3. Segment GE is an angle bisector of both
angle HEF and angle FGH. Prove triangle HGE is
congruent to triangle FGE.
F
H
G

The range is [tex]\boxed{-4 \leq y < 0}[/tex].

Answer:

1) undefined

2) 0

Step-by-step explanation:

Slope formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Problem 1:

(x1, y1) = (-7, 8)

(x2, y2) = (-7, -6)

Plug those 2 points into the slope formula and solve:

[tex]m=\frac{-6-8}{-7--7}\\\\m=\frac{-14}{0}[/tex]

Here, you can't divide by 0, so this slope is undefined. An undefined slope would make a completely vertical line on a graph. In this case, the equation of the line would be just:

[tex]x=-7[/tex]

Problem 2:

(x1, y1) = (-9, -8)

(x2, y2) = (3, -8)

[tex]m=\frac{-8--8}{3--9}\\\\m=\frac{0}{12}\\\\m=0[/tex]

The slope is 0, and that would make a horizontal line on a graph. The equation would be:

[tex]y=-8[/tex]

You don't actually need to fully work out the slope that way. If you ever have 2 points with the same x-coordinate, the slope has to be undefined. If you ever have 2 points with the same y-coordinate, then the slope has to be 0, assuming it's linear of course. You can see that in the points given, the first 2 have the same x and the second 2 have the same y.

Step-by-step explanation:

I'll try to get this out as as quickly as I can! In this scenario, we have a function m(x). We can also view m(x) as y to make everything easier to understand. It is said that m(x) = 1, which can also be interpreted as for whatever value x may be, the y value is 1. Whether x is -9, 0, 3, 1, or 2/3, the y-value will be 1. The table can be filled out with as many x-values as needed, with corresponding 1's for each.

Next, we have to graph. Try to visualize what this graph might look like. For whatever x-value given, the y-value will be 1. Our graph will have to be a horizontal line through the y-value (0, 1). This represents that for whatever x-value, the y-value will be 1.

Hopefully that's helpful! :)

The new balance is a credit of $ 48.78.

Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:

Therefore, the new balance is a credit of $ 48.78.

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Answer:

[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]

Step-by-step explanation:

[tex]\frac{dx}{dt}=2[/tex]

[tex]\frac{d\theta}{dt}=?[/tex]

[tex]x=12[/tex]

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(\theta)=\frac{x}{13}[/tex]

[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]

[tex]cos(\theta)=\frac{x}{13}[/tex]

[tex]cos(\theta)=\frac{12}{13}[/tex]

[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]

[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]

The value of θ is given by the inverse sine function, from which the rate of

change of θ with respect to x can be derived.

Reasons:

[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]

[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]

[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]

[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]

Using chain rule of differentiation, we have;

[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]

Therefore;

[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]

When x = 12, we get;

[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]

The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s

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Answer:

no

Step-by-step explanation:

1 x 7 = 7 but 2 x 7 does not equal 17

Answer:

7,200 words

Step-by-step explanation:

Answer: 4,800

I multiplied 120 by 20 because 60 divided by 3 is 20. Then I multiplied my answer by 2 because the question is asking how many words could they type in 2 hours

Answer:

x=3

Step-by-step explanation:

Answer:

75.36cm

Step-by-step explanation:

We use the pithagorean theorem: height^2 = 152^2 - 132^2 = 5680;

height = [tex]\sqrt{5680} = 75..36 cm[/tex]

Answer:

11/23

Step-by-step explanation:

B = 6

C = 5

6+5=11

11/23

Answer:

4 miles

Step-by-step explanation

If your mom can walk 1 mile in 14 minutes then 2 miles would take her 28 minutes 3 miles would take her 42 minutes and finally if she walked 4 miles it would take her 56 minutes.

14 + 14 + 14 + 14 = 56

14 x 4 = 56

Answer:

It suggests the days are intense but beautiful.

Step-by-step explanation:

According to the introductory paragraph that starts with breakfast and ends with the setting of Arctic sun. This short paragraph adds to the conflict in the story because It suggests the days are intense but beautiful.

Although the question is incomplete, i can infer that the story you are referring to is White Fang by Jack London, where the story is told of the people talking about events happening around them.

They talk about the sun and the work around them and also the cold. How thsir short conversation added to the conflict in the story is that It suggests the days are intense but beautiful

hi how have you been and i think u did get it right

[tex]3(x+9)-4x=11x-13x+23\\<=>3x+27-4x-11x+13x-23=0\\<=>x+4=0\\<=> x= -4[/tex]

Answer: this's true statement.

ok done. Thank to me :>

Answer:

The equation of this line is y = -3x + 7

Step-by-step explanation:

Remember that when writing an equation for a graphed linear line, we must write it in slope intercept form (y=mx+b). The m represents the slope, and the b represents the y-intercept.

(The slope determines the direction in which the line goes, and is written as rise/run.)

In this case the slope is going to be negative, since the line is going downwards to the right. Additionally the slope of this line is -3/1 or just -3.

(The y-intercept is the point in which the line crosses the y-axis.)

In this case, since the line crosses the y-axis at positive 7, the y-intercept will be 7.

So all together we have y = -3x + 7.

Hope this helps you :)

======================================================

Explanation:

PDF = probability density function

The given joint PDF is

[tex]f(x,y) = \begin{cases}ax \ \ \ \text{ if } 1 \le x \le y \le 2\\0 \ \ \ \ \ \text{ otherwise}\end{cases}[/tex]

Let's focus on the [tex]1 \le x \le y \le 2[/tex]. Specifically the x term for now. Erasing out the y term, we have the inequality [tex]1 \le x \le 2[/tex] which says x is between 1 and 2, inclusive. We have almost the same story for y, but there's another condition attached to it: y must also be equal to or larger than x.

So let's say x = 1.5. This would mean [tex]1.5 \le y \le 2[/tex]. As another example, x = 1.7  leads to [tex]1.7 \le y \le 2[/tex]. In general, we would say [tex]x \le y \le 2[/tex] where x is between 1 and 2.

As x gets bigger, the range of possible y values gets smaller. If x = 2, then y has no choice but to be 2 as well.

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

Based on that, we'll have a double integral that looks like this:

[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\[/tex]

The outer integral handles the x terms that range from 1 to 2, describing [tex]1 \le x \le 2[/tex]. Note the dx on the outside. The order of the dy and dx matters.

On the inside, we have the integral for dy ranging from x to 2 to describe the interval [tex]x \le y \le 2[/tex]

To have f(x,y) be a PDF, the volume under the f(x,y) surface must be 1, where the volume is based on the bounds set up. So we must have V = 1. We'll use this later.

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

Let's simplify the double integral.

We'll start by computing the inner integral with respect to y.

[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\\displaystyle V = \int_{1}^{2}\int_{x}^{2}\left(ax\right)dydx\\\\\displaystyle V = \int_{1}^{2}\left(axy\Bigg|_{x}^{2}\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(ax(2) - ax(x)\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\[/tex]

Then we'll finish it off by integrating with respect to x.

[tex]\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\\displaystyle V = \left(ax^2 - \frac{1}{3}ax^3\right)\Bigg|_{1}^{2}\\\\\displaystyle V = \left(a(2)^2 - \frac{1}{3}a(2)^3\right) - \left(a(1)^2 - \frac{1}{3}a(1)^3\right)\\\\\displaystyle V = \left(4a - \frac{8}{3}a\right)-\left(a - \frac{1}{3}a\right)\\\\[/tex]

[tex]\displaystyle V = 4a - \frac{8}{3}a-a + \frac{1}{3}a\\\\\displaystyle V = 3a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9}{3}a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9-8+1}{3}a\\\\\displaystyle V = \frac{2}{3}a\\\\[/tex]

Side note: We don't have to worry about the "plus C" integration constant when working with definite integrals.

Recall that V = 1. So,

[tex]\displaystyle V = \frac{2}{3}a\\\\\displaystyle \frac{2}{3}a = 1\\\\\displaystyle a = \frac{3}{2} = 1.5\\\\[/tex]

a = 3/2 is the final answer.

Answer:

A is the correct solution

Step-by-step explanation:

     3x³ + 4x² + 0x - 1  /  x - 2

             3      10    20

-2 | 3       4       0    -1

 -  (3      -6)

             10       0

      -     (10    -20)

                      20    -1

                 -   (20  -40)

                              39

3x² + 10x + 20 + 39/(x - 2)

The compound interest is applied to the remaining balance in the account

each subsequent year.

Reasons:

The given compound interest rate, r = 6.25% = 0.0625

The balance in the account after 2 years, A = $700

Required:

The required deposit, P, that gives the given account balance after 2 years.

Solution:

The following is the compound interest formula to use;

Where;

t = 2 years

We get;

[tex]\displaystyle P = \mathbf{ \frac{A}{(1 + r)^t}}[/tex]

Which gives;

[tex]\displaystyle P = \frac{700}{(1 + 0.0625)^2} \approx \mathbf{620.07}[/tex]

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Answer:

53

Step-by-step explanation:

—19 + 12 = —7

—7 + 12 = 5

5 + 12 = 17

.

.

.

so the n term of the sequence will be: 12n — 31

so 7th term will be: 12 × 7 — 31 = 53

Answer:

d. 53

Step-by-step explanation:

increases 12 units at each step:

17 + 12 = 29

29 +12 = 41

41 + 12 = 53  (7th term)

Hope this helps

Answer:

Put one point on -4 on the Y-axis (bottom middle) and one at (-2,2)

Answer:

C

Step-by-step explanation:

the angle opposite of it is 30

[tex]\huge\text{\bf Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{4x = 96}}\\\\\large\text{DIVIDE 4 to BOTH SIDES}\\\\\huge\boxed{\mathsf{\dfrac{4x}{4} = \dfrac{96}{4}}}\\\\\large\text{CANCEL out: }\rm{\dfrac{4}{4}}\large\text{ because it gives you 1}\\\large\text{KEEP: }\rm{\dfrac{96}{4}}\large\text{ because it helps solve for the x-value}\\\\\large\text{NEW EQUATION: }\huge\boxed{\rm{x = \dfrac{96}{4}}}\\\\\large\text{SIMPLIFY IT\textbf{!}}\\\\\huge\text{x = \bf 24}\\\\\\\huge\text{Therefore, your answer is: \boxed{\textsf{x = 24}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The equation of the line that is parallel to [tex]2\cdot x + 5\cdot y = 10[/tex] is [tex]y = -\frac{2}{5} \cdot x + 3[/tex] and the equation of the line that is perpendicular to [tex]4\cdot x + 3\cdot y =12[/tex] is [tex]y =\frac{3}{4}\cdot x - 1[/tex].

Let be a line whose equation is:

[tex]a\cdot x + b\cdot y = c[/tex] (1)

Whose explicit form is:

[tex]y = -\frac{a}{b} \cdot x +\frac{c}{b}[/tex] (2)

Where:

The slope and x-intercept of the line are [tex]-\frac{a}{b}[/tex] and [tex]\frac{c}{b}[/tex], respectively.

There are two facts:

Then, the equation of the line that is parallel to [tex]2\cdot x + 5\cdot y = 10[/tex] is [tex]y = -\frac{2}{5} \cdot x + 3[/tex] and the equation of the line that is perpendicular to [tex]4\cdot x + 3\cdot y =12[/tex] is [tex]y =\frac{3}{4}\cdot x - 1[/tex].

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Answer:

5

Step-by-step explanation:

I don't think I should have to explain this but if it's in between 4.5 and 5 it will be 5 and if it's 4.5-4 it would be 4

Answer:

x > 3

Step-by-step explanation:

And then, I believe you just need to solve that answer. But I'm not sure tho

The substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

A system of linear equation is a group of one or more linear equations which can be solved by using a simultaneous equation or elimination method.

From the information given;

3x + y = -2      ----- (1)

y = 2x +3        ----- (2)

By using substitution method, we will replace the value of equation (2) into equation (1), by doing so, we have:

3x + (2x + 3) = -2

3x + 2x + 3 = -2

5x + 3 = -2

5x = -2 - 3

5x = - 5

x = -5/5

x = -1

From equation (2), let's replace the value of x = - 1 into equation (2);

y = 2x + 3

y = 2(-1) + 3

y = -2 + 3

y = 1

Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

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Answer:

7.5lbs

Step-by-step explanation:

82/11 = 7.45454545lbs

Rounded to 7.4lbs

Hope that helps

Answer:

7 5/11

Step-by-step explanation:

you divide 82 and 11 and you get 7.45454545

Answer:

1. 7 to the square root of 3

2. negative square root of 3

Step-by-step explanation:

1. simplify 0.7 x 10 square of 3

2. Calculate: you get 7 to the square root of 3

1. simplify -0.125 x 8 to the square root of 3

2. Calcaute: you get negative square root of 3

The factors of the expression 0.7√300 and -0.125√192 will be 7 x √3 and - 1 x √3, respectively.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expressions are given below.

0.7√300 and -0.125√192

Simplify the expressions, then we have

0.7√300 and -0.125√192

7√3 and - √3

Factorize the expression, then we have

7 x √3 and - 1 x √3

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