You are doing a math quiz a need to complete at least 12 geometry problems in algebra problems within two hours

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

The average speed formula is given by:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)

Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is \(\displaystyle\sf 2 \times 120 = 240\) miles.

Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula \(\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}\).

For the journey from A to B:

\(\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4\) hours

For the return journey from B to A:

\(\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3\) hours

The total time for the round trip is the sum of the individual times:

\(\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7\) hours

Now, we can calculate the average speed:

\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29\) miles per hour.

Therefore, the average speed for the round trip is closest to 34.29 miles per hour.

Answer:

89

Step-by-step explanation:

178/2=89

The quotient of 6 and 1/4 is 24. In this question division operation applied.

What is a proper fraction?

A fraction is said to as a proper fraction if the numerator is less than the denominator. This implies that denominators will always be bigger than numerators for appropriate fractions.

When: Fractions are referred to as proper fractions.

Denominator < Numerator

(Or)

Numerator > Denominator

Given numerical expression is

6÷ 1/4

To convert the division sign into multiplication sign, take the reciprocal of 1/4.

The reciprocal of 1/4 is 4.

Therefore,

6÷ 1/4 = 6 × 4 = 24

The quotient of 6 and 1/4 is 24.

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50 units should the firm produce and sell each week to maximize its profit.

The cost per unit of producing a product is =60+0.2x dollars,

x is number of units produced per week.

The equilibrium price is determined by a competitive market is 80$.

Further we have to use the formula as,

\(\frac{d x^n}{d x}=n \cdot x^{n-1}\)

consider, cost for 1 unit of the product =60+0.2 x

Thus, for ' x ' units of the product,

The cost function is,c(x)=x(60+0.2x)

\(c(x)=60 x+0.2 x^2\)

Revenue eared from I unit of the product is  80$,

This, for ' x ' units of the product, the revenue function is represented as,

R(x)=880

So, the profit function is,

\(\Rightarrow P(x) & =R(x)-c(x) \\& =80 x-\left(60 x+0.2 x^2\right) \\& =80 x-(60+0.2 x) x \\& =-0.2 x^2+20\)

To find the maximum profit, differential profit function w.r.t ' x ',

\(& P^{\prime}(x)=\frac{d}{d x}\left(-0.2 x^2+20 x\right)=-2(0.2) x+20 \\& P^{\prime}(x)=-0.4 x+20\)

\(& p^{\prime}(x)=0 \\-0.4 x+20=0 \quad \\\Rightarrow \quad x & =\frac{20}{0.4} \\x & =50\)

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Hence, He had to pay $ 18.11 for the tip on a restaurant bill.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Josiah ate dinner at a restaurant and his bill was $15.75,

He wanted to leave  15% tip,

Then He had to pay,

=15.75+15 % of 15.75

=15.75 + 0.15*15.75

=18.11

Hence, He had to pay $ 18.11 for tip on the restaurant bill.

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To make a tree diagram, start by writing out the given information and drawing a box around it. Then draw two branches off of the box representing the two possible outcomes of selecting a student, male or female. Then draw two more branches off of each of the first two branches, representing the two possible outcomes of receiving aid.

Then draw two more branches off of each of the second two branches, representing the two possible outcomes of receiving federal aid. This will create a tree diagram that looks like this (see the image).

From the tree diagram, we can calculate the probability of selecting a student from the given information as follows:

P(selecting a student) = P(selecting a male) + P(selecting a female) = (of male students/total students) + (of female students/total students) = (of male students + of female students)/total students =

Therefore, the probability of selecting a student from the given information is .

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Just factor out the 3:

3m + 3n = 3 (m + n)

Suppose, Melissa makes deposits for 10 years, the total amount of deposited money in 10 years will be $61,070.14 by using geometric series.

A savings account is a type of bank account that is designed to help people save money. When you deposit money into a savings account, the bank pays you interest on your balance, which means that your money can grow over time.

To find the sum Sn of a geometric series of n terms, we can use the formula:

Sn = a(1 - \(r^{n}\)) / (1 - r)

where a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term is $1,000, and the common ratio is 1.02 (since each subsequent deposit is 2 percent greater than the previous deposit). So we can use: a = 1000 and r = 1.02

To find the number of terms, we need to know how many years Melissa plans to make deposits. Let's say she plans to make deposits for 10 years. Then we have: n = 10

Now we can use the formula to find the sum Sn:

Sn = 1000(1 - \(1.02^{10}\)) / (1 - 1.02)

Sn = 1000(1 - 1.221402758) / (-0.02)

Sn = 61070.138

Therefore, if Melissa makes deposits for 10 years as supposed, the total amount of deposited money will be $61,070.14.

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Answer:

Step-by-step explanation:

\(\tt 10x+37+9x+1+5x+12=360^o\)

Add like terms:-

\(\tt 10x+9x+5x=360^o+37^o-1^o-12^o\)

\(\tt 10x+9x+5x=\bf 24x\)

\(\tt 360+37-1-12=\bf 384\)

\(\tt 24x=384\)

Divide both sides by 24:-

\(\tt \cfrac{24x}{24}=\cfrac{384}{24}\)

\(\tt x=16^o\)

Now, let's find m∠BCA:-

m∠BCA = 180-(10x-37)

\(\tt 180-(10(16)-37)\)

\(\tt 180-123\)

\(\tt 57^o\)

Therefore, m∠BCA = 57°.

________________________

Hope this helps!

Answer:

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

Sum of exterior angles measures is 360°.

Set up the following equation and solve for x:

Find exterior angle measure at vertex C:

We know interior and exterior angles on the same vertex form a linear pair.

Find interior angle at vertex C, the ∠BCA:

Answer:

Step-by-step explanation:

f(x) = 2x2 − 12x + 24

      = 2(x^2 - 6x) + 24

      = 2[(x - 3)^2 - 9) + 24

      = 2(x - 3)^2 - 18 + 24

      = 2(x - 3)^2 + 6

- so the minimum cost is 6

Answer:

1st answer is right answer

Answer:

1134 ft^3

Step-by-step explanation:

Answer:

first is 2

second is 1

third is 5

fourth 3

and fifth is 4

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Answer:

Actually 21 of them are girls.

Step-by-step explanation:

Make a table with 3 and 7 like this

3|7

6|14

9|21

* remember to add together each side every time you multiply to make sure you get 30

The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

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The graph that shows the following system of equations and its solution is graph number C

A graph is the graphical representation of equations on a graph sheet

The given equations are

-4x-3y=4

4x-y=-4 Solving the equations

In equation 1

When x = 0

-3y = 4

y=-4/3                  (0, -4/3)

When y = 0

-4x = 4

x= -1            (-1, 0)

In equation 2 when x = 0

-y = -y = 4             (0, 4)

When y = 0

4x=-4 x=-1              (-1, 0)

When these coordinates are used to plot the graph, graph number is is obtained.

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Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

6 miles

2 1/4 + 3/4 = 3 whole miles. 3x2=6.

The expression that is equivalent to \(80^{(1/4}\) * x is \(80^{4/x}\)

To determine the equivalent expression to \(80^{1/4}\) * x, let's analyze each option:

\(80/4^{x}\)

This expression simplifies to \(20^{x}\), but it is not equivalent to the original expression.

Applying the power of a power rule, this expression simplifies to \(80^{x/4}\) , which is not equivalent to the original expression.

\(80/x^{4}\)

This expression can be simplified as \(80^{4 x^{4} }\) , which is not equivalent to the original expression.

Therefore, the expression that is option d.

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Answer:

please see answers below

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ².

angles in a triangle add up to 180°.

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

angle C = 90° (little square means 90).

if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.

using the Sine rule:

a/Sin A  =  c/Sin C

multiply both sides by Sin A:

a = (c Sin A) / Sin C

= (12 Sin 30) / Sin 90

= 6.

so a = 6.

Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),

c² = a² + b²

b² = c² - a²

= 12² - 6²

= 144 - 36

= 108

so b² = 108

b = √108

angle B is correct

Answer: 270 ft²

Step-by-step explanation:

The dimensions of 1 room is 10 ft x 12 ft

The other room is 10 ft x 15 ft

For area multiply the length and width and add the 2 areas

so A1 =  10x12=120 ft²

A2 = 10x15 =150 ft²

Total area is 150+120 =270 ft²

Answer:

Number of pieces in the puzzle

Step-by-step explanation:

The number of pieces in a puzzle determines how long it will take to complete.

The complete sentence will be;

''The amount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle.''

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The sentence is,

The amount of time it takes to complete a puzzle is most likely to be a

function of the ...

Now,

We know that;

The amount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle.

Hence, The complete sentence will be;

''The amount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle.''

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Answer:

slope = -7

Step-by-step explanation:

(1, 4) and (2, -3)

Slope = y^2 - y^1 / x^2 - x^1

m = -3 - 4 / 2 - 1

m = -7 / 1

m = -7 ---------> slope of the line through (1, 4) and (2, -3)

Answer:

slope is -7 for (1, 4) and (2, -3)

Answer:

depends on what your using it for but i think the 2 one

Step-by-step explanation:

Answer:

168 \(cm^{3}\)

Step-by-step explanation:

Start by finding the whole prism's volume. 9 x 3 x 8 = 216 Then find the volume of the missing part. 8 x 6 x 1 = 48. Subtract the missing volume from the whole volume. 216 - 48 = 168

Step-by-step explanation:

the answer is A.-3*6=-18