1/5 (x - 8) equals x - 16 ​

If two triangles are similar, that means their side lengths are proportional, so we get the equation

 [tex]\frac{AB}{AC} =\frac{FG}{FH} \\\frac{x}{17} =\frac{16}{20} \\20x = 16 * 17\\x=13.6[/tex]

Thus x = 13.6.

Hope that helped!

Answer:

  (25 -5√7)/3 ≈ 3.924 inches

Step-by-step explanation:

After removing squares from the corners and folding up the sides, the open-top box will have dimensions ...

  x × (20 -2x) × (30 -2x)

The maximum value for this cubic expression in the domain 0 < x < 10 is found easily by a graphing calculator to be at x = 3.924 inches.

__

You can solve this by expanding the cubic and finding the solution that makes its derivative equal to 0.

  V(x) = 4x^3 -100x^2 +600x

The derivative is ...

  V'(x) = 12x^2 -200x +600 = 0

Dividing by 12, we have ...

  x^2 -50/3x +50 = 0

Completing the square, we get the form ...

  (x -25/3)^2 = -50 +(25/3)^2 = (-450 +625)/9 = 175/9

Taking the square root gives ...

  x -25/3 = ±(5√7)/3

The solution in the desired range is ...

  x = (25 -5√7)/3 ≈ 3.924 . . . inches

_____

Additional comment

We limit the value of x to half the width of the cardboard material, as any longer cuts would overlap to create a negative box dimension. The graph shows the maximum volume to be about 1056.3 cubic inches. Box dimensions would be 3.924 in deep by 12.153 in by 22.153 in.

__

The generic solution can be found using a similar procedure. For cardboard dimensions a×b, it will be ...

x = ((a +b) -√((a -b)² +ab))/6

Assuming +800 represent RM800, then RM800 being debited into a saving account is represent as:-$800.

A saving account is an account that enables you to save you money while you earn interest on the amount save.

The amount +$800 being credited means that money is being deposited into the saving account  while on the other hand -$800 being debited represent a reduction  in the amount deposited into the saving account.

Inconclusion RM800 being debited into a saving account is represent as:-$800.

Learn more about saving account here:https://brainly.com/question/3877103

Answer:

553

Step-by-step explanation:

567 - 14 = 553

Answer:

Step-by-step explanation:

This is option A because the cos(x) has a y-intercept of (0, 1) only.

See attached to compare with other options.

Answer: A

Step-by-step explanation:

Edge 2025

The extra amount that Tim is expected to pay is approximately given by: Option D:  $57.88

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, the question is missing the fact that the size of the tank is 11.75 gallon and a gallon of gas costs $4.50.

So, the total cost of 11.75 gallon of gas is:

Cost of 11.75 gallon gas = 11.75 * 4.50 = 52.875 (in dollars)

Also from the question, the cost of refueling a vehicle is $5.00.

So, the total cost for refueling the car of Tim is:

Total cost = cost of gas + cost of refueling the car

Total cost  = 52.875 + 5.00

Total cost  = $57.875 ≈ $57.88

Thus, the extra amount that Tim is expected to pay is approximately  given by: Option D; $57.88

Learn more about forming equations here:

https://brainly.com/question/11938672

The point (3,22) lies on the graph of f(x) = 3ˣ - 5. The medication in an adult male reduces by half per hour can represent an exponential function.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Given the function:

f(x) = 3ˣ - 5

At point (3, 22):

f(3) = 3³ - 5 = 22

The point (3,22) lies on the graph of f(x) = 3ˣ - 5.

The medication in an adult male reduces by half per hour can represent an exponential function.

Both tables represent an exponential function.

Find out more on exponential function at: https://brainly.com/question/12940982

Answer:

The other endpoint is (-33, 17)

Step-by-step explanation:

The rule of the mid-point of a segment whose endpoints are

([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) is

In our question

∵ The coordinates of the endpoints of a segment are (-15, 13) and (x, y)

∴ [tex]x_{1}[/tex] = -15 and [tex]x_{2}[/tex] = x

∴ [tex]y_{1}[/tex] = 13 and [tex]y_{2}[/tex] = y

∵ The coordinates of the mid-point of this segment are (-24, 15)

∴ [tex]x_{M}[/tex] = -24 and [tex]y_{M}[/tex] = 15

→ Use the rule of the mid-point to find x and y

∵ [tex]-24=\frac{-15+x}{2}[/tex]

→ Multiply both sides by 2

∴ -48 = -15 + x

→ Add 15 to both sides

∴ -33 = x

∵ [tex]15=\frac{13+y}{2}[/tex]

→ Multiply both sides by 2

∴ 30 = 13 + y

→ Subtract 13 from both sides

∴ 17 = y

∴ The other endpoint is (-33, 17)

Answer:

15, 15, 15, 15, 24, 28, 36, 45, 75, 75, 76, 77, 80, 86

Step-by-step explanation:

you read the left side for each digit on the left side

The data set does this stem-and-leaf plot represent is

15, 15, 15, 15, 75, 76, 77, 80, 24, 28, 36, 45, 75, 86

Finding the Mean, Median, and Mode of a Data Collection Using Stem-and-Leaf Plots. A set of data's mean is its average. The midway value in a set of data is known as the median. The number that appears the most frequently in a piece of data is the mode. The mean, median, and mode of a collection of data can be determined using a stem-and-leaf plot.

we have given Stem and leaf plot.

then, the data from plot can be reframed as

15 15 15 15

24 28

36

45

75 75 76 77

80 86

So, the data set does this stem-and-leaf plot represent is

15, 15, 15, 15, 75, 76, 77, 80, 24, 28, 36, 45, 75, 86

Learn more about Leaf and Stem plot here:

https://brainly.com/question/12857419

#SPJ3

We can apply the process of solving percentiles of a grouped data in a purposeful way by using it to compare a performance to that of other students.

This is a statistical tool which measures the value below which a given percentage of observations in a group of observations fall.

Percentile Rank = L + (RN/100 – M) / F × C where

Read more about Percentile here https://brainly.com/question/2263719

Answer:

v=13

Step-by-step explanation:

3(13) = 39+11 = 50

Answer:

Our main goal is to isolate the variable here (v).

And if we want to solve this equation,

we must utilize inverse operations.

Given that:-

3v + 11 = 50

We always first get rid of the constants.

And in this case, 11 is our constant.

So the inverse operation of addition is subtraction (because 11 is being added)

-11        -11

3v = 39

Now, we are left with a co-efficient.

To isolate v, we must apply the inverse operation of multiplication which is division (because 3 and 'v' are being multiplied).

/3     /3

V = 13

Answer:

Solution

A=a2=52=25cm²

Step-by-step explanation:

[tex]\qquad \huge \underline{\boxed{\sf ǟռֆաɛʀ }}[/tex]

Area of a square is :

[tex] \qquad \sf  \dashrightarrow \: side {}^{2} [/tex]

that is ~

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {5}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {25}^{} \: cm {}^{2} [/tex]

Answer:

15

Step-by-step explanation:1 third of 9 is 3. Half of 10 is 5. Multiply 5 by 3. It is now 15.

Answer:

15

Step-by-step explanation:

Work backwards:

half of 10 = 10 ÷ 2 = 5

so ... nine times half of 10 = 9 × 5 = 45

so  ... ⅓ of nine times half of ten = ⅓ of 45 = 45 ÷ 3 = 15

Answer:

[tex]\huge\boxed{B)\ m=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-1, 3) and (3, 5).

Substitute:

[tex]m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{3+1}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}[/tex]

Answer:

(i) 0.15708

(ii) 0.432488

(iii) 3

Step-by-step explanation:

Given that, 99% of people who fracture or dislocate a bone see a doctor for that condition.

There is only two chance either the person having fracture or dislocation of bone will either see the doctor or not.

As per previous data, if one person got a fracture or dislocation of bone, the chance of seeing the doctor is 0.99. Assuming this chance is the same for every individual, so the total number of people having fractured or dislocated a bone can be considered as Bernoulli's population.

Let p be the probability of success represented by the chances of not seeing a doctor by any one individual having fractured or dislocated a bone.

So, p=1-0.99=0.01

According to Bernoulli's theorem, the probability of exactly r success among the total of n randomly selected from Bernoulli's population is

[tex]P(r)=\binom{n}{r}p^r(1-p)^{n-r}\cdots(i)[/tex]

(i) The total number of persons randomly selected, n=400.

The probability that exactly 5 of them did not see a doctor

So, r=5 , p=0.01

Using equation (i),

[tex]P(r=5)=\binom{400}{5}(0.01)^5(1-0.01)^{400-5}[/tex]

[tex]=\frac{400!}{(400-5)!\times 5!}(0.01)^5(0.99)^{395}[/tex]

=0.15708

(ii) The probability that fewer than four of them did not see a doctor

[tex]=P(r<4)[/tex]

[tex]=P(r=0)+P(r=1)+P(r=2)+P(r=3)[/tex]

[tex]=\binom{400}{0}(0.01)^0(0.99)^{400}+\binom{400}{1}(0.01)^1(0.99)^{399}+\binom{400}{2}(0.01)^2(0.99)^{398}+\binom{400}{3}(0.01)^3(0.99)^{397}[/tex]

[tex]=0.017951+0.072527+0.146154+0.195856[/tex]

[tex]=0.432488[/tex]

(iii) The expected number of people who would not see a doctor

[tex]=np[/tex]

[tex]=300\times 0.01[/tex]

=3

Answer: 12m by 4m.

Step-by-step explanation: You are looking for the dimensions of the room here, also known as the length and width.

Let’s make width equal to x since we don’t know what the value is. Length is going to be x + 8 since the diagonal is 8m MORE than the width.

w = x

l = x + 8

Use the equation for the perimeter.

P = 2l + 2w

Plug in your values:

32 = 2(x + 8) + 2(x)

Now, solve for x! First start by distributing the 2:

32 = 2x + 16 + 2x

Next, add like terms:

32 = 4x + 16

Subtract 16 from both sides:

16 = 4x

Divide by 4 on both sides:

4 = x

Now we have x, but remember, x is equal to the width. We just solved for width so now we need length.

l = x + 8

Plug in your x and solve:

l = 4 + 8

l = 12

Your length is 12m and your width is 4m, therefore, the dimensions of the rectangular room are 12m by 4m.

Answer:

sqrt(97)

Step-by-step explanation:

Answer:

x= 2/a (apex)

Step-by-step explanation:

Answer:

0.2830

Step-by-step explanation:

edge

The required proportion of red drum fish would be 0.2830 between 22 and 23.5 inches in length.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

As per the given condition, if the fish is between 22 and 23.5 inches,

P(22≤ X ≤ 23.5)

You can rewrite it as:

⇒ P(X ≤ 22) - P(X ≤ 23.5)

The first step is to standard both values before using population data and the standard normal distribution to get the probability:

The formula of the standard normal is Z=(X-μ)/σ

⇒ P(Z ≤  (23.5-24)/1.4) - P(Z ≤ (22-24)/1.4) = P(Z ≤-0.36) - P(Z ≤ -1.43)

Now you look at the table of the Z-distribution for the cumulative probabilities for both z-score

⇒  (1 - 0.6406) - (1 - 0.9236)

⇒ 0.3594- 0.0764 = 0.2830

Hence, the required proportion of red drum fish would be 0.2830 between 22 and 23.5 inches in length.

Learn more about the z-score here:

brainly.com/question/13793746

#SPJ2

Answer:Function modelling - It is based on the  variables like Quadratic expression, rational numbers as the setting of function depends the function modelling performs .Thus the option to the above ques is 16$

Step-by-step explanation: hope this helps!!! :)

Answer:

x = 5/2, -12

Step-by-step explanation:

(2x-5)(x+12) = 0

2x-5 = 0

2x = 5

x = 5/2

x + 12 = 0

x = -12

Answer:

x = 5/2          x = -12

Step-by-step explanation:

(2x-5)(x+12)=0.

Using the zero product property

2x-5 =0         x+12=0

2x=5              x = -12

x = 5/2          x = -12

Answer:

Below.

Step-by-step explanation:

a) Let the numbers be n, n + 2 and n + 4

Sum = n + n + 2 + n + 4

= 3n + 6.

As n must be even (2, 4, 6 and so on) , 3n must be divisible by 6  and 3n + 6 is divisible by 6 also.

b) 3n + 6 = 6000

3n =  5994

n = 5994/3 = 1998

So the numbers are 1998, 2000 and 2002.

Answer:

1/7 is less than 7/12

Step-by-step explanation:

please mark me as brainlest

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

15/k

15/3

5

how am I supposed to know????

Answer:

Ms.Manns, Office, and with the Crowbar

Step-by-step explanation:

Answer:

Today: Friday, 30 October 2020

Hour: 14.49 WIB (in Indonesia)

________________________

3 (2x - 7) + 1/3 (7x + 2)

= 6x - 21 + 7x/3 + 2/3

= 6x + 7x/3 + 2/3 - 21

= 25x - 61/3

Answer:

[tex]2x-5y=-40\\-5y = -40-2x\\y = \frac{-40}{-5}-\frac{2x}{-5} \\y = \frac{2x}{5}+8[/tex]

Slope of a line perpendicular is  [tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

Hey there!

The given equation is ; 2x - 5y = -40.

Or, 2x - 5y + 40 = 0

Slope of the equation is;

[tex]slope(m) = \frac{ - coeff. \: of \: x}{coeff. \: of \: y} [/tex]

[tex]m = \frac{ - 2}{ - 5} [/tex]

[tex]m = \frac{2}{5} [/tex]

Therefore, the slope of equation is 2/5.

Now; For the perpendicular lines:

Slope of equation * slope of next line = -1

i.e M1*M2= -1

[tex] \frac{2}{5} \times m2 = - 1[/tex]

[tex]2 \: m2 = - 5[/tex]

[tex]m2 = \frac{ - 5}{2} [/tex]

Therefore, the slope of the line which is perpendicular line to 2x - 5y + 40= 0 is -5/2.

Hope it helps....