Find the distance between the points (-7,6) and (3,0)

\(\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}\)

Answer:

d

Step-by-step explanation:

This is point-slope form, and these coordinates make both sides equal to 0.

The average total cost of producing 5 shirts by the firm is $35.

We can use the following formula to calculate the average total cost (ATC) of producing 5 shirts:

ATC = Total Cost / Quantity

We know that the firm produces 6 shirts at a total cost of $187, so the total cost of producing 5 shirts can be estimated by subtracting the marginal cost of the last shirt from the total cost of producing 6 shirts:

Total Cost of producing 5 shirts = Total Cost of producing 6 shirts - Marginal Cost of the last shirt

                                 = $187 - $12

                                 = $175

Now we can use the formula to find the average total cost of producing 5 shirts:

ATC = Total Cost / Quantity

   = $175 / 5

   = $35

Therefore, the average total cost of producing 5 shirts by the firm is $35.

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Answer:

$7,440.

Step-by-step explanation:

$0-$11,000 = no tax.

$11,000-$43,000 = 20%.

$43,000-$150,000 = 40%.

The earnings over $150,000 = 45%.  etc....

$45,600, = Revenue

Tax is 11000-43000  is = 0.20 * (32000)

= 11000-43000 = 6400

Tax  is 43000-45,600 is  = 0.40 *(2600)

=  45,600-43000 = 1040

=6400+1040 =7440

Answer:

f(x) + g(x) = 7x² - 4x + 2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 5x² - 3x - 1

g(x) = 2x² - x + 3

Step 2: Find f(x) + g(x)

Answer:

e(x)

Step-by-step explanation:

i think this is the answer

Answer:

The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:

standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7

To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:

z = (37.4 - 40) / (8 / 7) = -1.225

Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.

give thanks, your welcome <3

Step-by-step explanation:

Answer:

The cost per hour for renting the boat is $18 per hour.

A function is said to be linear if it is a straight line graph and it can be represented by the equation:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the total cost for renting the boat for x hours.

Given the equation:

y = 18x

Therefore the cost per hour for renting the boat is $18 per hour.

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40 + 30 + 18

= 70 + 18

= 88

Answer:

88

Step-by-step explanation:

40+30+18=70+18=88

Order the numbers smallest to largest and go to the middle, the middle number is your answer :)

Step-by-step explanation:

51 ,54 , 60 ,66 ,68 ,70 ,75 ,80

The answer is 67.

Hope this answer will help you.

Answer:

(i) \(80-x\)

(ii) \(S(x) = 40 - 0.10x\)

(iii) $36.5

Step-by-step explanation:

Given that:

1. Total Number of fruits = 80

2. Number of mangoes = x

3. Both mangoes and oranges are there in the basket.

Solution (i):

Only mangoes and oranges are there in the basket and the basket is full.

so, Number of mangoes + Number of oranges = Total number of fruits

x + Number of oranges = 80

Number of oranges = \(80 -x\)

Solution (ii):

Given:

Cost of an orange = 50 cents = $0.50

Cost of a mango = 40 cents = $0.40

Cost for x mangoes = \(\$ 0.40x\)

Cost for (\(80-x\)) oranges = \(\$ 0.50 \times (80-x)\)

\(\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x\)

Solution (iii):

Put value of x = 35 in S(x)

\(S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5\)

Hence, answers are:

(i) \(80-x\)

(ii) \(S(x) = 40 - 0.10x\)

(iii) $36.5

Answer:

I think that the answer may be volume = 169.65

Step-by-step explanation:

The volume of cylinder whose radius 3m and height 6m is 169.56 cm³ ≈ 170 cm³

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, π\(r^2h\), where r is the radius of the circular base and h is the height of the cylinder.

Here, Radius of Cylinder = 3 m.

         Height of Cylinder = 6 m.

Volume of Cylinder = πr²h

                                 = 3.14 X 3 X 3 X 6

                                 = 169.56 cm³

                                 ≈ 170 cm³

Thus, the volume of cylinder whose radius 3m and height 6m is 169.56 cm³ ≈ 170 cm³.

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Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

When the domain is substituted, the Range of the function will be

7 ≤ y < ∞

The range of a function is the the spread of minimum value of the function to maximum value. We can find the range by substituting different domains into the function.

Given a function  f(x) = |x| + 7

This |x| show that it is a modulus. That is, the domain will always be positive numerals.

The minimum domain = 0, so the minimum f(x) = 0 + 7 = 7

The maximum domain = ∞, so the maximum f(x) = ∞ + 7 = ∞

y = f(x)

Therefore, the range of of the function f(x) = |x| + 7 will be 7 ≤ y < ∞

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer:

Angle BPQ = 64°

Step-by-step explanation:

4x + 12 +2x = 90

6x + 12 = 90

     - 12    -12

6x = 78

x = 13°

BPQ = ((4(13) + 12)°

           (52 + 12)°

            64°

Answer:

A positive real number is 4 less than another.

So, the other number is a - 4

When 8 times the larger is added to the square of the smaller, the result is 96.

As a is positive, there is only one solution which is.

=4\square root of (5)

If a different positive real number is 4 smaller than the first. The number 96 is obtained by adding 8 times the bigger to the square of the smaller. The lower number is 4·(√5 - 1), whereas the larger number is 4·√5.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

Suppose x represent the large number, the smaller number is obtained s,

= x - 4

From the given condition when 8 times the larger is added to the square of the smaller, the result is 96.

=8 × x + (x - 4)² = 96

=8x + x² - 8x + 16 = 96

=8x - 8x + x² + 16 = 96

=x² + 16 = 96

⇒x² = 96 - 16 = 80

⇒x = ±√(80)

⇒x= ±4·√5

Thus, if a different positive real number is 4 smaller than the first. The number 96 is obtained by adding 8 times the bigger to the square of the smaller. The lower number is 4·(√5 - 1), whereas the larger number is 4·√5.

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Answer: 52 ounces

multiply the mass value by 16

Answer:

A) (3.5, 0.5)

Step-by-step explanation:

The small horizontal line represents that that digit is repeated to the right of the decimal point ad infinitum. Example would be the decimal equivalent of 1/9 = 0.11111111111... or 0.1 overbar

so 3.6 overbar  would be 3.6666666... or 3⅔

and 4.3 overbar would be 4.3333333... or 4⅓

With AB being 3 times longer than BC, the total distance from A to C is 4 units and AB is 3/4 of that distance.

The x value changes -2 units from 5 to 3.

The x value of B is -2(3/4) = - 1.5 from 5 or 3.5

The y value changes -6 units from A to C

The y value of B is -6(3/4) = -4.5  from 5 or 0.5

B = (3.5, 0.5)

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Answer:

0.75

Step-by-step explanation:

o = atan ( 7/8 ) = 41.18

cos ( 41.18 ) = 0.75

Answer:

Step-by-step explanation:

Hh

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer: 28.1x−3.1

Step-by-step explanation: 1.5(x+3)+3.8(7x−2)

=(1.5)(x)+(1.5)(3)+(3.8)(7x)+(3.8)(−2)

=1.5x+4.5+26.6x+−7.6

=(1.5x+26.6x)+(4.5+−7.6)

=28.1x+−3.1

=28.1x−3.1

Answer:

9x - 6

Step-by-step explanation:

9 times a number, x, is written as 9x

“6 less than” means to subtract 6 from something else.

Answer:

Step-by-step explanation:

9x-6

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Given the question image, we can infer the Alternate interior angles conjecture below using a paragraph proof.

Paragraph proof: The Alternate Interior Angle Conjecture states: "If two parallel lines are intersected by a transversal, then alternate interior angles are congruent."

Answer:

C. 3.33 moles

Step-by-step explanation:

Ammonia decomposes

\(2NH_3\rightarrow N_2+3H_2\)

We have to find the moles of hydrogen formed in 2.22 moles of ammonia.

From the reaction

2 moles of ammonia gives 3 moles of hydrogen

1 mole of ammonia  produce hydrogen=3/2 moles

2.22 moles of ammonia produces hydrogen=\(\frac{3}{2}\times 2.22\) moles

Number of moles of hydrogen formed by decomposition of 2.22 moles of ammonia

=\(\frac{6.66}{2}=3.33\)moles

Hence, 3.33 moles of hydrogen are formed in 2.22 moles of ammonia.

Option C is true.

C. 3.33 moles

The appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

The given data set is:

2, 10, 10, 12, 12, 20

To determine the appropriate measure of variability, we need to consider the spread or dispersion of the data. In this case, we can see that the range,

20 - 2 = 18.

A better measure of variability for this data set is the interquartile range (IQR), which is the range of the middle 50% of the data. To find the IQR, we first need to find the median of the data:

2, 10, 10, 12, 12, 20

The median is the middle value when the data set is arranged in order, which is 11. We can then divide the data set into two halves:

2, 10, 10 and 12, 12, 20

The lower half has a median of 10, and the upper half has a median of 12. The IQR is the difference between these medians:

IQR = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

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