Find the six trigonometric functions of theta. Be sure to simplify any radicals and rationalize denominators if needed.

y = 0.6x + 3

To determine the equation of the line, we need to determine the slope and the y-intercept. Then, we will substitute the slope and the y-intercept in the slope intercept form equation to obtain the equation in slope intercept form.

Two points that lie on line: (0, 3) and (-5, 0)

[tex]\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

[tex]\implies \text{Slope} = \dfrac{3 - 0 }{0- (-5)}\\[/tex]

[tex]\implies \text{Slope} = \dfrac{3 }{0+5}\\[/tex]

[tex]\implies \text{Slope} = \dfrac{3 }{5} = 0.6[/tex]

[tex]\implies \text{Intersection of line on y-axis: 3}[/tex]

[tex]\implies \text{y-intercept: 3}[/tex]

Slope intercept form:

[Where "m" is the slope and "b" is the y-intercept]

Substitute the slope (m) and the y-intercept (b) in the formula;

[tex]\implies \text{Slope intercept form: y = (m)x + (b)}[/tex]

[tex]\implies \text{Equation of line in slope intercept form: y = (0.6)x + (3)}[/tex]

Open the parenthesis in the equation;

[tex]\implies\text{Equation of line in slope intercept form: \boxed{\text{y = 0.6x + 3}}}[/tex]

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Answer: Explicit Rule: a_n=30,000 • 2^n-1

Recursive Rule: a_n = 2a_n-1; a_1 = 30,000

Step-by-step explanation: the explicit rule for a geometric sequence is a_n = a_1 • r^n-1 and the recursive rule is a_n= r • a_n -1.
a_1 is the first term of the sequence, which is this case is 30,000. R is the common ration, which is 2 since it doubles each time. Substitute those numbers into the formulas and that’s what you’ll get. Hope this helps. God bless you!!!

Answer:

88

Step-by-step explanation:

Answer:

8(4+7)

Step-by-step explanation:

The GCF of 32 and 56 is 8. Then you divide by 8.

Answer:

f(x) = -(x + 8)(x -14)

= -(x2 - 112 - 6x)

= -x2 + 6x + 112 --- (1)

We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.

The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation

a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is

x = -b/2a

= -(6)/[2(-1)]

= 3

Substituting the value of x = 3 in equation (1) we get,

Now y = -(3)2 + 6(3) + 112

= -9 + 18 + 112 = 121

So the vertex point coordinates are (3, 121) and the y value is 121.

The graph below verifies the vertex point.

vertex of the graph

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?

Summary:

The y-value of the vertex of the function f(x) = -(x +

Answer:

Step-by-step explanation:

D or 121  got it right on edgenuty

If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.

The law of cosines can be used to determine the measures of the triangle if the angles are known. The law is given by:

a² = b² + c² - 2bc*cosA

a,b,c are the sides and A, B, C are the angles.

The law of sines are used to determine the measures of the triangle if the angles are known. The law is given by:

a/sinA = b/sinB = c/sinC

If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.

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The equation of curve of best fit is y = -30.17x + 14.49. To find the curve of best fit, we would require two equations which are explained in details below.

Data;

The equation of straight line is y = ax + b

If we modify it to fit into this problem,

[tex]\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)[/tex]

Let's substitute the values into the equations and solve

[tex]\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)\\50.9 = 6*a + b*16 ...equ(i)\\24.6 = a*16 + b*35 ...equ(ii)\\50.9 = 6a + 16b ...equ(i)\\24.6 = 16a + 35b ...equ(ii)[/tex]

Let's solve both equation (i) and equation (ii)

[tex]50.9 = 6a + 16b...equ(i)\\24.6 = 16a + 35b ...equ(ii)\\a = -30.17, b = 14.49[/tex]

We can substitute the values of a and b into the equation

[tex]y = ax + b\\y = -30.17x + 14.49[/tex]

The equation of curve of best fit is y = -30.17x + 14.49

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Answer:

-24, -21, -19, -19, -19, -14, -13, -12, -7, -3, 2, 5, 6, 11, 11, 15

Step-by-step explanation:

Hey there!

To put the numbers in least to greatest form, you need to put the biggest numbers with a - sign in front of it

This means negative

Negative means below zero

Then after putting the big negative numbers, you put positive numbers going from smallest to largest

So the numbers in least to greatest is -24, -21, -19, -19, -19, -14, -13, -12, -7, -3, 2, 5, 6, 11, 11, 15

Answer:

X = 7.8

Step-by-step explanation:

First I will mark all the Information given to us:

Angle 1: 52 Degrees

Angle 2: 90 (Marked by the box) Degrees

Angle 3: 180-(90+52) Triangle Angle Sum Therom

Simplified Angle 3: 38 Degrees

Height: 10

Base: X
Hypo: ? (we will call this y)

In order to solve this problem we must use basic trig functions such as sin, cos and tan.

I will be applying sin for the degree measure of 52 as it is applicable there.

(Sin for refrence sin(angle measure)= side opposite to angle/hypo)

So this would be in our case:

Sin(52)=10/y

Simplify

y sin(52) = 10

y = 10/sin(52) (use a calculator make sure sin is in degrees not radians)

y=10/0.78801

y=12.69018 (We have our hypo value)

We can now apply a²+b²=c²

a²+10²=12.69018²

a²+100=161.040668432 (Calculator)

a²=61.040668432

a=√61.040668432 (calculator)

a=7.81285277168

Rounded to the nearest tenth

7.8 =a=x (X is the a value in this equation)

Answer:

C = 12.57 inches

Step-by-step explanation:

C=2πr

C=πd=π·4≈12.56637in

Using the scale factor, the volume of the larger similar shaped box is 497.6in³.

A scale factor is simply the ratio of the corresponding sides of two similar objects. A scale factor of 4 simply means that the new shape is multiply four times the size of the original shape.

Given the data in the question;

Since scale factor of 4 means that the new shape is multiply four times the size of the original shape.

Volume of the larger box V = V° × SF

V = 124.4in³ × 4

V = 497.6in³

Therefore, using the scale factor, the volume of the larger similar shaped box is 497.6in³.

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Answer:

575 mph

Step-by-step explanation:

The plane is traveling at 575 mph.

1725/3

575

Answer:

Borrowings = $0.10 Billion

Owner's Equity = $0.40 Billion

Step-by-step explanation:

Total liabilities = deposits + borrowings

Borrowings = total liabilities - deposits

Borrowings in 2017 = $14.60 - 11.90 = $2.70 billion

Borrowings in 2018 = $14.80 - $12.20 = $2.60 billion

Borrowings from 2017-2018= 2.60 - 2.70 = $0.10 billion

Owner's Equity= total assets - total liabilities

Owner’s equity in 2017 = $16.2 - $14.6 = $1.6 billion

Owner’s equity in 2018 = $16.8 - $14.8 = $2 billion

Owner's Equity from 2017-2018= 2 - 1.6 = $0.4 billion

Hope this helps!

The Owner's Equity for commercial banks in  2017-2018 is $0.4 billion.

The given is,

Borrowings = $0.10 Billion

Owner's Equity = $0.40 Billion

Total liabilities = deposits + borrowings

So we have Borrowings = total liabilities - deposits

Borrowings in 2017

= $14.60 - 11.90

= $2.70 billion

Borrowings in 2018

= $14.80 - $12.20

= $2.60 billion

Borrowings from 2017-2018

= 2.60 - 2.70

= $0.10 billion

Owner's Equity= total assets - total liabilities

Owner’s equity in 2017

= $16.2 - $14.6

= $1.6 billion

Owner’s equity in 2018

= $16.8 - $14.8

= $2 billion

Owner's Equity from 2017-2018

= 2 - 1.6

= $0.4 billion

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The series of questions is based on the entire concept of chemical equations. This is shown by balanced reaction equations.

A reaction equation shows the reactants and the products in a reaction. We shall now answer the questions individually;

1) The reactants in this equation are CaO and CO2. The product is CaCO3.

2) The simplest molecule that is formed between carbon and hydrogen is CH4 with the structure shown in the image attached.

3) The balanced equations are;

a) Na3PO4 + 3HCl -----> H3PO4 + 3NaCl

b) 2KClO3 → 2KCl  + 3O2

4)

a. 2NaBr + Ca  ----->CaBr2 + 2Na

b. 2Mg + O2  ------->2MgO

5) 3H2SO4 + 2Al -------> Al2(SO4)3 + 3H2

6) CH4 + 202 ---->CO2 + 2H2O

7)

a. molar mass of sucrose = 12(12) + 22(1) + 11(16) = 144 + 22 + 176 = 342 g/mol

b. molar mass of glucose = 6(12) + 12(1) + 6(16) = 72 + 12 + 96 = 180 g/mol

c. There are 6 * 10^23 molecules 1 mole of sucrose

d.  There are 6 * 10^23 atoms 1 mole of sucrose

8) The equation of the reaction is; NaHCO3 + HC2H3O2 → NaC2H3O2 + H2O + CO2

Number of moles of baking soda= 42.00 g/84 g/mol = 0.5 moles

Since  the reaction is 1:1, 0.5 moles of CO2 is formed.

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Answer:

health class

Step-by-step explanation:

when the mean absolute deviation (M.A.D) is lower, that means the data is closer together. When it is higher that means the data is more spread out.

Answer:

its health

Step-by-step explanation:

i took the k12 test and got it wrong and it showed this one was correct

Answer:

no. so the first answer I got was 4.12 and the other 16

Step-by-step explanation:

4×(1+3%)

3%=0.03

0.03+1= 1.03

1.03*4= 4.12

4*(1+3)

1+3=4

4*4=16

I hope that helps you

The equation represents the cost (in dollars) and shipping a package that weighs x pounds is y = 2(x - 1) + 6.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound.

Let x be the number of pounds and y be the total cost, then we have

y = 2(x - 1) + 6

This is the required equation that describes the condition.

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Answer:

Its A on edge, f(x)=6+2[x-1]

Step-by-step explanation:

, where x > 0

Answer

y = x + 2

hope this helped

lol

Answer:

X = 3

Step-by-step explanation:

(4x-6)+(4x-6)+12+12=36

Answer:

6

Step-by-step explanation:

pemdas=parenthesis, exponents, multiplication, division, addition, subtraction. with this, we multiply 2 x the absolute value of -3, which is just 3. therefore, 6. now we see we need to subtract the absolute value of 6 from the absolute value of 8, which gives us 2. and 2+4 is 6.

Answer: 6

Step-by-step explanation:

8-2 x 3+4

2x3=6

8-6+4

2+4

=6

hope this helps

Answer:

A

Step-by-step explanation:

To show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have two circles:

Circle A has a center of (2, 3) and a radius of 5

Circle B has a center of (1, 4) and a radius of 10

The standard circle's equation can be written as:

(x - h)² + (y - k)² = r²

The equation for circle A:

(x - 2)² + (y - 3)² = 5²

The equation for circle B:

(x - 1)² + (y - 4)² = 10²

To show that circle A is similar to circle B:

It is required to perform the geometric transformation:

Dilate circle A by a scale factor of 2.

The radius of circle A is 5 units and after dilation by a scale factor of 2, the radius of the circle becomes 10 which is the radius of circle B.

Thus, to show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.

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#SPJ5

Answer:

[tex](xy)^{7}[/tex]

 ↓

[tex]x^{7} y^{7}[/tex]

So the answer is [tex]x^{7} y^{7}[/tex].

The months where the difference in salinity of surface and bottom waters was the greatest was in April and September.

It should be noted that salinity simply means the accumulation of salt in land as well as water.

In this case, the months where the difference in salinity of surface and bottom waters was the greatest was in April and September.

This is because many events take place such as continuous flowing or river water into the sea, evaporation, and melting of ice.

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The annual yield on Frances’s stock approximately will be 0.0758. Then the correct option is A.

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

Frances bought 144 shares of Dwyn horticulture for $7.73 apiece. her broker charged her a commission of $46.15 for the purchase.

Then the total amount spent by the company will be

→ 144 × $7.73 + $46.15 = $ 1159.27

If the yearly dividend on Dwyn horticulture is 61 cents per share, then the annual yield on Frances’s stock will be

[tex]\Rightarrow \dfrac{0.61 \times 144}{11592.27} \\\\\Rightarrow 0.07577[/tex]

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By the definition of the polynomials, the expression  [tex]3.9x^3 - 4.1x^2 + 7.3[/tex] is the only polynomials.

Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

a. [tex]\pi x -\sqrt{3} +5y[/tex]

This expression consists of 2 variables so this is not a polynomial.

b. [tex]x^{2} y^{2} -4xy^{3} +12y[/tex]

This expression consists of 2 variables so this is not a polynomial.

c. [tex]\frac{4}{x} -4x^{2}[/tex]

Here variable x is in the denominator in term 4/x so this is not a polynomial.

d. [tex]3.9x^3 - 4.1x^2 + 7.3[/tex]

This expression satisfies all conditions of being a polynomial hence this is a polynomial.

e. [tex]\sqrt{x} -16[/tex]

Here the power of variable x is not an integer so it's not a polynomial.

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Answer:

A B E

Step-by-step explanation:

cuz i know

Answer:

y = 150x

Step-by-step explanation:

If y = savings and they save $150 each month then you can just multiply $150 by each month to get the total savings

Answer:

[tex]\huge\boxed{\bf\: \frac{93}{20}=4.65}[/tex]

Step-by-step explanation:

[tex]3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }[/tex]

Now,

[tex]3 \frac { 1 } { 4 } \\= \frac{4 * 3+1}{4}\\= \frac{13}{4}[/tex]

Then,

[tex]1 \frac { 2 } { 5 }\\= \frac{1* 5+2}{5} \\= \frac{7}{5}[/tex]

So,

[tex]3 \frac { 1 } { 4 } + 1 \frac { 2 } { 5 }\\= \frac{13}{4}+\frac{7}{5}\\ \\\mathrm{LCM = 20}\\\\= \frac{65}{20}+\frac{28}{20} \\=\boxed{\bf\: \frac{93}{20}=4.65}[/tex]

[tex]\rule{150pt}{2pt}[/tex]