Simplify the expression. [tex]\sqrt{32[/tex]

Answer:

  (i) gradient: 2/3

  (ii) equation: y -1 = 2/3(x +1)

  (iii) area: 10 square units

  (iv) length: 4.12 units

Step-by-step explanation:

The gradient of a line is found by using the slope formula with two points on the line. The length between points is found using the distance formula, which is based on the Pythagorean theorem. The equation of a line can be written in several forms. One is the point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

__

The points A and B can be used in the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (5 -1)/(5 -(-1)) = 4/6 = 2/3

The gradient of the line is 2/3.

__

Using the found slope in the point-slope equation with point A, we find the equation of the line to be ...

  y -1 = 2/3(x +1)

__

The area of a triangle is found from the formula ...

  A = 1/2bh . . . . . triangle with base b and height h

The base length will be the difference in x-coordinates of the horizontal segment AC: 4 -(-1) = 5.

The height will be the difference in y-coordinates from that horizontal segment and point B: 5 -1 = 4

Then the area of ABC is ...

  A = 1/2(5)(4) = 10 . . . . square units

The area of ΔABC is 10 square units.

__

The length of BC is found from the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((5 -4)² +(5 -1)²) = √(1 +16) = √17

  d ≈ 4.12 . . . . units

The length of BC is about 4.12 units.

Answer: (228.7, 241.3)

Step-by-step explanation:

Hello.

First, "twice a number" means we multiply 2 times that number.

Let the number be s.

Now, the sum of 2 times s and 5 is 21.

The product of 2 and s can be written like so:

[tex]\sf{2s[/tex]

Now, the sum of 2s and 5 is 21:

[tex]\sf{2s+5=21[/tex]

Subtract 5 from both sides:

[tex]\sf{2s=21-5[/tex]

[tex]\sf{2s=16}[/tex]

Now, divide both sides by 2:

[tex]\Large\boxed{\sf{s=8}}[/tex]

I hope it helps.

Have a nice day.

[tex]\boxed{imperturbability}[/tex]

x = 8

Step-by-step explanation:

Let the required number be x.

According to the given question,

=> 2x + 5 = 21

=> 2x = 21 - 5

=> 2x = 16

=> x = 16/2

=> x = 8

Answer:

[tex] \frac{4.1}{100} \times 714.73 = 29.30 \\ 714.73 - 29.30 = 685.43[/tex]

divide 4.1 with 100percent because per5 is always over 100 them multiply by the amount given

Step-by-step explanation:

subtract 29.30 from 714.30

subtract calculated amount from amount given

get yr final answer

Answer:

x = -2y

Step-by-step explanation:

Simplifying

600x + 200y = 500x

Solving

600x + 200y = 500x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-500x' to each side of the equation.

600x + -500x + 200y = 500x + -500x

Combine like terms: 600x + -500x = 100x

100x + 200y = 500x + -500x

Combine like terms: 500x + -500x = 0

100x + 200y = 0

Add '-200y' to each side of the equation.

100x + 200y + -200y = 0 + -200y

Combine like terms: 200y + -200y = 0

100x + 0 = 0 + -200y

100x = 0 + -200y

Remove the zero:

100x = -200y

Divide each side by '100'.

x = -2y

Simplifying

x = -2y

hope this helps!

ibrahim

Answer:

9b²-4

Step-by-step explanation:

(3b-2)(3b+2)

9b²+6b-6b-4

9b²+0-4

9b²-4

first to answer, pls brainliest.

Answer:

divide 8 and 398 and you will get ur answers

69 (x_x) (x_x) (x_x) (x_x) (x_x) (x_x) (x_x) (x_x) (x_x)

Answer:

i'm really not sure i'm sorry-

Step-by-step explanation:

ima get my smart friend to find the answer for you <3

Answer:

The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses. !!!!!

Step-by-step explanation:

A Control Chart is a tool that uses time-ordered values of a sample statistic to help detect the presence of correctable causes of variation in a process.

There are various kinds of control charts. They are:

The most commonly used control chart is the Individuals and Moving Range Chart.

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Answer:

65 coins

Step-by-step explanation:

Set this problem up with a porportion.

[tex]\frac{?}{260} \frac{25}{100}[/tex]

After that, cross multiple and divide.

25 times 260. Then divide by 100. That is then your answer.

Twice means two times

18.9 - 2x = 9.9

18.9 -18.9 -2x=9.9 - 18.9

-2x=9.9 - 18.9

(-2x= -9) divide both sides by negative two

-2x/-2 = -9/-2

x=4.5

Using linear function concepts, it is found that the maximum whole number of kilometres that can be travelled in one week with Carz if it is to cost less than it would with Renta is of 399.

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

For each car, Cart and Renta, the linear functions are given by:

C(k) = 90 + 0.15k

R(k) = 110 + 0.1k

Cart will cost less than Renta if:

C(k) < R(k)

Hence:

90 + 0.15k < 110 + 0.5k

0.05k < 20

k < 400

Hence, the maximum whole number of kilometres that can be travelled in one week with Carz if it is to cost less than it would with Renta is of 399.

More can be learned about linear function concepts at https://brainly.com/question/24808124

Answer:

Step-by-step explanation:

Sarah swam the diagonal length of a right-angled triangle with sides of river width, 193m and how far she was swept downstream, 67m.

By Pythagorean Theorem, distance swam = sqrt(193^2+67^2)

= 204.3 m

Apply Pythagorean theorem

[tex]\\ \rm\rightarrowtail H^2=P^2+B^2[/tex]

[tex]\\ \rm\rightarrowtail H^2=193^2+67^2[/tex]

[tex]\\ \rm\rightarrowtail H^2=41738[/tex]

[tex]\\ \rm\rightarrowtail H=204ft[/tex](Approx)

The value of x can be found by using the formula for the area of a trapezoid. The value of [tex]$x$[/tex] is [tex]$4$[/tex] inches.

Area is a two-dimensional measurement that is used to measure the size of a shape or surface. It is measured in square units, such as square centimeters, square meters, square kilometers, and so on. The formula for the area of a trapezoid is: [tex](a+b)/2 *h[/tex], where a and b are the lengths of the parallel sides, and h is the height. Mrs. Katz needs to calculate the value of x by plugging in the lengths of the parallel sides and the height into the formula.

We know that the opposite sides of a trapezoid are parallel, so we have [tex]AB \parallel DC.[/tex]

Using the given information, we can set up an equation in terms of [tex]$x$[/tex] and solve for it. We know that the height of the trapezoid is [tex]$8$[/tex] inches, and we know that the bases are [tex]$x$[/tex] inches and [tex]$16$[/tex] inches.

Using the formula for the area of a trapezoid, we have:

[tex]\text{Area} = \frac{1}{2}(AB+DC)(\text{height})[/tex]

Plugging in the values we know, we get:

[tex]\text{Area} = \frac{1}{2}(x+16)(8)[/tex]

We are also given that the area of the trapezoid is [tex]$100$[/tex] square inches, so we can set up an equation:

[tex]100 = \frac{1}{2}(x+16)(8)[/tex]

Simplifying and solving for [tex]$x$[/tex], we get:

[tex]100 &= \frac{1}{2}(x+16)(8)\20 &= (x+16)\x &= 4[/tex]

Therefore, the value of [tex]$x$[/tex] is [tex]$4$[/tex] inches.

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#SPJ1

The answer is 10.

Step-by-step explanation:

I have the same question on some tests of mine

Answer:

Step-by-step explanation:

(4sqrt2)/4 = 4/(projection)

sqrt2 = 4/(projection)

projection = 2sqrt2

So by the Pythagorean theorem, the altitude is also 2sqrt2.

Answer:

B

Step-by-step explanation:

Edge

The mean abosolute deviation of the given data set is: 42.9422.

The mean absolute deviation is the avergae of the distance of each data point from the mean of the data set.

Given:

23, 75, 79, 99, 105, 110, 110, 142, 149, 168, 168, 170, 183, 195, 202

Mean: (23 + 75 + 79 + 99 + 105 + 110 + 110 + 142 + 149 + 168 + 168 + 170 + 183 + 195 + 202)/15

Mean = 1978/15 = 131.8667

Mean aboslute deviation = [(23 - 131.8667) + ( 75 - 131.8667) + ( 79 - 131.8667) + ( 99 - 131.8667) + ( 105 - 131.8667) + ( 110 - 131.8667) + ( 110 - 131.8667) + ( 142 - 131.8667) + ( 149 - 131.8667) + ( 168 - 131.8667) + ( 168 - 131.8667) + ( 170 - 131.8667) + ( 183 - 131.8667) + ( 195 - 131.8667) + ( 202 - 131.8667)] / 15

Mean aboslute deviation = 644.1333/15 = 42.9422

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Answer:

help me

Step-by-step explanation:

Answer:

[tex]\frac{4}{15}[/tex] kilograms

Step-by-step explanation:

  We will take the total amount of beads and divide it by 3, since there are 3 friends.

[tex]\frac{4}{5}[/tex] kg / 3

[tex]\frac{4}{5}[/tex] kg * [tex]\frac{1}{3}[/tex]

[tex]\frac{4*1}{5*3}[/tex]

[tex]\frac{4}{15}[/tex] kg

Each friend recieves [tex]\frac{4}{15}[/tex] kilograms of the beads.

The rectangular prism having a length of 1 feet, width of 2 feet and that

is 1 feet deep, gives the area Mila stained as 8 square feet.

The given dimensions of the rectangular prism bin are;

Length of the bin = 2 foot

Width of the bin = 1 feet

Depth of the bin = 2 feet

Required:

The surface area of the rectangular prism bin.

Solution:

The surface area, S. A., of the rectangular prism bin is given as follows;

S. A. = Length × Width + Depth × Width + Length × Depth

Which gives;

S. A. = 2 × 1 + 2 × 1 + 2 × 2 = 8

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The probability is the ratio of the favorable event to the total number of events. The P(C|Y) is 0.5. Then the correct option is B.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

According to the problem, the table is made

                          X               Y               Z               Total

  A                    32              10             28                 70

  B                     6                5              25                 36

  C                    18               15              7                   40

Total                 56              30             60                146

Then the probability of will be

[tex]\rm P(C|Y) = \dfrac{15}{30}\\\\P(C|Y) = 0.5[/tex]

The P(C|Y) is 0.5. Then the correct option is B.

More about the probability link is given below.

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Answer: D

Step-by-step explanation: payment equals to money earned per hour (p=6.25h).

so the scatterplot will more or less look like the one in the picture below.

Answer:

5, -6

Step-by-step explanation:

We just need to find out the factors of -30 and they are 1 x -30, 2 x -15, 3 x 10 and 5 x -6. We can try out every factor to add  so it's either:

-29

-13

-7

-1

the last is the answer we're looking for so it's 5 x -6

The 2 numbers are 5 and -6