∠2= ∠5 , because they are
(I) Corresponding angles
(II) Alternate angles
(III) Co- interior angles
(IV) Linear pair
​

Answer:

[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]

Step-by-step explanation:

We want to find the maximum and minimum values of the function:

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

On the interval [0, 4].

First, evaluate its endpoints:

[tex]\displaystyle \begin{aligned} f(0) &= \sqrt{(0)+(0)^2} - 2\sqrt{0} \\ &= 0 \\ \\ f(4) &= \sqrt{(4)+(4)^2} - 2\sqrt{(4)} \\ &= 2\sqrt{5} -4 \end{aligned}[/tex]

Recall that the extrema of a function occurs at its critical points; that is, where its derivative equals zero (or is undefined).

Take the derivative of both sides:

[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ \sqrt{x + x^2} - 2\sqrt{x}\right][/tex]

Differentiate:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{1}{2\sqrt{x + x^2}} \cdot (1 + 2x) - 2\left(\frac{1}{2\sqrt{x}}\right) \\ \\ &= \frac{2x+1}{2\sqrt{x+x^2}} - \frac{1}{\sqrt{x}} \\ \\\end{aligned}[/tex]

Note that the derivative is undefined at x = 0. Hence, x = 0 is a critical point.

Solve for the zeros of the derivative:

[tex]\displaystyle\begin{aligned} \frac{2x+1}{2\sqrt{x + x^2}} - \frac{1}{\sqrt{x}} &= 0\\ \\ \frac{2x+1}{2\sqrt{x}\sqrt{1 + x }} - \frac{1}{\sqrt{x}} &= 0 \\ \\ \frac{2x+1}{2\sqrt{1+x}} - 1 &= 0\\ \\ 2x + 1 &= 2\sqrt{1+x} \\ \\ 4x^2 + 4x + 1 &= 4 + 4x \\ \\ x^2 &= \frac{3}{4} \\ \\ x= \frac{\sqrt{3}}{2} \end{aligned}[/tex]

Therefore, our only two critical points are at x = 0 and x = √3/2:

Evaluate the function at x = √3/2:

[tex]\displaystyle \begin{aligned} f\left(\frac{\sqrt{3}}{2}\right) &= \sqrt{\left(\frac{\sqrt{3}}{2} \right)+ \left(\frac{\sqrt{3}}{2}\right)^2} - 2 \sqrt{\left(\frac{\sqrt{3}}{2}\right)} \\ \\ &= \frac{\sqrt{3+2\sqrt{3}}}{2}- \frac{2\sqrt[4]{3}}{\sqrt{2}} \\ \\ &\approx -0.5900\end{aligned}[/tex]

In conclusion: the exact maximum and minimum values of f on the interval [0, 4] is:

[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]

Answer:

nose eee e e e e e e e e

Step-by-step explanation:

qhhabbejeheh0

Answer:

IS BIGGNER

Step-by-step explanation:

ABC WINNER ZILONG

ANSWERRR BY✏

SUGIONO REALL☠

Answer:

it's D

Step-by-step explanation:

2 dozen is 24 so we have 18 pnt butter and 24 choc chip.

they're putting 4 choc chp in each so do 24/4

they're putting 3 pnt butter in each so do 18/3

both are 6 so D is the answer

The property of real numbers that justifies the work done to simplify the expressions below is the distributive property of multiplication.

The distributive property of multiplication states that the same result is obtained by multiplying the sum of two or more addends by a number or multiplying each addend individually and adding the products.

The steps for the distributive property of multiplication are:

Thus, the property of real numbers that justifies the work done to simplify the expressions below is the distributive property of multiplication.

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Answer:

314ft²

Step-by-step explanation:

A = 3.14(10²)

A = 3.14 x 100

A = 314ft²

Answer:

Area is 314 ft²

Step-by-step explanation:

[tex]A = \pi {r}^{2} [/tex]

r is radius,

[tex]r = \frac{diameter}{2} = \frac{20}{2} = 10 \: ft[/tex]

therefore:

[tex]A = 3.14 \times {10}^{2} \\ A = 3.14 \times 100 \\ A = 314 \: {ft}^{2} [/tex]

Answer: 7-9

Step-by-step explanation: normal job hours

Like an 8, a 9-5 is what most people have so over 40 hours is overtime

Answer:

12

Step-by-step explanation:

1.2*10 = 1.2

Answer:

12

Step-by-step explanation:

the "normal form" to write numbers : just the digits and a decimal point when needed.

so, 1.2 × 10 = 12

12 is the normal, standard decimal notation.

in some cases it can be also 12.0 or 12.00 (especially with money).

the other form is the scientific notation, where a number is written with its leading digits and the power of 10 as the total value "weight". like in this example 1.2 × 10¹

hi <3

product means multiplication, therefore we know there has to be a '2k' and we can eliminate option A

also, there is a mention of subtraction, so we can also eliminate option B

now we are left with C and D

it is stated that it is being subtracted FROM 17, therefore the 17 would have to come first

in short, your answer is option C

hope this helps :)

The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

given that,

The product of 2 and a number k, subtracted from 17

we have to find the expression for given statement.

let the number be x

now, we have,

The product of 2 and a number k,

i.e. 2*k = 2k

then,  subtracted from 17

i.e. 17 - 2k

so, we get,

x = 17 - 2k

Hence, The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.

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Answer:

four hundred and thirty two million, five hundred and fifty three thousand, six hundred and two

Step-by-step explanation:

Answer:

Four hundred thirty-two million, five hundred fifty-three thousand, six hundred and two.

Step-by-step explanation:

Line 1-Line 2-Associative property .

Line 2-Line 3- Distributive property

Solution:-

[tex]\\ \rm\longmapsto (9+x)x[/tex]

[tex]\\ \rm\longmapsto x(x+9)[/tex]

[tex]\\ \rm\longmapsto x(9+x)[/tex]

[tex]\\ \rm\longmapsto x^2+9[/tex]

Answer:

123 456lcm divison method

Answer:

.75

Step-by-step explanation:

8 red marbles, 3 blue marbles, and 1 green marble = 12 marbles

P( not blue) = marbles that are not blue / total

                     =(8red+1 green) / 12

                     =9/12

                      = 3/4

                       .75

Answer:

angle f=147 degrees (alternate angles)

angle e=    33 degrees

Step-by-step explanation:

angle d =147 degrees

angle f=147 degrees (alternate angles)

angle e +angle d=180 (allied angles)

        e+ 147         =180

                   e      =180-147

                    e     =    33 degrees

Answer:

k = 70

Step-by-step explanation:

Since we have been given the value of x to be -ve5 (-5),

we multiply 6 and -5( value of x). Which gives;

-30.

Then add the answer (-30) to 100.

-

K = -30 + 100

= 100 - 30

=70

Note;

(+ * + = +)

( + * - = -)

(- * - = +)

I hope this helps you.

Answer:

[tex]k=70[/tex]

Step-by-step explanation:

[tex]k=6x+100[/tex]

[tex]x=-5[/tex]

[tex]k=6(-5)+100[/tex]

Remove parentheses:- [tex]\left(-a\right)=-a[/tex]

[tex]k=-6\times 5+100[/tex]

Multiply [tex]6\times5= 30[/tex]

[tex]k=-30+100[/tex]

Add [tex]-30+100=70[/tex]

[tex]k=70[/tex]

OAmalOHopeO

Answer:

33 & 27

I am positive !!!!!!!!!!!!

Answer:

$3480

Step-by-step explanation:

We know that the tax rate for the first $8000 is 15% and after $8000 the tax is 19%.

This means the total amount of money that Christine have to pay is equal to $8000 × 15% + ($20000 (the total) - $8000 (the amount that she already paid for the first $8000)) × 19%

This is equal to $1200 + $12000 × 19%

= $1200 + $2280

= $3480

Therefore, Christine must pay $3480 in income tax.

Answer: 2 pens and 4 pencils.

Step-by-step explanation:

If you buy 2 pens it is equal to $2.

If you buy 4 pencils it is also equal to $2.

2+2=4

and 2 pens and 4 pencils is equal to 6 in total.

Answer

[tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex] such that [tex]6[/tex] pens and pencils are bought for [tex]\$4[/tex] and each pen costs [tex]\$1[/tex] and each pencil costs [tex]\$0.50[/tex].

The equation whose variables' highest power is one is known as linear equation.

To find the unknown quantities, always assume it to be a variable and then form the equation based on the conditions given in the question.

Let the number of pens bought be [tex]x[/tex].

and the number of pencils bought be [tex]y[/tex].

The total number of pens and pencils [tex]=6[/tex].

So, the first equation is,

[tex]x+y=6[/tex]

[tex]x=6-y[/tex] ... (i)

And the costs per pen and pencil is [tex]\$1[/tex] and [tex]\$0.50[/tex] respectively.

So, the second equation is,

[tex]x+0.5y=4[/tex] ... (ii)

Now, solve the pair of linear equations.

Put the value of [tex]x[/tex] in the equation (ii),

[tex]6-y+0.5y=4\\-0.5y=-2\\y=4[/tex]

So,

[tex]x=6-4\\x=2[/tex]

Thus, [tex]2[/tex] pens and [tex]4[/tex] pencils were bought for [tex]\$4[/tex].

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Answer:

Range is 19.54

Step-by-step explanation:

I. If R = H - L

when R is Range, H is highest value and L is lowest value

R = 25.6 - 6.06

R = 19.54

Answer:

3.004

Step-by-step explanation:

If you were to round it like this: 3.0041, the thousands place would still be 4, so it would come out to be 3.004. Hope that helps!!

Answer:

B

Step-by-step explanation:

The other answers don't divide into rational numbers

Answer:

V=880

Step-by-step explanation:

V=π(R^2 − r^2)L

V=(22/7)*7*(11^2-9^2)

V=880

To test the validity of a given argument, we need to see if we can find a counter-example that makes one of the statements non-valid. If after analyzing the statements we can't find a counterargument, then we can conclude that the argument is valid.

Here we will find that the argument is valid.

We can write this as:

If he participates in a race then he is the winner.

Either he participates in the race, or he is sick.

He is not the winner, then, he is sick.

Now, from the first statement, we know that always that this person participates in a race, he wins.

From the second statement we know that he only participates if he is not sick, we can rewrite that one as:

"If he is sick, then he does not participate in the race".

Finally, from the third one, if he does not win, then he is sick.

This makes sense, he only does not participate when he is sick, then the only races where he is not the winner, are these races where he does not participate, and he does not participate only if he is sick, then this is a valid argument.

Concluding, the 3 statements are valid, as we can't find any counterargument to any of these 3.

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Answer:

2b - 14

Step-by-step explanation:

2(b – 7)

2b - 14

Answer:

[tex]2b-14[/tex]

Step-by-step explanation:

Using the distributive property, [tex]2(b-7)[/tex] can be written as [tex](2\cdot b)-(2\cdot7)[/tex] which solved/simplified is [tex]2b-14[/tex]

Man, it's late! Well, hope this helped you out and answered your question!

The probability that a randomly selected student is female or left-handed is 107/137.

Probability = required outcome / Total possible outcomes

Probability that student is female or left-handed = [(probability that student is female + probability that female is left-handed)]

Therefore,

Probability that student is female :

P(Female student) = number of female / total number of student

Number of female student = 81

Total number of student = 137

P(Female student) = 81 / 137

P(Left handed student) = number of lefthanded student / total number of student

Number of left handed student = 26

Total number of student = 137= 26 / 137

P(student is female or left-handed) :

P(student is female or left-handed) :[(81/137) + (26/137)] = 107/137

Probability that student is female or left-handed is 107/137

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Answer:

option b is the correct answer.

Explanation is beloe

Step-by-step explanation:

x²+y²=9

xy=8

x+y=?

Now,

(x+y)²=x²+2×x×y+y²

(x+y)²=x²+2xy+y²

(x+y)²=x²+y²+2xy

(x+y)²=9+2×8

(x+y)²=9+16

(x+y)²=25

(x+y)²=5²

x+y=±5

I hope it helped U

stay safe stay happy

Step-by-step explanation:

[tex]we \: have \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ here \: {x}^{2} + {y}^{2} = 9 \\ xy = 8 \\ then {(x + y)}^{2} = 9 + 2 \times 8 \\ {(x + y)}^{2} = 9 + 16 = 25 \\ {(x + y)}^{2} = 25 \\ x + y = \sqrt{25} = +/-5 \\ thank \: you[/tex]

Answer:

this answer could help you...

Step-by-step explanation:

make me brainiest

The speed where Trish is driving is 46 miles per hour.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

Given the table where a number of hours and miles are shown,

The unit rate of first data = 69/1.5 = 46

the unit rate of second data = 161/3.5 = 46

And so on

So, 46 will be constant of the function

It means the function will be y = 46x and the rate of the function will be y/x = 46.

Hence "The speed where Trish is driving is 46 miles per hour".

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Step-by-step explanation:

we first find the gradient

when y1=-4, x1=-5 and y2=1, x2=4

gradient={(y2-y1)÷(x2-x1)}

gradient={1-(-4)}÷{4-(-5)}

gradient=(1+4)÷(4+5)

gradient=5÷9 OR 0.5555

To find the equation interm of x

we substitute for the gradient in the formula

y-y1=gradient (x-x1)

y-(-4)=(5÷9)(x-×-5)

y+4=(5÷9)(x+5)

y+4=(5x+25)÷9 Cross multiply ✖️

9(y+4)=(5x+25)(1)

9y+36=5x+25 collect like terms

9y=5x+25-36

9y=5x-11 divide both sides by 9

y=(5x-11)÷9.......ans

Answer:

yes

Step-by-step explanation:

x - 4y = 15

Substitute the point into the equation and see if the equation is true

7 -4(-2) = 15

7+8 = 15

15 =15

This is true so the point is a solution to the equation