Use the distributive property to remove the parentheses.
-3(2v - 4w-6)
HELPPOO MEEE

Answer:

B

Step-by-step explanation:

Clearly BD is shorter than AE so that is false.

BD is clearly on the opposite end of EC so it is not bisecting, as bisecting would be DE bisecting AC

AC has to be perpendicular to something to be a perpendicular bisector however it is a straight line.

Answer:

B

Step-by-step explanation:

Answer:

61.3 meters

Step-by-step explanation:

Circumference of the circular = πd where d= diameter

= 3.14 x 20 m = 62.8 m

From this you have to subtract width of gate

Width of gate = 150 cm = 150/100 meters since 1 m = 100 cm

= 1.5 m

62.8 - 1.5 = 61.3 m

The total length of the safety fence around the circular pool, excluding the gate, is 61.3 meters. This has been calculated by first finding the circumference of the circular pool excluding the gate, then subtracting the width of the gate.

This question involves the application of the formula for the circumference of a circle. To find the total length of the fence around a circular pool not including the gate, you first need to calculate the circumference of the pool. To do this, you can use the formula C = 2πr, where C is the circumference, r is the radius (half of diameter), and π is 3.14. Given that the diameter = 20 meters, the radius r = 20/2 = 10 meters. Hence, the entire circumference of the fence without the gate = 2 * 3.14 * 10 = 62.8 meters.

To find the length of the fence excluding the gate, subtract the width of the gate from the entire circumference. The gate width is 150 cm, but remember that 1 meter = 100 cm so the gate width in meters is 150/100 = 1.5 meters. So, the length of the fence not including the gate = 62.8 - 1.5 = 61.3 meters.

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We have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

To prove that △ABD ≅ △CBD, we can use the SAS (Side-Angle-Side) congruence criterion.

Given:

∠BDA ≅ ∠BDC (Both are right angles)

D is the midpoint of AC¯¯¯¯¯

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯

BD¯¯¯¯¯ bisects ∠B

Proof:

Since D is the midpoint of AC¯¯¯¯¯, we have AD ≅ CD by the definition of a midpoint.

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯ (Given)

BD¯¯¯¯¯ is a common side for both triangles.

∠BDA ≅ ∠BDC (Given)

To apply the SAS congruence criterion, we need to show that one pair of corresponding sides and the included angle are congruent in both triangles.

AD ≅ CD (Side) - This is true as D is the midpoint of AC¯¯¯¯¯.

∠BDA ≅ ∠BDC (Included Angle) - Both are right angles.

By the SAS congruence criterion, we can conclude that △ABD ≅ △CBD.

Therefore, we have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

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For binomial probability mass function formula and compound interest formula, These both involve the use of exponents, they are not otherwise related to each other in any significant way.

What is Compound interest?

Compound interest is the interest that is earned not only on the initial principal amount of an investment, but also on any interest that has accumulated over time. In other words, it is interest that is "compounded" or added to the principal amount at specific intervals, such as daily, monthly, quarterly, or annually.

Now,

The binomial probability mass function formula and the compound interest formula are not directly related to each other, as they are used to model different types of phenomena.

The binomial probability mass function is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure) and the probability is same. The binomial probability mass function is

P(x) = pˣ (1-p)ⁿ⁻ˣ

where X is the number of successes, k is the specific number of successes we are interested in, n is the total number of trials, p is the probability of success on each trial, and represents the binomial coefficient.

The compound interest formula, on the other hand, is used to calculate the value of an investment over time, assuming a fixed interest rate and compounding periods. The future value is

FV = PV x (1 + r/n)ⁿˣ

where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), n = number of times interest is compounded per year, and x = number of years.

While both formulas involve the use of exponents, they are not otherwise related to each other in any significant way.

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The binomial probability mass function formula and the compound interest formula are not directly related to each other.

The binomial probability mass function formula is used to calculate the probability of observing a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across all trials. The formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where X is the random variable representing the number of successes, k is the number of successes we want to observe, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

On the other hand, the compound interest formula is used to calculate the value of an investment that earns a fixed interest rate over a certain period of time, assuming that the interest is compounded at regular intervals. The formula is:

A = P * (1 + r/n)^(nt)

where A is the final amount of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the number of years, and (1 + r/n)^(nt) represents the growth factor of the investment.

While both formulas involve exponents and use the terms (1 - p) and (1 + r/n), they are fundamentally different in their purpose and application.

Answer:B

Step-by-step explanation:

I just know k?

Answer:

B

Step-by-step explanation:

The dots form a line that passes through the orgin

The slope of a line perpendicular to the line whose equation is 2x + 3y = 24 is,

⇒ m = - 2/3

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 perpendicular line is,

⇒ 2x + 3y = 24

Now,

Since, Product of slopes of perpendicular line are - 1.

So, We need to find the slope of the line.

Hence, Slope of the line is,

2x + 3y = 24

y = - 2/3x + 8

m = dy/dx = - 2/3

m = - 2/3

Thus, The slope of a line perpendicular to the line whose equation is 2x + 3y = 24 is,

⇒ m = - 2/3

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Answer:

B: 8

Step-by-step explanation:

When you add a negative number, it means you subtract that number.

\(17+-9=17-9=8\)

Answer:

Graph A

Step-by-step explanation:

A linear association means that the dots form a line

Answer:

The answer is A

Step-by-step explanation:

A linear association is when the dots on the graph create a straight line. A creates a straight line therefore it is a linear association.

Answer:

11980

Step-by-step explanation:

This is simple interest.

We use the formula i=prt. Interest = price x rate x time

You just plug in your numbers, 10000 is your price, 5.5 years is the time, and 3.6% interest is rate.

Now our equation looks like this: i = 10000 x 5.5 x 0.036

(i converted the percent to a decimal)

So the interest is 1980, but the question asks for the final value, so we add the interest to the initial deposit, 1980 + 10000, and we get 11980 for our final value.

I apologize if my answer is wrong, but if it isn't I hope I helped :)

9514 1404 393

Answer:

  $12,190

Step-by-step explanation:

The formula for the balance in an account where continuous compounding occurs is ...

  A = Pe^(rt) . . . . where P is the principal invested at annual rate r for t years

  A = $10,000e^(0.036·5.5) = $10,000e^0.198

  A ≈ $12189.62 ≈ $12,190 . . . . rounded to the nearest dollar

The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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Answer:

Line A B and Line C G are parallel.

Line C G and Line R S are perpendicular

Line A B and Line R S must intersect

Line segment C G lies in plane X

Step-by-step explanation:

Given that Planes X and Y intersect at a right angle.

From the image attached, line AB and CG are on the same plane X while line RS is on plane Y. Hence, line CG lies on plane X.

Since both line AB and CG line on the same plane, this means that both lines are parallel to each other.

Since plane X and plane Y are perpendicular to each other and line CG is on plane X and line RS is on plane Y, this means that both Line C G and Line R S are perpendicular.

Also Since plane X and plane Y intersect and line AB is on plane X and line RS is on plane Y, this means that both Line C G and Line R S intersect with each other at right angle.

Answer:

A and  are parallel.

C   and  are perpendicular.

E  lies in plane X.

Step-by-step explanation:

ED22

The function that is graphed is (c) y = x² + 2    if x < 1 and y = -x + 2  if x ≥ 1

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

The graph

On the graph, we can see that the first curve is a quadratic function,

Also, it has an open circle at x = 1

So, we have:

x² + 2    if x < 1

Next, we have a linear equation with a closed circle at x = 1

So we have:

y = -x + 2 for x ≥ 1

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Answer: 2/5 Step-by-step explanation: The easiest approach is to realize that one hour is 3 times longer than 20 minutes. The longer the time, the more they will pave.  

Answer:

-2 - 24i

Step-by-step explanation:

a + bi + (7 - 3i) + (5 + 9i) + 13i = 10 - 5i

a + bi + 7 + 5  - 3i + 9i + 13i = 10 - 5i

                a + bi  + 12  + 19i = 10 - 5i

                         a + bi          = 10 - 5i - 12 - 9i

                                 a + bi = 10 - 12 - 5i - 9i

                                 a + bi = -2 - 24i

Answer: $22.8501

Step-by-step explanation:

Since their bill was $54.25 and they need to pay tax of 8% and leave a 17% tip, the total amount that will be paid will be:

= $54.25 + (8% × $54.25)

= $54.25 + (0.08 × $54.25)

= $54.25 + $4.34

= $58.59

We then add the 17% tip. This will be:

= $58.59 + (17% × $58.59)

= $58.59 + (0.17 × $58.59)

= $58.59 + $9.9603

= $68.5503

Since they want to split the bill evenly, we divide the total amount gotten by 3. This will be:

= $68.5503 / 3

= $22.8501

Each person will pay $22.8501

Answer:

91781052

Step-by-step explanation:

hope this helps mate

Answer: (5,3)

Step-by-step explanation:

the formula used for a reflection across the x-axis is (x,-y)

To find the limit of a convergent sequence, we can simply take the limit as n approaches infinity. Let's calculate the limits for each of the given sequences:

A. \(\sf\:\lim_{n \to \infty} \frac{5n}{n+7} \\\)

To find the limit, we divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{5n/n}{(n+7)/n} = \frac{5}{1} = 5 \\\)

Therefore, the limit of the sequence A is 5.

B. \(\sf\:\lim_{n \to \infty} \frac{4-7n}{8+n} \\\)

Again, divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{4/n - 7}{8/n + 1} = \frac{0 - 7}{0 + 1} = -7 \\\)

So, the limit of sequence B is -7.

C. \(\sf:\lim_{n \to \infty} \frac{8n - 500\sqrt{n}}{2n + 800\sqrt{n}} \\\)

Divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500\sqrt{n}/n}{2 + 800\sqrt{n}/n} \\\)

As n approaches infinity, the terms involving \(\sf\:\sqrt{n}/n \\\) tend to 0:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500(0)}{2 + 800(0)} = \frac{8}{2} = 4 \\\)

Therefore, the limit of sequence C is 4.

To summarize:

A. The limit of sequence A is 5.

B. The limit of sequence B is -7.

C. The limit of sequence C is 4.

Answer: 31.5

Step-by-step explanation:

Answer:

31.5

Step-by-step explanation:

\(45 \times .7 = 31.5\)

Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

The area of the shaped swimming pool is 25π square meters

A shape consisting of all points in a plane that are at a given distance from a given point which is the centre is described as a circle.

The formula for calculating the area of a circle is expressed as:

A = πr²

where:

r is the radius of the circle.

Given that radius = 5m, substitute to have:

A = π(5)²

A = 25π square meters

Hence the area of a circle shaped swimming pool with a radius of 5 m is 25π square meters

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Answer:

500

Step-by-step explanation:

20% of x = 100

Write 20% as a decimal - - > 0.2(x) = 100

Isolate and solve for x - - > x = 100/0.2

Therefore, x = 500

Answer:

500

Step-by-step explanation:

Let the no. be x

20% of x = \(\frac{20}{100} x\)

And ,

\(\frac{20}{100} x = 100\\=> 20x = 10000\\ => x = \frac{10000}{20} = 500\)

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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Answer: 21

Step-by-step explanation:  im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah

Answer:

21

Step-by-step explanation:

I did the test

Hope this helps :)

Answer:

16π

Step-by-step explanation:

2 * π * 8

16π

Answer:

16π

Hope this helps out!

Answer:

Step-by-step explanation:For what values of does the equation (2 + 1) have two 2

+ 2 = 10 − 6

real and equal roots?

A quadratic equation that has 2 roots that are equal means that the discriminant  of the equation is 0. The value of k that makes the equation have 2 real and equal roots is \(k = \frac{5}{6}\)

Given that:

\((2k + 1)x^2 + 2x = 10x - 6\)

Rewrite as:

\((2k + 1)x^2 + 2x - 10x + 6 = 0\)

\((2k + 1)x^2 - 8x + 6 = 0\)

A quadratic equation is represented as:

\(ax^2 + bx + c = 0\)

By comparison:

\(a=2k+1\\ b =-8\\\ c =6\)

If an equation has 2 real and equal roots, then:

\(b^2 = 4ac\)

So, we have:

\((-8)^2 = 4 \times (2k + 1) \times 6\)

\(64 = 4 \times (2k + 1) \times 6\)

Divide by 4

\(16 = (2k + 1) \times 6\)

Divide by 6

\(\frac{16}{6} = (2k + 1)\)

\(\frac{8}{3} = 2k + 1\)

Subtract 2 from both sides

\(2k = \frac{8}{3} -1\)

Take LCM

\(2k = \frac{8-3}{3}\)

\(2k = \frac{5}{3}\)

Divide by 2

\(k = \frac{5}{6}\)

Hence, the value of k that makes the equation have 2 real and equal roots is \(k = \frac{5}{6}\)

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Answer:

10 to 1

Step-by-step explanation:

if 0 went to up there 10 you'd have to

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

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

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

330 cubic feet

Step-by-step explanation:

The formula for Volume is L (length) x W (width)  x H (Hight)

So all we have to do is multiply the numbers for each floor and then add them together.

5 x 3 = 15 15 x 6 = 90

6 x 5 = 30 30 x 8 = 240

240 + 90 = 330

Now add you cubic feet since volume is cubed.

330 cubed feet

Thus, your answer is 330 cubed feet.

Hope this helps! :)