A function is graphed on the coordinate plane.

What is the value of the function when x = 2?

The number you must add to both sides of the equation and the solution are: B. 36, 6 ± √50.

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 12x = 14

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 12x + (-12/2)² = 14 + (-12/2)²

x² - 12x + 36 = 14 + 36

x² - 12x + 36 = 50

x² - 6x - 6x + 36 = 50

x(x - 6) - 6(x - 6) = 50

(x - 6)(x - 6) = 50

x = 6 + √50 or x = 6 - √50.

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Answer:

  14 4/9 km/h, about 14.4 km/h

Step-by-step explanation:

You want to know the average speed of a river cruise boat that travels upstream and downstream in one day if the boat's speed is 18 km/h and the current speed is 8 km/h.

When the boat travels the same distance upstream and back, its average speed is the harmonic mean of the speeds upstream and down. Those speeds are, respectively, the difference of the boat speed and current, and their sum.

  harmonic mean = n/(1/x1 +1/x2 +1/x3 +... +1/xn)

  average speed = 2/(1/(18-8) +1/(18+8)) = 2/(1/10 +1/26) = 2·10·26/(10 +26)

  average speed = 520/36 = 14 4/9 . . . . km/h

The average rate of speed of the cruise ship during the time it is moving is 14 4/9 km/h, about 14.4 km/h.

__

Additional comment

The average speed is the distance divided by the time. If the distance upstream is 'd', then the time upstream is d/(18 -8) = d/10. Similarly, the time downstream is d/26, and the total time is d(1/10 +1/26) = d(36/260).

Then the average speed over the distance 2d is ...

  2d/(d(36/260)) = 520/36 . . . . as above

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Answer:

The number is divisible by 2, 3, 4, 5, 6, 10.

Step-by-step explanation:

Number ends in 40. It is even. It is divisible by 2.

Sum of digits is 15. It is divisible by 3.

Last two digits are 40. It is divisible by 4.

Last digit is 0. It is divisible by 5 and 10.

It is divisible by both 2 and 3. It is divisible by 6.

Answer: The number is divisible by 2, 3, 4, 5, 6, 10.

The necessary condition for ordered pairs (a,b) is that the following characterizing property of them can be proved; (a,b)=(c,d)

And if and only if a=c and b=d

Since we can prove that

{{a},{a,b}}={{c},{c,d}} if and only if a=c and b=d

Thus defining (a,b)  as an abbreviation for {{a},{a,b}} suffices for ordered pairs.

We can also consider that

U = {ordered pairs on a coordinate plane}

A = {ordered pair solutions,y = x}

B = {ordered pair solutions to y = 2x}

if  (x,y) belongs to AnB then y = x and y = 2x

x = 0

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The height of the ladder to the top of the building is 14.4 feet.

The ladder leaned against the building. The base of the ladder is 12 ft from the base of the building. Marta is 6 feet tall.

Therefore, let's find how far up the building is the top of the ladder.

Hence, using similar triangle ratios,

x / 12 = 6 / 5

where

x = height of the building from the top of the ladder.

Therefore,

x / 12 = 6 / 5

cross multiply

5x = 72

divide both sides by 5

x = 72 / 5

x = 14.4

Therefore,

height of the building from the top of the ladder = 14.4 ft

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The correct option is C, this can be modeled with a linear function.

We know that the attendance increases by 15 units each time that the team wins a game.

So, if the initial attendance was A, then the attendance after the team wins x games is modeled by the linear function:

f(x) = A + 15x

Then the correct statement for this case is C, the best option is a linear function because the attendance increases by a constant rate, which is 15.

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The mean number of cars per family is 1.3.

Given table is

Number of cars           0     1      2      3      4

Number of families     5     8     4      2       1

a) From the given table, we can see that modal number of cars = 1 with highest frequency 8.

b) Mean = Sum of all the observations/Number of observations

= (0×5+1×8+2×4+3×2+4×1)/20

= (0+8+8+6+4)/20

= 26/20

= 1.3

So, the mean is 1.3

Therefore, the mean number of cars per family is 1.3.

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Total amount John has to pay = [tex]\$3 + (\$5.25 * X[/tex])

To determine the equation that represents the total amount John has to pay for tax, we need to consider the cost of the watermelon and the cost of the grapes he purchased.

The cost of the watermelon is $3, which remains constant regardless of the weight of the grapes.

The cost of the grapes is given as $5.25 per pound. Multiplying the price per pound by the number of pounds (X), we get the cost of the grapes:

Cost of grapes = $5.25 * X

To find the total amount John has to pay, including tax, we need to add the cost of the watermelon and the cost of the grapes:

Total amount John has to pay = Cost of watermelon + Cost of grapes

Total amount John has to pay =[tex]\$3 + (\$5.25 * X)[/tex]

Therefore, the equation that represents the total amount John has to pay for tax is:

Total amount John has to pay = [tex]\$3 + (\$5.25 * X)[/tex]

The simplified equation shows that the total amount John has to pay for the grapes depends on the cost per pound ($5.25), the tax rate (t), and the weight of the grapes (x).

Note that the specific value of the tax rate (t) is not provided in the question. To calculate the total amount accurately, the value of the tax rate needs to be known or specified.

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Answer: r = 3sinθ - 5cosθ

Step-by-step explanation:

To convert the equation x^2 + y^2 + 5x - 3y = 0 into polar form, we can substitute x = rcosθ and y = rsinθ. Let's rewrite the equation using these substitutions:

(rcosθ)^2 + (rsinθ)^2 + 5(rcosθ) - 3(rsinθ) = 0

Expanding and simplifying:

r^2cos^2θ + r^2sin^2θ + 5rcosθ - 3rsinθ = 0

Using the trigonometric identity cos^2θ + sin^2θ = 1, we can simplify further:

r^2 + 5rcosθ - 3rsinθ = 0

Now, let's rearrange this equation to express r in terms of θ:

r^2 = 3rsinθ - 5rcosθ

Dividing both sides by r:

r = 3sinθ - 5cosθ

Therefore, the equation in polar form that represents x^2 + y^2 + 5x - 3y = 0 is r = 3sinθ - 5cosθ. Hence, the correct option is r = 3sinθ - 5cosθ.

The rectangular equation x² + y² + 5x - 3y = 0 can be converted to polar form by substituting x = rcos θ and y = rsin θ. Simplifying yields the equation r = 5cos θ - 3sin θ.

To convert the given rectangular equation to polar form, we need to first establish the connection between rectangular coordinates (x, y) and polar coordinates (r, θ). This is given by x = rcos θ and y = rsin θ.

So, substitute these into the equation: x² + y² + 5x - 3y = 0 becomes (rcos θ)² + (rsin θ)² - 5rcos θ + 3rsin θ = 0, which simplifies to r² = 5rcos θ - 3rsin θ.

We can then factor r out of the equation to get r = 5cos θ - 3sin θ, which is the rectangular equation in polar form, and matches the last option.

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The value of r is 5 cm.

Given that, a right triangle has a base of r cm and hypotenuse of 10 cm with an angle 60 degrees we need to find the value of r,

The trigonometric function cosine (cos) can be used to determine the value of the right triangle's base (r).

We are aware of the hypotenuse (10 cm) and angle (60 degrees) in this situation.

The ratio of a right triangle's neighboring side to hypotenuse is known as the cosine function.

The base (r) in this instance is the opposite side, and the hypotenuse measures 10 cm.

Using the formula for cosine:

cos(angle) = adjacent/hypotenuse

cos(60 degrees) = r/10

60 degrees has a cosine of 0.5.

So,

0.5 = r/10

To solve for r, we can multiply both sides of the equation by 10:

0.5 x 10 = r

5 = r

Therefore, the value of r is 5 cm.

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Answer:

Option: C

Step-by-step explanation:

The center and radius of the circle with equation (x - 1)² + (y + 4)² = 4 are:

Center: (1, -4)

Radius: 2

So the correct answer is: Center (1, -4); r=2[tex][/tex]

The area of ΔEFG is approximately 916 square centimeters.

Given that,

In ΔEFG

f = 88 cm ,

g = 18 cm

∠E=68°

To find the area of ΔEFG,

Use the formula:

Area = (1/2)xfxgxsin(∠E)

First, we need to convert the angle from degrees to radians.

We can do this by multiplying by π/180.

∠E = 68° * π/180 ≈ 1.19 radians

Next, we can plug in the values we have:

Area = (1/2)x88x18xsin(1.19)

        ≈ 915.56 cm²

Rounding this to the nearest square centimeter,

we get,

Area ≈ 916 cm²

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The surface area of the rectangular prism given the length, width and height is 1800 square cm.

Surface area of a rectangular prism = 2(LW + LH + WH)

Where,

Length, L = 40 cm

Width, W = 10 cm

Height, H = 10 cm

Surface area of a rectangular prism = 2(LW + LH + WH)

= 2(40×10 + 40×10 + 10×10)

= 2(400 + 400 + 100)

= 2(900)

= 1800 square cm

Therefore, 1800 square cm is the surface area of the rectangular prism.

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Answer:

you will need to add the the two numbers and then double the total

(SORRY IF WORNG)

The variance of the data set can be found to be 169. 17.

The standard deviation would also be 13 .

The exam scores for the ten students are:

94 99 67 60 78 89 80 82 77 99

First, find the mean :

= ( 94 + 99 + 67 + 60 + 78 + 89 + 80 + 82 + 77 + 99) / 10

= 82. 5

Then the Sum of the squared deviations from the mean :

= ( 132.25 + 272.25 + 240.25 + 506.25 + 20.25 + 42.25 + 6.25 + 0.25 + 30.25 + 272.25 )

= 1, 522. 5

Variance is:

= Sum of squared deviations / n

= 1, 153. 50 / 10

= 169. 17

The standard deviation is :

= √Variance

= √ 151.35

=  13

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The area (A) of the trapezoid is 225 square kilometers.

The area of Figure #12 is 144 square centimeters.

Question 1:

To find the area (A) of a trapezoid, we can use the formula:

A = (1/2) x (a + b) x h

where 'a' and 'b' are the lengths of the parallel bases and 'h' is the height or the perpendicular distance between the bases.

Given:

Length of the parallel bases:

a = 11 km

b = 19 km

Length of the other two sides:

c = 17 km

d = 15 km

To find the height (h), we can use the Pythagorean theorem since the trapezoid is not necessarily a right trapezoid.

Let's consider the right triangle formed by the height (h), one of the other sides (c = 17 km), and the difference in lengths between the parallel bases (b - a = 19 km - 11 km = 8 km).

Using the Pythagorean theorem:

h² = c² - (b - a)²

h² = 17² - 8²

h² = 289 - 64

h² = 225

h = √225

h = 15 km

Now we have all the values to calculate the area (A):

A = (1/2) x (11 km + 19 km) x 15 km

A = (1/2) x 30 km x 15 km

A = 225 km²

Therefore, the area (A) of the trapezoid is 225 square kilometers.

Question 2:

The area of Figure #12 can be described as.

A  = (6 x 18) + (3 x 12)

A = 108 + 36 square centimeters

A = 144 square centimeters.

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Answer:

1:4

Step-by-step explanation:

4/17=1/4

7/28=1/4

9/36=1/4

Answer:

4

Step-by-step explanation:

Image (2) is 4x every measurement of image (1).

Answer:

Step-by-step explanation:

What are the other colors?

if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2

similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....

depends on how many colors are there

The area of the quadrilateral PQRS is (a) 48

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

The figure

We understand that

This means that

Height = 6

Base = √(10² - 6²) = 8

So, we have

Area = Height * Base

This gives

Area = 6 * 8

Evaluate

Area = 48

Hence, the area of quadrilateral PQRS is (a) 48

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Answer:

Step-by-step explanation:

1.8

20% of 9

= 1/5 of 9

= 9/5

= 18/10

= 1.8

The value of annual property tax on this home would be,

⇒ $3,221.52.

Since, We know that;

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The market value of a home is $316,000.

And, The assessed value is $254,000.

And, The annual property tax rate is $12.68 per $1,000 of assessed value.

Now, For the annual property tax on this home, the assessed value of the home in dollars:

= $254,000 assessed value / $1,000 per $1 of assessed value

= $254 dollars

And, For the annual property tax based on the assessed value:

= $254 dollars assessed value x $12.68 per $1,000 of assessed value

= $3,221.52 annual property tax

Therefore, We get;

The annual property tax on this home is,

⇒ $3,221.52

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The option at best represents the domain of the function, given the number of years would be B) x ≥ 0

The domain of a function encompasses the entirety of conceivable input values, often denoted by the variable x, which are capable of generating meaningful output within the function.

In the present context, the domain represents the plausible range of years subsequent to the car acquisition, wherein the car buyer contemplates the depreciation phenomenon.

The car buyer is considering depreciation after the purchase of the car. This suggests that the number of years, x, is greater than or equal to zero so the domain is:

x ≥ 0

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The volume of the cylindrical silo is V =  6,888 ft³

We can assume that the silo is a perfect cylinder. Remember that the volume of a cylinder of radius R and height H is given by:

V = pi*R²*H

Where we know that pi = 3.14

In this particular case, we know that the radius of the cylinder is 7.5ft, while the height is 39ft.

Replacing these values in the formula above, we will get:

V = 3.14*(7.5 ft)²*39ft

V = 6,888.375 ft³

Rounded to the next whole number we have V = 6,888 ft³

That is the volume.

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The perimeter of Sam's string is 178 inches.

Given information:

Sam has a rectangular shaped window.

Length = 65 inches.

Width = 24 inches.

To find the perimeter:

you can use the formula:

Perimeter = 2 x (Length + Width)

Substituting the values into the formula, we have:

Perimeter = 2 x (65 + 24)

Perimeter = 2 x 89

Perimeter = 178 inches

Therefore, the perimeter of the rectangular window is 178 inches.

So, the perimeter of the rectangular window is 178 inches. This means that if you were to walk along the outline of the window, you would cover a total distance of 178 inches. It's important to note that the perimeter represents the total length of all the sides combined, and it is measured in the same unit (in this case, inches) as the length and width of the window.

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The value of x and y in the right triangle is 4 and 2√2 respectively.

The figure is a right triangle:

Angle Y = 45 degrees

Adjacent to angle Y = 2√2

Hypotenuse = x

To solve for side length x, we the trigonometric ratio.

Note: cosine = adjacent / hypotenuse

Hence:

cos( Y ) = adjacent / hypotenuse

Plug in the values:

cos( 45° ) = (2√2)/x

Solve for x

x = (2√2)/cos( 45° )

x = 4

Next, to solve for y, we use Pythagorean Theorem:

c² = a² + b²

Hence:

x² = y² + (2√2)²

Plug in x = 4

4² = y² + (2√2)²

16 = y² + 8

16 - 8 = y²

y² = 16 - 8

y² = 8

y = √8

y = 2√2

Therefore, the value of side length y is 2√2.

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Based on the expression, Mr. Mbhalati's prediction is correct. His water bill will decrease in Polokwane.

Let's calculate Mr. Mbhalati's water bill in Polokwane and Tzaneen.

Polokwane

Monthly use: 50 kl

Rate: R15.10/kl

Total bill: 50 kl * R15.10/kl

= R755

Tzaneen

Monthly use: 50 kl

Rate: R23.70/kl

Total bill: 50 kl * R23.70/kl

= R1185

As you can see, Mr. Mbhalati's water bill will decrease in Polokwane. His bill in Tzaneen is R430 more than his bill in Polokwane.

Therefore, Mr. Mbhalati's prediction is correct. His water bill will decrease in Polokwane.

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Answer: (x−a)^2 + (y−b)^2 = r^2

Step-by-step explanation:BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB=7, BC= 18, and DC = 5. Find AD to the nearest tenth. B

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, 3 ) and (x₂, y₂ ) = (- 4, 2 )

m = [tex]\frac{2-3}{-4-(-7)}[/tex] = [tex]\frac{-1}{-4+7}[/tex] = - [tex]\frac{1}{3}[/tex]

The slope of the line that contains the points (-7, 3) and (-4, 2) is calculated using the formula for slope. The result of the calculation is negative one third.

The slope of a line is calculated by finding the change in y-values divided by the change in x-values between two points on the line. This is often described as 'rise over run'. For the points (-7, 3) and (-4, 2) given in the question, we can use the formula for slope which is (y2 - y1) / (x2 - x1).

Substituting the given coordinates into the formula, we would get the following: (2 - 3) / (-4 - (-7)) = -1 / 3 = negative one third.

Therefore, the slope of the line that contains the points (-7, 3) and (-4, 2) is negative one third.

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