\(one+one=\) yeet

Solving a system of equations, it is found that since the quadratic equation has two positive roots, they can be the values of the length and the width, and the design is possible.

The perimeter of a rectangle of length l and width w is given by:

\(P = 2(l + w)\)

The area is:

\(A = lw\)

In this problem, perimeter of 63.5 m, hence:

\(2l + 2w = 63.5\)

\(2l = 63.5 - 2w\)

\(l = 31.75 - w\)

Area of 225 m², hence:

\(lw = 225\)

\((31.75 - w)(w) = 225\)

\(w^2 - 31.75w + 225 = 0\)

Which is a quadratic equation with coefficients \(a = 1, b = -31.75, c = 225\).

Then:

\(\Delta = b^2 - 4ac = (-31.75)^2 - 4(1)(225) = 108.0625\)

\(w_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{31.75 + \sqrt{108.0625}}{2} = 21.1\)

\(w_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{31.75 - \sqrt{108.0625}}{2} = 10.68\)

Since the quadratic equation has two positive roots, they can be the values of the length and the width, and the design is possible.

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Answer: C. 00:00 $927; Vince wrote the wrong number to represent the interest rate.

Step-by-step explanation:

Given that:

Amount borrowed (p) = 900

Simple interest (r) = 1.5% = 0.015

Time (t) = 2 years

Amount he'll pay back (A) :

A = P(1 + rt)

A = 900(1 + 0.015(2))

A = 900(1 + 0.03)

A = 900(1.03)

A = $927

Answer:

Below

Step-by-step explanation:

Losing 27 % of value each year means it retains 73% each year

  we need to multiply 20 000 x  .73 x .73 x .73     ....  .73     (twelve times )

                  or   re-written as   20 000 * .73^12 = value =$ 458.04

The Probability that rose identifies all 3 cards in the correct order is 1/66300.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Number of Card drawn without replacement= 3

Total cards = 52

As, there is no description about cards then the total number of ways to choose is

= \(^{52}P_3\)

= 52!/ 3! 49!

= 66300

and, Favorable Condition= 1( pick one card at a time)

Now, Probability that rose identifies all 3 cards in the correct order

= 1/ \(^{52}P_3\)

= 1/ 66300

Hence, the probability is 1/66300.

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Answer:

i believe the answer is A.

Step-by-step explanation: Because the angle PQS is not a 90 degree angle it should equal 180 degrees, it is now lowered down to the answers A. and B. Answer B. has 2x and answer A. has just x. if it were to be 2x then the x would  have to represent 30 degrees but the point plotted x does not equal 30 degrees therefore leaving the last answer as A. x-60=180

Answer:

substitute a=-5 and c=5 into a=-3c

Step-by-step explanation:

a= -3c

(-5)= -3(5)

-5= -15

The width is 1 meter.

Given,

Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond.The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters

Let the border be width  = x

then the area of the border will be

2(6x) + 2(15x) +4x2 = 46

= 12x +30x+ 4x2 = 46

= 4x2 + 42x - 46 = 0

=> x =( -42 +- √42² +4*4*46)/8

x =1 , x = -11.5

since the width is 1 meter.

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Answer: A line that is parallel to the x-axis is a horizontal line. In this case, the horizontal line passes through a point, (1,2). All points on a horizontal line will have the same y value. Therefore, y=2  for every point on this line and that is the equation of the line.

Step-by-step  explanation i Hope this helps

Answer:

c

Step-by-step explanation:

\(\text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}\)

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

Reason:

The formula you can use is

\((a+b)^2 = a^2+2ab+b^2\)

This is the perfect square trinomial formula.

In this case,

The square of each gets us

Those form the outer terms, aka 1st and 3rd terms.

The 2ab term in the middle would be 2*x*(1/8) = (1/4)x

That leads us to be able to say \(\left(\text{x}+\frac{1}{8}\right)^2 = \text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}\)

You can use the FOIL rule or the box method as two ways to verify this answer. Also a graphing calculator can be used.

Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).

We know that for each bowl, she needs 1/2 cups of milk.

And we also know that she has a total of (3 + 3/5) cups of milk.

To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:

(3 + 3/5)/(1/2)

We can rewrite the total as:

3 + 3/5 = 15/5 + 3/5 = 18/5

Then the quotient becomes:

(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5

So she can make 7 bowls of cereal (and some leftover milk).

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The error interval for the combined mass, m, of the car and the person is: \($$2067.65 kg \leq m \leq 2068.75 kg$$\).

The mass of the car is given as 2006 kg rounded to the nearest kilogram, which means its actual mass could be as low as 2005.5 kg or as high as 2006.5 kg.

The mass of the person is given as 62.2 kg rounded to one decimal place, which means their actual mass could be as low as 62.15 kg or as high as 62.25 kg.

To find the error interval for the combined mass of the car and the person, we need to add the upper and lower bounds of each mass:

Lower bound of combined mass: 2005.5 kg + 62.15 kg = 2067.65 kg

Upper bound of combined mass: 2006.5 kg + 62.25 kg = 2068.75 kg

Therefore, the error interval for the combined mass, m, of the car and the person is: \($$2067.65 kg \leq m \leq 2068.75 kg$$\).

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the amount of work done is 5π².

The work done W is given by the line integral:

W = ∫ F · dr

where F is the force field and dr is the differential displacement along the curve r(t).

We can write r(t) as:

r(t) = (sin t, cos t, t), for 0 ≤ t ≤ 2π

The differential displacement dr is given by:

dr = (dx, dy, dz) = (cos t, -sin t, 1) dt

Now we can evaluate F · dr as:

F · dr = (5z, 5x, 5y) · (cos t, -sin t, 1) dt

= 5z cos t - 5x sin t + 5y dt

= 5t dt

since z = t, x = sin t, and y = cos t.

Therefore, the work done is:

W = ∫ F · dr = ∫₀²π 5t dt = [5t²/2] from 0 to 2π

= 5(2π²/2) - 5(0²/2)

= 5π²

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\(\bf \huge{Answer}\)

Answer:

True

True because as per the diagram the A is present in middle position between C and D we can also say A is midpoint of line CD

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.

Let's understand the concept behind this:

Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.

We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.

Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.

AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.

AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.

AB + BC = 3 + 3.5 cm  = 6.5 cm = AC.

However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.

Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.

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A study of accidents in a production plant has found that accidents occur randomly at a rate of one every 4 working days. A month has 20 working days. What is the probability that four or fewer accidents will occur in a month?

The probability that four or fewer accidents will occur in a month is 0.44 (option C).

Rate of accidents= 1 in 4 working days, working days in a month = 20, To find the probability of four or fewer accidents will occur in a month. We have to find the probability P(x ≤ 4) where x is the number of accidents that occur in a month.P(x ≤ 4) = probability of 0 accident + probability of 1 accident + probability of 2 accidents + probability of 3 accidents + probability of 4 accidentsFrom the Poisson probability distribution, the probability of x accidents in a time interval is given by: P(x) = e^(-λ) (λ^x) / x! Where λ = mean number of accidents in a time interval.

We can find λ = (total working days in a month) × (rate of accidents in 1 working day) λ = 20/4λ = 5. Using the above formula, the probability of zero accidents

P(x = 0) = e^(-5) (5^0) / 0!P(x = 0) = e^(-5) = 0.0068 (rounded off to four decimal places)

Using the above formula, the probability of one accidents P(x = 1) = e^(-5) (5^1) / 1!P(x = 1) = e^(-5) × 5 = 0.0337 (rounded off to four decimal places) Similarly, we can find the probability of two, three and four accidents. P(x = 2) = 0.0842P(x = 3) = 0.1404P(x = 4) = 0.1755P(x ≤ 4) = probability of 0 accident + probability of 1 accident + probability of 2 accidents + probability of 3 accidents + probability of 4 accidents= 0.0068 + 0.0337 + 0.0842 + 0.1404 + 0.1755= 0.4406 (rounded off to four decimal places)

Therefore, the probability that four or fewer accidents will occur in a month is 0.44 (option C).

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Answer:

.2 Cm

Step-by-step explanation:

Answer:

1190 jumps

Step-by-step explanation:

4200/60*17 = 1190 jumps

Answer:

C, D

Step-by-step explanation:

C is correct because the triangle is symmetrical which makes "AC" and "CD" equal.

D is correct because "BCE" is also symmetrical which makes it easier to determine whether the triangle has 2 equal sides, which is does. "BC" and "CE."

Comments for Improvement Please

Answer: Radius=19.2 diameter=38.39

Step-by-step explanation: :DDD

Answer:

Line a is parallel to line b:

m∠1=m∠ 5, because they are correspondent angles, then:

2x+44=5x+38

Solving for x:

2x+44-2x-38=5x+38-2x-38

6=3x

3x=6

Dividing both sides of the equation by 3

3x/3=6/3

x=2

Answer:

v = 1/3 x area of base x height

volume = 1/3 x (12 x 12) x 8

= 384 cm3

Jessica's statement is incorrect. The amount of silver in STEM Electrum is not one and a half times the amount of gold. Instead, there is 1.5 times more silver than gold, as the ratio of silver to gold is 3:2.

To determine if Jessica's statement is correct, we need to compare the proportions of gold and silver in STEM Electrum.

According to the given information, STEM Electrum is composed of 2/5 gold and 3/5 silver. This means that for every 2 parts of gold, there are 3 parts of silver.

Now let's examine Jessica's statement. She claims that the amount of silver is one and a half times the amount of gold.

If we compare the proportions of gold and silver, we can see that the ratio is 2:3. In other words, for every 2 parts of gold, there are 3 parts of silver.

To determine if Jessica's statement is true, we need to evaluate if the ratio of silver to gold is indeed 1.5:1.

If the ratio was 1.5:1, it would mean that for every 1.5 parts of silver, there would be 1 part of gold. However, in STEM Electrum, the actual ratio is 3:2, which means that for every 3 parts of silver, there are 2 parts of gold.

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Answer:

Shrub $7

Rose Bush $8

Step-by-step explanation:

First, write them as equations

10r + 4s = $108

5r + s = $47

Next, multiply

10r + 2s = $94

10r + 4s = $108

Then, Subtract

2s = $14

After, Divide

s = $7

Then, plug in and solve

5s + $7 = $47

$40/5s = 8$

$8 = r

$7 = s

Answer: The bushes cost $8 and the shrubs cost 7$

Step-by-step explanation:

For this question you must use system of equations, trial and error will take a very long time.

So yeah, here is how you solve it-

First set up equations (b represents the amount of bushes and s represents the amount of shrubs):

5b + 1s = 47

10b+4s=108

Next you can either solve via elimination or the substitution method. I will show elimination here. Elimination works by slightly modifying one of the equations so that it cancels when it is added to the other equation:

(I modified the first equation)

-4(5b+1s = 47) = -20b-4s=-188

(Then add)

     -20b-4s=-188

  +    10b+4s=108

This equals: -10b=-80

Next you just solve for b:

b=-80/-10

b=8

To then find s, plug b into one of the original equations and solve for s:

(I plugged it into the first equation)

5(8)+1s=47

40+s=47

s=7

So the bushes cost $8 and the shrubs cost 7$

Hope this helps :)

Answer:

(2,4)

Step-by-step explanation:

the solution to a system of equations is where two lines intersect.

The angle made by the vector is \(\theta\) such that

\(\tan(\theta) = \dfrac{18.4\,\rm m}{-28.7\,\rm m} \approx -0.6411\)

Before taking the inverse tangent of both sides, recall that \(\arctan\) returns a number between -π/2 and π/2 radians, or -90° and +90°. The vector in the diagram clearly makes an angle between 90° and 180°, however, so we use the fact that tangent has a period of π rad / 180° to write

\(\theta \approx \arctan(-0.6411) + 180^\circ n\)

where \(n\in\Bbb Z\).

Now,

\(\arctan(-0.6411) \approx -0.5701 \,\mathrm{rad} \approx -32.6639^\circ\)

Add 180° to this to recover the correct angle.

\(\theta = \arctan(-0.6411) + 180^\circ \approx \boxed{147.34^\circ}\)

Answer:

no solutions

Step-by-step explanation:

-7 does not equal 7, so there are no solutions.

Infinite solutions would be if it was two equal values, for example, 7 = 7.

Answer:

-3

Step-by-step explanation:

use the equation y = mx + b where m is the slope and b is the y-intercept so just plug in what you know. y = 2/3x + 2 then solve the equation for x . To do that, just put y = 0 so then it would be -2 = 2/3x then -2/ 2/3 = x and -2 divided by 2/3 would be -3