Determine whether each infinite geometric series diverges or converges.
If the series converges, state the sum. 1+ 1/4 + 1/16 + . . . .

Answer:

(1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7), (-4,8), (-5,9), & (-6,10)

Step-by-step explanation:

First, solve to alter the equation into a slope form instead of in standard form.

x+3y=12

Because x represents the slope, we need to transfer it to the other side of the equation. By subtracting it, it'll allow the equation to only have 3y on the left side of the equation and x will become negative x which will be added on to the 12 on the right side.

x+3y=12

-x       -x

+3y=-x+12

3y=-x+12

Next, you would divide the 3 underneath the y and the number 12 to allow the 3y to become y because y needs to be isolated in order for the slope intercept formula to work.

3y divided by 3 equals 3 and 12 divided by 3 is 4.

3y/3=-x+12/3

The final equation would look as follows:

y=-x+4

Hence, the y-intercept is 4 and the slope is -1.

You would then plot the origin coordinate of (0,4) and either go down one and right one or up one and left one; either way, you'll receive a negative slope looking like this: \

Some points on the graph would be: (1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7)

Hope this helps.

Answer:

1

Step-by-step explanation:

replace x with -7

f(-7) = 5 - (-7)

f(-7) = 5 + 7

f(-7) = 12

Answer:

70,951 rounded to the nearest hundred is 71,000.

Step-by-step explanation:

The sale price is $80.

Here the original price is $80.

there is no any valid data to find sale price so sale price should be$80

Profit and loss are expressions used to determine whether or not a sale is economic. In our diurnal lives, we use these expressions frequently. However, the difference between the two is appertained to as profit, If the selling price is advanced than the cost price. However, the difference is appertained to as the loss, If the selling price is lower than the cost price. The cost price of a product is the price at which it's bought. The selling price of a thing is the price at which it's vended. In this essay, we will study further about profit and loss.

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Answer:

B

Step-by-step explanation:

The rise is +7, and the run is -6

so, -6, +7

Answer:

w1= -1.4, w2= 3

Step-by-step explanation:

I will assume that "x" is a w since there is no x within the question

Solution

w

1

=−

5

7

,w

2

=3

Alternative Form

w

1

=−1.4,w

2

=3

Evaluate

5×∣4w−1∣=5w+40

Simplify

5∣4w−1∣=5w+40

Rewrite the expression

5∣4w−1∣−5w−40=0

Separate the equation into 2 possible cases

5(4w−1)−5w−40=0,4w−1≥0

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,4w−1≥0

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,w≥

4

1

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,w≥

4

1

w=−

5

7

,4w−1<0

Evaluate

w=3,w≥

4

1

w=−

5

7

,w<

4

1

Find the intersection

w=3

w=−

5

7

,w<

4

1

Find the intersection

w=3 w=− 57

Solution

w

1

=−

5

7

,w

2

=3

Alternative Form

w 1=−1.4,w 2

=3

Answer:

4521 is a rational number because it can be expressed as the quotient of two integers: 4521 ÷ 1.

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number

Hope this helps

The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the tree. Hence the distance to the top of tree = 3h + 2.

Using Pythagoras theorem:

(3h + 2)² = h² + 70²

9h² + 12h + 4 =  h² + 70²

8h² + 12h - 66 = 0

h = 2.22 feet

The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree

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The value of s in the given figure is 28

The given parameters are:

m<TUW = m<VUW =62 degrees

TW = s + 56 and VW= 3s

From the figure, we have the following congruent equation

TW = VW

This means that

s + 56 = 3s

Evaluate the like terms

So, we have

2s = 56

Divide both sides of the equation by 2

So, we have:

s = 28

Hence, the value of s in the given figure is 28

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The perimeter of the given rectangle is (A) 20 units.

The formula of the perimeter of the rectangle: 2(l + b)

Now, substitute values:

Therefore, (A) 20 units are the perimeter of the given rectangle.

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The correct question is given below:
What is the perimeter of the rectangle shown below?

Answer:

5(2) + 5(-3)

Step-by-step explanation:

10 + -15 = -5

A Canadian geese moved 4 miles every 7 minutes, consistently.

Part 1 out of 3.

Distance: 4,8,12,16,20,24,28

Time: 7,14,21,28,35,42,49

Time is an interval of time that is hours and minutes after midnight or noon.

Distance is a distance between two objects or individuals.

Given that,

A Canadian geese moved 4 miles every 7 minutes, consistently.

Distance: 4,8,12,16,20,24,28

Time: 7,14,21,28,35,42,49

Therefore, the table is

Distance: 4,8,12,16,20,24,28

Time: 7,14,21,28,35,42,49

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Answer:

-52

Step-by-step explanation:

fill in the x and y values and multiple it and then combine it

The supplementary angles are 60 degrees and 120 degrees

Two angles are said to be supplementary when their measure add up to 180 degrees.

Therefore, if x and y are supplementary angles,

x + y = 180

x represent the degree measure of the​ angle's supplement.

The measure of the angle is two times greater than its supplement.

Therefore, the algebraic expression of the angles is as follows:

x + 2x = 180

3x = 180

divide both sides by 3

3x / 3 = 180 / 3

x = 60

Therefore, the supplementary angles are 60 degrees and 120 degrees.

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A sketch of the required prism is as shown below.

In this question,

Josh is building a kaleidoscope using PVC pipe, cardboard, bits of colored paper, and a 12 -inch square mirror tile.

While making a kaleidoscope, the mirror tile is to be cut into strips and arranged to form an open prism, with a base like that of an equilateral triangle.

We need to make a sketch of the prism, giving its dimensions

As the base of the prism formed is an equilateral triangle, the mirror tile must be cut into three rectangular strips of equal width.

So, the width would be 12 ÷ 3 = 4 inches

The original tile is a 12-inch square, the length of each side of the square is 12 inches.

So the each rectangular strip will be 12 inches by  4 inches.

i.e., the length = 12 inches and width = 4 inches

Therefore, a sketch of the prism is as shown below.

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The value of 19 cubes is equal to 6859. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number is 19. The cube of 19 will be calculated as:-

19³ = 19 x 19 x 19

19³ = 6859

The cube of 19 is calculated by multiplying the number three times. Hence, the cube of 19 is 6859.

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The lengths of the diagonals are 8 and 24

Area of kite :

Area of kite is the space enclosed by a kite. A kite is a quadrilateral in which two pairs of adjacent sides are equal. The elements of a kite are its 4 angles, its 4 sides , and 2 diagonals.

In the given statement is :

Suppose the length of one diagonal of a kite is three times the length of the other diagonal. If the area of the kite is 96 square inches.

And, to find the lengths of the diagonals.

Now, Area of the kite is 96 sq. inches.

The length of one diagonal of a kite is x

and, other diagonal is three times to other diagonal

So, d2 = 3x

The area of a kite = 1/2 x (d1) x (d2)

96 = 1/2 × x × 3x

96 = [tex]\frac{3x^{2} }{2}[/tex]

192 = [tex]3x^{2}[/tex]

64 = x^2

x = [tex]\sqrt{64}[/tex]

x = 8

Therefore, The length of one diagonal is 8

and, other length of diagonal is 3x = 3x 8 = 24

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The value of -17-x is A. -13.

We are given the expression. To find the result, we need to solve the first expression. This will give the value of x. Further, we will be using the value of x to find the value of another expression.

-2 + x = -6

Shifting the value of -2 to the Right Hand Side of the equation

x = -6 + 2

Performing subtraction on Right Hand Side of the equation

x = -4

Now, keeping the value of x in second expression -

Value = -17 -(-4)

As there are two negative signs, the number 4 will be represented with positive sign

Value = -17 +4

Performing subtraction

Value = -13

Hence, the value of expression is A. -13.

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When you are given two sides but no measurement of the angle, such as a = 15 and b = 15, we can create an infinite number of triangles.

For instance:

How many different triangles can be made if we have side lengths of 15 and 15 and an angle value of 0 to 360 degrees?

Using a protractor, make one of the triangles with sides of 25 metres and 21 metres, an angle of 12 degrees, and a third side that can be changed to your preferred length. You've constructed a triangle.

Similar to this, we can create a completely different triangle by varying the third side's length and angle measurement.

It's crucial to remember that you select the side lengths and angle. This implies that you might choose differently. You may create an infinite number of distinct triangles by using the same angles.

As a result, we can make an infinite number of triangles using just one angle and one side length.

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9/4 cups of hot milk will be used by Chelsea.

As per the given information in question about custard, we know -

For 2/3 cups of sugar, the cups of hot milk required = 1(1/2)

Converting the number of cups of hot milk from mixed fraction to improper fraction -

Number of cups = (2×1 + 1)/2

Number of cups= (2 + 1)/2

Number of cups = 3/2

So, for 1 cup of sugar, the cups of hot milk required will be = (3/2) ÷ (2/3) × 1

Number of cups of hot milk required = (3×3) ÷ (2×2)

Number of cups of hot milk required = 9/4

Hence, for 1 cup of sugar 9/4 cups of hot milk will be used by Chelsea.

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Answer:1.052

Step-by-step explanation:

Answer:

45f - 42

Step-by-step explanation:

-5(-9f + 7) - 7

Expand -5(-9f +7) = -5(-9f) + (-5)(7) = +45f -35 or simply 45f - 35

5(-9f + 7) - 7  becomes 45f - 35 - 7 = 45f - 42

By elimination, the system of equations, 9a - 3d = 3 and -3a + d = -1, has infinite solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in a and d, a variable should be eliminated by adding/subtracting the two equations.

Simplifying the first equation by dividing it by -3,

9a - 3d = 3 ⇒ -3a + d = -1     (equation 1)

-3a + d = -1     (equation 2)

Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.

Hence, the system of equations has infinite solutions.

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The number of pensioners in the sample is 40.

Given,

Visitors to a cinema are either adults, children, or pensioners.

The ratio of children to adult visitors is 1:2.

The ratio of adults to pensioners is 3:4.

A stratified sample of 85 is to be taken from the cinema visitors.

We need to find out how many pensioners should be in the sample.

Example:

Out of 10 pens, the ratio of the red and blue pens is a:b

The number of blue pens = [ b / (a + b) ] x 10

The number of red pens = [ a / (a + b) ] x 10

We have,

Total number of visitors = 85

children:adult  = 1:2

adults:pensioners = 3:4

Here,

Let,

The number of children be C.

The number of adults be A.

Number of Pensioners be P.

Now,

1C : 2A

    : 3A : 4P

3C : 6A : 8P

Now,

3C + 6A + 8P = 85

This means 8 is the ratio of pensioners.

= 8 / (3 + 6 + 8) x 85

= (8 / 17)x 85

= 8 x 5

= 40

Thus the number of pensioners in the sample is 40.

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The property of real numbers illustrated by the equation  - [ -(x - 10)] = x-10 is Distributive property.

Distributive Property of real number is represented by the expression

a(b+c)=a*b+a*c.

For Example : 3(2+4)=3*2+3*4

                                  =6+12

                                  =18

In the given question ;

LHS  =-[-(x-10)]

First applying distributive property in side "[ ]".            

=  -[-x-(-10)]

= -[-x+10]   

Again applying distributive property , we get

= -(-x)-(+10)

= x-10  =RHS

Therefore , Distributive Property of Real numbers is illustrated by the equation  - [ -(x - 10)] = x-10.

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Answer:

8th grader

Step-by-step explanation:

They walked the the fastest since they walked 50 feet more than the 6th grader in 5 more seconds ( im sorry if you dont understand! i tried my best explaining it! hope this helps :) )

Answer:

The water cooler can hold approximately 23,6L

Answer: x=−8

Evaluate

2x−9=3x−1

Move the variable to the left side

2x−9−3x=−1

Subtract the terms

−x−9=−1

Move the constant to the right side

−x=−1+9

Add the terms

−x=8

Divide both sides

−1

−x

​

=

−1

8

​

Simplify

−1

−x =

−8

Solution

x=−8

Step-by-step explanation:

Hey!

2x-9=3x-1

Lets put the x on 1 side

2x 2x

- 2x -9= 3x-1

-9= x -1

-1 -1

-8 = x

X = -8 is your answer

Hope this helps!