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3 years ago

Type the correct answer in each box, If necessary, use / for the fraction bar(s).

Mathematics

1 answer:

user100 [1]3 years ago

6 0

Answer: -1/1

Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.

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I have a question about polynomial division it is in the picture

Cloud [144]

To answer this question, we have to do the long division process for polynomials. We can do the operation as follows:

To do this division process, we have:

1. Divide the first term of the dividend by the first element of the divisor. They are:

$\frac{-4x^3}{4x^2}=-x$

2. Now, we have to multiply this result by the divisor, and the result will change its sign since we have to subtract that result from the dividend as follows:

$-x\cdot(4x^2_{}-4x-4)=-4x^3+4x^2+4x$

And since we to subtract this result from the dividend, we end up with:

$-(-4x^3+4x^2+4x)=4x^3-4x^2-4x$

3. Then we have the following algebraic addition:

$\frac{\begin{cases}-4x^3+24x^2-15x-15 \\ 4x^3-4x^2-4x\end{cases}}{20x^2-19x-15}$

4. Again, we need to divide the first term of the dividend by the first term of the divisor as follows:

$\frac{20x^2}{4x^2}=5$

5. And we have to multiply 5 by the divisor, and the result will be subtracted from the dividend:

$5\cdot(4x^2-4x-4)=20x^2-20x-20$

Since we have to subtract this from the dividend, we have:

$-(20x^2-20x-20)=-20x^2+20x+20$

6. And we have to add this algebraically to the dividend we got in the previous step:

$\frac{\begin{cases}20x^2-19x-15 \\ -20x^2+20x+20\end{cases}}{x+5}$

And this is the remainder of the division, x + 5.

As we can see from the division process, we got as:

1. The quotient: -x + 5

$q=-x+5$

2. The remainder: x + 5.

$R=x+5$

Since we have that the dividend = divisor * quotient + remainder.

Therefore, the result for this division is:

$-4x^3+24x^2-15x-15=(4x^2-4x-4)\cdot(-x+5)+(x+5)$

4 0

1 year ago

Complete the identity. 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

Does anybody know how to solve the equation f(x)=-5/9(3)+b?

3241004551 [841]

Substitute either set of points into the equation:

(3, -1) and (-6,-4)

-1= -5/9(3)+b

-1= -15/9+b

-1+5/3= -5/3 +5/3 +b

2/3=b

So,

f(x)= -5/9 (x) + 2/3

4 0

3 years ago

2. The logo shown below was created by splitting a circle into 6 equal sections. Raphael is creating a stage-sized version of th

andrew11 [14]

From the shaded diagram, Raphael will need 3 of the 6 equal portions, or exactly 1/2 of the area of the circle. Given a radius of 12 ft, knowing that the area of any given circle is $\pi r^2$ , and knowing that the area of the fabric needs to be half of the total area, we can set up the equation for the area of the fabric $A$ :

$A= \frac{1}{2}\pi (12)^2$

Simplifying, we find that the area of the fabric is exactly

$\frac{1}{2} \pi (144)= \frac{144}{2} \pi=72\pi$ ft.² Using the approximation of 3.14 for π, we get an area of approximately $72(3.14)=226.08$ ft² of fabric.

6 0

4 years ago

In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old ar

Nataliya [291]

The answer is b.3x + 15 = 55 - x

x - Jill's present age
y - dad's present age

In 5 years, Dad will be three times as old as his daughter Jill will be then:
y + 5 = 3(x + 5)

The sum of their present ages is 50:
x + y = 50

We have the system of two equations now:
y + 5 = 3(x + 5)
x + y = 50

Let's rearrange the second equation:
If: x + y = 50
Then: y = 50 - x

Now, substitute y from the second equation (y = 50 - x) into the first one:
y + 5 = 3(x + 5)
50 - x + 5 = 3(x + 5)
50 + 5 - x = 3*x + 3*5
55 - x = 3x + 15

Rearrange it a bit:
3x + 15 = 55 - x
Therefore, the correct choice is b.

5 0

3 years ago