Express 16 1/3 in the simplest radical form

Answer:

y = 15

x = 43

Step-by-step explanation:

this is giving us a system of equations because we know two things:

x + y = 58

x - y = 28

take the second equation and format it where you have simplified it for one variable:

x = 28 + y

(we did this by adding y to both sides)

now substitute this new value of x into the first equation:

28 + y + y = 58

simplify this to get 2y = 30

divide both sides by 2: y = 15

now substitute your new value of y into the second equation:

x = 28 + 15

x = 43

Answer:

3611/12

Step-by-step explanation:

The measure of angle NMQ is 73 degrees

The given parameter is:

[tex]\angle MNP = 107[/tex]

From the given figure, angles MNP and NMQ are adjacent angles.

Given that the adjacent angles of a trapezoid add up to 180 degrees.

We have the following equation

[tex]\angle MNP + \angle NMQ = 180[/tex]

Make NMQ the subject

[tex]\angle NMQ = 180 -\angle MNP[/tex]

Substitute 107 for MNP

[tex]\angle NMQ = 180 -107[/tex]

[tex]\angle NMQ = 73[/tex]

Hence, the measure of angle NMQ is 73 degrees

Read more about adjacent angles at:

https://brainly.com/question/1149840

Answer:

The answer should be choice B.

Step-by-step explanation:

By using the process of elimination, you can cross out choices A and D.

According to the equation, the slope is of p(x) is smaller than q(x), thus q(x) will be steeper than q(x).

The valid answer is B because choice C is wrong.

Answer: x=9 1/3

Step-by-step explanation:

-5=-3x-33

-5+33=-3x

28=-3x

3x=-28

x=28/3

x=9 1/3

Answer: X=-28/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−5=−3(x+11)

−5=(−3)(x)+(−3)(11)(Distribute)

−5=−3x+−33

−5=−3x−33

Step 2: Flip the equation.

−3x−33=−5

Step 3: Add 33 to both sides.

−3x−33+33=−5+33

−3x=28

Step 4: Divide both sides by -3.

-3x/-3= 28/-3

X=-28/3

have a nice day :)

Answer:

See below and attached

Step-by-step explanation:

Given numbers

Greater than 3.1×10^-3

Between 3.1 × 10^-3  and 4.3 × 10^-5

Less than 4.3 × 10^-5

Answer:

3.2x 10-5 goes in the Less than 4.3 x 10-5 box

Step-by-step explanation:

Answer:0.03

Step-by-step explanation:

Answer:

The waste Suzanne is going to have is around 7.726.

8 if looking for nearest square foot.

Step-by-step explanation:

Area for a square - x*x (length times length)

Area for a circle - r^2*pi

Find the area of the circle first, which plug in r as 3.

3^2*pi

9pi

≈28.27433

Notice for a circle inside a square,  the length of the square is the diameter of the circle.

By knowing 2r=diameter, we know the length of the square is 6

substitute x as 6.

6*6=36

Find the waste= Area of square - Area of circle

36-28.27433

≈7.726

The image I attached should give you a clue on how the problem is being done and help you to understand what the 3 feet means.

Answer:

-2

Step-by-step explanation:

f(x) = –x– 5

f(x) = -(-3)– 5

f(x) = 3– 5

f(x) = -2

Answer:

Answer is -2 because - * - = + 3-5=-2

Answer:

equal in force, amount, or value also : equal in area or volume but not superposable a square equivalent to a triangle.

Step-by-step explanation:

Answer:

B:3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of bags required:

Total beans:-.

Answer:

Step-by-step explanation:

The answer would be 5 because 14/7=2 and 6/3=2 and 10/ 2 =5 so 5

Answer:

[tex]Scale = 1\ in : 8\ ft[/tex]

Step-by-step explanation:

Given

[tex]Scale\ Measurement = 20.5in[/tex]

[tex]Actual\ Measurement = 164ft[/tex]

Required

Determine the scale

The scale is calculated using the following ratio:

[tex]Scale = Scale\ Measurement : Actual\ Measurement;[/tex]

Substitute values for Scale and Actual Measurements

[tex]Scale = 20.5\ in : 164\ ft[/tex]

Divide ratio by 20.5

[tex]Scale = 20.5/20.5\ in : 164/20.5\ ft[/tex]

[tex]Scale = 1\ in : 8\ ft[/tex]

This implies that: 1 inch on scale represents 8 ft in actual measurement

Answer:

1.8

Step-by-step explanation:

Answer:

The height is 3791 ft.

Step-by-step explanation:

You need to make a drawing. Start with a vertical segment, 2 inches long, on the left side of the page. Label the top point A and the bottom point B. At the bottom endpoint, draw a longer horizontal segment, 4 inches long, to the right. Label the bottom right endpoint C. Connect A and C with a segment. Angle C is the original angle of elevation. On the bottom horizontal side, approximately 1 inch to the left of C, draw point D. Connect D and A with a segment. DA = 1000 ft. m<C = 34.8°. m<ABD = 40.4°. We are looking for AB, the height of the volcano.

We can work on triangle ADC.

m<C = 34.8°

Angles ADB and ADC are a linear pair, so m<ADC = 180° - 40.4° = 139.6°

m<DAC + m<ADC + m<C = 180°

m<DAC + 139.6° + 34.8° = 180°

m<DAC = 5.6°

Using the law of sines, we can find AC.

[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]

[tex]\dfrac{\sin 5.6^\circ}{1000} = \dfrac{\sin 139.6^\circ}{AC}[/tex]

[tex]AC = \dfrac{1000\sin 139.6^\circ}{\sin 5.6^\circ}[/tex]

[tex] AC = 6642~ft [/tex]

Now we use triangle ABC. AC = hypotenuse. AB = opposite leg. <C is known angle.

[tex] \sin C = \dfrac{opp}{hyp} [/tex]

[tex]\sin 34.8^\circ = \dfrac{AB}{6642~ft}[/tex]

[tex]AB = 6642~ft \times \sin 34.8^\circ[/tex]

[tex] AB = 3791~ft [/tex]

Answer: The height is 3791 ft.

Answer:

3125 bacteria.

Step-by-step explanation:

We can write an exponential function to represent the situation.

We know that the current population is 100,000.

The population doubles each day.

The standard exponential function is given by:

[tex]P(t)=a(r)^t[/tex]

Since our current population is 100,000, a = 100000.

Since our rate is doubling, r = 2.

So:

[tex]P(t)=100000(2)^t[/tex]

We want to find the population five days ago.

So, we can say that t = -5. The negative represent the number of days that has passed.

Therefore:

[tex]\displaystyle P(-5)=100000(2)^{-5} = 100000 \Big( \frac{1}{32}\Big) = 3125 \text{ bacteria}[/tex]

However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.

We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:

[tex]P(t)=A(2)^t[/tex]

After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:

[tex]100000=A(2)^5[/tex]

And solving for A, we acquire:

[tex]\displaystyle A=\frac{100000}{2^5}=3125[/tex]

So, our function in terms of the original day is:

[tex]P (t) = 3125 (2)^t[/tex]

So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.

Answer:

We can express the question in a exponential function

The current population is 100,000.

The population doubles each day.

The exponential function is given by: P(t)=a(r)^t

The current population is 100,000, a = 100000.

The rate is doubling, r = 2.

P(t)=100000(2)^t

As we know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, the function is:

P(t)=A(2)^t

After 5 days, the population reaches 100,000. So, when t = 5, P(t) = 100000:

100000=A(2)⁵

Now solving for A, we get

A=(100000)/(2⁵)=3125

So, the function in terms of the original day is:

P (t) = 3125 (2)^t

Hence, the initial population is 3125 bacteria.

Answer:

The perimeter of square will be 18 units

Step-by-step explanation:

We are given that the coordinates of three vertices of a square A (-2 1/2 , 1 1/2), B (-2 1/2 -3), and C (2,1 1/2 )

When point D is placed on this perimeter.

We have to find the perimeter of the square.

First we have to find the side of square by using the distance formula

Distance formula

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Coordinates of A=(-5/2,3/2)

Coordinates of B=(-5/2,-3)

Length of side AB=[tex]\sqrt{(-5/2+5/2)^2+(-3-3/2)^2}[/tex]

Length of side AB=[tex]\sqrt{0+(-9/2)^2}[/tex]

Length of side AB=9/2 units

Now, the perimeter of square=4 (side)

Using the formula

Perimeter of square=4(9/2)=18 units

Answer:

The best inequality describes the possible length of EG is 32 < EG < 56 ⇒ B

Step-by-step explanation:

In any triangle

In Δ EFG

∵ EF = 44 cm

∵ FG = 12 cm

→ Find their sum and difference

∴ The sum of their length = 44 + 12 = 56 cm

∴ The difference between their length = 44 - 12 = 32 cm

→ By using the rule above

∵ EG is the third side

∴ EG < 56

∴ EG > 32

→ Write them in one inequality

∴ 32 < EG < 56

∴ The best inequality describes the possible length of EG is 32 < EG < 56

Answer:

it's true...............

Answer:

y = 45 + 0.15x

Step-by-step explanation:

$45 is the initial cost

0.15 is the cost for each mile

we dont know the miles so miles is x, unknown

Answer:

It is clear that both equations are identical. Hence, the solution to the system of equations would contain infinitely many solutions.

Step-by-step explanation:

Given the system of equations

y = -4x + 2

y = -4x + 2

It is clear that both equations are identical. We know that when the system of equations is identical, then the system of equations will have infinitely many solutions.

Hence the given system of equations would contain infinitely many solutions.

solving the system of equations

[tex]\begin{bmatrix}y=-4x+2\\ y=-4x+2\end{bmatrix}[/tex]

Substitute y = -4x+2

[tex]\begin{bmatrix}-4x+2=-4x+2\end{bmatrix}[/tex]

For y = -4x+2

Express y in terms of x

[tex]y=-4x+2[/tex]

Thus, the solution to the system of equations would be:

[tex]y=-4x+2,\:x=x[/tex]

It is clear that x = x is true no matter what. Hence, the solution to the system of equations would contain infinitely many solutions.

Answer:

The co-ordinates of B (1,3 )

Step-by-step explanation:

Step(i):-

Given A( 3,4) and C( -9, -2)

Given  'B' partition AC such that

B divides AC in the ratio is 1:5 internally

Section formula

       [tex](\frac{mx_{2}+nx_{1} }{m+n} ,\frac{my_{2}_+ny_{1} }{m+n} )[/tex]

Step(ii):-

Given points are

     A( 3,4) and C( -9, -2) and ratio 1 : 5

(x₁ , y₁) = ( 3,4)     and (x₂, y₂) = (-9,-2)

m:n = 1 : 5

The co-ordinates of B

           = [tex](\frac{1(-9)+5(3) }{1+5} ,\frac{1(-2)+5(4) }{1+5} )[/tex]

         =  [tex](\frac{6}{6} , \frac{18}{6} )[/tex]

       = (1 , 3)

Final answer:-

The co-ordinates of B (1,3 )

The box has volume

11 in × 3 in × x in = 33x in³

and surface area

2 (11 in × 3 in + 11 in × x in + 3 in × x in) = (66 + 28x) in²

The volume and area have the same value if

33x = 66 + 28x

Solve this equation for x :

33x - 28x = 66

5x = 66

x = 66/5 = 13.2

Answer:

9

Step-by-step explanation:

if you have two negatives next to eachother, the equation now adds like 5+4. 5+4=9

Answer:

B I think

Step-by-step explanation:

Answer: Choice B

=========================================================

Explanation:

Let's say we had segment PQ. So the endpoints are P and Q. Let M be the midpoint of segment PQ.

Furthermore, let P have coordinates (x+6, y/3). Dividing by 3 is the same as multiplying by 1/3. So (1/3)y is the same as y/3.

Let Q have the coordinates (r,s). The goal is to express r and s in terms of x and y, as the answer choices indicate.

The midpoint M is located at (2,-5)

---------------------

For now, let's focus on the x coordinates of each point

If we average the x coordinates of P and Q, we'll get the x coordinate of M

So we add up (x+6) and r, then divide by 2, and we should get 2 as a result

( (x coord of P) + (x coord of Q) )/2 = x coord of M

( (x+6) + (r) )/2 = 2

(x+6+r)/2 = 2

Let's solve for r

(x+6+r)/2 = 2

x+6+r = 2*2

x+6+r = 4

r = 4-x-6

r = -2-x

The x coordinate of point Q is -2-x

----------------------

We'll follow the same basic idea for the y coordinates

We then get

( (y coord of P) + (y coord of Q) )/2 = y coord of M

( (y/3) + (s) )/2 = -5

(y/3) + s = -5*2

(y/3) + s = -10

Now solve for s

(y/3) + s = -10

s = -10-(y/3)

This is the y coordinate of point Q.

------------------------------

We found

Point Q is therefore located at (-2-x,  -10-(y/3) )

This points to choice B as the final answer.

Answer: 15a^5b^15

a^2 + a^3 = a^5

b^7 + b^8 = a^15

Answer:

The correct answer is  25 ¢(cents) (.25 of a dollar) Per Juice box

Step-by-step explanation:

34 divided by 136 is .25 or  25 ¢