how to construct a right triangle with a given hypotenuse and acute angle? (construction

The solution of the inequality, |x + 6| ≥ 5 is given as follows,

(A) x > -1

(B) It follows that x either belongs to the interval (-∞, -11) or to the interval (-1,∞) for the given absolute inequality.

(A) Solving the Given Inequality:

|x + 6| ≥ 5

x+6 ≥ 5 or x+6 ≤ (-5)

x+6-6 ≥ 5-6 or x+6-6 ≤ (-5)-6

x ≥ -1 or x ≤ -11

Hence the solution of the given inequality is given as,

x ∈ (-∞, -11] or x ∈ [-1, ∞)

(B) Description of the Solution

From the given absolute inequality, it can be concluded that x either belongs to the interval (-∞, -11] or to the interval [-1, ∞). Hence, on the number line, the solution of the inequality will be shown as a shaded region from -∞ to -11 and from -1 to ∞. The area between -1 and -11 will remain unshaded.

In the deduced solution, the interval is either open or closed on both sides. Open interval means the extreme value is not includes. On the other hand, closed interval indicates inclusion of the extreme point in the solution of the inequality.

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19 sweets are lefted.

Lets simplify the problem,

Maximum no. of bag filled by 4275 sweets

Through Simple Division we get,

4275/28 ~=152

Therefore , there is 4256 sweets in 152 bags

Therefore, 4275-4256=19 sweets are left

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Answer:

obtuse angle triangle

Step-by-step explanation:

please make me Brilliant for this correct answer

Answer:

y = - [tex]\frac{7}{4}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{7}{4}[/tex] x - 2 ← is in slope- intercept form

with slope m = - [tex]\frac{7}{4}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{7}{4}[/tex] x + c ← is the partial equation

to find c substitute (4, - 2 ) into the partial equation

- 2 = - 7 + c ⇒ c = - 2 + 7 = 5

y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line

The time that a member hold his/her position at the agency is approximately 0.1 year.

Given that twenty members are elected to an agency every two years and there are 100 members on a average overall.

We have to find the time that a member hold his position at the agency.

To calculate the time we have to use multiplication which means product of two numbers.

In 2 years agency elected 20 members. It shows like under:

2 years=20 members

We require 100 members at one end so we will multiply by 5 both sides.

10 years=100 members

Now take 100 to left side of equal to sign.

10/100=1 member

1 member=1/10

=0.1

Hence a member holds 0.1 year at the agency.

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Answer: G=4

Step-by-step explanation:

The expression is simplified to x

g(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)

First, we simplify the numerator

= [tex]\frac{x (x^2 - 3^2)}{x^2 - 6x + 9}[/tex]

Now, let's solve the quadratic equation in the denominator

= [tex]\frac{x(x^2 - 3^2)}{x^2 - 3x - 3x + 9}[/tex]

= [tex]\frac{x(x^2 - 3^2)}{x(x-3) - 3(x - 3)}[/tex]

= [tex]\frac{x(x - 3) (x -3)}{(x -3) ( x-3)}[/tex]

Divide the like factors

= x

The answer is x

Thus, the expression is simplified to x

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Mean = $ 4. 72

Median = $ 4. 5

Mode = No mode

MAD = $ 4. 8

IQR = $ 0. 5

Measure of center = $ 4. 5

Measure of variability = $ 2. 50

Given the data;

$3.50, $4.25, $6, $4.75, $5.80, $4

Mean = sum of data/ number of data values

Mean = [tex]\frac{3. 50 + 4. 25 + 6 + 4. 75 + 5. 80 + 4}{6}[/tex]

Mean = $ 4. 72

Median is the number in the center when the data is arranged in an ascending order

$3. 50, $4, $4. 25, $4. 75, $5. 80, $6

Median = [tex]\frac{4. 25 + 4. 75}{2}[/tex]

Median = $ 4. 5

Mode is the number with the highest repeats.

From the given data, none of the numbers was repeated.

Thus, there is no mode.

MAD, mean absolute deviation = |data value - mean|

MAD = [tex]|(3. 50 - 4. 72) + (4. 25 - 4. 72) + (6 - 4. 72) + (4. 75 - 4. 72) + (5. 80 - 4.72) + (4- 4. 72) |[/tex]

MAD = [tex]1. 22 + 0. 47 + 1. 28 + 0. 03 + 1. 08 + 0. 72[/tex]

MAD = $ 4. 8

IQR, interquartile range = Quartile 3 - quartile 1

IQR = 4. 75 - 4. 25

IQR = $0. 5

Note that  the mean and median are the most common measures of center.

A measure of variability is a single number that is  used to describe the spread of a data set

The measure of the center best for the data is the median = $4. 5

Measure of variability = range = highest value - lowest value = $6 - $3. 50 = $2. 50

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The length of the rectangular box is 0.67 feet

The given parameters are:

Length = ??

Width = 1.0 ft

Height = 1.5 ft

Volume = 1.0 ft^3

The volume is calculated as:

Volume = Length * Width * Height

Substitute the known values in the above equation

1 = Length * 1 * 1.5

Evaluate the product

1 = Length * 1.5

Divide both sides by 1.5

Length = 0.67

Hence, the length of the rectangular box is 0.67 feet

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See below for the solution to the questions

The given parameters are:

Area = 138

a = 4x - 1

b = x - 4

Height = 12

The area is calculated as:

Area = 0.5 * (a + b) * height

So, we have:

0.5 *(4x - 1 + x - 4) * 12 = 138

This gives

5x - 5 = 23

Add 5 to both sides

5x = 28

Divide by 5

x = 5.6

Recall that:

a = 4x - 1 = 4 * 5.6 - 1 = 21.4

b = x - 4 = 5.6 - 4 =  1.6

Hence,  the short base length is 1.6 meters and the long base length is 21.4 meters

The sides are given as:

x = 22

y = 24

z = 25

The largest angle always opposite the largest side.

This means that the largest angle is Z

The radius is given as:

r = 29

The circumference is calculated as:

[tex]C = 2\pi r[/tex]

So, we have:

[tex]C = 2\pi *29[/tex]

Evaluate

C = 182.21

Hence, the circumference is 182.21 inches

The measure of the arc is given as:

[tex]\theta = 69^o[/tex]

The angle LIK is calculated as:

[tex]m\angle LIK = \frac{\theta}2[/tex]

So, we have:

[tex]m\angle LIK = \frac{69^o}2[/tex]

Evaluate the quotient

[tex]m\angle LIK = 34.5^o[/tex]

Hence, the measure of the angle is [tex]m\angle LIK = 34.5^o[/tex]

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Using excel, we can determine that the likelihood that a randomly picked steel plate measuring 1 foot by 1 foot contains two or fewer faults is 0.862.

This is further explained below.

Generally, the characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.

In conclusion, In this section, we will make the assumption that the number of defects found in a steel plate measuring 1 foot by 1 foot has a Poisson distribution with a mean of 1.28.

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Answer:

Step-by-step explanation:

Day 1 = 2 birds

day 2 = 3 birds

day 3 = 9 birds

day 4 = 8 birds

day 5 = 1 bird

On day 1 the points are (1,2)

On day 5 the points are (5,1)

(I am picking these for the points because I don't know your options for the selecting area.)

we use this formula y2-y1/x2-x1

2-5/1-1

3/0

our answer is infinite which is the relation and this is an infinite function

Answer:

◘ (1, 2)

◘ (2, 3)

◘ 3

◘ is

◘ each value of Day corresponds to exactly one value of Number of birds

Explanation:

◘◘ In the graph, Days represents the x-axis, and Number of birds represents the y-axis. Therefore each marked point on the graph can be thought of as a Cartesian coordinate. This means that the answers for the first and second question could be any of (1, 2), (2, 3), (3, 9), (4, 8), or (5, 1).

◘ In the graph, we can see that the point above Day 2 corresponds to 3 on the Number of birds axis, which means on day 2, 3 birds visited the feeder.

◘ The relation shown is a function because each value of Day corresponds to exactly one value of Number of birds. A function is a relationship that provides one output for each input, and this graph follows that.

For two bathroom remodel estimate budget is $[tex]20000[/tex] for both remodels. when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $[tex]100[/tex] less than the budgeted .So the actual cost of two bathroom remodel is $ [tex]19800[/tex] and the different of actual and expected budgets is $[tex]200[/tex]

How can we find the actual costing of the bathroom remodel ?

Expected estimate budget of two bathroom's remodel is $[tex]20000[/tex]

So budget of one bathroom remodel is

[tex]20000/2\\=10000[/tex]

All supplies are come except for two vanities which were each $[tex]100[/tex]

So for two bathroom remodels

[tex]=2*100\\=200[/tex]

So the actual cost of remodel of both bathroom is

[tex]=20000-200\\=19800[/tex]

And difference between actual and estimated cost is

[tex]=20000-19800\\=200[/tex]

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Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf (C^{4})^{3} \end{gathered}$}[/tex]

To raise a power to another power, multiply the exponents.

[tex]\large\displaystyle\text{$\begin{gathered}\sf C^{4\times3} \ \to \ Multiply \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf C^{12} \end{gathered}$}}[/tex]

Therefore, the correct option is "C".

a. The rate of change = -25/month

b. Kamal's account balance reduces by 25$ per month.

c. To find the $725.

d. Kamal's opening balance or initial deposit.

e. The linear equation is: A = -25n + 725.

The rate of change (m) = change in y/change in x.

a. The rate of change (m) = change in A / change in n = (700 - 650)/(1 - 3) = -25/month.

b. -25 dollar per month means every month, Kamal's account balance reduces by 25$

c. To find the initial value (b), substitute m = -25 and (7, 550) = (n, A) into A = nm + b:

550 = 7(-25) + b

550 = -175 + b

550 + 175 = b

b = 725.

Initial value is: 725.

d. The initial value, $725, is Kamal's opening balance or initial deposit.

e. To write the linear equation, Substitute m = -25 and b = 725 into A = nm + b:

A = -25n + 725

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Answer:

Step-by-step explanation:

Answer

False but close.

The intercept arc and the central angle are equal.

Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.

From the given picture we can see the length of the sides. These are 7, 4 and 15.

The length of the two sides cannot join due to the fact that they are less than 15.

4 + 7 < 15

11< 15

Hence the answer is D.

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by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side

Answer:

A, B, F

- The radius of the circle is 3 units

- The center of the circle lies on the x-axis

- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

Step-by-step explanation:

The first option is correct because the standard equation of the circle is:

[tex](x - 1)^{2} + {y}^{2} = 9[/tex]

making the radius equal to 3.

The center is at (-1,0), therefore it lies on the x-axis.

And lastly, the last option is correct because both options have the radius of 3.

Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

Answer: 100

Step-by-step explanation:

The angles with measure 100° and x° are vertical angles, which are two opposite angles made from two intersecting lines. These vertical angles are always the same measure.

Hence, both x and 100 have the same measure.

Answer: [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.

Step-by-step explanation:

Finding the third angle in triangle XYZ,

[tex]m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ}[/tex],

Thus, [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.

The true mean expenditure per student is different from $10,337.

What is hypothesis in math?

Sample size is greater than 30 and the population standard deviation is given. Thus, in order to test

H0: µ =$10,337

H1: µ≠$10,337

The appropriate test is one sample z test.

The formula for one sample z test:

Z=   x−μ / σ √ n

x−μ

​x=10798

μ=10337

σ=1560

n=150

[tex]Z = \frac{10798 - 10337}{1560 / \sqrt{150} } = 3.62[/tex]

Computation of p-value:

The EXCEL formula to find the p-value for a two-tailed z-test is

“=2*(1-NORM.S.DIST(3.62, TRUE))”

Thus, the p-value obtained is 0.00029

Conclusion using α = 0.05:

Rejection rule using p-value:

If p-value ≤ α, then reject the null hypothesis.

Since, 0.00029 < 0.05, there is sufficient evidence to reject the null hypothesis.

Therefore, the true mean expenditure per student is different from $10,337.

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Answer:

[tex]5.5[/tex]

Step-by-step explanation:

Mean:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

[tex]\mu = \frac{{\sum}x}{N}[/tex]

The formula for the mean of a sample is

[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

[tex]\frac{55}{10} = 5.5[/tex]

The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.

We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;

|-x| = x

Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|

Thus, from the graph, we get;

Domain of both functions is the set of all real numbers.

Range of both functions is the set {y|y ≥ 0}

Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.

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The time it took the rider to reach the ground level is 171.651seconds

Quadratic functions are functions that has a leading degree of 2.

Given the equation that represents  roller coaster’s height as shown

h = –0.025t^2 + 4t + 50

The coaster will reach the ground when h = 0

Substitute

0 = –0.025t^2 + 4t + 50

Factorize

On factorizing, the time it took the rider to reach the ground level is 171.651seconds

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Answer:

171.65 seconds

Step-by-step explanation:

did the test and got it right

Answer:

120 ft cubed

Step-by-step explanation:

V=lwh

V=10(4)(3)

V=120 ft cubed

The difference between the tallest and shortest heights is 0.787 × 10

From tallest to shortest:

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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Answer:

[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]

Step-by-step explanation:

So the general formula for a circle is usually represented as: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h, k) is the center of the circle and r is the radius of the circle.

Since the diameter is 12, the radius is going to be 6, because the radius is half the diameter. We now square that value (since it's squared in the equation), you get 36, which is going to be on the right side.

The last thing to know is since it's on the y-axis, that means h=0, since if h didn't equal 1, it would either be to the right or left of the y-axis. So the equation should look something like this: [tex]x^2+(y-k)^2=36[/tex] where k can be any real number.

So this gives you the two equations:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]

Use a³+b³ +c³ - 3abc

Here a = 2a²

b= -a

And c = 1

Answer:

Step-by-step explanation:

See below for the converse, inverse, and contrapositive of the statement

The statement is given as:

If Brielle drives at exactly 30 mi/h, then she travels 10 mi in 20 mins

The speed is calculated as:

Speed = Distance/Time

So, we have:

Speed = 10 mi/20 mins

This gives

Speed = 10 mi/1/3 h

Speed = 30 mi/h

The converse

To do this, we simply switch the hypothesis and the conclusion

So, the converse is:

If Brielle travels 10 mi in 20 mins, then she drives at exactly 30 mi/h

The above statement is true

The inverse

To do this, we simply negate the hypothesis and the conclusion

So, the inverse is:

If Brielle did not drive at exactly 30 mi/h, then she did not travel 10 mi in 20 mins

The above statement is false

The contrapositive

To do this, we simply negate the hypothesis and the conclusion, and then switch them

So, the contrapositive is:

If Brielle did not travel 10 mi in 20 mins, then she did not drive at exactly 30 mi/h

The above statement is false

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