A banner maker was asked to redesign a squarebanner by increasing the width by 4 feet anddecreasing the length by 2 feet. The total area of thenew banner was 91 square feet.What was the length of the side of the original squarebanner?

The amount of ribbon needed to buy for the project in meters is (d) 5.

According to question,

1 centimeter = 0.01 meter

2.54 centimeter = 0.01*2.54

                           = 0.0254 meters

1 inches = 2.54 centimeters

              = 0.0254 meters

Amount of ribbon needed for project = 182 inches

                                                              = 182 * 0.0254 meters

                                                              = 4.62 meters

                                                              ≅ 5 meters

Hence, 5 meters of ribbon is needed for the project.

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Since the null hypothesis was not rejected, there is not enough evidence to conclude that under 46% of the residents favor construction of an adjoining bridge.

There are two decisions possible regarding the null hypothesis, as follows;

The hypothesis are given as follows:

The null hypothesis was not rejected, meaning that the conclusion regarding the mayor's claim is that there is not enough evidence from the sample of 190 voters to conclude that the percentage is below 46%.

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11

this is just words because it doesn't let me submit this with just the answer

Answer:

y = 2x + 1

Step-by-step explanation:

→ Find the gradient of this line

2

→ Write in standard format

y = 2x + c

→ Substitute in ( 0 , 1 )

1 = 0 + c ⇒ c = 1

The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.

Given that,

The library is getting new shelves built.

We have to find how long will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.

We know that,

We have to divide

4÷2÷5

2÷5

0.4

In percentage we write as 40%.

Therefore, The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.

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A scale factor of 0.1  was used to create the printed photo of the sandbox

A scale factor is the size by which a shape is enlarged or reduced. It is used in increasing or reducing the size of a 2D shape, such as circle, triangle, square, rectangle, hexagon, etc.

Given that: Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long, and in the photo, the sides of the hexagon are each 4 inches long

The scale factor will be:

4/40 = 1/10 = 0.1

This means the sandbox has been reduced by 10 times the original size

Therefore, the scale factor that was used to create the printed photo of the sandbox is 0.1

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Answer: y < -4

Step-by-step explanation:

Answer:1/3

Step-by-step explanation:

25/75

25/25=1

75/25=3

Answer is 25/75=1/3

Answer:

6y+12

Step-by-step explanation:

4(y+3)+2y

= 4y+12+2y

=6y+12

Answer:

Step-by-step explanation:

[tex]\sf 4(y+3)+2y[/tex]

Expand (Distributive property):-

[tex]\sf 4y+12+2y[/tex]

Combine like terms:-

[tex]\sf 4y+2y+12[/tex]

[tex]\sf (4y+2y)=6y[/tex]

[tex]\sf 6y+12[/tex]

__________________

Hope this helps!

Have a great day! :)

I believe it would be x = -5.

Hope this helps!

The equation of the line which is parallel to the other equation is;

[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].

What is the Relation between two Parallel Lines?

To determine whether two lines are parallel or not, apply the parallel line's formula. When we have the slope of two lines that we want to compare, the parallel line formula can be used. The separation between the parallel lines remains constant. Parallel lines are those that never cross each other. Since the two lines are equal in this situation and the angle is 180 degrees, they will never intersect.

In the given equation, we have:

The equation of the line is y = -5/7x-10.

and, Line k, which is parallel to the line of the equation :

[tex]y = \frac{-5x}{7} -10.[/tex]

[tex]y + \frac{5x}{7} +10. =0[/tex]

So, the equation of the line which is parallel to the line of the equation is:

[tex]y + \frac{5x}{7} +k. =0[/tex]

and since the two lines are parallels

So, the slope of equation 1 and the slope of equation two will be the same;

Also, It is given that the line includes the point  (-9, 5).

So,

[tex]5 + \frac{5 \times -9}{7} +k. =0[/tex]

⇒[tex]k = -\frac{5 \times -9}{7} -5[/tex]

⇒[tex]k = \frac{10}{7}[/tex]

So, The equation of the line which is parallel to the other equation is;

[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].

Hence,

The equation of the line which is parallel to the other equation is;

[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex]..

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As we know:

For:

Therefore:

Therefore, the statement is true

The addition of the given two functions  f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5 will be (f · g)(x) = 2x²-9

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

Given f(x)= -4x-2

g(x)=2x²+4x-5

For (f-g)(x) = -4x-2+2x²+4x-5

=2x²-9

(f-g)(x) = 2x²-9

Hence, The addition of the given two functions will be (f · g)(x) = 2x²-9

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Answer: 10 3\4

Step-by-step explanation:

I did the quiz

Answer: It is 14,596.

Answer:

V= 615 cm³

Step-by-step explanation:

the volume (V) of a rectangular box is calculated as

V = Ah ( A is the area of the base and h the height ) , then

V = 205 × 3 = 615 cm³

Answer:

Step-by-step explanation: In order to find the volume of box, we need to know the formula

The formula is

volume= LxBxH where L=length, B= breadth and H= height

SO, area= L x B

we can say,

Volume= area x height= 205 x 3=  615 cm^3

Hence, the volume of the box= 615 cm^3

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Answer:

0.53

Step-by-step explanation:

you just take 106 and divide it by 200

-4 is less than -3

so:

Solution

For this case we have the following system of equations:

x + y= 1

3x + 5y= 15

We can create the following plot:

Then the solution for this case is:

x= -5

y= 6

Answer:

It's very blurry, try sending one section at a time.

Step-by-step explanation:

Answer:

Step-by-step explanation:

35

The correct option is :

A package that weighs 7 pounds will cost $17 for both options.

The declaration that shows that the provided variables exist is a mathematical equation. When describing the scenario in this circumstance, two or more factors are taken into account.

The equation can be used to symbolize the price, y: Y is equal to 3 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $17, which is represented by the equation y = 17, in order to send the package.

We'll compare the equation as a whole.

In this case,

3 + 2x = 17

Compile similar terms

2x = 17 - 3

2x = 14

x = 14 divided by 2x = 7

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Okay, here we have this:

Considering the provided function, we are going to calculate the requested roots, so we obtain the following:

Finally we obtain that the roots of the function are x=8 and x=4.

Answer:

sometimes true

Step-by-step explanation:

Given, two straight lines intersect each other in such a way that one of the angles formed measure 90°.

We know that, lines which intersect to form a right angle are known as perpendicular lines

In the above figure , AB is perpendicular to CD

Considering ∠AOC=90°

Now,

∠AOC+∠AOD=180°     [Linear pair]

90°+∠AOD=180°

∠AOD=90°

Similarly,

∠AOC+∠BOC=180° and ∠BOD+∠AOD=180°   [Both making linear pair]

So, we get ∠BOC=90° and ∠BOD=90°

Hence, ∠AOC=∠AOD=∠BOC=∠BOD=90°

From the problem, we need to find the first five terms of the geometric sequence.

The first term, a1 = 16 and the common ratio, r = 3/2

Note that the succeeding term is the previous term multiplied by the common ratio.

This will be :

The geometric series is :

an = {16, 24, 36, 54, 81, ...}

The answer is B. an = {16, 24, 36, 54, ...}

A. The substance is in the gas phase only in region 5.

B. The substance is in both the liquid and the solid phase in region 2.

C. The substance is in only the liquid phase in region 3.

D. The melting point is the temperature at region 2.

E. The boiling point is the temperature at region 4.

For the given question, the correct depiction of the expressions are is;

Thus, the result for the graph will be-

A. The substance is in the gas phase only in region 5.

B. The substance is in both the liquid and the solid phase in region 2.

C. The substance is in only the liquid phase in region 3.

D. The melting point is the temperature at region 2.

E. The boiling point is the temperature at region 4.

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Answer:

A. The substance is in the gas phase only in region 5.

B. The substance is in both the liquid and the solid phase in Region 2.

C. The substance is in only the liquid phase in region 3.

D. The melting point is the temperature at region 2.

E. The boiling point is the temperature at region 4.

Step-by-step explanation:

The value of an irrational number  [tex]-16 + \sqrt{40}[/tex]  Is approximate, the nearest tenth is  -9.675.

Irrational numbers include all real numbers that cannot be stated as the ratio of two integers, or p/q, where p and q are both integers.

Given expression:

[tex]-16 + \sqrt{40}[/tex]

Factorize the square part as

[tex]-16 + \sqrt{10\times2^2 }[/tex]

Simplify the above expression as

[tex]-16 + 2\times \sqrt{10}[/tex]

We know that [tex]\sqrt{10} = 3.132[/tex]

Hence, -16 + 2 × 3.132

= -9.675

Therefore, the value of an irrational number  [tex]-16 + \sqrt{40}[/tex]  is approximately the nearest tenth is  -9.675.

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Answer:A

Step-by-step explanation:

The formula that can be used to find the nth term of the sequence is aₙ = 4n + 1

The sequence follows an arithmetic patterns. Therefore, the formula for arithmetic progression can be used to find the nth term as follows:

aₙ = a + (n - 1)d

where

Therefore, using the sequence 5, 9, 13, 17, 21

a = 5

d = 9 - 5 = 4

Hence,

aₙ = 5 + (n - 1)4

aₙ = 5 + 4n -4

aₙ = 5 - 4 + 4n

Therefore,

aₙ = 4n + 1

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We have 128 teams.

In each round, half of the teams remain, so if T is the number of teams and n is the number of rounds, we have:

and we start with n=0 so T(0)=128.

Then, we can use this recursive expression to find T after four rounds (n=4), but it is better if we derive an explicit formula for T in function of n (and not in function of the past terms of the sequence):

With the last expression we can calculate T for any value of n. Then, for n=4, we have:

NOTE: in this case, its better to express the factor 0.5 as a fraction instead of a decimal.

Answer: after 4 rounds there will be 8 teams left.