What is the slope of the line that passes through the points (8, 7) and (4, 5)

The general expression for the slope of a tangent line to the curve y = 3.5x - 2x^2 is given by the derivative of the function, which is -4x + 3.5. The slopes for the specific values of x (-1.5, -0.5, and 3).

To find the general expression for the slope of a tangent line to the curve y = 3.5x - 2x^2, we need to take the derivative of the function with respect to x. The derivative represents the rate of change of the function at any given point.

Differentiating y = 3.5x - 2x^2 with respect to x, we get dy/dx = 3.5 - 4x. This expression gives us the slope of the tangent line at any point P(x, y) on the curve.

Now, we can calculate the slopes for the given values of x (-1.5, -0.5, and 3) by substituting these values into the derivative expression.

For x = -1.5, the slope is m = 3.5 - 4(-1.5) = 10.

For x = -0.5, the slope is m = 3.5 - 4(-0.5) = 5.

For x = 3, the slope is m = 3.5 - 4(3) = -8.

These slopes represent the rates at which the curve is changing at the respective x-values. To sketch the curves and tangent lines, plot the points (x, y) on the graph and draw a line with the calculated slopes at those points.

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Answer:

Option B is the correct answer

Step-by-step explanation:

\(3 \bigg( \frac{7}{5} x + 4 \bigg) - 2\bigg( \frac{3}{2} - \frac{5}{4}x \bigg) \\ \\ = \bigg( \frac{7 \times 3}{5} x + 4 \times 3\bigg) - \bigg( \frac{3 \times \cancel 2}{\cancel 2} - \frac{5 \times 2}{4}x \bigg)\\ \\ = \bigg( \frac{21}{5} x + 12\bigg) - \bigg( 3 - \frac{5 }{2}x \bigg)\\ \\ = \frac{21}{5} x + 12 - 3 + \frac{5 }{2}x \\ \\ \frac{21}{5} x + \frac{5 }{2}x + 9 \\ \\ = \frac{42 + 25}{10} x + 9 \\ \\ \huge \purple{ = \frac{67}{10} x + 9}\)

Answer:

B, 67/10x + 9

Step-by-step explanation:

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Frank is a high school mathematics teacher. He is interested in what habits affect his student's final exam performance. He surveyed a random 60 out of 100 students in his classes and asked each one how many hours he or she spent studying. He also rated their class participation on a scale from 1 to 10. The response variable is exam performance

The response variable in this scenario is the students' final exam performance. Frank is interested in understanding how habits, such as studying hours and class participation, influence the students' performance on the final exam.

By surveying the students and collecting data on their studying hours and class participation ratings, Frank aims to analyze the relationship between these habits and the students' exam scores.

The final exam performance is the outcome or response variable that   Frank wants to examine and understand in relation to the habits of studying and class participation, Frank being a high school mathematics teacher.

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The solution to the model shown is 1.5

From the question, we have the following parameters that can be used in our computation:

The equation of the model is

2x - 1 = 2

Add 1 to both sides of the equation

So, we have

2x = 3

Divide both sides by 2

x = 3/2

Evaluate

x = 1.5

Hence, the solution to the model shown is 1.5

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Answer:

7

Step-by-step explanation:

26-2 = 24. 24/6 = 4. 53-4=49. The square root of 49 is 7.

The part of the plane 2x + 5y + z = 10 that lies inside the cylinder x2 + y2 = 9 is a half cylinder with a radius of 3 and height of 6. The area of this half cylinder is 9√30π.

The equation of the plane can be rewritten as z = 10 - 2x - 5y.

The equation of the cylinder can be rewritten as x2 + y2 = 9.

To find the part of the plane that lies inside the cylinder, we need to solve the system of equations z = 10 - 2x - 5y and x2 + y2 = 9.

Solving this system of equations, we find that the part of the plane that lies inside the cylinder is the set of all points (x, y, z) such that 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, and 10 - 2x - 5y ≥ 0.

The area of this half cylinder can be found using the formula for the area of a cylinder:

A = 2πr²h

where r is the radius of the cylinder and h is the height of the cylinder. In this case, r = 3 and h = 6, so the area of the half-cylinder is

A = 2π(3²)(6) = 9√30π

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The average value of P=f(t)=2.04(1.03)^t for 0≤t≤30 is approximately 3.236. The average value of P=f(t)=2.04(1.03) for 0≤t≤30 is 2.10.

To find the average value of the function P=f(t)=2.04(1.03)^t for 0≤t≤30, you'll need to evaluate the appropriate integral and use the formula for the average value of a function.
The formula for the average value of a function is:
Average value = (1/(b-a)) * ∫[f(t) dt] from a to b
In this case, a = 0, b = 30, and f(t) = 2.04(1.03)^t.
Step 1: Evaluate the integral.
∫[2.04(1.03)^t dt] from 0 to 30
Step 2: Use a calculator to find the definite integral value.
We should find that the integral value is approximately 97.091.
Step 3: Substitute the integral value, a, and b into the average value formula.
Average value = (1/(30-0)) * 97.091
Step 4: Calculate the average value.
Average value ≈ (1/30) * 97.091 ≈ 3.236
So, the average value of P=f(t)=2.04(1.03)^t for 0≤t≤30 is approximately 3.236.

To find the average value of P=f(t)=2.04(1.03) for 0≤t≤30, we need to first evaluate the integral of the function over the given interval.
∫(0 to 30) 2.04(1.03) dt
Using a calculator, we can simplify and solve this integral as follows:
2.04(1.03)∫(0 to 30) dt
= 2.10t |(0 to 30)
= 2.10(30) - 2.10(0)
= 63.00
So, the integral of P=f(t) over the interval 0≤t≤30 is 63.00.
To find the average value of P over this interval, we divide this integral by the length of the interval:
Average value of P = (1/30-0) * 63.00
= 2.10
Therefore, the average value of P=f(t)=2.04(1.03) for 0≤t≤30 is 2.10.

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Answer:

117

Step-by-step explanation:

Sum of all angles of pentagon = 540

x + 86 + 140 + 138 + 59 = 540

x + 423 = 540

x = 540 - 423

x = 117

Answer:

x= 117°

Step-by-step explanation:

In a Pentagon the interior angles are equal to 540° so, first we take the values we have which is:

140°+138°+59°+86°= 423° in total

To find x all you do is take 423 away from 540

540 - 423 = 117°

x= 117°

Hope it helped, ask any questions if you are unsure:)

The height of the object after 2.3 seconds is 107.08 feet. It will take 4.62 seconds for the object to hit the ground. The values are accurate to 2 decimal places.

The equation given is h(t) = -16t2 + 270. Since we are looking for the height of the object after 2.3 seconds, we need to replace the value of t with 2.3. So we have h(2.3) = -16(2.3)2 + 270. This simplifies to h(2.3) = -56.89 + 270, which is equal to 213.11. The height of the object after 2.3 seconds is therefore 213.11 feet. To calculate how long it will take for the object to hit the ground, we need to set h(t) = 0 and solve for t. This gives us 0 = -16t2 + 270, which simplifies to 16t2 = 270. Dividing both sides by 16 gives t2 = 16.875, and taking the square root of both sides gives t = 4.06. Since the object is falling, we need to take the positive value of t, which is 4.06. The time it will take for the object to hit the ground is therefore 4.06 seconds. The values are accurate to 2 decimal places, so the time it will take for the object to hit the ground.

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The equivalent expressions which depicts Mateo's spending are :

L(1 - 0.15L)

L - 3L/20

Using the following parameters:

The hours spent by Mateo can be written as :

L - 0.15L = L(1 - 0.15)

Also ;

0.15L = 3L/20

Hence, the equivalent expressions are :

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Answer:

1,778

Step-by-step explanation:

According to the problem, given data are as follows,

Number of hotdogs bought = 2,074

Number of hotdogs remaining = 296

So, we can calculate the number of hotdogs sold by using following method:

Number of hotdogs sold = Number of hotdogs bought - Number of hotdogs remaining

By putting the value, we get

Number of hotdogs sold = 2,074 - 296

= 1,778

Hence, total number of hotdogs sold are 1,778.

The real zeros for the polynomial function f(x) = 4x^3 - 21x^2 + 35x - 18 using the Factor Theorem and the factor x - 1 are 1, 2, and 9/4.

To find the real zeros using the Factor Theorem, we need to divide the given polynomial f(x) by the factor x - 1 and obtain a quotient and a remainder. If the remainder is zero, then x - 1 is a factor of f(x) and the roots can be found by setting the quotient equal to zero. The polynomial long division is shown below:

        4x^2 - 17x + 18

 __________________________

x - 1 | 4x^3 - 21x^2 + 35x - 18

- (4x^3 - 4x^2)

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

-17x^2 + 35x

+ (17x^2 - 17x)

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

18x - 18

- (18x - 18)

---------

0

Since the remainder is zero, we can write:

4x^3 - 21x^2 + 35x - 18 = (x - 1)(4x^2 - 17x + 18)

Now, we need to find the roots of the quadratic factor 4x^2 - 17x + 18. We can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 4, b = -17, and c = 18. Substituting the values, we get:

x = (17 ± √(17^2 - 4(4)(18))) / 8

Simplifying, we get:

x = (17 ± √73) / 8

Therefore, the real zeros of the polynomial function f(x) using the factor x - 1 are 1, (17 + √73) / 8, and (17 - √73) / 8. However, we need to check that the two irrational roots are real. Since 73 is positive, both roots are real. Finally, we can simplify the irrational roots as follows:

(17 + √73) / 8 ≈ 2.25

(17 - √73) / 8 ≈ 1.125

Hence, the real zeros of the polynomial function f(x) using the factor x - 1 are 1, 2, and 9/4.

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Answer:

71º

Step-by-step explanation:

since it is a complementary angle equal 90 degrees total

so 90° - 19 = 71

Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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Answer:

30.7

Step-by-step explanation:

Answer:

if the two angles are equal

we use sss therom to solve it

2ft/6ft=24ft/xft

x=(6*24)/2

=72

Answer:

5 miles

Step-by-step explanation:

distance = rate times time

distance = (10 miles per hour)( 30 minutes)  30 minutes is equal to 1/2 hour

distance = \(\frac{10 miles}{hour}\) \((\frac{1 hour}{2} )\)  You can cancel words, like like cancelling numbers  The hours cancel out and you are left with \(\frac{10 miles}{2}\)  which is equal to 5 miles.

Answer: 5 miles

Step-by-step explanation:

Jim runs 10 miles per hour, and 30 minutes is half an hour, so divide 10 by 2.

Step-by-step explanation:

Factor 98n2−200

98n2−200

=2(7n+10)(7n−10)

Answer:

2(7n+10)(7n−10)

The volume of the cube with the given side length is 64x⁶ + 144x⁴ + 108x² + 27 , the correct option is (a) .

The Volume of the cube with side length "a" is given by the formula

Volume = a³ .

In the question ,

it is given that ,

the length of the side (s) of the cube is 4x² + 3 .

By using the formula for Volume of the cube ,

we get

Volume = (4x² + 3)³

using the identity (a + b)³ = a³ + b³ + 3a²b + 3ab²

we get ,

Volume = (4x²)³ + 3³ + 3*(4x)²*(3) + 3*4x*3²

Simplifying further ,

we get

= 64x⁶ + 27 + 9*16x⁴ + 27*4x²

= 64x⁶ + 27 + 144x⁴ + 108x²

= 64x⁶ + 144x⁴ +  108x² + 27

Therefore , The volume of the cube with the given side length is 64x⁶ + 144x⁴ + 108x² + 27 .

The given question is incomplete , the complete question is

The side length s , of a cube is 4x² + 3 . If V = s³ , what is the Volume of the cube ?

(a) 64x⁶ + 144x⁴ + 108x² + 27

(b) 64x⁶ + 48x⁴ + 12x² + 1

(c) 4x⁶ + 36x⁴ + 108x² + 27

(d) 4x⁶ + 12x⁴ +12x² + 1

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Answer:

why does it say the answer is 165 on top?

The value of 1 cm : 1 km is 6.66666667e-7

The ratio expression is given as:

1 cm : 15 km

Convert km to cm

So, we have

1 cm : 1 km = 1 cm : 1500000 cm

Express as quotient

1 cm : 1 km = 1 cm/1500000 cm

Evaluate the quotient

1 cm : 1 km = 6.66666667e-7

Hence, the value of 1 cm : 1 km is 6.66666667e-7

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Answer:

C

Step-by-step explanation:

Answer:

x>15

hope this helps!!:)

Step-by-step explanation:

Answer:

√61

Step-by-step explanation:

Answer:

(5,6)

Step-by-step explanation:

3-(-2)=5

3-(-3)=6

Answer:

16 words per minute

Step-by-step explanation:

We can think of this problemas a fraction such as

\(\frac{80words}{5minutes}\)

to simplify the denominator to one you need to divide top and bottom by 5

\(\frac{16words}{1minute}\)

Using the exponential growth function, G(t) = 24(1.2314)^t, the first period or year the school can hire the geese-chasing dogs when the future number of geese in the school's sports fields increases to 70 in 2013.

We can use an online calculator to determine the number of years or periods, t, when a constant annual growth rate of 23.14% will increase to 70 (future value or number) from a population of 24.

We can also solve the given exponential growth function.

An exponential growth function is a mathematical function that shows a constant periodic growth.

The growth function can be expressed as G(t) = 24(1.2314)^t, where G(t) is the future population of the geese and t is the period when the current population grows to the expected number.

The annual growth rate of the Canada geese = 23.14%

PV (Present Number) of the Canada geese population = 24

FV (Future Number) of the Canada geese population = 70

Results:

Number of years (#) = 5.143

Total Increase in 5.143 years = 46 (70 - 24)

G(t) = 24(1.2314)^t

t = 5 years

(2008 + 5 years) = 2013

Thus, the school should be ready to hire the geese-chasing dogs in 2013.

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Answer:

  2 × (14 – 9) – (17 – 14) = 7

Step-by-step explanation:

Evaluate the choices to see which is true.

(2 x 14) – 9 – (17 – 14) = 7   ⇒  28 -9 -3 ≠ 7

2 x (14 – 9) + (– 17 – 14) = 7   ⇒  2(5) +(-31) ≠ 7

(2 x 14) – (9 – 17) – 14 = 7   ⇒   28 -(-8) -14 ≠ 7

2 x (14 – 9) – (17 – 14) = 7   ⇒   2(5)- 3 = 7 . . . . true

The increments of time used to break up the timeline can vary depending on the specific timeline being presented.

The increments of time used to break up the timeline can vary depending on the context and purpose.

However, common time increments include years, months, weeks, or days, which are displayed on the x-axis (horizontal) to divide the timeline into easily understandable segments.

For example, in a historical timeline, the increments might be years, decades, or centuries. In a project timeline, the increments might be weeks or months.

The x-axis (horizontal) is typically where these increments are marked and can help to visualize the timeline more clearly.

Ultimately, the increments chosen should be appropriate for the task at hand and allow for effective planning and tracking of progress.

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12 ≡ 7 + 5 ≡ 5 (mod 7)

so

12 + 12 + 12 + 12 ≡ 4•12 ≡ 4•5 ≡ 20 ≡ 14 + 6 ≡ 6 (mod 7)