The perimeter of a square is 4 times as
great as the length of any of its sides.
Determine if the perimeter of a square is proportional to its side length. Explain.

Money received in tenth month: $104.

A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

Money received in first four months: $50, $52, $55, %59.

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.

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Answer:

F(5)

Step-by-step explanation:

its right very sorry if its late

We have proved that , the ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE

It is given that AB║ CD and AB ≅ DC.

We have to prove that ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE.

What is the SAS rule of congruency of triangles ?

SAS axiom states that if two sides and the included angle of one triangle are equal to two sides and included angle of other triangle, then triangles are congruent.

As per the question ;

AB║ CD and AB ≅ DC

The two triangles are ΔABE and ΔCDE

So ,

AB = CD (from given data)

also ;

Included angles of two triangles are equal ;

∴

∠ABE = ∠CDE (from given data)

and

BE = BE (common)

∴ Both triangles are congruent to each other ;

i.e.,

ΔABE ≅ ΔCDE.

by SAS axiom.

Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

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The value of 'a' in the given expression is 11/2.

The square root formula can be used to calculate the square root of any number. The square root of any number is the value that, when multiplied by itself, yields the original number. Each number has two square roots, one positive and the other negative. For example, the number four has two square roots, -2 and 2.

Given [tex]$32 \sqrt{2}=2^a$[/tex]

We can write 32 as:

32 = 2 × 2 × 2 × 2 × 2

32 = [tex]2^{5}[/tex]

We can write [tex]$\sqrt{2}=2^{1 / 2}$[/tex].

Now,

[tex]$$\begin{array}{r}32 \sqrt{2}=2^a \\2^5 \cdot 2^{1 / 2}=2^a \\2^{5+1 / 2}=2^a \\2^{1 / 2}=2^a \\\end{array}$$[/tex]

Therefore, the value of a = 11/2.

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After solving each system, -6 = 3x - 6y, 4x = 4 + 5y, the values of x and y are calculated to be 6 and 4 respectively.

The two equations,  -6 = 3x - 6y, and 4x = 4 + 5y can be considered as linear equations as the highest power of the variables in these equations is one.

By rearranging the first equation, the value of x can be found to be,

-6 = 3x - 6y

3x = 6y - 6

x = 6y - 6 / 3

Putting the calculated value of x in the second equation,

4x = 4 + 5y

4(6y - 6 / 3) = 4 + 5y

24y - 24 / 3 = 4 + 5y

24y - 24 = 3 ( 4 + 5y)

24y - 24 = 12 + 15y

Rearranging,

24y - 15y = 12 + 24

9y = 36

y = 36 / 9

y = 4

To solve for x, put y = 4 in the first equation as follows,

-6 = 3x - 6y

-6 = 3x - 6(4)

-6 = 3x - 24

Rearranging,

24 - 6 = 3x

18 = 3x

x = 18/3

x = 6

Thus the value of x and y in these systems are calculated to be 6 and 4 respectively.

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Answer:

3, 5, 7, 9

Step-by-step explanation:

Give Brainliest if I helped!

The four consecutive odd integers that Zach found are x, x + 2, x + 4, and x + 6 are -11, -9, -7, and -5.

To solve this problem,  set up equations based on the given information.

"5 times the sum of the first and the third":

[tex]5(x + x + 4)[/tex]

"the product of 8 and the sum of the second and the fourth":

[tex]8((x + 2) + (x + 6))[/tex]

According to the problem, the first equation should be 22 greater than the second equation:

[tex]5(x + x + 4) = 8((x + 2) + (x + 6)) + 22[/tex]

Next,  simplify and solve the equation:

[tex]5(2x + 4) = 8(2x + 8) + 22[/tex]

Remove the bracket by multiplying the terms:

[tex]10x + 20 = 16x + 64 + 22[/tex]

Take the variables to LHS and constants to other side and solve it:

[tex]6x = -66[/tex]

On dividing by 6 on both sides:

x = -11

Now that the value of x, and  find the four consecutive odd integers:

x = -11

On substituting x value in the following terms:

[tex]x + 2 = -11 + 2 \\= -9\\x + 4 = -11 + 4\\ = -7\\x + 6 = -11 + 6 \\= -5[/tex]

Therefore, the four consecutive odd integers are -11, -9, -7, and -5.

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Answer:

15.71 cm

Step-by-step explanation:

circumference is [tex]\pi[/tex]d

diameter is 2r

radius = 2.5 cm so the diameter is 2.5*2 = 5 cm

circumference = [tex]\pi[/tex] (5) -> 15.707

rounded to the nearest hundredth is 15.71 cm

The given situation shows an arithmetic sequence and the number of sales in the week 50 can be determined by using the nth term formula of arithmetic sequence. The sales in all 50 weeks can be determined by using the formula for sum of finite arithmetic sequence.

An arithmetic sequence is an ordered set of numbers that have a constant difference called a common difference between consecutive terms. Each term is obtained by adding the common difference to the previous term.

In the given situation, the first term (a) is the number of sales to be made in the first week. Hence, a = 10

The common difference (d) is the number added to get the number of sales in the next week. Hence,

d = 1

Hence, in the 2nd week the number of sales should be 11 and in 3rd week it should be 12.

Using the formula for nth term and n = 50,

an=a+(n-1)d

a50=10+(50-1)1

a50=10+(49)1

a50=10+49=59

The formula of finding the sum of the finite arithmetic sequence:

Sn=(n/2)(a1+an)

S50=(50/2)(10+59)

S50=25(69)=1725

Hence, the number of sales in the 50th week is 59 and the total number of sales made in the 50 weeks is 1725.

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The triangle is an isosceles triangle with sides XY and XZ equal to [tex]\sqrt{29}[/tex] units and side YZ as 4 units.

Given that:-

Coordinates of X = (7,6)

Coordinates of Y = (5,1)

Coordinates of Z = (9,1)

We have to find the measures of the sides of ΔXYZ and classify the triangle by its sides.

Using distance formula, we can find the measure of the sides of the triangle.

Distance formula for the line segment with points (a,b) and (c,d):-

[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]

Hence,

XY = [tex]\sqrt{(1-6)^2+(5-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.

YZ = [tex]\sqrt{(1-1)^2+(9-5)^2} =\sqrt{0+16} =\sqrt{16}[/tex] = 4 units.

XZ = [tex]\sqrt{(1-6)^2+(9-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.

Here,

XY = XZ, hence it is an isosceles triangle.

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Answer:

14x+10

Step-by-step explanation:

The product means multiplication

Answer:

D 14x+10

Step-by-step explanation:

I should choose second or other campus, as it is cost effective.

We will begin with forming the equation according to the information provided in question. Let us represent the number of hours with t.

Cost on choosing first or one campus to play tennis-

Cost = 25 × t

Cost on choosing second or other campus to play tennis -

Cost = 10 + 20 × t

Now finding cost on each campus for duration of ten hours.

First campus -

Cost = 25 × 10

Cost = 250

Second campus -

Cost = 10 + 20 × t

Cost = 10 + 20 × 10

Cost = 10 + 200

Cost = 210

Therefore, to practice for a total of 10 hours, I should choose second or other campus, as it is cost effective.

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Using direct variation, the value of x for equation y = 5/-3 (x) is 3/5 when y = -1

When x is not equal to zero, an equation of the form y = kx describes the linear function known as direct variation. When x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.

Using direct variation,

y = kx

⇒ 5 = k(-3)

⇒ k = 5 / -3

for y = -1

y = 5/-3 (x)

⇒ -1 = 5/-3 × x

⇒ x = 3/5

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Answer:

12<6+n

this is the answer

[tex] \large \bf \implies{x = 4}[/tex]

[tex] \bf \longrightarrow{4.5x = 18}[/tex]

[tex] \bf \frac{ \cancel{4.5}x}{ \cancel{4.5}} = \frac{18 }{4 \cancel{.}5} = \frac{18 \times 10}{45} = \frac{180 \div 3}{45 \div 3} = \frac{60 \div 3}{15 \div 3} = \frac{20 \div 5}{5 \div 5} = \frac{4}{1} = 4 \\ [/tex]

[tex] \large \bf \implies \boxed{x = 4} \: ans.[/tex]

The population of Somerville is approximately 35047 after a depreciation of of 3% every year .

Depreciation is economics refers to two different aspects of the same idea: first, the actual decline in an asset's fair value as it is used and worn, such as the annual decline in value of factory equipment; and second, the allocation in accounting statements of the asset's original cost to the periods during which it is used.

Here depreciation is the gradual decline in population each year in the town.

The rate of depreciation or decline is the percentage amount of population that decreases every year.

The formula used to calculate depreciation is given by:

[tex]A=P(1-r)^t[/tex]

Given the rate of depreciation as 3%.

Population at present = 38400

Population after 3 years:

= 38400 (1 - 0.03 )³

= 38400 ( 0.97 )³

= 35046.6432

≈ 35047

Hence the population after 3 years will be approximately 35047.

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Answer: =35047

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the original speed of the cars be x.

When speed is x + 10 the distance in two hours is:

When speed = x - 10 the distance in three hours is:

Since the distance is same in both cases, set them equal and solve for x:

The original speed of the cars is 50 km/h

Answer:

Original speed = 50 km/h

Step-by-step explanation:

Given that,

→ first car travels 10 km faster than its current speed. It would travel in two hours the same distance.

→ second car travels 10 km per hour slower than its current speed. It would travel in 3 hours the same distance.

Then the equation will be,

→ 2(x + 10) => 1st car

→ 3(x - 10) => 2nd car

→ 2(x + 10) = 3(x - 10)

Now the original speed of the cars is,

→ 2(x + 10) = 3(x - 10)

→ 2x + 20 = 3x - 30

→ 2x - 3x = -30 - 20

→ -x = -50

→ [ x = 50 km/h ]

Hence, the original speed is 50 km/h.

Answer:

The area of each cookie is 254.3

Answer:

Step-by-step explanation:

Point slope form y-y₁ = m(x-x₁)

y-4 = 6(x + 1)

y-4 = 6x + 6

y = 6x + 10

Answer: Maybe f I'm not sure

Step-by-step explanation:

Plant P produced 15333 numbers of panels when the two plants together produced 1410 defective panels using unitary method.

It is a method for figuring out a single unit's value, then multiplying that value by itself to get the required value.

Given data

Plant produces defective panels = 1140

Plant A produce = 5%

Plant B produce = 4%

Assume,

Number panels Plant B produce = x

Number panels Plant A produce = x - 6000

[tex]\frac{5}{100}[/tex](x) + [tex]\frac{4}{100}[/tex](x-6000) = 1140

0.05x + 0.04x - 240 = 1140

0.09x = 1380

x = 15333

Plant P produced 15333 numbers of panels when the two plants together produced 1410 defective panels using unitary method.

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The result of the expression [tex]y^{2}+3[/tex]  for the variable y= [tex]\sqrt{7}[/tex] is 10

Given,

The algebraic expression = [tex]y^{2}+3[/tex]

The value of y = [tex]\sqrt{7}[/tex]

Substitute the values in the expression

[tex]y^{2}+3=(\sqrt{7} )^{2}+3[/tex]

=7+3

=10

Hence, the  result of the expression [tex]y^{2}+3[/tex]  for the variable y= [tex]\sqrt{7}[/tex] is 10

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We can construct an unlimited number of triangles when given only two sides and no indication of the angle, such as a = 10m and b = 15m

Consider this:

With 10m and 15m side lengths and an angle value ranging from 0 to 360 degrees, how many distinct triangles are possible?

Make one of the triangles with sides of 10 meters, 15 meters, a 30 degree angle, and a third side that may be adjusted to your preferred length using a protractor. A triangle has been built by you.

By changing the length and angle of the third side, we can produce a completely different triangle that is similar to this one.

Keep in mind that you choose the side lengths and angle. This suggests that you might make a different decision. Using the same angles, you can make an infinite number of different triangles.

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

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If TQ = 2x - 6 and RQ = x + 3 then the measure of TQ = 12.

The perpendicular bisector theorem states that if a point is on a segment's perpendicular bisector, it is equidistant from the segment's endpoints.

According to the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from both ends of the line segment on which it is drawn. If a pillar stands at an angle in the center of a bridge, all of its points will be equidistant from the bridge's end points.

Where, TQ = 2x - 6 and RQ = x + 3

By the Perpendicular Bisector Theorem, RQ = TQ.

2x - 6 = x + 3

x = 9

Substitute the value of x in TQ, we get

TQ = 2(9) - 6

= 18 - 6

= 12

Therefore, the value of TQ = 12.

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Answer:

Step-by-step explanation:

so first it would be -0.1 but that means you need to remove the 17th person and get 2 really light people because one can not be negative hope this helps

A translation in words and using vector notation that can be used to describe the change in their seating as-

In geometry, translation refers to a function which moves an object a specified distance. The object isn't otherwise altered. It has not been rotated, mirrored, or resized.

Now, as per the stated question.

In the previous year the seats given to Dexter's family were C3, C4, C5 , and C6.

Now, for current year, seats are at D16, D17, D18 , and D19.

Choose a seat from the new row & compare it to the seat with the previous row. Seat D16 is 13 seats to the right and 1 row back from C3.

As a result, the translation vector could be written as < 13, -10>.

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The cost of each small charcuterie boards is $6 and one medium charcuterie boards is $7.

A mathematical statement known as an equation is made up of two expressions joined together by an equal sign. It is a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Let small charcuterie boards = c

Let medium charcuterie boards = m

Therefore, the equation will be:

10c + 12m = 144

5c + 9m = 93

Multiply equation i by 5

Multiply equation ii by 10

50c + 60m = 720

50c + 90m = 930

Subtract

30m = 210

m = 210/30

m = 7

Therefore, 5c + 9m = 93

5c + 9(7) = 93

5c + 63 =93

5c = 93 - 63

5c = 30

Divide both sides by 5

c =  30 / 5

c = 6

Therefore, based on the information the cost of each small charcuterie boards is $6 and one medium charcuterie board is $7.

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Answer:

226.2 miles

Step-by-step explanation:

8.7 x 26 = 226.2

If f(x)=7-3 x and g(x)=3 x-7 , the value of f(1)+g(1) is 0

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

f(x)=7-3 x and g(x)=3 x-7

For, f(1) = 7 - 3(1)

            = 7 - 3

            = 4

For, g(1) = 3x - 7

             = 3(1) - 7

             = -4

f(1) + g(1) = 4 - 4

             = 0

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