Step by step solution

Answer:

[tex]\frac{wx}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{7wxy}{35y}[/tex]

Cancel y on numerator/ denominator and 7/ 35 by 7, leaving

[tex]\frac{xx}{5}[/tex]

Answer:

Solution given:

Sin[tex]\theta_{1}=\frac{1}{4}[/tex]

[tex]\frac{opposite}{hypotenuse}=\frac{1}{4}[/tex]

equating corresponding value

opposite=1

hypotenuse=4

adjacent=x

By using Pythagoras law

hypotenuse²=opposite²+adjacent²

4²=1²+x²

16=1+x²

x²=16-1

x=[tex]\sqrt{15}[/tex]

In II quadrant

Cos angle is negative

Cos[tex]\theta_{1}=\frac{-adjacent}{hypotenuse}[/tex]

Answer:

[tex]\displaystyle \cos ( \theta _{1} ) = - \frac{ \sqrt{15}}{ 4 }[/tex]

Step-by-step explanation:

on a unit circle there're 4 Quadrant. on Q:I sin and cos both are positive,on Q:II cos is negative and sin positive, on Q:III both sin and cos are negative and on Q:IV cos is positive and sin negative.

actually a unit circle is a coordinate plane but

it'll be required later

well to solve the problem we can consider Pythagorean theorem which states that the square of sin and cos is equal to 1. therefore,

[tex] \displaystyle \sin ^{2} ( \theta) + \cos ^{2} ( \theta) = 1[/tex]

[tex] \rm \displaystyle \implies \boxed{\cos ^{} ( \theta) = \sqrt{1 - \sin ^{2} ( \theta) }}[/tex]

in this case,

Thus substitute:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \left( \frac{1}{4} \right) ^{2} }[/tex]

simplify square:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \frac{1}{16} }[/tex]

simplify substraction:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{16 - 1}{16} }[/tex]

simplify numerator:

[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{15}{16} }[/tex]

recall redical rule:

[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ \sqrt {16} }[/tex]

simplify square root:

[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ 4 }[/tex]

since cos is negative on Q:II hence,

[tex]\displaystyle \cos ( \theta _{1} ) = \boxed{- \frac{ \sqrt{15}}{ 4 }}[/tex]

and we're done!

Answer:

50.24

Step-by-step explanation:

A = Area

Radius = 4 (The radius is half of the diameter

Diameter = 8

Pie = 3.14

A = (pie)r^2

A = (3.14)4^2

A = (3.14)16

A = 50.24

The uppercase letters are the angles, while the lowercase letters are the sides. We have side 'a' opposite angle A, side b opposite angle B, side c opposite angle C.

We have this given info:

Let's use the law of sines to find angle B

sin(B)/b = sin(A)/a

sin(B)/25.5 = sin(25)/13.2

sin(B) = 25.5*sin(25)/13.2

sin(B) = 0.81642164

B = arcsin(0.81642164) or B = 180 - arcsin(0.81642164)

B = 54.72817392 or B = 180 - 54.72817392

B = 54.72817392 or B = 125.27182608

When rounded to the nearest whole degree, we get B = 55 or B = 125.

However, I'll use the slightly more accurate values of B for the next two sections.

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

Let's consider the case that B = 54.72817392

This would have to mean

A+B+C = 180

C = 180-A-B

C = 180-25-54.72817392

C = 100.27182608  which rounds to C = 100

Through the law of sines we can say

c/sin(C) = a/sin(A)

c = sin(C)*a/sin(A)

c = sin(100.2718 2608)*13.2/sin(25)

c = 30.73327084 which rounds to c = 30.7

One solution is

A = 25, B = 55, C = 100

a = 13.2, b = 25.5, c = 30.7

As you can probably guess, the phrasing "solve the triangle" means find all sides and angle measures.

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

Now we'll consider the case that B = 125.27182608

We follow the same steps as the previous section

A+B+C = 180

C = 180-A-B

C = 180-25-125.27182608

C = 29.72817392 which rounds to C = 30

and

c/sin(C) = a/sin(A)

c = sin(C)*a/sin(A)

c = sin(29.72817392)*13.2/sin(25)

c = 15.48842618 which rounds to c = 15.5

The other solution is

A = 25, B = 125, C = 30

a = 13.2, b = 25.5, c = 15.5

Check out the diagrams below.

Answer:

56.52 mm

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *

C = 2 * 3.14 * 9

C = 56.52

Answer:

[tex]56.52\text{ mm}[/tex]

Step-by-step explanation:

The circumference of a circle with radius [tex]r[/tex] is given by [tex]A=2r\pi[/tex].

We're given a radius of 9 mm and told to use [tex]\pi=3.14[/tex]. Substituting these values, we get:

[tex]A=2(9)(3.14),\\A=\boxed{56.52\text{ mm}}[/tex]

Answer:

I know but I will not tell you have to do by self

Answer:

Step-by-step explanation:

Table I

Given function is,

f(x) = [tex]b^x[/tex]

From the table attached,

For x = 0.827, value of function f(0.827) = 5,

f(0.827) = [tex]b^{0.827}[/tex]

Therefore, [tex]b^{0.827}=5[/tex]

[tex]\text{log}(b^{0.827})=\text{log}(5)[/tex]

0.827[log(b)] = log(5)

log(b) = 0.8452

b = [tex]10^{0.8452}[/tex]

b = 7

Therefore, function 'f' will be,

f(x) = [tex]7^x[/tex]

For f(x) = 9,

9 = [tex]7^x[/tex]

log(9) = log([tex]7^x[/tex])

log(9) = x[log(7)]

x = 1.129

Table II

Given function is g(x) = [tex]\text{log}_b(x)[/tex]

From the given table,

For x = 7, g(x) = 1

1 = [tex]\text{log}_b(7)[/tex]

[tex]b^1=7[/tex]

b = 7

Therefore, the function 'g' will be,

g(x) = [tex]\text{log}_7(x)[/tex]

For g(x) = 1.318

1.318 = [tex]\text{log}_7(x)[/tex]

[tex]x=7^{1.318}[/tex]

[tex]x=12.9968[/tex]

[tex]x=13.997[/tex]

Answer:

i hope it will help

Step-by-step explanation:

I did not get the equation so I solve it with two methods

Answer:

9.8 cm

Step-by-step explanation:

Volume of a cylinder can be gotten with this formula

V=πr2h

h = height of the oil.

We were told that 3 litres of oil was removed, then, there is a falling in the level of oil by 10 cm, hence the height of the oil is now

h° =( h) - (0.1)

Then the new volume can be calculated as

V°= V - (3×10^-3)

But

volume= (π r2h°)

Then substitute we have

πr2h - 0.003 = π r2 (h-0.1)

If we open the bracket we have

0.003 = (πr2 ×0.1)

πr2=0.003/0.1

Then r=√ (0.03/0.1π)

=9.8 cm

Note that 1L = 10-3 m3

Answer:

[tex]6 * 7^3 = 2058[/tex]

Step-by-step explanation:

Given

[tex]6 * 7^3[/tex]

Required

Solve

App;y law of indices:

[tex]6 * 7^3 = 6 * 7*7*7[/tex]

Multiply

[tex]6 * 7^3 = 2058[/tex]

Answer:

C. [tex]-x-6>-3.5[/tex]

Step-by-step explanation:

One is asked to find which inequality has ([tex]x=-3[/tex]) in its solution set. Remember that an inequality is another way to represent a set of solutions. In essence, it states that all numbers less than; less than or equal to; greater than; or greater than or equal to, are a part of the solution. One simplifies an inequality in a similar manner to how one simplifies an equation, by using inverse operations and simplification. Just note that when multiplying or dividing the inequality by a negative number, one has to flip the inequality sign to ensure the expression remains true.

Simplify each of the inequalities, then evaluate to see which one has ([tex]x=-3[/tex]) as a part of its solution set.

A. [tex]-x -6<-3.5[/tex]

[tex]-x<2.5[/tex]

[tex]x>-2.5[/tex]

B. [tex]-x-6>3.5[/tex]

[tex]-x>9.5[/tex]

[tex]x<-9.5[/tex]

C. [tex]-x-6>-3.5[/tex]

[tex]-x>2.5[/tex]

[tex]x<-2.5[/tex]

D. [tex]x-6>-3.5[/tex]

[tex]x>2.5[/tex]

As can be seen, option (C [tex]-x-6>-3.5[/tex]) is the only one that fits this requirement. Since option (C) simplifies down to ([tex]x<-2.5[/tex]) or in words, (x) is less than (-2.5). This option is the only one that fits the solution since (-3) is less than (-2.5).

Answer:

Step-by-step explanation:

Given equation of the quadratic function is,

y = x² + 5x - 7

Convert this equation into vertex form,

y = x² + 2(2.5x) - 7

  = x² + 2(2.5x) + (2.5)² - (2.5)² - 7

  = (x + 2.5)²- 6.25 - 7

  = (x + 2.5)² - 13.25

Therefore, vertex of the function is → (-2.5, -13.25)

For the solutions,

y = 0

(x + 2.5)² - 13.25 = 0

x = (±√13.25) - 2.5

x = (±3.64) - 2.5

x = 1.14, -6.14

Solutions → (-6.14, 0) and (1.14, 0)

Answer:

answer is 10 (very easy)

Answer:

380. 1

Step-by-step explanation:

A=π r2=π. 11^2= 380.13271

Answer:

15x^9

Step-by-step explanation:

A=l x w

5x^4 times 3x^5 is basically 3*5*x^4*x^5

when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9

Answer:

Học sinh nam là 21 học sinh, số học sinh nữ là 15 học sinhH

Step-by-step explanation:

Tỉ số giữa nam và nữ là x/y = 7/5 => x/7 = y/5

áp dụng tính chất của dãy tỉ số bằng nhau, ta được:  

x/7 = y/5 => x-y =/7-5 = 6/2 = 3

Vì x/7 = 3 => x = 21

y/5 = 3 => y= 15

Vậy số học sinh nam là 21 học sinh, số học sinh nữ là 15 học sinh

Answer:

given values are:

1200 = 20×30 + 1/2 × 30²a

1200= 600 + 1/2 × 900a

600 = 450a

a = 600 / 450

a = 1.33 m/s²

v² = 20² +2 × 1.33 × 1200

v²= 400 + 3192

v = √3592

v = 59.9 ≈ 60 m/s

Answer:

Annual payment wil be 2,001 and total amount after compounded annually will be 27,001

Answer:

Step-by-step explanation: Hope this helps

Answer:

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Step-by-step explanation:

In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?

(1) The teacher distributed 180 candies and 40 bars.

(2) The total number of items received by each student was less than 20.

A Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked.

B Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient to answer the question asked.

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D EACH statement ALONE is sufficient to answer the question asked.

E Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

180 candies and 40 bars

The highest common factor of 180 candies and 40 bars = 20

Answer: 1 month = 500ml

4 month = 500ml × 4 = 2000ml = 2L

you should use the 2L container

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

Answer:

(E) [tex]y=x+3[/tex]

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).

1) Determine the slope (m)

[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-4,-1) and ( -1,2):

[tex]m=\displaystyle \frac{2-(-1)}{(-1)-(-4)}\\\\m=\displaystyle \frac{2+1}{-1+4}\\\\m=\displaystyle \frac{3}{3}\\\\m=1[/tex]

Therefore, the slope of the line is 1. Plug this into [tex]y=mx+b[/tex]:

[tex]y=1x+b\\y=x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=x+b[/tex]

Plug in one of the given points and solve for b:

[tex]2=-1+b\\2+1=b\\3=b[/tex]

Therefore, the y-intercept of the line is 3. Plug this back into the original equation:

[tex]y=x+3[/tex]

I hope this helps!

Step-by-step explanation:

the answer of the following is in the figure

Answer:

Decreases the variability of a sample

Step-by-step explanation:

Given that the items are unrelated random variables, we have that the total of the variances of variates is the variance of their sum, that is the variance of the mean of a distribution is the variance of a sample in the distribution divided by the square root of the number of subjects in the sample (the sample size)

Therefore, we have;

[tex]\sigma_{\overline x} = \dfrac{\sigma }{\sqrt{n} }[/tex]

Therefore, increasing the size of a probability sample, decreases the variability of a sample and increases precision and level of confidence

Answer:

[tex]3\left(8-4x\right)<6\left(x-5\right)[/tex]

[tex]3(8-4x)=241-2x[/tex]

[tex]6(x-5)=6x-30[/tex]

[tex]24-12x<6x-30[/tex]

Subtract 24 from both sides

[tex]-12x<6x-54[/tex]

Now, subtract 6x from both sides

[tex]-18x<-54[/tex]

Multiply both sides by -1

[tex]18x>54[/tex]

Divide 18 from both sides

[tex]x>3[/tex]

OAmalOHopeO

If you can show that the following two items are true

then you have shown that triangle A'B'C' is a translated or shifted copy of triangle ABC. In other words, they are the same triangle.

|x| basically means the count of how far from zero. It will always be a positive number.

So the answer is A. |-20| <  20

because 20 is not greater than 20