Which sequence is geometric and has `1/4` as its fifth term and `1/2' as the common ratio?
O A..., 1, 1/2", 1/4", 1/8"...
B..., `1/4,' 1/2,' '1, 2, ...
O C.., 1/72", 1/36', '1/18', '1/9 ,...
OD..., 8,' '4,' '2,' 1,' ....​

The Question is Incomplete, the Complete Question is with figure is below.

Answer:

Therefore,

The Measure of angle 6 is

[tex]\angle 6 =45\°[/tex]

Step-by-step explanation:

Given:

m∠1 = 135°

Lines b and c are parallel.

To Find:

m∠6 = ?

Solution:

Linear Pair:

A linear pair of angles is formed when two lines intersect.  

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.  

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.  

Example

∠ 1 and ∠ 2 ∠ 1 and ∠ 3 ,etc

[tex]\angle 1 + \angle 3 = 180\°[/tex]

Substituting the values we get

[tex]135 + \angle 3 = 180\\\\\angle 3 = 180-135=45\°[/tex]

Now,

Lines b and c are parallel.  .Given

When Two lines are Parallel Alternate interior angles are equal

∠ 3 and ∠ 6 are Alternate Interior angles

[tex]\angle 3 = \angle 6[/tex]

But [tex]\angle 3 =45\°[/tex]

[tex]\angle 6 =45\°[/tex]     ...Transitive Property

Therefore,

The Measure of angle 6 is

[tex]\angle 6 =45\°[/tex]

Step-by-step explanation:

Given:

Number of packets at the beginning of the day, Nb = 36 packets

Number of packets at the end of the day, Ne = 8 packets

A.

Number of packets sold, Ns = Nb - Ne

36 - Number of packets sold, Ns = Ne

8 = 36 - Ns

Ns = 28

B.

8 = 36 - Ns

8 = 36 - 28

Final answer:

The expression representing the number of juice boxes sold is 28 multiplied by x, where x is the number of juice boxes per package. Since x is unknown, the expression cannot be simplified further and remains as 28 × x.

Explanation:

Part A: Representing the Number of Juice Boxes Sold

To represent the number of juice boxes sold, let's denote the number of juice boxes in each package as x. The store started with 36 packages and ended with 8. We are looking for the number of juice boxes in the packages that were sold. The expression is:

28 × x (since 36 - 8 = 28, and 28 packages were sold)

Part B: Simplifying the Expression

To simplify the expression, we do not have further information to simplify 28 × x more because x represents an unknown number of juice boxes per package. The simplified expression remains as:

28 × x

Answer: 8 tablespoons

Step-by-step explanation:

If 1 doz muffins= 4 teapoons = 4/3 tablespoon

6 dozens muffin= 4/3 × 6

24/3 = 8 tablespoon

Answer:

8 tablespoons

Step-by-step explanation:

Answer:

HE will have 10 fingers

Step-by-step explanation:

Answer:

what region

Step-by-step explanation:

Square B

The complete question is written in a comment above. The doctor's office where you work needs to store eight filing cabinets with patient information in one of three secure storage rooms. We know that the filing cabinets need a total of 55 square feet of space. You need to identify in which room the filing cabinets will fit. So we have three rooms:

FIRST OFFICE:

[tex]Square \ A = 8 \times 5[/tex]

In other words, for this room we have the following area:

[tex]Square \ A =40ft^2[/tex]

SECOND OFFICE:

[tex]Square \ B = 9 \times 7.5[/tex]

In other words, for this room we have the following area:

[tex]Square \ B =67.5ft^2[/tex]

THIRD OFFICE:

[tex]Square \ C = 5 \times 10[/tex]

In other words, for this room we have the following area:

[tex]Square \ C =50ft^2[/tex]

How can we know what is the room we need to choose?

Well, the room we need to choose is the one whose area is greater than the area of the filling cabinets. In other words, let's call square x the unknown room, then:

[tex]Square \ x>55ft^2[/tex]

From the, choices the only room that meets our requirements is square B because:

[tex]Square \ B>55ft^2 \\ \\ 67.5ft^2>55ft^2[/tex]

Measure the length and width of a room in feet to calculate its area. Multiply these dimensions to get the area in square feet. The filing cabinets need a room with at least 55 square feet.

To determine whether the filing cabinets will fit into a room, we must calculate the area of the room and see if it is at least 55 square feet, the space required for the filing cabinets.

To calculate the area of a room in square feet, measure the length and width of the room in feet and then multiply these numbers together.

For example, if a room is 10 feet wide and 5.5 feet long, its area would be 10 feet times 5.5 feet, which equals 55 square feet. Therefore, the filing cabinets would fit in a room of this size.

Answer:

A.

Step-by-step explanation:

All of the other questions don't make sense because they are statistical

The length of SK = 10 units while the length of BK = 8.6602 units.

Step-by-step explanation:

Step 1:

In the given triangle, there are two right-angles triangles with 60° angles. The central line BK is the opposite side for both the triangles. For triangle RK the hypotenuse's length is 10 m. Assume BK = x units and SK = y units.

Step 2:

So first we calculate the length of BK (x).

As we have the values of the angle of the triangle and the hypotenuse, we can calculate the sine of the angle to determine the value of x.

[tex]sin R = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{x}{10}.[/tex]

[tex]sin 60 = 0.86602, x = 0.86602 (10) = 8.6602 units.[/tex]

So x = BK = 8.6602 units.

Step 3:

So now we calculate the length of SK (y).

As we have the values of the angle of the triangle and the opposite side's length, we can calculate the sine of the angle to determine the value of y.

[tex]sin S = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{86.602}{y}.[/tex]

[tex]sin 60 = 0.86602, y = \frac{8.6602}{0.86602} = 9.999units = 10 units[/tex]

So y = SK = 10 units.

Answer:

warm air toward high latitudes

Step-by-step explanation:

Known to sailors around the world as the doldrums, the Inter-Tropical Convergence Zone, (ITCZ, pronounced and sometimes referred to as the “itch”), is a belt around the Earth extending approximately five degrees north and south of the equator. From google

The atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.

An atmosphere is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body.

The atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.

This is because the Earth's surface is heated unequally due to differences in solar radiation and other factors.

The equator receives more direct sunlight and is therefore warmer, while the poles receive less direct sunlight and are cooler.

As a result, warm air rises at the equator and cool air sinks at the poles, creating a circulation pattern in the atmosphere known as the Hadley cell.

Hence, the atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.

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Answer:

$486

Step-by-step explanation:

Step 1:  Solve

(450 * 0.9) * 1.2

405 * 1.2

486

Answer:  $486

Answer: x=16

Step-by-step explanation:subtract 26 from 90 then divide 64 by 4 and you get 16

Answer:

X=16

Step-by-step explanation:

The answer is 16. 90-26/4=16

Answer:

$35

Step-by-step explanation:

To solve this problem you need to know how what and how is percentage work.

Percentage(%) is a unit that equals to 1/100 or one hundredths. So, 7% will be equal to 7*1/100= 7/100. The commission is given based on the price of the boat. If the boat sold at $500 the commission will be:

commission= percentage * boat price

commission= 7/100 * $500

commission= $35

x = 7 and x = –7.

Solution:

Given data:

[tex]$f(x)=x^{2}+15[/tex] and [tex]f(x)=64[/tex]

To find the solutions when f(x) = 64.

Both are equations of f(x), so equate the given equations, we get

[tex]x^2+15=64[/tex]

To isolate the constant term subtract 15 from both sides.

[tex]x^2+15-15=64-15[/tex]

[tex]x^2=49[/tex]

49 can be written as 7².

[tex]x^2=7^2[/tex]

Taking square root on both sides of the equation, we get

x = ±7

The solutions to f(x) = 64 is x = 7 and x = –7.

Answer: 2^4+7 -5^3

Step-by-step explanation:

Answer:

(2 to the power of 4 )plus 7 minus( 5 to the power of 3)

Step-by-step explanation:

Answer:

6x-15 = 4x+12

Step-by-step explanation:

3*2x = 6x

3*-5 = -15

4*x=4x

4*3=12

6x-15 = 4x+12

Answer:

6x - 15 = 4x + 12

Explanation:

Simplify 3 * 2x = 6x. 3 * -5 =  -15. 4 * x = 4x. And 4 * 3 = 12. Then just put 'em together! :D

The cost of wire to purchase is Rs 264.

Step-by-step explanation:

Given,

The diameter of the circular garden is 21 m

The radius(r) = [tex]\frac{21}{2}[/tex] m

To find, the length of wire of the fence we need to find the circumference.

Formula

The circumference of the circle = 2πr meter

=2×[tex]\frac{22}{7}[/tex] ×[tex]\frac{21}{2}[/tex] m

=66 meter

So, the length of the wire = 66 m

The cost of wire Rs 4 per meter.

The total cost = Rs 4 × 66

= Rs 264

Answer:

6

Step-by-step explanation:

The question might be trying to be tricky. If Prince Humperdinck has 17 henchmen and ALL BUT 6 die. That means that 6 are alive.

Answer:

x = 32

Step-by-step explanation:

Step 1:  Subtract 12 from both sides

x/8 + 12 - 12 = 16 - 12

x/8 = 4

Step 2:  Multiply both sides by 8

x/8 * 8 = 4 * 8

x = 32

Answer:  x = 32

Answer:

Step-by-step explanation:

[tex]\frac{x}{8}+12=16\\\\\frac{x}{8}=16-12\\\\\frac{x}{8}=4\\\\x=4*8\\\\x=32[/tex]

Answer: A. 80.61

Step-by-step explanation:

Answer:

[tex]0.125 \ in^3[/tex]

Step-by-step explanation:

Given the sides of the cube as 0.5 inch.

#the volume of a cube is calculated as the product of the three sides:

[tex]V=s^3, \ \ \ \ s=0.5in\\\\V=0.5\ in\times 0.5\ in\times 0.5\ in\\\\V=(0.5\ in)^3\\\\V=0.125\ in^3[/tex]

Hence, the volume of Mary's cube is 0.125 cubic inches

Answer:

Reflectional Symmetry

Answer:

9.86 / 0.85 = 11.6

Step-by-step explanation:

Answer:

t = 1/2

Step-by-step explanation:

6 - (3t+4) = t

Distribute the minus sign

6 - 3t -4 = t

Combine like terms

2 -3t = t

Add 3t to each side

2 -3t +3t = t+3t

2 = 4t

Divide each side by 4

2/4 =4t/4

1/2 =t

Answer:

6-(3t+4)=t

6-3t-4=t

6-4=t+3t

2=4t

t=2/4

Answer:

Part A) The graph in the attached figure

Part B) see the explanation

Step-by-step explanation:

Part A) Graph the function

we have the quadratic function

[tex]y=3x^2-12x-36[/tex]

This is a vertical parabola open upward

The vertex is a minimum

using a graphing tool

The graph in the attached figure

Part B) What are the values of a, b and c?

we know that

The values of a and b represent the x-intercepts of the quadratic equation

The x-intercepts are

(-2,0) and (6,0)

so

[tex]a=-2\\b=6[/tex]

Find the value of c

we know that

The x-coordinate of the vertex in a vertical parabola is equal to the midpoint of the roots

so

The value of c is equal to

[tex]c=\frac{a+b}{2}[/tex]

substitute the given values

[tex]c=\frac{-2+6}{2}=2[/tex]

see the attached figure

The solutions to quadratic equation are:

[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]

Solution:

Given is:

[tex]x^2 - 3x + 3 = 0[/tex]

We have to find the solutions to quadratic equation

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-3,\:c=3:\\\\x=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}[/tex]

[tex]x=\frac{3 \pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}\\\\x = \frac{3 \pm \sqrt{-3}}{2}\\\\x = \frac{3 \pm i \sqrt{3}}{2}[/tex]

We have two solutions :

[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]

The solutions to the quadratic equation x^2 - 3x + 3 = 0 can be found using the Quadratic Formula. The solutions are complex numbers: x = 3/2 ± (i*sqrt(3))/2.

The given equation is a quadratic equation of the form ax^2 + bx + c = 0. To find the solutions to this equation, we can use the Quadratic Formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here a=1, b=-3, c=3.

Plugging these values into the formula,

we get x = [3 ± sqrt((-3)^2 - 4*1*3)] / (2*1).

Simplifying this equation will give us x = [3 ± sqrt((9 - 12)] / 2.

Now, note that the value under the square root is negative, indicating that the solutions will be complex.

Finally, we have the solutions:

x = [3 ± sqrt(-3)] / 2

= 3/2 ± (i*sqrt(3))/2, where 'i' is the imaginary unit.

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8320 cubes can fit into the prism.

Solution:

Convert mixed fraction into improper fraction.

Length of the prism = 20 in

Width of the prism = 2 in

Height of the prism = [tex]3\frac{1}{4}=\frac{13}{4}[/tex] in

Volume of the prism = length × width × height

                                 [tex]$=20\times2\times\frac{13}{4}[/tex]

                                 = 130 in³

Volume of the prism = 130 in³

Length of the cube = [tex]\frac{1}{4}[/tex] in

Volume of the cube = length × length × length

                                 [tex]$=\frac{1}{4} \times\frac{1}{4} \times\frac{1}{4}[/tex]

                                 [tex]$=\frac{1}{64} \ \text{in}^3[/tex]

Volume of the cube = 0.015625 in³

[tex]$\text{Number of cubes}=\frac{\text{Volume of the prism}}{\text{Volume of cube}}[/tex]      

                            [tex]$=\frac{130}{0.015625}[/tex]

                            = 8320

Number of cubes = 8320

Hence 8320 cubes can fit into the prism.

Answer:

x = 4, y = -5 OR (4, -5)

Step-by-step explanation:

Step 1:  Solve for y in the first equation

2x + y - 2x = 3 - 2x

y = 3 - 2x

Step 2:  Plug in that into the second equation to get x

4x + 3(3 - 2x) = 1

4x + 9 - 6x = 1

-2x + 9 - 9 = 1 - 9

-2x / -2 = -8 / -2

x = 4

Step 3:  Use x to find y

y = 3 - 2(4)

y = 3 - 8

y = -5

Answer:  x = 4, y = -5 OR (4, -5)

Answer:x<29

Step-by-step explanation:

X<29