The vertex of the parabola below is at the point (2, -5). Which of the equations below could be the one for this parabola?   A. x = -4(y - 2)2  B. y = (x + 2)2 - 5

Answer:

x^2 - x + 2.

Step-by-step explanation:

Answer:

x² - x + 2

Explanation

Work out using the given functions to set up and simplify (f + g) (x)

The value of x found using the properties of the isosceles triangle is  92°.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Although this triangle's two sides are equal, the base of the triangle is the side that is not equal.

Given a = 22°

Since it is an isosceles triangle, a = 1 = 22°

One of the properties of a triangle is that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Here ∠2 is the exterior angle of the first isosceles triangle.

So ∠2 = ∠1 + a = 22 + 22 = 44°

Now∠ 3 = ∠2 = 44°

∠x = 180 - (∠2+∠3) = 180 - (44+44) = 92°

∠4 = 180 - (x+∠1) = 180 - (92+22) = 66°

∠5 = ∠4 = 66°

∠y = 180 - 66 -66 = 48°

∠6 = 180 - ∠y - ∠3 = 180 - 48 - 44 = 88°

∠7 = ∠6 = 88°

∠x = 180 - ∠7 = 180- 88 = 92°

Therefore the value of x found using the properties of the isosceles triangle is  92°.

To learn more about the isosceles triangle, follow the link.

https://brainly.com/question/1475130

#SPJ1

Answer:

Step-by-step explanation:

Firgure is out your self

From the given data, the answer is option B, 22 cans. Larissa should purchase minimum 22 cans of sport drink.

First, we need to calculate the volume of each cone-shaped cup using the given dimensions:

Radius of the cone = diameter / 2 = 7 cm / 2 = 3.5 cm

Height of the cone = 10 cm

Using the formula for the volume of a cone, we get:

Volume of each cone-shaped cup = (1/3) x π x radius² x height

Volume of each cone-shaped cup = (1/3) x π x (3.5 cm)² x 10 cm

Volume of each cone-shaped cup ≈ 128.68 cm³

Next, we need to calculate the total volume of sports drink needed for 900 servings:

Total volume of sports drink needed = 900 x 128.68 cm³

Total volume of sports drink needed ≈ 115811.2 cm³

Now, we need to calculate the volume of one economy can of sports drink using the given dimensions:

Radius of the can = diameter / 2 = 15 cm / 2 = 7.5 cm

Height of the can = 30 cm

Using the formula for the volume of a cylinder, we get:

Volume of one can of sports drink = π x radius² x height

Volume of one can of sports drink = π x (7.5 cm)² x 30 cm

Volume of one can of sports drink ≈ 5309.73 cm³

Finally, we can divide the total volume of sports drink needed by the volume of one can of sports drink to find the minimum number of cans Larissa should purchase:

Minimum number of cans of sports drink = Total volume of sports drink needed / Volume of one can of sports drink

Minimum number of cans of sports drink = 115811.2 cm³ / 5309.73 cm³ = 21.83

Since we need to purchase whole cans, the minimum number of cans Larissa should purchase is 22.

Learn more about volume here: brainly.com/question/23963432

#SPJ4

Answer:

to show how much rainfall there is between months in different regions

The equation y = -2x³ - 6 represents a nonlinear function.

What is linear function and nonlinear function?

The highest for linear functions is only one, whereas nonlinear functions have more.

The equation y = -2x³ - 6 represents a nonlinear function because the highest power of x, which is 3, is greater than 1. In general, a function is considered linear if it can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the equation cannot be written in that form because of the presence of x³, which makes the relationship between x and y nonlinear.

To know more about linear function and nonlinear function visit,

https://brainly.com/question/1418397

#SPJ1

As per the conversion factor, 5 foot 8 inches is equal to 172.72 centimeters

In this case, we're talking about converting from feet and inches to centimeters.

To convert 5 feet 8 inches to centimeters, we need to first convert the feet to inches, and then add the total number of inches. Since one foot is equal to 12 inches, we can multiply 5 feet by 12 to get 60 inches. Then, we add the remaining 8 inches to get a total of 68 inches.

Now, we need to use a conversion factor to convert inches to centimeters. One inch is equal to 2.54 centimeters, so we can multiply 68 inches by 2.54 to get the answer in centimeters.

To summarize, the conversion factors we used are:

1 foot = 12 inches

1 inch = 2.54 centimeters

=> (68 inches x 2.54 cm/inch) =  172.72 centimeters

To know more about conversion factor here.

https://brainly.com/question/30166433

#SPJ4

In 120 minutes, all the three boats will next meet at the starting location. The solution has been obtained by using the concept of least common multiple.

What is least common multiple?

Least Common Multiple is abbreviated as LCM. The smallest multiple shared by two or more different numbers is referred to as the least common multiple.

We are given that three boats start cruising around a small island starting at the same time and from the same location, and following the same route.

They take one full circle around the island which is 2 km.

First boat:

It covers 5 km in 60 minutes.

So, it will cover 2 km in 60/5 * 2 = 24 minutes

Second boat:

It covers 4 km in 60 minutes.

So, it will cover 2 km in 60/4 * 2 = 30 minutes

Third boat:

It covers 3 km in 60 minutes.

So, it will cover 2 km in 60/3 * 2 = 40 minutes

Now, taking the LCM of 24, 30 and 40, we get 120.

Hence, in 120 minutes all the three boats will next meet at the starting location.

Learn more about least common multiple from the given link

https://brainly.com/question/10749076

#SPJ1

Answer: $275,000

Step-by-step explanation:

Therefore , the solution of the given problem of linear equation comes out to be  129 sodas were sold.

The formula y=mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.

Here,

Let's start by defining some variables. Let s be the number of sodas sold and h be the number of hot dogs sold.

We know from the problem that:

s + h = 172 (the total number of sodas and hot dogs sold)

s = 3h (the number of sodas sold is three times the number of hot dogs sold)

We can substitute the second equation into the first equation to eliminate s and get an equation in terms of h:

3h + h = 172

4h = 172

h = 43

So, 43 hot dogs were sold. We can then use the second equation to find the number of sodas sold:

s = 3h = 3(43) = 129

Therefore, 129 sodas were sold.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

The probability of rolling a 7 with a pair of dice is 1/6. This is because there are six possible combinations that add up to 7.

Each of these combinations has an equal probability of occurring, so the probability of rolling a 7 is 1/6. (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

To explain further, when two dice are rolled, there are 36 possible outcomes, each with an equal probability of occurring. Of the 36 outcomes, 6 of them will result in the total number of dots appearing on top being 7. Since 6 out of 36 outcomes result in a 7, the probability of rolling a 7 is 6/36 or 1/6. This means that if two dice are rolled 36 times, there is a 1 in 6 chance that the total number of dots appearing on top will be 7 at least once.

Learn more about Probability:

https://brainly.com/question/24756209

#SPJ4

Answer:

68

Step-by-step explanation:

Looking at the pattern of what is given for the bottom section.  I can count two sections as being 6 blocks and then between those sections I would count 4 blocks.  This would be true for the bottom and the top.  The middle holding up the top and the bottom would need 4 more blocks for each "pillar"

2(6 + 6 + 4 + 4) + 4(4) = 56

If I use that same patter with the new structure

2(7 + 7 + 5 + 5) + 4(5) = 68

Answer:

68

Step-by-step explanation:

We know that a cube has 8 corners. So that's 8 cubes just for the corners. We also know that a cube has 12 edges. An edge can be calculated by subtracting 2 from the side length. Since the side length is 7 cubes long, the edge length is 5 cubes long. The total number of cubes is:

N = (number of corner * cubes per corner) + (number of edges * cubes per edges)

[tex]N = (8 * 1) + (12 * 5) = 8 + 60 = 68[/tex]

The full amount is $10.

Let x be the full amount.

We know that 40% of the amount is equal to $4, so we can set up the equation:

0.4x = 4

To solve for x, we can divide both sides by 0.4:

x = 4 ÷ 0.4

x = 10

Therefore, the full amount is $10.

In mathematics, an expression is a combination of numbers, variables, and operations that are grouped together. It can be a simple expression, like "2 + 3", or a more complex one, like "(x + 3) / (y - 2)".

Expressions can be evaluated to produce a result, but they are not necessarily equations, since they don't always include an equal sign. They can also be used as components in larger expressions or equations.

For example, the expression "2x + 3y" can be used as part of the equation "2x + 3y = 12" to represent a relationship between x and y, or it can be used as part of a larger expression, like "(2x + 3y) / 5".

To know more about expression visit :

https://brainly.com/question/1859113

#SPJ1

Answer:

60 Kilometers per hour

Step-by-step explanation:

To solve for how long it took Molly to get home, we can use this equation:

So, Molly took an hour and 30 minutes, or 90 minutes to travel 90km.

To get the number of km she traveled every hour, we can use this equation:

We multiply by [tex]\frac{2}{3}[/tex] because if we need to figure out the average speed for every hour (60) we need to convert 90 to 60, and to do that we multiply the 90 by [tex]\frac{2}{3}[/tex].

Therefore, Molly travels 60km every hour.

500 minutes are equal to 8 hours and 20 minutes.

Time is a valuable commodity that we must use wisely. We measure it in seconds, minutes, hours, days, weeks, months, and years. It is important to be able to convert time units so that we can manage our schedule efficiently.

To convert minutes to hours, we need to divide the number of minutes by 60, which is the number of minutes in an hour. Therefore,

500 minutes ÷ 60 minutes/hour = 8.33 hours

However, this answer is in decimal form, which is not a typical way to represent time. We want to express it in hours and minutes.

To do so, we will use the fact that there are 60 minutes in an hour. Therefore, we can multiply the decimal part of the answer by 60 to get the remaining minutes.

0.33 hours x 60 minutes/hour = 20 minutes

So, 500 minutes is equivalent to 8 hours and 20 minutes.

To know more about time here.

https://brainly.com/question/4199102

#SPJ4

Fraction of the volume of the cone = 1/4 0r 0.25

A cone is a solid that has a circular base and a single vertex.

To calculate its volume, you need to multiply the base area (area of a circle: π × r²) by height and by 1/3:

volume = (1/3) × π × r² × h

Volume of the cone using radius 12inches and height 8inches =

(1/3) × π × 12² × 8

= 0.6981inches³

Volume of the cone using radius 12inches and height 2inches =  

(1/3) × π × 12² × 2

= 0.17453inches³

in order to find the fraction filled with water, we use the

Volume of 2inches/Volume of 8 inches.

0.17453/0.6981

= 0.25 or 1/4

You can learn more about volume of a cone here https://brainly.com/question/22797929

#SPJ1

The requried first term of the sequence is $6.32.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
The amount of money Sally spends on breakfast each week forms an arithmetic sequence.

Let's use the formula for the sum of an arithmetic sequence to find the first term of the sequence. We know that Sally has already spent $31.64, which means that she has made 31.64/4.52 = 7 visits to the breakfast place. So the sum of the first 7 terms of the sequence is:

S₇ = 7/2 * (a₁ + a₇)

We know that a₇ = $4.52, so we can plug this into the formula and simplify

S₇ = 7/2 * (a₁ + 4.52)

a₁ = $6.32

Similarly, all the outcomes can be evaluated,
By the end of the year, Sally will have spent $891.36 on breakfast.

Therefore, the first term of the sequence is $6.32.

Learn more about arithmetic progression here: https://brainly.com/question/20334860
#SPJ1

54 degrees Celsius is equivalent to 129.2 degrees Fahrenheit.

A temperature unit developed from the SI (International System of Units) is the Celsius (symbol: °C).

Prior to the adoption of the metric system, the Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

Add 1.8 to the °C temperature.

To this number, add 32.

This is the response in degrees Fahrenheit.

To convert 54 degrees Celsius to Fahrenheit,

You can use the formula:

°F = (°C × 9/5) + 32

where °F is the temperature in Fahrenheit,

°C is the temperature in Celsius.

Substituting 54 for °C, we get:

°F = (54 × 9/5) + 32

°F = (486/5) + 32

°F = 97.2 + 32

°F = 129.2

Therefore, 54 degrees Celsius is equivalent to 129.2 degrees Fahrenheit.

For similar questions on Conversion from Celsius to Fahrenheit,

https://brainly.com/question/26351021,

#SPJ4

The estimate of 5/8 - 1/10 is 0.5, which is option B.

What is division in mathematics?

In mathematics, division is an arithmetic operation that is used to split a quantity into equal parts or to find the number of times one quantity is contained within another quantity. It is the inverse operation of multiplication, and is represented by the symbol "÷" or "/".

To estimate 5/8 - 1/10, we can round 5/8 to the nearest tenth, which is 0.6, and round 1/10 to the nearest tenth, which is 0.1. Then we can subtract them to get an estimate of the difference:

5/8 - 1/10 ≈ 0.6 - 0.1 = 0.5

Hence, the estimate of 5/8 - 1/10 is 0.5, which is option B.

To learn more about the division in mathematics, visit:

https://brainly.com/question/28119824

#SPJ1

The correct linear equation for the table is,

⇒ y = - 5x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shown in figure.

Now, Let two points from the table are (4, - 22) and (3, - 17).

Hence, Equation of linear function is,

⇒ y -  (- 22) = (- 17 - (-22)) / (3 - 4) (x - 4)

⇒ y + 22 = (5/- 1) (x - 4)

⇒ y + 22 = - 5 (x - 4)

⇒ y + 22 = - 5x + 20

⇒ y = - 5x + 20 - 22

⇒ y = - 5x - 2

Thus, The correct linear equation for the table is,

⇒ y = - 5x - 2

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ1

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

The cylindrical, which is frequently a lobed solid, comprises one of the most simple curvature geometric forms. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinders" is also used to refer to an infinitely curved surface in a number of modern domains of topology and geometries. A "cylinder" is a two half object made up of curved surfaces with circle tops and bases. A cylinder is a two half solid figure with two bases that are both similar circles connected at its height, which is controlled by the separation of the legs from the center. Cans of iced drinks and the wicks from toilet paper are example of cylinders.

given

r = d/2 = 40/2 = 20 cm

v = pi *r*r*h

100 = 3.14 * 20*20 *h

100 = 1256*h

h = 0.08 cm

strong box = surface area of cuboid = 45 * 90

= 4050 cm2

surface area of water heater = A=2πrh+2πr2=2·π·20·0.08+2·π·202

≈2523.3

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

To know more about cylinder visit:

https://brainly.com/question/16134180

#SPJ1

The value of (6022*1023) will be = 61,60,506

As per question,

We need to find the value of (6022*1023)

For finding the value of given expression, we will use the identity of multiplication.

So, applying the multiplication identity:

We can write the above as:

6022*1023 = (6000+22) * (1000+23)

As we know,

(a+b)*(c+d) = ac+ad+bc+bd

So, applying the identity in above expression,

We will get,

6022*1023 = (6000+22) * (1000+23)

=(6000*1000)+(6000*23)+(22*1000)+(22*23)

=(6000000+138000+22000+506)

=61,60,506

Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilise every day.

Multiplication is the process of taking one integer and multiplying it by a certain number of times. 5 multiplied by 4 is 5 + 5 + 5 + 5 = 20. We took the number 5 and multiplied it by four. This is why multiplication is often known as "times".

For more questions on Multiplication

https://brainly.com/question/10873737

#SPJ4

The value of x is 20, and the measures of the angles are:

H = 58°

I = 71°

J = 51°

We know that the sum of the interior angles of a triangle is always equal to 180°, and here we know that the measures are:

H = 3x - 2

I = 4x - 9

J = 3x - 9

Then we can write the linear equation:

3x - 2 + 4x - 9 + 3x - 9 = 180

And solve that for x.

10x - 20 = 180

10x = 180 + 20

10x = 200

x = 200/10 = 20

Then the measures of the angles are:

H = 3x - 2 = 3*20 - 2 = 58

I = 4x - 9 = 4*20 - 9 = 71

J = 3x - 9 = 3*20 - 9 = 51

So the correct option is C.

Learn more about interior angles at

https://brainly.com/question/24966296

#SPJ1

A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:

average rate of change = [g(2) - g(-2)] / [2 - (-2)]

First, we find the values of the function at the endpoints of the interval:

g(-2) = [tex]-2^{3}[/tex] - 6 = -14

g(2) = [tex]2^{3}[/tex] - 6 = 2

Substituting these values into the

average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4

Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:

g'(x) = 3[tex]x^{2}[/tex]

g'(-2) = 3[tex]-2^{2}[/tex] = 12

g'(2)  = 12

The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.

This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

Learn more about  instantaneous rate of change here:

https://brainly.com/question/30782681

#SPJ4

The total cost for each combination with the special offer would be:

Massage, leg wax, and manicure: £68.25

Massage, facial, and eyelash tint: £59.25

Massage, leg wax, and eyelash tint: £57.75

We can try out the different possibilities and calculate the total cost of each.

Let's start by listing the prices of the treatments she's interested in:

Massage: £35

Facial: £31

Leg wax: £29

Manicure: £27

Eyelash tint: £13

Now, we can try out the different combinations of 3 treatments and calculate their total cost:

Massage, facial, and leg wax:

Total cost = £35 + £31 + £29 = £95

With 25% off, the cost would be £71.25, which is over Lou's budget of £60, so this combination is not possible.

Massage, facial, and manicure:

Total cost = £35 + £31 + £27 = £93

With 25% off, the cost would be £69.75, which is still over Lou's budget of £60, so this combination is also not possible.

Massage, leg wax, and manicure:

Total cost = £35 + £29 + £27 = £91

With 25% off, the cost would be £68.25, which is within Lou's budget of £60. Therefore, this combination is possible.

Massage, facial, and eyelash tint:

Total cost = £35 + £31 + £13 = £79

With 25% off, the cost would be £59.25, which is within Lou's budget of £60. Therefore, this combination is also possible.

Massage, leg wax, and eyelash tint:

Total cost = £35 + £29 + £13 = £77

With 25% off, the cost would be £57.75, which is within Lou's budget of £60. Therefore, this combination is also possible.

From the above calculations, we can see that Lou can choose from three possible combinations of treatments that fit within her budget and qualify for the special offer:

Massage, leg wax, and manicure

Massage, facial, and eyelash tint

Massage, leg wax, and eyelash tint

The total cost for each combination with the special offer would be:

Massage, leg wax, and manicure: £68.25

Massage, facial, and eyelash tint: £59.25

Massage, leg wax, and eyelash tint: £57.75

Therefore, Lou can choose any of the above combinations and pay the corresponding total cost to enjoy the special offer.

Learn more about total cost here:https://brainly.com/question/29509552

#SPJ1

Answer:

Hi! In order to determine which answer is correct, remember that if an ordered pair is a solution of the inequality, then the ordered pair will satisfy the inequality. Let's plug each of these ordered pairs into the inequality.

A. 5, 0

Substitute 5 and 0 for x and y.

[tex]0 > \frac{3}{5} (5) - 2[/tex]

0 > 1 is not true. Therefore, A is NOT correct.

B. 0, -2

Substitute 0 and -2 for x and y.

[tex]-2 > \frac{3}{5} (0) -2[/tex]

-2 > -2 is not true. Therefore, B is NOT correct.

C. 1, 1

Substitute 1 and 1 for x and y.

[tex]1 > \frac{3}{5} (1) - 2[/tex]

1 > [tex]-\frac{7}{5}[/tex] is true. Therefore, C. 1, 1 is CORRECT.

D. -5, -6

Substitute -5 and -6 for x and y.

[tex]-6 > \frac{3}{5} (-5) - 2[/tex]

-6 > -5 is not true. Therefore, D is NOT correct.

Hope this helps!

The density of water is 1 gram per milliliter, which means that 1 milliliter of water weighs 1000 milligrams (1 gram).

Milligrams (mg) and milliliters (ml) are two different units of measurement used for different purposes. Milligrams are used to measure mass or weight, while milliliters are used to measure volume or capacity.

The conversion between milligrams and milliliters depends on the density of the substance being measured. The density is a measure of the amount of mass per unit of volume.

In general, the conversion between milligrams and milliliters is not straightforward and requires knowing the density of the substance being measured. However, for liquids with a density of approximately 1 gram per milliliter, 1 milliliter is equivalent to 1000 milligrams.

Learn more about milligrams at

https://brainly.com/question/29346047

#SPJ4

To find a point of inflection, take the second derivative of the function, set it equal to zero and solve for x, and verify the point by checking the sign of the second derivative on either side of the point.

Follow these steps to locate a point of inflection:

It is a point of inflection if the curve shifts from concave up to concave down at the point. It is also a point of inflection if it transitions from concave down to concave up.

Learn more about point of inflection at

https://brainly.com/question/29017999

#SPJ4

The sum of money lent out at 6 1/4 p.a. to get 75 rupees as interest in 8 months is 1800 rupees.

To find the sum of money lent out at 6 1/4 p.a. to get 75 rupees as interest in 8 months, we can use the formula for simple interest:

I = P × R × T

Where:
- I is the interest
- P is the principal (the sum of money lent out)
- R is the annual interest rate
- T is the time in years

In this case, we know that I = 75, R = 6.25% (6 1/4 p.a.), and T = 8/12 (8 months is 8/12 of a year). We can plug these values into the formula and solve for P:

75 = P × 6.25% × 8/12

75 = P × 0.0625 × 0.6666666666666666

75 = P × 0.041666666666666664

P = 75 ÷ 0.041666666666666664

P = 1800

Therefore, the sum of money lent out at 6 1/4 p.a. to get 75 rupees as interest in 8 months is 1800 rupees.

Learn more about sum of money here: https://brainly.com/question/12243828

#SPJ11

im positive the answer is x<3