Solving a word problem using a system of linear equations

Select all expressions that are equivalent to (2n + 6)(n + 3)

we have

(2n + 6)(n + 3)

apply distributive property

2n^2+6n+6n+18

2n^2+12n+18

Verify each option

option A

2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok

option B

is not correct

option C

is correct

option D

is not correct

option E

2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct

option F

2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok

therefore

The average cost per minute which the shop runs is $1.50

To find the shop's cost per minute, we can write down equations and proceed to solve.

In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.

But we were not given the average cost per cupcake.

To do that, let's write an equation for this.

[tex]y = mx + c[/tex]

Let's find the slope to this equation which determines the average cost per minute.

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]

The shop's cost per minute was calculated to be $1.50.

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y= 2x+4

Slope-intercept form

y=mx+b

Where:

m= slope

b= y-intercept

y=2x+4

Slope = m= 2

Perpendicular lines have negative reciprocal slopes.

So, the slope of the new line = -1/2

New equation:

y= -1/2x+b

Replace x,y by the point (4,2) and solve for b:

2 = -1/2(4)+b

2= -2 + b

2+2 = b

4 = b

New line equation:

y= -1/2x+4

The factor by which the current changes if the resistance increases 10% is; 90.9% reduction

Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;

I = V/R

Now, we are told that the resistance increases by 10%.

Thus, New value of resistance = 1.1R

Thus, new current/old current = 1/1.1 = 0.909 = 90.9%

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given: 100 cm = 1 meters

We need to convert 4 m to cm

so,

The total number associated to barre class is 207 + 196 = 403

Therefore, the probability that a attendee does not attend a barre class is given by 403/2153 = 0.1872

If Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

The interest rate = 4.6%

The final amount = $1610

The time period = 15 years

The compound interest

A = [tex]P(1+\frac{r}{100})^{t}[/tex]

Where A is the final amount

P is the principal amount

r = interest rate

t is the time period

Substitute the values in the equation

1610 = [tex]P(1+\frac{4.6}{100})^{15}[/tex]

1610 = P×1.96

P = 1610/1.96

P = $820.06

Hence, if Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years

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If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:

That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:

Jenna bought a coat on sale for $120

The price of the coat is the 2/3of the original price

Let the original price is $x

So, the equation will be :

2/3 of x =120

So, The original price of the coat is $180

Using the Fundamental Counting Theorem, the number of length-n sequences that have at least one pair of adjacent LEDs that light up with the same color is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In the context of this problem, there are n LEDs, each with 4 possible colors, hence he total number of sequences is:

[tex]T = 4^n[/tex]

For sequences with no repeating LEDs, we have that:

Hence the number is:

[tex]T_n = 4 \times 3^{n-1}[/tex]

(n - 1) as the first LED is not included on those with 3 possibilities.

Having at least one repeating and no repeating are complementary events, hence the number of sequences is:

[tex]N = 4 - 4 \times 3^{n - 1}[/tex]

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Formula for the trigonometry is y = b sin ( πx/2 - π/2) + 4

y = A sin( ωx + δ) + b

period: t = 4

ω = 2π/t = 2π/4 = π/2

A = 10 -(-2)/ 2

  = 6

b = (10-2)/2

  = 4

y = b sin (πx/2 + δ) + 4

x = 0, y = bsinδ + 4 = -2

sinδ = -1   => δ = -π/2

y = b sin( πx/2 - π/2) + 4

Therefore the formula for the trigonometry function is y = b sin(πx/2 - π/2) + 4.

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Answer:

L x W =   8.5 x 24    or     12 x 17

Step-by-step explanation:

x  (41 -2x) =204

-2x^2 + 41x -204 = 0      Use Quadratic Formula to find x = 8.5 or 12

(x-8.5)(x-12) = 0

         two sides = 8.5       and river/third side =  24

      or  two sides 12     and river/thirdside = 17

Given

the age of the winner for best actor was 38 and the age of the winner for best actress was 51.

For all best​ actors, the mean age is 46.8 years and the standard deviation is 5.7 years.

For all best​ actresses, the mean age is 31.9 years and the standard deviation is 10.8 years.​

Find

who had the more extreme age when winning the​ award, the actor or the​ actress

Explanation

the Z- score is given by

Best Actor

X = 38

mean = 46.8 years

standard deviation = 5.7 years.

so ,

Best Actress

X = 51

mean = 31.9 years

standard deviation = 10.8 years.

so ,

the best actress's age is farther from the mean so he has the more extreme age when the winning the award.

Final Answer

Hence , the z- score for best actor is -1.54 and for best actress = 1.77

Actress has more extreme age

The general form of a quadratic equation is given by the expression:

A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero

(a < 0). Such a graph opens downwards

Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point

Mathematically expressed as:

Answer: y = -2x + 5

Step-by-step explanation:

y = _x + 5

(5,0) (3,4)

(y2 - y1) / (x2 - x1)

(4 - 0 ) / (3 -5)

4 / -2

-2

y = -2x + 5

The coat of the dress based on the percentage is $66.

From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.

Let the cost of the dress be represented as x

Therefore, the appropriate information given I'll be expressed as:

= 55% × 120 = x

0.55 × 120 = x

Multiply

x = 66

The amount spent is $66.

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In order to simplify an equation we want to add all the terms with the same unkowns.

In the equation

4 - 2y + (-8y) + 7.3

we can see that there are terms with y and numbers alone.

We combine like terms:

Terms with y: -2y,

Let's simplify the following equation

The expected value of the proposition is $22.6

The given parameters are

Represent the proportion as a fraction

So, we have

p = 359/449

The expected value is then calculated as

E(x) = p * Amount paid for making a throw - (1 - p) * Amount collected for losing a throw

Where p represents the proportion defined above

So, we have

E(x) = 359/449 * 39 - (1 - 359/449) * 43

Evaluate the difference

E(x) = 359/449 * 39 - 90/449 * 43

So, we have

E(x) = 22.6

Hence, the proposition has an expected value of $22.6

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Answer:

-1.09

The problem requires one to calculate the win payoff and win probability as well as the lose payoff and probability. You would then do a calculation like this:

[(Win Payoff) x (Win Probability)] + [(Lose Payoff) x (Lose Probability)]

The various algebraic properties used for each of the given expressions are;

1) Symmetric property of equality.

2) Distributive property of equality.

3) Addition property of equality.

4) Division property of equality.

5) Addition property of equality.

6) Transitive property of equality.

7) Associative property of equality.

8) Multiplication property of equality

9) Commutative property of equality.

There are different properties of equality or algebra such as;

1)  If AB=CD, then CD=AB; Property used here is Symmetric property of equality because it suits the definition.

2) 5(x-4) = 5x-20; Property used here is Distributive property of equality because it suits the definition.

3) 3x - 17 = 8, then 3x = 25; Property used here is Addition property of equality because it suits the definition.

4) 22m=440, then m=20; Property used here is Division property of equality because it suits the definition.

5) :(2a+3a)-4a=7a+55, then (5a)-4a=7a+55; Property used here is Addition property of equality because it suits the definition.

6) If GH=2x+17, and 2x+17=JK, then GH=JK; Property used here is Transitive property of equality because it suits the definition.

7) 2b+(b-7)=17, then (2b+b)-7=17; Property used here is Associative property of equality because it suits the definition.

8) (x+7)/3=13, then x+7=39.; Property used here is Multiplication property of equality because it suits the definition.

9) m 10:4+x=13, then x+4=13; Property used here is Commutative property of equality because it suits the definition.

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Answer:

x-intercept: (-0.5,0)

y-intercept: (0,1)

Slope: 2

Domain: All real values

Range: All real values

Step-by-step explanation:

x-intercept:

The x-intercept is the value of x when y = 0. In this graphic, we have that when y = 0, x = -0.5. So the x-intercept is given by: (-0.5,0)

y-intercept:

The y-intercept is the value of y when x = 0. In this graphic, we have that when x = 0, y = 1. So the y-intercept is given by: (0,1).

Slope:

To find the slope, we select two points. The slope is given by the division of the change in y by the change in x.

Two points: (-0.5, 0) and (0,1)

Change in y: 1 - 0 = 1

Change in x: 0 - (-0.5) = 0 + 0.5 = 0.5

Slope: 1/0.5 = 2

Domain and range:

In a line, the domain is all real values, the same for the range.

Answer:

26 centilitres.

Explanation:

First, we start by recalling the standard conversion between millilitres and centilitres.

Let 260 milliliters = x centiliters

We express it as a ratio:

Cross multiply to solve for x:

Therefore, 260 millilitres is 26 centiliters.

Answer:

11

Step-by-step explanation:

A = lw

l = A/w

l = 77/7

l = 11

Hope that helps

Top left: Yes, each input corresponds to only one output.

Top right: Yes, each input corresponds to only one output.

Bottom left: Yes, each input corresponds to only one output.

Bottom right: No, the input of -1 corresponds to three different outputs.

(4x -2) yd, 2x yd, 2(x + 7) yd, 2.5x yd. The triangle's perimeter is the same as the square's perimeter. The value of x=6

Given that,

The graphic displays the yards-long sides of a triangle and a square. The triangle's perimeter is the same as the square's perimeter.

We have to find the value of x in the given side.

In the picture we can see the triangle and square.

The perimeter of the triangle is sum of the three sides of the triangle.

The perimeter of the square is 4 times the side of the square.

4x-2+2x+2(x+7)=4×2.5x

4x-2+2x+2x+14=10x

8x+12=10x

10x-8x=12

2x=12

x=12/2

x=6

Therefore, the value of x=6

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Hello!

First, let's rewrite the expression here:

We will have to find the coefficients a, b and c:

• a ,= -2;

• b ,= 12;

• c ,= -15;

As we can see, coefficient a is negative. It means that the parabola will face downwards and have a maximum value.

We can obtain this point by using the two formulas below to calculate the coordinates (x, y) of this point, look:

As we know the coefficients, let's replace the values in the formulas:

Xv:

Now let's find Yv:

Doing this, we obtained the coordinate of the maximum point (x, y) = (3, 3).

As it doesn't have any restrictions, the domain will be: [-∞, +∞].

The maximum value will be when y = 3, so the range is [-∞, 3].

Look at the graph of this function below:

Given data:

First squaring both sides we get,

Therefore, the value for the solution which satisfies the above equation are

Thus, the ans is (a) , (b) , (d) , (e)

The expresion for the correlation coefficient is :

summation of x = 5 + 7 + 10 + 15 + 19

Summation of x = 56

Summation of y = 19 + 17 + 16 + 12 + 7

Summation of y = 71

Summation of prodcut xy

Summation of x^2 = 25 + 49 + 100 + 225 + 361

Summation of x^2 = 760

Summation of y^2 = 361 + 289 + 256 + 144 + 49

Summation of y^2 = 1099

Substitute tha value in the expression of correlation coefficient

Answer: A) Correlation coefficient is 0.985

The measure of the fourth angle that is x and the value is 133°

A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.

Let the 8 interior angles of the octagon be:

x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.

Their sum = 8x+16 = 1080, or

this implies 8x = 1080–16 = 1064  

thus on further solving we get x = 133

Hence the sixth angle = x+8 =141 degrees.

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