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Using the coordinate geometry formula, the exact area of triangle DEF is: B. 18 square units.

The coordinate geometry formula is used to find the rea of a triangle with given coordinates of its vertices. It is given as: the absolute value of [Dx(Ey - Fy) + Ex(Fy - Dy) + Fx(Dy - Ey)]/2.

Dx = -3

Dy = 4

Ex = 3

Ey =-2

Fx = 3

Fy = 4

Plug in the values:

[-3(-2 - 4) + 3(4 - 4) + 3(4 - (-2))]/2.

[-3(-6) + 3(0) + 3(6)]/2.

[18 + 0 + 18]/2.

36/2

= 18 units²

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Answer:

{(-2, 5), (1, -1), (2, -2), (5, 2)}

The system of equations modeling the number of imports and the number of exports is given as follows:

The solution f(x) = g(x) represents the month at which the number of imports and the number of exports was the same.

The system of equations is modeled by linear functions in slope-intercept form, as follows:

y = mx + b.

In which:

Hence the equations are given as follows:

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Hiiiiiii

The answer is 1 1/9

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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Answer/Step-by-step explanation:

We are given the following coordinates of two points on the line of the graph shown in the question as: A(2, 1) and B(4, 2)

Vertical change from point A = \( y_2 - y_1 = 2 - 1 = 1 \)

Horizontal change from point A = \( x_2 - x_1 = 4 - 2 = 2 \)

Rate of change = \( \frac{y_2 - y_1}{x_2 - x_1} = \frac{1}{2} = 0.5 \)

The period of the sound wave created by the tuba is approximately 0.0134 seconds.

The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:

v = λ × f

Where:

v = speed of sound (343 m/s)

λ = wavelength (4.61 m)

f = frequency (unknown)

To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:

v = λ / T

Rearranging the equation to solve for the period (T), we get:

T = λ / v

Substituting the given values, we have:

T = 4.61 m / 343 m/s

Calculating the value, we find:

T ≈ 0.0134 seconds

Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.

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Answer:

Step-by-step explanation:

( 2 , 26 )

( 0 , 4 )

m = (26 - 4 ) / ( 2 - 0 ) = 11

Cost of each game is $11

We can Add 7 black beads to make ratio 3 : 1.

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)b : 3

Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3    

Both sides divisible by 3; reduce ratio

= 3 : 1        

Which is Correct ratio

Hence, There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore , we need to add 7 black beads.

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Answer:

94

Step-by-step explanation:

Answer:

Percent of Change

Step-by-step explanation:

The ratio of the change in an amount to the original amount expressed as a percent is known as the change of percent.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

Final amount - initial amount = change

And, change / initial amount = change of percentage

Hence "The ratio of the change in an amount to the original amount expressed as a percent is known as the change of percent.".

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There are 462 different ways can be done for a promotional program.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

Selection of menu, food, clothes, subjects, the team are examples of combinations.

The formula for combinations is: nCr = n!/[r! (n-r)!]

nCr represents the number of combinations from “n” objects taken “r” at a time.

given that

select 6 restaurants from 11.

nCr = n!/[r! (n-r)!]

we are looking at a Combination of 11 things takes 6 at a time, or 11C6

11C6=11!/(6!5!)

11C6=11×10×9×8×7 / 5×4×3×2×1.

11C6=55440 / 120

11C6=462

Thus, there are 462 different ways in which the manager can choose 6 restaurants at a time out of 11.

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The amount after 4 years is $15036

Interest is the amount of money u receive when you invest certain amount of money for certain period of time .

It is given that

Principal = $10,000

Interest = 6% compounded yearly,

time =4 years.

\(\rm Amount = P (1 + \dfrac{r}{n})^{nt}\)

Amount = 10000(1+ (6/100))⁴

Amount = $15036

Therefore the amount after 4 years is $15036.

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Answer: $12,624.77

Step-by-step explanation:

Applying the angle of intersecting secants and tangents theorem, m(KNL) is: A. 264°.

The angle of intersecting secants and tangents theorem states that the angle formed outside a circle has a measure that equals 1/2 the positive difference of the measures of the intercepted arcs.

60 = 1/2(18x - 6 - 5x - 17) [angle of intersecting secants and tangents theorem]

Solve for x

2(60) = 13x - 23

120 = 13x - 23

120 + 23 = 13x

143 = 13x

x = 143/13

x = 11

m(KNL) = (18x - 6 + 5x + 17)

m(KNL) = 23x + 11

Plug in the value of x

m(KNL) = 23(11) + 11

m(KNL) = 264° (option A)

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The interquartile range of the stem and leaf plot is 6.

The table given is a stem and leaf plot. A stem and leaf plot is a table that divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the unit digit.

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1) = 61

First quartile = 1/4 x (n + 1) = 55

Interquartile range = 61 - 55 = 6

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The perimeter of the rectangular floor is the sum of its dimensions

The perimeter function is \(\mathbf{P(x) = \frac{2x^2 + 3000}x}\)

The area of the rectangular floor is given as: 1500

The area of a rectangle is calculated as:

\(\mathbf{Area = xy}\)

Where: x and y represents the width and the length of the floor, respectively.

So, we have:

\(\mathbf{xy = 1500}\)

Make y the subject

\(\mathbf{y = \frac{1500}x}\)

The perimeter of the rectangular floor is:

\(\mathbf{P = 2(x + y)}\)

Substitute \(\mathbf{y = \frac{1500}x}\)

\(\mathbf{P = 2(x + \frac{1500}x)}\)

Take LCM

\(\mathbf{P = 2(\frac{x^2 + 1500}x)}\)

Open bracket

\(\mathbf{P = \frac{2x^2 + 3000}x}\)

Express as a function

\(\mathbf{P(x) = \frac{2x^2 + 3000}x}\)

Hence, the perimeter function is \(\mathbf{P(x) = \frac{2x^2 + 3000}x}\)

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Answer:

\(f = \frac{1}{ {d}^{2} } \)

Answer: 48

Step-by-step explanation: 60-12=48

Answer:

36 %

Step-by-step explanation:

Convert the fraction to a decimal, then multiply by  100 .

Answer:

36%

Step-by-step explanation:

The same explanation as she said

Answer:

The antiderivative is \(F(X) = 6x + 6x^4 + 3x^6 - 15\).

Step-by-step explanation:

Antiderivative F(x)

This is the integral of \(F^{\prime}(x)\)

So

F′(x) = f(x) = 6 + 24x^3 + 18x^5

Then:

\(F(x) = \int (6 + 24x^3 + 18x^5) dx\)

\(F(x) = 6x + \frac{24x^4}{4} + \frac{18x^6}{6} + K\)

\(F(x) = 6x + 6x^4 + 3x^6 + K\)

F(1)=0

\(F(X) = 0\) when \(x = 1\). We use this to find K.

\(F(x) = 6x + 6x^4 + 3x^6 + K\)

\(0 = 6 + 6 + 3 + K\)

\(K = -15\)

Thus

The antiderivative is \(F(X) = 6x + 6x^4 + 3x^6 - 15\).

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer:

Step-by-step explanation:

shes fastr

Answer:

B

Step-by-step explanation:

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

x = 45

Step-by-step explanation:

Note that:

The sum of the interior angles of a quadrilateral is 360°.

Angle: ADC+BAD+ABC+BCD = 360°

Thus, Substitute  ∠ABC = 3x, ∠BAD = (2x-5) , ∠ ADC = (x+15), ∠ BCD = 80 turn into ADC+BAD+ABC+BCD = 360° :

Also known as :

(x+15) +(2x-5) + 3x+80=360

Solving for x

Add the numbers

x + 90+2x+3x=360

Combine like terms

6x + 90=360

subtract 90 from both sides

6x = 270

x = 45

Hence the value of x = 45

Kavinsky

Answer:

C. 45

Step-by-step explanation:

1) Sum of the interior angles of any shape:

(n - 2) x 180, where n is the number of vertices of a shape. In this case, we have 4 vertices.

= (4 - 2) x 180

= 2 x 180

= 360°

2) Add all the given values equating to 360.

2x - 5 + 3x + 80 + x + 15 = 360

6x + 90 = 360

6x = 360 - 90

6x = 270

x = 270/6

x = 45

Answer:

They ordered 432 bottles of water

Step-by-step explanation:

1 multipack = 6 bottles

3 multipacks = 1 box

24 boxes = 24 (3 multipacks)

24 boxes = 72 multipacks

72 multipacks = 72 (6 bottles)

72 multipacks = 432 Bottles