Use the compass and ruler to inscribe a circle in the triangle.

Rational expressions are those that have fractional terms. We state restrictions because it may cause the equation to be undefined in some values of x. The most common restriction for rational expressions is N/0. This means any number divided by zero is undefined.

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions.

To find the restrictions on a rational function, find the values of the variable that make the denominator equal 0.

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Answer:

We can tell by looking at the graph that it is a positive slope, so we can eliminate answers b and d.

It is rise over run. from a point, it goes up 4, and over 1.

4/1

which would be 4. The answer is C! Hope this helps!

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's consider two points on the line and calculate its Slope ~

Slope (m) of a line is :

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:m = \dfrac{2 - 1}{8 - 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \:m = \dfrac{1}{4} [/tex]

Answer:

96 days. Divide 3072 by 32 and you get 96.

Yes

Step-by-step explanation:

Because the sides of this triangle follow the Pythagorean Theorem.

i.e.

[tex]52^{2} = {20}^{2} + {48}^{2} [/tex]

[tex]\boxed{\textbf{Therefore it IS a right triangle}} [/tex]

Answer:

x= -64°, y= -63°, z=-57°

Step-by-step explanation:

→Solution,

Here,

60°=(-y-3)°[The opposite sides of a parallelogram are equal]

⇒y= -60°-3°

⇒y= -63°

⇒60°+(-2x-8)°=180°[Sum of co-interior angles is 180°]

⇒52°-2x=180°

⇒52°-180°=2x

⇒x= -128°/2

⇒x= -64°

⇒60°+(-2z+6)°=180°[Sum of co-interior angles is 180°]

⇒66°-2z=180°

⇒66°-180°=2z

⇒z= -114°/2

⇒z= -57°

Answer:

Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:

[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].

[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].

[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].

Step-by-step explanation:

Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].

Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].

Since [tex]\cos(\theta) \ne 0[/tex]:

[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].

Substitute this equality into the expression:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].

By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:

[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].

Substitute this equality into the expression:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].

Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].

Answer:

she could buy 5 outfits

Step-by-step explanation:

you multiply 7.17 by 3 = 21.51

700 - 21.51 = 678.49

678.49 - 242.33 = 436.16

436.16 - 33.68  = 402.48

402.48 divided by 77.40 = 5

Answer:

Step-by-step explanation:

1) Opposite angles in a parallelogram are congruent, so angle B measures 82 degrees.

2) Opposite sides of a parallelogram are congruent, so 12=6x. Hence, x=2.

3) Opposite sides of a parallelogram are congruent, so by the alternate interior angles theorem, the answer is 62 degrees.

Answer:

see explanation

Step-by-step explanation:

the opposite angles of a parallelogram are congruent , then

∠ B = ∠ D = 82°

the opposite sides of a parallelogram are parallel and congruent , then

AD = BC , that is

6x = 12 ( divide both sides by 6 )

x = 2

∠ BCA and ∠ DAC are alternate angles and are congruent , then

∠ BCA = ∠ DAC = 62°

Answer: $32

Step-by-step explanation:

Answer:

the area of ∆ABC = 9

Step-by-step explanation:

[tex]CA=\sqrt{\left( -1-2\right)^{2} +\left( 2-5\right)^{2} } = \sqrt{18} =3\sqrt{2}[/tex]

[tex]CB=\sqrt{\left( 5-2\right)^{2} +\left( 2-5\right)^{2} } = \sqrt{18} =3\sqrt{2}[/tex]

Since CA = CB  then  A(-1,2), B (5,2) and C (2,5) are the vertices of an isosceles triangle.

Area calculation:

Let The point H be the midpoint of side AB

[tex]x_{H}=\frac{-1+5}{2} =2\\y_{H}=\frac{2+2}{2} =2[/tex]

Then

H(2 , 2)

therefore,

[tex]CH=\sqrt{\left( 2-2{}\right)^{2} +\left( 2-5\right)^{2} } =3[/tex]

Finally,

[tex]\text{the area of triangle ABC} =\frac{\text{CH} \times \text{AB} }{2} =\frac{3\times 6}{2} =9[/tex]

Answer:

m<1 = 94

m<2 = 132

Step-by-step explanation:

This is a right trapezoid

Since the base lines are parallel, the facing angles would be supplementary and their sum is equal to 180 which means:

m<1 + 86 = 180 so m<1 = 94

and

m<2 + 48 = 180 so m<2 = 132

Answer:

y = 12 mm

Step-by-step explanation:

Volume of a rectangular prism: length × width × height

V = L×W×H

Substitute the values above and solve for y:

2,016 = 14 × 12 × y

2,016 = 168y

2,016/168 = 1395v/168

12 = y

Final answer: 12 mm

Hope this helps!

A B and F seem like questions that make sense :)

Answer:

Abc

Step-by-step explanation:

they make the most reasonable answers

Answer:

see explanation

Step-by-step explanation:

(a)

∠ XBC = 55° because it corresponds to ∠ AXY

(b)

since XB = XC then Δ XBC is isosceles with base angles congruent, that is

∠ XBC = ∠ XCB = 55°

the sum of the 3 angles in Δ XBC = 180° , then

∠ BXC + 55° + 55° = 180°

∠ XBC + 110° =180° ( subtract 110° from both sides )

∠ XBC = 70°

Answer:

x=-1

Step-by-step explanation:

x+2-1=0

-1+2=1

1-1=0

y=0

Answer:

X = -2

Step-by-step explanation:

Y = | (-2) + 2 | - 1

Y = |0| - 1

y = -1

Answer:

y=4x-3

Step-by-step explanation:

Using y - intercept form:

y=mx+b

Slope goes up by 4 squares and to the right by 2 squares. This means the slope is 4. The y intercept is -3, thus b is -3.

The triangle PAT is an isosceles triangle because the side lengths PA and AT are congruent

The points are given as:

P = (1,6)

A = (4,5)

T = (5,2)

Calculate the distance between both points as follows:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]PA = \sqrt{(1 -4)^2 + (6-5)^2}[/tex]

[tex]PA = \sqrt{10}[/tex]

[tex]PT = \sqrt{(1 -5)^2 + (6-2)^2}[/tex]

[tex]PT = \sqrt{32}[/tex]

[tex]AT = \sqrt{(4 -5)^2 + (5-2)^2}[/tex]

[tex]AT = \sqrt{10}[/tex]

Because the side lengths PA and AT are congruent, i.e. √10, then the triangle is an isosceles triangle

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Answer:

Soup A

Step-by-step explanation:

For this we need to find the number of sodium per cup. To do this, we divide the ratios by the number of cups. 8:10 would be 10/10 (1 cup) and 8/10 (.8 g per cup). 7:14 would be 14/14 (1 cup) and 7/14 (.5 g per cup). So, soup A has .8 g of sodium per cup and soup B has .5 g of sodium per cup. .8>.5, so soup A has more sodium.

Hope this helps!

Probability = option(s) that we want / total number of possibilities

Options that we want = cash or credit card  = 50 + 4 = 54

Total number of possibilities = cash, debit card, credit card = 50 + 2 + 4 = 56

54 / 56 = 0.96

Answer: 0.96

Hope this helps!

   [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

    Find the slope using the following points:

        (20, -10) (6, -20)

[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Use the slope formula:-

                    [tex]\LARGE\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]

Replace letters with numbers as follows:-

                             [tex]\Large\text{$\displaystyle\frac{-20-(-10)}{6-20}$}[/tex]

On simplification,

                                  [tex]\Large\text{$\displaystyle\frac{-20+10}{-14}$}[/tex]

On further simplification,

                                        [tex]\Large\text{$\displaystyle\frac{-10}{-14}$}[/tex]

Reducing the fraction,

                               [tex]\large\text{$\displaystyle\frac{10}{14}$}[/tex]

               [tex]\large\text{$\displaystyle\frac{5}{7}$}\leftarrow\:slope[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

13/40.

Step-by-step explanation:

We add the probability in this case.

So it is 1/5 + 1/8

=  8/40 + 5/40

= 13/40.

100 teeth / 20 teeth = 5

5 x 10 rpm = 50 rpm

answer: 50 rpm

Answer:

6x+54 should be the answer

Step-by-step explanation:

Answer:

We are 90% confident that the population mean height of college football players is between 65.6 and 67.1 inches.

Step-by-step explanation:

90% Confidence interval means that out of 100 different samples, for example, 90 out of 100 confidence intervals with include the true mean value (average height).

The option (C)  20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, —, ×, and ÷.

We have:

= (20 x 100)

= 2000

4 times smaller will be:

=2000/4

= 500

A) (20×100) 4 = 4000

B) 204×100 = 20400

C) 20 – 25 = -5

D) 5×25​ = 100

-5 < 500

100 < 500

Thus, the option (C)  20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.

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The critical points for the inequality x²-5x+6 is x= 2 and x = 3.

In calculus, a critical point of a function is a point where the derivative of the function is either zero or undefined.

These points are important in determining the maximum and minimum values of a function, and can also help identify points of inflection and other important features of a curve.

To find the critical points for the inequality x²-5x+6, we need to find the values of x that make the expression equal to zero (i.e., the roots of the quadratic equation).

We can factor the expression as (x-2)(x-3) and set each factor to zero to find the critical points:

x-2 = 0 or x-3 = 0

x = 2 or x = 3

So the critical points are x = 2 and x = 3.

Therefore, the answer is x= 2 and x = 3.

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