Solve this system of equations please it’s giving me fits

According to the information we ca infer that the equation associated with answer is the graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7) (option D).

To find the graph that corresponds to the equation, we must check that the option matches all four criteria and has the right vertex. In accordance with the above, we must read each of the options and analyze whether they meet these requirements.

According to the previous instruction we can infer that the following function is the one that provides a correct answer to the equation:

y = x2 - 6

Additionally, we can calculate the vertex of the parabola by finding the derivative of the equation when assigned the value of 0.

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Answer:

do u still need help?

Step-by-step explanation:

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

\( \sqrt[3 \\ ]8 + \sqrt{114} {?} \)

Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)

Step-by-step explanation:

Answer:

(-∞,1)∪(1,∞)

Step-by-step explanation:

Domain stretches to positive and negative infinity with an asymptote at 1.0. Different places use different ways to denoting domains, but this should be it!

Answer:

Equation to find radius = Diameter divided by 2

Area is 1319.585

Step-by-step explanation:

Diameter = 41 cm

Radius = 41÷2 = 20.5cm

Area = πr^2

Area = 3.14×(20.5)^2

Area = 3.14×420.25

Area = 1319.585cm^2

Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

Answer:

\(x = y = z = 20\)

Step-by-step explanation:

Given

\(Volume = 8000cm^3\)

Required

Determine the dimensions that minimizes the surface area.

Surface area of a box is;

\(S = 2(xy + xz + yz)\)

Volume of a box is:

\(V = xyz\)

Make z the subject

\(z = \frac{V}{xy}\)

Substitute 8000 for V

\(z = \frac{8000}{xy}\)

Substitute 1000/xy for z in \(S = 2(xy + xz + yz)\)

\(S = 2(xy + x\frac{8000}{xy}+y\frac{8000}{xy})\)

\(S = 2(xy + \frac{8000}{y}+\frac{8000}{x})\)

Expand:

\(S = 2xy + \frac{16000}{y}+\frac{16000}{x}\)

\(S = 2xy + 16000(\frac{1}{y}+\frac{1}{x})\)

Differentiate S w.r.t x

\(\frac{dS}{dx} = 2y - \frac{16000}{x^2}\)

Differentiate S w.r.t y

\(\frac{dS}{dy} = 2x - \frac{16000}{y^2}\)

Equate both differentiation to 0

\(2x - \frac{16000}{y^2} = 0\)

Multiply through by \(y^2\)

\(2xy^2 - 16000 = 0\)

\(2xy^2 = 16000\)

Divide through by 2

\(xy^2 = 8000\) -- (1)

\(2y - \frac{16000}{x^2} = 0\)

Multiply through by x^2

\(2x^2y - 16000 = 0\)

\(2x^2y = 16000\)

Divide through by 2

\(x^2y = 8000\) --- (2)

Divide (1) by (2)

\(\frac{x^2y = 8000}{xy^2 = 8000}\)

\(\frac{x}{y} = 1\)

\(x = y\)

Substitute y for x in (1)

\(x^2y = 8000\)

\(x^2 * x = 8000\)

\(x^3 = 8000\)

Take cube roots

\(x =20\)

Hence;

\(x = y = 20\)

Recall that:

\(z = \frac{8000}{xy}\)

\(z = \frac{8000}{20 * 20}\)

\(z = 20\)

Hence, the dimension of the box that minimizes the surface area of the box is:

\(x = y = z = 20\)

Answer:

2 4/9

Step-by-step explanation:

Get common denominators:

1/3= 3/9

Then subtract:

7/9-3/9=4/9

8-6=2

Then add:

2+4/9= 2 4/9

Hope this helps! :)

Pls mark brainliest if correct:)

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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The product below is equivalent when x > 0 is 1/9

Square root is a real number x multiplied by itself - which results in a perfect value, where it is possible to calculate the real proof (which is the square root).

Given the expression, \(\large \sf \sqrt{\dfrac{1}{x^{2} } } \cdot \sqrt{\dfrac{x^{2} }{81} }\), first step: we will calculate the root of the numerator and denominator of this fraction:

\(\\\large \sf \sqrt{\dfrac{1}{x^{2} } } \cdot \sqrt{\dfrac{x^{2} }{81} }\)

\(\large \sf \dfrac{\sqrt{1} }{\sqrt{x^{2} } } \rightarrow \dfrac{1}{x}\)

\(\large \sf \dfrac{\sqrt{x^{2} } }{\sqrt{81 } } \rightarrow \dfrac{x}{9}\\\\\)

Step two: rearranging the expression and canceling the common factors x, we will have,:

\(\\\large \sf \dfrac{1}{\not x} \cdot \dfrac{\not x}{9}\)

\(\pink{\boxed{\large \sf \dfrac{1}{9} }}\\\)

Therefore, the final answer to this multiplication will be 1/9.

Answer:

447

Step-by-step explanation:

The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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Answer: 9.44 seconds

Step-by-step explanation:

A movement equation in the vertical axis is usually written as follows:

p(t) = (-g/2)*t^2 + v0*t + p0

where:

g is the gravitational acceleration, in this case is 32 ft/s^2, then -g/2 = -16ft/s^2

v0 is the initial velocity, in this case, 24 ft/s

p0 is the initial height, in this case, 1200ft

Then, when p(t)  = 0ft will mean that the pebble will hit the ground, then we need to calculate:

p(t) = -16t^2+24t+1200  = 0

and find the value of t, this is a quadratic equation, then we can use the Bhaskara equation to find the two solutions, these are:

\(t = \frac{-24 +- \sqrt{24^2 - 4*(-16)*1200} }{2*-16} = \frac{-24 +- 278.2}{-32}\)

Then the two solutions are:

t = (-24  + 278.2)/-32 = -7.94 seconds (we can discard this one, because the negative time is not really defined)

t = (-24 - 278.2)/-32 = 9.44 seconds

Then the pebble needs 9.44 seconds to hit the ground

Answer:

Three examples are 0.471, 0.472, 0.473.

Always remember there are more than 2 place values in decimals! Do not be afraid to extend it. Have a nice day and mark brainliest if possible :)

Most samples of 6 adults would differ from mean by no more than 1.0

In our culture, computer equations are also employed to define the systems that truly influence the social or political reality we live in. This kind of prescriptive usage of statistical equations is described.

(a) The creation of approaches and procedures utilizing statistical as well as other mathematical treatments for the quantitative analysis of data in order to investigate political structures and behavior. Questions pertaining to probability models, probability theory, measurement, and data are included.

Here n=6

p=0.77

q=1-p=1-0.77=0.23

mean=np=6*0.77=4.62=4.6

variance=npq=6*0.77*0.23=1.0626=1.1

standard deviation=sqrt(variance)=sqrt(1.0626)= 1.030825=1.0

M = 4.6

o2 = 1.1

0= 1.0

Most samples of 6 adults would differ from  mean by no more than 1.0

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Answer:

Here we have:

IxI < 7

This also can be written as:

-7 < x < 7

and:

IyI < 2.

As above, we can write this as:

-2 < y < 2.

Then the graph of this region will be a rectangular area, where the perimeter is a dashed line (because here we use the strictly smaller or strictly larger symbols)

Such that the vertical component goes from -2 to 2, and the horizontal component goes from -7 to 7.

The area would be the area inside that rectangle, where i did not shade it so it is easier to read.

Answer: 1/2x -5

Step-by-step explanation:

Half of x , less 5. (5 less just means subtract)

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

p<4

Step-by-step explanation:

4p+2< 2(p+5)

Distribute: 4p+2<2p+10

Subtract 2 from both sides: 4p<2p+8

Subtract 2p from both sides: 2p<8

Divide and we get: p<4

Answer:

p<4

Step-by-step explanation:

subtract 2 from both sides

subtract 2p from both

dont get them confused

divide

Step-by-step explanation:

the answer is

\(x = \sqrt{3} \)

Answer:

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Replace the 2b with 10 and then do the parenthesis, so 10-4=6

now multiply it with the 6 outside the parenthesis and you get 36

Hi! I'm happy to help!

First of all, we need to substitute b into the expression.

6(2b-4)

6((2×5)-4)

Now we use the order of operations, or PEMDAS (Parenthesis, Exponents, Multiplication or Division, and Addition or Subtraction) to finish simplifying.

We see that 2×5 is inside two sets of parenthesis, so we solve that first

6((2×5)-4)

6((10)-4)

We cam remove the extra set of parenthesis because there isn't an expression inside of it any more.

6(10-4)

Now, we look inside of the parenthesis again and we see 10-4

6(10-4)

6(6)

The six next to the parenthesis has no sign next to it, which means to multiply.

6×(6)

Now we can remove the parenthesis.

6×6

Now, we just simply multiply.

6×6

36

To sum it up: The value of 6 (2b-4) When b=5 is 36

I hope this was helpful, keep learning! :D

Answer:

Logistic growth is like growth statistics only known when the population size is affected by limited resources. Logistic growth is a mix of math and science, and comes helpful for studying populations.

One example of logistic growth formula is f(P) = rP(1 - P / K)

Where K is your relative growth rate co-efficient(only when K is lowercased. Otherwise, K is carrying capacity.)

And P is your initial population.

Answer:

500 boxes an hour?

Step-by-step explanation:

Answer:

The machine can pack 500 boxes in one hour

You can add +500 in case for more hours

Step-by-step explanation:

2,500 divided by 5 is 500.

Answer: b=11

Step-by-step explanation:

2x^2+11x-40=0

here

a=2 ,  b=11 and c= -40

The rental cost in dollars per square foot is $11,00

Cost of renting 1.250 square feet = $13, 750 per month

Rental cost per square foot = Total renting cost / total renting area

= $13, 750 per month / 1.250 square feet

= $11,000

Hence, $11,000 is the rental cost in dollars per square foot.

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