4x – 20 = 2(x – 1) + 8

Based on the given value of pitch (slope), the bottom number simply means the horizontal distance an object runs through.

A pitch is also referred to as slope and it can be defined as the ratio of the vertical distance (rise) measured to the horizontal distance (running) measured.

Mathematically, the pitch (slope) of a roof can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Given the following data:

Vertical distance (rise) = 2 units.

Horizontal distance (running) = 7 units.

By critically observing the given value of pitch (slope) as 2/7, we can infer and logically deduce that the bottom number simply means the horizontal distance an object runs through.

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Solving the equation (6x)(9x) using the zero product property we get the solution is x = 2.

To find the solution to the equation, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, the product of (6x) and (9x) is given as 88 square feet. So, we have the equation (6x)(9x) = 88.

To solve this equation, we can first simplify it by multiplying the terms inside the parentheses. (6x)(9x) becomes 54x^2. Now our equation is 54x^2 = 88.

To isolate x, we divide both sides of the equation by 54. This gives us x^2 = 88/54. Simplifying further, we have x^2 = 22/27.

Taking the square root of both sides of the equation, we get x=±√(22/27). However, since the length and width of the rectangular patio are increased, we are only interested in the positive value of x.

Approximating the value of √(22/27), we find that x ≈ 0.832. This value represents the amount by which both the length and width of the patio should be increased to obtain an area of 88 square feet.

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Answer:

0.80 m/s

Step-by-step explanation:

rate = 40 m / 50 s = 0.8 m/s

Answer:

Step-by-step explanation:

f(x) = (x+2)² - 2    

-f(x-4)    means multiply the whole function by -1 and substitute x for x-4

-f(x-4) = -[((x-4)+2)² - 2]          simplify the -4 and 2

         = -[(x-2)² -2]                  distribute the -

          = -(x-2)² + 2

1. the new function is now facing down, reflected across the x-axis

2.  the new vertex is (2, 2)  the old one was (-2, -2)

     -shifted 4 units right

    - shifted 4 units up

Answer:

Answer on a graph

Answer:

y = 51.32º

Step-by-step explanation:

z = 180 - 47 - 90

z = 43º

sin43 = opp/hyp

sin43 = 35/y

y = 35/sin43

y = 51.32º

Law of Cosines

Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:

We have a = 14, b = 9, θ = 71°. Substituting:

The length of CD is 13.96

Answer:

zero

Step-by-step explanation:

If you multiply a number by 0, the result is zero

Answer:

The answer is A

Anything multiplied by Zero is Zero

Answer:

3(3x + 5)

Step-by-step explanation:

9x + 15

find a common factor, 3

3(3x + 5), this is the answer as u can't factorize anymore

Answer:

Carmela made $9 per hour

270÷30=9

Hope this helps !

Answer:

answer is 69 degree

Step-by-step explanation:

a+33+78=180 degree

a+111=180

a=180-111

a=69

Answer: 9 gallons per minute

Step-by-step explanation:

36/4=9/1 9 gallons per minute

Answer:

48m^2-72mn

Step-by-step explanation:

I'm quite sure that 48m^2=72mn is the answer that you want, but if you are calculating the factors, the answer is, 24m(2m-3n).

Hope this helped! :)

The ratios of the segments of both the polygons are not same hence the polygons are not similar. Option 4 is the correct answer.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides).

To create a closed figure, a minimum of three line segments must be connected end to end. As a result, a polygon with at least three sides is known as a triangle and is also known as a 3-gon. An n-gon is a polygon with n sides.

Given that the two polygons which are parallelogram with the opposite sides 2.5 and 1.5, and 9 and 4.8.

For the polygons to be similar, ratios of both the polygons must be equal.

2.5 / 1.5 = 1.66

9 / 4.8 = 1.875

The ratios of the segments of both the polygons are not same hence the polygons are not similar. Option 4 is the correct answer.

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The formula to calculate probability is favourable outcomes/total outcomes.

a. The probability of getting two heads with the toss of two coins can be calculated using the formula for probability: Probability = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is 2 x 2 = 4 (since there are 2 possible outcomes for each coin toss, and 2 coins are being tossed). The number of favorable outcomes (getting two heads) is 1. Therefore, the probability of getting two heads is 1/4 or 0.25.

b. The probability of not getting two heads is simply the complement of getting two heads, which is 1 - 0.25 = 0.75 or 75%.

c. The expected value can be calculated by multiplying the probability of each outcome by its corresponding payoff, and then adding up these values. In this case, there are two possible outcomes: getting two heads and not getting two heads. The probability of getting two heads is 0.25, and the payoff is $2. The probability of not getting two heads is 0.75, and the payoff is -$1 (since you lose $1 if you fail). Therefore, the expected value is:

Expected value = (0.25 x $2) + (0.75 x -$1) = $0.25 - $0.75 = -$0.50

This means that on average, you can expect to lose $0.50 for every coin toss.

d. To calculate how much you can expect to lose if you toss the coin 100 times or 500 times, you simply need to multiply the expected value by the number of coin tosses.

For 100 tosses: Expected loss = -$0.50 x 100 = -$50
For 500 tosses: Expected loss = -$0.50 x 500 = -$250

Therefore, if you were to play this game 100 or 500 times, you can expect to lose an average of $50 or $250, respectively.

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Answer:

Electrons are atoms that are magnetic.

Step-by-step explanation:

Answer:

Electrons are atoms that are magnetic

Question 1 : Janae can find out when she first hit the water by finding out the distance of travel, as well as her speed of travel

Question 2 :

Given that her height above the water can be modeled using the function below:

We can obtain her vertical distance of travel from the diving board to the point where she starts to descend

At the turning point,

Hence, Jane travelled a distance of 10 units upwards and (10 + 15)unit downwards

At the turning point, her velocity is zero, using the relation below we can find her initial velocity and then the time it took

From the turning point, her velocity changes from 0

Answer:

Step-by-step explanation:

The desired formula parameters for Newton's Law of Cooling can be found from the given data. Then the completed formula can be used to find the temperature at the specified time.

__

  \(T(t)=T_a+(T_0-T_a)e^{-kt}\\\\T_a=68,\ T_0=208,\ (t,T)=(3,185)\)

  k

  T(4)

Filling in the given numbers, we have ...

  185 = 68 +(208 -68)e^(-k·3)

  117/140 = e^(-3k) . . . . . subtract 68, divide by 140

  ln(117/140) = -3k . . . . . . take natural logarithms

  k = ln(117/140)/-3 ≈ 0.060

__

The temperature after 4 minutes is about ...

  T(4) = 68 +140e^(-0.060·4) ≈ 68 +140·0.787186

  T(4) ≈ 178.205

After 4 minutes, the final temperature is about 178 °F.

Answer:

5

Step-by-step explanation:

4(5+n)=4(n+p)

20+4n=4n+4p

4p=20

p=20/4

p=5

Answer:

the value of p is 5

Step-by-step explanation:

the expression 4(5 + n) is equivalent to 4(n + p)

4(5+n)=4(n+p)

5+n=n+p

n+5=n+p

comparing each other

we get p=5

\(\\ \sf\longmapsto sin44=\dfrac{x}{48}\)

\(\\ \sf\longmapsto 0.69=\dfrac{x}{48}\)

\(\\ \sf\longmapsto x=48(0.69)\)

\(\\ \sf\longmapsto x=33.12\)

_________

\( \: \)

Sin (44°) = x/48

0.69 = x/48

x = 48 × 0.69

x ≈ 33.12

By solving a system of equations and a quadratic equation, we will see that x = 2.

We know that x and y are positive integers, that x < y and:

x*y = 56

We also know that "seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4"

Then we can write the equation:

7*(1/x) + 14*(1/y) = 4

So we have a system of equations:

x*y = 56

7*(1/x) + 14*(1/y) = 4

We can rewrite the first equation to get:

x = 56/y

And the second equation as:

14/y = 4 - 7/x

Then the system becomes:

56/y = x

14/y = (4 - 7/x)

Taking the quotient between these, we can remove the variable y:

(56/y)/(14/y) = x/(4 - 7/x)

56/14 = x/(4 - 7/x)

4*(4 - 7/x) = x

4*(4x - 7)/x = x

4*(4x - 7) = x^2

So now we have a quadratic equation:

x^2 - 16x + 28 = 0

Using the quadratic formula, we will get:

\(x = \frac{16 \pm \sqrt{(-16)^2 -4*1*28} }{2*1} \\\\x = \frac{16 \pm 12 }{2}\)

So the solutions are:

x = (16 - 12)/2 = 2

x = (16 + 12)/2 = 14

But notice that if x = 14, then:

14 = 56/y

y = 56/14

y = 4

And y is larger than x, then x = 14 can be discarded.

The solution is x = 2.

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Answer:

Step-by-step explanation:

4

The three-period moving average forecast for period 6 is 5215, rounded to the nearest whole number. This is calculated by averaging the last three periods of actual sales data, which are 5035, 4886, and 5724.

The three-period moving average forecast is a simple forecasting method that takes the average of the last three periods of actual sales data. This is a relatively easy method to calculate, and it can be a good starting point for forecasting future sales.

In this case, the three-period moving average forecast for period 6 is 5215. This is calculated by averaging the last three periods of actual sales data, which are 5035, 4886, and 5724. To calculate the average, we simply add these three numbers together and then divide by 3. This gives us a forecast of 5215.

It is important to note that this is just a forecast, and the actual sales for period 6 may be different. However, the three-period moving average forecast is a good starting point for estimating future sales.

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So,

Based in the information, we could draw:

Let "x" be the length of the longer leg.

We could find the dimentions of the triangle using the Pythagorean theorem:

As you can see, we could solve this quadratic equation factoring:

Note that the solution x=0 has not any sense in the context of the problem.

Therefore, the appropiate value of x is 28.

Now, we have found that the length of the longer leg is 28cm.

The shorter leg of the right triangle is 7 cm shorter than the longer leg, so its value is 21cm.

The hypotenuse is 7 cm longer than the longer leg, so, the value of the measure of the hypotenuse is 35cm.

Answer:

week number: 11 if you do count the first time they got the money or week number 10 if you don't count the first time they got the money

Step-by-step explanation:

First time they got money: Julie: 41,200 Kelsey: $400

week 1: Julie : $1,180  Kelsey: $440

week 2: Julie: $1,140  Kelsey: $480

week 3: Julie: $1,100  Kelsey: $520

week 4: Julie: $1,060  Kelsey: $560

week 5: Julie: $1,020  Kelsey: $600

week 6: Julie: $980    Kelsey: $640

week 7: Julie: $940    Kelsey: $680

week 8: Julie: $900    Kelsey: $720

week 9: Julie: $860    Kelsey: $780

week 10: Julie: $820   Kelsey: $820

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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The value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

Given data

A soft- drink machine can be regulated so that it discharges an normal of? oz. per mug. The ounces of filler are typically distributed with a standard divagation of0.4 oz.

What value should be set at so that 98 of 6- oz. mugs won't overflow?

Let μ be the mean ounces of filler per mug.

μ can be attained by using the formula

μ = 6 oz. = 6/8 = 0.75 mugs.

Now, given σ = 0.4 oz.

The Z- score for a 6- oz mug can be calculated as follows

z = ( x- μ)/ σ

Then, x = 6 oz = 6/8 = 0.75 mugs.

μ = 0.75 mugs

σ = 0.4 oz.

z = (0.75-0.75)/0.4 = 0

For 98 of 6- oz mugs to not overflow, we need to find the value of μ similar that P( z Since the Normal distribution is symmetric about the mean, we have

P( 0< z We can look up the value of

z_score for P( 0< z

standard normal distribution table or use the inverse function on a calculator similar as Excel.

Using a table, we get the value ofz_score = 2.33.

Now, z = ( x- μ)/ σ2.33 = (0.75- μ)/0.4

μ = 0.75-0.4 ×2.33

μ = 0.75-0.932

μ = -0.182 oz.6 oz in terms of ounces = 6 *0.125 = 0.75 oz.

oz per mug in terms of ounces = ? *0.125 oz.

Using the values from above

μ = -0.1820.75 = 0.568 oz. ≈0.57 oz.

= 0.57/0.125 = 4.56 or 5

So, the value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

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If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.

To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).

The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:

C = πr = π(10) = 31.4 inches.

The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:

P = 3s = 3(20) = 60 inches

Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:

Perimeter = C + P = 31.4 + 60 = 91.4 inches.

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Complete Question

This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.

You can use 3.14 as an approximation for π. help i don't know it.

\(a(n) = 3 + 5n\)

\(b(n) = - 2 + 6n\)

\(a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)\)

\(a(5) \: or \: b(5) = 3 + 5(5) = 28\)

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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