You have a 3-gallon and a 5-gallon jug that you can fill from a fountain of water. The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?

Answer:

[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]

Step-by-step explanation:

Accorded to trigonometric formula, we know that:

[tex]\displaystyle \large{\cos \theta = \dfrac{x}{r}}\\\\\displaystyle \large{\csc \theta = \dfrac{1}{\sin \theta} = \dfrac{1}{\frac{y}{r}} = \dfrac{r}{y}}\\\\\displaystyle \large{\tan \theta = \dfrac{\sin \theta}{\cos \theta} = \dfrac{y}{x}}[/tex]

We know what x and y are but not yet knowing what r is. We can find r (radius) using the formula:

[tex]\displaystyle \large{r=\sqrt{x^2+y^2}}[/tex]

Input x = -3 and y = 5 in.

[tex]\displaystyle \large{r=\sqrt{(-3)^2+(5)^2}}\\\\\displaystyle \large{r=\sqrt{9+25}}\\\\\displaystyle \large{r=\sqrt{34}}[/tex]

Hence, radius is √34 and we know all we need now. Substitute x = -3, y = 5 and r = √34 in respective areas.

[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]

These are the answers to your question. Please let me know if you have any questions regarding my answer or explanation!

Answer:

5. m<STP = 134

6. m<PTS = 158

Step-by-step explanation:

5. Since ray TR bisects <PTS, angles PTR and STR are congruent.

m<PTR = m<STR

3x - 8 = 2x + 17

Subtract 2x from both sides.

x - 8 = 17

Add 8 to both sides.

x = 25

m<STP = 2m<PTR

m<STP = 2(3x - 8)

m<STP = 2(3 × 25 - 8)

m<STP = 2(67)

m<STP = 134

6.

2m<PTR = m<PTS

2(x - 23) = x + 56

2x - 46 = x + 56

x = 102

m<PTS = x + 56

m<PTS = 102 + 56

m<PTS = 158

Answer:

The slope would also be 2/7.

Step-by-step explanation:

The two lines are parallel, meaning that they follow the same slope. If line / has a slope of 2/7, then line M must have the same slope as well. I hope this helps! :)

Answer:

(x-9)(x-5)

Step-by-step explanation:

x²-5x-9x+45

x(x-5)-9(x-5)

(x-9)(x-5)

Answer:

(x-9)(x-5)

Step-by-step explanation:

To factor this expression, you need to find two values that have a sum of -14 and also have a product of 45. The values -5 and -9 meet these requirements and become the constants in the two factors of the expression,

x2 − 14x + 45 = (x − 9)(x − 5).

Answer:

5x + [tex]\frac{1}{8}[/tex]y = 3/8

Step-by-step explanation:

Add [tex]\frac{5x}{8}[/tex] to both sides

[tex]\frac{5x}{8}[/tex] + y = 3

Divide both sides by 8

5x +  [tex]\frac{1}{8}[/tex]y = 3/8

Step-by-step explanation:

standard form is given by Ax + By = C

hence,

the answer is:

5x + 8y = 24

Answer: <1 = 26°

Step-by-step explanation:

given that:

• <ABD = 66°

• <2 = 14° + <1 (since ''more than' means we add)

• Find <1

Since it is obvious that <ABD is a sum of <1 and <2:

⇒ <ABD = <1 + <2

now we know that <2 is 14° more than <1 and that <ABD = 66°

⇒ 66° = <1 + (14° + <1)

⇒ 66° = <1 + 14° + <1

⇒ <1 = (66° - 14°) ÷ 2

⇒ <1 = 26° ...Answer...

hope that helps...

Answer:

y = x + 1

Step-by-step explanation:

Step 1: Find the slope.

Parallel lines have the same slope. That means that the line we are seeking is going to have the same slope as line x - y = 7.

To find the slope of the line x - y = 7 let's change it to the slope-intercept form.

Slope-Intercept Form

y = mx + b

m ... slope

b ... y-intercept

Let's change the equation of the parallel line to slope-intercept form (isolate y).

x - y = 7

Add y on both sides.

x - y + y = 7 + y

x = 7 + y

Subtract 7 on both sides.

x - 7 = 7 + y - 7

x - 7 = y

y = x - 7

Let's read the slope from the equation.

Instead of y = x - 7 we can write y = 1x -7.

Now it's obvious that m (slope) is 1.

m = 1

So far, our equation of the line is:

y = 1x + b

which is te same as

y = x + b

Step 2: Find y-intercept.

To find out y-intercept (b), we substitiute the point (-7, -6) in the equation. Points are in form (x, y) so -7 is x and -6 is y.

y = x + b

-6 = -7 + b

Solve for b.

1 = b

Step 3: Substitute slope and y-intercept in general formula for slope-intercept form of the line.

Now substitute m and b in slope-intercept form y = mx + b.

m = 1

b = 1

Equation of the line:

y = x + 1

Answer:B

Step-by-step explanation:

The amoeba splits 24 times, meaning that the number of amoebas will be

2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24

Answer:

yes

Step-by-step explanation:

2/3=6/9

2/3=2/3

it is because 6 and 9 is divided by 3

Answer:

4/8

Step-by-step explanation:

15 1/8 - 1/2(4/8) = 14 5/8

Answer:

2,4,8,11,22, or 44

Step-by-step explanation:

To figure out how many rings would be in each full row with no leftovers, we need to find all the factors of 88 (outside of 1 and 8) which are 2,4,8,11,22, and 44. Since the question does not give any more information on how big the rows need to be, I can't narrow this down any further, however if I had to choose I would say rows of 8 by 11 would be the best.

Hope this helps! :)

The total amount Sam will pay in all will be $2,400,000

From the question, we are to determine the interest Sam pays in all

Using the simple interest formula,

I = PRT

From the given information,

P = $2,000,000

R = 5% = 0.05

T = 4

Putting the parameters into the formula,

I = $2000000 × 0.05 × 4

I = $400000

The interest Sam will pay is $400,000

The total amount Sam will pay in all will be $2,000,000 + $400,000

= $2,400,000

Hence, the total amount Sam will pay in all will be $2,400,000

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Answer:

Step-by-step explanation:400000

Line segment AB is the same length as line segment CD.

A line segment is defined as the part of a line that is divided in parts using two or more end points for easy observation.

From the given diagram, the line segment AB is the same as the line segment CD because the line segment CD was shifted a bit from the point of origin of line segment AB.

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Answer:

69

Step-by-step explanation:

420

Answer:

The Median

Step-by-step explanation:

i did the quiz

Answer:

A. the median only

Step-by-step explanation:

Answer:

2000.

Step-by-step explanation:

The hundreds digit is 9 so we round up the 1 so the answer is 2000.

Completing the squares, the correct statements regarding the equation of the circle are given by:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem, the equation is given by:

x² + y² - 2x - 8 = 0.

Completing the squares:

(x - 1)² + y² = 8 + 1²

(x - 1)² + y² = 9.

Hence the center is (1,0), the radius is 3, and the correct statements are:

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Answer:

[tex]1\frac{1}{9}[/tex]

Step-by-step explanation:

Given the following question:

[tex]1\frac{2}{3} \times\frac{2}{3}[/tex]

In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.

[tex]1\frac{2}{3} =3\times1=3+2=\frac{5}{3}[/tex]
[tex]\frac{5}{3} \times\frac{2}{3}[/tex]
[tex]5\times2=10[/tex]
[tex]3\times3=9[/tex]
[tex]=\frac{10}{9}[/tex]

Convert the improper fraction into a mixed number:

[tex]\frac{10}{9}[/tex]
[tex]\frac{10}{9} =10\div9=1\frac{1}{9}[/tex]
[tex]=1\frac{1}{9}[/tex]

Your answer is "1 1/9."

Hope this helps.

Answer:

a 75% chance the weather will stay dry

Step-by-step explanation:

3/4

Step-by-step explanation:

the domain is the set or interval of all valid x values.

the range is the set or interval of all valid y values.

1.

domain = {-1, 2, 5}

range = {0, 2, 3, 7}

function : no, because x = -1 has 2 different y values assigned (7 and 2). that violates the definition of a function.

2.

domain = {-3, -2, -1, 1, 4}

range = {-5, -1, 0, 2}

function : yes. every x bake has exactly one y value assigned.

3.

domain = {4, 6, 7}

range = {-1, 2, 3, 5}

function : no, because x = 4 has 2 different y values assigned (2 and 5).

4.

domain = [-3, 3) "3" is not included, hence the empty dot

range = [-4, 5]

function : yes

5.

domain = (-infinity, +infinity) "infinity" is not a possible value, so the limits are not included.

range = [-1, 2]

function : yes

6.

domain = [-2, +infinity)

range = (-infinity, +infinity)

function : no. except for x = -2 all x values have 2 different y values assigned.

This  is an equilateral triangle, therefore, all the angles  are 60 degrees.

3 times  60 is  180.

180 is the answer

The value of sin⁻¹ (sin 17°) is 17° or 17 degree after applying the trigonometric identity sin⁻¹ (sinx) = x

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

= sin⁻¹ (sin 17°)

The above expression represents an angle.

Let's suppose the angle is x and sin of x is sinx

sinx is a ratio of side opposite to the angle to hypotenuse.

If we take sin inverse of sinx we get an angle of x.

sin⁻¹ (sinx) = x

sin⁻¹ (sin 17°) = 17 degree

Thus, the value of sin⁻¹ (sin 17°) is 17° or 17 degree after applying the trigonometric identity sin⁻¹ (sinx) = x

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Answer:

22.50

Step-by-step explanation:

25 percent 30

= (25/100)30

= (25*30)/100

= 750/100 = 7.50

$30 - $7.50 = $22.50

Answer:

x ≤ 1/2

Step-by-step explanation:

Domain:  input values (x-values)

We cannot take a square root of a negative number, therefore

3 - 6x ≥ 0

Solving the inequality:

⇒ 3 - 6x ≥ 0

⇒ 3 ≥ 6x

⇒ 1/2 ≥ x

⇒ x ≤ 1/2

Therefore, the domain is x ≤ 1/2

An equation is formed of two equal expressions. The equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation 7*e^0.1t=47 in terms of logarithm in terms of base-e can be solved as,

[tex]7e^{0.1t}=47\\\\e^{0.1t}=\dfrac{47}{7}\\\\0.1 t = {\rm ln}(\dfrac{47}{7})\\\\t = \dfrac{ {\rm ln}(\frac{47}{7})}{0.1}[/tex]

Hence, the equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.

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Answer:

angle A=30°

Step-by-step explanation:

[tex]9x + 6 + 4x + 6 + 90 = 180 \\ 13x + 102 = 180 \\ 13x = 180 - 102 \\ 13x = 78 \\ \frac{13x}{ 13} = \frac{ 78}{13} \\ x = 6 \\ 4x + 6 = a \\ 4(6) + 6 = a \\ 24 + 6 = a \\ 30 = a[/tex]