prove sin^2 π/6 + cos^2 π/3 - tan^2 π/4 = -1/2​

Answer:

3000 students

Step-by-step explanation:

If 48% of the students are female, and there are 1440 female students, we can set up a percentage proportion, assuming x is the total amount of students.

[tex]\frac{1440}{x} = \frac{48}{100}[/tex]

We can use the cross products property to find the value of x.

[tex]1440\cdot100=144000\\\\144000\div48=3000[/tex]

Hope this helped!

Answer:

y=1 and x=2

Step-by-step explanation:

Add the two linear equation and you will have 2y=2, y=1. Plugging this in any equation, we have x=2

Answer:

The solution is (2,1)

Step-by-step explanation:

Set the two equations equal

y=3x-5 and y=-3x+7

3x-5 = -3x+7

Add 3x to each side

3x-5+3x = -3x+7+3x

6x-5 = 7

Add 5 to each side

6x-5+5 = 7+5

6x = 12

Divide by 6

6x/6 = 12/6

x=2

Now find y

y =3x-5

y=3(2)-5

y = 6-5

y=1

The solution is (2,1)

Answer:

Ross = 15 hours

Russel = 40 hours

Step-by-step explanation:

Let Ross have used their sprinklers for x hours

Let Russell  have used their sprinklers for y hours

Together they used 55 hours

x+y = 55 hours

The output of Ross is 35 liters per hour and Russell is 30 liters per hour for a total of 1725

35x + 30y = 1725

Multiply the first equation by -30

-30(x+y=55)

-30x -30y = -1650

Add this to the second equation to eliminate y

-30x -30y = -1650

35x + 30y = 1725

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

5x =75

Divide each side by 5

x = 15

Now find y

x+y = 55

y = 55-15

y = 40

Answer: 2.31

Step-by-step explanation:

Answer:

see below (I hope this makes sense!)

Step-by-step explanation:

Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x  =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.

Let daughter be x years old. Then, Shyam is (x + 28) years old.

So,

x(x + 28) = 204

=> x² + 28x = 204

=> x² + 28x - 204 = 0

=> x² - 6x + 34x - 204 = 0

=> x(x-6) + 34(x-6)

=> (x - 6) (x + 34) = 0

=> x - 6 = 0 or x + 34 = 0

=> x = 6 or x = -34

Since any age cannot be negative, daughter's age is 6 years old.

Step-by-step explanation:

We need to say that [tex]9^{3/4}[/tex] is equivalent to what.

We know that, (3)² = 9

So,

[tex]9^{3/4}=((3)^2)^{3/4}\\\\=3^{3/2}[/tex]

We can write [tex]3^{3/2} =3\times 3^{1/2}[/tex]

And [tex]3^{1/2}=\sqrt{3}[/tex]

So,

[tex]3\times 3^{1/2}=3\sqrt{3}[/tex]

So, [tex]9^{3/4}[/tex] is equivalent to [tex]3\sqrt{3}[/tex].

Hence, this is the required solution.

Answer:

if 5 people =1 hour. which is 60 minutes.

so 8people.52 minutes ...it wont take hours .since an hour is 60 min.

Answer:

Step-by-step explanation:

Let's solve:

[tex] \mathsf {people \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: time( \: in \: minutes) }[/tex]

[tex] \mathsf{5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 hour = 60 minutes}[/tex]

[tex] \mathsf{8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x}[/tex]

Here, Let 8 people take x minutes to complete the work.

Since, the number of people and their working minutes are indirect proportional. So,

Here, the ratio of people = 5 : 8

The ratio of minutes = 60 : x

So,

[tex] \mathsf{ \frac{5}{8} = \frac{x}{60} }[/tex]

Apply cross product property

⇒[tex] \mathsf{8x = 60 \times 5}[/tex]

Multiply the numbers

⇒[tex] \mathsf{8x = 300}[/tex]

Divide both sides of the equation by 8

⇒[tex] \mathsf {\frac{8x}{8} = \frac{300}{8} }[/tex]

Calculate

⇒[tex] \mathsf{x = 37.5 \: minutes}[/tex]

Hope I helped!

Best regards!

Answer:

100%+15% = 115%

proportionally:

x - 100%

161 - 115%

x = (161 * 100%) / 115% = 140

Answer:

[tex]\Large\boxed{140}[/tex]

Step-by-step explanation:

[tex]\sf Let \ x \ be \ the \ number.[/tex]

[tex]\sf x \ increased \ by \ 15\% \ is \ 161.[/tex]

[tex]x \times (1+15\%)=161[/tex]

[tex]x \times (1+0.15)=161[/tex]

[tex]x \times (1.15)=161[/tex]

[tex]\displaystyle \frac{x \times (1.15)}{1.15}=\frac{161}{1.15}[/tex]

[tex]x=140[/tex]

Answer:

1)  502.65"

2) 367.57 yd

3)  141.37'  

4) 471.24'

Step-by-step explanation:

Formula: volume of a cylinder = πr²h

1) v= πr²h                     2) v= πr²h                      

  v= π x 4² x 10                v= π x 3² x 13

  v=  502.65"                   v= 367.57 yd

3) v= πr²h                       4) v= πr²h

    v=  π x 3² x 5                 v= π x 5² x 6

     v= 141.37'                       v= 471.24'

I hope this helped

Answer:

1. 502.5 [tex]in^{3}[/tex]

2. 367.38 [tex]yd^{3}[/tex]

3. 141.3 [tex]cm^{3}[/tex]

4. 471 [tex]cm^{3}[/tex]

Step-by-step explanation:

The solution to finding the volume of a cylinder is: [tex]\pi r^{2} h[/tex].

They give us a diameter but no radius. So, we just need to divide the diameter, 8, by two. That leaves us with a radius of 4.

We can also see that the height of the first cylinder is 10. That gives us all our information to find the volume!

3.14 · [tex]4^{2}[/tex] · 10 = 502.5

So, the volume of the first cylinder is 502.5[tex]in^{3}[/tex]

This, hopefully explains how to find the volume of the rest of the cylinders!! :)

Hope this helps!! <3

Answer:

57 units^2

Step-by-step explanation:

First find the area of the triangle on the left

ABC

It has a base AC which is  9 units and a height of 3 units

A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5

Then find the area of the triangle on the right

DE

It has a base AC which is  6 units and a height of 1 units

A = 1/2 bh = 1/2 ( 6) *1  = 3

Then find the area of the triangle on the top

It has a base AC which is  3 units and a height of 3 units

A = 1/2 bh = 1/2 ( 3) *3  = 9/2 = 4.5

Then find the area of the rectangular region

A = lw = 6*6 = 36

Add them together

13.5+3+4.5+36 =57 units^2

Answer:

Total Area = 57 sq. units

Step-by-step explanation:

will make it simple and short

Total Area = A1 + A2 + A3

A1 = (7 + 6) * 6/2 = 39 sq. units  (area of a trapezoid)

A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)

A3 = 1/2 (3 * 3) = 4.5 sq. units  (area of a triangle)

Total Area = 39 + 13.5 + 4.5 = 57 sq. units

Answer:

1) La opción correcta es;

c) 0

2) La opción correcta es;

c) x = 2

Step-by-step explanation:

1) La forma general de una ecuación cuadrática se puede escribir en la forma;

a · x² + b · x + c = 0

Dónde;

a, y b son los coeficientes de x², x y c es el término constante

Por tanto, para que exista un polinomio de 2º grado es necesario que el coeficiente a sea diferente de 0

De lo que tenemos;

(0) × x² + b · x + c = 0, lo que da;

(0) × x² + b · x + c = b · x + c = 0 que es una ecuación lineal o un polinomio de primer grado

Por tanto, la opción correcta es c) 0

2)

La ecuación dada se presenta como sigue;

f (x) = x² - 5 · x + 6 = 0

Usando el método de prueba y error, tenemos;

Cuando x = 0

f (0) = 0² - 5 · (0) + 6 = 6 que no es igual a 0 y, por lo tanto, no es una solución

Cuando x = 1

f (1) = (1) ² - 5 · (1) + 6 = 1 que no es igual a 0 y por lo tanto, no es una solución

Cuando x = 2

f (2) = (2) ² - 5 · (2) + 6 = 0 que es igual a 0 y por lo tanto, es una solución

Cuando x = -2

f (1) = (-2) ² - 5 × (-2) + 6 = 20 que no es igual a 0 y por lo tanto, no es una solución

Por tanto, la opción correcta es c) x = 2

Answer:

54 inches

Step-by-step explanation:

First, let's convert the measurements into a common measurement.

Since inch is the smallest measurement here, let's use that.

Ella's pet snake is 42 inches long.

Roya's pet snake is 8 feet long. There are 12 inches in one foot. Therefore, 8 feet would mean 12 times 8 or 96 inches.

Therefore, Roya's snake is 96 inches long.

To find out how many inches longer is Roya's snake, subtract:

96 - 42 = 54.

Therefore, Roya's snake is 54 inches longer than Ella's.

Answer:

because of its bark

Step-by-step explanation:

the answers have corresponding letters so answer the questions and put the letter next to the question above the answer

some of the answers are repeated

Answer:

51

Step-by-step explanation:

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

The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.

--------

tan(angle) = opposite/adjacent

tan(theta) = AC/BC

tan(theta) = 12.3/8.4

theta = arctan(12.3/8.4)

theta = 55.6697828044967

theta = 55.7 degrees approximately

--------

arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]

make sure your calculator is in degree mode

Answer:

Parallel: AC and DB, BA and CD

Perpendicular: AC and CD, DB and CD, DB and BA, BA and AC

Neither: None

Step-by-step explanation:

Step 1: Find Slopes

Let's first find the slopes of each side of the rectangle, as that will helps us determine which sides are parallel, perpendicular, or neither.

Recall that the formula for finding the slope between two points is [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the two points. To avoid confusion, I will be taking the first point I list as [tex](x_1,y_1)[/tex] and the second point as [tex](x_2,y_2)[/tex].

Slope of [tex]BA[/tex]:

[tex]\frac{-7-(-3)}{-1-(-4)}\\=\frac{-7+3}{-1+4} \\= -\frac{4}{3}[/tex]

Slope of [tex]AC[/tex]:

[tex]\frac{-4-(-7)}{3-(-1)} \\=\frac{-4+7}{3+1} \\=\frac{3}{4}[/tex]

Slope of [tex]CD[/tex]:

[tex]\frac{0-(-4)}{0-3} \\=\frac{4}{-3} \\=-\frac{4}{3}[/tex]

Slope of [tex]DB[/tex]:

[tex]\frac{-3-0}{-4-0} \\=\frac{-3}{-4} \\=\frac{3}{4}[/tex]

Step 2: Determine which sides are parallel, perpendicular, or neither

Now that we found the slopes of the sides, we can determine which sides are parallel, perpendicular, or neither.

Recall that parallel lines have the same slope. [tex]\bf AC[/tex] and [tex]\bf DB[/tex], along with [tex]\bf BA[/tex]and [tex]\bf CD[/tex], have the same slope, so they are parallel. No other pair of sides has the same slope, so these are our only parallel pairs.

For two lines to be perpendicular, the product of their slopes must be [tex]-1[/tex]. [tex]\bf AC[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf CD[/tex], [tex]\bf DB[/tex] and [tex]\bf BA[/tex], and [tex]\bf BA[/tex] and [tex]\bf AC[/tex] [tex]\bf[/tex]meet that criteria, so they are perpendicular. No other pair of sides meets the criteria, so these are our only perpendicular pairs. Hope this helps!

Answer:

Does the answer help you?

Answer:

[tex] (x+4)^2=4[/tex]

Step-by-step explanation:

[tex]x^2+8x+12=0\\

\implies (x^2+8x+16)+12=16\\

\implies (x+4)^2=16-12\\

\implies \boxed{(x+4)^2=4}[/tex]

Answer:

(x +4)^2 = 4

Step-by-step explanation:

if we add 4 to the expression x^2 + 8x + 12 we will have a perfect square which is shown as (x +4)^2

so (x +4)^2 = 4 is equivalent to the expression x^2 + 8x + 12

Step-by-step explanation:

526 133 3821

P: 12345

j _o _I _n g _I _r l

o. n z-oo-o-m

Answer:

C

Step-by-step explanation:

sqrt(a^7) = sqrt(a^6 * a)

Answer:

Stick 2: [tex] \frac{1}{2} [/tex]

Stick 3: [tex] \frac{4}{10} [/tex]

Step-by-step explanation:

To determine which of the lengths are less than ⅗ meters, you would compare each given length with ⅗ meters.

Stick 1: Comparing ⁹/10 and ⅗

Find The common denominator of both fractions. 10 is the common denominator. Multiply the numerator and denominator of ⅗ by 2 to create a fraction equivalent to ⁹/10.

Thus,

[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]

Compare the numerator of [tex] \frac{9}{10} [/tex] and [tex] \frac{6}{10} [/tex].

9 is greater than 6. This means [tex] \frac{9}{10} [/tex] > [tex] \frac{6}{10} [/tex].

Therefore, [tex] \frac{9}{10} [/tex] > [tex] \frac{3}{5} [/tex]

Stick 2: comparing ½ and ⅗

Common denominator = 10

Make both fractions equivalent to each other as follows,

[tex] \frac{1*5}{2*5} = \frac{5}{10} [/tex]

[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]

5 < 6. This means, [tex] \frac{5}{10} [/tex] < [tex] \frac{6}{10} [/tex].

Therefore, [tex] \frac{1}{2} [/tex] < [tex] \frac{3}{5} [/tex]

Stick 3: comparing ⁴/10 and ⅗

Common denominator = 10

Make the fractions equivalent as follows,

[tex] \frac{4*1}{10*1} = \frac{4}{10} [/tex]

[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]

4 < 6. This means, [tex] \frac{4}{10} [/tex] < [tex] \frac{6}{10} [/tex].

Therefore, [tex] \frac{4}{10} [/tex] < [tex] \frac{3}{5} [/tex]

Stick 4: comparing ⅘ and ⅗

Common denominator = 5

Since both denominators are already the same, both fractions are equivalent. Comparing their numerator, 4 > 3. Therefore, ⅘ > ⅗.

Answer:

10x - 15

Step-by-step explanation:

5(2x-3) = 10x - 15

Answer:

option 2 with radius of 1.4 in, and height of 1.2 in.

Step-by-step explanation:

If two cylinders are similar, the ratio of one cylinder's radius to its height must be the same as that of the other.

To know which cylinder is similar to the given cylinder with radius 2.8 in and height of 2.4 in, find the ratio, and compare with the ratio of the options provided. The option with the same ratio, is the cylinder that is similar.

This,

The given cylinder => radius : height = [tex] \frac{2.8}{2.4} = \frac{0.7}{0.6} = \frac{7}{6} [/tex]

First option:

Radius : height = [tex] \frac{1.8}{1.4} = \frac{0.9}{0.7} = \frac{9}{7} [/tex]

Second option:

Radius : height = [tex] \frac{1.4}{1.2} = \frac{0.7}{0.6} = \frac{7}{6} [/tex]

Third option:

Radius : height = [tex]\frac{5.6}{4.2} = \frac{0.8}{0.6} = \frac{0.4}{0.3} = \frac{4}{3}[/tex]

Fourth option:

Radius : height = [tex] \frac{2.4}{2.8} = \frac{0.6}{0.7} = \frac{6}{7} [/tex]

The correct option with the cylinder that is similar with the given cylinder is option 2 with radius of 1.4 in, and height of 1.2 in.

Answer:

C

Step-by-step explanation:

In the equation y = -x - 4, the gradient is -1.

While in the second equation,

5x + 5y = 20

y = -x + 4

So the gradient is -1 too

Both sides are not perpendicular to each other because if you apply the formula, m1m2 = -1, and if substitute both gradient, (-1)(-1) = 1 ≠ -1

Therefore, no they are not perpendicular but parallel instead.

Answer: C

Step-by-step explanation:

Look above fool

Answer: B) different y intercepts; same end behavior

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

Explanation:

The graph shows the y intercept is 4 as this is where the green curve crosses the vertical y axis.

The y intercept of g(x) is 6 which can be found by plugging x = 0 into the g(x) function

g(x) = 4(1/4)^x + 2

g(0) = 4(1/4)^0 + 2

g(0) = 6

So we can see the y intercepts are different.

----------

However, the end behaviors are the same for each function. The left side of f(x) goes up forever to positive infinity. The same is true for g(x). You could use a graphing calculator or a table to see this. As x heads to negative infinity, y goes to positive infinity.

In terms of symbols, [tex]x \to -\infty, y \to \infty[/tex]

----------

For the right side of f(x), it slowly approaches the horizontal asymptote y = 2. It never actually reaches this y value. The same happens with g(x). The portion 4(1/4)^x gets smaller but never gets to 0 so overall 4(1/4)^x+2 gets closer to 2. We can say that as x approaches infinity, y approaches 2.

In terms of symbols, [tex]x \to \infty, y \to 2[/tex]

Answer:

The right option is definitely the first one

Hope this helps

Answer:

x < -6

Step-by-step explanation:

-2x - 4 > 8

-2x > 12

x < -6, you have to flip the inequality when you multiply or divide by a negative

Answer:

a

Step-by-step explanation:

Answer:

A 0.6 0.9 1.2 1.5 1.8

B 3/8 5/8 7/8 9/8 11/8

C -7 -5 -3 -2 -1

D 1, 1 1/3, 1 2/3, 2, 2 1/3

E 0.61 0.72 0.83 0.94 1.05

Step-by-step explanation:

Answer:

A.  x  x   1.2  1.5  1.8

B.  3/8   x   x  x  1 2/8

C.  x  x  -3  -2  -1

D.   0  x  x  x  5 1/3

E.   x  x   0.83  0.94  1.05

Step-by-step explanation:

hope it helped

The answer is Or + 12

Answer:

2n+2

Step-by-step explanation:

the common difference is 4,6,8

again the common difference of 4,6,8 is 2,2

hence its common difference is 2

now, nth term,=a+(n-1) *d

4+(n-1)*2

4+2n-2

2n+2