Sharon started with $42 in her bank account and
added $16 per week. Neil started out $70 in debt and deposited $30 per week. Determine how many weeks it will take them to have saved the same amount of money.

Simplifying the expression gives 0 = 6

An algebraic expression is defined as an expression made up of variables and constants, with algebraic operations like addition, subtraction, and division.

Given the expression;

1/2 (x + 4) = 1/2x + 1

\(\frac{1}{2(x + 4)} = \frac{1}{2(x+ 1)}\)

cross multiply

2(x + 1) = 2(x+ 4)

Expand the bracket

2x + 2= 2x + 8

collect like terms

2x - 2x = 8 - 2

0 = 6

Thus, simplifying the expression gives 0 = 6

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Answer:

diameter 12mm

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

They are exact and you can't mess up or accidentally slide the compass or straightedge around. This is just my opinion though.

Answer

it depends

Step-by-step explanation:

The GCF of 30x²y^5 and 24x^3y^4y^4 and 18x^2y^3 is 6xy^3.

1) To determine the GCF of 30x²y^5 and 24x^3y^4, we need to factor each expression.

30x²y^5 = 2 × 3 × 5 × x² × y^5

24x^3y^4 = 2 × 2 × 2 × 3 × x^3 × y^4

The common factor is:

GCF = 2 × 3 × x² × y^4

2) To determine the GCF of 4y^4 and 18x^2y^3, we again factor each expression.

4y^4 = 2 × 2 × y^4

18x^2y^3 = 2 × 3 × 3 × x^2 × y^3

The common factors are 2 and y^3.

The GCF is 2y^3.

Therefore, the GCF of 30x²y^5 and 24x^3y^4y^4 and 18x^2y^3 is 6xy^3.

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Answer:

Answer:

The principal, real, root of:

9–√2

=3

All roots:

3

−3

9 is a perfect square

Answer:

The principal, real, root of:

25−−√2

=5

All roots:

5

−5

25 is a perfect square

Step-by-step explanation:

the first one is for the 9 and the second one is for the 50

As stated in the assertion The ladder will be able to climb up the building around 34.64 feet.

We can use the Pythagorean theorem to address this issue by referring to "height" and taking into account the 40-foot ladder that is situated 20 feet from the building's base. According to the theorem, the square root of the length of the hypotenuse, or side opposite the side with the right angle, in a right-angled triangle, is equal to the sum of each square of the lengths of each of the other two sides.

In this instance, the height of the ladder on the building serves as the hypotenuse, with the distance to the building's base serving as one of its sides. These sides should be labelled as follows:

The Ladder's hypotenuse measures 40 feet

- Side 1 is 20 feet away from the base.

Side 2 (height attained) equals h

The Pythagorean theorem yields the following result: 402 = 202 + h2.

1600 = 400 + h2 h2 = 1200 h 34.64 feet when h is solved for.

The ladder may therefore climb the building to a height of about 34.64 feet.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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The height of water left in the can  is determined as 9.9 cm.

option B.

The height of water left in the can is calculated by the difference between the volume of a cylinder and volume of a cone.

The volume of the cylindrical can is calculated as;

V = πr²h

where;

V = π(4.6 cm)²(13.5 cm)

V = 897.43 cm³

The  volume of the cone is calculated as;

V = ¹/₃ πr²h

V = ¹/₃ π(5.1 cm)²( 8.7 cm )

V = 236.97 cm³

Difference in volume =  897.43 cm³ - 236.97 cm³

ΔV = 660.46 cm³

The height of water left in the can  is calculated as follows;

ΔV = πr²h

h = ΔV /  πr²

h = ( 660.46 ) / (π x 4.6²)

h = 9.9 cm

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Answer:

19

Step-by-step explanation:

5w+3°=98°

5w=98°-3°

5w=95°

therefore w=95/5=19

Answer:

- \(\frac{5}{3}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{3}{5}\) x - \(\frac{12}{5}\) ← is in slope- intercept form

with slope m = \(\frac{3}{5}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{3}{5} }\) = - \(\frac{5}{3}\)

When a fold axis is lying on its side (horizontal), the fold is said to be recumbent.

Folds are bends or curves in rock layers caused by tectonic forces. The axis of a fold is an imaginary line that runs through the highest point of each layer in the fold. A recumbent fold is a type of fold in which the axial plane is horizontal, and the layers are nearly horizontal as well.

This means that the fold axis is lying on its side, and the layers on either side of the axis are essentially parallel to each other. Recumbent folds can be difficult to recognize in the field, as they may look like flat-lying layers rather than folds.

They are typically formed by intense tectonic forces that cause the layers to be bent and deformed.

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An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.

D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.

D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.

D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.

D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.

The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.

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Answer and Step-by-step explanation:

The cubed root of -343 has ONE real roots.

That root is -7.

When you multiply -7 by itself 3 times, you get -343.

-7 times -7 = 49

49 times -7 = -343.

#teamtrees #WAP (Water And Plant)

a. To calculate the expected value of how much money you’ll get if you bet $10 on number 12 in Roulette, we can use the formula: Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Lost)

In this case, the probability of winning is 1/38, and the amount won is $350. The probability of losing is 37/38, and the amount lost is $10. Substituting these values into the formula, we get: Expected Value = (1/38 * $350) - (37/38 * $10)
Expected Value = $9.21 Therefore, the expected value of how much money you’ll get if you bet $10 on number 12 in Roulette is $9.21. b. Based on the expected value from part a, it is not a good idea to play Roulette over and over again. The reason is that the expected value is positive but small. This means that on average, you will win $9.21 for every $10 you bet, but the variance in the game can cause you to lose money in the long run.
For example, if you play 100 rounds of Roulette with a $10 bet on number 12 each time, you would expect to win $921 on average. However, there is a significant chance that you could lose money over these 100 rounds. The more you play, the greater the likelihood of experiencing a losing streak that would offset your winnings.

Therefore, while playing Roulette can be fun and exciting, it is not a sustainable way to make money. The small expected value means that over time, the casino will always come out ahead.

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Answer:

120

Step-by-step explanation:

25 + 35 = 60

60 + 60 = 120

Answer:

To find the odds in favor of Cody being first, we need to divide the probability of him winning (25%) by the probability of him not winning (75%).

Odds in favor of Cody winning = 25% / (100% - 25%) = 25% / 75%

Simplifying, we get:

Odds in favor of Cody winning = 1/3

Therefore, the odds in favor of Cody being first in the 50m backstroke are 1 to 2 (or 1:2).

I was in a rush so I couldn't write fown the steps. If you need the explanations for how they were gotten, please say.

Answer: 66

Step-by-step explanation:

0 - 12 = -12

54--12 = 66

66 is the difference

Given

Procedure

Now for y

The answer would be x = 2.75 and y = 1.25

Answer:

Step-by-step explanation:

We know that the permiter is defined as

\(P=L+S+M\)

Where \(L\) is the longest side, \(S\) is the smallest and \(M\) is the middle side.

If \(L=x\) then, \(S=x-20\), where we need to find an expression for \(M\) using the law of cosines.

\(M^{2} =L^{2}+S^{2}-2 \times L \times S \times cos(60\°)\\M=\sqrt{x^{2}+(x-20)^{2}-x(x-20)}\\M=\sqrt{x^{2} +x^{2}-40x+400-x^{2}+20x}=\sqrt{x^{2}-20x+400}\)

Replacing all expression, the perimeter is

\(P=x+x-20+\sqrt{x^{2}-20x+400}\\P=2x-20+\sqrt{x^{2}-20x+400}\)

Using a calculator, the perimeter is 20 units centimeters.

The Verdicts on each value of u according to the given inequality are as follows; 11, 13 and 8.

It follows from the task content that the values which are solutions to the inequality; u ≤ 13 are to identified.

To determine the solution of an inequality on a number line, the number line representation of such inequality is very pivotal.

Therefore, the inequality given; u ≤ 13 simply implies that; the solution set of u includes 13 and all numbers to the left of 13 on the number line.

Hence, by considering each of the given values of u; we have;

Ultimately, the solutions to the inequality among the answer choices are; 11, 13 and 8 respectively.

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Answer:

\(\huge\boxed{\sf Yes.}\)

Step-by-step explanation:

y = 6x - 9 ---------------(1)

y = 2x + 3 --------------(2)

So,

x = 3, y = 9

Put this in Eq. (1) to verify.

9 = 6(3) - 9

9 = 18 - 9

9 = 9 [Equation satisfied]

Now, put x = 3, y = 9 in Eq. (2)

9 = 2(3) + 3

9 = 6 + 3

9 = 9 [Equation satisfied]

Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.

\(\rule[225]{225}{2}\)

Answer: Yes, it is a solution

Step-by-step explanation:

Plug (x,y) values into the equations.

Plug in (3,9)

y=6x-9  ---->.  (9)=6(3)-9 ----> 9=18-9 ----->   9=9

y=2x+3 ------>.  (9)=2(3)+3 ----> 9=6+3 ----> 9=9

When know (3,9) is a solution because each side has the same value.

Example:

8=9 Not a solution

5=5 A solution

Answer:

Option 2. That is the best option for this problem

The equation of line passes through the points (3, -4) will be;

⇒ y = - x - 1

What is Equation of line?

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 point on the line are (3, -4).

And, the parallel line is,

⇒ y = - x + 8

Now,

Since, The equation of line passes through the points (3, -4) and  parallel to the line y = -x + 8

And, Slope of parallel lines are always same.

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

Hence, Slope of the line is,

y = - x + 8

m = dy/dx = - 1

Thus, The equation of line with slope - 1 and passes through the points

(3, -4) is,

⇒ y - (-4)= -1 (x - 3)

⇒ y + 4 = - x + 3

⇒ y = - x + 3 - 4

⇒ y = - x - 1

Therefore, The equation of line passes through the points (3, -4) is;

⇒ y = - x - 1

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Answer:

128:72

Or

16:9 (simplified)

Hope this helps!

It will take approximately 51.25 minutes for the man to get home at his usual speed of 9 kilometers per hour.

Step 1: Convert the given time in minutes to hours
26 minutes = 26/60 hours = 0.4333 hours
10 minutes = 10/60 hours = 0.1667 hours

Step 2: Calculate the distance covered during each time interval
First interval: 6.76 km/h * 0.4333 hours = 2.9276 km
Second interval: 5.55 km/h * 0.1667 hours = 0.9256 km

Step 3: Add the distances together to find the total distance covered
2.9276 km + 0.9256 km = 3.8532 km

Step 4: Calculate the remaining distance to reach home
11.54 km - 3.8532 km = 7.6868 km

Step 5: Calculate the time it takes to cover the remaining distance at the usual speed
Time = Distance / Speed
Time = 7.6868 km / 9 km/h = 0.8541 hours

Step 6: Convert the time in hours back to minutes
0.8541 hours * 60 = 51.246 minutes

So, it will take approximately 51.25 minutes for the man to get home at his usual speed of 9 kilometers per hour.

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Answer:

(7-4)+17-14+2×5

3+17-14+2×5

3+17-14+10

3+27-14

30-14

16