Find HCF and LCM

100
60

Answer:

1. 3x + 2y = -4

2. y = 1/2x + 3

3. y = 3/14x - 3/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Tim shirts cost = 3*45

Craig shirts cost = 5*45

Total cost = 135+225

                  =360

Answer:

a = - 3

Step-by-step explanation:

Since the point (- 3, 2) is on the line then its coordinates make the equation true.

Substitute x = - 3, y = 2 into the equation and solve for a

a(- 3) - 2(2) = 5, that is

- 3a - 4 = 5 ( add 4 to both sides )

- 3a = 9 ( divide both sides by - 3 )

a = - 3

Answer:

Step-by-step explanation:

-3x-2•2=5

-3x=5+4

-3x=9

X=9:(-3)

X=-3

The Height of the frame having area of 560cm² is 50cm.

By splitting a rectangle into two equal-sized right triangles, the formula for calculating the area of a rectangle may be obtained. For instance, a diagonal is drawn from vertex A to vertex C in the rectangle ABCD that is supplied.

The rectangle is split into two identical right-angled triangles by the diagonal AC.

(ABCD) Area = b × h

Given,

The area of the frame = 560cm²

Width of the frame = 11 1/5

Length = ?

Area of the rectangle = Length × Breadth

560 = 11 1/5 × L

⇒ L = 560 × 5/56

⇒ L = 50cm

The frame is 50cm tall.

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Correct question -

Claire is making a frame to display a drawing she made. The frame is 11 1/5 cm wide. The frame has a rectangular shape and an area of 560cm². How tall is the frame?

a. The future value after 7 years is approximately $139,485.49.

b. The amount found with continuous compounding yields approximately $18,075.04 more than the amount found with annual compounding.

a. To find the future value of $90,000 invested at 8% compounded annually for 7 years, we can use the formula for compound interest:

Future Value = Principal * (1 + Rate/100)^Time

Future Value = $90,000 * (1 + 8/100)^7

Future Value ≈ $139,485.49

Therefore, the future value after 7 years is approximately $139,485.49.

b. In part (b), it is stated that the future value of $90,000 invested at 8% interest, compounded continuously, is $157,560.53.

To compare the result from part (a) to part (b), we calculate the difference:

Difference = Future Value (Continuous Compounding) - Future Value (Annual Compounding)

Difference = $157,560.53 - $139,485.49

Difference ≈ $18,075.04

Therefore, the amount found with continuous compounding yields approximately $18,075.04 more than the amount found with annual compounding.

The result from part (b) shows that continuous compounding generates a higher future value compared to annual compounding. The difference between the two approaches is approximately $18,075.04.

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Answer:

x =  9(a+g)

Step-by-step explanation:

x/9 - g = a

Add g to each side

x/9 - g+g = a+g

x/9 = a+g

Multiply each side by 9

x/9 * 9 = 9(a+g)

x =  9(a+g)

An equation of the parabola with the given focus and directrix is (x - 4)² = -16(y - 1).

Given that, focus of a parabola at (-4,3) and a directrix at y = 5.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where

The vertex of the parabola is (h, k)

The focus is (h, k + p)

The directrix is at y = k - p  

Here, the focus of the parabola is (4, -3)

The focus is (h, k + p)

So, h = 4

Then, k + p = -3 --------(1)

It has a directrix of y = 5

The directrix of the parabola is y = k - p

∴ k - p = 5 --------(2)

Add equations (1) and (2) to find k and p, that is

(k + k) + (p - p) = (-3 + 5)

⇒ 2k + 0 = 2

⇒ 2k = 2

Divide both sides by 2

k = 1

Substitute the value of k in equation (1), we get

1 + p = -3

Subtract 1 from both sides, we get

1 - 1 + p = -3 - 1

⇒ p = -4

Substitute the values of h=4, k=1 and p=-4 in (x - h)² = 4p(y - k), that is

(x - 4)² = 4(-4)(y - 1)

⇒ (x - 4)² = -16(y - 1)

Therefore, an equation of the parabola with the given focus and directrix is (x - 4)² = -16(y - 1).

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Answer:

x = 145°

Step-by-step explanation:

x and 35° are a linear pair and sum to 180° , that is

x + 35° = 180° (subtract 35° from both sides )

x = 145°

Answer:

y = -11

Step-by-step explanation:

Equation formula: y = mx + b

y = y-point

mx = slope

b = y-int

The equation has no slope since it's a straight line so the equation is y = -11

y = 0 + (-11)

y = -11

The equation of a line can be written in both slope-intercept form and standard form.

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Weight represents the top 10% of the zucchinis is 5.9

The formula for calculating a z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We're looking for:

Weight is 10% of zucchinis at the top.

Top 10% = 90% of the population

90th percentile Z score is 1.282.

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

5.9 ounces, roughly.

The top 10% of the zucchinis have a weight of 5.9 ounces.

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Perimeter = 2 (l + b)

2x² + 4x - 4y = 2 {(2x - 3y) + b}

2x² + 4x - 4y = (4x - 6y) + 2b

2x² + 4x - 4y - (4x - 6y) = 2b

2x² + 4x - 4y - 4x + 6y = 2b

2x² + 2y = 2b

(2x² + 2y)/2 = b

x² + y = b

Breadth = x² + y

Answer:

6 to 48

Step-by-step explanation:

i just did that question in a test

Answer:

DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-step explanation:

To divide decimals, use a standard division formula. First, write the decimal number as a fraction. Then, divide the numerator by the denominator. The result will be the decimal number.

To illustrate, let's divide 0.8 by 0.2. First, convert the two decimal numbers into fractions. 0.8 is equal to 8/10, and 0.2 is equal to 2/10. Now, we can divide 8/10 by 2/10. We can do this by dividing the numerators, 8 and 2, and then dividing the denominators, 10 and 10.

8/10 divided by 2/10 is equal to 4/5. To express this as a decimal, divide 4 by 5. The result is 0.8.

We can also use a graphical method to divide decimals. To do this, draw a number line, label each tick mark with a tenth, and use a ruler to draw a line from the first decimal to the second. Count the number of tenths between the two points to find the answer.

For example, let's divide 0.7 by 0.3 on a number line. Draw the number line and mark the two points at 0.7 and 0.3. Count the number of tenths between the two points. There are four tenths, so the answer is 0.4.

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The average gradient of the stream is 0.3 meters/kilometer (m/km).

To calculate this, we need to determine the change in elevation over the distance of 200 kilometers. Therefore, the difference in elevation is 600 meters (the starting elevation) minus the elevation at the ocean (assumed to be 0 meters). Dividing this difference (600 meters) by the distance (200 kilometers) gives us the average gradient: 0.3 m/km.

It is important to remember that this is only an average, and the gradient of a stream is not constant throughout its course. Factors such as terrain, obstacles, and rainfall will all affect the gradient of the stream, making it higher or lower at certain points. It is also important to note that a negative gradient means the elevation of the stream is decreasing, while a positive gradient indicates that the elevation is increasing.

In conclusion, the average gradient of the stream beginning at 600 meters and flowing 200 kilometers to the ocean is 0.3 m/km.

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Answer: 8 mi

Step-by-step explanation: 2*1*4=8

Answer:

\(4 {q}^{3} \times 9 {q}^{4} \)

\(36 {q}^{7} \)

Answer:

Step-by-step explanation:

4*q^3*9*q^4

4*9*q^4+3

36q^7

in multiplication if the base are same we add their power.

The vector -601 - 902 can be represented as (-603, -1503) in component form.

The vector -601 - 902 can be found by subtracting the components of 601 and 902 from the corresponding components of the vectors ₁ and 72. In component form, the result is -601 - 902 = (1 - 6) - (-2 + 9) = (-5) - (7) = -5 - 7 = (-12).

To find -601 - 902, we subtract the x-components and the y-components separately.

For the x-component: -601 - 902 = -601 - 902 = -603

For the y-component: -601 - 902 = -601 - 902 = -1503

Therefore, the vector -601 - 902 in component form is (-603, -1503).

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Answer:

im a current alcoholic

Step-by-step explanation:

ion een no

Answer:

10 to 1

Step-by-step explanation:

create a table of x-y values:

when x = 1, y = 10

when x = 2, y = 20

etc.

Answer:

1:10

Step-by-step explanation:

The sample space of the experiment of rolling three fair coins consists of all possible outcomes when three coins are tossed simultaneously. Therefore, there are 2 x 2 x 2 = 8 possible outcomes in the sample space.

In this experiment, we are rolling three fair coins. To find the number of elementary events in the sample space, we need to consider all possible outcomes.

An elementary event is an individual outcome in the sample space. The sample space is the set of all possible outcomes for an experiment. In this case, each coin can have 2 possible outcomes: heads (H) or tails (T).
Each outcome in the sample space is an elementary event, which is an outcome that cannot be further broken down into simpler outcomes. Therefore, there are 8 elementary events in the sample space of this experiment.

Since there are three coins, we can determine the number of elementary events in the sample space by multiplying the number of outcomes for each coin: 2 (for the first coin) x 2 (for the second coin) x 2 (for the third coin) = 8.

So, there are 8 elementary events in the sample space of this experiment. The correct answer is c. 8.

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An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.

These steps are used to determine the Z score:

z = (x - μ)/σ

As mentioned in question-

x > 550 and μ = 500, σ = 40:

z = 550 - 500 / 40

z = 1.25

Obtain the p-value from normal distribution chart,

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.

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Answer:

24

Step-by-step explanation:

the answer is 24 because the 3 and 12 u divide

Answer: the answer is choice c which is 24 .

Step-by-step explanation: HOPE IT IS CORRECT .THANKS .

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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Answer:

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Step-by-step explanation:

Answer:310.45

Step-by-step explanation:

The interval notation for all real numbers between and including -1 and 8 is [-1, 8].

In interval notation, we use brackets to indicate whether the endpoints are included or excluded from the interval. The square brackets [ ] denote that the endpoints are included in the interval. In this case, we want to include both -1 and 8, so we use square brackets for both.

The interval is written in the form [a, b], where a represents the lower bound or starting point, and b represents the upper bound or ending point of the interval. In this case, the lower bound is -1 and the upper bound is 8. The comma separates the lower and upper bounds. It indicates that the numbers between -1 and 8, as well as -1 and 8 themselves, are included in the interval.

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Transmittivity = I_transmitted / (I_reflected + I_transmitted) & Reflectivity = I_reflected / (I_reflected + I_transmitted)

Hi! To derive the expressions for intensity transmittivity and reflectivity given in equations (10.29) and (10.30), respectively, follow these steps:

1. Define the terms:
  - Transmittivity (T): The fraction of incident light transmitted through a medium.
  - Reflectivity (R): The fraction of incident light reflected by a medium.
  - Intensity (I): The power per unit area of light.

2. Consider a light wave incident on a medium with intensities I_incident, I_reflected, and I_transmitted.

3. Based on the conservation of energy, the sum of the reflected and transmitted intensities should equal the incident intensity:
  I_incident = I_reflected + I_transmitted

4. Define the transmittivity and reflectivity expressions:
  - Transmittivity (T) = I_transmitted / I_incident
  - Reflectivity (R) = I_reflected / I_incident

5. Substitute the intensity values into the expressions from step 4:
  - T = I_transmitted / (I_reflected + I_transmitted)
  - R = I_reflected / (I_reflected + I_transmitted)

6. Rearrange the equations to isolate I_reflected and I_transmitted:
  - I_transmitted = T * (I_reflected + I_transmitted)
  - I_reflected = R * (I_reflected + I_transmitted)

These are the expressions for intensity transmittivity (Equation 10.29) and reflectivity (Equation 10.30) based on the given information. Note that these expressions may vary depending on the specific context or system being analyzed.

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Answer:

D

Step-by-step explanation:

Typical price is the average of highest and lowest

The best representation of the typical price of a home in this town is the median price, which is $132,500.

The best representation of the typical price of a home in the town can be determined using different measures of central tendency.

1. Mode: The mode represents the most frequent value in a dataset. In this case, none of the prices appear more than once, so there is no mode.

2. Median: The median is the middle value when the data is arranged in ascending or descending order.

To find the median, we arrange the prices in ascending order: $125,500, $130,000, $132,500, $135,000, and $350,000.

The middle value is $132,500, which is the median price.

3. Mean: In this case, the mean price is calculated as follows: ($125,500 + $130,000 + $132,500 + $135,000 + $350,000) / 5 = $174,800.

4. Average of the lowest and highest prices: To find the average of the lowest and highest prices, we add the lowest price ($125,500) and the highest price ($350,000) and divide by 2.

The average is ($125,500 + $350,000) / 2 = $237,750.

Therefore, the best representation of the typical price of a home in this town is the median price, which is $132,500. This value represents the middle price when all the prices are arranged in order.

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Answer:

248 mph (miles per hour)

Step-by-step explanation:

744 miles (in 3 hours) ÷ 3 hours = 248 mph (miles per hour)

Check if answer is correct:

248 mph × 3 hours = 744 miles in 3 hours

Final answer:

248 mph

Hopefully this helps! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee