please answer correctly
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The given quadratic equations by solving using inverse operations gives,

(a) x = ±2√2, (b) x = ±3√2 + 5, (c) x = ±4√2, (d) x = ±√90 - 2 and (e) x = 4 ±3√3.

Given are some quadratic equations.

We have to solve this using the inverse operations.

Inverse operations are operations which undo the operation which is done to the equation.

(a) 1/2 x² - 4 = 0

Adding both sides by 4,

1/2 x² = 4

Multiplying both sides by 2,

x² = 8

Taking the square root on both sides,

x = ±√8 = ±2√2

(b) (x - 5)² = 18

Taking the square root on both sides,

x - 5 = ±√18

x - 5 = ±3√2

Adding 5 on both sides,

x = ±3√2 + 5

(c) 2x² + 7 = 71

Subtracting by 7 on both sides,

2x² = 64

Dividing by 2 on both sides,

x² = 32

Taking the square root on both sides,

x = ±4√2

(d) 5 (x + 2)² + 37 = 487

Subtracting by 37 on both sides,

5 (x + 2)² = 450

Dividing by 5 on both sides,

(x + 2)² = 90

Taking the square root on both sides,

x + 2 = ±√90

Subtracting by 2 on both sides,

x = ±√90 - 2

(e) (x - 4)² /3 + 8 = 17

Subtracting by 8 on both sides,

(x - 4)² /3 = 9

Multiplying both sides by 3,

(x - 4)² = 27

Taking the square root on both sides,

x - 4 = ±3√3

Adding both sides by 4,

x = 4 ±3√3

Hence the values are found.

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The number of heart cakes that were sold at the cake sale was 28

According to the question,

Cost of circular-shaped cake = $7

Cost of heart shaped cake = $5

Total sale = $238

Let the number of circular cakes shaped be x

Since the number of heart cakes was sold twice as many as the circular cake, the number of heart cakes will be 2x

Cost of x circular-shaped cake = $7 * x

Cost of 2x heart shaped cake = $5 * 2x

Total sale = Cost of x circular cake + Cost of 2x heart cake

Thus, we get the following equation,

238 = 7x + 10x

238 = 17x

x = 14

Thus, the number of heart cakes sold was 2x that is 28.

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The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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The radius of the sphere is approximately 3.634 inches.

We have,

The formula for the volume of a sphere is:

V = (4/3)πr³

where V is the volume of the sphere and r is its radius.

We know that the volume of the sphere is 36π cubic inches.

Substituting this value into the formula, we get:

36π = (4/3)πr³

Multiplying both sides by 3/4π, we get:

r³ = (36π)/(3/4π) = 48

Taking the cube root of both sides.

r = (48)^(1/3)

r = 3.634 inches (rounded to three decimal places)

Therefore,

The radius of the sphere is approximately 3.634 inches.

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To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms

2. Use the given information

3. Determine when the object is stopped

4. Calculate the distance traveled

Identify the terms:

For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:

Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:

To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.

Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:

Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.

We can use the equation s = ut + 0.5at²,

where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.

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The total area of the rectangle and the two right-angled triangles is 50 square units.

What is meant by area?

Area refers to the measurement of the size or extent of a two-dimensional surface or shape. It is usually expressed in square units, such as square meters or square feet.

What is meant by a rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides and four right angles. The opposite sides of a rectangle are equal in length, and the area can be calculated as length x width.

According to the given information

Area of rectangle = h * x

Area of one right-angled triangle = (1/2) * h * y

Total area of two right-angled triangles = 2 * (1/2) * h * y = h * y

Adding the area of the rectangle and the area of the triangles, we get the total area:

Total area = Area of rectangle + Total area of two right-angled triangles

Substituting the given values, we get:

Total area = (5 * 4) + (5 * 6)

Total area = 20 + 30

Total area = 50 square units

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Given statement "3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors." is true. Because the rise and run of a gable roof allows you to calculate the slope factor, which can then be used to calculate the rake length and area of the roof.

If you know the rise and run of a gable roof, you can calculate the rake length and area using slope factors. The slope factor is a ratio that relates the length of the roof to the height of the roof.

The slope factor is calculated by dividing the rise of the roof by the run of the roof. Once you have the slope factor, you can use it to calculate the rake length and area of the roof.

The rake length is the length of the diagonal edge of the roof, and it can be calculated by multiplying the slope factor by the run of the roof.

For example, if the run of the roof is 10 feet and the slope factor is 0.5 (which corresponds to a 6:12 pitch), then the rake length would be 5 feet (0.5 x 10).

The area of the roof can be calculated by multiplying the rake length by the width of the roof.

For example, if the width of the roof is 20 feet and the rake length is 5 feet, then the area of the roof would be 100 square feet.

Statment is true.

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The linear equation have the following results: f(- 2) = 0, f(0) = 2, f(1) = 3.

In this problem we find a linear equation that must be evaluated at x = - 2, x = 0 and x = 1. Linear equations are expressions of the form:

y = m · x + b

Where:

Now we proceed to evaluate the function, the results are described:

x = - 2

f(- 2) = - 2 + 2

f(- 2) = 0

x = 0

f(0) = 0 + 2

f(0) = 2

x = 1

f(1) = 1 + 2

f(1) = 3

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An expression that represents the amount of money Henry would have saved in w weeks is $95 + ($5 x w)

Henry already has $95, and he can save an additional $5 per week. So after one week of saving, Henry would have a total of $100 ($95 + $5). After two weeks, he would have $105 ($100 + $5), and so on.

To find out how much total money Henry would have after 10 weeks of saving, we can use the same method. After 10 weeks, Henry would have saved a total of $145 ($95 + ($5 x 10)). So, Henry would have a total of $145 after 10 weeks of saving.

Now, let's talk about an expression that represents the amount of money Henry would have saved in w weeks. We can use the formula:

Total amount saved = $95 + ($5 x w)

This formula takes into account the $95 that Henry already has, and the additional $5 he can save each week. The "w" in the formula represents the number of weeks Henry has been saving for. By plugging in different values of "w", we can determine how much money Henry would have saved at different points in time.

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Elevation on ramp B is more steep than ramp A.

"Elevation" typically refers to the height of a location above sea level. It is often used in geography and topography to describe the height of a mountain or the altitude of a city or other location. Elevation is usually measured in feet or meters, and it can have a significant impact on climate, weather patterns, and other environmental factors.

"Steep" can have a few different meanings depending on the context. It can refer to a steep slope or incline, such as a steep hill or mountain. It can also mean a high price or cost, as in "the price is too steep for me." Additionally, "steep" can refer to the act of soaking something in hot water in order to extract flavor, as in steeping a tea bag in hot water.

For RampA:

tanα=36/30

tanα=1.2

For Ramp B:

tanβ=36/20

tanβ=1.8

Therefore for Ramp B angle is more than Ramp A and incase of tangent function value of angle increases with the angle measures.

So β>α.

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Answer:

a) What is her GROSS pay for a week? 1,400

b) What is her GROSS pay for a year? 67,200

c) What are her TOTAL DEDUCTIONS for a week? 351.39

d) What is her NET pay for a week? 1,048.61

e) What is her NET pay for a year? 50,333.28

f) What does she pay in Income Tax per YEAR? 13,535.52

g) What does she pay in CPP contributions per YEAR? 2,537.28

h) What does she pay in El contributions per YEAR? 793.92

i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%

Step-by-step explanation:

 GROSS

 NET

 There are 4 weeks in a month, 52 weeks in a year.

a) What is her GROSS pay for a week? 1,400

b) What is her GROSS pay for a year? 67,200

c) What are her TOTAL DEDUCTIONS for a week? 351.39

d) What is her NET pay for a week? 1,048.61

e) What is her NET pay for a year? 50,333.28

f) What does she pay in Income Tax per YEAR? 13,535.52

g) What does she pay in CPP contributions per YEAR? 2,537.28

h) What does she pay in El contributions per YEAR? 793.92

i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%

The distance from Earth to Mercury is approximately 5.7 x 107 miles, which is less than the fuel capacity of Spigot to travel 125% of the distance from Earth to Mars. Therefore, Spigot has enough fuel to travel from Earth to Mercury and return to Earth before refueling. The correct option is D.

Distance refers to the amount of space between two points, objects, or locations. It is typically measured in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line or along a curved path, depending on the context.

Distance is often used in conjunction with time to calculate speed and velocity. For example, the distance traveled by a car in a certain amount of time can be used to calculate its speed.

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a) i) The pressure on the ground by snowshoe hare is 0.07 N/cm².

ii) The pressure on the ground by European hare is 0.15 N/cm².

b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet.

a) The pressure on the ground can be calculated by dividing the force on the ground due to weight by the total surface area of the feet.

i) For the snowshoe hare, the pressure on the ground is:

Pressure = Force on ground / Total surface area of feet

Pressure = 14 N / 200 cm²

Pressure = 0.07 N/cm²

ii) For the European hare, the pressure on the ground is:

Pressure = Force on ground / Total surface area of feet

Pressure = 38 N / 250 cm²

Pressure = 0.15 N/cm²

b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet than the European hare and exerts less pressure on the ground. This allows the snowshoe hare to move more easily over the snow without sinking.

Additionally, the snowshoe hare has fur on the soles of its feet, which provides additional insulation against the cold snow. These adaptations help the snowshoe hare survive in its snowy environment by allowing it to move and find food more easily.

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Answer:

£78.75

Step-by-step explanation:

An easy way step but longer way to do this is

10% of 75 is 7.5 ((75/10= 7.5))

divide by 2 on both sides

5% = 3.75

then just add it, its increasing 75 by 5%

so 75 + 3.75 = 78.75

Answer:

linear

Step-by-step explanation:

i js took the test

The kind of model that best describes the data is a linear relation

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

{(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)}

In the above dataset, we can see that

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

The relation has a constant rate of -3/-1

Evaluate

The relation has a constant rate of 3

Only linear relations have constant rates

Hence, the kind of model that best describes the data is a linear relation

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The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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Answer: 75%

have a good day/night and crush that homework/class!! you are loved

brainliest??

Answer: 75%

Step-by-step explanation: 56 - 14 = 42. So, 42 people are not wearing red. 42/56 is .75, which is the decimal form for 75%. Also, if you simplify 42/56, you get 3/4 which is also 75%

The inequality to find the number of tablespoons of flour actually used in a recipe is |t - 48| <= 4. The correct answer is D.

Since the recipe calls for 3 cups of flour with a variation of up to 4 tablespoons, the total amount of flour used can vary between 3 cups - 4 tablespoons and 3 cups + 4 tablespoons. Converting tablespoons to cups, this becomes 3 cups - 1/4 cup and 3 cups + 1/4 cup.

Thus, the range of cups of flour used is [3 - 1/4, 3 + 1/4], which is [2.75, 3.25]. Multiplying by 16 to convert back to tablespoons, we get the range [44, 52].

So, the inequality that could be used to find the number of tablespoons of flour actually used in the recipe is

|t - 48| <= 4

where t is the number of tablespoons of flour used. So, the correct option is D).

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The absolute maximum value of f(x)=2x³ +3x² +1 on the closed interval [-3, 1] is 6, which occurs at x=1.

To find the absolute maximum value of the function f(x) on the closed interval [-3, 1], we need to evaluate the function at the endpoints of the interval and at any critical points in the interior of the interval.

First, we evaluate the function at the endpoints of the interval

f(-3) = 2(-3)³ + 3(-3)² + 1 = -17

f(1) = 2(1)³ + 3(1)² + 1 = 6

Next, we find the critical points of the function f(x) by taking its derivative and setting it equal to zero

f'(x) = 6x² + 6x

6x(x+1) = 0

x = 0 or x = -1

Now we evaluate the function at these critical points

f(0) = 1

f(-1) = 2(-1)³ + 3(-1)² + 1 = 2

Therefore, the absolute maximum value of f(x) on the closed interval [-3, 1] is 6, which occurs at x=1.

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The given question is incomplete, the complete question is:

Let f be the function given by f(x)=2x³ +3x² +1. What is the absolute maximum value of f on the closed interval [-3,1] ?

The measure of side ‘b’ in the given triangle ABC, with angle A measuring 54 degrees and angle C measuring 59 degrees and side BC measuring 11 is option-c:12.516, which is found using Sine-law.

In a scalene or oblique triangle (a non-right triangle), the law of sine describes the relationship between the sides and angles. Trigonometric laws such as the law of sines and law of cosines are crucial when "solving a triangle" by calculating the unknown angles or sides. The ratio of a triangle's side lengths to the sine of each of its opposite angles must be equal in order for the sine rule to apply. Triangle side length ratios to their corresponding opposite angles are connected by the law of sines. All three sides and the diagonal angles maintain the same ratio.

Given that ∠A= 54° ,∠C= 59° & side BC=a=11

We know that ∠A + ∠B + ∠C = 180°   {angle sum property}

Consider △ABC,

54° + 59° +  ∠B = 180°

113° +  ∠B = 180°

∠B = 180°- 113°

∠B = 67°

Applying Sine-Law,

[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B} = \frac{C}{sin\ C}[/tex]

By using,

[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B}[/tex] , we get:

[tex]\frac{11}{sin\ 54} =\frac{B}{sin\ 67}\\ \\\frac{11}{0.80901} =\frac{B}{0.92050} \\\\B=\frac{11}{0.80901} \times 0.92050[/tex]

B = 13.59686 x 0.92050

B = 12.5159

B = 12.516

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Refer to the attachment for the complete question.

The height of given parallelogram is 5 units.

Given that, the parallelogram shown below has an area of 15 units.

The base is 3 units.

We know that, the area of a parallelogram is Area = Base × Height

Here, Area = 3×Height

15 = 3×Height

Height = 15/3

Height = 5 units

Therefore, the height of given parallelogram is 5 units.

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"Your question is incomplete, probably the complete question/missing part is:"

The parallelogram shown below has an area of 15 units. Find the missing height.

The value of k is approximately 0.034. The projected Hispanic resident population in 2015 is approximately 73.9 million. The Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.

To find k, we can use the fact that A = 35.3 million when t = 0 (i.e., in 2000), and A = 50.5 million when t = 10 (i.e., in 2010). Substituting these values into the exponential growth function, we get

35.3 = 35.3e^0k

50.5 = 35.3e^(10k)

Dividing the second equation by the first equation, we get

50.5/35.3 = e^(10k)

Taking the natural logarithm of both sides, we get

ln(50.5/35.3) = 10k

Solving for k, we get

k ≈ 0.034

Therefore, the exponential growth function is A = 35.3e^(0.034t).

To project the Hispanic resident population in 2015, we need to find A when t = 15 (i.e., 15 years after 2000). Substituting t = 15 into the exponential growth function, we get

A = 35.3e^(0.034*15) ≈ 73.9 million

Therefore, the projected Hispanic resident population in 2015 is approximately 73.9 million.

To find the year in which the Hispanic resident population reaches 70 million, we need to solve the exponential growth function for t when A = 70. Substituting A = 70 into the exponential growth function, we get

70 = 35.3e^(0.034t)

Dividing both sides by 35.3, we get

e^(0.034t) = 70/35.3

Taking the natural logarithm of both sides, we get

0.034t = ln(70/35.3)

Solving for t, we get

t ≈ 24.7

Therefore, the Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.

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The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.

The probability of landing on a green section is 0/16, which simplifies to 0.

The probability of landing on a red section is 4/16, which simplifies to 1/4.

The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.

In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.

The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.

Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.

The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.

Since there are no green sections, the probability of landing on a green section is 0.

There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.

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Answer:

His confidence is transformed by the crowd’s response.

Step-by-step explanation:

Scotty is described as being a "quavering husk...just moments before." This shows his lack of confidence and anxiety about being on stage.

The slope of the cathedral ceiling is 0.83.

To calculate the slope of the cathedral ceiling, we need to find the rise over the run. The rise is the difference in ceiling heights between the two points. The run is the horizontal distance between the two points.

From the problem statement, we know that the ceiling is 8 feet high at the west wall and 10.5 feet high three feet from the west wall. So the rise is:

rise = 10.5 - 8 = 2.5 feet

The run is the horizontal distance between the two points, which is:

run = 3 feet

Now we can calculate the slope:

slope = rise/run = 2.5/3 = 0.83

Therefore, the slope of the cathedral ceiling is 0.83.

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According to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.

Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product.

To compare 7 yards and 19 feet, we need to convert them to the same unit. Since 1 yard is equal to 3 feet, we can convert yards to feet by multiplying by 3, and we can convert feet to yards by dividing by 3.

In the first answer, we converted 7 yards to feet by multiplying by 3, which gave us 21 feet. Then we compared 21 feet to 19 feet, and found that 21 feet is greater than 19 feet. Therefore, we concluded that 7 yards is more than 19 feet.

In the second answer, we converted 19 feet to yards by dividing by 3, which gave us approximately 6.33 yards (rounded to two decimal places). Then we compared 7 yards to 6.33 yards, and found that 7 yards is greater than 6.33 yards. Therefore, we concluded that 7 yards is more than 19 feet.

Therefore, according to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.

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Answer:

Both 2B and 2A are not similar.

Step-by-step explanation:

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

Let me be helpful!

Let's start with 2B. It is easier to understand the subject that way.

->for a triangle to be similar, it's angles and sides must be the same.

-2B's triangle shows that line TW got scaled by x2.2 (22/10)

-Line ZW got scaled by 1.18

-2b are not similar.

Now on it 2A!

- line JK got scaled by 0.75

- Line JL got scaled by 0.5

-they are not similar

Let me know if I am incorrect!

-A friendly 8th grader :)

answer is : x 25. y = 20 both y's will cancel . 2x =50.=x=25

The function rule that could model this situation is f(x)=sin(x)+3. The correct answer is (c).

The sine function is a mathematical function that describes a periodic oscillation. It is one of the basic trigonometric functions, along with cosine, tangent, cotangent, secant, and cosecant.

Let us relate this to our given question.

The midline of a sine function is the horizontal line that the graph oscillates around.

In this case, the midline is y=3, which means that the sine function oscillates between y=3+1=4 and y=3-1=2.

The function rule that could model this situation is c. f(x)=sin(x)+3, because adding 3 to the sine function shifts the midline up to y=3, and the sine function oscillates between y=4 and y=2.

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The probability that two of those selected will be from the manufacturing department and one will be from the accounting department is approximately 0.409.

To solve the problem, we first need to find the total number of ways to select 3 people out of the 12 people in the company, which is given by the combination formula:

C(12,3) = 12! / (3! * (12-3)!) = 220

Next, we need to find the number of ways to select 2 people from the manufacturing department and 1 person from the accounting department. We can do this by using the combination formula again:

C(6,2) * C(4,1) = (6! / (2! * (6-2)!)) * (4! / (1! * (4-1)!)) = 90

Finally, we can find the probability by dividing the number of desired outcomes by the total number of possible outcomes:

P(2 manufacturing, 1 accounting) = 90 / 220 ≈ 0.409

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