Reduce to Standard form : (a) -21/91 (b) 32/(-256)​

Answer:

2 sin(2x)

Step-by-step explanation:

sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.

The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.

so, we get,

However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.

Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

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Answer:

31 PTS

Step-by-step explanation:

Answer:

what's the problem!?......

angle CDT is the opposite angle of ADN

and the segment DF=FN, so AD= AN

and thats why angle FAN= angle FAD

here, Angle FAN =60,

therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree

and the opposite of ADN is CDT, and the opposite angles are equal.

Hope u got it.

Answer:

B) 3

Step-by-step explanation:

4+5+1/3=10/3=3.333~3

Answer:

B) 3

Step-by-step explanation:  

[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]

Now

[tex]\\ \sf\longmapsto x+\dfrac{1}{x}=12[/tex]

[tex]\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2[/tex]

[tex]\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144[/tex]

[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144[/tex]

[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142[/tex]

Answer:

122

Step-by-step explanation:

x+1/x = 12

x + 1 = 12x

x = 1/11

（1/11）² + 1 / （1/11）² = 1/121 +1 /1/121 = 122

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

Explanation:

At 95% confidence, the z critical value is roughly z = 1.960

The population standard deviation is given to be sigma = 3.7

The error is E = 2 since we want to be within 2 inches of the population mean mu

The min sample size needed is:

n = (z*sigma/E)^2

n = (1.960*3.7/2)^2

n = 13.147876

n = 14

We always round up to the nearest whole number to ensure that we clear the hurdle (otherwise, the sample is too small). It doesn't matter that we're closer to 13 than to 14.

Answer:

0

Step-by-step explanation:

for y= -2*(3^x), as x is greater, the slope is steeper, and since the two graphs don't intercept in the picture we can see, they won't ever intercept because the slop of y=-2x+3 stays the same. as x becomes greater the distance between the two graphs is larger

Answer: (x+4) ( x-4i)(x+4i)

Discussion:

Factor the polynomial:

x^3+4x^2+16x+64 =  (x +4 ) ( x^2 + 16)     (*)

Factor x^2 +1 6 over the complex numbers:

x^2 + 16 = (x -4i)(x+4i)                               (**)

Combing (*) and (**) gives the full factorization

(x+4) ( x-4i)(x+4i)

9514 1404 393

Answer:

   $40,615.20

Step-by-step explanation:

The amortization formula will tell you Michelle's monthly payment.

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . loan value P at interest rate r for t years

  A = $124,500(0.059/12)/(1 -(1 +0.059/12)^(-12·10)) ≈ $1375.96

__

The total of Michelle's 120 monthly payments is ...

  12 × $1375.96 = $165,115.20

This amount pays both principal and interest, so the amount of interest she pays is ...

  $165,115.20 -124,500 = $40,615.20

Michelle will pay $40,615.20 in interest over the course of the loan.

__

A calculator or spreadsheet can figure this quickly.

Answer:

[tex] \frac{2 \sqrt{7} + \sqrt{3}}{3 \sqrt{7} - \sqrt{3} } = \frac{2 \sqrt{7} + \sqrt{3}}{3 \sqrt{7} - \sqrt{3} } . \frac{3 \sqrt{7} + \sqrt{3} }{3 \sqrt{7} + \sqrt{3} } \\ \\ = \frac{(2 \sqrt{7} + 3)(3 \sqrt{7} + \sqrt{3}) }{(3 \sqrt{7} - 3)(3 \sqrt{7} + \sqrt{3} ) } \\ \\ = \frac{(42 + 2 \sqrt{21} + 9 \sqrt{21} + 3 \sqrt{21} )}{63 - 3} \\ \\ = \frac{42 + 2\sqrt{21} + 9 \sqrt{21} + 3 \sqrt{21} }{60} [/tex]

Answer:

9514 1404 393

Answer:

  1 11/49 ≈ 1.224 miles

Step-by-step explanation:

Let m represent the length of the morning walk. Then the length of the evening walk is 2.5m, and the total each day is m+2.5m = 3.5m.

The total for 7 days is ...

  7(3.5m) = 30

  m = 30/24.5 = 60/49 ≈ 1.224 . . . . miles

Mia's morning walks are 1 11/49 miles, about 1.224 miles.

Answer:

It will take Sophia 1 hour to run 6 miles.

And 1 1/2 hours for 9 miles.

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  8 km

Step-by-step explanation:

Let m represent the distance (in kilometers) Michelle has walked. Then Janet walked a distance of (m-2). These distances are at right angles, so the distance between them can be found using the Pythagorean theorem.

  m² +(m -2)² = 10²

  m² +m² -4m +4 = 100

  2m² -4m = 96 . . . . . . subtract 4, collect terms

  m² -2m +1 = 49 . . . . . divide by 2 and add 1

  (m -1)² = 7² . . . . . . .write as squares

  m -1 = 7 . . . . . . positive square root

  m = 8

Michelle walked 8 km.

After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

"It is a polynomial equation with degree two."

"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "

For given example,

We have been given a quadratic equation.

[tex]3x^{2} -12x-15=0[/tex]

First we divide above quadratic equation by 3,

[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex]                             ................(i)

Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]

[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]

Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),

[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]

Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

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Answer:

hello thereeeee

ans is 23.5

Step-by-step explanation:

so lets start

first of all remove decimal of divisor 1.1/25.85 multiplying by 10

11/258.5

now first multiply by 2

now we get 22 and subtract with 25 => 25-22 = 3

so left is

38

now 11*3 = 33

so now by 3

38-33= 5

bringing another 5 down

we get 55

now quotient is 23. something ( as we bought .5 down)

and now 11*5 = 55

so

23.5 is answer

Answer:

[tex]216\ km^2[/tex]

Step-by-step explanation:

1. Approach

The surface area of a three-dimensional figure is the two-dimensional distance around the figure.  The easiest way to find the surface area of a figure is to find the area of each of its facets, then add up the area to get the total surface area. The given pyramid is composed of four congruent triangles and a square. Find the area of one of the triangles, and then the area of the rectangle. Multiply the area of the triangle by four to account for the fact that there are four congruent triangles. Then add the area of the base to the result, the result attained is the surface area of the prism.

2. Find the area of the triangles

The formula to find the area of a triangle is the following:

[tex]A_t=\frac{b*h}{2}[/tex]

Where (b) represents the base and (h) represents the height of the triangle. Substitute the given values into the formula and solve for the answer.

[tex]A_t=\frac{b*h}{2}[/tex]

[tex]A_t=\frac{9*7.5}{2}[/tex]

[tex]A_t=\frac{67.5}{2}[/tex]

[tex]A_t=33.75[/tex]

3. Find the area of the rectangle

The formula to find the area of a rectangle is the following,

[tex]A_r=b*h[/tex]

Substitute the given values in and solve,

[tex]A_r=b*h[/tex]

[tex]A_r=9*9[/tex]

[tex]A_r=81[/tex]

4. Find the total surface area

Multiply the area of the triangle by four to account for the fact that there are four triangles. Then add its area to the area of the rectangle.

[tex]A_t+A_t+A_t+A_t+A_r=A[/tex]

[tex]4(A_t)+(A_r)=A[/tex]

[tex]4*33.75+81=A[/tex]

[tex]135+81=A[/tex]

[tex]216=A[/tex]

Answer:

a) 0

b) 2,3,4,5,6,7

c)3,4,6,7

Step-by-step explanation:

Answer:

[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystlye F(x) = x^2 - 2x + 4[/tex]

And we want to find F(b + 3).

We can substitute:

[tex]\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4[/tex]

Expand:

[tex]\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4[/tex]

Rearrange:

[tex]\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)[/tex]

Combine like terms. Hence:

[tex]\displaystyle = b^2 +4b + 7[/tex]

In conclusion:

[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]

Coordinates of point A is (-2 and 1)

Coordinates of point B is (1 and -1)

[tex] \begin{cases}\large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{(x_2 - x_1 ) \: + \:(y_2 - y_1 )} \\ \\ \large\bf\red{ \longrightarrow} \rm \:Distance \: = \:\sqrt{(1 - [ - 2]) ^{2} \: + \:( - 1 - 1)^{2} } \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{( - 3) ^{2} \: + \:( - 2) ^{2}} \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{6 \: + \: 4} \\ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \: \sqrt{10} \ \\ \ \\ \large\bf\red{ \longrightarrow} \rm \: Distance \: = \:3.1622 \: \: units \end{cases}[/tex]

Answer:

15 months old.

Step-by-step explanation:

Let m = months and h = height:

h = 1/3(m + 75) ⇔ h = 1/3m + 25

Let h = 30:

[tex]30=\frac{1}{3}m+25\\5=\frac{1}{3}m\\15=m[/tex]

Therefore, when Asia is 30 inches tall, she will be 15 months old.

Answer:

D

Step-by-step explanation:

0.0015

hope this helps

Answer:

C

Step-by-step explanation:

using the theorem of Pythagoras

x = sqrt * 10.2^2 - 9.6^2 *

using the calculator

x = 3.4 units

rounded to 1 decimal place

Answer:

100000

Step-by-step explanation:

Answer:

R35625

Step-by-step explanation:

(R30,000×.125×18/12)+R30000

=R35625

Answer:

It's 28 3/4

Step-by-step explanation:

Answer:

Answer is 19.5

Step-by-step explanation:

27-9+(12-5)÷4

27-9+6÷4   [BOD MAS Rule]

27-9+1.5

28.5-9

19.5

Answer:

990/23

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

23 × 43 = 989

Step 2

Add the answer from Step 1 to the numerator

989 + 1 = 990

Step 3

Write answer from Step 2 over the denominator

990/23

Answer:

Remainder is -53/8

Step-by-step explanation:

the divisor is (2x - 3):

make x the subject:

[tex]2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} [/tex]

substitute for x in the function:

[tex]f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} [/tex]

Answer:

750,. is answer

I hope it helps