Santiago is solving the system of equations.5x – 4y = 604x + 5y = 60Which description shows a way to solve the system of equations correctly ?

Considering the expression of a line, the price of the guitar in 2011 is $354.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

Being:

the slope can be calculated as:

m= (300 - 246)÷ (2008 - 2005)

m= 54÷ 3

m= 18

Considering point 2 and the slope m, you obtain:

300= 18×2008 + b

300= 36,144 + b

300- 36,144 = b

-35,844 = b

Finally, the equation of the line is Price= 18×Year - 35,844

Now, you want to know the price of the guitar in 2011. Replacing in the linear equation, you get:

Price= 18×2011 - 35,844

Solving:

Price= 36,198- 35,844

Price= 354

In summary, the price of the guitar by 2011 is $354.

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Answer: -x^2-2x-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

well just go throught the factors as far as you can ik from my personal mindset that 14*14= 196 so if i go bk and  calculate 13*13=169 which means its gonna be in between 13 and 14. so to figure this out we have to write it out. so we can try 13.5*13.5=182.25 so we have to go higher  13.89*13.89=192.9321 which means it has to be 13.89 rounded to the nearest hundreth.

The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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Answer:

Step-by-step explanation:

3y - x = - 12 ⇔ y = \(\frac{1}{3}\) x - 4

y - 2 = \(\frac{1}{3}\) ( x - 18 )

y = \(\frac{1}{3}\) x - 4

Answer:

y=1/3x-4

Step-by-step explanation:

Refer to the picture that given

Answer:

-5

Step-by-step explanation:

f(g(-2)

solve g(-2) first

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

now solve f(1)

-7(1)+2=-5

OR

put g(x) into f(x)

f(g(x)= -7(x+3)+2   then plug in the -2

f(g(-2)=-7(-2+3)+2

f(g(-2)= -7(1)+2= -5

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer:

C on Edge 2021

Step-by-step explanation:

Answer

Your answer should be C.

Step-by-step explanation:

Step-by-step explanation:

1) angle 2 and 4

2)angle 2 and 3

3)angle 1 and 4

Hope it helps

Using ratio we can conclude that Recipe 1 and recipe 2 tastes the same.

The multiplicity of two integers is shown by a ratio. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Let us consider the ratio of the orange juice top the pineapple juice for the 3 recipes.

Recipe 1 = 4 : 6 = 2 : 3

Recipe 2 = 6 : 9 = 2 : 3

Recipe 3 = 9 : 12 = 3 : 4

Hence from the above ratios we can conclude that Recipe 1 and recipe 2 tastes the same.

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Answer:

2

Step-by-step explanation:

terms are separated by addition or subtraction signs so this expression can be simplified to be \(\frac{m}{5}\) + 24, therefore two terms:

m/5 and 24

Answer:

6yx

Step-by-step explanation:

Answer:

c. SA = 596 ft²

Step-by-step explanation:

Area of the rectangular pyramid = Base area + area of the 2 equal lateral faces + area of the 2 lateral faces

Base area = length × width

Length = 16 ft

Width = 12 ft

Base area = 16 × 12 = 192 ft²

Area of the 2 lateral faces with the following dimension:

base = 12 ft

height = 15 ft

Area = 2(½bh) = 2(½*12*15) = 180 ft²

Area of the 2 lateral faces with the following dimensions:

base = 16 ft

height = 14 ft

Area = 2(½*14*16) = 224 ft²

✅Total surface area = 192 + 180 + 224 = 596 ft²

Answer:

c

Step-by-step explanation:

Is is right?

Answer:

45

Step-by-step explanation:

Answer:

The length of the body is 45.

Step-by-step explanation:

The violin and bass have an equal ratio, to find the ratio find the two given lengths and divide them, 72 ÷ 24 = 3. So the ratio is 3:1. To find the body of the bass you just have to do 15 × 3. Which is 45.

\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

Every function is a relation but not every relation is a function.

Step-by-step explanation:

A function is only that relation in which each input or the relation has exactly one output.

The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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Thomas is buying football jerseys for his high school football team.

The cost of each jersey is $80.

The company also charges a processing fee of $100.

We could write an equation that models Thomas's total cost for purchasing x

number of jerseys.

Since for every x jerseys Thomas buys, he pays

But he also has to pay the company's processing fee, this is independent of the quantity bought.

So, the total cost for buying x number of jerseys is;

ii. What is Thomas's total cost, if he buys 55 jerseys?

We can use our formula,

Therefore, Thomas's total cost for 55 jerseys is $4500

Answer:

Step-by-step explanation:

<SRQ = 270 degrees

<RPQ is just 31 degrees short of that amount.

<RPQ = <SRQ - 31

<RPQ = 270 - 31

<RPQ = 239

Answer:

n = 9

Step-by-step explanation:

24 = -3 + 3n

24 + 3 = 3n

27 = 3n

9 = n

Answer: n = 9

Step-by-step explanation:

24 = -3+ 3n  - so + 3 on both sides - you get

27 = 3n - then divide both sides by 3 - which is

9 = n

n = 9

in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x\)

Answer:

268m²

Step-by-step explanation:

given,

l= 10m

b= 8m

h= 3m

A = ?

we know,

A = 2 (lb + bh + lh)

= 2 (10m×8m + 8m×3m + 10m×3m)

= 2 ( 80m² + 24m² + 30m² )

= 2 ( 134m² )

= 268m²

Answer: \(4\sqrt{5}x^7\)

Step-by-step explanation:

\(\sqrt{80}x^7\)

\(=\sqrt{2^4\cdot \:5}x^7\)

\(=\sqrt{2^4}\sqrt{5}x^7\)

\(=4\sqrt{5}x^7\)

Answer:

Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

Step-by-step explanation:

hourly pay: $5/hour

number of hours: 24 hours

total pay = hourly pay × number of hours

total pay = $5/hour × 24 hours

total pay = $120

MP3 player costs $100.

Total pay is $120.

Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.