Write the word sentence as an inequality. A number y minus 1/2 is no more than −3/2 .

Note that √((1 - x)/x) is defined only as long as 0 < x ≤ 1.

Consider a right triangle with reference angle θ such that

[tex]\cot(\theta) = \sqrt{\dfrac{1-x}x}[/tex]

In other words, on an appropriate domain,

[tex]\theta = \cot^{-1}\left(\sqrt{\dfrac{1-x}x}\right)[/tex]

In such a triangle, you would find that

[tex]\sin(\theta) = \sqrt x[/tex]

so f(x) reduces a bit to

[tex]f(x) = \cos\left(2 \tan^{-1}(\sqrt x)\right)[/tex]

Now consider another triangle with reference angle ɸ such that

[tex]\tan(\phi) = \sqrt x \implies \phi = \tan^{-1}(\sqrt x)[/tex]

In this triangle, you would find

[tex]\cos(\phi) = \dfrac1{\sqrt{1+x}}[/tex]

Recalling the double angle identity for cosine, it follows that

[tex]f(x) = \cos(2\phi) = 2 \cos^2(\phi) - 1 = \dfrac{1-x}{1+x}[/tex]

Differentiating with respect to x yields

[tex]f'(x) = -\dfrac2{(1+x)^2}[/tex]

while

[tex]f(x)^2 = \dfrac{(1-x)^2}{(1+x)^2}[/tex]

It follows that

[tex]f'(x)(x-1)^2 - 2f(x)^2 = 0[/tex]

so B is the correct choice.

Answer:

[tex]20[/tex].

Step-by-step explanation:

In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:

[tex]a + b > c[/tex],

[tex]a + c > b[/tex], and

[tex]b + c > a[/tex].

In this question, the length of the sides are [tex]10[/tex], [tex]24[/tex], and [tex]x[/tex]. The length of these sides should satisfty the following inequalities:

[tex]10 + 24 > x[/tex],

[tex]10 + x > 24[/tex], and

[tex]24 + x > 10[/tex].

Since [tex]x > 0[/tex], the inequality [tex]24 + x > 10[/tex] is guarenteed to be satisfied.

Simplify [tex]10 + 24 > x[/tex] to obtain the inequality [tex]x < 35[/tex].

Similarly, simplify [tex]10 + x > 24[/tex] to obtain the inequality [tex]x > 14[/tex].

Since [tex]x[/tex] needs to be a whole number, the greatest [tex]x[/tex] that satisfies [tex]x < 35[/tex] would be [tex]34[/tex]. Similarly, the least [tex]x\![/tex] that satisfies [tex]x > 14[/tex] would be [tex]15[/tex]. Thus, [tex]x\!\![/tex] could be any whole number between [tex]15\![/tex] and [tex]34\![/tex] (inclusive.)

There are a total of [tex]34 - 15 + 1 = 20[/tex] distinct whole numbers between [tex]15[/tex] and [tex]34[/tex] (inclusive.) Thus, the number of possible whole number values for [tex]x[/tex] would be [tex]20[/tex].

[tex]\text{Area of square} = \text{Side}^2 = \left(\dfrac{7}{12}\right)^2 = \dfrac{49}{144}=0.3402\overline{7}~ \text{Units}^2[/tex]

Answer:

They were out side for 21 minutes

Step-by-step explanation:

you just add 11:43 and add 21 minutes  to it and you get 12:04

Answer:

Sunday

Step-by-step explanation:

Friday  

[(13.5 + 8.5) ÷ 2] = [(22) ÷ 2] = 22 ÷ 2 = 11 miles

Saturday

[18 − (2 × 4)] = 18 - (8) = 18 - 8 =  10 miles

Sunday

[20 − (5 − 3)] = 20 - (2) = 18 miles

18 > 11 > 10

Then She rode her bicycle the most on Sunday

Try:

Rereading your lessons, getting help from your tutor or others.

Answer:

Sundays

Hope this helps and don't forget to hit the thanks button! <3

Written by: RiBu

Answer: Stacy: 30 Naomi: 18

Step-by-step explanation:

Stacy- ratio of oat to blueberry is 6:2 we want to find x:10

10 is 5 times 2, and whatever you do to the bottom you have to do to the top, and 6 times 5 is 30

Naomi- ratio of oat to blueberry is 9:5 we want to find x:10

The 10 is 2 times 5, and whatever you do to the bottom you have to do to the top, and 9 times 2 is 18

Answer:

1728 ft³

Step-by-step explanation:

Lower part:

volume = 19 ft × 12 ft × 6 ft = 1368 ft³

Upper part:

volume = 10 ft × 12 ft × 3 ft = 360 ft³

Total Volume = 1728 ft³

Answer:

His profit was 15%

Step-by-step explanation:

120*2€ = 240€

72*2.5€ = 180€

120-72 = 48

48*2€ = 96€

And now a simple proportion:

240€ = 100%

276€ = x

x = (276*100)/240 %

x = 115%

115%-100% = 15%

His profit was 15%

ray is x years old

Ron is x+y years old

in 5 years ron will be 5 years older than now, so x+y+5 years old

 orAnswer:

x - x + y + 5 - 5 = y  or   x + y - x = y

Step-by-step explanation:

The difference now,

x + y - x = y

The difference in 5 years,

(x + y + 5) - (x + 5) = x - x + y + 5 - 5

x - x + y + 5 - 5 = y

The difference in their ages never changes

The total balance in Raul's account after 40 years when he retires is $65,714.90.

The formula that can be used to determine the balance of the accout is: monthly amount saved x annuity factor.

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$100 x [(1.00125^480) - 1 ] / 0.00125 = $65,714.90

Here is the complete question:

Raul is a saver. He sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns 1.5% interest per year. What is the balance in the account after 40 years?

To learn more about annuites, please check: https://brainly.com/question/24108530

Answer:

true

hope that helps

Step-by-step explanation:

Hello!

_____

The quotient of two numbers means we divide one number by another number.

Example :-

The quotient of 6 and a number:-

6÷x

According to the example above, the algebraic expression looks like so:-

69÷x

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

5.56 ft

Step-by-step explanation:

30.48 cm per foot

170 cm ÷ 30.48 cm/ft = 5.56 ft

Hope this helps!

Answer:

33.69°

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

Answer:

33.69°

Step-by-step explanation:

Let's take ∡CBA as y

Tan y =  [tex]\frac{opposite}{adjacent}[/tex]

         =  [tex]\frac{6}{9}[/tex]

         = 0.6666

y = 33.69°

Answer:

J=118

L=62

M=62

Step-by-step explanation:

In an isoseles trapezoid, the top angles are congruent to each other and the bottom angles are congruent to each other. Opposite angles are supplementary, and all angles together add up to 360.

Answer:

1. 20 km/hr (60km / 3h)

2. 70 m/hr (170m / 2h)

3. 6.5 hr (260cm / 40km)

4. 4.5 s (72cm / 16cm)

5. 184 km (46km * 4h)

Step-by-step explanation:

We'll use d = distance, t = time, s = speed.

Speed over time can be found by dividing distance by time

s = d / t

We can take this formula and manipulate it to find either distance or time if we know two of the values. Keeping in mind division and multiplication cancel each other.

If we wanted to find d for instance we can multiply both sides by t to get

s * t = d

For time we can divide both sides of the above formula by s to get

t = d / s

Answer:

1. 20 km/h

2. 70 m/h

3. 6.5 h

4. 4.5 s

5. 184 km

Step-by-step explanation:

For first two questions, you can use the following formula:

[tex]\displaystyle \large{s = \frac{d}{t}}[/tex]

I denote ‘s’ be speed, ‘d’ be distance and ‘t’ be time. Some books may use ‘v’ for speed instead of ‘s’ but I use ‘s’ variable instead so it makes the equation easier to memorize.

Therefore, speed = distance/time

( 1 ) The first question is given both distance be 60 km and time be 3 hours. Therefore:

[tex]\displaystyle \large{s=\frac{60}{3}}\\\displaystyle \large{s=20 \ \ \sf{km / h}}[/tex]

So for the first question, the speed is 20 km/h

( 2 ) The second is given both distance be 140 m and time be 2 hours. Therefore:

[tex]\displaystyle \large{s=\frac{140}{2}}\\\displaystyle \large{s=70 \ \ \sf{m / h}}[/tex]

Therefore, speed is 70 m/h

For the third and four questions, we will be finding time. From the speed formula:

[tex]\displaystyle \large{s=\frac{d}{t}}[/tex]

Multiply both sides by t.

[tex]\displaystyle \large{st=d}[/tex]

Divide both sides by s.

[tex]\displaystyle \large{t=\frac{d}{s}}[/tex]

Therefore, time = distance/speed

( 3 ) The question is given speed be 40 km/h and distance be 260 km. Therefore:

[tex]\displaystyle \large{t=\frac{260}{40}}\\\displaystyle \large{t=\frac{13}{2} \ \ \sf{h}}\\\displaystyle \large{t = 6\frac{1}{2} \ \ \sf{h}}\\\displaystyle \large{t= 6.5 \ \ \sf{h}}[/tex]

Therefore, time is 6.5 h

( 4 ) The question is given speed be 16 cm/s and distance be 72 cm. Therefore:

[tex]\displaystyle \large{t=\frac{72}{16}}\\\displaystyle \large{t=\frac{9}{2} \ \ \sf{s}}\\\displaystyle \large{t=4\frac{1}{2} \ \ \sf{s}}\\\displaystyle \large{t=4.5 \ \ \sf{s}}[/tex]

Therefore, time is 4.5 s

For the last question, we have to find distance. From the speed formula:

[tex]\displaystyle \large{s=\frac{d}{t}}[/tex]

Multiply both sides by t.

[tex]\displaystyle \large{st=d}\\\displaystyle \large{d=st}[/tex]

Therefore, distance = speed * time

( 5 ) The question is given time be 4 hours and speed be 46 km/h. Therefore:

[tex]\displaystyle \large{d=46 \cdot 4}\\\displaystyle \large{ d=184 \ \ \sf{km}}[/tex]

Therefore, distance is 184 km.

Answer: X+Y+5

Step-by-step explanation:

There is no single answer you have to write an equation.

Answer:

[tex]Hi!~I~am~beinggreat78~and~I~will~help~you.\\[/tex]

To solve problems, you first must find the source of the conflict, and attempt to let the situation play out, or use a strategy yourself. To solve math problems, go by PEMDAS.

With this strategy, PEMDAS, you can solve math problems quickly, and like a pro!

The probability that an outcome is greater than 5 is the likelihood of the outcome

The probability that the sum of the numbers showed on the dice is greater than 5 is 13/18

The sample size of a roll of two dice is:

n(S) = 36

The number of outcomes that have a sum greater than 5 is:

Greater than 5 = 26

So, the required probability is:

P = 26/36

Simplify

P = 13/18

Hence, the probability that the sum of the numbers showed on the dice is greater than 5 is 13/18

Read more about probability at:

https://brainly.com/question/251701

Answer:

Pt A: D. Pt B: D

Step-by-step explanation:

You can multiply 5x2 which easily equals 10. 6x6 equals 36 and you cannot multiply anything other than one and itself for 7, 13, 23, or 67. for part B, you can multiply 4x 11 to equal 44 and you can multiply 9x5 to equal 45 so it would be composite

44 and 45 are composite numbers.

A prime number has only two factors, itself and one.

A composite number has at least three factors, and sometimes a lot more.

1.  Prime:7, 13, 23, 67

Composite:10, 36, 55

As, 7, 13, 23 and 67 have only two factors : one and number itself

and 10, 36, 55 have more than 2 factors like 2.

2. 44 and 45 both have more than 2 factors.

Learn more about this concept here:

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Answer: See below

Step-by-step explanation:

Question 3:

[tex]a) \ $S=1$ \ yields \ $(1,3)$ \\ \\b) \ $S=3$ \ yields \ $(3,1)$ \\ \\ c) \ $x(\sqrt{10})=\sqrt{10}$ \\ \\d) $y(\sqrt{10}+\sqrt{5})=1$ \\ \\e) $x(2)=2$ \\ \\f) $y(2,5)=1$ \\[/tex]

Challenge:

[tex]\begin{aligned}&x(s)=s \quad ,s \in[0,4] \\&y(s)=\left\{\begin{array}{cc}3 s & , s \in[0,1] \\5-2 s &, s \in[1,2] \\1 & s \in[2,4]\end{array}\right.\end{aligned}[/tex]

Answer:

precio antes De impuestos 1563.60 impuestos 5.4%

Answer:

GH = 15

Step-by-step explanation:

In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. Therefore:

[tex]9x - 3 = \frac{1}{2} (19 + 5x + 1)[/tex]

[tex]18x - 6 = 5x + 20[/tex]

[tex]13x = 26[/tex]

[tex]x = 2[/tex]

[tex]9(2) - 3 = 18 - 3 = 15[/tex]

Answer:

2.054

Step-by-step explanation:

put the value of x in f(x)

Answer:

1, 4, 6.

Step-by-step explanation:

[tex]\left(2n+8\right)\left(n+4\right)=2n^2+16n+32[/tex]

1. [tex]2(x+4)^2=2n^2+16n+32[/tex]

2. [tex]2\left(n+4\right)\left(n+4\right)=2(n+4)^2[/tex]

3. [tex]16n+32=16n+32[/tex]

4. [tex]2n^2+16n+32=2n^2+16n+32[/tex]

5. [tex]2n^2+8n+32=2n^2+8n+32[/tex]

6. [tex]2(n^2+8n+16)=2n^2+16n+32[/tex]

As you can see from the answers it is 1, 4, and 6.

Answer:

The answer is 156cm^2

Step-by-step explanation:

Solution:

The shape given is a trapezium.

The area of the green region = Area of the outer trapezium - Area of the inner trapezium.

[tex]Area\: of\:a\:trapezium\:=\frac{1}{2}\:(a+b)h[/tex]

[tex]Where\: a,b\:are\:the\:bases,\:h=height[/tex]

[tex]For,\:outer\:trapezium,[/tex]

[tex]a=10cm,\:b=14cm,h=16cm[/tex]

[tex]Area\:of\:the\:outer\:trapezium=\frac{1}{2}\:(10+14)16[/tex]

[tex]=\frac{1}{2}(24)(16)=192cm^{2}[/tex]

[tex]For\:inner\:trapezium,[/tex]

[tex]a=3cm,b=6cm,h=8cm[/tex]

[tex]Area\:of\:the\:inner\:trapezium=\frac{1}{2}(3+6)8[/tex]

[tex]=\frac{1}{2}(9)(8)=36cm^{2}[/tex]

[tex]193cm^{2}-36cm^{2}[/tex]

[tex]=156cm^{2}[/tex]

The answer is 156cm^2



Answer: 70

Step-by-step explanation:

Answer:

9 and 21

Step-by-step explanation:

First we can write the factors of 108:

1,108

2,54

3,36

4,27

6,18

9,12        - these 2 numbers add up to 21 so these 2 numbers is our answer.

Answer:

12 and 9

[tex]108 / 12 = 9[/tex]

[tex]9 * 12 = 108[/tex]

________________________________________________________

We learned alternative ways to find the sum and product of a number using a similar method.

Questions related to the topic? Ask me in the comments box.

Answer:

3.6% or B quack quack quack quack

The unemployment percentage is 3.6 percent. Therefore, option B is the correct answer.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, the labor force is 740 workers, but 27 are unemployed.

Here, percentage = 27/740 ×100

= 2700/740

= 3.6%

Therefore, option B is the correct answer.

To learn more about the percentage visit:

brainly.com/question/24159063.

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