what is its first derivative

The coordinates of the 4th vertex of the rhombus are (-2,3)

The diagonals are given as:

(-7, -2) and (-1, -4)

The 3rd vertex is given as: (-6,-9)

Calculate the distance between the vertices of the diagonals and the 3rd vertex using:

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

So, we have:

[tex]d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50[/tex]

[tex]d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50[/tex]

Let the 4th vertex be (x,y)

So, we have:

[tex]d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50[/tex]

[tex]d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50[/tex]

Equate d3 and d4

[tex]\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}[/tex]

Take the square of both sides

[tex](-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2[/tex]

Expand

[tex]1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2[/tex]

Evaluate the like terms

1 + 2x  + 16 + 8y  = 49 + 14x + 4 + 4y

Collect like terms

14x - 2x + 4y - 8y = 1 + 16 - 49 - 4

12x - 4y = -36

Divide through by 4

3x - y = -9

Next, we test the options in the above equation

Point (-8,13) means x = -8 and y = 13

So, we have:

3x - y = -9

3(-8) - 13 = -9

-37 = -9 --- this is false

Point (-2, 3) means x = -2 and y = 3

So, we have:

3x - y = -9

3(-2) - 3 = -9

-9 = -9 --- this is true.

Hence, the coordinates of the 4th vertex are (-2,3)

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Answer:

In terms of Pi: [tex]3\pi + 6[/tex] km

Exact value (rounded): 15.42477 km

Approximated (3.14): 15.42 km

Step-by-step explanation:

Hello!

A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]

We can plug in the values to solve for the perimeter.

In terms of Pi, it is [tex]3\pi + 6[/tex],

Exact value of Pi, it is 15.42477

Approximation of Pi (3.14), it is = 15.42

Since diagonals bisect each other, both halves of a diagonal have the  same length.

[tex]5y-5=y+23\\4y=28\\y=7\\\\2x-0=x+2\\x=2[/tex]

Therefore b)

Answer: g(x)

Step-by-step explanation:

Seniors in the class = total number of students - total number of juniors

30 - 24 = 6

Juniors that went on the field trip = 2/3 x 24 = 16 students

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Step-by-step explanation:

13 pounds of sugar for $6.

for a single pound of sugar we need to divide everything by 13 to keep the same ratio (relationship).

1 pound cost then 6/13 = 0.461538462... ≈ $0.46

Answer: 0.05

Step-by-step explanation:

Since 95 out of 100 were closed, the closed window is 95% = 0.95.

5 open windows = 5% = 0.05

Answer: The save $1134.48

Step-by-step explanation:

3912 x 0.29 = 1134.48

The amount of money that the family saves in a month will be $1,017.12.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

A family has a month-to-month payment of $3912. Their month-to-month uses are displayed in the diagram underneath.

Rent 21%

Food 24%

Transportation 11%

Other Expenses 18%

Savings 26%

Then the amount of money that the family saves in a month is calculated as,

⇒ $3,912 x 0.26

⇒ $1,017.12

The amount of money that the family saves in a month will be $1,017.12.

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Answer:

  68 texts per day

Step-by-step explanation:

The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).

__

Substitute the number (15) for the variable (a) and do the arithmetic:

  t = -1.63a +92.14

  t = -1.63(15) +92.14 = -24.45 +92.14

  t = 67.69

Keiko's trend line estimates a 15-year-old would send about 68 texts per day.

Answer:

8x

Step-by-step explanation:

(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.

Answer:

8x

Step-by-step explanation:

got it right!!!

Answer:

x = 3.6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Formula:

Let b be the base (circle) of the cone

and h be the height of the cone

[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]

……………………………………………

→ b = π × r²

  = π × 6²

  = (22÷7) × 36

  = 113.142857142857 cm²

→ h = 7

[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]

The volume = (1÷3)×(113,142857142857)×(7)

                    = 264 cm³

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

 METHOD 2 :

Volume = (1÷3)×(22÷7)×36×7

             = (1÷3)×22×36

             = 22×12

             = 264

Answer:

Decimal = 0.05

Percentage = 5%

Explanation:

Total count : 20

Sarah count : 1

probability = favorable outcomes/total outcomes

                   =     1/20

                   =     0.05

The given quadratic expression; 5b² -6b -2 is prime because the discriminant is not a perfect square.

According to the task content; it is required to identify if the expression is prime.

On this note, it follows that the discriminant of the expression can be evaluated as follows;

= 36 -(4× 5 × -2)

= 76.

Hence, the expression is prime since 76 is not a perfect square.

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Answer:

[tex]log_2(10)[/tex]

Simplify the equation using logarithms.

[tex]2^3x=10[/tex]

[tex]log_1_0(2^3x)=log_1_0(10)[/tex]

log rule ⇩

[tex]log_a(x^y)=y*log_a(x)[/tex]

move exponent out of log.

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

isolate variable further

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]

formula for combining logs. ⇩

[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]

the result ⇩

[tex]x=log_2(10)[/tex]

Answer:

0.1235

Step-by-step explanation:

I'm not exactly sure what you mean, but I'm guessing that it's how much is needed to get 10 as the whole number. In that case, you just do 10-9.8765 to get 0.1235. So, 9.8765+0.1235=10. Hope this helped!

Answer:

D) [tex]22\:\text{m/s}^2[/tex]

Step-by-step explanation:

Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:

Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]

Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]

Acceleration of Particle: [tex]a(t)=6t-8[/tex]

After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]

The acceleration of the particle after 5 seconds is 38 m/s².

Acceleration is the rate of change of velocity or the slope of velocity.

We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.

∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.

Now, s = t³ + 4t² + 2t + 8 meters.

ds/dt = 3t² + 8t + 2 m/s.

d²s/dt² = 6t + 8m/s²

Now, at t = 5 seconds d²s/dt² = 6t + 8 is,

d²s/dt² = 6(5) + 8 m/s².

d²s/dt² = 38 m/s².

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Since, Maxwell wants to know how much space his globes occupies he has to find its volume.

Volume is the amount of space an object or substance occupies.

Every three dimensional object occupies a space.

Volume is measured in cubic units.

Therefore, the three dimensional object that has a width, length and height will have its volume as follows;

volume = lwh

where

Therefore, the space occupied by the globe is the volume of the globe.

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Answer:

Step-by-step explanation:

If x = 3

then

5x² = 5×(3)² = 5 × 9 = 45

and 45 > 40

Therefore

3 is not a solution to the inequality 5x² < 40.

Hi Student!

This question is fairly simply and the main goal of this question is to determine whether x = 3 is a solution of the expression that was provided or not.  The first step that we take is to plug in all of the values or in this case we input the value 3 for everywhere we see x in the equation.  The next step is to simplify the expression on both sides and finally compare the expression to see if it evaluates to true.  If it evaluates to true then x = 3 is a solution but if it evaluates to false then x = 3 isn't a solution.

Plug in the values

Simplify the expression

Looking at the final expression that was simplified, we can see that it states that 45 is less than 40 when we know that is not the case.  Therefore, this would evaluate to the expression being false and x = 3 not being a solution of the expression that was given in the problem statement.

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.

The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]

Thus, we can compute the confidence interval:

[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]

Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.

Part B

The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]

Resolviendo un sistema de ecuaciones veremos que se vendieron 900 boletos de $15 y 3600 boletos de $10.

Primero definamos las variables:

Sabemos que se vendieron 4500 boletos, entonces:

x + y = 4500

Y se recaudo un total de $49,500, entonces:

x*$10 + y*$15 = $49,500

Entonces tenemos un sistema de ecuaciones:

Para resolver esto, primero debemos aislar una de las variables en la primer ecuación, voy a aislar x:

x = 4500 - y

Ahora reemplazamos esto en la otra ecuación:

(4,500 - y)*$10 + y*$15 = $49,500

Ahora debemos resolver estoy para y.

$45,000 - y*$10 + y*$15 = $49,500

y*$5 = $49,500 - $45,000 = $4,500

y = ( $4,500)/$5 = 900

Entonces:

x = 4500 - 900 = 3600

Se vendieron 900 boletos de $15 y 3600 boletos de $10.

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The solution to the given system of inequality is (-12, 6).

These are equations that contains unknown variables.

Given the equations

x + 4y > 12

3y > x + 6

__________

x + 4y > 12

3y - x > 6

Subtract

4y - 3y > 12 - 6

y > 6

Substitute y = 6 into the equation

x + 4y >12

x + 4(6) > 12

x > -12

Hence the solution to the given system of inequality is (-12, 6)

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The true statement about the functions is (d) the range of g(x) includes more values than the ranges of f(x) and h(x).

The attached image represents the missing part of the question

From the attached image, we have the following properties:

The property 2 above is calculated as follows:

Range of g(x) =|-4 + 19| = 15

Range of f(x) =|1 + 2| = 3

Range of h(x) =|2 + 8| = 10

Hence, the true statement about the functions is (d) the range of g(x) includes more values than the ranges of f(x) and h(x).

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Answer:

Step-by-step explanation:

1) Reflection over [tex]\overline{BC}[/tex]

2) The triangles are congruent by SAS, so when [tex]\triangle GBC[/tex] is mapped onto [tex]\triangle ABC[/tex], because points [tex]G[/tex] and [tex]A[/tex] are corresponding, [tex]G'[/tex] will correspond with [tex]A[/tex].

3) Yes, because [tex]\overline{BG} \cong \overline{AB}, \overline{GC} \cong \overline{AC}, \angle BAC \cong \angle BGC[/tex], so the triangles are congruent by SAS.

Answer:

Calculator soup can help just search for whatever your learning and add a calculator at the end

Answer: x-axis

Explanation:

Hope that helps!

this is your answer.

Answer: 68.0389

Answer:

68.04 is the correct answer

I looked it up