Given the equations of the lines 2x – y = 4 and 3x + 2y = -1. Do these lines intersect? If
they do, find the point of intersection.

Answer: a c e are the correct ones i think

Answer:

1⁸,2⁴,5²,3³

Step-by-step explanation:

so its 1,16,25,27

An equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is \(7x > -22.\)

To find an equivalent inequality, we can start by simplifying the given inequality and then make adjustments to preserve its truth.

Let's simplify the given inequality step by step:

\(-4(x + 7) < 3(x - 2)\)

Expanding both sides:

\(-4x - 28 < 3x - 6\)

Grouping like terms:

\(-4x - 3x < -6 + 28\)

Simplifying:

\(-7x < 22\)

To maintain the direction of the inequality, we need to multiply both sides by -1.

However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.

Therefore, we need to flip the inequality sign:

\(7x > -22\)

Hence, an equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is

\(7x > -22.\)

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Answer:

38 units

Step-by-step explanation:

We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.

Thus, see attachment below for the number of units of each length of the figure that we have counted.

The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38

Perimeter of the shaded figure = 38 units

Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

------------

Extra info:

Answer:

325m = c

Step-by-step explanation:

Each meeting room has 325 chairs.

Since we don't know how many meeting rooms there are, the number is replaced with the variable, m.

An equation is a problem with an equals sign so you need to put what it would equal.

Since you don't know how many meeting rooms there are you use the variable, c which represents the total number of chairs.

The population of US is 330 million approx.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.

Given

population of new york = 2.727272% population of US

population of new york = 9 million

population of US = 1/2.727272% of new york

population of US =  36.6666 x 90,00,000

population of US = 33,00,00,087.9 = 330 million approx

Hence population of US is approx 330 million.

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Answer:

1. 7

2. 3

3. 7

4. 3

5. 7/3

Step-by-step explanation:

Answer:

1. 7

2. 3

3. 7

4. 3

5. 7/3

Step-by-step explanation: Hope this helped

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.

Fixed costs: $34,000

Variable costs per widget: $5.00

Total costs = Fixed costs + (Variable costs per widget × Number of widgets)

Total costs = $34,000 + ($5.00 × 7,000)

Total costs = $34,000 + $35,000

Total costs = $69,000

Average cost per widget = Total costs / Number of widgets

Average cost per widget = $69,000 / 7,000

Average cost per widget ≈ $9.86

Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.

Step-by-step explanation: :)

Answer:

The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.

Step-by-step explanation:

Let's assume the speed of the passenger train is represented by x mph.

According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.

Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.

Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.

Since speed = distance/time, we can set up the following equation based on the distances covered by each train:

Distance covered by passenger train = Distance covered by freight train

Using the formula, distance = speed × time, we get:

x × 3 = (x - 18) × 5

Simplifying the equation:

3x = 5x - 90

90 = 5x - 3x

90 = 2x

Dividing both sides by 2:

45 = x

So, the speed of the passenger train is 45 mph.

The speed of the freight train is 45 - 18 = 27 mph.

Answer:

C

Step-by-step explanation:

This is the answer because you have to use the formula of volume

which is L x W x H then you get your answer

Let a be the first term in the sequence, and d the common difference between consecutive terms. If aₙ denotes the n-th term in the sequence, then

a₁ = a

a₂ = a₁ + d = a + d

a₃ = a₂ + d = a + 2d

a₄ = a₃ + d = a + 3d

and so on, up to the n-th term

aₙ = a + (n - 1) d

The sum of the first 10 terms is 100, and so

\(\displaystyle \sum_{n=1}^{10} a_n = 100 \\ \sum_{n=1}^{10} (a + (n-1)d) = 100 \\ (a-d) \sum_{n=1}^{10} 1 + d \sum_{n=1}^{10} n = 100 \\ 10a+45d = 100\)

where we use the well-known sum formulas,

\(\displaystyle \sum_{n=1}^N 1 = 1 + 1 + 1 + \cdots + 1 = N\)

\(\displaystyle \sum_{n=1}^N n = 1 + 2 + 3 + \cdots + N = \frac{N(N+1)}2\)

The sum of the next 10 terms is 300, so

\(\displaystyle \sum_{n=11}^{20} a_n = 300 \\ (a-d) \sum_{n=11}^{20} 1 + d \sum_{n=11}^{20} n = 300 \\ (a-d) \left(\sum_{n=1}^{20} 1 - \sum_{n=1}^{10} 1\right) 1 + d \left(\sum_{n=1}^{20} n - \sum_{n=1}^{10} n\right) = 300 \\ 10a+145d = 300\)

Solve for a and d. Eliminating a gives

(10a + 145d) - (10a + 45d) = 300 - 100

100d = 200

d = 2

and solving for a gives

10a + 145×2 = 300

10a = 10

a = 1

So, the given sequence is simply the sequence of positive odd integers,

{1, 3, 5, 7, 9, …}

given recursively by the relation

\(\begin{cases}a_1 = 1 \\ a_n = a_{n-1} + 2 & \text{for }n>1\end{cases}\)

and explicitly by

\(a_n = 1 + 2(n-1) = 2n - 1\)

for n ≥ 1.

Answer:

f(3) = 3 + 1 = 4

Step-by-step explanation:

Since 3 > 0, we need to focus on the part of the function where x > 0. So:

f(3) = 3 + 1 = 4.

Answer:

f = 4/3

f = 1.3

f = 1 1/3

Step-by-step explanation:

Move all terms that don't contain f to the right side and solve.

Answer:

y=70 degrees

Step-by-step explanation:

If 2 angles are complimentary, they add up to 90 degrees.

x+y=90 degrees

x=20 degrees

y=90-20 degrees

y=70 degrees

If that is wrong, try this. Let's say the questions gives us the fact that x is 20 degrees greater than y.

y=x

Substituting x for y, the equation is x+x+20=90

Since y is x, x would also be y, which is 35. then x+20 would be 55.

So y would be 35.

THE ANSWER WOULD BE 70 DEGREES, BUT IF THAT IS WRONG, DO THE SECOND ONE, WHICH IS 35

The graph of y =g(x)-6 is a graph that shows a line cutting across -6 on the y axis.

The graph of the y =g(x)-6

to solve this, first of all rewrite this as a function

y = x - 6

The y intercept is given as 0 and - 6

you would graph the line using the intercept and the slopes of the points

slope = 1

y intercept is given as (0 , -6)

x (0 , 1 )

y (-6 , -5)

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The probability of getting at least 7 questions correct on this test is 0.08665%.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

The probability of getting an answer right is 1/5, while the probability of getting it wrong is 4/5. Therefore, the probability of getting at least 7 questions correct on this test is,

P(X≥7) = P(X=7) + P(X = 8) + P(X=9) + P(X = 10)

= ¹⁰C₇ (1/5)⁷ (4/5)³ + ¹⁰C₈ (1/5)⁸ (4/5)² + ¹⁰C₉ (1/5)⁹ (4/5)¹ + ¹⁰C₁₀(1/5)¹⁰(4/5)⁰

= 0.0007886 + 0.000073728+ 0.000004096 + 0.0000001024

= 0.0008665264

= 0.08665%

Hence, the probability of getting at least 7 questions correct on this test is 0.08665%.

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Answer:

a + c = 30

8a + c = 100

a=10, c= 20

Step-by-step explanation:

cost = 8a + 1c  since it is 8 dollars for adult and 1 for child where a is the number of adults and c is the number of children

a+c = 30  since we know that 30 adults and children went

100 = 8a + 1c   and it cost 100 dollars

Let c =30 -a

100 = 8a + (30-a)

100 = 7a +30

Subtract 30 from each side

70 = 7a

Divide by 7

10 =a

Then a+c = 30

10+c = 30

c = 30-10

c = 20

Answer:

eqn1 : a +c=30

eqn2: 8a+c=100

20 children and 10 adults

a. C = 5.00 + 0.75t

b. It will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we can use the following equation:

C = 5.00 + 0.75t

In this equation, the constant term 5.00 represents the flat fee for parking, and the term 0.75t represents the additional cost per hour based on the number of hours (t) the car is parked. By adding the flat fee to the hourly cost, we get the total parking cost for t hours.

(b) To find out how much it will cost Elaine to park her car for a full 24 hours, we can substitute t = 24 into the equation:

C = 5.00 + 0.75 * 24

Calculating this expression, we get:

C = 5.00 + 18.00

C = 23.00

Therefore, it will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

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Percentages can be expressed as decimals. Percentage of something can be found by multiplying the number by the decimal.

20% = 0.20

20%(18.5)
0.20(18.5)
3.7

Since this is a 20% increase, we will add this to the original value.

18.5 + 3.7 = 22.2

Step-by-step explanation:

Find slope

m = (y2 - y1)/(x2 - x1)

m = (-9 - 5)/(4 - 8)

m = -14/-4

m = 7/2

Slope → 7/2

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

The total cost of chocolate sprinkles is $800

This is an implementation of the numeral system that shows the value of each digit in a number using their positions

From the complete question, we have the following parameters:

So, the total cost of chocolate sprinkles is calculated using the following formula

\(Unit = \frac{Total}{Pounds}\)

This gives

\(\$8.00= \frac{Total}{100}\)

Multiply both sides of the equations by 100

\(Total = \$8.00 \times 100\)

\(Total = \$800\)

Hence, the total cost of chocolate sprinkles is $800

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Answer:

32.5 is greater than 30.8

Answer: greater than

Step-by-step explanation:

32.5 is greater than 30.8

32.5-30.8=1.7

The difference is positive, which means 32.5 is greater than 30.8

EXTRA: 32.5 is 1.7 more than 30.8

Hope this helps!! :)

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