Evaluate 5x2−9 when x=−2

The measure of the angle between tangent and secant AB in a circle with arcs in a 1:5 ratio is 120°, calculated using arc measures.

Let's denote the measures of the arcs subtended by chord AB as x and 5x, where x is the measure of the smaller arc.

Now, according to the properties of angles formed by a tangent and a secant, the measure of the angle formed between the tangent and the secant AB is equal to half the difference of the measures of the intercepted arcs.

So, the measure of the angle [tex]\( \angle A \)[/tex] formed between the tangent and the secant AB is:

[tex]\[ \angle A = \frac{1}{2} \left|5x - x\right| \\\[ \angle A = \frac{1}{2} \left|4x\right| \][/tex]

Now, since x represents the measure of the smaller arc, it must be greater than 0. Thus, the expression simplifies to:

[tex]\[ \angle A = 2x \][/tex]

Now, we need to find the value of x. Since the sum of the measures of the arcs in a circle is 360°, we have:

[tex]\[ x + 5x = 360^\circ \\\[ 6x = 360^\circ \\\[ x = \frac{360^\circ}{6} \\\[ x = 60^\circ \][/tex]

Now, we can find the measure of the angle [tex]\( \angle A \)[/tex]:

[tex]\[ \angle A = 2x \\\[ \angle A = 2(60^\circ) \\\[ \angle A = 120^\circ \][/tex]

So, the measure of the angle between the tangent and secant AB is 120°.

Answer:

The measure of the angle between the tangent and secant AB is [tex]\(120\°\).[/tex]

Explanation:

To solve this problem, let's denote the measures of the two arcs subtended by chord AB as [tex]\(x\)[/tex]  and [tex]\(5x\)[/tex], respectively.

We know that when a tangent line intersects a secant line, the angle formed between the tangent and the secant is equal to half the difference of the measures of the intercepted arcs.

So, the angle between the tangent and secant AB, let's call it [tex]\(\theta\)[/tex], is given by:

[tex]\[ \theta = \frac{1}{2}(5x - x) = \frac{1}{2}(4x) = 2x \][/tex]

Now, let's find the value of [tex]\(x\).[/tex]

Since chord AB subtends two arcs with measures in the ratio of [tex]\(1:5\)[/tex], the total angle around the circle is [tex]\(1x + 5x = 6x\)[/tex], which is [tex]\(360\°\)[/tex](since the total angle around a circle is [tex]\(360\°\)[/tex]).

So, we have:

[tex]\[ 6x = 360\° \][/tex]

Solving for [tex]\(x\):[/tex]

[tex]\[ x = \frac{360\°}{6} = 60\° \][/tex]

Now, we can find the measure of the angle [tex]\(\theta\):[/tex]

[tex]\[ \theta = 2x = 2 \times 60\° = 120\° \][/tex]

So, the measure of the angle between the tangent and secant AB is [tex]\(120\°\).[/tex]

Final answer:

The probability of getting a 2 and then a 1, given that the first number rolled was 2, is 1/5 or 0.2 (20%).

Explanation:

The probability of getting a 2 and then a 1, given that the first number rolled was 2, can be calculated using the concept of conditional probability.

Since we know that the first number rolled was a 2, the sample space is reduced to {2, 3, 4, 5, 6}. The probability of rolling a 2 from this reduced sample space is 1/5.

Now, since we want to find the probability of rolling a 1 after rolling a 2, the reduced sample space is further reduced to {1}. The probability of rolling a 1 from this reduced sample space is 1/1, since there is only one outcome.

Therefore, the probability of getting a 2 and then a 1, given that the first number rolled was 2, is 1/5 * 1/1 = 1/5 or 0.2 (20%).

The probability of rolling a 2 and then a 1 on a six-sided number cube, given that the first number rolled was a 2, is [tex]\(\frac{1}{6}\)[/tex].

To solve this problem, we need to consider the probability of each event separately and then combine them, keeping in mind that the outcome of the first roll affects the probability of the second roll.

1. The probability of rolling a 2 on the first roll is [tex]\(\frac{1}{6}\)[/tex], since there is only one '2' on a six-sided die and there are six possible outcomes.

2. Given that the first roll is a 2, the probability of rolling a 1 on the second roll is still [tex]\(\frac{1}{6}\)[/tex]. This is because the die has no memory, and each roll is independent of the previous one. The fact that a 2 was rolled first does not change the probability of rolling a 1 on the second roll.

3. Since the rolls are independent events, we multiply the probabilities of the two events to find the combined probability:

[tex]\[ P(\text{2 and then 1} | \text{first roll is 2}) = P(\text{first roll is 2}) \times P(\text{second roll is 1}) \][/tex]

4. Substituting the probabilities we found:

[tex]\[ P(\text{2 and then 1} | \text{first roll is 2}) = \frac{1}{6} \times \frac{1}{6} \][/tex]

5. Multiplying these probabilities:

[tex]\[ P(\text{2 and then 1} | \text{first roll is 2}) = \frac{1}{36} \][/tex]

However, since we are given that the first number rolled was a 2, we do not need to consider the probability of rolling a 2 on the first roll. We only need to consider the probability of rolling a 1 on the second roll, which is [tex]\(\frac{1}{6}\)[/tex].

Therefore, the probability of getting a 2 and then a 1, given that the first number rolled was a 2, is [tex]\(\frac{1}{6}\)[/tex].

Answer:

B 6x - 4y = 2

Step-by-step explanation:

Stand form of a linear equation is

Ax + By =C

8 - 4(x-y) = 2x+6

Distribute the -4

8 -4x +4y = 2x+6

Subtract 2x from each side

8 -4x-2x +4y = 2x-2x+6

8 -6x +4y = 6

Subtract 8 from each side

8-8-6x+4y = 6-8

-6x+4y = -2

We like to have x with a positive coefficient

Multiply by -1

6x -4y = 2

Answer:   a) -240

Step-by-step explanation:

[tex]2\sqrt{-32}\cdot 5\sqrt{-18}\\\\=2\cdot 5\sqrt{-32\cdot -18}\\\\=10\sqrt{-1\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot -1\cdot 2\cdot 3\cdot 3}\\\\\\=10(-1\cdot 2\cdot 2\cdot 2\cdot 3)\\\\=10(-24)\\\\=\boxed{-240}[/tex]

Answer:

3 cups of pancake mix and 2 cups of water

Step-by-step explanation:

For the family of 6 to have 3 pancakes each, Arjun must make at least 18 pancakes. If 1 cup of pancake mix makes at least 6 pancakes, Arjun would need three cupes of pancake mix to make at least 18 pancakes.

Now if each cup of pancake mix requires 2/3 cups of water, the amount of water needed for 3 cups of pancake mix would be

3 x 2/3 = 2 cups of water

Answer:

3 cups of pancake mix and 2 cups of water

Step-by-step explanation:

We are given that a box of pancake mix requires 1 cup of mix and 2/3 cups of water which makes at least 6 cupcakes.

If each person in Arjun's family of 6 wants to have 3 pancakes, it means that he needs to make 18 cupcakes.

To make 18 cupcakes, we need [tex]1 \times 3 =[/tex] 3 cups of pancake mix and [tex]3 \times \frac{2}{3} =[/tex] 2 cups of water.

Answer: [tex]\frac{x+5}{x+3}[/tex]

Step-by-step explanation:

The problem gives you the following expression:

[tex]\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}[/tex]

Therefore, to add the fractions with equal denominator, you must rewrite the denominator (x+3) and add the numerators of each one of the fractions.

Then, keeping the above on mind, you obtain the sum shown below (You must remember to add the like terms):

[tex]\frac{x+3+2}{x+3}=\frac{x+5}{x+3}[/tex]

Answer:

The correct answer is (x + 5)/(x + 3)

Step-by-step explanation:

It is given an expression,

x/x+3 + 3/x+3 + 2/x+3

From the above expression we can see that, sum of three fractions

To find the sum

The above expression is sum of three fraction. The denominators are same which is (x + 3)

So we can add numerators

x/x+3 + 3/x+3 + 2/x+3 = ( x + 3 + 2)/(x + 3) = (x + 5)/(x + 3)

Therefore the correct answer is (x + 5)/(x + 3)

Answer:

94.97.

Step-by-step explanation:

➷ Use the multiplier version:

40% ==> 0.4

Multiply it by the multiplier:

55 x 0.4 = 22

The answer is 22.

➶ Hope This Helps You!

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↬ ʜᴀɴɴᴀʜ ♡

I can try it depends on what the question is

Answer:

That's right!

Step-by-step explanation:

All of the points are in the right places! :P

Answer:

All four points are in the right place.

Step-by-step explanation:

Here's what you need to check.

The coordinate of each point is a set of two number in a round bracket.

Taking point A (9, 7) as an example.

Repeat these steps for the rest of the four points. See if every single point is in their place.

Here, current (I) = 1.6A

resistance(R) = 240 ohm

we know, voltage(v) =I×R

=1.6×240

=384 VOLTS

Hope i am clear and correct

Answer:

380 V

Step-by-step explanation:

The explicit formula for the sequence 5, 9, 13, 17 is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

The given sequence is 5, 9, 13, 17. To find the explicit formula, we need to determine the pattern or rule that generates these numbers. In this case, the pattern can be observed by adding 4 to the previous term to get the next term. So, the explicit formula for this sequence is:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term (5 in this case), n is the position of the term in the sequence, and d is the common difference (4 in this case).

Using this formula, we can find any term in the sequence by plugging in the values for n and a1.]

Answer:

[tex]2\frac{5}{8}\ gal[/tex]

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

so

[tex]5\frac{1}{4}\ gal=\frac{5*4+1}{4}=\frac{21}{4}\ gal[/tex]

step 2

Divide the total gallons of paint by two

[tex]\frac{(21/4)}{2}=\frac{21}{8}\ gal[/tex]

step 3

Convert improper fraction to mixed number

[tex]\frac{21}{8}\ gal=\frac{16}{8}+\frac{5}{8}=2+\frac{5}{8}=2\frac{5}{8}\ gal[/tex]

Answer:

Option D is correct

Step-by-step explanation:

According to Geometry, A circle is a round plane figure whose boundary (that is the circumference) consists of points equidistant from a fixed point (that is the centre).

Thus, according to the definition of circle in geometry, option D is correct because it gives the correct description about circle while all other options are not correct because they are giving the incorrect description of circle.

Answer:

The answer is -2/3.

Answer:

18π in²

Step-by-step explanation:

We need to find the circumference of the edge of the cylinder.  The formula for circumference is C = 2πr, where r is the radius.

Here, the circumference is 2π(3 in) = 6π in.

To find the surface area covered by the label, multiply this circumference by the can height, 3 in:

V = (6π in)(3 in) = 18π in²

Approximately 18.85 square inches of paper is used for the label that covers the Lateral surface area of the soup can.

Let's find the amount of paper used for the label that covers the lateral (side) surface area of the soup can, you can calculate the lateral surface area of the cylinder.

The formula for the lateral surface area of a cylinder is:

Lateral Surface Area = 2πrh

Where:

π (pi) is approximately 3.14159

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius (r) of the soup can is 1 inch, and the height (h) is 3 inches. Plug these values into the formula:

Lateral Surface Area = 2π(1 inch)(3 inches)

Lateral Surface Area = 2π(3 square inches)

Lateral Surface Area = 6π square inches

Now, you can calculate the approximate value:

Lateral Surface Area ≈ [tex]6 \times 3.14159[/tex] square inches

Lateral Surface Area ≈ 18.84954 square inches

For more such questions on Lateral surface area

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Answer:

false

Step-by-step explanation:

What is your gender

Are you married

What is your gender?

Are you married?

A cylinder can be cut parallel to the base, the result will give the set of parallel cross-sections that are congruent circles.

A sphere is a three-dimensional shape analouge of a circle.

The sphere is a round shape that has no vertex.

The cross-section is generally a two-dimensional plane figure.

If the cone is cut parallel to the base, the result would be the base of the cone, which in cross-section, is just a circle.

A cylinder can be cut parallel to the base, the result will give the set of parallel cross-sections that are congruent circles.

Learn more about shapes;

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Final answer:

Among a sphere, cylinder, and cone, the cylinder is the only shape that possesses a set of parallel cross sections that are congruent circles, as the cross-sections made perpendicular to its base are identical in shape and size.

Explanation:

The question asks which shape among a sphere, cylinder, and cone possesses a set of parallel cross sections that are congruent circles. The cylinder is the shape that fits this description. When you make parallel cuts perpendicular to the base of a cylinder, each of the resulting cross-sections is a circle.

Moreover, these circles are congruent, meaning they are identical in shape and size. In contrast, a sphere's parallel cross-sections vary in size (getting smaller as you move towards the poles), and a cone's parallel cross-sections also vary in size (getting smaller as you move from the base to the point).

the answer to Y/8=5 Y=40

Answer:

y=40

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-6)}{-3-0}\implies \cfrac{0+6}{-3}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-6)=-2(x-0) \\\\\\ y+6=-2x\implies y=-2x-6[/tex]

Answer:

64 cubes

Step-by-step explanation:

The square is 12x12x12 inches, meaning it is 1,728 cubic inches in volume. A 3x3x3 inch cube is 27 cubic inches in volume. Divide 1,728 by 27 and you'll find that 64 3x3x3 cubes can fit inside one of the 12x12x12 cubes.

Final answer:

To fill a cube-shaped container with an edge length of 12 inches, 64 small cubes with an edge length of 3 inches each are required.

Explanation:

The student is asking how many small cubes, with an edge length of 3 inches, are required to fill a larger cube-shaped container with an edge length of 12 inches. First, we calculate the volume of the large cube which is 12 inches x 12 inches x 12 inches, resulting in 1728 cubic inches. Then, we find the volume of one small cube which is 3 inches x 3 inches x 3 inches, resulting in 27 cubic inches. To determine the number of small cubes that can fit into the larger cube, we divide the large cube's volume by the small cube's volume: 1728 cubic inches / 27 cubic inches which equals 64. Therefore, 64 small plastic cubes are needed to fill the container.

here are the answers to this question

Answer:

The zeroes are {-4, 13}

Step-by-step explanation:

Your best bet here is to determine the zeros using the quadratic formula or "completing the square."

Completing the square,

y = x² - 17x                         +52, or

y = (x - 17/2)² - (17/2)²         +52, or

y = (x - 17/2)² - 289/4          +208/4, or

y = (x - 17/2)²  - 81/4

We set this = to 0, as we want the zeros.  Then:

(x - 17/2)²  - 81/4 = 0, or

x - 17/2 = ±9/2, after having taken the square root of both sides.

Thus, one root is x = 17/2 + 9/2, or 26/2, or 13, and the other is

                             x = 1/2 - 9/2, or -8/2, or -4.

The zeroes are {-4, 13}.

Answer:

(7,-2)

Step-by-step explanation:

First, you move to the right of y-axis like 5 to 7,

then you movie to the up of x-axis like -5 to -2.

So the answer was (7,-2)

Final answer:

The image point of (5,-5) after a translation right 2 units and up 3 units is (7, -2).

Explanation:

The image point of (5,-5) after a translation right 2 units and up 3 units can be found by adding the respective translation values to the x and y coordinates of the original point. To move the point right by 2 units, you add 2 to the x-coordinate, and to move the point up by 3 units, you add 3 to the y-coordinate.

Therefore, the new coordinates after the translation will be:

So the image point after the translation is (7, -2).

Answer: One hour costs 7.25 $

Step-by-step explanation:

The charge for 2 hours is 14.50 $, then 14.50 $ / 2 hours = 7.25 $ / hour

The charge for 5 hours is 36.25 $, then 36.25 $ / 5 hours = 7.25 $ / hour

Answer: One hour costs 7.25 $

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Answer:

The angular velocity is 10π rad/s or 600 rad/min.

Step-by-step explanation:

angular velocity = angle/time

0.5 revolution = 0.5 × 2π = π rad

ω = θ/t = π rad/0.1 s = 10π rad/s

Convert time to minutes

ω = 10π rad/1 s × (60 s/1 min) = 600π rad/min

Answer:

The area of the kite is [tex]42\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a kite is half the product of the diagonals

so

[tex]A=\frac{1}{2}(D1*D2)[/tex]

we have

[tex]D1=2*(3)=6\ units[/tex]

Find the length side of diagonal D2

Applying the Pythagoras Theorem

[tex]D2=\sqrt{5^{2}-3^{2}} +10\\ \\D2=4+10\\ \\D2=14\ units[/tex]

Find the area of the kite

we have

[tex]D1=6\ units[/tex]

[tex]D2=14\ units[/tex]

substitute

[tex]A=\frac{1}{2}(D1*D2)[/tex]

[tex]A=\frac{1}{2}(6*14)=42\ units^{2}[/tex]

100%-15%=85% -- 0.85

A. doesn't work because it is increasing

B. works because your finding 85 percent since you decrease by 15 percent

C. doesn't work because you are not taking 15 percent from value of t

D. doesn't work because finging 15 percent of t and them subtracting from one won't give you the right answer

E.doesnt work because all you have to do is find 85 percent not subtract that from the original value

F.works because subtracting 15 percent from one and multiply by t would give the equation from B

So the answers are B and F