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Answer:

Part A)

The slope is two.

Part B)

[tex]\displaystyle y = 2x - 7[/tex]

Step-by-step explanation:

Part A)

We want to find the slope of the curve:

[tex]\displaystyle y = x^2 - 2x - 3[/tex]

At the point P(2, -3) by using the limit of the secant slopes through point P.

To find the limit of the secant slopes, we can use the difference quotient. Recall that:

[tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]

Since we want to find the slope of the curve at P(2, -3), x = 2.

Substitute:

[tex]\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}[/tex]

Simplify. Note that f(2) = -3. Hence:

[tex]\displaystyle \begin{aligned} f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h} \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}[/tex]

(Note: I evaluated the limit using direct substitution.)

Hence, the slope of the curve at the point P(2, -3) is two.

Part B)

Since the slope of the curve at point P is two, the slope of the tangent line is also two.

And since we know it passes through the point (2, -3), we can consider using the point-slope form:

[tex]\displaystyle y - y_1 = m(x-x_1)[/tex]

Substitute. m = 2. Therefore, our equation is:

[tex]\displaystyle y + 3 = 2(x-2)[/tex]

We can rewrite this into slope-intercept if desired:

[tex]\displaystyle y = 2x - 7[/tex]

We can verify this by graphing. This is shown below:

Answer:

the difference between the temperatures is -50.9. f=-50.9

Step-by-step explanation:

33.6°F+17.3°F=50.9

33.6°F+F= -17.3°F

33.6°F+(-50.9°F= -17.3°F

so, F=-50.9°F

Step-by-step explanation:

d=T2-T1=(-17.3-33.6)=-50.9°F

Answer:

-5/4

Step-by-step explanation:

C is at the point (2,3) and D is at the point (6,-2)

-2-3 = -5 which would be the top part and 6-2=4 and that's the bottom part.

Answer: x = 1

Step-by-step explanation:

Given

3/2 + (1/2)x = 2x

Multiply 2 on both sides to cancel out the denominator

2 · [3/2 + (1/2)x] = 2 · 2x

3 + x = 4x

Subtract x on both sides

3 + x - x = 4x - x

3 = 3x

Divide 3 on both sides

3 / 3 = 3x / 3

[tex]\boxed {x=1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

exponent is -3 and coefficient is 4

Answer:

13.6122

Step-by-step explanation:

(x-18.6)/15.3=-0.326

x-18.6=-0.326*15.3

x-18.6=-4.9878

x=-4.9878+18.6

x=13.6122

Answer:

r = (-4,9]

Step-by-step explanation:

hope this will help

Answer:

-4<y≤2

Step-by-step explanation:

The range of a graph is the range of the y values.

First take a derivative,

[tex]\frac{d}{dx}-5t^2+10t+30=-10t+10=-10(t-1)[/tex]

Now compute the critical point where the slope is 0,

[tex]-10(t-1)=0\implies t-1=0\implies t=1[/tex]

And done.

The maximum height is at [tex]t=1[/tex] of [tex]h(1)=-5+10+30=35[/tex].

Hope this helps :)

Answer:

(m - 43)/2m

Step-by-step explanation:

Answer:

f(x) = [tex]-2^{x+1}-1[/tex]

Step-by-step explanation:

I. If you see (0, -3) point on the green line

II. Perform x = 0, if y = -3 means the statement is true

    = [tex]-2^{0+1} - 1[/tex]

    = [tex]-2^{1}[/tex] - 1

    = -2 - 1

  y = -3

Got more question or somethin to discuss? Leave comment below

Answer:

c

Step-by-step explanation:

thats the anser

Answer:

Below

Step-by-step explanation:

DO=15

OB=3x+7

DB=9x-2

O is between D and B

So,

OB+DO=DB

or, 9x-2+3x+7=15

or, 12x=15-5

or, x=10/12

Thus, x=5/6

Answer:

It'll be the same figure- an acute isoceles triange

Step-by-step explanation:

Reflection is just copying the same shape across the x-axis (the main horizontal line on graphs) or the y-axis (the main vertical line on graphs). It's like looking at yourself in the mirror, like a reflection!

let length be x

ATQ

[tex]\\ \sf\longmapsto \dfrac{2}{8}\times x=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{8}=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{4}=28[/tex]

[tex]\\ \sf\longmapsto x=4(28)[/tex]

[tex]\\ \sf\longmapsto x=112[/tex]

Answer:

B

Step-by-step explanation:

It just is

B

if it is not correct sory

Diagram B is a proper demonstration of an angle bisector.

Letter A is wrong because they are a set of intersecting ines.

Letter C is wrong because they are a set of parallel lines.

Letter D is wrong because they are also a set of perpendicular lines.

So, now, we know that Letter B is the correct answer. The reason for this is also because ∠ACD is bisected by line B.

I hope that this helped answer your question. Have a good day!

Step-by-step explanat

(g) 3[(3)²-2]+4=3(9-2)=3×7=21+4=25

Answer:

It is not hard

Step-by-step explanation:

•Once you get familiar with the lesson you understand it in a much easier way by doing problems pretty often

•If you want get more comfortable with it just search for a few questions in internet specifically educational platforms in schools like teachers

•But if your still confused you can always study it for free by byjus or vedantu and the best option in my opinion is ask your teacher to explain it once more

•It is very hard to solve questions if you are not freindly with the chapter

• Do not hesitate to ask questions if your doubting or anything you might face problems in higher grades with the topic

Answer: B

Step-by-step explanation:

The most likely the next pattern in the series is 2 lines with red color. Therefore, option B is the correct answer.

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

From the given patterns

Figure 1 has 5 lines and it is blue in color.

Figure 2 has 4 lines and it is red in color.

Figure 3 has 3 lines and it is blue in color.

So, Figure 4 must has 2 lines and red in color.

Therefore, option B is the correct answer.

Learn more about the pattern here:

https://brainly.com/question/23136125.

#SPJ7

Step-by-step explanation:

a²=b²

since a=b, therefore we can write a in place of b or b in place of a,

a²=a² or b²=b²

Hence, it is proved.

I hope it helped U

I hope it helped Ustay safe stay happy

Answer:

3/15

Step-by-step explanation:

-2/5=-6/15

(-6-(-9))/15=(-6+9)/15=3/15

9514 1404 393

Explanation:

Add sin(θ)

  cos(θ) = sin(θ)

Divide by cos(θ)

  1 = sin(θ)/cos(θ) = tan(θ)

Square both sides

  1 = tan²(θ)

Add 1

  2 = tan²(θ) = sec²(θ)

Take the square root

  √2 = sec(θ) . . . . for 0 < θ < π

_____

Additional comment

The equation cos(θ) -sin(θ) = 0 has two solutions: θ = π/4 and θ = 5π/4. For the first-quadrant solution, sec(θ) = √2. For the third-quadrant solution, sec(θ) = -√2.

Answer:

Step-by-step explanation:

There are 420 students.

41% are first year students.

41% = 41/100

420 * 41/100 = 172.4

What do you do about the 0.4? I would just round to the nearest whole number which is 172.

There are 420 - 172 = 248 who are not first year students.

Answer:

A

Step-by-step explanation:

X^3+1

Y int = 1

X int = -1

We can clearly see that the x int(when y = 0) for c = -3 so C is incorrect.

b is wrong because it's a quadratic(ax^2+bx+c) and d wrong because it linear(y=mx+c).

Knowing all this we can safely say that A is the correct answer choice.

Answer:

we firstly need to find x intercept and y intercept

9514 1404 393

Answer:

  x = -4

Step-by-step explanation:

Put the given point in the equation and solve for x.

  4x = 5(-3) -1

  4x = -16 . . . . . . simplify

  x = -4