Work out 1/2 x 7 giving your answer as a mixed number.

Answer:

k = y/x

Step-by-step explanation:

1/5, 2/10, 3/15 . . . all equal to 1/5 which is what the value of k is; 'k' stands for constant of proportionality

Answer:

The solutions to the quadratic function are:

[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]

Step-by-step explanation:

Given the function

[tex]f\left(x\right)\:=\:4x^2\:-\:4x\:+\:3[/tex]

Let us determine all possible solutions for f(x) = 0

[tex]0=4x^2-4x+3[/tex]

switch both sides

[tex]4x^2-4x+3=0[/tex]

subtract 3 from both sides

[tex]4x^2-4x+3-3=0-3[/tex]

simplify

[tex]4x^2-4x=-3[/tex]

Divide both sides by 4

[tex]\frac{4x^2-4x}{4}=\frac{-3}{4}[/tex]

[tex]x^2-x=-\frac{3}{4}[/tex]

Add (-1/2)² to both sides

[tex]x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{3}{4}+\left(-\frac{1}{2}\right)^2[/tex]

[tex]x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{1}{2}[/tex]

[tex]\left(x-\frac{1}{2}\right)^2=-\frac{1}{2}[/tex]

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

solving

[tex]x-\frac{1}{2}=\sqrt{-\frac{1}{2}}[/tex]

[tex]x-\frac{1}{2}=\sqrt{-1}\sqrt{\frac{1}{2}}[/tex]                 ∵ [tex]\sqrt{-\frac{1}{2}}=\sqrt{-1}\sqrt{\frac{1}{2}}[/tex]

as

[tex]\sqrt{-1}=i[/tex]

so

[tex]x-\frac{1}{2}=i\sqrt{\frac{1}{2}}[/tex]

Add 1/2 to both sides

[tex]x-\frac{1}{2}+\frac{1}{2}=i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]

[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]

also solving

[tex]x-\frac{1}{2}=-\sqrt{-\frac{1}{2}}[/tex]

[tex]x-\frac{1}{2}=-i\sqrt{\frac{1}{2}}[/tex]

Add 1/2 to both sides

[tex]x-\frac{1}{2}+\frac{1}{2}=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]

[tex]x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]

Therefore, the solutions to the quadratic function are:

[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]

Step-by-step explanation:

the price charged for 100 students reflects the cost per student that applies to the order as a whole.

100 * 6 = $600, so the fixed cost is 750-600 = 150.

...

We can check this by substituting in the other equation.

Does 150*6 + 150 = 1050?

150*6=900

900+150 = 1050.

Yes, it does

...

We can express this relationship by the equation:

y = mx + b

where

y = total cost

m = $6 per student

x = number of students

b = fixed costs = 150

y = 6x + 150

The caterer’s fixed cost and the rate per student served is $6 and $150

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

[tex]a_1x + b_1y = c_1\\a_2x + b_2y = c_2[/tex]

then, if we want to eliminate variable x, then we have to multiply equation 1 with

[tex]-\dfrac{a_2}{a_1}[/tex]

which will make coefficient of x in first equation as

[tex]a_1 \times - \dfrac{a_2}{a_1} = -a_1[/tex]

Then adding both equation will eliminate the variable x.

Given;

Cost of 100 students= $750

Cost of 150 students= %1050

Let the fixed cost of caterer be x

and the cost per student be y

x+100y=750...(1)

x+150y=1050...(2)

solving the above equations;

50y=300

y=6

x=750-600=150

The fixed cost is $150, while the per-student cost is $6.

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Answer:

97.43cm³

Step-by-step explanation:

h = 22cm

d = 10cm

r = d/2

= 10/2

= 5

dh = 2(0.4)

= 0.8

dr = 0.05

V = πr²h

dV = d(πr²h)

Such that

πd(r²h)

= π[(r²dh + hd(r²)]

dV = π[(r²dh + 2rhdr]------(1)

When we put the values above in this equation 1 above:

dV = π[(5)²*0.8 + 2*5*22*0.05]

= π(25*0.8+11)

= π31cm³

Multiply the value of pi with 31cm³

= 97.43cm³

Answer: 9/1

Step-by-step explanation:

Selah needs to save 35.7% of her weekly pay she will need to save if she wants to sign her lease in 8 weeks.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Starting from the bottom in 8 weeks Selah will earn $(8×650).

= $5200.

The cost of renting the property for 2 months is $(2×825).

= $1650.

And 25% of one month's rent as a security deposit is,

= (25/100)×825.

= $206.25.

So, The total amount she needs to sign is $(1650 + 206.25).

= $1856.25.

Therefore, The percentage of her weekly pay she will need to save is,

= (1856.25/5200)×100.

= 35.69% or 35.7%

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Answer:

$104

Step-by-step explanation:

First find how much 1 ticket costs

65/5= 13

Times that by 8

8x13=104

The chances he chooses the 3 specific marbles he was told to find is 1/20.

It should be noted that there are 60 marbles and he wants to find 3.

In this case, he poured out 20. Therefore, his chances of picking the three marbles will be 1 out of 20.

Therefore, the chances will be 1/20.

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Answer:

Pretty sure its D.

Step-by-step explanation:

Whenever I made t something higher than 0 I got something less than 40|

(Sorry if I didn't make it in time and if I did I'm taking the same test rn gl homie)

The value of function W(t) will be less then 40 if t > 0 thus option (D) is correct.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

W(t) = 40[tex]e^{-0.35t}[/tex]

By the law of indices,

W(t) = 40/[tex]e^{.035t}[/tex]

When t > 0 the value of  [tex]e^{.035t}[/tex] > 1

Thus, t > 0 the value of W(t) < 40

Hence "The value of function W(t) will be less then 40 if t > 0".

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Answer:

80 ft^2

Step-by-step explanation:

The area of a rectangular walkway = L x W = 20 ft x 4ft =  80 ft

Answer:

[tex]\dfrac{dy}{dx}=\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex]

Step-by-step explanation:

[tex]y^3+x^2\ln y=4x+2[/tex]

Diferenciando con respecto a [tex]x[/tex]

[tex]3y^2\dfrac{dy}{dx}+2x\ln y+\dfrac{x^2}{y}\dfrac{dy}{dx}=4\\\Rightarrow (3y^2+\dfrac{x^2}{y})\dfrac{dy}{dx}=4-2x\ln y\\\Rightarrow (\dfrac{3y^3+x^2}{y})\dfrac{dy}{dx}=4-2x\ln y\\\Rightarrow \dfrac{dy}{dx}=\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex]

La derivada de la función dada es [tex]\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex].

i can't read it, its too blurry

anyways have a great day/night :)

Answer:

70 ish

Step-by-step explanation:

Answer:The correct answer is 16

Step-by-step explanation:

4^2= 16

16-6/2+3

16-3+3

13+3=16

Answer:

x=3 and x=-1

Step-by-step explanation:

Given Descartes' Rule of Signs, there is only one positive root and one negative root.

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient.

So P could be +1, -1, +3, or -3, while Q could be 1 or -1.

Therefore, P/Q could be +1, -1, +3, or -3.

Then we use synthetic division to find the correct factor(s):

1 | 1 -1 -5   -3

___ 1_0_ -5

   1  0 -5 | -8

So (x-1) is not a factor

-1 | 1 -1 -5   -3

___-1_2_  3

    1 -2 -3 |  0

So (x+1) is a factor where the quotient is x^2-2x-3 or (x-3)(x+1)

3 | 1 -1 -5   -3

___ 3_6_ 3

    1  2  1 |  0

So (x-3) is a factor where the quotient is x^2+2x+1 or (x+1)^2

Given (x-3) and (x+1) are factors, we now use the Zero Product Property:

(x-3)(x+1)=0

x-3=0

x=3

x+1=0

x=-1

So the roots are x=3 and x=-1

Answer:

The last one

Step-by-step explanation

x is greater than six so you would go to the right and it has to be an open dot since it can't be the same as 6

Answer:

hello

Step-by-step explanation:

Answer:

The non-equivalent ratio is 4:5.

Step-by-step explanation:

2/3 4/6 and 8/12 are equivalent because they are all multiples of each other.

As given triangle ABC, angle C is a right angle if a=6, c=10 then value of trigonometric function is  sin A = 3/5.

As given in the question,

In triangle ABC,

∠C  = 90°

Side a is opposite to angle A

c is the hypotenuse opposite to angle C

a = 6

c = 10

sin A = ( opposite side) / Hypotenuse

⇒sin A = a/c

⇒sin A = 6/10

⇒sin A = 3/5

Therefore, as given triangle ABC, angle C is a right angle if a=6, c=10 then value of trigonometric function is sin A = 3/5.

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the correct answer is C. 3/8

Answer:

damm thats really good

Step-by-step explanation:

Answer:

ooooooo me :)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Probably C but I sure wouldn't bet the farm on it. It looks like C is about 1.5 times the size of X

Answer:

5 singles

Step-by-step explanation:

5 $20= 100

2 $20= 40

remainder is 5 singles

Answer:

5 $1 bills.

Step-by-step explanation:

The expression to reflect this problem is:

145 = 20(5) + 20(2) + 1x

145 = 100 + 40 + 1x

145 = 140 + 1x

145 - 140 = 140 + 1x - 140

5 = 1x

5 ÷ 1 = 1x ÷ 1

5 = x

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

15% off $30

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

5 hours

Answer:

[tex] = 4(32) + (2) \\ = 128 + 2 \\ = 130[/tex]

HOPE THIS HELPS

Using trigonometric ratios we calculate the value of the variables as approximately x and y are 5.1 units and 3.1 units respectively .

Trigonometry is the branch of mathematics that is used for solving a right angled triangle if only one data is given.

Let us consider a triangle ABC right angled at B. BC is the base of the triangle and AC is the hypotenuse , therefore AB is the perpendicular.

The various trigonometric ratios used for solving a triangle are :

sin C = AB ÷ AC

cos C = BC ÷ AC

tan C = AB ÷ BC

Now in the given figure we can see that :

In ΔABC , using the trigonometric ratio of sin

sin ∠A = BC ÷ AB

or , sin 51° × AB = BC

or, BC = 10.102...

or, BC ≈ 10.1

Again in Δ BCD ,  using the trigonometric ratio of cos

cos ∠D = CD ÷ BD

or, CD ≈ 5.1

In ΔABC , using the trigonometric ratio of tan

tan ∠A = BC ÷ AC

or, tan 51° = 10.1 ÷ AC

or, AC = 8.178...

or, AC ≈ 8.2

Therefore the value of y is AC-DC = 8.2 - 5.1 = 3.1 units

The values of x and y are 5.1 units and 3.1 units respectively .

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