 3/5 like the other options.

To determine which of the given ratios is not equivalent to 6:10, we can simplify the ratio 6:10 or convert it to a fraction and then reduce it to its simplest form. In fraction form, 6:10 can be written as 6/10, which simplifies to 3/5 when both the numerator and the denominator are divided by their greatest common divisor, which is 2.

Therefore, the ratio that is not equivalent to 6:10 is 24/45.

To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), you can use implicit differentiation and solve for dy/dx.

To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), we need to use implicit differentiation. We differentiate both sides of the equation with respect to x, treating y as a function of x. Thus, we get:

12x^2 - 3y^2 - 3x(2y(dy/dx)) + 3y^2(dy/dx) = 0

Now we substitute x = 3 and y = 4 into the equation and solve for dy/dx:

12(3)^2 - 3(4)^2 - 3(3)(2(4)(dy/dx)) + 3(4)^2(dy/dx) = 0

Answer:

C.[tex]8.22 h\geq[/tex]$ 623

Step-by-step explanation:

We are given that Sophia is saving money for a new bicycle.

The bicycle will  cost atleast $623.

Sophia makes $8.22 per hour.

We have to find the inequality that could be used to find the number of hours Sophia needs to work to make enough money to buy a new bicycle.

Let Sophia works h hours to make enough money to buy a new bicycle.

Sophia makes money per hour =$8.22

Total money made by Sophia in h hours =[tex]8.22 h[/tex]

According to question

[tex]8.22 h\geq [/tex]$623

Hence, option C is true.

The student is required to combine three algebraic fractions with different denominators using factoring to find a common denominator and then simplify the expression.

The question entails a topic in algebra, specifically with respect to combining expressions with different denominators, which requires finding a common denominator, and working with signs and exponents. The problem presents three fractions that should be combined: (x+6)/(x^2+8x+15), (3x)/(x+5), and (x-3)/(x+3).

Firstly, note that the denominator x^2+8x+15 can be factored into (x+3)(x+5). This will allow us to identify a common denominator for all three fractions, which is (x+3)(x+5). We rewrite the fractions so that each has the common denominator:

Now we simply combine these three fractions over the common denominator:

After the combination, the terms must be simplified and ordered in descending powers of x, which is the final answer.

Descending powers of x is [tex]\[ \frac{2x^2 + 8x + 15}{(x + 3)(x + 5)} \][/tex].

To combine the given expressions, we need to find a common denominator and then combine the numerators. Here are the expressions given:

[tex]\[ \frac{x}{x^2 + 8x + 15} + \frac{3x}{x + 5} - \frac{x - 3}{x + 3} \][/tex]

First, let's factor the quadratic denominator in the first term if possible and identify the common denominator:

The quadratic [tex]\( x^2 + 8x + 15 \)[/tex] can be factored into [tex]\( (x + 3)(x + 5) \)[/tex], since 3 and 5 are factors of 15 that add up to 8.

Now we have:

[tex]\[ \frac{x}{(x + 3)(x + 5)} + \frac{3x}{x + 5} - \frac{x - 3}{x + 3} \][/tex]

The common denominator will be [tex]\( (x + 3)(x + 5) \)[/tex].

Now, let's rewrite each fraction with the common denominator:

The second term already has [tex]\( x + 5 \)[/tex] in the denominator, so we multiply the numerator and denominator by [tex]\( x + 3 \)[/tex]to have the common denominator.

[tex]\[ \frac{3x}{x + 5} \rightarrow \frac{3x(x + 3)}{(x + 5)(x + 3)} \][/tex]

The third term has [tex]\( x + 3 \)[/tex] in the denominator, so we multiply the numerator and denominator by \( x + 5 \) to have the common denominator.

[tex]\[ \frac{x - 3}{x + 3} \rightarrow \frac{(x - 3)(x + 5)}{(x + 3)(x + 5)} \][/tex]

Now all terms have a common denominator, and we can combine them as follows:

[tex]\[ \frac{x}{(x + 3)(x + 5)} + \frac{3x(x + 3)}{(x + 3)(x + 5)} - \frac{(x - 3)(x + 5)}{(x + 3)(x + 5)} \][/tex]

Combine the numerators while keeping the denominator the same:

[tex]\[ \frac{x + 3x(x + 3) - (x - 3)(x + 5)}{(x + 3)(x + 5)} \][/tex]

Now, let's expand and simplify the numerator:

[tex]\[ x + 3x^2 + 9x - (x^2 + 2x - 15) \][/tex]

[tex]\[ x + 3x^2 + 9x - x^2 - 2x + 15 \][/tex]

Combine like terms:

[tex]\[ 3x^2 - x^2 + x + 9x - 2x + 15 \][/tex]

[tex]\[ 2x^2 + 8x + 15 \][/tex]

Now, let's put it all over the common denominator:

[tex]\[ \frac{2x^2 + 8x + 15}{(x + 3)(x + 5)} \][/tex]

This is the simplified expression in descending powers of \( x \). Since the numerator is already in descending powers of \( x \), this is the final answer. There is no further simplification possible because the numerator and the denominator do not have common factors other than 1.

Final answer:

The values of m and n that satisfy the equation 15 - 28i = 3m + 4ni are m = 5 and n = -7 after equating and solving the real and imaginary parts separately.

Explanation:

To find the values of m and n that make the equation 15 - 28i = 3m + 4ni true, we must equate the real parts and the imaginary parts of both sides of the equation separately. The real part of the left side of the equation is 15, and the imaginary part is -28i. Similarly, for the right side, the real part is 3m, and the imaginary part is 4ni.

Equate the real parts: 15 = 3m
Dividing both sides by 3, we get m = 5.

Equate the imaginary parts: -28i = 4ni
Dividing both sides by 4i, we get n = -7.

Hence, the values that satisfy the equation are m = 5 and n = -7.