Add: (3x^3-3x^2+9) and (-7+5x^2+7x^3)​

The calculation 62°23' - 31°57' simplifies to 30°26'. This means that the difference between 62 degrees 23 minutes and 31 degrees 57 minutes is 30 degrees 26 minutes.

To subtract two angles expressed in degrees and minutes, we perform the subtraction separately for degrees and minutes. For the degrees, subtract 31 from 62, which gives us 31 degrees.

For the minutes, subtract 57 from 23. Since 23 is smaller than 57, we need to borrow 1 degree from the degree part, making it 61 degrees and adding 60 minutes to 23. Subtracting 57 from 83 (61°60' + 23') gives us 26 minutes. Putting the results together, we have 31°26' as the difference between 62°23' and 31°57', which simplifies to 30°26' by reducing the minutes.

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Answer:

2/3

Step-by-step explanation:

that does not say + it a division sign  how to got 2/3

(3/4) / x = (9/8)

To solve this equation, we want x alone so we start by multiplying x on both sides like this:

((3/4) / x)x = (9/8)x

Which equals:

(3/4) = (9/8)x

Then we divide each side by 9/8 to like this:

(3/4) / (9/8) = ((9/8)x) / (9/8)

(3/4) / (9/8) is 2/3 and ((9/8)x) / (9/8) leaves x which means we end up with x = 2/3. Therefore, the answer to "3/4 divided by what equals 9/8?" is as follows:

2/3

It is always good to double-check your math to make sure you did it right. When we entered 2/3 for x in this equation (3/4) / x = (9/8), we get the following true equation which means our math is correct.

(3/4) / (2/3) = (9/8)

The value of x will be 2/3

What is an equation?

Equation: An equation is basically a statement that equates two expressions.

An equation must contain an "equality" sign.

Given,

3/4 + x = 9/8

Let us make it correct . Replace + sign with / to get the required answer.

(3/4) / x = (9/8)

To solve this equation, we want x alone so we start by multiplying x on both sides like this:

((3/4) / x)x = (9/8)x

(3/4) = (9/8)x

Then we divide each side by 9/8 to like this:

(3/4) / (9/8) = ((9/8)x) / (9/8)

(3/4) / (9/8) is 2/3 and ((9/8)x) / (9/8) leaves x which means we end up with x = 2/3.

Therefore, the answer to "3/4 divided by what equals 9/8?" is as follows:2/3

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Mr. Jones will be able to eat at the buffet restaurant approximately 4 times in a month.

To determine how many times Mr. Jones will be able to eat at the buffet restaurant based on his budget, we need to divide his monthly budget by the cost per visit.

Mr. Jones budgets $42 for the month, and the cost per visit is $9.

Number of visits = Monthly budget / Cost per visit

= $42 / $9

≈ 4.67

Since we cannot have a fractional number of visits, we round down to the nearest whole number because Mr. Jones cannot have a partial visit. Therefore,

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The area of the polygon become 24.5.

According to the statement

We have to find that the area of the polygon.

So, For this purpose, we know that the

Polygon is a plane shape (two-dimensional) with straight sides.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

From the given information:

The given vertices are:

J(-3,\ 4),\ K(4,\ 4),\ L(3,-3)

And then the base of the polygon become:

Base = \(\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} }\)

Then

Base = \(\sqrt{(-3 - 4)^{2} + (4 -4)^{2} }\)

Base = 7

Then

Height = \(\sqrt{(y_{1} - y_{2})^{2} +(z_{1} - z_{2})^{2} }\)

Height = \(\sqrt{(4 - 4)^{2} +(4 - (-3))^{2} }\)

Height = 7

Then the area of the polygon becomes:

Area = 1/2 *Base*Height

Area = 1/2 *7*7

Area = 1/2*49

Area = 24.5

Thus, The area of the polygon become 24.5.

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Answer:

because as long as it's the same number, the equation is still the same as long as you have the same numbers and you're using the same subtraction/addition properly

Step-by-step explanation:

Answer:

I think its A

Step-by-step explanation:

I eliminated C and D but am not 100% sure between a and b i think its right im not sure sorry

Answer:

39

Step-by-step explanation:

Okay so there are 52 cards in a deck and there are 4 of each card. 4 kings 4 Queens 4 Jacks 4 Ace 4 Twos 4 Threes 4 fours 4 fives 4 sixes 4 sevens 4 eights 4 nines 4 tens. One from each group is a heart there are 13 groups so therefore subtract 13 from 52.

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.

Probability that dice rolled shows a 5 once =  1/36

Probability that dice rolled shows a 5 twice =  2/36

Probability that the sum is 8 = 5/36

Total probability = 1/36 + 2/36 + 5/36 = 0.22

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Answer: 36

Step-by-step explanation:

\(\overline{AB} \cong \overline{BC}\) (Triangle ABC is isosceles)

\(m\angle CAB=m\angle CBA=30^{\circ}\) (base angles of an isosceles triangle are congruent)

\(\angle MCB=90^{\circ}\) (In triangle CMB, angles in a triangle add to 180 degrees)

\(\angle ACM=30^{\circ}\) (triangle sum theorem)

\(MB=24\) (30-60-90 triangle CMB)

\(AB=12\) (sides opposite congruent angles in a triangle are congruent)

\(AB=36\) (segment addition postulate)

Answer:

Step-by-step explanation:

-Start by distributing the 2, -2(3m+1/2).

-Getting -6m-1, your equation should look like -40-6m-1=7m-2

-Combine -40 and -1 to get -41, and then add the -6m to the other side.

-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.

-Now, we have -39=13m. divide both sides by 13 to get m=-3.

Answer:

4, 6, and 475

Step-by-step explanation:

See attached image.

In interpreting effect size, the meaning of effect size at 0.3 is small effect size. So, the correct answer is A).

In interpreting effect size, an effect size of 0.3 is typically considered to be a small effect size. This means that there is a small but still measurable difference or relationship between two variables.

The interpretation of effect size can vary depending on the context and the discipline in which it is being used, but as a general rule, effect sizes of 0.2 or smaller are considered small, effect sizes of 0.5 are considered medium, and effect sizes of 0.8 or larger are considered large. Therefore, an effect size of 0.3 falls in the small effect size range. So, the correct option is A).

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The numerical length of the line segment FG is 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Point G is on FH, hence:

FH = FG + GH

Given that GH = 8, FH = 3x + 3, FG = 2x, hence:

3x + 3 = (2x) + 8

x = 5

FG = 2x = 2(5) = 10

The numerical length of the line segment FG is 10 units.

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Answer:

468.75 = Volume B

Step-by-step explanation:

The volume of two similar figures is related to the scale factor by cube

Volume A          

----------------- = scale factor ^3

Volume B

30                  2^3

-------------- = ---------

Volume B        5^3

Using cross products

30 * 125 = 8 Volume B

3750 = 8 Volume B

Divide by 8

3750/8 = Volume B

468.75 = Volume B

Answer:

67 900000199l

Step-by-step explanation:

Answer:68

Step-by-step explanation:

Three labeled points on the line are (-2, -2m), (0, 0), and (2, 2m), where m is the slope of the line.

A line passing through the origin but not contained in any of the three coordinate planes can be represented by the equation y = mx, where m is the slope of the line. Since the line passes through the origin, the y-intercept is 0.

To find labeled points on the line, we can choose different values for x and calculate the corresponding y-values using the equation y = mx. Let's choose three values for x: -2, 0, and 2.

For x = -2:

y = m(-2) = -2m

So, one labeled point on the line is (-2, -2m).

For x = 0:

y = m(0) = 0

Another labeled point on the line is (0, 0).

For x = 2:

y = m(2) = 2m

So, the third labeled point on the line is (2, 2m).

These three labeled points (-2, -2m), (0, 0), and (2, 2m) lie on the line passing through the origin, and they are not contained in any of the coordinate planes.

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Finding the six trigonometric functions of θ: Since (-3,3) is a point on the terminal side of θ, we can use the coordinates of this point to determine the values of the trigonometric functions.

Let's label the legs of the right triangle formed as opposite = 3 and adjacent = -3, and use the Pythagorean theorem to find the hypotenuse.

Using Pythagorean theorem: hypotenuse² = opposite² + adjacent²

hypotenuse² = 3² + (-3)²

hypotenuse² = 9 + 9

hypotenuse² = 18

hypotenuse = √18 = 3√2

Now we can calculate the trigonometric functions:

sin θ = opposite/hypotenuse = 3/3√2 = √2/2

cos θ = adjacent/hypotenuse = -3/3√2 = -√2/2

tan θ = opposite/adjacent = 3/-3 = -1

csc θ = 1/sin θ = 2/√2 = √2

sec θ = 1/cos θ = -2/√2 = -√2

cot θ = 1/tan θ = -1/1 = -1

Therefore, the exact values of the six trigonometric functions of θ are:

sin θ = √2/2, cos θ = -√2/2, tan θ = -1, csc θ = √2, sec θ = -√2, cot θ = -1.

Part 2: Finding the remaining trigonometric functions given tan θ and sin θ:

Given that tan θ = and sin θ < 0, we can deduce that θ lies in the third quadrant of the unit circle where both the tangent and sine are negative. In this quadrant, the cosine is positive, while the cosecant, secant, and cotangent can be determined by taking the reciprocals of the corresponding functions in the first quadrant.

Since tan θ = opposite/adjacent = sin θ/cos θ, we have:

sin θ = -1 and cos θ =

Using the Pythagorean identity sin² θ + cos² θ = 1, we can find cos θ:

(-1)² + cos² θ = 1

1 + cos² θ = 1

cos² θ = 0

cos θ = 0

Now we can calculate the remaining trigonometric functions:

csc θ = 1/sin θ = 1/-1 = -1

sec θ = 1/cos θ = 1/0 = undefined

cot θ = 1/tan θ = 1/-1 = -1

Therefore, the exact values of the remaining five trigonometric functions of θ are:

sin θ = -1, cos θ = 0, tan θ = -1, csc θ = -1, sec θ = undefined, cot θ = -1.

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Answer:

√2

Step-by-step explanation:

Angle ( θ ) = 45

Hypotenuse side = 2

Opposite side = x

Formula : -

sin θ = Opposite side / Hypotenuse side

Note :

The value of sin 45 = 1/√2

sin 45 = x/2

1/√2 = x/2

Cross multiply,

x*√2 = 2*1

x√2 = 2

2 can be simplified as √2 * √2

x√2 = √2*√2

Divide √2 on both sides,

x = √2

The value of x is 19.79.

Given base of a right angled triangle as 14, hypotenuse is marked as x.

Firstly calculate the perpendicular of the right angled triangle with the help of trigonometric functions,

tanα= perpendicular/base

tan45°= 14/base

tan45°=1

1= 14/base

base=14

Now using Pthagorean theorem,

We know by Pythagoras theorem, square of the hypotenuse is equal to the sum of the squares of the legs,

Hypotenuse² = Perpendicular² + Base ²

Substitute the values of perpendicular and base in the pythagorean theorem,

x² = 14² + 14²

x² = 196 +196

x=√392

x= 19.79

Hypotenuse of a right angled triangle is 19.79 .

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Answer:

C

Step-by-step explanation:

The area of the regular octogon is 196.15 square inches.

For a regular octogon with apothem A and side length L, the area is given by:

area =(2*A*L) * (1 + √2)

Here we know that:

A = 7in

L = 5.8 in

Replacing these values in the area for the formula, we will get the area:

area = (2*7in*5.8in) * (1 + √2)

area = 196.15 in²

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The additional information required to prove  that ΔXYZ and ΔFEG are congruent is  ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE. So option 1 and 5 are correct.

Here in the figure it is given that ∠F and ∠X are congruent. To prove the triangle is congruent we have to prove that either two sides including the angles are congruent or another angle and included side is congruent.

When ∠Z ≅ ∠G and XZ ≅ FG, two angles and included sides are congruent, so triangles are congruent.

∠Z ≅ ∠G and ∠Y ≅ ∠E , we can not apply ASA, since three angles are mentioned

XZ ≅ FG  and ZY ≅ GE , Two sides are given, ASA cannot be applied, we need two angles

XY ≅ EF and ZY ≅ FG, is not possible.

∠Z ≅ ∠G and XY ≅ FE, one corresponding side and two angles are equal, so ΔXYZ ≅ ΔFEG according to ASA.

So, the correct answer is option 1 and option 5.

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The complete question is as follows and image is given below

What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and ∠Y ≅ ∠E

XZ ≅ FG and ZY ≅ GE

XY ≅ EF and ZY ≅ FG

∠Z ≅ ∠G and XY ≅ FE

Answer:

1 and 5 are correct

Step-by-step explanation:

The answer  is that there are 165 ways to distribute eight identical bottles of water to three friends.

We can use the formula for distributing identical objects to distinct groups, which is (n+r-1) choose (r-1), where n is the number of objects and r is the number of groups. In this case, n=8 and r=3.

So the formula becomes (8+3-1) choose (3-1), which simplifies to 10 choose 2. Using the combination formula, 10 choose 2 equals 45. However, this only accounts for cases where all three friends receive at least one bottle of water.

To account for cases where some friends may receive no water, we need to add the number of ways where two friends receive water and one friend receives no water, and the number of ways where one friend receives water and two friends receive no water.

There are three ways to choose which friend receives no water, and then we need to distribute the remaining eight bottles of water among the remaining two friends. Using the formula from earlier, this gives us (8+2-1) choose (2-1) = 9.

So for the case where two friends receive water and one friend receives no water, there are 3 * 9 = 27 ways. Similarly, for the case where one friend receives water and two friends receive no water, there are 3 * 9 = 27 ways.

Adding these cases to the initial case where all three friends receive at least one bottle of water, we get a total of 45 + 27 + 27 = 99 ways. However, we still need to account for cases where all eight bottles of water go to a single friend, which is just 3 ways.

So the final answer is 99 + 3 = 102 ways to distribute eight identical bottles of water to three friends, where some friends may receive no water.

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Answer:

75.6

Step-by-step explanation:

100% - 73% = 27%  

27% = 0.27

280 × 0.27 = 75.6

There are 358,800 different ways that a 4-letter password might be used.

For the stated question-

For the fourth letter, we might select any letter between A and Z besides the first, second, and third letters.

SO;

Number of possible combinations for 4-letter passwords

= 26 × 25 × 24 × 23

= 358,800

Thus, there are 358,800 different ways that a 4-letter password might be used.

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The complete question is-

To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible.