Miles is renting a meeting room at a college. There is a reservation fee of $21 and an additional fee of $4 per hour. He needs to spend no more than $85. What is the possible number of hours for which Miles could rent the meeting room? Use t for the number of hours.
t ≤26.5
t<4
t ≤ 16
t<21.25

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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The value of Quotient from the given terms is 9.6* 10^8

According to the statement

we have given that the two terms and we have to find the quotient of the these terms.

So, we know that the

Quotient is a the number resulting from the division of one number by another.

And for find the quotient we have to divide the terms with each other.

So, The given terms are \(7.536*10^7\)and \(7.85*10^2\)

divide both terms with each other.

Quotient = \(\frac{7.536*10^7}{7.85*10^2}\)

Then

The value of quotient becomes

Quotient = \(0.96 * 10^9\)

After removing the decimal from the answer it will become

Quotient = \(9.6* 10^8\).

So, The value of Quotient from the given terms is 9.6* 10^8

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Answer: its 7.85x10^-9

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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Answer:

cos L = 55/73

Step-by-step explanation:

The triangle KLM is a right angle triangle. The ∠M = 90°. The side KM = 48, LK = 73, and ML = 55. The ratio that represents the cosine of ∠L can be solved below.

The right angle triangle formed has an hypotenuse , opposite and an adjacent side. Using the SOHCAHTOA principle one can find the ratio that represent the cosine of ∠L.

opposite side = 48

adjacent = 55

hypotenuse = 73

cos L = adjacent/hypotenuse

cos L = 55/73

Answer:

B. line

Step-by-step explanation:

A line would fit this description best. A ray wouldnt work because it goes on infinitely in one direction. A point wouldnt work because it is a dot that marks a location, and a segment is bound by 2 points, and cannot go on forever.

The given description would be best fitting to a "line", which is the correct answer would be an option (B).

A Line is formed by a set of points traveling in a straight line but in opposite directions. It has no breadth, no depth (curvature), and no termination, which implies 'it will not finish,' hence it moves in a straight line in opposing directions indefinitely.

This object goes forever in opposite directions. It is infinitely skinny, as it is a set of points that are all lined up.

This description would be best suited to a line.

A ray would not operate since it extends in one direction indefinitely. A point would not work since it is a dot that indicates a position, but a segment is constrained by two points and cannot continue indefinitely.

Hence, the correct answer would be an option (B).

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Answer:

(−3  2/3 )(x)+57

Step-by-step explanation:

Ayyy I remember this question.

(−3  2/3 )(x)+57

Answer:

8/15 gallons or 0.5333 gallons

Step-by-step explanation:

x = total

0.4 = 0.75x

0.4/0.75 = x

0.533 = x

0.533 = 8/15

Answer:

Step-by-step explanation:

Given the expression u= av + bw where u = 2i + j, v = i + j, and w = i - j, to find the scalars a and b, we will first substitute the vectors into the expression given as shown;

u= av + bw

2i + j = a( i + j)+b(i-j)

open the parenthesis

2i + j = ai+aj+bi-bj

collect like terms at the right hand side of the equation

2i + j = ai+bi+aj-bj

2i + j = (a+b)i+(a-b)j

compare the coefficient of complex value i and j on both sides

a+b = 2 ............... 1

a-b = 1................. 2

solve the resulting equation simultaneously using elimination method

Subtract both equation from each other.

(a-a) +(b-(-b))= 2-1

0+2b = 1

b = 1/2

Substitue b = 1/2 into equation 2 to get a

From equation 2, a = 1+b

a = 1 + 1/2

b = 3/2

Hence the scalars a and b are 1/2 and 3/2 respectively

\(a=\frac{3}{2},b=\frac{1}{2}\)

A complex number is of the form \(\boldsymbol{a+ib}\) where \(a,b\) are real numbers.

\(u=2i+j\)

\(v=i+j\)

\(w=i-j\)

\(u=av+bw\)

So,

\(2i+j=a(i+j)+b(i-j)\)

\(2i+j=(a+b)i+(a-b)j\)

Therefore,

\(2=a+b\\1=a-b\)

Add these equations.

\(3=2a\\\frac{3}{2}=a\)

So,

\(1=\frac{3}{2}-b\\\\b=\frac{3}{2}-1\\\)

  \(=\frac{1}{2}\)

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In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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Answer:

there are no outlier in this data set beacuse

1.  Put the data in numerical order.

2.  Find the median.

3.  Find the medians for the top and bottom parts of the data.  This divides the data into 4 equal parts.

The median with the smallest value is called Q1.  The median for all the values - usually just called the median is also called Q2.  The median with the largest value is Q3.

4.  Subtract...Q3 - Q1.  This value is the InterQuartileRange or IQR.  Remember that the range means taking the largest minus the smallest.  This is a special range having to do with the quartiles.

5.  Multiply...1.5 * IQR

6.  Take your answer from #5 and do 2 things with it.  A). Subtract it from Q1 and B)  Additional to Q3.

7.  Look at all your data points.  If any are SMALLER than Q1 - 1.5 *IQR, they are outliers.  If any are LARGER than Q3 + 1.5 *IQR, they are also outliers.

For your data....the median, Q2 is

(43+38)/2 = 40.5.

Q1 = (30+26)/2 = 28.

Q3 = (54+52)/2 = 53

The IQR is 53 - 28 = 25

1.5 * IQR = 37.5

Q1 - 37.5 = 28 - 37.5 = -9.5. There is no data value less than -9.5.

Q3 + 37.5 = 53 + 37.5 = 90.5.  there is no data value greater than 90.5.

My conclusion is that there are no outliers in this data.

I hope this helps!

Answer:

700

Hope this helps!!

Answer:

700

Step-by-step explanation:

Answer:

No, but they add up to 180 degrees.

Step-by-step explanation:

Take one of the angles, interior or exterior and subtract it from 180 and you should have your other angle.

Answer:

2sqr3, the first option

Step-by-step explanation:

Answer:

m = w/g

Step-by-step explanation:

Step 1: Write equation

w = gm

Step 2: Divide both sides by g

w/g = m

Step 3: Rewrite

m = w/g

Answer:

w/g = m

Step-by-step explanation:

w = gm

Divide each side by g

w/g = gm/g

w/g = m

The solution to the given inequality -3(x - 2) ≤ 1/3 is x ≤ 17/9

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3x ≤ 1/3 - 6

-3x ≤ (1-18) / 3

-3x ≤ -17/3

x ≤ -17 /3 ÷ -3

x ≤ -17/3 × 1/-3

x ≤ -17/-9

x ≤ 17/9

A verbal statement describing the solution to the inequality is x is less than equal to 17 over 9

Verifying the solution of the inequality:

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3(17/9) + 6 ≤ 1/3

-51/9 + 6 ≤ 1/3

(-51+54) / 9 ≤ 1/3

3/9 ≤ 1/3

1/3 ≤ 1/3

Therefore, the -3(x - 2) ≤ 1/3 to the inequality -3(x - 2) ≤ 1/3 in verbal statement is x is less than equal to 17 over 9.

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Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,

Lemonade left = 14,000 - 9,500 = 4,500 ml

Hence, the lemonade left with Tony is 4500ml.

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Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°

Answer:

D. 221.7 cm

Step-by-step explanation:

Surface area of a sphere is: \(SA=4\pi r^2\)

'r' - radius

We are given the radius of 4.2 centimetres.

\(SA=4\pi 4.2^2\\4 * \pi * 4.2^2\\\rightarrow 4.2^2 =17.64\\\text {Using 3.14 for pi: }\\4 * 3.14 *17.64\\12.56*17.64\\\boxed {221.5584}\)

221.5584 ≈ 221.6

The closest answer is Option D, therefore it should be the correct answer.

Answer:

Step-by-step explanation:

Answer:

A. is the answer

Step-by-step explanation:

A. Since there is one value of  y  for every value of  x

B. is not a function x  =  − 4  produces  y  =  4  and  y  =  3

C. is not a function x  =  6  produces  y  =  6  and  y  =  3

D. is not a function   x  =  6  produces  y  =  3  and  y  =  5

The relation that is a function is D (see image below).

If any vertical line passes through more than one point on a graph, then the relation is not a function. Conversely, if every vertical line intersects the graph at most one point, then the relation is a function.

Applying the vertical line test, if we place a vertical line across each graph given, only the graph in option D (as shown in the image below) will have the the vertical line intersects it at most one point.

Therefore, the correct option is D. (see image below).

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Answer:

0.75 .................

By direct multiplication of fractions, we will see that she uses 1/30 of the original container of applesauce to bake the muffins.

Remember that the product of two fractions is just:

\(\frac{x}{y} \frac{a}{b} = \frac{x*a}{y*b} \)

Now, we know that Sasha gets 1/3 of the applesauce, and she uses 1/10 of what she gets to make the muffins. So the fraction that she uses is just the product of these two:

\(\frac{1}{3}* \frac{1}{10} = \frac{1}{30} \)

This means that she uses 1/30 of the original container of applesauce to bake muffins.

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Answer:

yes

Step-by-step explanation:

d f xcdg

Answer:

maybe uh forgot to copy complete question.

The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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The measure of the angles in bold are as follows;

25. 90° and 90°

26. 60° and 60°

When two parallel lines are cut by a transversal , angle relationship are formed. They are alternate angles, corresponding angles etc.

Therefore,

x + 96 + x + 96 = 180

2x  = 180 - 192

2x = -12

x = -6

Hence, the angles are 90 and 90 degrees.

6x = 5x + 10(corresponding angles)

6x - 5x = 10

x = 10

Therefore, the angles are 60 degrees and 60 degrees

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x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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Answer:

D.) Sheba

Step-by-step explanation:

Divide all their incomes by the number of hours they worked.

Santana:

205.85/23=8.95

$8.95 per hour

Zomi:

370.50/38=9.75

$9.75 per hour

Priya

156.10/14=11.15

$11.15 per hour

Sheba

282.45/21=13.45

$13.45 per hour