Brian wants to purchase a piece of fabric that is between 49 and 53 inches long. He can choose between three pieces of fabric. Choice A is 4 3/4 feet long. Choice B is 4 1/2 feet long. Choice C is 4 1/4 feet long. Which price of fabric should Brian purchase?

Answer:

C

Step-by-step explanation:

the legs of a 30-60-90 triangle are 1 and [tex]\sqrt{3}[/tex], while the hypotenuse is 2.

the ratio of the legs is therefore 1 : [tex]\sqrt{3}[/tex] → C

[tex]l-length\\w-width\\\\\text{The formula of an area of a rectangle:}\ V=lw\\\\\text{We have the area}\ 540\ m^2\to lw=540\\\\\text{New rectangle}\\\\l-5-length\\w+5-width\\\\\text{We have the area}\ 540\ m^2+35\ m^2=575\ m^2\to (l-5)(w+5)=575\\\\\text{Therefore we have the system of equation:}\\\\\left\{\begin{array}{ccc}lw=540&\to w=\dfrac{540}{l}&(*)\\(l-5)(w+5)=575&&(**)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**)[/tex]

[tex](l-5)\left(\dfrac{540}{l}+5\right)=575\qquad\text{use distributive property}\\\\(l)\left(\dfrac{540}{l}\right)+(5)(l)-(5)\left(\dfrac{540}{l}\right)-(5)(5)=575\\\\540+5l-\dfrac{2700}{l}-25=575\\\\515+5l-\dfrac{2700}{l}=575\qquad\text{subtract 575 from both sides}\\\\-60+5l-\dfrac{2700}{l}=0\qquad\text{multiply both sides by }\ l\neq0\\\\-60l+5l^2-2700=0\\\\5l^2-60l-2700=0\qquad\text{divide both sides by 5}\\\\l^2-12l-540=0\\\\l^2+30l-18l-540=0\\\\l(l+30)-18(l+30)=0\\\\(l+30)(l-18)=0\iff l+30=0\ \vee\ l-18=0\\\\l=-30<0\ \vee\ \boxed{l=18\ cm}[/tex]

[tex]\text{Substitute the value of}\ l\ \text{to}\ (*):\\\\w=\dfrac{540}{18}\\\\\boxed{w=30\ cm}[/tex]

[tex]Answer:\ \boxed{length=18\ cm,\ width=30\ cm}[/tex]

The original dimensions of the rectangle are 30 meters in length and 18 meters in width.

We need to find the dimensions of the original rectangle given an area of 540 sq m and the changes in area after altering the dimensions. Let's represent the length of the rectangle as L meters and the width as W meters.

From the information provided:
Original Area: L * W = 540
New Area: (L - 5) * (W + 5) = 540 + 35

By solving these equations step-by-step:

L  * W = 540

(L - 5)(W + 5) = 575
LW + 5L - 5W - 25 = 575
LW - 5(W - L) - 25 = 575
Substitute the original area (LW = 540):
540 - 5(W - L) - 25 = 575
-5(W - L) = 60
W - L = -12

Now we have two simultaneous equations:
L * W = 540
W - L = -12

We can solve these equations for L and W.

Solving the system of equations, we get:

L = 30 meters
W = 18 meters

Therefore, the original dimensions of the rectangle are 30 meters in length and 18 meters in width.

Answer:

sales tax = 2.25

Step-by-step explanation:

To find the sales tax, we multiply the list price by the tax rate

We need to convert the tax rate of 5% to decimal form 5% = .05

sales tax = 45 * .05

sales tax = 2.25

Answer:

70

Step-by-step explanation:

The simplest way to find the number is work backwards. If you know the final answer is 10, start with 10 and make the number x. Then set up the original equation.

0.5x-25=10

Then start working backwards(isolate).

0.5x-25=10

      +25  +25

in other words, 10+25=0.5x. (the 25 cancels out because -25+25=0)

10+25=35, so 35=0.5x.

Now, instead of dividing by 2, multiply by 2(opposite again).

35=0.5x

/0.5(aka *2)     /0.5(cancels out)

now you are left with 70=x, so the number is 70.

Answer:

(A)

Step-by-step explanation:

The Postulate states that corresponding sides of similar triangles are in proportion.

We know that similar triangles are the triangle which have congruent triangles and and the corresponding sides are in proportion

Now in ΔSTP and ΔRPQ, corresponding sides are : (RP,TP); (RQ,TS) ;  (PQ,PS)

So we have RP:TP = PQ:PS

TP= 51; RP= 85; PS = 3x; PQ = 3x+24

PQ : PS = RP : TP

3x+24 : 3x = 85 : 51

Hence 5 statement represents (A) equation

Answer: A) (3x + 24):3x = 85:51

The sum of 4 yards 2 feet 8 inches, 3 feet 11 inches and 6 yards 6 feet and 6 inches is 11 yards and 1 foot or 11 1/3 yards and 7 inches, using standard conversions between inches, feet, and yards.

To solve this problem, we first need to recall the relationships between inches, feet, and yards. There are 12 inches in a foot, and 3 feet in a yard.

Starting with the yards, you have 4 yards plus 6 yards giving you a total of 10 yards. Moving on to feet, you have 2 feet from the first measurement, and 6 feet from the third measurement. Also, remember to convert the 3 feet in the second measurement into 1 yard and add it to your yards total, which makes 11 yards and leaves you with no feet. For inches, add 8 inches from the first measurement and 11 inches from the second measurement for a total of 19 inches.

Then, convert these measurements to the highest unit possible. Your 19 inches equals 1 foot and 7 inches. Add this foot to your feet total and you have 1 feet and 11 yards. Finally, convert feet to yards: 1 foot is 1/3 of a yard, so you finish with a total of 11 1/3 yards and 7 inches.

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I would have to that it would be about 9 miles because is you go up from oceanfront the it is 9 but if you going sideways it is more then 10. I am so sorry if i get this wrong. Good luck

Answer:

He can feed 5 people

Step-by-step explanation:

divide pizzas in the number of people to how much people will eat.

divide 5 by invisible number, x. getting the answer of 5/6

x=6

Answer:6

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

hm this is a  little tricky!

so on a number line, -3 will be behind -2 because it is less than the two since it is negative. If we have 4/5 and 1/5 we will need to think what comes between them.

5/5 and 0/5  

which means that -3 comes between them both

First and foremost, notice that because the two integers are negative,  [tex]- 2\frac{4}{5}[/tex] is greater than the other number [tex]-3 \frac{1}{5}[/tex] .  As just a result, a number less than  [tex]- 2\frac{4}{5}= -\frac{14}{5}[/tex] and greater than [tex]- 3 \frac{1}{5}= -\frac{16}{5}[/tex]  means a value between such two integers.

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Answer:

Step-by-step explanation:

A

and

D

Answer:

A) WU and ZX

Step-by-step explanation:

Answer:

64 plants/32 seed packets =

2 plants/seed packet

90 plants ÷ 2 plants/seed packet =

45 seed packets

A) B=3V/h

Multiply both sides by 3 to get 3V=Bh. Divide both sides by h, and you get 3V/h=B

Answer:

A) B = 3V/h

Step-by-step explanation:

Given: The formula for the volume of a pyramid is V=1/3Bh.

From the above equation, we have to solve for B.

We use inverse operation to find B.

Multiply by reciprocal of 1/3 on both sides. the reciprocal of 1/3 is 3.

So, multiply by 3 on both sides, we get

3V = 3*1/3*B*h

3V = B*h

Now divide both sides by h, we get

3V/h = Bh/h

3V/h = B

Therefore, the answer is A) B = 3V/h

Answer: -12 < x < [tex]-\frac{9}{2}[/tex]

Step-by-step explanation:

2x + 9 < 0    and      x > -12

2x       < -9

 x        < [tex]-\frac{9}{2}[/tex]

Since it is an "and" statement, x is between -12 and [tex]-\frac{9}{2}[/tex], so -12 < x < [tex]-\frac{9}{2}[/tex]

Graph: -12 o-----------------o [tex]-\frac{9}{2}[/tex]

Interval Notation: (-12, [tex]-\frac{9}{2}[/tex])

The integers that satisfy the inequalities 2x + 9 < 0 and x > -12 are -11, -10, -9, -8, -7, -6, and -5.

To find integers that satisfy both inequalities 2x + 9 < 0 and x > -12, we first solve each inequality separately.

For the inequality 2x + 9 < 0, we subtract 9 from each side to get 2x < -9. Then we divide each side by 2 to find x < -4.5. Since we are looking for integers, x must be less than or equal to -5.

For the inequality x > -12, since x must be greater than -12 and is an integer, the least integer x can be is -11.

Putting these together, the integers that satisfy both inequalities are the set of all integers from -11 through -5. Therefore, we list the integers on one line as: -11, -10, -9, -8, -7, -6, -5.

Answer:

The answer is C. 0.60b + 0.30w = 150; 60 + 0.30w = 150

Step-by-step explanation:

Answer:

2.5 hours

Step-by-step explanation:

25 miles/10 mph= 2.5 hours

Answer:

The awnser is 2.5 because,

Step-by-step explanation:

.25 divided by 10 = 2.5

The decimal moves one time to the left because there is ONE zero (0) in 10.

Hey there!

You could solve those equations many ways but, here's a more "Easier way" to  solve that

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

Answer:

avg speed is 3.5 miles per hour

Step-by-step explanation:

1.75 x 2 = 3.5 miles per hour

Answer:

3 and 1/2

Step-by-step explanation:

hope this helps

Answer:

Given the system of equation:

[tex]y = -x + 2[/tex] and

[tex]y =4x+7[/tex]

Table for the equation [tex]y = -x + 2[/tex] ;

x                y

-1               -3

0              2

1                1

2               0

Then, the points for this equations are: (-1, -3), (0, 2) , (1, 1 ) and (2, 0)

Also, table for the equation: [tex]y =4x+7[/tex]

x               y

-1.75         0  

-1              3

0              7

1               11

Then, the points for this equations are: (-1.75, 0) , (-1, 3) , (0, 7) and ( 1, 11)

Using Point tool , we plot these points of the given system of equation on the Cartesian plane.

You can see the graph as shown below in the attachment.

Also, the two lines intersects at (-1, 3)      

Therefore, the apparent solution for the given system of equation is; (-1, 3)

Final answer:

To find the apparent solution to the system of equations, you need to solve the equations simultaneously. The apparent solution to the given system of equations is (-1, 3).

Explanation:

To find the apparent solution to the system of equations, we need to solve the equations simultaneously. The given equations are:

y = -x + 2

y = 4x + 7

We can solve these equations by setting them equal to each other:

-x + 2 = 4x + 7

Now, we can solve for x:

-x - 4x = 7 - 2

-5x = 5

x = -1

Substituting this value of x back into either of the original equations, we can find the corresponding value of y:

y = -(-1) + 2

y = 3

Therefore, the apparent solution to the system of equations is (-1, 3).

Answer:

causes the growth of peaches with multiple pits

Step-by-step explanation:

I got a 100% on the test :)

Option 3 "causes the growth of peaches with multiple pits" is the correct answer.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

A study revealed that most orchards that used a new fertilizer harvested peaches with multiple pits.

In this study the cases are as follows:

Case 1: Adding fertilizer

The end result is that peaches are plucked while still full of pits.

Case 2: Leaving out fertilizer

As a result, no peaches are picked up with multiple pits.

Thus, option 3 "causes the growth of peaches with multiple pits" is the correct answer.

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Answer: P(G even and W>2) = 1/3 or 0.333 or 33.3%

Step-by-step explanation:

Independent events multiply probabilities,

P(G even)=1/2, P(W>2)=2/3, P(G even and W>2)= 1/2 × 2/3 = 1/3.

Without using definition of "independent events", or rules referring to them, I use sample space S of 36 points, and P(event) = #(event)/#(sample space).

Points are labeled with two digits, left is green die, right is white die. S = {11,12,13,14,15,16,21,...26,...,61,...,66}, and #(S)=36.

An event E is a subset of S, and

0 <= #(E) <= #(S) = 36.

Event G even is GE={21,22,23...,41,42,...,61,...,66},

#(G even)=18

Event "W>2" = W2 ={13,14,15,16,23,24...,63,64,65,66},

#(W>2)=24.

Event G even and W>2 GEW2={23,24,25,26,43,44,45,46,63,64,65,66),

#(GEW2)=12

P(GEW2)=#(GEW2)/#(S)=12/36=1/3=33.3%

To find the probability of the green cube landing with an even number face up and the white cube landing with a number greater than 2 face up, multiply the probabilities of each event happening. The probability is 1/3.

To find the probability that the green cube will land with an even number face up and the white cube will land with a number greater than 2 face up, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The green cube has 3 even numbers (2, 4, and 6) out of 6 faces, so the probability of the green cube landing with an even number face up is 3/6 or 1/2.

The white cube has 4 numbers greater than 2 (3, 4, 5, and 6) out of 6 faces, so the probability of the white cube landing with a number greater than 2 face up is 4/6 or 2/3.

To find the probability of both events happening, we multiply the probabilities: (1/2) * (2/3) = 1/3.

Therefore, the probability that the green cube will land with an even number face up and the white cube will land with a number greater than 2 face up is 1/3. Option C, 1/3, is the correct answer.

Answer:

12) tax rate is 8%

13) convert percent to decimal format

Step-by-step explanation:

12)   4.32/4.00 = 1.08

1.08 - 1 = 0.08

0.08 * 100 = 8%

13) Convert all % to decimal format.

Do this by dividing the percent by 100

e.g. 10% = 10/100 = 0.10

Answer:

Hola,

1, 2, 4, 5, 10, 20

Step-by-step explanation:

Answer:

x=56

The exterior angle is 116

Step-by-step explanation:

The three angles of a triangle add to 180 degrees.

Lets call the unknown angle in the triangle y

y ,2x+4 make a straight line so they are supplementary.  That means they add together to make 180 degrees

y + 2x+4=180

Lets solve for y by subtracting 2x+4 from each side

y + 2x+4 - (2x+4) = 180 - (2x+4)

y = 180 -2x-4

y = 176 -2x

The three angles x , 60 and y   add together to make 180 degrees.

x + 60 + y = 180

Substituting in for y

x + 60 + 176 -2x = 180

Combine like terms

-x + 236 = 180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Divide by -1

x = 56

The exterior angle is 2x+4

2(56) +4

112+4

116

Answer: 1) x=56

2) value of the exterior angle: 116

Step-by-step explanation:

1. to solve for x, set up the equation that equals to the exterior angle

60 + x = 2x + 4

-x + 60 = 4

-x = -56

x = 56

2. now insert x (56) to the exterior angle expression

2 (56) + 4

112 + 4

116 degrees

I can't help you out my brother It's too hard

Answer: d=sc/6. that's what i got.

Step-by-step explanation:

The area of the school banner is approximately 5 times larger than the sign. Area was calculated by multiplying length by width for each, then the ratio was found by dividing the banner area by the sign area.

The subject of this question is mathematics, mostly involving geometrical comparison and proportions between squares. First, you would need to calculate the area of both the banner and the sign. The area of a rectangle is calculated by multiplying its length by its width, so the areas would be 40 inches x 24 inches = 960 square inches for the banner and, the sign would have similar proportions, so width = 18 inches x (24/40) = 10.8 inches, so the area of the sign would be 18 inches x 10.8 inches = 194.4 square inches. Finally, the ratio of the area of the school banner to the area of the sign would be 960/194.4 = 4.94 (approximately). This means the banner is about 5 times larger than the sign.

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Answer:

A.) 10c≤50

Step-by-step explanation:

This inequality shows less than or equal to 10 chairs can be bought with $50

Answer: A.) 10c≤50

Step-by-step explanation:

Hi, to answer this question we have to write an inequality using the information given:

So, if the number of chairs is "c", we can multiply "c" by $10 to obtain the cost of buying "c" number of chairs.

She only has $50, so, the cost of the chairs must be less or equal to 50.

Mathematically speaking:

10c≤50  (option A)

Feel free to ask for more if needed or if you did not understand something.  

Answer: the slope is -5/8 so the mid point would be 2,1.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are half way there when you record the endpoints from the graph correctly. Nice work.

The midpoint is found by this formula

(x_mid,y_mid) = (x1 + x2)/2 , (y1 + y2)/2

Givens

Solution

(x_mid,y_mid) = (-2 + 6)/2, (4 + - 1)/2

(x_mid,y_mid) = (2, 1.5)  Answer

Graph

Answer:     9.6

Step-by-step explanation: A percent is like a decimal so 15% would be 0.15 so if you use that for this you must multiply 32 hours by the 30%/0.30 to find the answer