Simplify the expression 3^-8× 34.

Answer:

Step-by-step explanation:

-2x + 3 = -x + 6

-x + 3 = 6

-x = 3

x = -3

y = 3 + 6

y = 9

(-3, 9)

Answer:

3 (5x+2y = 0)

2 (2x – 3y = -19)

Step-by-step explanation:

5x+2y=0 (1)

2x-3y=-19 (2)

To eliminate y from the first two equation when applying the linear combination method

We will multiply y Equation (1) and (2) with 3 and 2 respectively so that the coefficients of y in the two equations +6 and -6 respectively

3(5x+2y=0)

2(2x-3y=-19)

We have,

15x+6y=0 (3)

4x-6y= -38 (4)

Add Equation (3) and (4)

19x=-38

x= -2

Substitute x= -2 into (1)

5x+2y=0

5(-2)+2y=0

-10+2y=0

-10= -2y

y=-10/-2

=5

y=5, x=-2

Answer:

12.65

Step-by-step explanation:

In the case of the blue triangle, to calculate the rise, which would be the increase, therefore it would be the hypotenuse formed by the arrow.

We have to Pythagoras is:

h ^ 2 = a ^ 2 + b ^ 2

In this case:

a (x-axis) = 4

b (y-axis) = 12

replacing:

h ^ 2 = 4 ^ 2 + 12 ^ 2

h ^ 2 = 160

h = 12.65

Which means that the rise in the blue triangle is 12.65 units

Answer:

E.  y = 2/3x

Step-by-step explanation:

You need to make an equation in slope-intercept form.  

First, you need to find the slope.  You can do this by taking two points and dividing the difference of the y's by the difference of the x's.  I will use the first two points, but you can pick whichever points you want and still get the right answer.  Also, the values in the left column will be x's, and the values in the right column will be y's.

8 - 2 = 6

12 - 3 = 9

6/9 = 2/3

The slope is 2/3.  The only equation with this value is E.

Answer:

Quantity of fuel is 24 L, based on the model S=2400/Q when S=100

Step-by-step explanation:

If the output power of the car remains constant, the speed would reduce as the masses increase, which is the shown in the observed data.

Hence S does NOT vary directly with the mass and quantity, but varies INVERSELY with the mass and fuel (which has a mass).

Many models are possible to fit the results.  Product models with a single constant k

S(m,q) = kmq  and S(m,q) = k/mq  

do not fit both observation, hence rejected.

A possible  model with two constants is shown below

S(m,q) = k1/m + k2/q..................(1)

1.  m=220, q=30 =>  80 = k1/220 + k2/30 ..........(2)

2. m=300, q=40 =>  60 = k1/300 + k2/40 ..........(3)

Solve system (2) and (3) gives k1=0, k2 = 2400.

So it appears that the speed is independent of the mass (m) [unlikely], but inversely proportional to the quantity (q) of fuel, giving

S(q) = 2400/q

When speed = 100 km/h, and mass = 250 kg,  substitute

100 = 2400/q => q=2400/100 = 24

Answer:

The answer is option A.

The number of friends you invited to your last party

Hope this helps you

Answer:

x = 2

Step-by-step explanation:

5(2x- 6) + 20 = 10

10x - 30 = -10

10x = 20

x = 2

Answer:

O2

Step-by-step explanation:

5(2x-6)+20=10

Use distirbutive property:

10x-30 because, 5×2 = 10, and 5×6=30

Now we have

10x-30+20=10

Now combine the like terms

10x-10=10

Send the 10 to the other side(it turns into positive 10 because it was negative 10 on the other side)

10x = 10+10

10x=20

Divide 10 by both sides

x/10 = 20/10

x=2

Hope that helped

Answer:

Step-by-step explanation:

The Area of the rectangular field is expressed as A = LB and its perimeter

P = 2(L+B)

L is the length of the rectangular field

B is the Breadth of the rectangular field

If the length of a rectangular field is twice its breadth i.e L = 2B and the area is 98m² then;

98 = LB

98 = 2B*B

98 = 2B²

B² = 98/2

B² = 49

B = √49

B = 7m

if B = 7m

L = 98/B

L = 98/7 = 14m

The perimeter of the field P = 2(L+B)

P = 2(14+7)

P = 2*21

P = 42m

The perimeter of the field is 42m.

The length of the diagonal of the field can be expressed using Pythagoras theorem.

d = √L²+B²

d = √14²+7²

d = √196+49

d = √245

d = 15.7m ≈ 16m

Hence, the approximate length of the diagonal of the field is 16m

Answer:

7.3 mi

Step-by-step explanation:

*Make sure your calculator is in degree mode*

Do this with the SOHCAHTOA method using angle V. Since we are trying to find the side that is the opposite of angle V (WY) and since the hypotenuse is already given, you would use SOH (sinΘ=[tex]\frac{opposite}{hypotenuse}[/tex])

sin(27)=[tex]\frac{x}{16}[/tex]

Multiply by 16 on both sides to cancel out the fraction:

16sin(27)=x

7.3=x

Answer:

[tex]\boxed{3520\ ft/min}[/tex]

Step-by-step explanation:

1 miles per hour = 88 feet per minute

Multiplying both sides by 40

40 miles per hour = 88*40 ft/min

40 mi./hr = 3520 ft/min

Answer:

3520 feet/min

Step-by-step explanation:

the speed of the car in feet per minute:

first convert miles to feet ( 1 mile =5280 feet) and hours to minutes(1hr=60min.)

(40*5280)/1*60=3520 feet/min

a) The number of bacteria in the initial population is 34.

b) The exponential growth model is y = 34 * e^(kt)

Given data:

(a) To find the initial population, we can use the exponential growth formula:

y = A * e^(kt)

Where:

y = population at time t

A = initial population

k = growth rate

t = time

Given that there are 105 bacteria after 2 hours, so plug in these values into the formula:

105 = A * e^(k*2)

Similarly,  given that there are 325 bacteria after 4 hours:

325 = A * e^(k*4)

We now have a system of equations:

105 = A * e^(2k)

325 = A * e^(4k)

To solve for A, divide the second equation by the first equation:

325/105 = e^(4k)/e^(2k)

Simplifying further:

325/105 = e^(2k)

Taking the natural logarithm of both sides:

ln(325/105) = ln(e^(2k))

ln(325/105) = 2k

Solving for k:

k = 0.56493

Substitute it back into one of the original equations to solve for A. Let's use the first equation:

105 = A * e^(2k)

Substituting k = ln(325/105) / 2:

105 = A * e^(2 * ln(325/105) / 2)

Simplifying:

105 = A * (325/105)

A = 105 * (105/325)

A ≈ 34 (rounded to the nearest whole number)

Hence, the initial population is approximately 34 bacteria.

(b) Now that we have the initial population, A, and the growth rate, k, we can write the exponential growth model for the bacteria population:

y = 34 * e^(kt)

where t represents the time in hours.

Hence, the exponential equations are solved.

To learn more about exponential growth factor, refer:

https://brainly.com/question/13674608

#SPJ4

Answer:

Step-by-step explanation:

[tex] {4}^{ \frac{3}{4} } \times {2}^{x} = {16}^{ \frac{2}{5} } [/tex]

In order to solve the equation express each of the terms in the same base .

in this case we express each of the terms in base 2

That's

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

And

[tex] {16}^{ \frac{2}{5} } = {2}^{4 \times \frac{2}{5} } = {2}^{ \frac{8}{5} } [/tex]

So we have

[tex] {2}^{ \frac{3}{2} } \times {2}^{x} = {2}^{ \frac{8}{5} } [/tex]

Since the left side are in the same base and are multiplying, we add the exponents

[tex] {2}^{ \frac{3}{2} + x } = {2}^{ \frac{8}{5} } [/tex]

Since they have the same base we can equate them

That's

[tex] \frac{3}{2} + x = \frac{8}{5} [/tex]

[tex]x = \frac{8}{5} - \frac{3}{2} [/tex]

[tex]x = \frac{1}{10} [/tex]

Hope this helps you

Answer:

D

Step-by-step explanation:

Answer:d

Step-by-step explanation:

D

Answer:

{-3.5, 3.5}

Step-by-step explanation:

Interpreting

|-x| = 3.5

gives

3.5 = +(-x)  or 3.5 = -(-x)

or

x = + / - 3.5

so the answer is

{-3.5, 3.5}

Answer:

A

Step-by-step explanation:

Answer:

[tex]p = \frac{1}{2}[/tex]

[tex]q = 5[/tex]

[tex]h^{-1}(h(3)) = 3[/tex]

Step-by-step explanation:

Given

[tex]h(x) = px - \frac{5}{2}[/tex]

[tex]h^{-1}(x) = q + 2x[/tex]

Solving for p and q

Replace h(x) with y in [tex]h(x) = px - \frac{5}{2}[/tex]

[tex]y = px - \frac{5}{2}[/tex]

Swap the position of y and d

[tex]x = py - \frac{5}{2}[/tex]

Make y the subject of formula

[tex]py = x + \frac{5}{2}[/tex]

Divide through by p

[tex]y = \frac{x}{p} + \frac{5}{2p}[/tex]

Now, we've solved for the inverse of h(x);

Replace y with [tex]h^{-1}(x)[/tex]

[tex]h^{-1}(x) = \frac{x}{p} + \frac{5}{2p}[/tex]

Compare this with [tex]h^{-1}(x) = q + 2x[/tex]

We have that

[tex]\frac{x}{p} + \frac{5}{2p} = q + 2x[/tex]

By direct comparison

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

[tex]\frac{5}{2p} = q[/tex]  --- Equation 2

Solving equation 1

[tex]\frac{x}{p} = 2x[/tex]

Divide both sides by x

[tex]\frac{1}{p} = 2[/tex]

Take inverse of both sides

[tex]p = \frac{1}{2}[/tex]

Substitute [tex]p = \frac{1}{2}[/tex] in equation 2

[tex]\frac{5}{2 * \frac{1}{2}} = q[/tex]

[tex]\frac{5}{1} = q[/tex]

[tex]5 = q[/tex]

[tex]q = 5[/tex]

Hence, the values of p and q are:[tex]p = \frac{1}{2}[/tex];  [tex]q = 5[/tex]

Solving for [tex]h^{-1}(h(3))[/tex]

First, we'll solve for h(3) using [tex]h(x) = px - \frac{5}{2}[/tex]

Substitute [tex]p = \frac{1}{2}[/tex];  and [tex]x = 3[/tex]

[tex]h(3) = \frac{1}{2} * 3 - \frac{5}{2}[/tex]  

[tex]h(3) = \frac{3}{2} - \frac{5}{2}[/tex]

[tex]h(3) = \frac{3 - 5}{2}[/tex]

[tex]h(3) = \frac{-2}{2}[/tex]

[tex]h(3) = -1[/tex]

So; [tex]h^{-1}(h(3))[/tex] becomes

[tex]h^{-1}(-1)[/tex]

Solving for [tex]h^{-1}(-1)[/tex] using [tex]h^{-1}(x) = q + 2x[/tex]

Substitute [tex]q = 5[/tex] and [tex]x = -1[/tex]

[tex]h^{-1}(x) = q + 2x[/tex] becomes

[tex]h^{-1}(-1) = 5 + 2 * -1[/tex]

[tex]h^{-1}(-1) = 5 - 2[/tex]

[tex]h^{-1}(-1) = 3[/tex]

Hence;

[tex]h^{-1}(h(3)) = 3[/tex]

Answer:

Step-by-step explanation:

x  - the width of the barn

She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:

y = 32 - 2x

Area of the fencing:  A = x•y

A(x) = x•(32 - 2x)

A(x) = -2x² + 32x             ←  quadratic function

The maximum value of quadratic function occurs at:  [tex]x=-\frac b{2a}[/tex]

a = -2,  b = 32

[tex]x=-\frac b{2a}=-\frac{32}{2\cdot(-2)}=-(-8)=8[/tex]

32-2x = 32 - 2•8 = 16

Answer:

23/30

Step-by-step explanation:

x/y

(3 5/6)/(3 3/4)

((3*6)+5/6)/((3*4)+ 3/4)

(18+5/6)/(12+3/4)

(23/6)/(15/4)

(23/6)*(4/15)

(23*3)/(6*15)

(69/90)

23/30

Answer:

1 1/45

Step-by-step explanation:

Answer:

9 lb 4 oz

Step-by-step explanation:

Justin weighed 8 lb 12 oz at birth. He gained 8 ounces by his two-week checkup. So,

8 lb 12 oz + 8 oz = 8 lb 20 oz

But, 16 oz equals one pound. So,

20 oz = 1 lb with 4 oz remaining

Now add them together.

8 lb + 1 lb 4 oz = 9 lb 4 oz

Justin's weight is 9 lb 4 oz.

Hope that helps.

Answer:

It will take 0.989 second to attain this speed

Step-by-step explanation:

In this question, we want to calculate the time it will take for the wheel of the machine to attain the given rotational speed

We proceed as follows;

From the question, we can identify the following parameters

Rotational acceleration of the wheel is, α = 180 rad/s^2

Initial spinning rotational speed of the wheel is, ω= 0 rpm

1 rpm = (1/60) revolution per second = 2π * (1/60) rad/s

Thus,

initial rotational speed ωi = 0 rad/s

Final spinning rotational speed ωf of the wheel is, = 1700 rpm =178.02 rad/s

Now, from the equations of motion (for rotational motions),

ωf = ωi + αt

where t is the time taken by the wheel to attain its final rotational speed.

178.02= 0 + 180 * t

t = 178.02/180

t = 0.989 second

Answer:

To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts

Step-by-step explanation:

To create the sketch of a polynomial function there are key features are necessary and these are the vertex, axis of symetry, x and y intercepts

One of the key features arte the vertex and this shows where it changes concativity.

While the x and y intercepts give you a couple of points of reference.

Also, the axis of symetry is only applicable to even degree polynomials

Answer:

Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.

Step-by-step explanation:

A is the intersection of angle bisectors, so is the incenter of triangle EFG. It is also the intersection of the perpendicular bisectors of the sides of triangle EFG, so is the circumcenter.

The altitudes at X, Y, and Z are perpendicular to sides EF, EG, and FG, and pass through the incenter, so X, Y, Z are points on the incircle.

A is the center of circles through E, F, and G, and through X, Y, and Z.

Answer:

Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.

C on edg2020

Answer:

8000 lei

Step-by-step explanation:

Ni se spune la întrebarea de mai sus să găsim suma depusă în bancă.

Ni se oferă următoarele valori

R = rata = 2% = 0.02

T = Timp = 1 an

Suma totală = A = 8160 lei

Trebuie să găsim principalul (suma depusă la bancă).

Formula de utilizat este dată ca:

P (Principal) = A / (1 + rt)

P = 8160 lei / 1 + 0.02 × 1

P = 8160 lei / 1.02

P = 8000 lei

Prin urmare, suma depusă în bancă este de 8000 de lei.

Answer:

the two percent of 8160 its 163.2 so its 7996.8

Step-by-step explanation:

Answer:

b = [tex]\frac{2A}{h}[/tex]

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] bh

Multiply both sides by 2 to clear the fraction

2A = bh ( divide both sides by h )

[tex]\frac{2A}{h}[/tex] = b

Answer:

r = 1.59inch

the radius of the cylinder is

1.59inch

Step by step Explanation

lateral surface of a cylinder can be calculated using the below formula

Surface Area= 2 πr h

We were given area as 400inch^2 and height as 40inch then substitute we have

400 = 2 ×π × r ×40

400= 2×22/7×40

Then do the calculation, where, π

=22/7

400 = r × 251.2

Make r subject of formula we have

r = 400 / 251.2

r = 1.59inch

Therefore, the radius of the cylinder is

1.59inch

CHECK THE ATTACHMENT FOR THE FIGURE

Answer:

X= 618079825.9

Y= 6.18 crystals

Step-by-step explanation:

It takes Lily a crystal to raise 999 zombies.

It will take her x crystals to Raise 617461746174 zombies

Mathematically

One crystal= 999 zombies

X = 617461746174

X=( 617461746174*1)/999

X= 617461746174/999

X= 618079825.9

Again

It took one crystal to raise 999 zombies

It will take y crystal to raise 6174 zombies

Mathematically

One = 999

Y =( 6174*1)/999

Y= 6.18 crystals

Answer:

They would be perpendicular to each other.

One would have a slope of 0 (horizontal line) and the other would have an undefined slope (vertical line)

Step-by-step explanation:

Notice that

2010 ≡ 1 mod 2009

2011 ≡ 2 mod 2009

2012 ≡ 3 mod 2009

...

4017 ≡ 2008 mod 2009

4018 ≡ 0 mod 2009

So really, S is just the sum of the first 2008 positive integers:

[tex]S=\displaystyle\sum_{n=1}^{2008}n=\frac{2008\cdot2009}2[/tex]

where we invoke the formula

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]

and so S ≡ 0 mod 2009.

Answer:

The angle created between the ladder and tree is [tex]15.5^{0}[/tex].

Step-by-step explanation:

The required sketch is shown in the attachment to this answer.

Applying the appropriate trigonometric function to the question, we have;

Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]

         = [tex]\frac{5}{18}[/tex]

         = 0.2777777777

⇒ θ = [tex]Tan^{-1}[/tex] 0.2777777777

      = 15.5241

      = [tex]15.5^{0}[/tex]

Therefore, the angle created between the ladder and tree is [tex]15.5^{0}[/tex].

Answer:

4(four)

Step-by-step explanation:

You take the number 10×2=20

Then,20÷5=4

Four{4}is your answer

Answer:

Step-by-step explanation:

[tex]10 \times 2 \div 5[/tex]

Multiply the numbers

[tex] = 20 \div 5[/tex]

Divide :

[tex] = 4[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

D y = 9/x

Step-by-step explanation:

An inverse variation is of the form

xy = k where k is a constant

We can write this as

y = k/x

The only equation that is of this form is

D y = 9/x

Answer:

[tex]\boxed{\mathrm{Option \: D}}[/tex]

Step-by-step explanation:

Inverse variation is written as:

[tex]y=\frac{k}{x}[/tex]

Where k is the constant of proportionality.