CL 6-131. Solve each system using the method of your choice.
I. 2x + 3y = 7
−3x − 5y = −13
II. 8 − y = 3x 2y + 3x = 5

It will take [tex]20\frac{5}{6}[/tex] minutes to fill a 50 gallon tub.

Step-by-step explanation:

Time taken to fill 3 gallons bucket = [tex]1\frac{1}{4}=\frac{5}{4}\ minutes[/tex]

We have to find time required to fill 50 gallons tub.

3 gallons = [tex]\frac{5}{4}\ minutes[/tex]

1 gallon = [tex]\frac{5}{4}*\frac{1}{3}\ minutes[/tex]

1 gallon = [tex]\frac{5}{12}\ minutes[/tex]

To find the time required for 50 gallons;

50 gallons = 50 * Time per gallon

50 gallons = [tex]50*\frac{5}{12}[/tex]

50 gallons = [tex]\frac{250}{12}[/tex] = [tex]\frac{125}{6}[/tex]

50 gallons = [tex]20\frac{5}{6}\ minutes[/tex]

It will take [tex]20\frac{5}{6}[/tex] minutes to fill a 50 gallon tub.

Keywords: fraction, division

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Final answer:

It takes approximately 20.83 minutes to fill a 50 gallon tub if it takes 1 1/4 minutes to fill a 3 gallon bucket, considering a constant rate of filling.

Explanation:

The question asks us to determine how long it will take to fill a 50 gallon tub if it takes 1 1/4 minutes to fill a 3 gallon bucket. To solve this, we can set up a proportion since the rates of gallons per minute will be the same for both the bucket and the tub.

First, let's convert the time from minutes to seconds to match the unit for seconds provided in the example. There are 60 seconds in a minute, so 1 1/4 minutes is equal to 75 seconds.

Now, we know it takes 75 seconds to fill 3 gallons. Let's calculate the number of seconds it takes to fill 1 gallon, and then we will use that rate to find out how many seconds it will take to fill 50 gallons.

We divide 75 seconds by 3 gallons, to get 25 seconds per gallon. Then we multiply this rate by 50 gallons to find the total time needed to fill the tub:

25 seconds/gallon × 50 gallons = 1250 seconds.

Finally, to convert seconds back to minutes, we divide 1250 seconds by 60:

1250 seconds ÷ 60 seconds/minute = 20 5/6 minutes or approximately 20.83 minutes.

So, it takes approximately 20.83 minutes to fill a 50 gallon tub at the given rate.

Answer:

1/6

Step-by-step explanation:

Answer:

1. x = 12

2. 3∛4 feet.

Step-by-step explanation:

1. We are given the equation of x as [tex]\sqrt{x - 3} + x = 9[/tex] and we have to find the extraneous solution of the equation.

Now, [tex]\sqrt{x - 3} + x = 9[/tex] ............. (1)

⇒ [tex]\sqrt{x - 3} = 9 - x[/tex]

Squaring both sides we get,

⇒ x - 3 = 81 - 18x + x²

⇒ x² - 19x + 84 = 0

⇒ x² - 12x - 7x + 84 = 0

⇒ (x - 12)(x - 7) = 0

⇒ x = 12 or 7.

Now, putting x = 12 in the equation (1) we get,

[tex]\sqrt{12 - 3} + 12 \neq 9[/tex]

Again, putting x = 7 in the equation (1) we get,

[tex]\sqrt{7 - 3} + 7 = 9[/tex]

Therefore, x = 12 is an extraneous solution of this equation. (Answer)

2. The volume of a cube with side lengths a ft. is given to be 108 ft³.

So, a³ = 108

⇒ a = 3∛4 feet.

Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)

Answer:

10x+20

Step-by-step explanation:

Answer: The equation is 10x+20

(x is a variable, not a multiplication symbol)

Step-by-step explanation:

10 times a number, that is unknown, plus 20.

x is the unknown number.

10x plus 20.

10x+20

I will have "x" represent the unknown number, or you could use a "?", doesn't matter.

[tex]8\leq \frac{x}{-4}[/tex]     [8 is less than or equal to (≤) the quotient (÷) of a number and -4, so the number is being divided by -4]

If you need to solve this, you need to isolate/get the variable "x" by itself in the inequality:

[tex]8\leq \frac{x}{-4}[/tex]   Multiply -4 on both sides to get rid of the fraction and get "x" by itself

[tex](-4)8\geq \frac{x}{-4} (-4)[/tex]    When you multiply/divide by a negative number, you flip the sign (< >)

-32 ≥ x          [-32 is greater than or equal to x, or x is less than or equal to -32]

Answer:

[tex]3\sqrt{2} \sqrt{x}[/tex]

The solution for (x^2+x-17) / (x-4) is (x + 5) + 3/(x-4)

Step-by-step explanation:

The given polynomial is (x^2+x-17) divided by (x-4)

Steps for long division method :

Using long division method :

        x + 5                  

x-4 |  x^2 + x - 17  

    (-)(x^2 - 4x)

                 5x - 17

              (-)(5x -20)      

                         3    

The quotient is (x+5).

The remainder is 3.

The solution is written in the form of quotient + remainder/ divisor

∴ The final answer is (x^2+x-17) / (x-4) = (x + 5) + 3/(x-4)

Final answer:

To divide (x²+x-17) by (x-4) using polynomial long division, divide the highest order term of the dividend by the highest order term of the divisor, multiply the divisor by the result, subtract the result from the dividend, and repeat until there are no more terms or the remainder has lower degree. The quotient is x+5 and the remainder is -3.

Explanation:

To divide (x²+x-17) by (x-4) using polynomial long division:

Write the dividend (x²+x-17) and the divisor (x-4) in the division format.

Divide the highest order term of the dividend (x²) by the highest order term of the divisor (x). The result is x.

Multiply the entire divisor (x-4) by the result from step 2 (x) and write the result below the dividend.

Subtract the result from step 3 from the dividend.

Repeat steps 2-4 until there are no more terms to bring down or the degree of the remainder is less than the degree of the divisor.

The final quotient is x+5 and the remainder is -3.

MI ≅ MR proved by using ASA postulate of congruence

Step-by-step explanation:

Let us revise the cases of congruence

∵ M is the mid-point of TE

∴ MT = ME

In Δs TMI and EMR

∵ ∠T ≅ ∠E ⇒ given

∵ ∠TMI ≅ EMR ⇒ vertical opposite angles

∵ MT = ME ⇒ proved

∴ Δ TMI ≅ ΔEMR by ASA postulate of congruence

- From congruence, corresponding sides are equal

∴ MI ≅ MR

MI ≅ MR proved by using ASA postulate of congruence

Learn more;

You can learn more about the cases of congruence in brainly.com/question/6108628

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The question is about a geometry proof related to congruent angles and midpoints, but additional information is needed to provide a specific solution.

The question appears to be a geometry proof involving congruent angles and midpoints. The goal is to prove that two line segments MI and MR are congruent given ∠E ≅ ∠T, and M is the midpoint of TE.

To prove this, one would need to provide more information about the points I and R, such as their positions relative to point E, T, and M.

Without this additional information, it is difficult to give a specific proof. However, typical proof strategies might involve showing that triangles EMI and TMR are congruent by Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS) postulates, depending on the position of points I and R.

Answer:

[tex]b+g=26[/tex]

[tex]b=g-3[/tex]

Step-by-step explanation:

Let the number of boys be reprented by [tex]b[/tex]

Let the number of girls be represented by [tex]g\\[/tex]

↓ Total number of boys + girls must be 26

[tex]b+g=26[/tex]

↓ Number of boys is 3 less than the number of girls

[tex]b=g-3[/tex]

The system of equations that represents the number of boys and girls are [tex]x+y=26[/tex] and [tex]x = y-3[/tex] and this can be determined by forming the linear equation.

Given :

The following steps can be used in order to determine the system of equations that represents the number of boys and girls:

Step 1 - Let the total number of boys be 'x' and the total number of girls be 'y'.

Step 2 - So, the linear equation that represents the total number of students in Mrs. Augello's math class is:

[tex]x+y=26[/tex]    --- (1)

Step 3 - The linear equation that represents the situation "number of boys is three less than the number of girls" is:

[tex]x = y-3[/tex]   --- (2)

For more information, refer to the link given below:

https://brainly.com/question/11897796

[tex]\( f(2) = \ln \left( \frac{14}{3} \right) \)[/tex]. You can calculate this value to get a numerical result.

To find the particular solution [tex]\( y = f(x) \)[/tex] to the given differential equation [tex]\( \frac{dy}{dx} = \frac{x^2 + 1}{e^y} \)[/tex] with the initial condition [tex]\( f(1) = 0 \)[/tex] and then evaluate [tex]\( f(2) \),[/tex] we can follow these steps:

1. Separate variables:

[tex]\[ e^y dy = (x^2 + 1) dx \][/tex]

2. Integrate both sides:

[tex]\[ \int e^y dy = \int (x^2 + 1) dx \][/tex]

[tex]\[ e^y = \frac{1}{3} x^3 + x + C \][/tex]

3. Apply the initial condition [tex]\( f(1) = 0 \):[/tex]

[tex]\[ e^0 = \frac{1}{3} (1)^3 + 1 + C \][/tex]

[tex]\[ 1 = \frac{1}{3} + 1 + C \][/tex]

[tex]\[ C = \frac{2}{3} \][/tex]

So, the particular solution is:

[tex]\[ e^y = \frac{1}{3} x^3 + x + \frac{2}{3} \][/tex]

4. Solve for  y :

[tex]\[ y = \ln \left( \frac{1}{3} x^3 + x + \frac{2}{3} \right) \][/tex]

Now, we need to find f(2), which means finding the value of y when  x = 2:

[tex]\[ y = \ln \left( \frac{1}{3} (2)^3 + 2 + \frac{2}{3} \right) \][/tex]

[tex]\[ y = \ln \left( \frac{8}{3} + 2 + \frac{2}{3} \right) \][/tex]

[tex]\[ y = \ln \left( \frac{14}{3} \right) \][/tex]

Answer:

SinB = Sin30 = 0.5

Step-by-step explanation:

Ok lets use sine rule

a/SinA = b/SinB = c/SinC

a/Sin60 = b/SinB = 12/Sin90

b/Sin30 = 12/Sin90

b = (12 × Sin30) ÷ Sin90

b = (12 × 0.5) ÷ 1

b = 6cm

SinB = Sin30 = 0.5

To evaluate the expression[tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) for \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\),[/tex]let's substitute these values into the expression:

[tex]\[3\left(\frac{2}{3}\right)^3 - \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 + \frac{2}{3} \times \frac{1}{2}\][/tex]

Let's simplify this step by step.

1. [tex]\(3\left(\frac{2}{3}\right)^3 = 3 \times \frac{8}{27} = \frac{24}{27} = \frac{8}{9}\)[/tex]

2.  [tex]\(- \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 = - 2 \times 2^6 \times \frac{1}{3^2} \times \frac{1}{2^2} = - 2 \times 64 \times \frac{1}{9} \times \frac{1}{4} = - \frac{128}{9}\)[/tex]

3   .[tex]\(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\)[/tex]

Now, let's add these results together:

[tex]\[\frac{8}{9} - \frac{128}{9} + \frac{1}{3} = \frac{8 - 128 + 3}{9} = \frac{-117}{9} = -\frac{13}{3}\][/tex]

So, [tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) evaluated at \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\) is \(-\frac{13}{3}\).[/tex]

Answer:

the graph of the equation will  be symmetric about option b.) x axis

Step-by-step explanation:

i) the given equation is x = [tex]y^2[/tex] + 4

ii) therefore [tex]y^{2}[/tex] = x - 4

iii) the equation is that of a parabola with vertex at (4,0)

iv) the graph of the equation will  be symmetric about option b.) x axis

Answer:

55

Step-by-step explanation:

The two shortest sides added up need to be longer then the longest angle so 48 + 55 = 103>73

Answer:

Plane B is closer.

The distance for Plane A is 7.9 km.

The distance for Plane B is 7.4 km.

Step-by-step explanation:

To find the distance to the tower, altitude must be converted to kilometers. Each 1000 ft is 0.3048 km, so the heights of the planes are ...

-- Plane A: (20 thousand ft)*(0.3048 km/thousand ft) = 6.096 km

-- Plane B: (8 thousand ft)*(0.3048 km/thousand ft) = 2.4384 km

The Pythagorean theorem can be used to find the distance from each plane to the tower:

-- distance = √((ground distance)² + (height)²)

-- Plane A distance = √(5² +6.096²) ≈ √62.16 ≈ 7.9 . . . km

-- Plane B distance = √(7² +2.4384²) ≈ √54.95 ≈ 7.4 . . . km

The distance for Plane B is shorter, so Plane B is closer to the tower.

Square of m reduced by 49 = m²- 49

Step-by-step explanation:

Let us consider the variable as m.

Square of m is given as m².

Reduction factor is 49.

So the expression for the square of m reduced by 49 is given as m²- 49.

Answer:

42)  122.72 square inches

43) 212.83 additional feet of fabric

Step-by-step explanation:

42)

Diameter = [tex]12\frac{1}{2}[/tex] = 12.5 inches

Radius = (1/2) * Diameter = (1/2) * 12.5 = 6.25 inches

The formula for calculating the area of a circle is π * Radius²

π * Radius²

Substitute radius and pi into formula

3.14159265359 * 6.25²

Solve exponent

3.14159265359 * 39.0625

Multiply

122.7184630309

Round to the nearest hundredth

122.72 square inches

43)  Clarissa needs 500 feet of fabric

She has these pieces

3 pieces of fabric that are each 18 yards long

1 piece of fabric that is [tex]16\frac{1}{2}[/tex] yards long

1 piece of fabric that is [tex]75\frac{2}{3}[/tex] feet long

Convert all yard measurements to feet and all fractions to decimals

(1 yard = 3 feet)

3 pieces of fabric that are each 54 feet long

1 piece of fabric that is 49.5 yards long

1 piece of fabric that is 75.67 feet long

Add all lengths

3(54) + 49.5 + 75.67

162 + 49.5 + 75.67 = 287.17

Subtract from 500 to find missing length

500 - 287.17 = 212.83

212.83 additional feet of fabric

Hope this helps :)

Answer:

Therefore Afon can read 0.75 pages per minute.

Step-by-step explanation:

Afon read 22 1/2 pages in 30 minutes

Therefore Afon read 22.5 pages in 30 minutes.

Therefore the number of pages Afon can read in 1 minute

[tex]= \dfrac{22.5}{30} = \dfrac{45}{60} = \dfrac{9}{12} = \dfrac{3}{4} = 0.75 pages[/tex]

Therefore Afon can read 0.75 pages per minute.

Answer: 1,360

Step-by-step explanation:

20 * 20 = 400

20 * 12 = 240

240 * 4 = 960

960 + 400 = 1,360

Answer:

approximately 2,800

Step-by-step explanation:

you would round 691 to 700 then multiply by 4

Answer:

2,800

Step-by-step explanation:

In saying "largest number," I believe the question means that you should round 691 up to 700 (nearest hundreds). Multiple 700 by 4, and you will get 2,800! Hope this helps! :)

Answer:45

Step-by-step explanation:

it is 45

Step-by-step explanation:

Answer:

[tex]11\frac{3}{8}\ yd[/tex]

Step-by-step explanation:

we know that

To find out the total yards of fabric used, add up the yards of fabric used for Nickys' room and the yards of fabric used for Linda's room

so

[tex]4\frac{3}{4}+6\frac{5}{8}[/tex]

Convert mixed number to an improper fraction

[tex]4\frac{3}{4}\ yd=4+\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}\ yd[/tex]

[tex]6\frac{5}{8}\ yd=6+\frac{5}{8}=\frac{6*8+5}{8}=\frac{53}{8}\ yd[/tex]

Adds the fractions

[tex]\frac{19}{4}+\frac{53}{8}=\frac{2*19+53}{8}= \frac{91}{8}\ yd[/tex]

Convert to mixed number

[tex]\frac{91}{8}\ yd= \frac{88}{8}+ \frac{3}{8}= 11\frac{3}{8}\ yd[/tex]

Answer:

There's no picture. Is it D.√3 / 2

Step-by-step explanation:

Answer:

lool at the picture shown

Answer:

The amount of stock for which both brokers would charge the same commission is $2500.

Step-by-step explanation:

i) Let the amount of stock to be traded be worth $x

ii) therefore for both the brokers to charge the same commission we can write

   1% of x  = $25 [tex]\RIghtarrow[/tex][tex]\Rightarrow[/tex]  0.01 [tex]\times[/tex] x  = 25  [tex]\therefore[/tex]   x = [tex]\frac{25}{0.01} = 2500[/tex]

The amount of stock for which both brokers would charge the same commission is $2500.

Final answer:

By setting up an equation based on the given information that Jim is 2 years older than 3 times Tommy's age and their combined ages are 18, we find that Tommy is 4 years old and Jim is 14 years old.

Explanation:

The question is about finding the ages of Jim and his younger brother Tommy given that Jim is 2 years older than 3 times Tommy's age and together their ages add up to 18. Let's denote Tommy's age as T years. Therefore, Jim's age would be 3T + 2 years. According to the problem, if we add both ages, the sum is 18. So, we can set up the following equation to find their ages:

T + (3T + 2) = 18

Simplifying this equation gives:

4T + 2 = 18

4T = 16

T = 4

Thus, Tommy is 4 years old. To find Jim's age, we substitute Tommy's age back into the equation for Jim's age:

Jim's age = 3(4) + 2 = 12 + 2 = 14

Therefore, Tommy is 4 years old, and Jim is 14 years old.

-1/2x < -12

Divide both sides by -1/2

Also because you are dividing by a negative number you need to reverse the inequality sign.

X > 24

[tex](-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )[/tex]

Solution:

Given [tex]f(x)=6\left(\frac{2}{3}\right)^{x}[/tex]

Domain = {–1, 0, 1, 2, 3}

Substitute the given values in the function.

At x = –1,

[tex]f(-1)=6\left(\frac{2}{3}\right)^{-1}[/tex]

         [tex]=6 \times \frac{3}{2}[/tex]

         = 9

[tex](x, f(x))=(-1, 9)[/tex]

At x = –0,

[tex]f(0)=6\left(\frac{2}{3}\right)^{0}=6[/tex]

[tex](x, f(x))=(0,6)[/tex]

At x = 1,

[tex]f(1)=6\left(\frac{2}{3}\right)^{1}=4[/tex]

[tex](x, f(x))=(1,4)[/tex]

At x = 2,

[tex]f(2)=6\left(\frac{2}{3}\right)^{2}[/tex]

       [tex]=\frac{24}{9}[/tex]

      [tex]=2\frac{6}{9}[/tex] (Cancel the common terms)

      [tex]=2\frac{2}{3}[/tex]

[tex](x, f(x))=(2, 2\frac{2}{3} )[/tex]

At x = 3,

[tex]f(3)=6\left(\frac{2}{3}\right)^{3}[/tex]

       [tex]=\frac{48}{27}[/tex] (Cancel the common terms)

       [tex]=\frac{16}{9}[/tex]

      [tex]=1\frac{7}{9}[/tex]

[tex](x, f(x))=(3, 1\frac{7}{9} )[/tex]

Plot the points in the graph.

The image of the graph is attached below.