Which of the following are properties of the incenter of a triangle? Choose all that apply.
A. The incenter is where all of the bisectors of the angles of the triangle meet.
B. The incenter of an obtuse triangle lies on the outside of the triangle.
C. The incenter is equidistant from each vertex of the triangle.
D. The incenter of a triangle is always inside it.

Answer

Find out the what is the minimum simple interest rate Maggie needs to reach her goal .

To proof

Formula

[tex]Simple\ interest = \frac{principle\times rate\times time}{100}[/tex]

As given

Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years.

put all the values in the formula

[tex]4000 = \frac{14100\times rate\times 8}{100}[/tex]

Solving

[tex]rate = \frac{4000\times 100}{14100\times8}[/tex]

solving the above

[tex]rate = \frac{400000}{112800}[/tex]

rate =3.55% (approx)

the minimum simple interest rate Maggie needs to reach her goal is 3.55% .

Option (b) is correct .

Hence proved

The answer is  

x ≥ 4

x + y ≤ 10

y ≥ 0

Answer:

720 is correct

Final answer:

One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. The conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.

Explanation:

One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. This involves setting up conversion factors to cancel out the unwanted units. Here's an example:

Therefore, the conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.

Answer: A. 210

Step-by-step explanation:

We know that the number of combinations of n things taking r at time is given by expression :-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]  (1)

The given expression : [tex]^{10}C_{6}[/tex] which basically gives the number of combinations of 10 things taking 6 at a time.

Using (1) , we have

[tex]^{10}C_{6}=\dfrac{10!}{6!(10-6)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}\\\\=\dfrac{10\times9\times8\times7}{4!}\ \ [\text{Cancel }6!\text{ from numerator and denominator}]\\\\=\dfrac{10\times9\times8\times7}{4\times3\times2\times1}\\\\=210[/tex]

Hence, the correct answer is A. 210 .

For a rectangle with a given area, the smallest possible perimeter is achieved when the rectangle is a square. Hence, for a rectangle with an area of 343 m², the dimensions that give the smallest perimeter are approximately 18.5 m x 18.5 m.

The subject of this question is related to the optimization problems in Calculus. Given that the area of a rectangle is 343 m², we are looking for the smallest possible perimeter. The area of a rectangle can be defined as the product of its length and width (l*w), and the perimeter is defined as the sum of all sides (2l + 2w).

According to the properties of rectangles, a rectangle will have the smallest possible perimeter if it is a square, because rectangles with the same area have larger perimeters as their shapes become more elongated.

So, if the rectangle is a square, its area is side² or s². Given that the area is 343 m², s² = 343, thus the side s equals the square root of 343, which is approximately 18.5202591775 meters. Therefore, the dimensions of the rectangle with the smallest possible perimeter are approximately  18.5 m × 18.5 m.

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The flash on Casey's camera needs to be set stronger when it is darker outside.

The subject of this question is Physics. In physics, the behavior of light and the properties of a camera flash can be studied. When it is darker outside, Casey needs to set her flash stronger to compensate for the lack of natural light. This is because the flash provides an additional burst of light that illuminates the subject, making it clearer in the photo.

Hence, the value of x is:

[tex]x=\dfrac{1}{3}[/tex]

We have to solve for x i..e we have to find the value of 'x' by solving this equation.

The equation is given as:

[tex]-4(3x-2)=6x+2[/tex]

firstly we will solve the bracket term as:

[tex]-4\times 3x-4\times (-2)=6x+2\\\\-12x+8=6x+2[/tex]

Now we take like terms together i..e the variable term is taken to the right hand side of the equation and the constant term is kept on the left side of the equation as:

[tex]8-2=6x+12x\\\\\\6=18x[/tex]

on dividing both side of the equation by 18, we obtain:

[tex]x=\dfrac{6}{18}\\\\x=\dfrac{1}{3}[/tex]

Hence, the value of x is:

[tex]x=\dfrac{1}{3}[/tex]

Answer:

B

Step-by-step explanation:

To maximize profit, derive the profit equation ((120 - 0.1x) * x - (60x + 4000)) and set it to zero to find the critical points. These points will dictate the number of smartphones the company needs to manufacture and sell each day.

The subject of this question is the maximization of profit, which is a concept in economic mathematics. To maximize the profit, you'll need to determine the number of smartphones that the company should produce and sell each day.

The profit is the revenue (the money earned from selling goods) minus the costs. Revenue is given by the equation R = (120 - 0.1x) * x, and the total cost is given by the equation C = 60x + 4000, where x is the number of smartphones produced.

So, the profit P becomes P = R - C = (120 - 0.1x) * x - (60x + 4000). To maximize this profit, we'd take the derivative of P in terms of x and set it equal to zero to find the critical points. After finding the critical points, we then test these values back in the profit equation to find which gives the highest value and hence maximizes the profit.

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Answer:

Arc length XPY =28.26 m.

Step-by-step explanation:

Given : A circle with two arc XY and XPY and radius 6 m.

To find  : Arc length XPY.

Solution : We have given that arc XY and XPY .

Radius = 6 m.

Central angle formed by arc XPY = 360 - 90 = 270.

Arc length = 2 *pi* r ( [tex]\frac{central\ angle}{360}[/tex].

Plugging the values

Arc length = 2 *3.14 * 6 ( [tex]\frac{270}{360}[/tex].

Arc length =37.68 ( [tex]\frac{3}{4}[/tex].

Arc length =37.68 * 0.75

Arc length XPY =28.26 m.

Therefore, Arc length XPY =28.26 m.

Answer:

The length of arc XPY=28.26 m

Step-by-step explanation:

We are given that a circle in which

Radius=6 m

Central angle made by arc XPY=[tex]360-90=270^{\circ}[/tex]

We have to find the length of arc XPY.

We know that

Arc length formula:[tex]\frac{central\;angle}{360^{\circ}}\times 2\pi r[/tex]

Substitute the value in the formula then we get

Length of arc XPY=[tex]\frac{270}{360}\times 2\times 3.14 \times 6=28.26 m[/tex]    ([tex]\pi=3.14[/tex])

Hence, the length of arc XPY=28.26 m

Learning the proper order in which to read algebraic expressions and solve algebraic equations is important in algebra for understanding the order of operations, developing logical reasoning, and ensuring consistency in mathematical communication.

It is important to learn the proper order in which to read algebraic expressions and solve algebraic equations in algebra for several reasons:

Using the straight-line depreciation method, the linear equation for the equipment's value over time is y = -175t + 875. After 2 years, the equipment's value is $525. To find when the equipment's value is $200, solve for t and get approximately 3.86 years.

To calculate the depreciation of the equipment using a linear equation, we'll use the straight-line depreciation method. The business purchases the equipment for $875 and it will be worthless after 5 years, so it depreciates $875 over 5 years.

Part A

To write the linear equation representing the value of the equipment y over time t, we need to find the slope (m) of the line which in this case is the annual depreciation. The slope is the change in value divided by the time, thus m = -$175/year. The initial value (intercept) is $875. The equation is:

y = -175t + 875

Part B

Substitute t = 2 into the equation to find the value of the equipment at year 2:

y = -175(2) + 875

y = -350 + 875

y = $525

Part C

We want to find the time t when the value y is $200. Substitute y = $200 into the equation:

200 = -175t + 875

-175t = 200 - 875

-175t = -675

t = [tex]\frac{-675}{-175}[/tex]

The linear equation to find the area of the carpet after applying Felix's $50 discount is 3.50 × A = 180, where A represents the area in square feet. After solving the equation, we find that the area is 51.43 square feet.

To find the area, A, of the carpet that Felix buys, we can set up a linear equation based on the total cost after the discount and the cost per square foot. The original price of the carpet is $230, but Felix has a coupon for a $50 discount, reducing the cost to $180. Since the cost per square foot of the carpet is $3.50, we can denote the area of the carpet as A, and set up the equation:

3.50 × A = 180

To solve for A, we divide both sides of the equation by 3.50:

A = 180 / 3.50

A = 51.43 square feet

The correct answer is the first option: All real numbers.

I just did the quiz and got it right.

For all the non BrainlyPlus members

The moment of inertia of the thin rectangular sheet of metal about the specified axis is[tex]\( \frac{Ma^2}{4} + \frac{Mb^2}{12} \).[/tex]

To find the moment of inertia  I of the thin rectangular sheet of metal about an axis passing through its center and parallel to the side with length b, we can use the parallel axis theorem.

This theorem states that the moment of inertia about any axis parallel to the axis passing through the center of mass can be found by adding the moment of inertia about the center of mass and the product of the mass and the square of the perpendicular distance between the two axes.

The moment of inertia of a thin rectangular plate about its center and perpendicular to its plane is given by:

[tex]\[ I_c = \frac{M}{12}(a^2 + b^2) \][/tex]

where M is the mass of the plate, a and b are the lengths of the sides of the rectangle.

Now, let's denote d as the perpendicular distance between the axis passing through the center and the axis parallel to the side with length b. Since the axis is passing through the center of the rectangle, d is half the length of side a, so [tex]\( d = \frac{a}{2} \)[/tex].

Using the parallel axis theorem, the moment of inertia about the desired axis is:

[tex]\[ I = I_c + Md^2 \][/tex]

[tex]\[ I = \frac{M}{12}(a^2 + b^2) + M\left(\frac{a}{2}\right)^2 \][/tex]

[tex]\[ I = \frac{M}{12}(a^2 + b^2) + \frac{M}{4}a^2 \][/tex]

[tex]\[ I = \frac{Ma^2}{12} + \frac{Mb^2}{12} + \frac{3Ma^2}{12} \][/tex]

[tex]\[ I = \frac{Ma^2}{4} + \frac{Mb^2}{12} \][/tex]

Thus, the moment of inertia of the thin rectangular sheet of metal about the specified axis is[tex]\( \frac{Ma^2}{4} + \frac{Mb^2}{12} \).[/tex]

The real number resulting from the expression x-y/xy is positive when x is negative and y is positive. This is determined by following the rules of signs in arithmetic where subtracting a positive number from a negative results in a negative and dividing a negative number by another negative results in a positive.

The given expression in question is x-y/xy. To understand the sign of the resulting real number we have to discern the signs of x, y and the result of subtraction, x-y.

As mentioned, x is less than 0 and hence negative and y is greater than 0, thus positive. So when you subtract a positive number y from the negative number x, the result will obviously be negative. This is due to the 'rules of signs' in arithmetic.

Then, for the division, when you divide this negative result by the multiplication of x (which is negative) and y (which is positive), the answer will be positive. This is again because of the 'rules of signs' for division - a negative number divided by a negative number yields a positive number.

So, the sign of the result of the real number expression x-y/xy is positive when x<0 and y>0.

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