Points A, B, and C are collinear. Point B is between A and C. Find the length indicated. Find BC if AB=2x-12, AC=14, and BC=x+2

Answer:

4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Step-by-step explanation:

Simplify the following:

(2^(1/3))^7

Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.

Multiply exponents. (2^(1/3))^7 = 2^(7/3):

2^(7/3)

Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.

2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):

2^(6/3) 2^(1/3)

Hint: | Divide 6 by 3.

6/3 = (3×2)/3 = 2:

2^2 2^(1/3)

Hint: | Evaluate 2^2.

2^2 = 4:

Answer:  4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Answer: terminating

Step-by-step explanation:

Answer:

7.2 is a terminating decimal.

Step-by-step explanation:

Terminating decimals are decimals that have an end point. The decimal does not continue to go on and on with numbers but, it stops at one number which makes it terminating.

Repeating decimals are decimals that go on and on with the same number or same patterns of numbers.

So, since 7.2 has an endpoint, then it is a terminating decimal.

Answer:

 y = -1/2x + 4

Step-by-step explanation:

We have two points ( 8,0) and ( 0,4)

We can find the slope

m =(y2-y1)/(x2-x1)

    = (4-0)/(0-8)

    4/-8

   -1/2

We can use the slope intercept form

 y = mx+b where m is the slope and b is the y intercept

 y = -1/2x + 4

Answer:

Step-by-step explanation:

eq. of line with intercepts a and b is

[tex]\frac{x}{a} +\frac{y}{b} =1\\here ~eq. ~of ~line~ is ~ \frac{x}{8} +\frac{y}{4} =1\\or x+2y=8\\[/tex]

Answer:

The answer is (3×7) + (12×2) .

[tex](3 \times 7) + (12 \times 2)[/tex]

[tex] = 21 + 24[/tex]

[tex] = 45[/tex]

Answer:

  lies in the shaded regions of both the top and bottom inequalities

Step-by-step explanation:

For a point to be a solution of two inequalities, it must lie in both solution sets. It ...

  lies in the shaded regions of both the top and bottom inequalities

We want to define when a point is a solution of a system of inequalities, we will see that the correct option is: "lies in the shaded regions of both the top and bottom inequalities."

Just like in a system of equations, a solution of the system is must be a solution of both equations.

Here, a solution ot the system of inequalities must be at the same time a solution of each inequality.

Remember that the solutions of the inequalities are represented by shaded regions, so the point must belong to the intersection of the two shaded regions.

So the correct option is:

"lies in the shaded regions of both the top and bottom inequalities."

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Answer:

60 miles per hour

Step-by-step explanation:

Total distance= 180 miles

Total time =3 hours

Average rate of change= ?

Distance= Rate × time

Make Time the subject of the formula

Time= Distance / Rate

Make average rate of change the subject of the formula

Average rate of change = Distance / time

= 180 miles / 3 hours

= 60 miles per hour

Answer:

(A) [tex]y = x+3[/tex]

Step-by-step explanation:

Using the values of (-6, -3), (3,6), and (5,8) we can substitute the values into each equation and see if the equation meets the requirements for all 3.

Let's test A first.

[tex]-3 = -6+3[/tex]

Correct, let's try the second pair.

[tex]6 = 3+3[/tex]

Correct, let's try the third pair.

[tex]8 = 5+3[/tex]

So yes, this equation works.

For fun, let's try the other equations.

Let's test B.

[tex]-3 = -6-3[/tex]

This is not true as -6 -3 = -9. So this equation is immediately ruled out.

Let's test C.

[tex]-3 = 2\cdot-6[/tex]

Again this doesn't work, as -6 times 2 is -12. So this equation is also ruled out.

Let's try D.

[tex]-3 = \frac{1}{2}\cdot-6[/tex]

This works, as half of -6 is -3 - however the equation will only work if all 3 pairs work for it.

Let's try the second pair.

[tex]6 = \frac{1}{2}\cdot3[/tex]

This doesn't work, as half of 3 is 1.5. This equation is also ruled out.

Therefore, A is the only equation that works with these pairs.

Hope this helped!

Answer:

a. quarter and eighth notes is the best option

Step-by-step explanation:

you can get help from this attachment

hope it will help you :)

Answer:

11.8%

Step-by-step explanation:

Here in this question, we want to find the probability of no success in the binomial experiment for 6 trials.

Let p = probability of success = 30% = 30/100 = 0.3

q = probability of failure = 1-p = 1-0.3 = 0.7

Now to calculate the probability, we shall need to use the Bernoulli approximation of the binomial theorem.

That would be;

P(X = 0) = 6C0 p^0 q^6

6C0 is pronounced six combination zero

= 6 * 0.3^0 * 0.7^6 = 1 * 1 * 0.117649 = 0.117649

This is approximately 0.1176

If we convert this to percentage we have 11.76%

But we want our answer rounded to the nearest tenth of a percent and that is 11.8%

Answer:

About 706.5 square inches.

Step-by-step explanation:

Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]

The radius is half the diameter. So, the radius of the given sphere is 7.5 in.

15/2 = 7.5

Find the surface area:

I use 3.14 for pi.

[tex]SA=4*3.14*7.5^2\\\\SA=4*3.14*56.25\\\\SA=12.56*56.25\\\\\boxed{SA=706.5}[/tex]

The surface area is about 706.5 square inches.

Hope this helps.

Answer:

SA=706.86 in²

Step-by-step explanation:

surface area of a sphere = 4πr²

radius r=d/2=15/2=7.5

SA=4(π)(7.5)²

SA=706.86 in²

Answer:

48 portions of salad

Step-by-step explanation:

4 bags spinach = 18 cherry tomatoes = 7.2 lb of chicken

7.2/.75 = 9.6 x 5 = 48

Answer:

When x = -4 and y = -6, p = 37.75

Step-by-step explanation:

Given that p = x² - y²/x² + x·y, we have;

p = (x² × x² -y² + x·y×x²)/x²

p = (x²⁺² - y² + x¹⁺² × y)/x²

p = (x⁴ - y² + x³·y)/x²

Therefore, p in the simplest form is given as follows;

[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]

To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;

[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]

Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.

[tex]_{10}C_3=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot 3}=120[/tex]

Question :-

Answer :-

[tex] \rule{200pt}{3pt}[/tex]

Combinations refers to the number of ways of selecting from a set when the order is not important. The number of combinations of n objects taken r at a time is given by [tex]\sf C(n, r) = \dfrac{n!}{(n - r)!r!}, n \geqslant r[/tex].

Solution :-

As per the provided information in the given question, we have been given that the number of combinations of 10 students taken 3 at a time. We have been asked to calculate the ways that she can choose 3 of the 10 students.

To calculate the ways that she can choose 3 of the 10 students, we will apply the formula below :-

[tex] \qquad \bigstar \: \: \: \boxed{ \sf{ \: \: C(n, r) = \dfrac{n!}{(n - r)!r!} \: \: }}[/tex]

Substitute the given values into the above formula and solve for C:

[tex]\sf:\implies{ C(n, r) = \dfrac{n!}{(n - r)!r!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{(10 - 3)!3!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{7!3!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8 \cdot \cancel{7!}}{ \cancel{7!}3!}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8}{3 \cdot 2}}[/tex]

[tex]\sf:\implies{ C(10, 3) = \dfrac{720}{6}}[/tex]

[tex]\sf:\implies \bold{ C(10, 3) = 120 \: ways}[/tex]

Therefore :-

[tex]\\[/tex]

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Have a great day! <33

Answer:

At   90% confidence interval, the estimate of the mean breaking weight is (770.45, 778.15)

Step-by-step explanation:

Given that:

sample size n =43

sample mean x = 774.3

standard deviation = 15.4

confidence interval = 90%

At C.I of  90% , the level of significance ∝ = 1 - C.I

the level of significance ∝ = 1 - 0.90

the level of significance ∝ = 0.10

The critical  value for z at this level of significance is [tex]z_{\alpha/2} = z_{0.10/2}[/tex]

[tex]z_{0.05}[/tex] = 1.64

The margin of error can be computed as follows:

Margin of error = [tex]\mathtt{z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}}[/tex]

Margin of error =  [tex]\mathtt{1.64 \times \dfrac{15.4}{\sqrt{43}}}[/tex]

Margin of error = [tex]\mathtt{1.64 \times \dfrac{15.4}{6.5574}}[/tex]

Margin of error  = [tex]\mathtt{1.64 \times2.3485}[/tex]

Margin of error = 3.8515

The mean breaking weight  for the 90% confidence interval is = [tex]\mathtt{\overline x \pm E < \mu }[/tex]

=  [tex]\mathtt{\overline x - E < \mu < \overline x + E}[/tex]

= ( 774.3 - 3.8515  < μ < 774.3 + 3.8515 )

= (770.4485, 778.1515)

[tex]\simeq[/tex] (770.45, 778.15)

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

Answer:

'y', "addition", '9'.

Step-by-step explanation:

The variable is an unknown value in an algebraic equation or expression. It is represented by a letter.

'y' would be the variable in the given equation.

The operation in the expression is addition. The '+' sign represents addition, which means 9 and 'y' would be added together to get the sum.

Constants are terms in a expression or equation that contains no variables. This means that constants are only numbers.

'9' would be the given constant in the expression.

Hope this helps.

Answer:

y

+

9

Step-by-step explanation:

Answer:

1.132d

Step-by-step explanation:

Cost of the dinner=$d

Coupon=10% after

Tax=8%

Tax=0.08d

Tax + cost of dinner= d + 0.08d

Coupon for 10% discount after tax

10% coupon discount means she will pay 100% - 10%( coupon)

=90%

Price=90%(d + 0.08d)

=0.9(1.08d)

She added 16% tip to the total cost before any price or discount was applied

16% of d

=0.16*d

=0.16d

New price= 0.09(1.08d) + 0.16d

=0.972d + 0.16d

=1.132d

Answer:

(4,2) is the answer on AP EX

The coordinate of the image of point A is (-4,-2)

Transformation is the process of changing the graph to a new graph by Rotation, Reflection, Translation, and Dilation.

The coordinate of A is (4,-2)

When it is reflected across y axis, the coordinate (x,y) changes to ----> (-x,y)

So, the coordinates of A (4,-2) changes to (-4,-2)

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Answer:

The measure of one angle is 81.3° and the other angle is 8.7°.

Step-by-step explanation:

We are given that two angles are complementary. One angle's measure is 3 more than 9  times the other angle.

Let the measure of one angle be 'x' and the measure of other angle be 'y'.

So, according to the question;

                                 x + y = 90°

                                 x = 90° - y  ---------------- [equation 1]

                             x = 3 + 9y ------------ [equation 2]

Now, both the equations we get;

90 - y = 3 + 9y

9y + y = 90 - 3

10y = 87

[tex]y=\frac{87}{10}[/tex] = 8.7°

Now, putting the value of y in equation 1 we get;

                x = 90° - y

                x = 90° - 8.7° = 81.3°

Hence, the measure of one angle is 81.3° and the other angle is 8.7°.

Answer:

Reflection.

Step-by-step explanation:

Reflection moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding pre-image and image points.

On the other hand, "Translation" moves points the same distance along lines that are parallel to each other while "Rotation" moves points along concentric circles and through the same angle of rotation.

At an angle of 90°, a line of reflection intersects the line segments connecting corresponding points of the pre-image under a reflection.

Basically, a reflection allows us to flip an object or figure across a line, point or plane without any change in its shape or size.

Hence, to reflect an object or a figure such as a triangle simply means that its mirror image would be produced with respect to a line; this line is generally referred to as the line of reflection.

Answer:

1001.66 in²

Step-by-step explanation:

radius=r=diameter/2

r=22/2=11

l is the slant =18

surface area of a cone= area of circle + area of the curved part of cone

SA=πr²+πrl

SA=3.14(11)²+3.14(11)(18)=1001.66 in²

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Hi my lil bunny!

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If an octagon is 24, how many is a pentagon?

Ans : Pentagon has 5 sides.

( A five-sided shape is called a pentagon. A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has eight sides. The names of polygons are derived from the prefixes of ancient Greek numbers. )

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

The pentagon is 15, when octagon is 24.

What is Polygon?

A polygon is a figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides).

Polygon with 8 sides known as Octagon and polygon with 5 sides known as Pentagon.

Here, given that, Octagon = 8 sides = 24

So, 1 side= 3

Then, we get, pentagon = 5 sides = (5×3) = 15

Hence, the pentagon is 15.

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Answer:

h = 108.8 m

Step-by-step explanation:

x = tanФ h

x = 68m

Ф = 32°

h = unknown

68 = tan(32°) * h

h = 68 / tan(32°)

h = 108.8 m

Answer:

1. u = 2, v = -1.5

2. y = -7, x = -3

Step-by-step explanation:

1) For the following simultaneous equation, we have;

5·u + 2·v = 7....................(1)

2·u - 2·v = 7......................(2)

Adding equation (1) to equation (2), gives;

5·u + 2·v + 2·u - 2·v = 14

5·u + 2·u + 2·v- 2·v   = 14

7·u = 14

u = 14/7 = 2u = 2

u = 2

From equation (1), we have;

5·u + 2·v = 7 substituting u = 2 gives;

5×2 + 2·v = 7

2·v = 7  - 5×2 = 7 - 10 = -3

v = -3/2 = -1.5

v = -1.5

2.

3·x - 4·y = 19....................(1)

4·x - 5·y = 23.......................(2)

Multiplying  equation (1) by 4 and equation (2) by 3 gives;

For equation (1)

4 × (3·x - 4·y) = 4 ×19

12·x - 16·y = 76...........................(3)

For equation (2)

3 × (4·x - 5·y) = 3 × 23

12·x - 15·y = 69...........................(4)

Subtracting equation (3) from equation (4) gives;

12·x - 15·y - (12·x - 16·y) = 69 - 76 = -7

12·x - 15·y - 12·x + 16·y = 69 - 76 = -7

12·x - 12·x - 15·y + 16·y = -7

y = -7

Substituting the value of y = -7 in equation (1), we have;

3·x - 4·y = 19 = 3·x - 4×(-7) = 19

3·x - 4×(-7) = 19

3·x + 28 = 19

3·x = 19- 28  = -9

x = -9/3 = -3

x = -3.

Answer:

134

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

x = 1/2 ( m DH + m BC)

x = 1/2 (144+ 124)

x = 1/2 ( 268)

x = 134

Answer:

x = 24

Step-by-step explanation:

We know that lines s and t are parallel. Then by definition, the two labelled angles, which are same-side angles, are congruent and equal in measure.

Then, we set the expressions equal to each other:

7x - 48 = 5x

Subtract 5x from both sides:

7x - 5x - 48 = 0

2x - 48 = 0

Add 48 to both sides:

2x = 48

Divide by 2:

x = 48/2 = 24

Thus, x = 24.

~ an aesthetics lover

Answer:

x² + 4x + 4 = 0

Step-by-step explanation:

x² + 4x + 4 = 0

( x + 2 )² = 0

x + 2 = 0

x = -2

x² + x = 0

x ( x + 1 ) = 0

x = 0 or x = -1

x² - 1 = 0

x² = 1

x = 1 or x = -1

Answer:

10.5 m²

Step-by-step explanation:

Given:

∆ with 2 side lengths, 4.7m, 6.1m, and an included angle, 47°.

Required:

Area of the triangle

SOLUTION:

Area of such triangle that has 2 known sides and an included angle between them is given as ½*a*b*sin(θ).

Where,

a = 4.7 m

b = 6.1 m

θ = 47°

Area = ½*4.7*6.1*sin(47)

Area = 10.5 m² (to the nearest tenth)

Answer:

Step-by-step explanation:

if x is the bill and y is the tip ten

x+y>14.50

x<2   and  x≤ 2

when the sign is< then the dot has to be clear , because 2 does not count and x is less than 2 and not equal to 2

when the sign is ≤ the dot on the graph is solid which represent the equal to.