ACTIVITY 1. Evaluate the following (a) sin60° (b) tan 34° (c)cos 124°​

Answer:

40.4502 billion dollars

51.3432 billion dollars

Step-by-step explanation:

Given :

Total amount spent in billions in pets x years after year, 2000 ;

P(x)=2.1786x + 25.2

Amount spent in 2007 ;

x = 2007 - 2000 = 7 years

Put x = 7 in the equation :

P(7)=2.1786(7) + 25.2 = 40.4502

Amount spent in 2012 :

x = 2012 - 2000 = 12 years

Put x = 12 in the equation :

P(12) = 2.1786(12) + 25.2 = 51.3432

The amount spent in billik dollars on pets in :

2007 = $404502 billion

2012 = $51.3432 billion

Answer:

The answer would be -7x^2 - 14!

Step-by-step explanation:

We can remove the parentheses by distributing the subtraction sign! -2x^2 + x + 1 - x^2 + x - 7 - 4x^2 - 2x - 8. Simplifying this gives us -7x^2 - 14. Hope this helped! :)

Answer:

m<1 = 55°

m<2 = 125°

m<3 = 55°

m<5 = 55°

m<6 = 125°

m<7 = 55°

m<8 = 125°

Step-by-step explanation:

m<4 = 125° (given)

✔️m<8 = m<4 (alternate exterior angles are congruent)

m<8 = 125° (substitution)

✔️m<1 = 180° - m<8 (supplementary angles/linear pair)

m<1 = 180° - 125° (substitution)

m<1 = 55°

✔️m<2 = m<8 (vertical angles are congruent)

m<2 = 125° (substitution)

✔️m<7 = m<1 (vertical angles are congruent)

m<7 = 55° (Substitution)

✔️m<3 = m<7 (alternate interior angles are congruent)

m<3 = 55° (substitution)

✔️m<5 = m<3 (vertical angles are congruent)

m<5 = 55°

✔️m<6 = m<4 (vertical angles)

m<6 = 125°

Answer:

Step-by-step explanation:

The current world population is 7.9 billion as of July 2021 according to the most recent United Nations estimates elaborated by Worldometer. The term "World Population" refers to the human population (the total number of humans currently living) of the world.

Answer:

El cuadrado de la suma de dos números es igual a (a + b) ² = a² + 2ab + b²Un producto notable: es una expresión matemática que conocemos ya el resultado, a pesar de la operación ser sencilla tenemos

Step-by-step explanation:

Answer:

1250000cm

Step-by-step explanation:

1:500000

1x2.5 : 500000x2.5

2.5:1250000

Answer:

multiply the numerator together and denominator together

Answer:

shifting to the right is just an east/west movement

not a north/south

an east west movement is on the "X" ais, a north/south is on the "Y"

axis...

so just ADD 10 units to all the "X" values

a" = (9,-3)

b"=  (6,-1)

c"=  (4,-4)

Step-by-step explanation:

Answer:

1/2 in fractions if you nees it in decimal just transfer

Answer:

answers in the explanation cz I'm too lazy to type :(

not entirely sure tho

Step-by-step explanation:

w²+2w-42=0

*quadratic formula*

w= -1+ square root 43 m

or w= -1- square root 43 m

then since the length is 2m more than w

add 2 to both answers

l= 1+ square root 43 m

l=1- square root 43 m

9514 1404 393

Answer:

Step-by-step explanation:

Given:

  a rectangular patio of width w meters, length w+2 meters, and area 42 m²

Find:

  width and length

Solution:

The area is ...

  A = LW

  42 = w(w +2)

  43 = w² +2w +1 . . . . . . add 1 to complete the square

  √43 = w+1

  w = √43 -1 ≈ 5.557 . . . meters

  l = w+2 = √43 +1 ≈ 7.557 . . . meters

The width and length of the patio are 5.557 m and 7.557 m, respectively.

Answer:

The numbers are 18 and 25

Step-by-step explanation:

Given

[tex]\bar x_1 = 14[/tex]     [tex]n_1 = 17[/tex]

[tex]\bar x_2 = 13[/tex]     [tex]n_2 = 15[/tex]

[tex]a - b = 7[/tex] --- the difference of the 2 numbers

Required

Find a and b

We have:

[tex]\bar x = \frac{\sum x}{n}[/tex] -- mean formula

So, we have:

[tex]\bar x_1 = \frac{\sum x_1}{n_1}[/tex]

[tex]14 = \frac{\sum x_1}{17}[/tex]

Cross multiply

[tex]\sum x_1 = 14 * 17[/tex]

[tex]\sum x_1 = 238[/tex]

When the two numbers are removed, we have:

[tex]\bar x_2 = \frac{\sum x_2}{n_2}[/tex]

[tex]13 = \frac{\sum x_2}{15}[/tex]

Cross multiply

[tex]\sum x_2 = 13 * 15[/tex]

[tex]\sum x_2 = 195[/tex]

The two numbers that were removed are:

[tex]a + b = \sum x_1 - \sum x_2[/tex]

[tex]a + b = 238 - 195[/tex]

[tex]a + b = 43[/tex]

Make a the subject

[tex]a= 43 - b[/tex]

We have:

[tex]a - b = 7[/tex]

Substitute [tex]a= 43 - b[/tex]

[tex]43 - b - b = 7[/tex]

[tex]43 - 2b = 7[/tex]

Collect like terms

[tex]2b = 43 - 7[/tex]

[tex]2b = 36[/tex]

Divide by 2

[tex]b = 18[/tex]

Substitute [tex]b = 18[/tex] in [tex]a= 43 - b[/tex]

[tex]a = 43 - 18[/tex]

[tex]a = 25[/tex]

no the square root of 113 is rounded to 56x2

Answer:

1 length ityoughkdds hshlkb

Let it be x

[tex]\\ \sf\longmapsto \dfrac{x}{10}=\dfrac{3}{6}[/tex]

[tex]\\ \sf\longmapsto 6x=10(3)[/tex]

[tex]\\ \sf\longmapsto 6x=30[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{30}{6}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

The maximum number of minutes to keep the cost at $50 or less is 110 minutes

Step-by-step explanation:

Given

[tex]C(x) = 30[/tex] ---- [tex]x < 60[/tex]

[tex]C(x) = 30 + 0.40(x - 60)[/tex] --- [tex]x \ge 60[/tex]

Required

[tex]C(x) = 50[/tex] ---- find x

We have:

[tex]C(x) = 30 + 0.40(x - 60)[/tex]

Substitute 50 for C(x)

[tex]50 = 30 + 0.40(x - 60)[/tex]

Subtract 30 from both sides

[tex]20 = 0.40(x - 60)[/tex]

Divide both sides by 0.40

[tex]50 = x - 60[/tex]

Add 60 to both sides

[tex]110 = x[/tex]

[tex]x =110[/tex]

9514 1404 393

Answer:

  ₱6400

Step-by-step explanation:

Let 'b' represent the amount invested in scheme B. Then 13900-b is the amount invested in scheme A. The total interest for 2 years is then ...

  14%(13900-b)(2) +11%(b)(2) = 3508

  1946 -0.03b = 1754 . . . . . . divide by 2, simplify

  -0.03b = -192 . . . . . . . . . subtract 1946

  b = 6400 . . . . . . . . . . . divide by -0.03

The amount invested in scheme B was ₱6400.

Answer:

f(g(x)) = 9x^2 + 15x - 6

Step-by-step explanation:

We are using function g(x) = 3x - 1 as the input to function f(x) = x^2 + 7x.

Starting with f(x) = x^2 + 7x, substitute g(x) for x on the left side and likewise substitute x^2 + 7x for each x on the right side.  We obtain:

f(g(x)) = (3x - 1)^2 + 7(3x - 1).

If we multiply this out, we get:

f(g(x)) = 9x^2 - 6x + 1 + 21x - 7, or

f(g(x)) = 9x^2 + 15x - 6

Answer:

Not a function

Domain: {3,4}

Range: {4,5}

Step-by-step explanation:

A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function

For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function

Now let's find the domain and range.

Domain is the set of x values in a relation.

The x values of the given relation are 3 and 4 so the domain is {3,4}

The range is the set of y values in a relation

The y value of the given relation include 4 and 5

So the range would be {4,5}

Notes:

The values of x and y should be written from least to greatest when writing them out as domain and range.

They should be written inside of brackets

Do not repeat numbers when writing the domain and range

9514 1404 393

Answer:

  (e) f′(x)=2xg(x)+x²g′(x)

Step-by-step explanation:

The product rule applies.

  (uv)' = u'v +uv'

__

Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).

  f(x) = x²·g(x)

  f'(x) = 2x·g(x) +x²·g'(x)

Answer:

x = 7[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Pytago:

[tex]7^2 + 7^2 = x^2\\x = \sqrt{7^2 + 7^2} \\x = 7\sqrt{2}[/tex]

Step-by-step explanation:

In a right triangle, you can find the leg of the triangle by using the Pythagorean theorem.

[tex]a^2+b^2=c^2[/tex]

In this case, we have [tex]7^2+7^2=c^2[/tex], or

[tex]c^2=98[/tex]

[tex]\sqrt{98}[/tex]≅[tex]9.9[/tex]

Answer:

So, remember that:

cos(x) > 0   for  -pi/2 < x < pi/2

cos(x) < 0 for  pi/2 < x < (3/2)*pi

and

sin(x) > 0 for 0 < x < pi

sin(x) < 0 for -pi < x <0  or  pi < x < 2pi

Also, we have the periodicty of the sine and cocine equations, such that:

sin(x) = sin(x + 2pi)

cos(x) = cos(x + 2pi)

Now let's solve the problem:

[tex]sin(\frac{13*\pi}{36} )[/tex]

here we have:

x = (13/36)π

This is larger than zero and smaller than π:

0 < (13/36)π < π

then:

[tex]sin(\frac{13*\pi}{36} )[/tex]

Is positive.

The next one is:

[tex]cos(\frac{7*\pi}{12} )[/tex]

Here we have x = (7/12)*pi

notice that:

7/12 > 1/2

Then:

(7/12)*π > (1/2)*π

Then:

[tex]cos(\frac{7*\pi}{12} )[/tex]

is negative.

next one:

[tex]sin(\frac{47*\pi}{36} )[/tex]

here:

x = (47/36)*π

here we have (47/36) > 1

then:

(47/36)*π > π

then:

[tex]sin(\frac{47*\pi}{36} )[/tex]

is negative.

the next one is:

[tex]cos(\frac{17*\pi}{10} )[/tex]

Here we have x = (17/10)*π

if we subtract 2*π (because of the periodicity) we get:

(17/10)*π - 2*π

(17/10)*π - (20/10)*π

(-3/10)*π

this is in the range where the cosine function is positive, thus:

[tex]cos(\frac{17*\pi}{10} )[/tex]

is positive.

the next one is:

[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]

here we have:

x = (41/36)*π

Notice that both functions, sine and cosine are negatives for that value, then we have the quotient of two negative values, so:

[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]

is positive.

The final one is:

[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]

Here:

x = (5/9)*π

The sin function is positive with this x value, while the cosine function is negative, thus:

[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]

Is negative.

Answer:

D Replace on equation with sum /difference of both equations

The systems are still the same

Step-by-step explanation:

5x + y = 3

4x - 7y = 8

Subtract the second equation from the first

5x + y = 3

-(4x - 7y = 8)

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

x    +8y = -5

The second equation in system B is the first equation in system a minus the second equation in system A

We added the same thing to each side of the equation so the the system is still the same

Answer and Step-by-step explanation:

The random point on the line is between A and B, and to find the probability of the A, let's find the probability that is distance A and more than times the distance B. Let's have the probability that A and distance to A are more than the distance to B. The distance C is the interval of A to B. If she is closer and landed in the interval, the equation can be (A, A+B/2). This is the interval length, and the probability is 0.5. If the distance to A is more than the distance B, then the interval is as follows in the given equation (A + 3B/2, B ). The probability of the given interval is 0.25.

Answer:

[tex](a)\ V = \{(N,30),(R,37),(S,17)\}[/tex]

[tex](b)[/tex]

[tex]Domain = \{N,R,S\}[/tex]

[tex]Range = \{37,30,17\}[/tex]

Step-by-step explanation:

Given

[tex]V(R) = 37,\ V(N) = 30,\ V(S) = 17[/tex]

Solving (a): Set of ordered pair

A function y = f(x) is represented as (x,y)

So, the ordered pair of V is:

[tex]V = \{(R,37),(N,30),(S,17)\}[/tex]

Order the alphabets in increasing order

[tex]V = \{(N,30),(R,37),(S,17)\}[/tex]

Solving (b): The domain and the range

In a function [tex]\{(x_1,y_1),...,(x_n,y_n)\}[/tex]

The domain and the range are represented as:

[tex]Domain = \{x_1,x_2....x_n\}[/tex]

[tex]Range = \{y_1,y_2....y_n\}[/tex]

So, we have:

[tex]Domain = \{N,R,S\}[/tex]

[tex]Range = \{37,30,17\}[/tex]

Step-by-step explanation:

Ru Tu yulyryosuyyyhlsgjpcbmb kvjvlcykxnlvdlbvhck

chgkbhlxyovk m.

chchhlzixhvkh

Let the number be x

ATQ

[tex]\\ \sf\twoheadrightarrow 6x-18=96[/tex]

[tex]\\ \sf\twoheadrightarrow 6x=96+18[/tex]

[tex]\\ \sf\twoheadrightarrow 6x=112[/tex]

[tex]\\ \sf\twoheadrightarrow x=\dfrac{112}{6}[/tex]

[tex]\\ \sf\twoheadrightarrow x=7[/tex]