Use substitution to write an equivalent quadratic equation.
(3x + 2)2 + 7(3x + 2) – 8 = 0


ANSWER IS ✔ u² + 7u - 8 = 0, where u = 3x + 2

There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Answer:

1/27000

Step-by-step explanation:

Use your calculator

Answer:

one elven? do you mean eleven? if so, the answer is 11.00900 hope this helps

Step-by-step explanation:

Answer:

11.091000

Step-by-step explanation:

Answer:

The answer is letter B

Step-by-step explanation:

We know obviously when you are multiplying (since it is how MANY he ran that we are multiplying to get total distance), you don't add 1 or 3 to the numbers. We also know he did not run the 26 mile course 13 times, so the only answer choice that is feasible and/or even remotely correct would be B.

Answer:

0

Step-by-step explanation:

\(2\sqrt[3]{(1-3x)} =6-4=2\\\sqrt[3]{(1-3x)}=\frac{2}{2} =1\\\sqrt[3]{(1-3x)}^{3} =1^{3} \\(1-3x)=1\\-3x=0\\x=0\)

Answer:

length=22 [cm].

Step-by-step explanation:

1) if the length is 'l' and the width is 'w', then it is possible

2) to write the given perimeter: 62=2(l+w), - this is the 1st equation of system;

3) to write the condition 'the length of a rectangle is 5 cm less than 3 times its width' as 3w-5=l, - this is the 2d equation of the system.

4) using two equations above it is possible to make up the next system:

\(\left \{ {{2(w+l)=62} \atop {3w-5=l}} \right. \ = > \ \left \{ {{w+l=31} \atop {3w-l=5}} \right. \ = > \ \left \{ {{l=22} \atop {w=9}} \right.\)

5) finally, the length=22 [cm].

Solving the system of equations with the substitution method, we have:

- x - y - z = -8 Equation (1)

- 4x + 4y + 5z = 7 Equation (2)

2x + 2z = 4 Equation (3)

2x=4 - 2z (Subtracting 2z from both sides of the equation 3)

x=2- z (Dividing by 2 on both sides of equation 3)

-x-z=-8+y (Adding y to both sides of equation 1)

-x-z+8=y (Adding 8 to both sides of the equation 1)

Replacing the previous results in the equation 2, we have:

-4(2-z) + 4(-(2-z)-z+8)+ 5z = 7

-8+4z+4(-2+z-z+8)+5z = 7 (Distributing)

-8+4z+4(-2+8)+5z=7 (Subtracting like terms)

-8+4z-8+32+5z=7 (Distributing)

9z+16=7 (Adding like terms)

9z=-9 (Subtracting 16 from both sides of the equation)

z=-1( Dividing by 9 on both sides of the equation)

Replacing z in the equation x=2-z

x=2-(-1)=2+1=3

Replacing x=3 and z=-1 in the equation -x-z+8=y

-3-(-1)+8=y

-3+1+8=y

6=y

The answers are:

x=3

y=6

z=-1

Given:

A right angle triangle ABC, right angled at C.

To find:

The measure of θ.

Solution:

In a right angle triangle,

\(\tan \theta=\dfrac{Opposite}{Adjacent}\)

In triangle ABC,

\(\tan \theta=\dfrac{AC}{BC}\)

\(\tan \theta=\dfrac{2.7}{5}\)

\(\tan \theta=0.54\)

It can be written as

\(\theta=\tan^{-1}0.54\)

\(\theta\approx 28.369\)

Therefore, the measure of θ is 28.369.

We are given two curves on a graph paper and we have to find the y values for the given x.

From the graph we can check for a value of x, what is the value of y from the curve.

x     -3     -2     -1    0      1         2        3

Exp  8      4      2    1      0.5  0.25  0.125

Lin.   7.5   6    4.5   3      1.5     0     -1.5

We find that the two have the same values where the two curves intersect.

From the graph we find that near to -3 and near to 2 both have the same values.

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The missing graph is attached below.

Answer:

......______.......

....._______..........

Answer:

(F+G)(x)= x²+2x+2

Step-by-step explanation:

Finding the answer is pretty simply:

The given equations are

F(x) = 2x

G(x) = x²+2

Finding  (F+G)(x).

Now we simply have to add the values of both functions F(x) and G(x).

(F+G)(x) = F(x) + G(x)

All we have to do is substitute the values of both functions F(x) and G(x) into the given equation.

(F+G)(x) = (2x) + (x² +2)

Rearranging the terms

(F+G)(x)= x²+2x+2

P.S. thanks to AmeerAbdullah for the awesome answer.

The credit term 3/15, n/45 states that the buyer will receive a 3% discount if the payment is made within 15 days. Otherwise, full payment is expected within 45 days from the invoice date.

This term can be expressed as a formula and calculation as follows:

Discount = 3% of Invoice Total

Payment due within 15 days = Invoice Total - Discount

Payment due within 45 days = Invoice Total

For example, if the invoice total is $500, then the buyer will receive a 3% discount (Discount = 3% x $500 = $15) if the payment is made within 15 days. The payment due within 15 days is then equal to the invoice total minus the discount ($500 -$15 = $485). On the other hand, if the payment is not made within 15 days, the buyer is expected to pay the full invoice total within 45 days ($500).

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Answer:

Step-by-step explanation:

25

Answer:

A is no, B is yes, and I can't see the rest of the options

Answer:

I think you got to time it all togther and the answer would be 531.44m^3

Step-by-step explanation:

(5.2×7×14.6)mmm

(36.4×14.6)mmm

531.44m^3

The number of miles planned on Saturday is 19 milea

This means the sequence where the difference between one term and the next term is a constant.

In this case, the following information are illustrated:

Sunday: 1 miles

Monday: 4 miles

Tuesday: 7 miles

Wednesday : 10 miles

Thursday: 13 miles

Friday: 16 miles

As we can see there's a difference of three between them. This can be seen as:

= 4 miles - 1 mile

= 3 miles

Therefore, the number planned on Saturday will be:

= Friday + 3 miles

= 16 miles + 3 miles

= 19 miles

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a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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The missing side length on the figure is 9 yards

From the question, we have the following parameters that can be used in our computation:

The figure

The missing length on the figure is represented with ?

Using the above as a guide, we have the following equation

? + 7 = 16

Evaluate

? = 9

Hence, the missing side length is 9 yards

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The missing side length is equal to 9 yd.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: length and width (W). Due to its characteristics, the rectangle presents two lengths (L) and two widths (W).

For solving this question, you should:

        The figure is composed of two rectangles:

          Rectangle 01 whose sides are: 6 yd (W) and 16 yd (L).

          Rectangle 02 whose sides are: 8 yd (W) and 7 yd (L).

If the length (L) of rectangle 01 is 16 yd, which is equal to the sum between the missing side and the length of rectangle 02 (7 yd). Thus

      16=s+7

      s=16-7

      s=9

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The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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Using equations, the time for the main engine 14.4 seconds and 21.6 seconds for the auxiliary engine

Let's call the time each engine takes to consume its allotted fuel supply as "t₁" for the main engine and "t₂" for the auxiliary engine.

From the first piece of information, we know:

t₁ = (2/3)t₂

From the second piece of information, we know that the combined fuel consumption time for both engines is 36 seconds:

t₁ + t₂ = 36

Now we can substitute the first equation into the second:

t₁ + (2/3)t₂ = 36

Combining like terms:

t₂ = 21.6

Finally, substituting t₂ back into the first equation:

t₁ = (2/3)(21.6) = 14.4

So the main engine alone could be fired for 14.4 seconds and the auxiliary engine alone could be fired for 21.6 seconds.

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Answer: exponential growth function

Step-by-step explanation:

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Answer:

3x+1=3x+1

0x=0

no solution

3x+1=3x+2

0×=1

no solution

3x+1=2x+1

x=0

X IS THE SOLUTION BTW

Answer:

  $42

Step-by-step explanation:

You want the price with tax of a $35 pair of shoes subject to a 20% tax.

The tax is the cost of the shoes multiplied by the tax rate. The final price is the sum of the cost of the shoes and the tax:

  final price = price + price × tax rate

  final price = price × (1 + tax rate) = $35 × 1.20 = $42

The final price of the shoes is $42.

Answer:

42$

Step-by-step explanation:

tax increase will be

20% of 35$

= 20/100 × 35

= 7$

Final price = Old price + Tax

= 35 + 7

= 42$

Answer: x=1, y=-4

Step-by-step explanation:

There are different ways to solve system of equation

In your case, since they are all put y on one side, then we should use substitution.

we should substitute y

-7x+3=-x-3

-7x+x=-3-3

  -6x=-6

      x=1

--------------------------

substitute x into any one of the equation to find y

y=-7x+3

y=-7×1+3

y=-7+3

y=-4

y=-x-3

y=-1-3

y=-4

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This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.

Given that,

For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.

We have to find what percentage of the initial purchase price was represented by the auction price.

Let us take the percentage as x%.

Necklace sold at auction=the percentage multiplied by the actual price

We get,

$11,379,600 =x%($54,000)

x%=$11,379,600/$54,000

x%=2.1%

Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.

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Answer:

The angles are 87 degrees and 93 degrees.

Im not sure if its correct-

Step-by-step explanation:

x+(x-6)=180

2x=174

x=87