Solve the inequality |6x + 2| < 10 and graph its solution.

Answer:

5 cm

Step-by-step explanation:

ΔABC is equilateral, so BC = AB = 5 cm.

____

AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.

The length of BC is 5cm

Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]

Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:

[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]

OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)

Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.

Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.

Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.

But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').

Diameter = 2 * OB = 2 * 2.5 cm = 5 cm

BC = 5cm

Answer:

A). Sometimes.

Step-by-step explanation:

Sometimes a translation  because it might be a rotation or a reflection.

Translation in geometry always results in a similar figure. Hence, the correct answer is C.

A similar figure compared to the original figure is **always** a translation.

Translation in geometry involves moving a figure without rotating or flipping it. When a figure is translated, all the points move in the same direction by the same distance. This means that a translation produces a figure that is congruent to the original figure.

Answer:

1282.82ft³

Step-by-step explanation:

To find the volume of the entire shape, we first need to find the volume of the cone and the cylinder separately.

Let's begin by getting the volume of the cylinder.

The formula to find the volume of a cylinder is:

[tex]V=\pi r^{2}h[/tex]

r = 7 ft

h = 6 ft

Let's plug in our values into the formula.

[tex]V=\pi (7)^{2}6[/tex]

[tex]V=\pi (49)6[/tex]

[tex]V=\pi (294)[/tex]

[tex]V=923.63[/tex]ft³

Now that we have the volume of our cylinder we need to find the volume of the cone.

The volume of the cone can be found by using the formula:

[tex]V=\dfrac{1}{3}\pi r^{2}h[/tex]

Our variables for the cone are:

r = 7 ft

h = 7 ft

[tex]V=\dfrac{1}{3}\pi (7)^{2}(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (49)(7)[/tex]

[tex]V=\dfrac{1}{3}\pi (343)[/tex]

[tex]V=\dfrac{1}{3}1077.57[/tex]

[tex]V=359.19[/tex]ft³

Now that we found both of the volumes of the two shapes, we can then simply get the sum of both volumes to get the total volume of the shape.

Total Volume = 923.63ft³ + 359.19ft³

Total Volume = 1282.82ft³

Answer:

a: 27 apples

b: $0.40 apples

Step-by-step explanation:

a: another way of saying that the price of an apple one-third that of an orange is that you can get 3 apples for the price of 1 orange. If he bought 5 oranges, he could have gotten 15 apples, so 27 apples total.

b:  $10.80/27 = $0.40 per apple

Answer:

6a. -8

8b. 1/125

Step-by-step explanation:

If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)

___

6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8

___

8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)

= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)

= (5^2)^(-3/2) = 5^(-3) = 1/5^3

= 1/125

Answer: - 2.5n+13.5

Explanation:

[tex]11 - 8.5 = 2.5 \\ - 2.5n \times 1 = - 2.5 \\ it \: is \: negative \: as \: the \: sequence \: \\ decreases\\ 11 - - 2.5 = 13.5 \\ - 2.5n + 13.5[/tex]

The explicit rule for the sequence 11, 8.5, 6, 3.5, 1 is to subtract 2.5 from the previous term.

To find the explicit rule, we look for a pattern in the sequence. We can see that each term is decreasing by a constant amount. Let's calculate the difference between consecutive terms:

- The difference between the second term (8.5) and the first term (11) is 8.5 - 11 = -2.5.

- The difference between the third term (6) and the second term (8.5) is 6 - 8.5 = -2.5.

- The difference between the fourth term (3.5) and the third term (6) is 3.5 - 6 = -2.5.

- The difference between the fifth term (1) and the fourth term (3.5) is 1 - 3.5 = -2.5.

Since the difference is constant and equal to -2.5, we can express the nth term of the sequence, [tex]\( a_n \)[/tex], as:

[tex]\[ a_n = a_{n-1} - 2.5 \][/tex]

where [tex]\( a_{n-1} \)[/tex] is the previous term in the sequence. To express this in terms of n, we need to find the first term of the sequence and then apply the pattern. The first term, [tex]\( a_1 \)[/tex], is 11. Since we are subtracting 2.5 each time, the nth term can be written as:

[tex]\[ a_n = a_1 - (n - 1) \cdot d \][/tex]

where [tex]\( d \)[/tex] is the common difference, which is -2.5. Substituting [tex]\( a_1 = 11 \) and \( d = -2.5 \)[/tex], we get:

[tex]\[ a_n = 11 - (n - 1) \cdot (-2.5) \][/tex]

[tex]\[ a_n = 11 + 2.5n - 2.5 \][/tex]

[tex]\[ a_n = 8.5 + 2.5n \][/tex]

Therefore, the explicit rule for the nth term of the sequence is:

[tex]\[ a_n = 8.5 + 2.5n \][/tex]

This rule gives us the terms of the sequence when we substitute n = 1, 2, 3, 4, 5, etc. For example, for n = 1:

[tex]\[ a_1 = 8.5 + 2.5(1) = 8.5 + 2.5 = 11 \][/tex]

which matches the first term of the sequence.

Answer:

1800

Step-by-step explanation:

Given in the question a polygon of 12 sides

Formula to calculate sum of interior angles of 12-gon is

where n is the number of sides

which in this case = 12

plug values in the formula above

(12 - 2)180

12*180 - 180(2)

2160 - 360

1800

Sum of measurements of the interior angles of a 12sided polygon is 1800

Answer:

=1800°

Step-by-step explanation:

A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)

n represents the number of sides of the polygon.

Therefore, the sum of all angles= 180(12-2)

=1800°

Answer:

Step-by-step explanation:

Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...

  9/(n -1) - 9/n = 3/4 . . . . . minutes

Multiplying by (4/3)n(n -1), we get

  12n -12(n -1) = n(n -1)

  12 = n(n -1)

Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...

  (4·450 m)/(9 min) = 200 m/min

Brian completes 3 laps in that 9-minute time, so his rate is ...

  (3·450 m)/(9 min) = 150 m/min

Answer:

  $5.25

Step-by-step explanation:

If the friend tripled the first purchase and subtracted twice the second purchase, he would have the cost of 3·8-2·5 = 14 notebooks. 7 notebooks would cost half that amount:

  (3·$11 -2·11.25)/2 = $5.25 . . . . . cost of 7 notebooks

Answer:

x = 2

Step-by-step explanation:

The minimum occurs where the value being squared is zero. x-2 = 0 when x=2.

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:

 [tex](48inches)(\frac{1foot}{12inches})=4feet[/tex]

- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that  correctly compares 2 feet to 48 inches, you can write:

[tex]ratio=\frac{2feet}{4feet}[/tex]

- Reduce the fraction, then:

[tex]ratio=\frac{1}{2}[/tex]

- You can rewrite it as following:

[tex]ratio=1:2[/tex]

Answer:

D

Step-by-step explanation:

Answer:

184

Step-by-step explanation:

1st step

we simplify (5-1) which is just 4 and (3+7) which is 10

and we also simply 6^2 which is 36

now we plug the simplified terms back in

(4)(36+10)

(4)(46)

184

Answer:

184

Step-by-step explanation:

Subtract: 5 - 1 = 4

Power: 6 ^ 2 = 36

Add: 36 + 3 = 39

Add: 39 + 7 = 46

Multiple: 4 * 46 = 184

Please mark as brainiest

Answer:

  √13 units

Step-by-step explanation:

Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.

In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used.  It is expressed as BC^2 = AB^2 + AC^2.

In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).

Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.

https://brainly.com/question/35911509

#SPJ2

Answer:

1.2g+0.4

Step-by-step explanation:

The equivalent expression should be 1.2g+0.4.

The equation is (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)

= (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)

= 0.7g + 0.6h - 0.4 + 0.8 - 0.6h + 0.5g

= 1.2g + 0.4

Learn more about the expression here: https://brainly.com/question/24422266

Answer:

5/2

Step-by-step explanation:

The multiplicative inverse is what me need to multiply by to get 1

2/5 * what = 1

Multiply by the reciprocal

5/2 *2/5 * what = 1 *5/2

what = 5/2

The multiplicative inverse is 5/2

5/2 is the multiplicative inverse

Answer:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]

Step-by-step explanation:

We want to evaluate:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]

When x=0, we obtain the first term of the geometric series as

[tex]a_0=2(\frac{1}{3})^0[/tex]

The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]

The sum of the first n-terms of a geometric series is

[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

From x=0 to x=15, we have 16 terms.

The sum of the first 16 terms of the geometric series is

[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.

Answer:

  b² -2ab +a²

Step-by-step explanation:

The first factor can be rearranged to put the minus sign in the middle. Then you have

  (b -a)(b -a) = (b -a)² = b² -2ab +a²

___

If you like, you can also write this as ...

  a² -2ab + b² . . . . . . terms in lexicographical order

_____

The "special product" of interest here is the square of a binomial:

  (p +q)² = p² +2pq +q²

You have p=b, q=-a, so the result is as shown above.

Answer:

  80

Step-by-step explanation:

The square of a binomial is ...

  (a +b)^2 = a^2 + 2ab + b^2

You have a=8q, b=5, so the square is ...

  (8q)^2 + 2(8q)(5) + (5)^2

  = 64q^2 +80q +25

The coefficient missing from your given expression is 80.

Answer:

(x, y) ⇒ (-x, y)

Step-by-step explanation:

Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.

The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.

_____

Comment on rotations

A rotation about the origin can be written in the form ...

(x, y) ⇒ (ax -by, bx +ay)

where a^2 +b^2 = 1 and b/a = tan(angle of rotation)

This rigid transformation is an exception to the statement above about multiplication by something other than ±1.

Answer:

The correct answer option is B. c = 25 + 2m.

Step-by-step explanation:

We are given that a movie rental club charges a one time fee of $25 to join and $2 for every movie rented.

We are to determine whether which of the given equations in the answer options represent how much you would spend to join the club and rent movies for a year.

The correct answer option is B. c = 25 + 2m.

One time charges = 25 plus $2 multiplied by the number of movies rented.

Answer:

Since 2 inches represent 8 feet then 2.5 would represent x feet so  

2/8 = 2.5/x  

By doing cross multiplication :  

2 x = 20 --> x = 10 feet

Step-by-step explanation:

Given dimensions:

Height of the cylinder = 2 m

Volume is increasing at a rate of = 10 m³/min

Radius = 4 inches

Converting radius in meters.

1 inch = 0.0254 meters

4 inches = [tex]4\times0.0254=0.1016[/tex] meters

[tex]\frac{dv}{dt}=10[/tex]

we have to find, [tex]\frac{dr}{dt}=?[/tex]

Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]

= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]

Now differentiating with respect to 't'

[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]

[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]

[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]

[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]

= 7.83 meter per minute.

Answer:

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

||Vel_jet_r|| =  465.993 mph

Step-by-step explanation:

We need to decompose the velocity of the wind into a component that can be added  (or subtracted from the velocity of the jet)

The velocity of the jet

500 mph North

Velocity of the wind

50 mph SouthEast = 50 cos(45) East + 50 sin (45) South

South = - North

Vel_ wind = 50 cos(45) mph  East  -  50 sin (45) mph North

Vel _wind =  35.35 mph  East  -  35.35 mph North

This means that the resulting  velocity of the jet is equal to

Vel_jet_r =  (500 mph - 35.35 mph) North + 35.35 mph East

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

An the jet has a magnitude velocity of

||Vel_jet_r|| =  sqrt ((464.645 mph)^2 + (35.35 mph)^2)

||Vel_jet_r|| =  465.993 mph

Answer:

C. 2

Step-by-step explanation:

Point B is 6-(-4) = 10 units up from point A. A point (F) that partitions that distance in the ratio 3:2 will be 3/(3+2) = 3/5 of the distance from A to B. That is, it will be ...

3/5 · 10 units = 6 units

above A. The y-coordinate of F will be 6 units added to the y-coordinate of point A, -4 +6 = 2.

Answer:

D. (2, 5)

Step-by-step explanation:

On a graph, (2, 5) is the only point in the solution space.

___

You can evaluate the inequality for each of the points to see which works.

A. 4 > 2·4 -3 . . . . false

B. 12 > 2·9 -3 . . . . false

C. 2 > 2·3 -3 . . . . false

D. 5 > 2·2 -3 . . . . TRUE

Answer:77

32+27+22+17+12+7+2-3-8-13-15-18=77

Answer:

54

Step-by-step explanation:

The first twelve terms would be, in decreasing order, 32, 27, 22, 17, 12, 7,2, -3, -8,-13,-18,-23.

1. -23+22 = -1

2. -13+12 = -1

3. -18+17 = -1

4. -8+7 = -1

5. -3+2 = -1

Using these five facts, we can simplify this to 32+27 -5(1) = 32+27-5 = 54

Answer: function b has a greater rate of change

Answer:

Step-by-step explanation:

27

The observed value when x = 3, estimated to the nearest half unit is y = 4.5.

The observed value is the actual value of the variable. The points on the regression line are called predicted values.

Therefore, the observed value of y when x = 3, estimated to the nearest half unit is y = 4.5. The correct answer is option C.

Learn more about observed values here: https://brainly.com/question/11888173

#SPJ2