(3,7), (1,8)
find the distance between each pair of points ​

Answer:

[tex]12k^3 -k^2-36k-20[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex](4k + 5)(3k^2 - 4k - 4)[/tex]

[tex](4k * 3k^2)+(4k*-4k)+(4k*-4)+(5*3k^2)+(5*-4k)+(5*-4)[/tex]

[tex]12k^3-16k^2-16k+15k^2-20k-20[/tex]

Step 2:  Combine like terms

[tex]12k^3+(-16k^2+15k^2)+(-16k-20k)-20[/tex]

[tex]12k^3 -k^2-36k-20[/tex]

Answer: [tex]12k^3 -k^2-36k-20[/tex]

Answer:

[tex]\boxed{\bf 7 \times 10 {}^{ - 3}} [/tex]

Step-by-step explanation:

Write 0.7 *10^-2 into scientific notation:

Hope this helps! ^^"

Answer:

[tex]7 \times 10^{-3}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}\dfrac{6.3 \times 10^{-5}}{9 \times 10^{-3}} & =\dfrac{6.3}{9} \times \dfrac{10^{-5}}{10^{-3}}\\\\& = 0.7 \times \dfrac{10^{-5}}{10^{-3}}\end{aligned}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\begin{aligned}\implies 0.7 \times \dfrac{10^{-5}}{10^{-3}} &=0.7 \times 10^{-5-(-3)}\\& = 0.7 \times 10^{-2}\end{aligned}[/tex]

[tex]\textsf{Rewrite}\:0.7\:\textsf{as}\: 7 \times 10^{-1}:[/tex]

[tex]\implies 0.7 \times 10^{-2}=7 \times 10^{-1} \times 10^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \times a^c=a^{bc}:[/tex]

[tex]\implies 7 \times 10^{-1} \times 10^{-2}=7 \times 10^{-3}[/tex]

Using an exponential function, it is found that it will take 3,252 years for the sample to degrade to 4.5kg.

It is given by:

[tex]A(t) = Pe^{-kt}[/tex]

In which:

The half-life is of 21,400 years, hence, A(21400) = 0.5P, and this is used to find k.

[tex]A(t) = Pe^{-kt}[/tex]

[tex]0.5P = Pe^{-21400k}[/tex]

[tex]e^{-21400k} = 0.5[/tex]

[tex]\ln{e^{-21400k}} = \ln{0.5}[/tex]

[tex]-21400k = \ln{0.5}[/tex]

[tex]k = -\frac{\ln{0.5}}{21400}}[/tex]

k = -0.00003239005

Hence, considering the initial mass is of P = 5 kg, the amount after t years is given by:

[tex]A(t) = 5e^{-0.00003239005t}[/tex]

The amount will be of 4.5 kg at t for which A(t) = 4.5, hence:

[tex]4.5 = 5e^{-0.00003239005t}[/tex]

[tex]e^{-0.00003239005t} = 0.9[/tex]

[tex]\ln{e^{-0.00003239005t}} = \ln{0.9}[/tex]

[tex]-0.00003239005t = \ln{0.9}[/tex]

[tex]t = -\frac{\ln{0.9}}{0.00003239005}[/tex]

t = 3252.

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Answer: Heyaa! ~

Your Answer is... 26.8

Step-by-step explanation:

The estimated answer is D. 27!

Hopefully this helps you! ^^

Answer:

27

Step-by-step explanation:

12.18 + 14.62= 26.80

if the number after the point is greater than 5 or equal to 5, we will add 1 to the number before the point, so now the number is 8 we will add 1 to the number before the point

26+1=27

therefore the sum of 12.18+14.62 = 27

Answer:

[tex]\boxed{\bf \sf number : \ \frac{4}{5} }[/tex]

Explanation:

Let the number be n

According to students Condition:

[tex]\rightarrow \sf \dfrac{3}{2} \ x \ n \quad = \quad \dfrac{3n}{2}[/tex]

What He actually Did:

[tex]\rightarrow \sf n \div \dfrac{3}{2} \quad = \quad n \ x \ \dfrac{2}{3} \quad = \quad \dfrac{2n}{3}[/tex]

He got a smaller number by 2/3, so:

[tex]\rightarrow \sf \dfrac{3n}{2} - \dfrac{2n}{3} = \dfrac{2}{3}[/tex]

make the denominator's same

[tex]\rightarrow \sf \dfrac{3(3n)}{6} - \dfrac{2(2n)}{6} = \dfrac{2}{3}[/tex]

multiply the integers

[tex]\rightarrow \sf \dfrac{9n}{6} - \dfrac{4n}{6} = \dfrac{2}{3}[/tex]

Join the fractions

[tex]\rightarrow \sf \dfrac{9n-4n}{6} = \dfrac{2}{3}[/tex]

Subtract integers

[tex]\rightarrow \sf \dfrac{5n}{6} = \dfrac{2}{3}[/tex]

Cross multiply

[tex]\rightarrow \sf n = \dfrac{6 \ * \ 2}{5 \ * \ 3} \quad = \quad \dfrac{4}{5}[/tex]

Lets see

the number be x

The expression is

Step-by-step explanation:

[tex]\huge{\color{black}{\fbox{\color{pink}{\colorbox{pink}{\color{red}{Answer ✨☑️}}}}}}[/tex]

The number of terms are 8. Step-by-step explanation: Given : The sum n terms of an A.P is 136 the common difference is 4 and last term is 31.

Answer:

Sn=2n{2a+(n−1)d}

a+(n−1)d=31⇒a=31−4(n−1)

∴136=2n{2[31−4(n−1)]+(n−1)d}

n[70−8n+4n−4]=272

n(66−4n)=272

4n2−66n+272=0

2n2−33n+136=0

2n(n−8)−17(n−8)=0

(2n−17)(n−8)=0

∴n=8

The correlation coefficient is 0.92

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

In other words, it reflects how similar the measurements of two or more variables are across a dataset.

When one variable changes, the other variables change in the same direction or opposite direction.

Perfect positive correlation :When one variable changes, the other variables change in the same direction.

Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.

[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]

After calculation we get

r = 0.92

Therefore it is a Perfect positive correlation

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Step-by-step explanation:

Triangle MŇO is congruent to Triangle UŤS

NO=4

MN=4

MO=5.6( Which is 140% bigger than 4)

UT=10

TS=10(Therefore this also should be 10)

US=14(Which is 140% bigger than 10)

I think this is the solution but I am not 100% sure

Answer:

x=14

Step-by-step explanation:

Answer:

21 cats!

Step-by-step explanation:

the ratio is 3:4

4 being dogs    -     28/4 = 7      -      7 * 3 = 21

hope this helps!!! <3

Answer:

Your first step in solving the system would be to substitute the value of a variable into one of the equations

Step-by-step explanation:

We know that x = 2y + 2 and y = -1/3x + 4, so we could insert one of these values as the variable in one of the equations

If we were to insert -1/3x + 4 for y, our new equation would be:

x = 2(-1/3x + 4) + 2 (as you can see, the value of y was inserted into the equation)

Answer: 48

Step-by-step explanation: 50 is the hypotenuse

14 is the opposite side - its opposite of angle Q

If the function is h(t) = - 4.9t² + 39.2t + 5. Then the maximum height will be 83.4 meters.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given as

h(t) = - 4.9t² + 39.2t + 5

Then the differentiation of the function will be

h'(t) = - 9.8t + 39.2

For the maximum height, put h'(t) equals zero. Then we have

              h'(t) = 0

- 9.8t + 39.2 = 0

                  t = 4

Then the maximum height will be

h(t) = - 4.9(4)² + 39.2 x 4 + 5

h(t) = - 4.9 x 16 + 39.2 x 4 + 5

h(t) = - 78.4 + 156.8 + 5

h(t) = 83.4 meters

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Answer:

8 then 2 and reflection on y axes

Answer:

The answer is attached.

Part A

The yard is a quadrilateral with the following corner points

I'll label those points A through D in the order presented above.

From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.

In short: side AB is 40 feet long.

The length of side BC is not as simple. We'll need the distance formula.

[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]

Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.

Use the distance formula again to find the distance from point C(40,50) to D(50,0)

[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]

Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.

We have these side lengths:

AB = 40

BC = 41.2311 (approximate)

CD = 50.9902 (approximate)

AD = 50

Add up those four sides and we'll get the perimeter of the quadrilateral.

AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213

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

Part B

The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).

This 15 by 20 rectangle has an area of 15*20 = 300 square feet.

The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.

The area of the trapezoid is

A = h*(b1+b2)/2

A = 15*(20+35)/2

A = 412.5

That decimal value is exact.

Add it onto the area of the rectangle

412.5+300 = 712.5

[tex]~~~5 \log 3 + \log4 \\\\=\log 3^5 + \log 4~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log(3^5 \cdot 4)~~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\=\log(972)[/tex]

Answer:

The area of triangle ABC is 60 mm^2

Step-by-step explanation:

x = the area of triangle ABC

15/6 * x/24

x=60

Answer:

  (d)  150 mm²

Step-by-step explanation:

The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.

__

ΔABC is larger than ΔPRT by the factor ...

  AC/PT = 15/6 = 5/2

The area of ΔABC is the square of this factor times the area of ΔPRT:

  area ABC = (5/2)²×area PRT

  area ABC = (25/4)×(24 mm²)

  area ABC = 150 mm²

Answer:

To the nearest 100 miles, Jessica drove about 300 miles since we haven't reached 350 miles.  If we have a number that is greater than 350 miles than we would've rounded it up to 400 but since ours is less than that we round down to the nearest hundred which is 300 miles.

The surface area of solid Y given the ratio of volume to surface area of solid X is 2,369.25cm²

Volume:

Surface area:

Ratio of volume to surface area of solid X and Y respectively

64 : 208 = 729 : x

64/208 = 729/x

64 × x = 208 × 729

64x = 151,632

x = 151,632 / 64

x = 2,369.25cm²

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Answer:

y = 1/5x + 3

Step-by-step explanation:

y = mx + b

m: slope = 1/5

b: y - intercept

(x, y): (-5, 2)

2 = 1/5(-5) + b

2 = -1 + b

add 1 to both sides to get b alone

2 + 1 = -1 + b + 1

3 = b

Answer:

IT IS 43./45455/.34 LIKE WHEN U ADD 10 TIMES 10 AND DIVIDED 2,000 FROM 20 U THAT ANSWER

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score is given by:

z = (raw score - mean) / (standard deviation / √sample size)

Given mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages, hence, for x > 10:

z = (10 - 8.6) / (4.3 / √39) = 2.03

P(x > 10) = P(z > 2.03) = 1 - P(z < 2.03) = 1 - 0.9788 = 0.0212

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

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Answer:

A. .0210

Step-by-step explanation:

I'm taking the test... could be wrong though...

Answer:

  (B)  38.4 m³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height.

__

The picture tells you the area of the pool is 24 m² and its height is 1.6 m. The volume formula tells you its volume is ...

  V = Bh = (24 m²)(1.6 m) = 38.4 m³

The volume of the prism is 38.4 cubic meters.

Answer:

10.5 baskets

Step-by-step explanation:

The median is the middle value, but for this one just add the two in the middle and divide by 2.

4+3 = 7

Each ball is 3 baskets

7×3 = 21

21/2 = 10.5

Answer:

A) 2¹²

Step-by-step explanation:

Given :

Equate the equation to y :

Substituting in the expression :

Answer:

potential to kinetic energy

Answer:

B

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Because.....

  -11 - 10 = -21

-32 - (-11) = -21

This tells us that the sequence is adding by -21, which is why the next 2 terms will be -53 and - 74 since....

-32 + -21 = -53

-53 + -21 = - 74

Hence, the answer is A.

Find the perimeters of all the figures. = ADD all four sides of shape.

(Length + Width + Height + Base)

Answer:

Here is the solution...hope it helps:)