What is the explicit rule for this geometric sequence?

a1=4; an=13·an−1




an=4(1/3)n−1

an=1/3⋅4n

an=1/3⋅4^n−1

an=4(1/3)n

      Statement                      Reason

1. AB = CD, AD = CB           1. Given

2. AC = AC                          2. Reflexive Property

3. ΔADC ≅ ΔCBA                3. SSS

4. ∠1 = ∠4                             4. CPCTC

5. DC || AB                            5. Alternate Interior Angles Converse Thm

Answer:

2l + 3 = 39

Step-by-step explanation:

the equation is 3 + 2L = C, where L is Lindsay's age and C is Carol's age

3 + 2L = 39

Answer:

B

Step-by-step explanation:

We have perpendicular bisector through a chord of the circle. We know the length, so either side of the chord is 11 due to the bisector cutting it directly in half. Since the radius is a fixed distance from the center to any point on the edge of the circle, we can draw the radius x from the circle to the end of the chord to form a right triangle.

We can use Pythagorean Theorem [tex]a^{2} +b^{2} =c^{2}[/tex] to find the missing side length x. a=6, b=11 and c=x.

[tex](6)^{2} +(11)^{2} =x^{2}[/tex]

[tex]36+121=x^2\\157=x^2\\\sqrt{157}=x\\ 12.5=x[/tex]

Answer:

x = 32

Step-by-step explanation:

This is an equilateral triangle, all three sides equal.  Since all three sides are equal, all three angle are equal.  180/3 = 60.  That means each angle is equal to 60 degrees.

2x-4 = 60

Add 4 to each side

2x-4+4 = 60+4

2x =64

Divide each side  by 2.

2x/2 = 64/2

x = 32

Answer:

14.4 yards

Step-by-step explanation:

Each shirt needs 0.8 yards so 18 shirts needs 18 * 0.8 = 14.4 yards of material.

14.4 yards of material will be needed to make 18 shirts.

Multiplication is when you take one number and add it together a number of times.

Given that, one shirt is of 0.8 yards of material,

18*0.8 = 14.4

Hence, 14.4 yards of material will be needed to make 18 shirts.

For more references on Multiplication, click;

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The first thing to notice is that the smaller triangle on the left is equilateral, because of the same single tickmarks on each of the three sides. For any equilateral triangle, each interior angle is 60 degrees as you have marked it on the drawing.

Once you determine that, you would solve for the 120 degree angle (60+120 = 180). Afterward, solve the equation 120+x+x = 180 to find that x = 30. The equation 120+x+x = 180 refers to adding up the three angles of the smaller triangle on the right side (with angles 120, x, x). The two missing angles are both x due to the fact that this triangle is isosceles.

Answer:

Step-by-step explanation:

Since ∆ABC is equilateral, all of its angles would be the same (60°). Since a line is 180°, the other part of ∠C is 120°. Since we also know that △BCD is isosceles, we know that angles ∠B and ∠D are equal. If a triangle is 180°, and we already know that ∠C is 120°, we can do 180-120, which is 60°. If angles ∠B and ∠D are equal, we can do 60/2=30. Therefore, ∠D is 30°.

Answer:

angle C is 60 degrees

Step-by-step explanation:

First you would solve for X

once you have that plug it in angle C

2(30)=60

Answer:

60°

Step-by-step explanation:

∠B is a right angle and all right angles are 90°, so if ∠B = 3*x then to find x you divid 3 by 90 to get x because 3*x = 90 once you do that you get 30 so x=30 then to find ∠C you just multiply 2 by 30 which gives you 60 which means the measure of ∠C = 60°

hope this helps :D

Answer:

(D)

Step-by-step explanation:

Two triangles are similar if it satisfies the following properties:

1) Corresponding angles are congruent.

2) Corresponding sides are all in same proportion.

Here, ΔSTU and ΔVWX are given, where ∠S is congruent to ∠V.

To prove these two triangles similar, we need one more corresponding angle to be congruent.

And from all the options, (d) Angle U is congruent to angle X. will help in proving ΔSTU and ΔVWX similar triangles.

Therefore, (d) is correct.  

Answer:

d)Angle U is congruent to angle X.

Step-by-step explanation:

25 friends because 7*5=35

Answer:

hello :

the graph passes by ( -4; 7/128)  : f(-4) = 7/128

a/ (-4)^4 = 7/128

a / 256 = 7/128

a/2 = 7

a = 14

We have the point:

[tex]\left(-4,\ \dfrac{7}{128}\right)[/tex]

Put the coordinates of the point to the equation of the function f:

[tex]f(x)=\dfrac{a}{x^4}\to y=\dfrac{a}{x^4}\\\\\left(-4,\ \dfrac{7}{128}\right)\to x=-4,\ y=\dfrac{7}{128}\\\\\dfrac{a}{(-4)^4}=\dfrac{7}{128}\\\\\dfrac{a}{256}=\dfrac{7}{128}\qquad\text{multiply both sides by 256}\\\\a=\dfrac{7}{128}\cdot256\\\\\boxed{a=14}[/tex]

Answer:

190 percentage of the weight limit is 114 pounds.

Step-by-step explanation:

Given: A rocking horse has a weight limit of 60 pounds.

We have to find what percentage of the weight limit is 114 pounds.

x percentage of the weight limit is 114 pounds.

⇒ x% of 60 = 114

[tex]\frac{x}{100} \times 60 = 114[/tex]

Solve for x;

[tex]\frac{6x}{10} = 114[/tex]

Multiply both sides by 10 we get;

[tex]\frac{6x}{10} \times 10 = 114 \times 10[/tex]

[tex]6x = 1140[/tex]

Divide both sides by 6 we get;

[tex]x = \frac{1140}{6}[/tex]

Simplify:

x = 190%

Therefore, 190 percentage of the weight limit is 114 pounds.

To find the percentage, divide the given weight by the weight limit and multiply by 100. 114 pounds is 190% of the weight limit of 60 pounds.

To find the percentage of the weight limit, we need to divide the given weight (114 pounds) by the weight limit (60 pounds) and then multiply the result by 100. So, the calculation would be:

Percentage = (114 pounds / 60 pounds) * 100

Simplifying this equation, we get:

Percentage = 190%

Therefore, 114 pounds is 190% of the weight limit of 60 pounds.

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Answer: [tex]\bold{\dfrac{1}{36}}[/tex]

Step-by-step explanation:

The first die can be any number:  [tex]P = (\dfrac{6}{6}) = 1[/tex]

The second die must match the first die: [tex]P = \dfrac{1}{6}[/tex]

The third die must also match the first die: [tex]P = \dfrac{1}{6}[/tex]

1st die   and   2nd die   and    3rd die  =  Probability of success

   1          x          [tex]\dfrac{1}{6}[/tex]             x          [tex]\dfrac{1}{6}[/tex]         =               [tex]\dfrac{1}{36}[/tex]

Answer:

2

Step-by-step explanation:

We can find the average rate of change by using the formula

rate of change = (y2-y1) /(x2-x1)

                         = (5-3)/(1-0)

                         = 2/1

                            =2

Answer:

A. 2

Step-by-step explanation:

average rate of change from x1 to x2 is

[f(x2) - f(x1)]/(x2 - x1)

Here we have x1 = -3; f(x1) = -3; x2 = 1; f(x2) = 5

average rate of change from x1 to x2 =

= [f(x2) - f(x1)]/(x2 - x1)

= [5 - (-3)]/(1 - (-3))

= 8/4

= 2

Answer:

3 brownies

Step-by-step explanation:

To find this answer we need to divide the 0.81 by 0.27 to find out how many brownies total 0.81:

0.81 ÷ 0.27 = 3

So he needs to sell 3 brownies.

Answer:

3187.59

Step-by-step explanation:

Add 4250 - 25% + 9% and u should have this exact answer

- The one guy who has a F in math

Answer: D

Step-by-step explanation:

Inverse is when the x's and y's are swapped

x   |   y        Inverse

-3 |   5         (5, -3)

-2 |  -3         (-3, -2)

0 |   3          (3, 0)

1  |  -5         (-5, 1) ← this matches choice D

2  |   6          (6, 2)

3  |  10          (10, 3)

well, we don't have to use the pythagorean theorem per se, only the distance formula, since the distance formula is really the pythagorean theorem in disguise.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MN=\sqrt{[4-5]^2+[-8-(-3)]^2}\implies MN=\sqrt{(4-5)^2+(-8+3)^2} \\\\\\ MN=\sqrt{(-1)^2+(-5)^2}\implies MN=\sqrt{26}[/tex]

Answer: [0, 6) ∪ (6, 15]

Step-by-step explanation:

The particle is moving to the right when the velocity is positive.

[tex]s(t)=\dfrac{t^3}{3} -\dfrac{12t^2}{2}+36t[/tex]

v(t) = s'(t)

     = t² - 12t + 36

First, find the zeros of v(t): ⇒ v(t) = 0

  0 = t² - 12t + 36

     = (t - 6)²

0 = t - 6

6 = t

The zero occurs when t = 6

Next, find when v(t) > 0

Choose a test point between 0 and 6:

v(5) = (5 - 6)²

     =     (-²)

     =      (+)

Since velocity is positive between 0 and 6, the particle is moving to the right during that interval.

Choose a test point between 6 and 15:

v(7) = (7 - 6)²

     =    (+)²  

     =    (+)

Since velocity is positive when t > 6, the particle is moving to the right.

Answer:

When f(x) is 0, then x is -1.8.

Step-by-step explanation:

To find this, you simply have to look for the place where the line crosses the x axis. This is where y (or f(x)) is equal to 0. Since this graph only crosses that axis at x = -1.8, that is the number we are looking for.

Answer: 6.3093

Step-by-step explanation:

[tex]3^{\frac{x}{5}} = 4[/tex]

[tex]ln3^{\frac{x}{5}} = ln4[/tex]

[tex]\frac{x}{5} ln3 = ln4[/tex]

xln3 = 5ln4

[tex]x = \frac{5ln4}{ln3}[/tex]

x = 6.3093

************************************************************

Answer: 5, 3, [tex]\frac{1}{5}[/tex], D

Step-by-step explanation:

a) x ≤ 0 so, f(-5) = | -5 | = 5

   x ≤ 0 so, f(-3) = | -3 | = 3

   x > 0 so, f(5) = [tex]\frac{1}{5}[/tex]

b) graph D

************************************************************

Answer: [tex]\frac{\pi}{12}[/tex]

Step-by-step explanation:

 [tex]\frac{25\pi}{12} - \frac{2\pi}{}[/tex]

=  [tex]\frac{25\pi}{12} - \frac{24\pi}{12}[/tex]

=  [tex]\frac{\pi}{12}[/tex]

TJKL - different letters

for the first place you have 4 letters to choose from

for the second place you have 3 letters to choose from

for the third place you have 2 letters to choose from

for the last place you have only one letter

Therefore your answer is:

[tex]\boxed{4}\cdot\boxed{3}\cdot\boxed{2}\cdot\boxed{1}=24\to\boxed{D)}[/tex]

[tex]2)\\\\6+5k+2=18\\\\(6+2)+5k=18\\\\8+5k=18\qquad\text{subtract 8 from both sides}\\\\5k=10\qquad\text{divide both sides by 5}\\\\\boxed{k=2}\\\\4)\\\\-8(a-8)=96\qquad\text{divide both sides by (-8)}\\\\a-8=-12\qquad\text{add 8 to both sides}\\\\\boxed{a=-4}[/tex]

[tex]6)\\7m+35=7(5m-3)\qquad\text{divide both sides by 7}\\\\m+5=5m-3\qquad\text{subtract 5 from both sides}\\\\m=5m-8\qquad\text{subtract 5m from both sides}\\\\-4m=-8\qquad\text{divide both sides by (-4)}\\\\\boxed{m=2}[/tex]

Answer:

A

Step-by-step explanation:

The transformation is [tex]h(x)=4*g(x+5)[/tex].

The answer is A.  The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the left.

Answer: A for plato users

Answer: The meaning y-intercept is the initial value of a rare coin is 6.

Step-by-step explanation:

Given : The graph of [tex]f(t) = 6\times 2^t[/tex] shows the value of a rare coin in year t.

The y- intercept is the point on Cartesian plane when the graph intersects y axis. It given the initial value of the function by substituting the value of independent variable as zero.

i.e. , we need to put t=0, we get

[tex]f(0) = 6\times 2^0=6[/tex]

The meaning y-intercept is the initial value of a rare coin is 6.