A 50kg mass is shot from a cannon straight up with an initial velocity of 10m/s off a bridge that is 100 meters above the ground. If air resistance is given by 5v, determine the velocity of the mass when it hits the ground.

The correct option c ) m∠5 + m∠2 = m∠3 + m∠2, is the missing statement in step 4.

When a transversal divides two parallel lines, the resulting alternate interior angles are congruent.

Thus,  m∠5 + m∠2 = m∠3 + m∠2, is the missing statement in step 4.

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Answer:

i believe its 24500

Step-by-step explanation:

Answer:

(1/48)ax

Step-by-step explanation:

We can use the proportion of the lengths of the model and the actual locomotive to determine the scale factor for this similarity transformation.

The model is 18 inches long, which is equivalent to 1.5 feet (since 1 foot = 12 inches). The actual locomotive is 72 feet long. So, the scale factor can be calculated as:

scale factor = actual length / model length

scale factor = 72 feet / 1.5 feet

scale factor = 48

This means that each measurement on the model is 1/48th the size of the corresponding measurement on the actual locomotive. We can express this similarity transformation using the notation x* ax as: x* (1/48)ax

So, if a measurement on the model is x, the corresponding measurement on the actual locomotive would be (1/48)ax.

We have a right triangle with sharp angles measuring 30 and 60 degrees, proving the assertion "Triangle with angles A= 30 degrees, B= 60 degrees, C= 90 degrees" to be true.

To assess whether the supplied angles may form a triangle, we can use the knowledge that the total of the angles in a triangle is always 180 degrees. Let's figure up the angles' total:

180 degrees is equal to A + B + C = 30 + 60 + 90.

The supplied angles can definitely form a triangle because the sum of the angles is 180 degrees. We can now utilise the data to identify the kind of triangle.

The angles indicate that a right triangle with a 90-degree angle (angle C) and acute angles of 30 degrees and 60 degrees (angles A and B) exists (angle B).

The measurements of angles A and B are compatible with the available information since the total of the acute angles in a right triangle is always 90 degrees.

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The image reflected by the line of the triangle is attached below.

What is an image?

A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The coordinates of the vertices of the triangle are (1, -2), (8,1), (4,-9).

The rule of reflection across the y = x line is (x,y) → (y,x).

The reflection of (1, -2) across the y = x line is (-2,1).

The reflection of (8,1) across the y = x line is (1,8).

The reflection of (4,-9) across the y = x line is (-9,4).

The coordinates of the vertices of the reflected triangle are (-2,1), (1,8), and (-9,4).

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The heaviest fish caught weighed more than 12 pounds.

What is mean in statistics?

In statistics, the mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. The mean is also called the arithmetic mean or the average. It is commonly used to describe the typical value of a group of numbers.

To determine which statement is supported by the data, we need to analyze the weights of the fish that Terri and her father caught. Here are some possible statements that could be supported by the data:

A. The average weight of the fish caught was less than 7 pounds.

B. The heaviest fish caught weighed more than 12 pounds.

C. The total weight of the fish caught was more than 60 pounds.

D. The range of weights of the fish caught was between 4 and 12 pounds.

To determine which statement is supported, we can calculate some basic statistics:

Mean (average) weight: (5.6 + 11.0 + 4.0 + 12.2 + 7.0 + 10.0 + 4.2) / 7 = 7.8 pounds

Maximum weight: 12.2 pounds

Minimum weight: 4.0 pounds

Range of weights: 12.2 - 4.0 = 8.2 pounds

Total weight: 5.6 + 11.0 + 4.0 + 12.2 + 7.0 + 10.0 + 4.2 = 54 pounds

Based on this analysis, we can see that statement C ("The total weight of the fish caught was more than 60 pounds") is not supported by the data, as the total weight was only 54 pounds.

Statement A ("The average weight of the fish caught was less than 7 pounds") is also not supported, as the average weight was 7.8 pounds.

Statement B ("The heaviest fish caught weighed more than 12 pounds") is supported, as the heaviest fish weighed 12.2 pounds.

Finally, statement D ("The range of weights of the fish caught was between 4 and 12 pounds") is also supported, as the weights ranged from 4.0 to 12.2 pounds.

Therefore, the correct answer is either B or D, depending on the context of the question.

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Answer:

Refer to pic..........

The number of touchdowns scored by the defense of the professional football team in the season was C. 10 touchdowns.

The team scored a total of 242 points, and the defense scored about 24% of those points, which is:

0.24 x 242 = 58.08

This means that the defense scored approximately 58 points during the season. If a touchdown is worth 6 points, we can find the number of touchdowns scored by the defense by dividing the total number of points scored by 6:

58 / 6 = 9.67

So the defense scored approximately 9.67 touchdowns during the season. Since we can't have a fraction of a touchdown, the closest whole number answer would be 10 touchdowns.

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Answer:

Step-by-step explanation:

I'm unable to solve this, The photo is unclear and to small.

The answer as a fraction in lowest terms is 4/81, and the denominator is 81.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

There are 4 green card, 2 red cards, 3 blue cards

Now,

If the first card drawn is red and is replaced before the second draw, then the probability of drawing a red card on the second draw is the same as the probability of drawing a red card on the first draw, which is 2/9 (since there are 2 red cards out of a total of 9 cards).

To find the probability of drawing two red cards, we need to multiply the probability of drawing a red card on the first draw (which we know is 2/9) by the probability of drawing a red card on the second draw, which is also 2/9 (since the first card is replaced).

So the probability of drawing two red cards with replacement is:

(2/9) * (2/9) = 4/81

Therefore, the probability and denominator will be 4/81 and 81.

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Answer:

The answer is 1/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]7 \times 3 + 2 = 23 [/tex]

[tex]2 \times 3 + 2 = 8[/tex]

[tex] \frac{23}{8}[/tex]

so if want to have improper fraction this is the answer but to get proper fraction i am continuing

[8 \div 23 \sqrt[23]{80} to get the correct answer.you can get a mixed fraction too when you multiply 8 how many times you will get 23 8×2=16=2whole number 16 as the numerator and 8 as the denominator

The factors of given expression are (a+b+2) and (a+b+2).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is (a+b)²+4(a+b)+4.

Here, take x=a+b

Now, x²+4x+4

= x²+2×2×x+4 (Algebraic identity (a+b)²=a²+2ab+b²)

= (x+2)²

= (a+b+2)²

= (a+b+2)(a+b+2)

Therefore, the factors are (a+b+2) and (a+b+2).

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Answer:

A) (5 , 1)

Step-by-step explanation:

The x coordinate goes first, then the y coordinate: (x , y)

In this case, locate Chewy. Chewy is found in the x-coordinate of 5, and a y-coordinate of 1. Therefore, (5 , 1) or A) is your answer.

~

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By taking the quotient between the volume of the sink and the volume for each cone, we will see that both of your answers are correct.

How many coops does Carissa need to scoop out in each case?

First, we know that the sink has a volume V = (2000/3)*pi in^3

A) First she uses a cone of a diameter of 4 in and a height of 8 in.

Remember that the volume of a cone of diameter D and height H is:

V = pi*(D/2)^2*H/3

Then this cone has a volume of:

V' = (pi/3)*(4in/2)^2*8in = (pi/3) 32 in^3

The number of scoops needed to completely remove the water out of the sink is given by the quotient between the two volumes, it is:

Rounding it, we get 63, so she needs to scoop 63 times.

B) This time the diameter is 8 in and the height 8 in, so the volume of the cone is:

V'' = (pi/3)*(8in/2)^2*8in = (pi/3)*128 in^3

This time, she needs to scoop:

Rounding to the next number we get 16, she needs to scoop 16 times.

So yes, both of your answers are correct.

l be beneficial both in school and in other parts of your life.[1]

Answer:

Step-by-step explanation:

To determine how many conical cups of water Carissa must scoop out of the half-sphere sink to empty it, divide the volume of the sink by the volume of each cup.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

To determine the volume of conical cup 1 (in terms of π) given it has a diameter of 6 in and a height of 14 in, substitute r = 3 and h = 14 into the volume of a cone formula:

[tex]\begin{aligned}\implies V_{\sf cup\:1}&=\dfrac{1}{3} \pi (3)^2(14)\\\\&=\dfrac{1}{3} \pi (9)(14)\\\\&=\dfrac{126}{3} \pi\\\\&=42 \pi\;\sf in^3\end{aligned}[/tex]

Divide the given volume of the sink by the volume of conical cup 1 to calculate the number of cups of water Carissa must scoop out of the sink to empty it.

[tex]\begin{aligned}\implies \dfrac{4500}{3}\pi \div 42 \pi &=\dfrac{4500}{3}\pi \times \dfrac{1}{42 \pi}\\\\ &=\dfrac{4500 \pi}{126 \pi}\\\\&=\dfrac{4500}{126}\\\\&=35.7142867...\\\\&=36\;\sf(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, Carissa must scoop out 36 cups of water to empty the sink.

To determine the volume of conical cup 2 (in terms of π) given it has a diameter of 10 in and a height of 12 in, substitute r = 5 and h = 12 into the volume of a cone formula:

[tex]\begin{aligned}\implies V_{\sf cup\:2}&=\dfrac{1}{3} \pi (5)^2(12)\\\\&=\dfrac{1}{3} \pi (25)(12)\\\\&=\dfrac{300}{3} \pi\\\\&=100\pi\;\sf in^3\end{aligned}[/tex]

Divide the given volume of the sink by the volume of conical cup 2 to calculate the number of cups of water Carissa must scoop out of the sink to empty it.

[tex]\begin{aligned}\implies \dfrac{4500}{3}\pi \div 100 \pi &=\dfrac{4500}{3}\pi \times \dfrac{1}{100 \pi}\\\\ &=\dfrac{4500 \pi}{300\pi}\\\\&=\dfrac{4500}{300}\\\\&=15\end{aligned}[/tex]

Therefore, Carissa must scoop out 15 cups of water to empty the sink.

Answer: It doesn't really matter

Step-by-step explanation: This is more of an opinion question, but failing math tests doesn't mean you aren't good at math, some people have different reasons why they don't try at math. Math tests don't define how good or bad you really are in math. You can fail a math test and be good at math, but not passing math tests might also create a lot of issues in the careers you're trying to persuade in because math is one of the most useful subjects. If colleges see your math scores and how badly you performed in them, they won't pick you, which is why is always nice to try no matter how easy or hard it is.

The easiest way to solve problems involving "two unit multipliers" is to use a technique called unit conversion or dimensional analysis.

To solve such problems, you need to convert the given value from one unit to another by multiplying it by a series of conversion factors or unit multipliers. A conversion factor is a fraction that has the same value as one, but its numerator and denominator are expressed in different units.

For example, to convert 10 meters to feet, you can use the conversion factor:

1 meter = 3.28 feet

To convert 10 meters to feet, you would multiply 10 by the conversion factor:

10 meters * (3.28 feet/1 meter) = 32.8 feet

The meters unit cancels out, leaving you with the desired unit of feet.

In some cases, you may need to use multiple conversion factors to get from one unit to another. In these cases, you can multiply or divide the conversion factors to cancel out the unwanted units until you get to the desired unit.

Using unit conversion or dimensional analysis is an effective way to solve problems involving two unit multipliers because it ensures that the units cancel out correctly, and you end up with the desired unit in your final answer.

Answer: (3,-1) = (0,2) (5,-2) = (2,1) (3,-5) = (0,-2) (-5,-5) = (-2,-2)

Step-by-step explanation:

Using displacement, His unit rate every mile per hour will be 4 miles/hours.

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

Mario walked at a rate of 2/3 mile every 10 minutes.

We have,

Distance = 2/3 miles

Time = 10 minutes

On substituting these values in the above formula, we get

speed = 2/10.3

We have to find the unit rate in mile per hour, so we need to multiply it by 60, 1/15 × 60 = 4 miles/hours

Hence, his unit rate every mile per hour will be 4 miles/hours.

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Answer:

x = 20

Step-by-step explanation:

We know that the vertically opposite angles are equal.

Accordingly,

41 = 2x + 1

Subtract 1 from both sides.

41 - 1 = 2x

40 = 2x

Divide both sides by 2.

x = 20

Answer: 2%

Step-by-step explanation:

annual interest rate is based off a year
monthly is based off month
there are 12 months in a year, so to find the monthly interest you just divide the annual interest by 12.

Answer: 38

Hope this helps!

Answer:$0.85

Step-by-step explanation: 4.25/5=0.85

The sum of the solutions for the equation 4x²- 8x - 12 = 0 will be 2. The correct option is C.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

To find the sum of the solutions of the equation 4x^2-8x-12=0, we first need to find the solutions of the equation. We can start by factoring in the left-hand side of the equation:

4x²-8x-12=0

4(x²-2x-3)=0

4(x-3)(x+1)=0

So the solutions of the equation are x=3 and x=-1. The sum of these solutions is:

3 + (-1) = 2

Therefore, the answer is C) 2.

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16 oranges can be purchased in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                      Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

cost of 12 oranges = 45

Thus, number if oranges we will get for ₹1 = 12/45 oranges.

Thus, the number of oranges that we can buy fro ₹60 = (12/45) × 60 = 16.

Thus, 16 oranges can be purchased.

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Answer:

Step-by-step explanation:

The 8 is in the hundreds place.

Answer:

The 8 is in the hundreds place.

Step-by-step explanation:

2,000 (Thousands Place)

800 (Hundreds Place)

90 (Tens Place)

4 (Ones Place)

0.0 (Tenths Place)

2,894.0

The factored form of the polynomial  f(x) = x³ - 7x² + 9x - 63 is,

(x - 7)(x² + 9).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A polynomial f(x) = x³ - 7x² + 9x - 63.

Now, If x = 7 is an x-intercept then one root(cuts the x-axis) is 7 and one factor is (x - 7).

Now, Factoring(long division) f(x) = x³ - 7x² + 9x - 63 by (x - 7) we have,

(x³ - 7x² + 9x - 63) = (x - 7)(x² + 9).

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The restaurant location problem as a nonlinear optimization model is given below.

The restaurant location problem can be formulated as a goal programming model with the following components:

Decision variables:

x1: the x-coordinate of the restaurant location

x2: the y-coordinate of the restaurant location

Goals:

Minimize the total distance from the restaurant to the three suburbs, calculated as follows:

Distance from suburb 1: |x1 - 1| + |x2 - 2|

Distance from suburb 2: |x1 - 6| + |x2 - 18|

Distance from suburb 3: |x1 - 12| + |x2 - 8|

Maximize the accessibility of the restaurant to the three suburbs, measured as the sum of the reciprocals of the distances from the restaurant to each suburb:

Accessibility = 1 / (|x1 - 1| + |x2 - 2|) + 1 / (|x1 - 6| + |x2 - 18|) + 1 / (|x1 - 12| + |x2 - 8|)

Constraints: None

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Answer: x> -28/13

Step-by-step explanation:

1.

Simplify the expression

2. Combine multiplied terms into a single fraction

3. Distribute

4. Rearrange terms

5. Combine multiplied terms into a single fraction

6. Multiply by 1

7. Multiply all terms by the same value to eliminate fraction denominators

8. Cancel multiplied terms that are in the denominator

9. Distribute

10. Distribute

negative five-sevenths ( 21 x plus 35 ) < 1/3 ( 9-6 x )

negative 315 x minus 525 is less than negative 42 x plus 63

2

Add

525

to both sides

3

Simplify the expression

4

Add

42 x

to both sides

5

Simplify the expression x> -28/13