Every week, Estella has guitar lessons.
A guitar is shown. The caption says that Guitar Lessons are thirty-five dollars per lesson.
Question 1
Part A

Complete the expression to represent the change in Estella’s account balance due to guitar lessons after 2 years.

Answer:

x = 10 (yes)

x = 14 (yes)

x = 6 (no)

x = 4 (no)

Step-by-step explanation:

Plug in each x value into the function and determine if it is true or not.

44 [tex]\leq[/tex] 35 + x

44 [tex]\leq[/tex] 35 + (10)

44 [tex]\leq[/tex] 45

45 is greater than or equal to 44, so it is a solution

44 [tex]\leq[/tex] 35 + (14)

44 [tex]\leq[/tex] 49

49 is greater than or equal to 44, so it is a solution

44 [tex]\leq[/tex] 35 + (6)

44 [tex]\leq[/tex] 41

41 is not greater than or equal to 44, so it is not a solution

44 [tex]\leq[/tex] 35 + (4)

44 [tex]\leq[/tex] 39

39 is not greater than or equal to 44, so it is not a solution

I hope this helps! :)

Answer:

Step-by-step explanation:

It is impossible to accurately estimate the size of the crowd without knowing how many people are standing in each foot of space. However, if we assume that 16 people fit in a 9 ft x 8 ft area, then we can estimate the size of the crowd in a 2-mile section of the parade route that is 5 feet deep on both sides of the street.

Assuming a 5-foot deep crowd on both sides of the parade route, we can estimate that there would be 40 feet of crowd on one side of the parade route and 40 feet of crowd on the other side of the parade route. This means that there would be a total of 80 feet of crowd across the 2-mile parade route.

Using the assumption that 16 people fit in a 9 ft x 8 ft area, we can estimate that there would be 1280 people across the 2-mile parade route (80 feet x 16 people). This is a rough estimate, as it does not account for the gaps between people, which would likely reduce the total number of people in the parade route.

The geom_ jitter () method creates a scatter plot and then it adds a small amount of random noise to every point in the plot to make the points easier to find.

Therefore, the geom_jitter is shortcut that creates a scatterplot and add random variation in each point.

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Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

57

Answer: 25%

Step-by-step explanation:

The profit from Lube for Store A would be = $8.31.

Unit profit can be obtained by subtracting the cost of the product from the selling price.

Data and calculations:

Selling price for oil change = $275

Percentage of total oil revenue = 39.1%

Cost of oil per gallon = $21.25

Selling price per gallon = $29.56 ($21.25 x $1,391)

Total income = $8.31 ($29.56 - $21.25)

Therefore, the profit from Lube for Shop A would be= $8.31.

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Complete question:

Shop A charges $275.00 for an oil change and has a gross oil profit percent of 39.1% for its total oil gross profit %. Shop B charges $275.00 for an oil change and has a gross oil profit percent of 28.4% for its total oil gross profit %. Both shops pay $21.25 per gallon of oil. What is the Profit per Lube for Shop A?

Answer:

We can use the equation:

amount of a given nutrient / % of recommended daily amount = recommended daily amount

Here, we know that 69 grams of carbohydrates is 22% of the recommended daily amount, so we can plug in the given values and solve for the recommended daily amount:

69 / 0.22 = Recommended Daily Amount

Recommended Daily Amount = 69 / 0.22 = 313.64 grams (rounded to one decimal place)

So, the total recommended daily amount of carbohydrates in grams is 313.6 grams.

Answer:

a)

i) To calculate the profit if 0 cakes are made per day, we can substitute x = 0 into the function:

P(x) = -x²+36x - 40

P(0) = -0² + 36(0) - 40 = -40 dollars

So, the profit from making 0 cakes per day is -40 dollars.

ii) To calculate the profit if 20 cakes are made per day, we can substitute x = 20 into the function:

P(x) = -x²+36x - 40

P(20) = -20² + 36(20) - 40 = 760 dollars

So, the profit from making 20 cakes per day is 760 dollars.

b) To find out how many cakes need to be made per day for the profit to be $270, we need to solve the equation P(x) = 270.

We can substitute the function P(x) into this equation:

-x²+36x - 40 = 270

Next we can solve this equation for x by using any method you prefer ( factoring, Quadratic formula, etc)

x = (36 +/- √(36² -4*(-40)(-1)))/ 2(-1)

x = (36 +/- √(1296 + 320))/ -2

x = (36 +/- √1616)/ -2

x = (36 +/- 40)/ -2

x = -2 +/- 20

x = 18 or -22

The number of cakes need to be made per day for the profit to be $270 is 18 or -22, but -22 is not a valid solution because the number of cakes must be a non-negative value, so the number of cakes need to be 18

Answer: 24/14 or 1 10/14

Step-by-step explanation:

11/14 + 9/14 = 20/14

Add the 11 and nine first.

Then add 20/14 + 4/14 and that = 24/14 or you can turn it into a mixed fraction of 1 10/14.

You're Welcome!

Answer:

Since slope of line passing through two points (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) is m=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

We now find the slope of the line passing through the points (2,3) and (4,6) as shown below:

m=

4−2

6−3

​

=

2

3

​

Therefore, the slope of the line is  

2

3

​

.

Now use the slope and point (2,3) to find the y-intercept.

y=mx+b

⇒3=(

2

3

​

×2)+b

⇒3=3+b

⇒b=3−3=0

Write the equation in slope intercept form as:

y=mx+b

⇒y=

2

3

​

x+0

⇒y=

2

3

​

x

Step-by-step explanation:

Answer:

7x2−4x/5

Step-by-step explanation:

7x2−4x over 5

Answer:

Step-by-step explanation:

242424

A relative maximum is a highest point in that little area.  Think of it as a top to a mountain in a mountain range.  It's a peak, but it might not be the tallest peak.

A relative minimum is the lowest point in that little area.  Think of it as a the bottom of a valley in some area.  It's possibly one of many valleys, so might not be the deepest valley.

When we talk about where these things happen, we describe them based on their x-values.  They happen at the x-value of that peak or valley.

There's a little peak on the left side and the x-value of that peak is x = -1.2.

There's a little valley on the right side and the x-value of that valley is x = 1.2.

The answer is A.

Answer:

-9

Step-by-step explanation:

The constant doesn't have a letter attached to it

Answer:

2× radius of the circle

Step-by-step explanation:

The line segment joining two points on the circle and passing through the centre is the diameter.

Answer:

x=-3

Step-by-step explanation:

I showed my work in the picture

Answer:

[tex]\boxed{\sf x=-3}[/tex]

Step-by-step explanation:

[tex]\sf -2x+1=3x+16[/tex]

Subtract 3x from both sides:-

[tex]\sf -2x+1-3x=3x+16-3x[/tex]

[tex]\sf -5x+1=16[/tex]

Subtract 1 from both sides:-

[tex]\sf -5x+1-1=16-1[/tex]

[tex]\sf -5x=15[/tex]

Divide both sides by -5:-

[tex]\sf \cfrac{-5x}{-5}=\cfrac{15}{-5}[/tex]

[tex]\sf x=-3[/tex]

Therefore, x = -3!

______________________

Hope this helps!

Have a great day!

a) The percentage change in nominal GDP between 2010 and 2019 is;

47.54%

b)  Real GDP in 2019 at prices of 2010 is; 20,597.113 billions

c)  The percentage change in real GDP between 2010 and 2019; 72.4%

d)  The percentage change in nominal GDP between 2010 and 2019 attributed to changing prices is; 24.45%

The formula to calculate percentage change is;

Percentage change = (Final Value - Original Value)/Original Value * 100%

a) The percentage change in nominal GDP between 2010 and 2019 is;

(21433 - 14527)/14527 * 100%

= 47.54%

b) Real GDP in 2019 at prices of 2010 is;

21433 * 0.961

= 20,597.113 billions

c)  The percentage change in real GDP between 2010 and 2019;

real GDP in 2010 = 14527 * 0.961

= 13,960.447 billion

Real GDP in 2019 = 21433 * 1.123

= 24,069.259 billion

Percentage change =  (24069.259 - 13960.447)/13960.447 * 100%

= 72.4%

d)  The percentage change in nominal GDP between 2010 and 2019 attributed to changing prices is;

Percentage change = [(21433/1.123) - (14527/0.961)]/(14527/0.961) * 100%

= 24.45%

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The expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In a right triangle, the hypotenuse (the longest side) is opposite the right angle, and the other two sides are called the legs. In this case, the hypotenuse is 2p + 8 and one of the legs (the base) is p - 5.

To find the third side (the other leg), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. In other words:

(hypotenuse)^2 = (leg 1)^2 + (leg 2)^2

Substituting the given values, we get:

(2p + 8)^2 = (p - 5)^2 + (leg 2)^2

Simplifying and solving for leg 2, we get:

leg 2 = sqrt((2p + 8)^2 - (p - 5)^2)

Now we can use the perimeter formula, which is the sum of the lengths of all the sides of the triangle. In this case, the perimeter of the triangle is:

perimeter = (leg 1) + (leg 2) + (hypotenuse)

Substituting the given values and the expression we found for leg 2, we get:

perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

Therefore, the expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

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Answer:

Have a good day!:)

Step-by-step explanation:

When two lines intersect at a point, they form two pairs of angles that do not share a side. These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.

Answer:

8:39 is the answer.

The rest, when simplified, change to 1:5.

A graph of the absolute function y = |x + 2| - 4 with five points that fit on the axes is shown in the image attached below.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).

Next, we would use an online graphing calculator to plot the given absolute value function y = |x + 2| - 4 as shown in the graph attached below.

By observing critically the graph (see attachment), the five ordered pairs (points) that fit on its axes include the following:

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Answer:

It can be represented as a fraction, 276/1000. It isn't non-terminating.

0.276 is a rational number because we can write it as a fraction, where both denominator and numerator are integers.

The amount of water in Casandra's bowl, given the gallons of water it can hold and the fraction full it is, is 0.6 gallons

Casandra' s fish bowl is able to hold a total of 9 / 10 gallons of water which is also 0.9 gallons of water. This means that you can find out how much water is in the bowl if told the fraction of the bowl that is currently full up to.

This time, the bowl is said to be 2 / 3 full which means that out of the capacity of 9 / 10 gallons or 0 . 9 gallons, the bowl is two - thirds full.

The amount of water in the bowl is therefore:

= Capacity of fish bowl x Proportion of water in the bowl

= 9 / 10 x 2 / 3

= 0. 9 x 2 / 3

= 0 . 6 gallons

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The required correct product is (x + 4)/(x - 4)(x  + 1) for the rational expressions.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Anderson multiplies two rational expressions with the given results.

His error is the inequivalent can't be canceled out.

The two rational expressions are given in the question, as follows:

(x² - 16)/(x² - 8x + 16) × (x + 1)/(x² + 2x + 1)

(x² - 4²)/(x² - 2 × 4 × x + 4² ) × (x + 1)/(x² + 2 × 1 × x + 1²)

(x + 4)(x - 4)/(x - 4)² × (x + 1)/(x + 1)²

(x + 4)/(x - 4)(x  + 1)

Thus, the required correct product is (x + 4)/(x - 4)(x  + 1).

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Answer:

Part A:

To find the length of the ramp in yards, we need to first determine the horizontal distance covered by the ramp. The slope of the ramp is 1/12, meaning that for every 12 inches of horizontal distance, the height of the ramp increases by 1 inch. Since the height of the ramp when it connects to the house is 9 inches, we can use this information to determine the horizontal distance covered by the ramp.

9 inches / (1/12) = 108 inches

To convert inches to yards, we divide by 36, so

108 inches / 36 inches/yard = 3 yards

Part B:

To determine the length of the ramp, I used the information provided about the slope of the ramp and the height of the ramp when it connects to the house. I used the slope of the ramp (1/12) to calculate the horizontal distance covered by the ramp. Then I converted the horizontal distance from inches to yards by dividing by 36. Finally, I obtained 3 yards as the length of the ramp.

Answer:

Part A = 3 yards

Part B = 9 x 12 = 108 inches = 9 feet = 3 yards

Step-by-step explanation:

Part A

1 inch height - 12 inches length

9 inches height - 9 x 12 = 108 inches length

36 inches = 1 yard

108 inches = 108/36 = 3 yards

Part B

Shown above

The ramp is 9 inches tall, so the length of the ramp is 9 x 12 = 108 inches.

1 feet = 12 inches

108 inches = 108/12 feet = 9 feet

1 yard = 3 feet

9 feet = 3 yards.

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Step-by-step explanation:

what is the usual formula for the area of a triangle ?

it is

base × height / 2

so, we know the area (10 cm²).

when we use the formula, we get

10 = 5 × w / 2

20 = 5 × w

w = 20/5 = 4 cm

Answer:

the height is equal = 4 cm

Answer:

The slope is -1

The y-intercept is -8

The equation is y = -x -8

Step-by-step explanation:

The slope is the change in y over the change in x.  As the y is decreasing by 1.  The x is increasing by 1

-1/1 = -1  

The slope is -1.

The y-intercept is the y value when the x value is 0.  When x = 0, y = -8

The y-intercept is -8.

y = mx + b

y = -1x - 8  I don't nee the 1 so I am going to write it without it.

y = -x - 8

Answer:

To find the value of x, we can substitute the value of y in the equation:

-2X + (-3) = 9

We can then solve for X by isolating it on one side of the equation:

-2X = 12

X = -6

So, the value of X is -6.

Step-by-step explanation: