Which of the following are possible side lengths
for a triangle?
A. 8, 16,4
B. 3, 6, 9
C. 3, 12, 10

Answer: the area of the triangle is (1/2) * √20 cm

Step-by-step explanation:

The area of a triangle is equal to one half of the product of the base and the height. In this case, the base of the triangle is √20 cm and the height is √8 cm, so we can find the area by doing this:

Area = (1/2) * (√20 cm) * (√8 cm)

To simplify this expression, we can first multiply the numerator and denominator by the square root of the denominator:

Area = (1/2) * (√20 cm * √8 cm) / (√8 cm)

This gives us:

Area = (1/2) * (√160 cm^2) / (√8 cm)

Now we can cancel out the square root of 8 in the numerator and denominator:

Area = (1/2) * √160 cm^2 / √8 cm

Area = (1/2) * √20 cm

Thus, the area of the triangle is (1/2) * √20 cm, which is the simplified radical form of the answer.

Answer:   [tex]2\sqrt{10} \ \ \text{square cm}[/tex]

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

Work Shown:

[tex]\text{area} = 0.5*\text{base}*\text{height}\\\\\text{area} = 0.5*\sqrt{20}*\sqrt{8}\\\\\text{area} = 0.5*\sqrt{20*8}\\\\\text{area} = 0.5*\sqrt{160}\\\\\text{area} = 0.5*\sqrt{16*10}\\\\\text{area} = 0.5*\sqrt{16}*\sqrt{10}\\\\\text{area} = 0.5*4*\sqrt{10}\\\\\text{area} = 2\sqrt{10}\\\\[/tex]

The area units are in square centimeters.

----------------------------

Explanation:

As the steps above indicate, I used this rule

[tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex]

This is to combine the roots in the 3rd step, but also to pull them apart in the 6th step. The idea is to pull out the largest perfect square factor to simplify the square root.

The probability P(A and B) has a value of (d) 0.2

From the question, we have the following parameters that can be used in our computation:

These mean that

P(A) = 0.4

P(B) = 0.5

From the question, we have

The events are independent events

This means that

P(A and B) = P(A) * P(B)

So, we have

P(A and B) = 0.4 * 0.5

Evaluate

P(A and B) = 0.2

Hence, value is 0.2

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The income tax can be paid by the teacher =$ 9212.

An income tax is a sort of tax that is levied on the earned and unearned income of an individual or corporation.

For instance, the United States levies a federal income tax on its residents, regardless of where they reside—in the country or overseas. The majority of the money the US government receives comes from this income tax.

Here we have

The annual salary of a teacher is $ 65,800

The rate of income tax = 14%

The income tax can be paid = 14% of 65800  

=> [tex]\frac{14}{100} \times 65800[/tex]

= [tex]14 \times 658[/tex]

= 9212

Therefore,

The income tax can be paid by the teacher =$ 9212  

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Answer:

c

Step-by-step explanation:

If the sales tax is 6. 35% then Claire's total is $15.63

In this questiion we have been given Claire buys a pair of earrings for $4, a necklace for $10, and a ring for $7.

So, her total purchase is:

4 + 10 + 7 = 21 dollars

She has a 30% off coupon for her whole transaction.

We find the 30 percent of 21

(30/100) * 21 = 6.3 dollars

So, she will get discount of 6.3 dollars.

So, the amount would be,

21 - 6.3 = $14.7

The sales tax is 6. 35%

Now we find 6.35 percent of 14.7

6.35% of 14.7

= 0.0635 × 14.7

= 0.933

So, the total purchase amount would be,

$14.7 + $0.933 = $15.63

Therefore, the total is $15.63

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When we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept. The correct answers is concept

A concept is an abstract idea that takes form in your mind. This is known as the structures of thoughts and beliefs. They are important because it gives a clear explanation of a particular subject.

An automobile, byname auto, also called motorcar or car, a usually four-wheeled vehicle designed primarily for passenger transportation and commonly propelled by an internal-combustion engine using a volatile fuel, this term is generally used for an vehicle when refering to its category.

When we think of the word automobile, the first thing that comes to your mind is a category of transport. The mind connects the thoughts around the structures build. That’s a concept

Thus, when we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept.

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The slower pipe if working alone can fill the tank in 10.5 hours.

A cuboid is a three-dimensional solid that has 6 faces (rectangular), 8 vertices, and 12 edges. A cuboid has three dimensions such as length, width, and height. A perfect cuboid is said to be a cuboid that has integer edges and the formula for its volume is: V = length ×breadth× width

Given here dimensions of the swimming pool as 30 feet long, 14 feet wide, and an average depth of 8 feet, therefore the volume of the swimming pool V = 30×14×8

  = 3360 feet³

Again the two pipes working together can fill the pool in 3.5 hours and let their speeds 2x and x then, their relative speed = 3x

thus we have 3.5 = 3360/3x

                  ⇒   x  = 320 feet³/hr

Therefore the individual speeds are equal to 320 feet³/hr and 640 feet³/hr

Accordingly, the time taken by the slower pipe to fill the entire tank alone is = 3360/320

             = 10.5 hours

Hence, the time taken by the slower pipe is 10.5 hours

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a. The solution to the equation 1/3(5x - 9) = 2(1/3x + 6) is x = 15.

b. The solution to the 4(3x + 5) - 3 = 9x - 7 is x = -8.

c. The solution to the equation 5(x + 7) - 3(x - 4) = 7x + 2 is 9

a. Give the equation 1/3(5x - 9) = 2(1/3x + 6)

We want to find the value of x

5/3x - 3 = 2/3x + 13

x - 3 = 12

Collect the like terms

x = 12 + 3

x = 15

b. 4(3x + 5) - 3 = 9x - 7

12x + 20 - 3 = 9x - 7

Collect the like terms

3x + 17 = -7

3x = -24

Divide

x = -24 / 3

x = -8

c. 5(x + 7) - 3(x - 4) = 7x + 2

5x + 35 - 3x + 12 = 7x + 2

2x + 47 = 7x + 2

Collect the like terms

5x = 45.

Divide.

x = 45 / 5

x = 9

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Answer:

[tex] \sf \: -2x² + 6x + 4 [/tex]

Step-by-step explanation:

Given problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

Let's solve the problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

→ 3x² + 8x - 7 - 5x² - 2x + 11

→ (3x² - 5x²) + (8x - 2x) + (-7 + 11)

→ (3 - 5)x² + (8 - 2)x + 4

→ -2x² + 6x + 4

Hence, answer is -2x² + 6x + 4.

Answer:

84 Degrees

Step-by-step explanation:

This is because they are alternate interior angles

Which means they are both the same angle and are both inside the parallel line

The percentage of the guests at this hotel who called for room service yesterday is 40%

When provided,

170 visitors in total requested room service.

The total number of visitors who did not request room service was 255.

We can now determine the overall number of guests.

Total guests equal (total guests who requested room services) plus (total number of guests who did not call for room services)

so,

there are overall guests of

=170+255

=425

We can now find the percentage

the proportion of visitors to this hotel who requested room service yesterday is

170/425 *100%

=40

The percentage of the customers at this hotel who called for room service yesterday is 40%.

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Answer:

£2.94

Step-by-step explanation:

1500g = 750g x 2 = 2 boxes

£1.96 = price for 1 box

÷ by 2 = 98p

add that to £1.96 = £2.94

The median score for the whole semester is 85. Thus, option a is correct.

It is given to us that -

The grades on first 7 tests of a statistics student are -

76, 80, 91, 94, 78, 85. 90

We have to find out the median score for the whole semester.

To find out the median, we have to first arrange the grades in ascending order from lowest to highest. Thus, arranging them in ascending order, we have -

76, 78, 80, 85, 90, 91, 94

Now, from this arrangement from lowest to highest, the median can be found out as the middle number in the given order which is equal to 85.

Therefore, the median score for the whole semester is 85. Thus, option a is correct.

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Answer:

Step-by-step explanation:

do your work ok you go it  and who still do ixl

An equation for the line parallel to the given line that contains C(2,4) is y = (3/4)x + (1/2).

We may use the slope-intercept version of the expression of a line, which is provided by "y = mx + b," where m seems to be the slope of the line & b is the y-intercept, to express the linear function that is perpendicular to a given line as well as contains a particular point.

We may easily utilize the same value of m again for the equation of a parallel line if the slope-intercept form of a line's equation is provided. For instance, if the provided line's equation is "y = 2x + 1," a parallel line's equation would be "y = 2x + c," where c is a constant.

By restructuring the equation in slope-intercept form if the equation of a line is provided in another form, such as "ax + by + c = 0," it is possible to determine the slope of the line. If the expression of the single sequence is "3x - 4y + 5 = 0," for instance, we may rewrite it in slope-intercept form by focusing just on y on one side of the equation:

3x - 4y + 5 = 0

-4y = -3x - 5

y = (3/4)x + (5/4)

The slope of the line is 3/4.

4 = (3/4)(2) + b

4 = (3/2) + b

b = 4 - (3/2)

b = (4 - 3/2)

b = (4 - 3)/2

b = (1/2)

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The length of p is 411 cm.

Every three-sided polygon having three edges and three vertices is referred to as a triangle in geometry. The most important attribute of a triangle is that its internal angles sum to 180 degrees. The triangle's angle sum attribute is what is known as.

As per the given data:

We are given a triangle, and we know 2 angles of the triangle and one side.

In ΔPQR:

r = 38 cm

∠P = 49°

∠Q = 127°

From the angle sum property for a triangle:

∠P + ∠Q + ∠R = 180°

49° + 127° + ∠R = 180°

∠R = 180° - 176°

∠R = 4°

By using the sine rule in a triangle:

sin(∠P)/p = sin(∠R)/r

p = [sin(∠P)/sin(∠R)] × r

p = [sin(49°)/sin(4°)] × 38

p = 411 cm

The length of p is 411 cm.

Hence, the length of p is 411 cm.

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Answer:

in order of going down:
1) 77
2) 103
3) 77
4) 37
5) 53

Step-by-step explanation:

Answer:

77°

103°

77°

37°

Step-by-step explanation:

The outer quadrilateral in black is a rectangle because of the angles it has at the vertices.

Look at the upper green line. It intersects the vertical sides of the outer rectangle.

The upper green line intersects the left vertical segment of the outer rectangle at a 103° angle. That makes the top yellow box 77°.

The top yellow box is an angle of a quadrilateral.

360 - 77 - 66 - 114 = 103

The second yellow box is 103°.

The third yellow box is 77°.

The bottom yellow box is 180 - 66 - 77 = 37°

Answer:

To find an equivalent expression for the area of the cement walkway, we can first distribute the 32 on the right side of the equation to get 32(5x-1 + 8) = 32(5x-1) + 32(8). Then, we can subtract the area of the courtyard, 24(5x-1), from this expression to get 32(5x-1) + 32(8) - 24(5x-1) = 8(5x-1) + 32(8). This is an equivalent expression that represents the area of the cement walkway in square yards.

The general form of an equation having vertex and point is y=a(x-h)²k. Then, the general form equation with the vertex of (-4,1) and point (-3,3) is y=3x²+24x+48.

The vertex form is an alternative way to state a parabola's equation. The equation y=a(x-h)²k is the formula for this, where k denotes the vertical translation, h is the horizontal translation, and a is a vertical stretch factor.

Here, given the vertex (h,k) is (-4,1) and the point (x,y) is (-3,3)

Start by substituting the values of h and k in the vertex equation, we get,

y=a(x+4)²(1)

Given that the point where the vertex meets is (-3,3). If we substitute this point into the equation above, we obtain,

3=a(-3+4)

a=3

To obtain the general form, now substitute the values of a and (h,k) in the vertex equation. We get,

y=3(x+4)²

y=3(x²+8x+16)

y=3x²+24x+48

Therefore, the required answer is y=3x²+24x+48.

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The correct statement about the plotted value on the number line is given as follows:

The stock is 5.5 less than the original value, and the absolute value is 5.5.

The value plotted on the number line is given as follows:

-5.5.

The fact that the value is negative means that the stock is now less than the original amount, and the amount that it is less is the absolute value of the number plotted.

The absolute value of a number is represented by the number without the signal, hence the absolute value of -5.5 is given as follows:

|-5.5| = 5.5.

(just removed the negative symbol).

Hence the second statement is correct about the interpretation of the number line in this problem.

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Answer:

n=2/5

Step-by-step explanation:

look it up

Answer:

n = 6

Step-by-step explanation:

8 x 6 = 48

48 + 9 = 57

=

7 x 6 = 42

42 + 15 = 57

So n = 6

By using the property of triangle, it can be calculated that-

A triangle is possible for case b) and c)

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.

We know that sum of two sides of a triangle is always greater than the third side

For a)

CA + BC = 3 + 1 = 4 which is not greater than AB = 4

A triangle is not possible in this case

For b)

CA + BC = 10 + 8 = 18 > AB = 8 cm

AB + AC = 8 + 10 = 18 > BC = 8cm

AB + BC = 8 + 8 = 16 > AC = 10 cm

A triangle is possible in this case

For b)

CA + BC = 8 + 10 = 18 > AB = 7 cm

AB + AC = 7 + 8 = 15 > BC = 10cm

AB + BC = 7 + 10 = 17 > AC = 8 cm

A triangle is possible in this case

So a triangle is possible for case b) and c)

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The equation of the perpendicular line is y = (7/3)x - 2/3. And the slope of the line is 7/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

y = -(3/7)x + 4

The equation of the line that is perpendicular to y = -(3/7)x + 4 will be given as,

y = (7/3)x + d

The equation passes through (2, 4) will be given as,

4 = (7/3) × 2 + d

c = - 2/3

Then the equation of the perpendicular line is given as,

y = (7/3)x - 2/3

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Answer:

See below

Step-by-step explanation:

5z/(z-2) = - 1/z

1)  z [tex]\neq[/tex] 2  the expression (z-2) in 5z/(z-2) would be 0, leaving 5/0.  Division by 0 is undefined.

2)  Similiarly, the expression - (1/z) requires that z [tex]\neq[/tex] 0, since division by 0 is not allowed (undefined).

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0 is True statement.

In exponential smoothing, a weight is assigned to each data point in the series.

If a small weight is assigned, close to 0, it means that the more recent data points will have a lesser influence on the overall result.

This will therefore show the overall long-term tendency of the series.

in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0 is True statement.

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Answer:

Step-by-step explanation:

answer is A. n is parallel to both l and m

Correct formatting for a nested function is

=IF(AND(B2>3000,02>2000),"Bonus","No Bonus")

A nested If statement is used when 1 or more conditions are to be tested. The result of the nested function depends based on the true value of the function.

i.e. If the nested statement is true, certain operations are to be done otherwise, do something else. In other words, the IF function allows you to make a logical comparison between a value and what you expect by testing for a condition and returning a result if True or False.

The syntax of a nested function goes thus

IF( condition1, value_if_true1, IF( condition2, value_if_true2, value_if_false2 ))

This would be equivalent to the following in Excel

= IF(condition1,"value_if_true",value_if_false)

Base on the above explanation, only option B is right.\

And what it does is that

it checks if cell B2 is greater than 3000 AND cell 02 is greater than 2000.

If both statement are true, "Bonus" will be the output result

If one ore both statement are false, "No Bonus" will be the output result

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Answer: B

Step-by-step explanation:

i just did it

Answer:

y = 8x

Step-by-step explanation:

The amount of sugar in grams is 8 times the number of portions.

For example, 1 portion has 8 grams of sugar.

Two portions have 16 grams of sugar.

If you let y = number of grams of sugar and x = number of portions, then

y = 8x