Find the value of each variable.
4V3
b
60°
45°
C
d

Answer:

√3+√7 is irrational.

Step-by-step explanation:

Let us assume that √3+√7 is rational.

That is , we can find coprimes a and b (b≠0) such that \sqrt{3}+\sqrt{7}=\sqrt{a}{b}

3

+

7

=

a

b

Therefore,

\sqrt{7}=\frac{a}{b}-\sqrt{3}

7

=

b

a

−

3

Squaring on both sides ,we get

7=\frac{a^{2}}{b^{2}}+3-2\times \frac{a}{b}\times \sqrt{3}7=

b

2

a

2

+3−2×

b

a

×

3

Rearranging the terms ,

\begin{gathered}2\times \frac{a}{b}\times \sqrt{3}=\frac{a^{2}}{b^{2}}+3-7\\=\frac{a^{2}}{b^{2}}-4\end{gathered}

2×

b

a

×

3

=

b

2

a

2

+3−7

=

b

2

a

2

−4

\implies 2\times \frac{a}{b}\times \sqrt{3}=\frac{a^{2}-4b^{2}}{b^{2}}⟹2×

b

a

×

3

=

b

2

a

2

−4b

2

\begin{gathered}\implies \sqrt{3}=\frac{a^{2}-4b^{2}}{b^{2}}\times \frac{b}{2a}\\=\frac{a^{2}-4b^{2}}{2ab}\end{gathered}

⟹

3

=

b

2

a

2

−4b

2

×

2a

b

=

2ab

a

2

−4b

2

Since, a and b are integers , \frac{(a^{2}-4b^{2})}{2ab}

2ab

(a

2

−4b

2

)

is rational ,and so √3 also rational.

But this contradicts the fact that √3 is irrational.

This contradiction has arisen because of our incorrect assumption that √3+√7 is rational.

Hence, √3+√7 is irrational.

Answer:

2 + sqrt(3)

Step-by-step explanation:

Roots that contain square roots come in pairs

If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)

2 -sqrt(3) means there is a root 2 + sqrt(3)

Answer:

1st option is decreased 2nd is increased

Step-by-step explanation:

Because you add a liquid to dilute a solution, it makes the solution weaker (less concentrated) you also added more liquid which would increase the volume

Answer:

decreased; increased

Step-by-step explanation:

when you dilute something you make it less concentrated by adding something else (usually water i think). so the concentration decreases while the volume increases

Step-by-step explanation:

to find this angle you can use the sin ratio seeing that the opposite has been given which is 35 and the hypotenuse which is 48.so the solution will be

sin?=opposite/hypotenuse

sin?=35/48

sin?=0.729

?=sin inverse of 0.729

?=46.8 rounded off to 47°

I hope this helps

Hi

in application of sinus formula : ( must learn your trigonimetric formulas by heart !)

value of ? is sin^(-1) = (35/48) = 46,8. so 47 when rounded to the nearest degree

Because it's +-, the - cancels out the +.

We can rearrange the equation to 6-47.

Or -47+6.

Then the answer is -41

If this was helpful hit the thanks :D

6+(-47)

Remove the parentheses

6-47

= -41 as your answer

Answer:

5

Step-by-step explanation:

Based on the given conditions, formulate

Evaluate the expression:

Calculate the power:

Calculate the first two terms:

Answer:

9514 1404 393

Answer:

  C.  16

Step-by-step explanation:

UV is a diameter of the circle. If it is perpendicular to the chord XS, then it bisects that chord. This means ...

  XT = TS

  3b -1 = b +5

  2b = 6

  b = 3

  TS = b +5 = 8

The chord length is 2·TS = 2·8 = 16 units.

Answer:

C,XS=16

Step-by-step explanation:

3b-1=b+5

3b-b=5+1

2b=6

b=6/2=3

TS=b+5=3+5=8

XS=2 TS=2×8=16

Answer:

$3072

Step-by-step explanation:

It is given that :

I work for 4 hours everyday, working 2 days a week.

And in 1 hour , I get $8.

Therefore,

1 hour = $8

4 hours = 4 x  8

             = $32

So, in 1 day working for 4 hours, I get $32.

∴ Working 2 days = 32 x 2

                              = $64

In 1 month, there are 4 weeks

So, in 4 weeks (or 1 month), I work for = 4 x 2

                                                               =  8 days

Therefore, in 8 days, I get = 8 x 32

                                            = $256

Now there are 12 months in a year.

So, in 12 months , I will get = 12 x 256

                                            = $3072

Therefore, in 1 year , I will get $3072.

Answer:

a) 10

b) 2.5

Step-by-step explanation:

2^n = 1024

2^n = 2^10

n = 10

4^(2n-3) = 16

4^(2n-3) = 4^2

2n-3 = 2

2n = 5

n = 2.5

Solution:-1:-

[tex]\\ \sf\longmapsto 2^n=1024[/tex]

[tex]\\ \sf\longmapsto 2^n=2^10[/tex]

[tex]\\ \sf\longmapsto n=10[/tex]

Solution:-2:-

[tex]\\ \sf\longmapsto 4^{2n-3}=16[/tex]

[tex]\\ \sf\longmapsto 4^{2n-3}=4^2[/tex]

[tex]\\ \sf\longmapsto 2n-3=2[/tex]

[tex]\\ \sf\longmapsto 2n=2+3[/tex]

[tex]\\ \sf\longmapsto 2n=5[/tex]

[tex]\\ \sf\longmapsto n=\dfrac{5}{2}[/tex]

[tex]\\ \sf\longmapsto n=2.5[/tex]

Answer:

B.

Step-by-step explanation:

Since i is in the denominator, if i = 0, then the result will be undefined. Therefore, B cannot be a value of θ.

Answer: The number would be 18

Step-by-step explanation:

18/2=9 9-3=6 6*3=18

The equation be (x/2) - 3 = x/3 then, the number of x = 18.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let x be the number

From the given information, we get

(x/2) - 3 = x/3

The set all the fractions on one side and constants on another side

(x/2) - (x/3) = 3

Multiply by LCM

3x - 18 = 2x

Add 18 to both sides

3x - 18 + 18 = 2x + 18

simplify

3x = 2x + 18

Subtract 2x from both sides

3x - 2x = 2x + 18 - 2x

x =18.

Therefore, the number is x = 18.

To learn more about algebraic expression refer to:

https://brainly.com/question/4541471

#SPJ2

Answer:

Yes, it will overflow after 16 minutes..

Step-by-step explanation:

The tub fills at a rate of 5 gallons every minute, but it drains at a rate of 2.5 gallons every minute. This means that it fills twice as fast as it drains, so it would take 16 minutes for the tub to overflow. If you subtract the rate of draining from the rate of filling then the net rate of water going up is 2.5 gallons a minute.

Answer:

I can help you with C and I tis non-linear because to make it linear it needs to be a straight line and shouldn't have any curves.

Step-by-step explanation:

[tex]\\ \sf\longmapsto 72^{\frac{3}{4}}[/tex]

[tex]\\ \sf\longmapsto 72^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}[/tex]

[tex]\\ \sf\longmapsto 2.91+2.91+2.91[/tex]

[tex]\\ \sf\longmapsto 3.73[/tex]

Step-by-step explanation:

A n L =null

A U L= a,b,c,e,k,j

Step-by-step explanation:

I=PRT/100

p=I/RT×100

p=2240/10×2×100

p=11200

B is an upside down image of A and is 2 units below A.

The image of A is mirrored across the y axis at y = 2.

Answer: A was mirrored across y= 2 to form B.

The seller sold 120 single-scoop cones and 130 double-scoop cones to make $565.

250 cones were used while selling yogurt and made $565.

There are two types of cones:

Single-scoop cone that cost $2.

Double-scoop cone that cost $2.50.

We need to know how many cones of each type were used while selling yogurt that made $565.

We will have to make two linear equations using the given statements and apply the substitution method to get our answer.

Consider,

x = single-scoop cone.

y = double-scoop cone.

Now, we can make two linear equations:

x + y = 250............(A)

2x + 2.50y = 565...............(B)

Apply substitution method.

From (A) we get,

x = 250 - y...............(C)

And putting x = 250 - y in (B) we get,

2 ( 250 - y ) + 2.50y = 565

500 - 2y + 2.50y = 565

0.50y = 565 - 500

0.50y = 65

y = 65 / 0.50
y = 6500 / 50

y = 130

Putting y = 50 in (C) we get,

x = 250 - 130

x = 120

We have,

x = 120 and y = 130

We see that we need 120 single-scoop cones and 130 double-scoop cones to make $565.

Learn more about the system of the linear equations here:

https://brainly.com/question/8062932

#SPJ2

Answer:

u is 17√2 and v is 17

Step-by-step explanation:

To find u:

[tex]{ \bf{ \sin( \theta) = \frac{opposite}{hypotenuse} }}[/tex]

feed in the terms:

[tex] \sin(45 \degree) = \frac{17}{u} \\ \\ u = \frac{17}{ \sin(45 \degree) } \\ \\ u = 17 \sqrt{2} [/tex]

To find v:

[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

feed in the terms:

[tex] \cos(45) = \frac{v}{u} \\ \\ v = u. \cos(45) \\ v = (17 \sqrt{2} )÷( \sqrt{2} ) \\ v = 17[/tex]

Answer:

A) both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.

Answer:

At least 7 girls: 0.5^7 OR 0.0078125

At least 8 girls: 0.5^8 OR 0.00390625

Answer:

A.

Step-by-step explanation:

'The difference' means minus or subtraction. 'plus' and 'increased' are both for addition.

Brainliest please!

Answer:

b i think

Step-by-step explanation:

Answer:

128 ft^2

Step-by-step explanation:

each drapery has an area of 8*4 feet^2 and there are four panes so the total area is 8*4*4= 128

Answer:

75 degrees maybe.......

Answer:

75 degrees

Step-by-step explanation:

the external angle is between the outside of one of the sides of the angle and the continued line of the second side of the angle.

and because it is measured against a line, where we have a total of 180 degrees for angles, we have

exterior angle = 180 - interval angle = 180-105 = 75

Answer:

Hope it will helps you

.

.

Answer:

and w = –2 w = 0, w = 2, and w = 6 w = 0 and w = Three-halves w = 2 and w = 6

hope it's help you...!!!

#rishu

Answer:

t+d/2

Step-by-step explanation:

Answer:

18h +4

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)  where l is the length and w is the width

  =2( 7h+8 + 2h-6)

Combine like terms

  = 2( 9h+2)

Distribute

   = 18h +4

Answer:

dame like y muchísimas estrella