Checking number 2( Solving inequalities)

Let [tex]x,y[/tex] be the legs of the triangle, with [tex]x[tex]\mathrm{area}_{\rm square} = y^2[/tex]

[tex]\mathrm{area}_{\rm triangle} = \dfrac12 xy[/tex]

The square has 3 times the area of the triangle, so

[tex]y^2 = \dfrac32 xy[/tex]

Meanwhile, in the triangle we have

[tex]\tan(\theta) = \dfrac xy[/tex]

Now,

[tex]y^2 = \dfrac32 xy \implies \dfrac23 = \dfrac xy \implies \boxed{\tan(\theta) = \dfrac23}[/tex]

Answer:

15/17

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

I'm assuming that ED is an exactly straight line, that would mean the angle is 180 degrees. So the sum of the angles in between should also equal 180. This gives you the equation

100 + 20 + x = 180

120 + x = 180

60  = x

Answer:

Step-by-step explanation:

Answer:

The solution to the inequality |x-2|>10 in interval notation is given by -8<x<12

Step-by-step explanation:

An absolute value inequality |x-2|>10 is given.

It is required to solve the inequality and write the solution in interval form.

To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.

Step 1 of 2

The given absolute value inequality is $|x-2|>10$.

The inequality can be written as

x-2<10 and x-2>-10

First solve the inequality, x-2<10.

Add 2 on both sides,

x-2<10

x-2+2<10+2

x<12

Step 2 of 2

Solve the inequality x-2>-10.

Add 2 on both sides,

x-2>-10

x-2+2>-10+2

x>-8

The solution of the inequality in interval notation is given by -8<x<12.

Answer:

[tex] - \frac{2}{3} [/tex]

Step-by-step explanation:

Given (6x18)(3x+2) = 0

[tex]108(3x + 2) = 0 \\ 324x + 216 = 0 \\ 324x = - 216 \\ x = \frac{ - 216}{324} \\ = - \frac{2}{3} [/tex]

Work Shown:

16% of x = 17

0.16x = 17

x = 17/(0.16)

x = 106.25

Answer:

OC. 39.3 cm²

Step-by-step explanation:

Area of a circle = πr²    (π ≈ 3.14)

45 degrees = 1/8 of a full circle

Area of the full circle : 3.14 × 10² =

3.14 × 100 = 314 cm²

Area of the sector : 314 × 1/8 = 39.25 cm² ≈ 39.3 cm²

Answer:

F = 2

Step-by-step explanation:

Answer:6

Step-by-step explanation:i did the quiz

Answer:

Step-by-step explanation:

The true statements are :

the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.

The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.

A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers and a box. The whiskers represents the minimum and maximum scores. The difference between the minimum and maximum scores is the range.

On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.

Range for New Orleans = 85 - 50 = 35

Range for Indianapolis = 75 - 25 = 50

Median for New Orleans = 70

Upper quartile for  Indianapolis = 70

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Answer:

680π dm² = 2136.28 dm²

Step-by-step explanation:

Recall:

lateral area of cone = πrs; where s = slant height = 17 dm

area of circle = πr²

lateral area of cylinder = πdh

Lateral area of cone: (3.14159)(8 dm)(17 dm) = 427.26 dm²

Area of base of cylinder: (3.14159)(8 dm)² = 201.06 dm²

Lateral area of cylinder: (3.14159)(16 dm)(30 dm) = 1507.96 dm²

Total surface area = 427.26 dm² + 201.06 dm² + 1507.96 dm²

Total surface area = 680π dm² = 2136.28 dm²

Answer:

144

Step-by-step explanation:

Base:16

Height: 18

Triangle area formula: (bxh)/2

16x18=288

288/2=144

Answer:

(2,3),(4,3),(-2,-3),(-4,-3)

Step-by-step explanation:

A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).

This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.

The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.

A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.

In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:

(5,1),(5,2),(5,3),(5,4)

Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.

Answer:

The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].

Step-by-step explanation:

A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).

It is asked to find a linear equation satisfying the given condition.

To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.

Step 1 of 2

Determine the slope of the line.

The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]$$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$$[/tex]

Step 2 of 2

Write the equation in the slope-intercept form.

The slope-intercept form of a line is given as follows,

[tex]$$y=m x+b$$[/tex]

The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.

So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,

[tex]$y=\frac{4}{5} x+4$$[/tex]

This is the required linear equation.

Using the triangle midsegment theorem, x = 5; BC = 10 units.

According to the triangle midsegment theorem, ED = 1/2(BA).

Given the following:

ED = x + 2

BA = 4x - 6

x + 2 = 1/2(4x - 6)

2(x + 2) = 4x - 6

2x + 4 = 4x - 6

2x - 4x = -4 - 6

-2x = -10

x = 5

BC = 2(BE)

BC = 2(x)

BC = 2(5)

BC = 10 units

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Answer:

D

Triangle Midsegment

5

10

Step-by-step explanation:

E2020 Geometry B!!:3

From the given graph, and using the scatter plot function of a graphing calculator, the residuals are;

-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578

From the diagram, the given points are;

(14, 4), (15, 4), (16.5, 3.5), (18, 4), (18, 3.9), (19.5, 3.85), (20, 4), (26.8, 3.8)

Utilizing a graphing calculator, using the scatter plot function we have the following predicted values;

Best fit line; y = 5.032 - 0.0676•x

Residuals = Actual - Predicted from equation

The residuals are;

y1 = 4 - 4.08693 = -0.08693

y2 = 4 - 4.019376 = -0.019376

y3 = 3.5 - 3.918 = -0.518

y4 = 4 - 3.817 = -0.183

y5 = 3.9 - 3.817 = -0.083

y6 = 3.85 - 3.715 = 0.135

y7 = 4 - 3.682 = 0.318

y8 = 3.8 - 3.222 = 0.578

The residuals are therefore;

The residuals are;

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[tex] - 4y = v - 4x \\ y = \frac{ - v}{4} + x[/tex]

[tex]\\ \rm\dashrightarrow V=-4y+4x[/tex]

[tex]\\ \rm\dashrightarrow -4y=V-4x[/tex]

[tex]\\ \rm\dashrightarrow y=\dfrac{V-4x}{-4}[/tex]

[tex]\\ \rm\dashrightarrow y=x-\dfrac{V}{4}[/tex]

In a binomial​ experiment to say that each trial is independent of the other​ trials means that the outcome of one trial does not affect the other trial.

An experiment with a set number of independent trials and just two results is referred to as a binomial experiment.

To say that in a binomial experiment, each trial is independent of the other trials means that the outcome of one trial does not affect the other trials.

This means that whatever we get in the first trial, does not affect the outcome of the second or any other trial.

For example, in the tossing of a coin 10 times, the outcome of the first trial doesn't affect any of the other nine trials.

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There are 16 red counters there.

If one-quarter of the counters in a tub are red and the rest are green, then there are three-quarter of the counter in the tub.

Let the total counter be x such that

3/4x = 48

3x = 4 * 48

x = 4 * 16

x = 64

Determine the amount of red counter

Red counter = 64 - 48

Red counter = 16

Hence there are 16 red counters there.

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The volume of the square pyramid is: B. One-third s^2h units^3.

An example of a square pyramid is given in the image attached below. It has a square base and 4 triangular faces.

A right pyramid that has a square base has a volume that can be calculated using the following volume formula, given as: 1/3(a² × h), where "a" is the length of the edge of the square base, and "h" is the height of the square pyramid.

Given the following parameters for a square pyramid:

The length of the edge of the square base (a) = s units

The height of the square pyramid = h units.

Plug in the values into 1/3(a² × h) to find the expression that represents the volume of the pyramid:

Volume of the square pyramid = 1/3(a² × h) = 1/3(s² × h)

Volume of the square pyramid = 1/3s²h units ³.

The expression that represents the volume of the square pyramid is: B. One-third s^2h units^3.

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Answer:

The answer would be C

Answer:

The rate of growth of the population is -400, this means the growth of the population from year 1960 to 1989 has dropped by 400 per city.

Step-by-step explanation:

It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .

It is required to compute the rate of growth of population and make a statement about the population rate of 1989 with the year 1989 and the time taken to change the population.

Step 1 of 1

It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .

To find the rate of growth of population and make a statement about the population rate of change in people per year.

Now let f(x) be the number of population and x be the year and use formula of rate of change to find the change in population,

[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$[/tex]

Now substitute, 275900 for [tex]$f\left(x_{2}\right)[/tex], 287500 for  then,

[tex]$$\begin{aligned}m &=\frac{275900-287500}{1989-1960} \\&=\frac{-11600}{29} \\&=-400\end{aligned}$$[/tex]

The rate of growth of population -400, so there is a drop in the population by 400 per city.

Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Given:

Substituting it in the relationship we get,

Distance = Speed x Time

Distance =  5 1/2 miles per hour  x 2 3/4 hours

Distance = [tex]\frac{11}{2} X \frac{11}{4}[/tex] miles

Distance =  [tex]\frac{121}{8}[/tex] miles or 15[tex]\frac{1}{8}[/tex] miles

Thus Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours

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Answer:

1136/295 cm

Step-by-step explanation:

Corresponding lengths of similar figures are proportional.

If we let the radius of the second cylinder be x,

x/6.4 = 7.1/11.8

x = 6.4(7.1/11.8) = 1136/295 cm

Answer:

324.3mi

Step-by-step explanation:

Given Space Shuttle height above ground = 330mi

Airplane height above ground = 5.7mi

Difference between two aircrafts = Space Shuttle height - airplane height above ground

= 330 - 5.7

= 324.3mi

Answer:

-2

Step-by-step explanation:

The solution to the system of equations is (x, y) = (-2, 1).

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The second equation tells us that x = -2.

Substituting this value into the first equation, we get:

y = -2 + 3

Simplifying, we get:

y = 1

Therefore,

The solution to the system of equations is (x, y) = (-2, 1).

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Answer:

she would be 20 years old if lily is 22