Adding Positive & Negative Integers

(+3) + (+2) =

The most reasonable unit of measurement for 3) is option (C): \(m^2\), 4) is option (B): \(km^2\), 5) is \(in^2\).

3) The most reasonable unit for the measurement of the baseball field is \(m^2\) because the baseball field covers a large distance which is not accurately measured by small units  \(cm^2\) or \(mm^2\)  where it is not that big to be measured in large units like \(km^2\). So option C is the correct option.

4) The most reasonable unit for the measurement of a lake is \(km^2\) because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like \(cm^2\) , \(mm^2\) , and \(m^2\). So option B is the correct option.

5) The most reasonable unit for the measurement of the area of a door is \(in^2\) because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.

Therefore the correct answers question-wise are:

3) \(m^2\)

4) \(km^2\)

5) \(in^2\)

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Answer:

He computes the mean as $1,022.

Step-by-step explanation:

Answer:

57.45% increase

Step-by-step explanation:

The formula for percent change is (new - old)/new x 100.

The new value is $282 and the old value is $120.

Plug that into the formula:

(282 - 120)/282 x 100

= 57.45%

I hope this helped!

Answer:

Step-by-step explanation:

Oil 3 parts in the basic relationship. So try 12

Vinegar 2 parts so call it x.

3/12 = 2/x                    Cross multiply

3x = 2*12                     Combine the right

3x = 24                        Divide by 3

3x/3= 24/3

x = 8

So 12:8  is the same as 3:2

We are given an equation d = 65 t, where d represents the distance, in miles, that the car travels at this speed in t hours.

We know distance, speed and time relation

d = s * t.

Where  d represents the distance, that the car travels at this speed in t  at the speed s.

If we compare that relation with the given equation, we can see s = 65.

So,

a) The 65 tell us speed of 65 miles per hour in this situation.

b) Second part seems to be incorrect. Please check it again.

c) We are given distance = 26 miles.

Plugging d= 26 in the given equation.

26 = 65 t

Dividing both sides by 65, we get

26/65 = t

t= 0.4 hours.

So, it takes 0.4 hours or 0.4 * 60 = 24 minutes o travel 26 miles at this speed.

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer:

$685.30

Step-by-step explanation:

Her hourly pay is $15.40

Her overtime pay is 1.5 x $15.40 = $23.10

She works 37 normal hours = 37 x $ 15.40 = $569.80

She works 5 overtime hours = 5 x $23.10 = $115.50

Adding her normal + overtime = $569.80 + $115.50 = $685.30

Hope this helps! Let me know if you have any questions :)

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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we have

3(x-4)=24

solve for x

step 1

apply distributive property left sides

3(x)-3(4)=24

3x-12=24

step 2

adds 12 both sides

so

3x-12+12=24+12

simplify

3x=36

step 3

divide by 3 both sides

3x/3=36/3

x=12

Answer:

Hello I'm sorry but I have a question and I have to give ans and I can ask my question

Answer:

x+(x+4)=52

I think this is it

Answer:

The company lost 3 dollars

9-6= (-3)

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

The sum of internal angles in a triangle is equal to 180

58 + 47 + x = 180

105 + x = 180 subtract 105 from both sides

x = 75

This is an acute triangle so each angle has to be less than 90 degrees in total we already have 105 and then lastly you can find out the last angle is kind of the same angle of angle 58 so its closer to 58 than 47 this is just a clue to the answer because I cant measure the angle from over the screen.

Answer:

110 :)

Step-by-step explanation:

Triangle total angle measurement: 180

Now lets solve!

28 + 42 + ? = 180

70 + ? = 180

Now we have to subtract!!

180 - 70 = 110

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Here is one solution to the puzzle:

Squares: 2, 8, 16

Circles: 5, 7, 14

Total: 26

You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

Therefore, the correct answer is as given above

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Paula's account will earn a total of $282,546.60 in interest over the next 20 years, in addition to her initial investment of $250,000.

The monthly yield on Paula's account can be calculated using the following formula:

Monthly Yield = (Account Balance x Annual Percentage Rate) ÷ (12 x 100)

Monthly Yield = (250,000 x 5.63) ÷ (12 x 100) = $1,177.29

So, Paula's account will earn a monthly yield of $1,177.29 for the next 20 years. To calculate the total amount earned over the 20-year period, we can multiply the monthly yield by the number of months in 20 years (i.e., 240):

Total Earnings = Monthly Yield x Number of Months

Total Earnings = $1,177.29 x 240

Total Earnings = $282,546.60

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Answer:

ios a

Step-by-step explanation:

Answer:

\(\Large \boxed{\sf A. \ True}\)

Step-by-step explanation:

Absolute value is the number's distance from zero.

The absolute value of a number is always non-negative because distance is not negative (without considering direction).

Answer:

3/4

Step-by-step explanation:

If she has 3 pans and pours 1/4 in each that's 3/4

Answer:

3/4 cups of choclate chips

Step-by-step explanation:

1/4+1/4+1/4=3/4

Answer:

Step-by-step explanation:

1399 rounds to 1400 so A is not the answer

1449 rounds to 1400 so B is not the answer

1589 rounds to 1600 so D is not the answer

The hundreds place is second from the left. Third from the left determines what happens to second from the left. 5 and over round up. Less than 5 just use the first 2 digits left and 2 zeros.

The answer is C

1457 rounds to 1500

1547 rounds to 1500

The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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Answer:

Amount received per brother based on number of children plus debt is given as

Roberto, S/ 55,333.33

Luis, S/ 46,000

Armando, S/ 74,666.67

Step-by-step explanation:

English Translation

A prestigious businessman decides to distribute his inheritance of S / 176,000 among his three brothers Roberto, Luis and Armando, DP to the number of his children and IP to the amount of his debts. How much corresponds to each brother?

Roberto: No of children 4, Amount of debts (S /): 2 000

Luis: No. of children 3, Amount of debts (S /): 6,000

Armando: No of children 5, Amount of debts (S /): 8,000

Solution

The man shares the inheritance according to the number of children per person and according to each brother's debts.

Assuming the debts are first settled,

The total debts = 2000 + 6000 + 8000 = S/ 16,000

We assume that each brother receives the respective debt amounts first, then the remaining cash is divided amongst the 3 brothers according to the number of their children.

Total amount available = S/ 176,000

total debt = S/ 16,000

Amount available less debts = 176,000 - 16,000 = S/ 160,000

There are 4, 3 and 5 children respectively for the 3 brothers.

Total number of children = 4+3+5 = 12.

Amount corresponding based on a per child basis =( S/ 160,000/12) = S/ 13,333.33

Meaning that each brother receives the following amount based on their children's sake

Roberto, 4 × S/ 13,333 = S/ 53,333.33

Luis, 3 × S/ 13,333.33 = S/ 40,000

Armando, 5 × S/ 13,333 = S/ 66,666.67

Total amount each brother then receives when the amount received due to debts are added

Roberto, 53,333.33 + 2,000 = S/ 55,333.33

Luis, 40,000 + 6,000 = S/ 46,000

Armando, 66,666.67 + 8,000 = S/ 74,666.67

To check, 55,333.33 + 46,000 + 74,666.67 = 176,000 (total inheritance!)

Hope this Helps!!!

Queremos ver como se reparte una dada suma entre 3 hermanos, siendo que tenemos unas dadas restricciones, donde debemos trabajar con relaciones directamente proporcionales e inversamente proporcionales.

Veremos que:

Roberto recibe: $112,640

Luis recibe: $28,160

Armando recibe: $35,200

Sabemos que lo que se reparte es directamente proporcional al número de hijos de cada hermano, e inversamente proporcional a las deudas de cada hijo.

Entonces, definamos las variables:

R = lo que recibe Roberto.

L = Lo que recibe Luis

A = lo que recibe Armando.

Tendremos que:

R + L + A = $176,000

Entonces como lo que recibe cada hermano es directamente proporcional al número de hijos (x) e inversamente proporcional a la deuda (z) lo que cada hermano recibe será:

Entonces podemos escribir:

R + L + A = $176,000

k*4/2,000 +  k*3/6,000 + k*5/8,000 = $176,000

k*(4/2,000 + 3/6,000 + 5/8,000) = $176,000

k*(0.003125) =  $176,000

k = $176,000/(0.003125) = $56,320,000

Ahora que conocemos el valor de k, podemos calcular lo que cada hermano recibe:

R = $56,320,000*(4/2,000) = $112,640

L = $56,320,000*(3/6,000) = $28,160

A = $56,320,000*(5/8,000) = $35,200

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Answer:

Step-by-step explanation:

The figures are similar, therefore they have equal ratio of corresponding sides:

So

\(\\ \tt\hookrightarrow \dfrac{12}{16}=\dfrac{x}{24}\)

\(\\ \tt\hookrightarrow \dfrac{3}{4}=\dfrac{x}{24}\)

\(\\ \tt\hookrightarrow 4x=72\)

\(\\ \tt\hookrightarrow x=18\)

The equation of the line passing through the point (-4, 1), and having a slope of m = -3/2 is 2y = -3x - 10.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

The equation of the line passing through the points (x1, y1), with a slope of m is given by the formula:

(y - y1) = m (x - x1)

Given that the point is (-4, 1) and the slope, m = -3/2.

Substituting the values we have:

(y - y1) = m (x - x1)

y - 1 = -3/2 (x - (-4))

2(y - 1) = -3(x+ 4)

2y - 2 = -3x - 12

2y = -3x - 10

Hence, the equation of the line passing through the point (-4, 1), and having a slope of m = -3/2 is 2y = -3x - 10.

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Chloe can travel 4.4 miles less than Jin on one gallon of gas.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

Chloe travels 93 miles on 5 gallons of gas, hence the constant is given as follows:

k = 93/5

k = 18.6 miles per gallon.

Jin's ratio is of 23 miles per gallon, hence he can travel more and the difference is given as follows:

23 - 18.6 = 4.4 miles per gallon.

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