Find the distance from the vertices of AABC to the corresponding vertices of the other three triangles, and enter them in the table. For AJKL-
you'll need to use the distance formula da (01 – 12) + (y1 - y2) . Verify your calculations using the tools available in GeoGebra.

Answer:

y = 54/25 when x = 4.

Step-by-step explanation:

y is given by the equation:

[tex]\displaystyle y = p\times q^{x-1}[/tex]

Where p and q are numbers.

We are also given that when x = 1, y = 10 and when x = 6, y = 0.7776.

And we want to determine the value of y when x = 4.

Since y = 10 when x = 1:

[tex]\displaystyle (10) = p\times q^{(1)-1}[/tex]

Simplify:

[tex]10 = p \times q^0[/tex]

Any number (except for zero) to the zeroth power is one. Hence:

[tex]p=10[/tex]

Thus, our equation is now:

[tex]y = 10\times q^{x-1}[/tex]

When x = 6, y = 0.7776. Thus:

[tex](0.7776) = 10\times q^{(6)-1}[/tex]

Simplify and divide both sides by ten:

[tex]\displaystyle 0.07776 = q^5[/tex]

Take the fifth root of both sides:

[tex]\displaystyle q = \sqrt[5]{0.07776}[/tex]

Use a calculator. Hence:

[tex]\displaystyle q = \frac{3}{5} = 0.6[/tex]

Our completed equation is:

[tex]\displaystyle y = 10\times \left(\frac{3}{5}\right)^{x-1}[/tex]

Then when x = 4, y equals:

[tex]\displaystyle \begin{aligned} y &= 10\times \left(\frac{3}{5}\right)^{(4)-1} \\ \\ &= 10\times \left(\frac{3}{5}\right)^3 \\ \\ &= 10\times \left(\frac{27}{125}\right) \\ \\ &= \frac{54}{25}\end{aligned}[/tex]

Answer:

x=(-2,0) and x=(5/2,0)

Step-by-step explanation:

To find x-intercepts you set f(x), or y, to 0 and then solve.

[tex]0=2x^2-x-10\\Factor!\\0=(x+2)(2x-5)\\x+2=0\\x=2\\2x-5=0\\2x=5\\x=\frac{5}{2}[/tex]

The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).

The function is given as:

[tex]f(x) = 2x^2 - x - 10[/tex]

We need to find the points at which the given function crosses the x-axis.

It is the point at which the given function crosses the x-axis.

The x-intercept is found by setting y = 0 or f(x) = 0.

Given function,

[tex]f(x) = 2x^2 - x - 10[/tex]

Let's set f(x) = 0.

[tex]2x^2 - x - 10 = 0[/tex]

Solve the equation for x.

[tex]2x^2 - x - 10\\2x^2 - (5 - 4)x - 10\\2x^2 - 5x + 4x - 10\\x(2x-5) +2(2x - 5)\\(x+2)(2x-5)[/tex]

Now we have,

x+2 = 0 and 2x - 5 = 0

x = -2 and x = 5 / 2

We already know that y = 0 so the points at which the function intercepts with the x-axis are:

(-2, 0) and (5/2, 0).

The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).

Learn more about x-intercepts of a function here:

https://brainly.com/question/28019177

#SPJ2

Answer:

C

Step-by-step explanation:

The slope of the line will be (2) and the equation will be C

Answer:

i thank the ans id 450

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

93/3=31

So UV is equal to 31

Answer:

31

Step-by-step explanation:

Answer:

Male-19&Female-13

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

Step-by-step explanation:

Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).

Then the total differential is

[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]

[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]

Answer:

67

Step-by-step explanation:

DM=JM-JD=84-17=67

Answer:

Step-by-step explanation:

Answer:

3 times 10 ^ 9

Step-by-step explanation:

3 × 10 ^ 9 = 3000000000

Answer:

18 divided by nine is two. so for every one table spoon of oil there's two table spoons of vinegar. Please give brainliest

Answer:

2

Step-by-step explanation:

Make a ratio:

Oil : Vinegar

9 : 18

1 : 2

For each tablespoon of oil, 2 tablespoons of vinegar is needed.

Hope this helped.

Answer:

290.44

Step-by-step explanation:

The whole figure area can be calculated by assuming that the whole floor is a complete square of 18.2 x 18.2 and subtracting the area of the rectangular cutout which is 10.2 x 4

Area of the the flooring=18.2 x 18.2 - (10.2*4)=290.44

Answer:

The 95% confidence interval for the population mean is ($6510, $7138).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{340}{\sqrt{7}} = 314[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 6824 - 314 = $6510.

The upper end of the interval is the sample mean added to M. So it is 6824 + 314 = $7138.

The 95% confidence interval for the population mean is ($6510, $7138).

Answer:

2 is the factor of every even number hope this help you

Answer:

Hello,

in order to simplify, i have taken the inverses functions

Step-by-step explanation:

[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]

Answer:

?

Step-by-step explanation:

Answer:

x=–2

Step-by-step explanation:

x-8=-10

x=-10-8

x=–2

Answer:

-8= -10

, = -10+8

, = -2

1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.

Answer:

C. The representative failed to have Tim initial by the fuel level on the Check-Out sheet.

Step-by-step explanation:

After reading the paragraph, we can eliminate B, by seeing that the representative did give him a copy of the Check-Out sheet, as quoted. "Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.".

We can also eliminate A and D, as the contract stated nothing about dents or the oil level in the car.

The answer is C, as the representative failed to have Tim initial on the Check-Out sheet. That is a requirement for the contract to be valid, as stated. "The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter.". However, Tim never initialed by the fuel level, as stated here. "...the agency representative turned on the car, took note of the fuel level, and indicated it on the Check-Out sheet. Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.". No where here does it state that Tim initialed on the Check-Out sheet, meaning that he didn't. Him not doing so invalidates the contract.  

Answer:

Step-by-step explanation:

there are function that "invert" each other..

subtraction inverts addition...

3+2 = 5 ... 5-2 = 3

division inverts multiplication

5*2 = 10 ... 10/2 = 5

Using that concept, "factoring" is basically the inverse of multiplication

3x^2 + 9x can be factored to 3x(x+3)

if you multiply that out it reverts back to the original equation

so  x^2 + 5x + 6 factors to (x+3)(x+2)

if you multiply that out (foil it)

you get x^2 + 5x + 6

Answer:

$54

Step-by-step explanation:

10% of $60 is $6

$60-$6=$54

Answer:

17.5ml- of 10 percent solution, 17.5ml- of 20 percent solution

Step-by-step explanation:

35:100*15=5.25- ml of alkali in the base solution

Suppose we need x ml of 10 percents solution and 35-x - of 20 percents.

Then The quantity of alkali in the first one (10 percents) is x/100*10=0.1x

when in the second one we have (35-x)/100*20= 7-0.2x of alkali

0.1x+7-0.2x=5.25

7-0.1x= 5.25

0.1x=1.75

x=17.5- 0f 10 percents

35-17.5=17.5 - of 20 percents

Answer:

the union of l and m is minus 1,1,2,4,5,7,8.....and the intersection of l and m is 1.......

Answer:

[tex]125 \: \: degrees[/tex]

Step-by-step explanation:

As the 2 lines are parallel

<A = <B ( Alternative Angles)

[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = 20[/tex]

[tex]<A = 6x + 5 \\ = 6 \times 20 + 5 \\ = 120 + 5 \\ = 125[/tex]

<A=6x+5

=6×20+5

=120+5

=125

<B=4x+45

=4×20+45

=80+45

=125

it is alternate angle they are equal each other

<A = < B

[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20 \\ \\ [/tex]

Answer:

"Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample"

Step-by-step explanation:

In cluster random sampling, "the population is divided, usually geographically, into groups that generally have the same size.  A certain number of groups are randomly chosen, and every individual in the chosen groups are chosen for the sample."

In accord with this logic, the second choice, "Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample" seems to be correct.

NOTE: This may not be the correct answer. I am simply basing my answer on the definition I have learnt.

Answer:

B

Step-by-step explanation:

Answer:

Dependent event

[tex]P(Red = 2) = \frac{5}{588}[/tex]

Step-by-step explanation:

Given

[tex]Total = 49[/tex]

[tex]Red = 5[/tex]

Solving (a): Are the events dependent?

Yes, they are.

When the first red candy is selected and eaten, the total number of candies reduced to 48 and the number of red candies also reduced to 4.

So, the probability of selecting a 2nd candy is dependent on the first candy selected.

Solving (b): P(Red = 2)

This is calculated as:

[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]

The first selection has the following probability:

[tex]P(Red) = \frac{Red}{Total}[/tex]

[tex]P(Red) = \frac{5}{49}[/tex]

The second selection has the following probability:

[tex]P(Red|Red) = \frac{Red - 1}{Total - 1}[/tex]

[tex]P(Red|Red) = \frac{5 - 1}{49 - 1}[/tex]

[tex]P(Red|Red) = \frac{4}{48}[/tex]

So, we have:

[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]

[tex]P(Red = 2) = \frac{5}{49} * \frac{4}{48}[/tex]

Reduce fraction

[tex]P(Red = 2) = \frac{5}{49} * \frac{1}{12}[/tex]

Multiply

[tex]P(Red = 2) = \frac{5}{588}[/tex]

Answer: 15

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The cost of the ends of the can will be ...

  c1 = 0.07(2πr²)

The cost of the side of the can will be ...

  c2 = 0.04(2πrh)

The volume of the can will be ...

  v = πr²h

We want the derivative of the total cost to be zero, and we want the volume to be 550 cm³. We can take the derivatives of both equations to find a relation between r and h.

  d(c1 +c2) = 0.28πr·dr +0.08π(h·dr +r·dh) = 0

  d(v) = 2πrh·dr +πr²·dh = 0

Solving the first equation for dh/dr gives ...

  dh/dr = -π(0.28r +0.08h)/(π(0.08r)) = -(7r+2h)/(2r)

Solving the second equation for dh/dr gives ...

  dh/dr = -2πrh/(πr²) = -2h/r

Equating these expressions, we get ...

  -(7r +2h)/(2r) = -2h/r

  7r +2h = 4h . . . . . . . multiply by -2r

  h = 7/2r . . . . . . . . . . subtract 2h, divide by 2

__

Now, we can find the can dimensions from the volume equation.

  550 = πr²(7/2r)

  r³ = 1100/(7π)

  r ≈ ∛50.02 ≈ 3.685 . . . . . cm

  h = 7/2(3.685 cm) = 12.896 cm

The can cost will be a minimum when the radius is 3.685 cm and the height is 12.896 cm.

_____

Additional comment

You may notice that the ratio of height to diameter is the same as the ratio of end cost to side cost: 7/4. This is the generic solution to this sort of problem.