Find the slope of the line.

Given:

4, x, y, 108 are the consecutive terms of a G.P.

To find:

The x and y.

Solution:

The nth term of a G.P. is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Let us consider 4, x, y, 108 are the first 4 terms of the G.P. Here 4 is the first term of the given G.P.

Suppose r  the common ratio, then 4th term of the given G.P. is:

[tex]a_4=4(r)^{4-1}[/tex]

[tex]a_4=4(r)^{3}[/tex]

The 4th term of the G.P. is 108.

[tex]4(r)^{3}=108[/tex]

[tex]r^{3}=\dfrac{108}{4}[/tex]

[tex]r^{3}=27[/tex]

[tex]r^{3}=3^3[/tex]

On comparing both sides, we get

[tex]r=3[/tex]

The common ratio is 3.

The second term of the given G.P. is:

[tex]x=4r[/tex]

[tex]x=4(3)[/tex]

[tex]x=12[/tex]

The third term of the given G.P. is:

[tex]y=xr[/tex]

[tex]y=12(3)[/tex]

[tex]y=36[/tex]

Therefore, the value x is 12 and the value of y is 36.

Answer:

A and D

option A is correct because if you do 4/5 times 2/2 you get 8/10

so that means they both are Equal.

option D is also correct

because

after 6/10 It’s 7/10, 8/10..

Step-by-step explanation:

1100-825= Markup

Markup= 275

Answer:

For a regular polygon, the perimeter is equal to the product of one side length and the number of sides of the polygon. For example, the perimeter of a regular pentagon whose side length 8 cm, is given by; Perimeter of a regular pentagon = 8 x 5 = 40 cm.

Step-by-step explanation:

I hope I've helped :).

Answer:

perimeter = number of sides x the length of any side.

Step-by-step explanation:

brainliest pls

Answer:

7%

Step-by-step explanation:

Add up all of the hot drinks that were ordered:

5 + 48 + 22 = 75

So 75 total hot drinks were ordered.

Of those, only 5 were small. So 5/75 were small drinks.

Then find that as a percentage.

5/75 = x/100

To get to 100, 75 is multiplied by 4/3. So multiply 5 by the same number and you get 6.66666667, which rounds 7% and that is your answer,

On one tank of gas Charlie will drive 612 km

At a cost of 149.9, Charlie will fill the tank with the sum of 8994

Annual cost of filling the tank 467688

Information from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L

Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride

= 60 * 10.2

= 612 km

Cost of filling the tank

The cost per liter is 149.9 for 60 L we have

= 149.9 * 60

= 8994

Filling the tank once week, the cost for filling in one year is

1 year is 52 weeks

= 8994 * 52

= 467688

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Answer:

SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system. ...

Check the solution in both equations.

Step-by-step explanation:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

9514 1404 393

Answer:

  90

Step-by-step explanation:

10! = 10 × 9 × 8!

so 10!/8! = 10×9 = 90

__

The factorial of an integer is the product of that integer and all the positive integers less than it. So, 3! = 3×2×1, for example. 0! is defined as 1.

Answer:

Step-by-step explanation:

You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.

The total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.

Multiplying the ratio units by £5, we find the distribution to be ...

  Laura : Tom : Alex = £40 : £35 : £20

Answer:

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Step-by-step explanation:

Given ,

To Find : How much money will each of them receive

Let us take the variable as 'x' to find the money received by them

When we convert it to a equation

8x+7x+4x = 95

19x = 95

x = [tex]\frac{95}{19}[/tex]

x = 5

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Hence, the money received by each of them is  £40, £35 and  £20

Answer: x-100 < 115

Step-by-step explanation: X is less then 215

The end behavior of the function f(x) = 1/9 x¹² is

The end behavior of the function f(x) = -1/10 x¹⁸ is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1/9 x¹²

The positive exponents will mean that x will always yield positive values hence f(x) is always positive

f(x) = -1/10 x¹⁸

The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative

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Answer:

Number of people fit in 6 feet by 6 feet room = 12 people

Step-by-step explanation:

Given:

Number of people fit in 9 feet by 4 feet room = 12 people

Find;

Number of people fit in 6 feet by 6 feet room

Computation:

Surface area of 9 feet by 4 feet room = 9 x 4

Surface area of 9 feet by 4 feet room = 36 feet²

So,

Surface area of 6 feet by 6 feet room = 6 x 6

Surface area of 6 feet by 6 feet room = 36 feet²

Surface area of both rooms are equal. so number of people are also equal

Number of people fit in 6 feet by 6 feet room = 12 people

Answer:

[tex] \frac{1}{-2} [/tex]

equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

( y - y1 ) = m( x - x1 )

y - 7 = 2 (x-8)

2x - y - 1 = 0

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Using the pythagoras theorem in the given figure, the required length of c is [tex]49\sqrt{6}[/tex].

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean Theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides.

The pythagoras theorem is named after the Greek mathematician-philosopher Pythagoras.

To solve for c, first taking the small triangle in the left of the figure,

since one of the angle is 45 degree and another is 90 degree, the unlabelled angle is 45 degree. Which makes this triangle a isosceles triangle, hence the sides a and b are equal in length. i.e a = b

Using pythagoras theorem in this triangle,

[tex](7\sqrt{2} )^{2} = \sqrt{a^{2}+\ a^{2} }[/tex]

Therefore, a = 49[tex]\sqrt{2}[/tex]

Now Taking the small triangle in the right of the given figure,

tan 30 = a/c

or, [tex]\frac{1}{\sqrt{3} }[/tex] *c = 49[tex]\sqrt{2}[/tex]

Therefore , c = 49[tex]\sqrt{6}[/tex]

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Answer:

no

Step-by-step explanation:

Answer:

6 ft

Step-by-step explanation:

The ratio of the square of the sides of two similar figures = the ratio of their area

Let x represent the missing side corresponding side length

Therefore,

Area of figure B/area of figure A = square of side length of figure B/square of the side length of figure A

Thus:

98/18 = 14²/x²

98/18 = 196/x²

Cross multiply

98*x² = 196*18

98x² = 3,528

Divide both sides by 98

x² = 3,528/98

x² = 36

x = √36

x = 6

Therefore, missing corresponding side length = 6 ft

The corresponding side length is 2.57 feet

Given that figures A and b are, hence the ratio of the area to the length is equal to a constant as shown:

Substitute the given parameters into the formula to have:

A = 98 square feet

L = 14 square feet

a  18 square feet

[tex]\frac{98}{14} = \frac{18}{l}\\98l=252\\l = 2.57 feet[/tex]

Hence the corresponding side length is 2.57 feet

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Answer:

8 27/28 or 251/28

Step-by-step explanation:

Find common denominators then simply add.

Answer:

it would be the first answer

Step-by-step explanation:

you can draw the net of the shapes, and count each corner there

Answer:

8% is equivalent to the fraction 8/100

Step-by-step explanation:

when f(x)=4, then the value of x is 2

A relation is a function if it has only One y-value for each x-value.

Given that A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs:

The ordered pairs are (2, 4), (-3, 0), (- 1, -1), (4, 3)

We need to find value of x when f(x)=4

In the (x, y) ordered pair the x place represents the domain value and y place represents the range.

In the order pairs we have to look for the y value which has 4.

The corresponding element of 4 is the x value

So the value of x is 2 if f(x)=4

Hence, when f(x)=4, then the value of x is 2

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Answer:

M - 2

Step-by-step explanation:

Decreased is a math term indicating that we’re deal with subtraction

Answer:

Step-by-step explanation:

The m should be a variable.

Variable is a symbol like x or y that is used in mathematical or logical expressions to represent a variable quantity.

Decreased is subtract should have a minus sign.

Decreased is to reduced made less in size or amount or degree.

Decreased: ⇒ - (minus sign)

m-2, which is our answer.

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given : PQRS has the length 12

and TUVW has length 15.

thus ,

To find the perimeter of PQRS:

we find,

TUVW = 35 units

and

PQRS = 35 - 6

=> PQRS  = 29

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

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Therefore , the solution of the given problem of triangle comes out to be the distance of  the drone from the start point is  13feet.

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Height of drone  = 5 feet

and  distance of drone covered is 12 feet

Thus ,

to calculate the distance of  the drone from the start point

distance can be represented as H

Since it forms right triangle.

By using pythagoras theorem,

=> 5² + 12² = H²

=> H² = 169

=> H = √169

=> H = 13

Therefore , the solution of the given problem comes out to be the distance of  the drone from the start point is  13feet.

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Answer:

3x-2x-6=4x-7

x-6. =4x-7

3x=1

X=1/3

Answer:

4w² + 82w + 400

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients involving addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A quadratic function is a polynomial of degree 2. The standard form of a quadratic equation is:

ax² + bx + c

The moat has width of w inch. Therefore:

combined width of castle and moat = 16 in + w in + w in = 16 + 2w in

combined length of castle and moat = 25 in + w in + w in = 25 + 2w in

The combined area = length * width = (16 + 2w)(25 + 2w) = 400 + 32w + 50w + 4w² = 4w² + 82w + 400

Answer:

A(w) = 4 w^2 + 82 w + 400

Step-by-step explanation:

Person above me is correct. :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3^3\times3^3\times3}[/tex]

[tex]\mathsf{3^3 = 3 \times3\times3 = 9\times 3 = \bf 27}[/tex]

[tex]\mathsf{27\times27\times3 =\ ? }[/tex]

[tex]\mathsf{27\times27 = \bf 729}[/tex]

[tex]\mathsf{729\times 3}[/tex]

[tex]\mathsf{= \bf 2,187}[/tex]

[tex]\large\text{So you are looking for: \bf 2,187}[/tex]

[tex]\large\text{Option A.}[/tex]

[tex]\mathsf{3^6}[/tex]

[tex]\mathsf{= 3\times3\times3\times3\times 3\times3}[/tex]

[tex]\mathsf{3\times 3 = \bf 9}[/tex]

[tex]\mathsf{= 9\times 9\times 9}[/tex]

[tex]\mathsf{9\times9 = \bf 81}[/tex]

[tex]\mathsf{= 81\times9}[/tex]

[tex]\mathsf{= \bf 729}[/tex]

[tex]\large\text{So Option A is NOT equivalent because it is too small }[/tex]

[tex]\large\text{Option B.}[/tex]

[tex]\mathsf{3^7}[/tex]

[tex]\mathsf{= 3\times3\times3\times3\times3\times3 \times3}[/tex]

[tex]\mathsf{3\times 3 = \bf 9}[/tex]

[tex]\mathsf{= 9\times9\times9\times3}[/tex]

[tex]\mathsf{9\times9 = \bf 81}[/tex]

[tex]\mathsf{81\times9\times3}[/tex]

[tex]\mathsf{81\times 9 = \bf 729}[/tex]

[tex]\mathsf{729\times3}[/tex]

[tex]\mathsf{= \bf 2,187}[/tex]

[tex]\large\text{Option B. could possibly be your answer}[/tex]

[tex]\mathsf{3^9}[/tex]

[tex]\mathsf{= \bf 19,683}[/tex]

[tex]\large\text{Option C. Can’t be your answer because it’s too big!}[/tex]

[tex]\mathsf{3^{12}}[/tex]

[tex]\mathsf{= \bf 531,441}[/tex]

[tex]\large\text{Option D. cannot be your answer because it is way too big}\\\ \large\text{similar to your original answer (2,187)}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge Option B.}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: ur answer is B mark me brainliest

Step-by-step explanation:

(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that the side of the square must be equal to the width of the rectangle, x feet.

The length of the rectangle must be 50 feet longer than its width

The field the farmer wants to build the two fenced sections in has an area of y square feet.

The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet

the sum of the fenced areas must be less than the area of the field.

y≥x²+1000

y>2x²+50x

(20, 2,200) and (5, 3,000) are the viable solutions

Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

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