What is the value of sinY?

If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.

This situation can only occur if the two numbers have opposite signs. In other words, one number must be positive, and the other must be negative.

When we divide a positive number by a negative number or a negative number by a positive number, the resulting quotient will always be negative. So, to satisfy the given condition, the two numbers must have opposite signs—one positive and one negative.

Therefore, If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.

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Final answer:

For the quotient of two numbers to be negative, one of the numbers must be positive and the other must be negative. This principle follows the general rules for multiplication and division involving signed numbers.

Explanation:

For a quotient of two numbers to be negative, one number must be positive and the other negative. This rule aligns with the multiplication and division rules for signs, whereby the product or quotient of two numbers with opposite signs results in a negative outcome.

Essentially, this can be understood by considering examples of multiplication, such as (-3) x 2 = -6 and 4 x (-4) = -16, which similarly apply to division. The same principle holds when dividing two numbers; if their signs are opposite, the result is negative.

This mathematical rule is fundamental and applies universally across mathematics, ensuring consistency in the calculation and understanding of operations involving signed numbers.

Answer:

100

Step-by-step explanation:

100% of a number + 30% of a number is 130% of a number.

This means 130 = 1.3x.

Now we simplify:

130=1.3x

/1.3   /1.3

100=x

x=100

Therefore, the number is 100.

The unknown number is 100.

Given that, 30% of a number is added to the number, the result is 130.

The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of the whole is always taken as 100.

Let the unknown number be x.

30% of x+x=130

⇒0.3x+x=130

⇒1.3x=130

⇒x=100

Therefore, the unknown number is 100.

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Answer:

543.7

Step-by-step explanation:

.67 is closer to .7 than to .6

Answer:

543.7

Step-by-step explanation:

The 7 rounds up to a 6 in the tenth place.

Answer:

The ordered pair that is a solution to the equation  (5, 2)

Step-by-step explanation:

It is given that,

2x + 5y = 20

To find the ordered pairs

Multiples of 2 are,

2, 4, 6, 8, 10, 12....

Multiples of 5 are,

5, 10, 15, 20,...

20 can be written as,

20 = 2x + 5y

2x is the multiple of 2 and 5y is the multiple of 5

From the above data we get, 20 = 10 + 10

2x = 10 then x = 5

5y = 10 then y = 2

Therefore  the ordered pair that is a solution to the equation  (5, 2)

Final answer:

To determine if an ordered pair is a solution to the equation 2x + 5y = 20, substitute the values into the equation and check if the simplified result equals 20.

Explanation:

To find an ordered pair that is a solution to the equation 2x + 5y = 20, we need to check which pair (x, y) satisfies the equation when we substitute the values of x and y into it. This involves basic algebraic skills, including substitution and simplification.

Step-by-Step Explanation

If the left side of the equation equals the right side after substitution, then the ordered pair is a solution to the equation. For example, if we substitute x = 2 and y = 4, we get 2(2) + 5(4) = 20 which simplifies to 4 + 20 = 24, not equal to 20. Thus, (2,4) is not a solution. Find an ordered pair where, after the substitution and simplification, the equation is satisfied.

Answer:

x=30

Step-by-step explanation:

The two angles form a straight line

4x+2x = 180

6x= 180

Divide each side by 6

6x/6 = 180/6

x = 30

Answer:

X=30

Step-by-step explanation:

the degree of a straight line is 180

Add 2x and 4x together = 6x

Then divide 6x = 180 by 6 to get the x value.

The answer is 30

Answer with explanation:

 [tex]\rightarrow \frac{\frac{2y^2-6 y-20}{4 y+12}}{\frac{y^2+5 y+6}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{y^2-3y-10}{2 y+6}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{\frac{(y-5)(y+2)}{2 (y+3)}}{\frac{(y+2)(y+3)}{3 y^2+28 y+27}}\\\\\rightarrow \frac{(y-5)(y+2)}{2 (y+3)}} \times {\frac{3 y^2+28 y+27}{(y+2)(y+3)}}\\\\ \rightarrow\frac{(y-5)\times(3 y^2+28 y+27)}{2 (y+3)^2}}[/tex]

→y²+5y+6

=y²+3 y+2 y+6

=y×(y+3)+2×(y+3)

=(y+2)(y+3)

→y² -3 y-10

=y² -5 y+2 y -10

=y×(y-5)+2×(y-5)

=(y+2)(y-5)

Answer:

B. 3(y-5)/2 on edge

Step-by-step explanation:

[tex]\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{y}{xy}+\dfrac{x}{xy}=\dfrac{x+y}{xy}=\dfrac{12}{-5}=-\dfrac{12}{5}=-2,4[/tex]

Answer:

fast bike speed = 41/3= 17mph

slower bike speed = 37/3 =12.33 mph

Final answer:

The slower biker's speed is 12 mph and the faster biker's speed is 14 mph, determined by setting up an equation with their combined distances equating to 78 miles after 3 hours.

Explanation:

To resolve the puzzle of the two bikers departing from the same location and traveling in opposite directions, we can apply concepts of rate, time, and distance. We are given that the two bikers are 78 miles apart after 3 hours and that one biker is traveling at a speed that is 2 mph faster than the other.

Let's denote the speed of the slower biker as $x$ mph. Consequently, the speed of the faster biker would be $x + 2$ mph. Considering that they have been traveling for 3 hours, the slower biker would have covered 3$x$ miles and the faster biker 3($x + 2$) miles. The sum of these distances is the total distance between the bikers after 3 hours, which is 78 miles.

Mathematically, we can represent the situation as:

3$x$ + 3($x + 2$) = 78

Simplifying the equation:

3$x$ + 3$x$ + 6 = 78

6$x$ + 6 = 78

6$x$ = 72

$x$ = 12

Thus, the slower biker's speed is 12 mph and the faster biker's speed is 12 mph + 2 mph = 14 mph.

Answer: The faster biker travels at 14 mph and the slower biker travels at 12 mph

Answer:

[tex]\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }[/tex]

To solve this quotient, we just have to apply a rationalization, which consists in eliminating every root in the denominator. To do so, we multiply and divide the expression by the opposite binomial of the denominator, as follows

[tex]\frac{\sqrt{6}+\sqrt{11}}{\sqrt{5}+\sqrt{3} }=\frac{\sqrt{5}-\sqrt{3} }{\sqrt{5}-\sqrt{3} }\\\\\frac{(\sqrt{6}+\sqrt{11})(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}\\\\\frac{\sqrt{30}-\sqrt{18}+\sqrt{55}-\sqrt{33} }{5-3}\\ \\\frac{\sqrt{30}-3\sqrt{2}+\sqrt{55}-\sqrt{33} }{2}[/tex]

Therefore, the right answer is the second option.

Answer:

Option C is correct.

Step-by-step explanation:

We are given the expression:

[tex](\frac{3^2a^{-2}}{3a^{-1}})^k[/tex]

The value of a =5 and k = -2

Putting the values and solving

[tex]=(\frac{3^2*5^{-2}}{3*5^{-1}})^-2\\=(\frac{3^{2-1}}{5^{-1+2}})^-2\\=(\frac{3^{1}}{5^{1}})^-2\\\\=(\frac{3}{5})^-2\\if \,\,a^{-1} \,\,then\,\, 1/a\\=\frac{(3)^{-2}}{(5)^{-2}}\\ Can\,\,be\,\,written\,\,as\\\\=\frac{(5)^{2}}{(3)^{2}} \\=\frac{25}{9}[/tex]

Option C is correct.

Answer: [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

We need to remember that equivalent fractions are  defined as fractions whose numerators and denominator are different but both fractions represent the same value.

To find an equivalent fraction, we must multiply the numerator and the denominator by the same number (Which must be a nonzero whole number).

In this case, to find a fraction equivalent to [tex]\frac{1.5}{9}[/tex],  with a whole number in both numerator and the denominator, we can multiply the numerator and the denominator by 2. Then you get:

[tex]\frac{1.5*2}{9*2}=\frac{3}{18}[/tex]

Reducing the fraction, you get:

[tex]=\frac{1}{6}[/tex]

the simplified whole number fraction equivalent is 1/6.

To find a fraction equivalent to 1.5 over 9 with a whole number in both the numerator and the denominator, first convert the decimal in the numerator to a fraction by expressing it as 1.5 or 15/10. Then, you can write the original fraction as (15/10)/9 which simplifies to 15/90 by multiplying the numerator and the denominator by 10. Finally, you simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 15 in this case. Thus, the simplified whole number fraction equivalent is 1/6.

[tex]\bf \cfrac{x-2}{x^2+4x-12}\implies \cfrac{\begin{matrix} x-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{(x+6)~~\begin{matrix} (x-2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies \cfrac{1}{x+6}\qquad \{x|x\in \mathbb{R};x\ne 2,x\ne -6\}[/tex]

Answer:

[tex]\boxed{\text{1172 in}^{2}}[/tex]

Step-by-step explanation:

SA = SA(prism) + SA(cylinder) – 2SA(cylinder base)

1. Surface area of rectangular prism

The formula for the surface area of a rectangular prism is

S = 2(lw + lh + wh)

Data:  

 l = 16 in

w = 11  in

h = 11  in

Calculations:

2(Top + Bottom) = 2lw  = 2 × 16 × 11 = 352 in²

 2(Front + Back) = 2lh   = 2 × 16 × 11 = 352 in²

   2(Left + Right) = 2wh = 2 × 11 × 11  = 242 in²

                                        Total area =  946 in²

2. Surface area of cylinder

A = A(top) + A (base) + A(side)  = 2A(base) + A(side)

Data:

d = 8 in

h = 9 in

Calculations:

r = ½d  = ½ × 8 = 4 in

[tex]\begin{array}{rcl}SA & = & 2\pi r^{2}+ 2\pi rh \\& = & 2 \times 3. 14\times 4^{2} +2\times 3. 14 \times 4\times 9\\& = & 6.28\times 16 + 226.08\\& = & 100.48 + 226.08\\& = & 326.56 \text{ in}^{2}\\\end{array}[/tex]

3. Excluded area

Excluded area = 2A(base) = 100.48 in²

4. Total area  

[tex]A = 946 + 326.56 - 100.48 \approx \boxed{\textbf{1172 in}^{2}}[/tex]

Answer:

there is no graph

Step-by-step explanation:

Answer:

{-6,4}

Step-by-step explanation:

Given

x-4y=-22      Eqn 1

x-y=-10         Eqn 2

Subtracting both equations:

The left hand side of equation 2 will be subtracted from left hand side of eqn 1 and the right side of equation 2 will be subtracted from right hand side of eqn 1.

[tex](x-4y)-(x-y)=-22-(-10)\\x-4y-x+y=-22+10\\-4y+y=-12\\-3y=-12\\\frac{-3y}{-3}=\frac{-12}{-3}\\ y=4[/tex]

Putting y=4 in eqn 2

[tex]x-4=-10\\x=-10+4\\x=-6\\So,\\Solution Set = \{-6,4\}[/tex]

Answer:

{x, y} = {-6, 4}

Step-by-step explanation:

It is given that,

x - 4y = -22    ------(1)

x -  y= -10   -------(2)

To ind the value of x and y

subtract eq(2) from eq(1)

x - 4y = -22    ------(1)

x -  y= -10   -------(2)

0  -3y = -12

3y = 12

y = 12/3 = 4

Substitute the value of y in eq (1)

x - 4y = -22    ------(1)

x - (4*4) = -22

x - 16 = -22

x = -22 +16 = -6

Therefore {x, y} = {-6, 4}

The answer is 9.5

You tube is awesome for explaining this

Answer:

Step-by-step explanation:

Write the explanation x-4

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Answer:

The answer in the procedure

Step-by-step explanation:

Let

x ----> the number of gigabytes used in a month

C(x)------> the monthly cost in dollars

step 1

For the interval ----> [0,2]

[tex]0\leq x\leq 2[/tex]

[tex]C(x)=15[/tex]

step 2

For the interval ---->(2,6]

[tex]2< x\leq 6[/tex]

Find the equation of the line

Find the slope

we have

[tex](2,20),(6,40)[/tex]

[tex]m=(40-20)/(6-2)=5[/tex]

The equation of the line in to point slope form is equal to

[tex]y-20=5(x-2)\\ y=5x-10+20\\ y=5x+10[/tex]

therefore

[tex]C(x)=5x+10[/tex]

step 3

For the interval ----> (6,∞]

[tex]x> 6[/tex]

[tex]C(x)=50[/tex]

Answer:

C(x)=[tex]15, 0\leq x\leq 2[/tex]

        [tex]5x+10, 2<x\leq 6[/tex]

          [tex]50, [/tex] 6<x≤∞

Step-by-step explanation:

C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month

Lets find C(x) on each interval (for every line graph)

first interval 0 to 2

the value of y is 15 on the interval 0 to 2

Its horizontal line . So equation is c(x)=the constant y value

[tex]C(x)= 15, 0\leq x\leq 2[/tex]

Second interval 2 to 6

Pick two points to get the equation of that line

(3,25) and (6,40)

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{40-25}{6-3} =5[/tex]

Equation of the line is using m=5 and (3,25)

[tex]y-y1=m(x-x1)[/tex]

[tex]y-25=5(x-3)[/tex]

[tex]y-25=5x-15[/tex]

[tex]y=5x+10[/tex]

[tex]C(x)= 5x+10, 2<x\leq 6[/tex]

Now we look at the third interval

6 to infinity

For the third graph , the value of y is 50 (constant)

It is a horizontal line

So [tex]C(x)= 50, [/tex] 6<x≤∞

We got three equations for C(x)

C(x) is a piecewise function

C(x)=[tex]15, 0\leq x\leq 2[/tex]

        [tex]5x+10, 2<x\leq 6[/tex]

          [tex]50, [/tex] 6<x≤∞

Answer:

Step-by-step explanation:

A isn't. You have that right. A sinusoidal wave is one that creates a sine curve.

Absolute value curves look sort of like a spear head.

Answer:

I would say the correct answer is 2^3 • 5 • 11

Step-by-step explanation:

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 440 by 2

440 ÷ 2 = 220 -  No remainder! 2 is one of the factors!

220 ÷ 2 = 110 -  No remainder! 2 is one of the factors!

110 ÷ 2 = 55 - No remainder! 2 is one of the factors!

55 ÷ 2 = 27.5 - There is a remainder. We can't divide by 2 even anymore. Let's try the next prime number

55 ÷ 3 = 18.3333 - This has a remainder. 3 is not a factor.

55 ÷ 5 = 11 - No remainder! 5 is one of the factors!

11 ÷ 5 = 2.2 -There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number

11 ÷ 7 = 1.5714 - This has a remainder. 7 is not a factor.

11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

If we put all of it together we have the factors 2 x 2 x 2 x 5 x 11 = 440. It can also be written in exponential form as 2^3 x 5^1 x 11^1.

here is also the factor tree method : -

Answer:

A.) 1/81

Step-by-step explanation:

This is your equation:

f(x) = 9^x

They want you to solve for x = -2, so substitute -2 in for x.

f(-2) = 9^-2

When you solve this, you get, 1/81.

So, the answer is A.)

I hope this helps! :)

Answer:

6cm

Step-by-step explanation:

[tex]A = \frac{h_b b}{2}[/tex]

[tex]38.4 = \frac{12.8_b b}{2}[/tex]

[tex]b = 2\frac{A}{h_b}[/tex]

[tex]b = 2\frac{38.4}{12.8}[/tex] = 6

The total space enclosed by the three boundaries of the triangle is called the area of the triangle.

The length of the base of the triangle is 6 cm.

A triangle has an area of 38.4 cm2.

The height of the triangle is 12.8 centimeters.

The total surface or space enclosed by the three boundaries of the triangle is called the area of the triangle.

The formula to calculate the area of the triangle is given by;

[tex]\rm Area \ of \ the \ rectangle = \dfrac{1}{2} \times Base \times Height\\\\[/tex]

Substitute all the values in the formula;

[tex]\rm Area \ of \ the \ triangle= \dfrac{1}{2} \times Base \times Height\\\\\rm 38.4 = \dfrac{1}{2} \times Base \times 12.8\\\\ Base = \dfrac{38.4 \times 2}{12.8}\\\\Base = 3 \times 2\\\\Base = 6 \ cm[/tex]

Hence, the length of the base of the triangle is 6 cm.

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Answer:

13 Cars Have Been Loaded, Equation: 12x + 6 = 162

Step-by-step explanation:

If a car holds 12 people, and there are 162 people waiting divide 162 by 12. This gives you 13.5,  which means that 13 total cars have been loaded, while .5 or 6 are left waiting on the line. So 13!

Answer:

162

Step-by-step explanation:

ADD EMMM UPPP GIRLLLLLGET IT TOGETHER

Answer:

14 yds

Step-by-step explanation:

To find the perimeter, we add up all the sides

P = s1 + s2+ s3 + s4

38 = 5.8+7+11.2 + s4

Combine like terms

38 = 24+s4

Subtract 24 from each side

38-24 = 24-24 +s4

14 = s4

The 4th side is 14 yds

Answer:

14yd

Step-by-step explanation:

Final answer:

A linear equation represents a straight line and is written in the form y = mx + b. A quadratic equation represents a parabolic curve and is written in the form y = ax² + bx + c.

Explanation:

A linear equation is an equation that represents a straight line when graphed. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope describes the rate of change between the independent and dependent variables, while the y-intercept is the point where the graph crosses the y-axis.

On the other hand, a quadratic equation is an equation that represents a parabolic curve when graphed. It is typically written in the form y = ax² + bx + c, where a, b, and c are constants. The graph of a quadratic equation is symmetric around a vertical line called the axis of symmetry, and it has either a maximum point or a minimum point.

Answer:

Domain of a geometric or arithmetic sequence is the counting numbers unless otherwise noted.

Answer: Set of Natural numbers.

Step-by-step explanation:

We know that the domain of a function is the set of all values for x for which the function must be defined.

The domain of the geometric sequence is always the set of natural numbers , since each term has a particular position in the sequence according to an order which can only represent by natural numbers.

Hence, the domain for the given geometric sequence = Set of natural numbers.

For this case, we can discard options B and C because they do not have coefficients. Also, we discard option D because it has 4 roots given by -4.1, -1,2 each with multiplicity "1".

The multiplicity indicates the number of times a root is repeated.

Then, we have that the correct option is option A, we have a coefficient of "3", in addition to three roots (-4,1,2) with multiplicity "1", because they only repeat once.

Answer:

Option A

Answer: A

Step-by-step explanation:

Answer:

negative angles are clockwise

Step-by-step explanation:

negative angel: An angle whose generating line is rotated clockwise.

hope this helps!!

Clockwise and counterclockwise are used to indicate the direction of an angle.

The terminal quadrant of -400 degrees is in the clockwise direction

The angle is given as:

[tex]\mathbf{\theta = -400^o}[/tex]

The condition for clockwise direction is: [tex]\mathbf{\theta < 0}[/tex]

While the condition for counterclockwise direction is:[tex]\mathbf{\theta > 0}[/tex]

By comparison:

[tex]\mathbf{-400 < 0}[/tex]

Hence, the terminal quadrant of -400 degrees is in a clockwise direction

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ANSWER

The correct answer is B.

EXPLANATION

If the point B(x,y) partitions

[tex]A(x_1,y_1)[/tex]

and

[tex]C(x_2,y_2)[/tex]

in the ratio m:n then, then we have

[tex]x = \frac{mx_2+nx_1}{m + n} [/tex]

and

[tex]y= \frac{my_2+ny_1}{m + n} [/tex]

We want to find the coordinates of the point B(x,y) that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.

This implies that:

[tex]x = \frac{5 \times 11+3 \times - 5}{5 + 3} [/tex]

[tex] \implies \: x = \frac{55 - 15}{8} [/tex]

[tex] \implies \: x = \frac{40}{8} = 5[/tex]

[tex]y = \frac{5 \times 0 + 3 \times 2}{5 + 3} [/tex]

[tex]y = \frac{0 + 6}{8} [/tex]

[tex]y = \frac{6}{8} = \frac{3}{4} [/tex]

Therefore the coordinates of B are

[tex](5, \frac{3}{4} )[/tex]

Answer:

B. (5,3/4)

Step-by-step explanation:

Since, when a segment having end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is divided by or partitioned by a point, that lies on the segment, in the ratio of m : n,

Then the coordinates of that points are,

[tex](\frac{mx_2+nx_1}{m+n}, \frac{my_2+my_1}{m+n})[/tex]

Here, point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3,

Thus, the coordinates of B are,

[tex](\frac{5\times 11+3\times -5}{5+3}, \frac{5\times 0+3\times 2}{5+3})[/tex]

[tex](\frac{55-15}{8}, \frac{0+6}{8})[/tex]

[tex](\frac{40}{8}, \frac{6}{8})[/tex]

[tex](5, \frac{3}{4})[/tex]

Option 'B' is correct.