Solve each problem below by writing an equation that matches the situation. Then solbe your equation to find the solution to the problem. (It's been almost a day and these two questions baffled me.)

To solve this triangle, we cannot use either the Pythagorean Theorem or the Law of Cosines. We need more information.

Conversely, we can use SOHCAHTOA, in the sense that we can use the SOH part of this (Sine = opposite side over hypotenuse), that is, we can use angle 33 as the reference angle, and we have a right triangle here. Then, using trigonometric ratios, we can use:

We also can use the Law of Sines to solve it:

Therefore, we can solve this triangle using both Law of Sines and SOHCAHTOA. (We can select two options: c and d.)

The common differences of arithmetic sequence are;

For a) -3

For b) - 20

For c) - 30

For d) - 10

What is Arithmetic sequence?

An arithmetic sequence is ordered set of numbers that have common difference between each consecutive term.

Given that;

The Arithmetic sequence are;

a) 35, 32, 29, 26 ...

b) - 3, -23, - 43, -63

c) -34, -64, -94, - 124

d) - 30, - 40, - 50, -60

Now, The common difference of an arithmetic sequence is calculated by the difference between each consecutive term.

For Arithmetic sequence a;

Common difference = 32 - 35 = -3

And, For Arithmetic sequence b;

Common difference = - 23 - (-3)

                               = - 23 + 3

                               = - 20

For Arithmetic sequence c;

Common difference = - 64 - (-34)

                               = - 64 + 34

                               = - 30

For Arithmetic sequence d;

Common difference = - 40 - (-30)

                               = - 40 + 30

                               = - 10

Thus, The common differences of arithmetic sequence are;

For a) -3

For b) - 20

For c) - 30

For d) - 10

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Answer:

Step-by-step explanation:

first you need to figure out what your solving for We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

The given information is:

ABCD is a rhombus.

1 Statement: Rhombus ABCD

Reason: given

2. Statement: AB=AD

Reason: Definition of rhombus (all four sides are congruent)

3. Statement: AE=AE

Reason: Reflexive property

4. Statement: BE=DE

Reason: Diagonals bisect each other

5. Statement: Triangle ABE=Triangle ADE

Reason: SSS congruency (Side-Side-Side).

Based on the probability of the macro-economic probabilities and the share returns, the expected share return can be found to be 10%.

The expected share return based on the economic probabilities can be found by the formula:

= (Probability of recession x Share return in recessions) + (Probability of steady state x Share return in steady state) + (Probability of boom x Share return in boom)

Solving for the expected share return gives:

= (20% x 5%) + (60% x 10%) + (20% x 15%)

= 1% + 6% + 3%

= 10%

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Answer: Divisor

Step-by-step explanation:

The the answer to a division problem is called the quotient. The number that is doing the dividing is called the divisor. The number that gets divided up is called the dividend.

Example: If 3 boys ask to mow your yard for $24, then each boy would get $8.

24 divided by 3 is 8. (24 / 3 = 8 )

24 is the dividend (the number getting divided up)

3 is the divisor (the number that is doing the dividing)

8 is the quotient.

Answer:

[tex]1 \div 6 = 0.16 \times 100 = 16.6 percent[/tex]

that's all I know

Answer:

The volume of the cylinder is;

Explanation:

Given the figure in the attached image;

Recall that the volume of a cylinder can be calculated using the formula;

Substituting the given values;

Therefore, the volume of the cylinder is;

Answer:

A - 35 copies

B - $4050

Step-by-step explanation:

A-

2300 + 70c = 4750

70c = 4750 - 2300

70c = 2450

c = 35

He sold 35 copies

B-

P = 2300 + 70(25)

P = 2300 + 1750

P = $4050

Total if he sold 25 copies: $4050

Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.

What is Coordinate?

Total coordinates son number line from -7 to +7 =15

Number line ratio that has to be provided = 3:2

Let the coordinate be provided is x.

Therefore, 3x+2x=15

⇒5x=15

⇒x=3

Coordinate X

3x=3(3)=9

9th coordinate from -7 = 1 i.e. D

Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.

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Answer:

-4

Step-by-step explanation:

-3(x+3)+11=14

-3·x-3·3+11=14

-3x-9+11=14

-3x+2=14

-3x=14-2

-3x=12

x=12÷(-3)

x=-4

ANSWER:

2

STEP-BY-STEP EXPLANATION:

We have the following equation of line:

The equation of the line in its slope and intercept form is like this:

Therefore, we must solve for y to know the value of the slope (m), like this:

The slope is 2

Answer:

x< 3 this is for inequality and interval (inf,3)

The Slope of the line through the points (4, -5) and (2, 2) then graph it. Slope [tex]m=-\frac{7}{2}$$[/tex]

Slope between two points: [tex]$\quad$[/tex]Slope [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]

[tex]$$\begin{aligned}&\left(x_1, y_1\right)=(4,-5),\left(x_2, y_2\right)=(2,2) \\&m=\frac{2-(-5)}{2-4}\end{aligned}$$[/tex]

Refine

[tex]m=-\frac{7}{2}$$[/tex]

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

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The range of the function is determined as 1 ≤ M ≤ 6.5 kg.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

Also we can defined a domain of a function as all the possible values that go into a function.

From the  graph the range of the function of the mass of the bucket is calculated as follows;

The minimum value of the mass of the bucket = 1

The maximum value of the mass of the bucket = 6.5 kg

The range of the function (mass, M of the bucket) = {1, 2, 3, 4, 5, 6.5 kg}

1 ≤ M ≤ 6.5 kg

Thus, the range of the function includes numbers ranging from 1 to 6.5 kg. That is  {1, 2, 3, 4, 5, 6.5 kg}.

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Given that line segment, GC bisects ∠FGH

I made a sketch of the angles, they are not at scale.

That segment GC is an angle bisector indicates that it divides ∠FGH into halves. To determine the measure of the ∠FGC and ∠CGH you have to divide the measure of FGH by 2.

a) ∠FGH=86º

So, in this case, the measure of ∠FGC is 43º.

b) For this item you have to determine the measure of ∠FGH given that the measure of one of the angles determined by the bisector is ∠CGH. To determine the measure of ∠FGH you have to multiply ∠CGH by 2

The dimension of minimum paper size would be 18 inches by 9 inches.

Let the paper size be x inches in length and y inches in width.

The length of the printed space would be x-8 inches and width would be y-4 inches.

Print area would thus be (x-8)(y-4)=50.

From this [tex]$y=4+\frac{50}{x-8}=\frac{4 x+18}{x-8}$[/tex]

Also from the same equation on simplifying, it is x y-8 y-4 x+32=50.

Since the area of the paper of size x inches by y inches is xy, let it be denoted as A.

Thus

[tex]$A-8 y-4 x=18$[/tex] Or [tex]$A=8 y+4 x+18$[/tex]

[tex]$A=\frac{32 x+144}{x-8}+4 x+18$[/tex].

For minimum paper size [tex]$\frac{d A}{d x}$[/tex] must be =0, hence,

[tex]$\frac{d A}{d x}=\frac{32(x-8)-(32 x+144)}{(x-8)^2}+4=0$[/tex]

[tex]$\frac{-400}{(x-8)^2}+4=0$[/tex]

(x-8)² = 100

x-8 = 10

[tex]$\mathrm{x}=18$[/tex], hence [tex]$\mathrm{y}=4+\frac{50}{x-8}=9$[/tex]

Dimension of minimum paper size would be 18 inches by 9 inches.

The complete question is:

You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?

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Well the principals patterns are that the equations are quadratic equations, and the graphs are parables and that the equations and the graphs are related.

Answer:

257 kg

Step-by-step explanation:

Hello!

The mass of the cow is 257 kg.

Solution

Note: The event here is Mutually Exclusive,, meaning the 2 events can happen at the same time

Total number = 4 + 3 + 3+3 = 13

Note ; We multiplied each of the x-values with their probabilities and obtain the sum of all. This gives the expected value.

We know that the half life of this element is 41.3 days.

We have to find how much will remain of a sample of 2 grams after 86 days.

The half life of 41.3 days means that the mass after 41.3 days will become half of what it was.

We can express this as:

As this is represented with an exponential model like this:

we can use the half-life to find the parameter b:

Then, knowing that the initial mass M(0) is 2 grams, we can express the final model as:

We then can calculate the mass after t = 86 days as:

Answer: the mass after 86 days will be 0.472 grams.

Given,

The expression of the function is,

Required

The graph of the function.

Take x = 1 then the value of y is,

Take x = 2 then the value of y is,

Take x = 0 then the value of y is,

Take x = -1 then the value of y is,

Take x = -2 then the value of y is,

The graph of the function is,

The vertex of the graph is (-2, -1).

The x - intercept of the graph is -1 and -3.

The y - intercept of the graph is at 3.

Hence, the graph of the function is obtained.

Answer:

For f(x);

The domain is;

The range is;

Graphing those points for function A, we have;

The domain and range of the given function A is;

Graphing those points for function B, we have;

The domain and range of the given function B is;

Explanation:

Given the function in the attached image;

The function is a square function and can be written as;

The domain is;

The range is;

A.

B.

Graphing the functions;

For A;

Graphing those points for function A, we have;

The domain and range of the given function A is;

For B;

Graphing those points for function B, we have;

The domain and range of the given function B is;

Answer:

P(A and B) = 0.25

Step-by-step explanation:

Since P(A) and P(B) are independents events, The probability P(A) and P(B) occurs consecutively is P(A)*P(B):

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

P(A and B) = 0.512*0.488

P(A and B) = 0.25

Answer:

A. S = 65 + 10x

B. 3.3 hours

Step-by-step explanation:

A. S=f(T)

65 = f(0)

85 = f(2)

S₂ - S₁

85 - 65 = 20

T₂ - T₁

2   -   0  = 2

20 / 2 = 10

For every hour you study, you will score an additional 10 points with a baseline of 65 points.

S = 65 + 10x where x is the amount of time (in hours) that you studied for.

B. S = 65 + 10x

Since we want a specific score of 98, we plug it in for S and solve for x.

98 = 65 + 10x

33 = 10x

3.3 = x

If we wanted a score of 98, we would need to study for 3.3 hours.

Since question is incomplete, I will try my best to complete it my way:

It is given that 2 cups of blue with 10 cups of yellow make up green.

Question asks how many cups of yellow would i need to mix with 1 cup of blue to make same shade of green.

So,

2 cup with 10 cup

We divide each by 2, to get:

2/2 = 1

10/2 = 5

This means:

1 cup with 5 cup

Or,

1 cup blue with 5 cup yellow.

So, we arrive at our answer:

with 1 cup of blue, we need to fix 5 cups of yellow to get same shade of green.

Drawing the diagram of option D we have

Which means that 5/6 and 10/12 are equivalent fractions.

We have the next given information:

-18.5% is the percentage of methyl alcohol

- The bottle contains 1.43 L

Now, we need to convert the percentage into a decimal.

Then 18.5% = 0.185

We need to determinate the volume in millimeters for methyl alcohol:

If 143L of solution contains 18.5% of methyl alcohol. Therefore:

The volume of methyl alcohol = 1.43 * 0.185

= 0.26455 L

Then, we need to convert Liters to milliliters:

1L ---------------------------- 1000ml

0.26455 L ------------------ x

Where x = (0.26455 L*1000ml)/1L

x =264.55ml

Answer:

A

Step-by-step explanation:

45/2