The sine ratio of an angle is the opposite side over the adjacent side.

always
never
sometimes

Answer:

Part 1)  [tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]

Part 2)  [tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

Part 1)

in this problem we have

[tex]x^{2} -2x-2=0[/tex]

so

[tex]a=1\\b=-2\\c=-2[/tex]

substitute in the formula

[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}\\\\x=\frac{2(+/-)\sqrt{12}} {2}\\\\x=\frac{2(+/-)2\sqrt{3}} {2}\\\\x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}\\\\x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}[/tex]

therefore

[tex]x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))[/tex]

[tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]

Part 2)

in this problem we have

[tex]x^{2} -6x+4=0[/tex]

so

[tex]a=1\\b=-6\\c=4[/tex]

substitute in the formula

[tex]x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(4)}} {2(1)}[/tex]

[tex]x=\frac{6(+/-)\sqrt{20}} {2}[/tex]

[tex]x=\frac{6(+/-)2\sqrt{5}} {2}[/tex]

[tex]x_1=\frac{6(+)2\sqrt{5}}{2}=3+\sqrt{5}[/tex]

[tex]x_2=\frac{6(-)2\sqrt{5}}{2}=3-\sqrt{5}[/tex]

therefore

[tex]x^{2} -6x+4=(x-(3+\sqrt{5}))(x-(3-\sqrt{5}))[/tex]

[tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]

Answer:

B 122

Step-by-step explanation:

just thinking ur her

There are about 1866 seats left to fill before the game.

Step-by-step explanation:

Number of people hold be basketball arena = 7000

Tickets bought by fans = 5134

Seats left to fill = Total capacity of arena - tickets bought by fans

Seats left to fill = [tex]7000-5134[/tex]

Seats left to fill = 1866

There are about 1866 seats left to fill before the game.

Keywords: subtraction

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Answer:

Step-by-step explanation:

The general form of an equation of a line:

Ax + By + C = 0

We have

y = -3              add 3 to both sides

y + 3 = -3 + 3

y + 3 = 0

where A = 0, B = 1, C = 3

Answer:

Rob is 76 cm tall.

Step-by-step explanation:

Let b = height of bill.

Let m = height of Mary.

Let r = height of Rob.

"the total heigh of bill mary and rob is 180 cm"

b + m + r = 180         Equation 1

"bob* is twice as tall as bill"

*I think you meant Rob is twice as tall as Bill.

r = 2b

"mary is 28 cm taller than bill"

m = b + 28

Substitue r = 2b and m = b + 28 into Equation 1.

b + b + 28 + 2b = 180

4b + 28 = 180

4b = 152

b = 38

r = 2b

r = 2(38) = 76

Rob is 76 cm tall.

Rob height is 76cm.

Given that,

According to the given data, computation of the data are as follows,

Let Bill height be X, then Rob height is 2X and Mary height is X + 28.

So, X + 2X + X + 28 = 180cm

4X = 180 - 28

X = 152 [tex]\div[/tex] 4

X = 38

Hence, Bill height = X = 38cm

Rob height = 2X = 76cm

Mary height = X + 28 = 66cm

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Answer:

The average number of tornado's in December is 22 and the average number of tornado's in June is 226

Step-by-step explanation:

The complete question is

The average number of tornado's in June is 16 less than 11 times the average number of tornado's in December. If the difference between the average number of tornado's in June and December is 204,determine the average number of tornado's in December and June.

Let

x ----> the average number of tornado's in June

y ----> the average number of tornado's in December

we know that

[tex]x=11y-16[/tex] ---> equation A

[tex]x-y=204[/tex] ----> equation B

solve the system by substitution

substitute equation A in equation B

[tex]11y-16-y=204[/tex]

solve for y

[tex]10y=204+16[/tex]

[tex]10y=220[/tex]

[tex]y=22[/tex]

Find the value of x

[tex]x=11y-16[/tex] ----> [tex]x=11(22)-16=226[/tex]

therefore

The average number of tornado's in December is 22 and the average number of tornado's in June is 226

Answer:

100 meters in 1 minute

Step-by-step explanation:

500/5=100

To find the unit rate of a question, divide.

500 / 5 = 100

100 meters per minute.

______

Best Regards,

Wolfyy :)

Answer:

0.

Step-by-step explanation:

If you take these two equations to a graphing calculator, you'll find that they are parallel. I. E. they don't intercept.

A solution to a system of equations is when they intercept, so if they don't intercept, that means no solution.

Answer: No solution

Step-by-step explanation:

LCM is 3 (x + 1)(x - 5)(x + 2)

Step-by-step explanation:

Given polynomials are:

x2 - 4x – 5 and x2 – 3x – 10.

Factorizing x^2-4x-5

[tex]x^2-4x-5\\= x^2-5x+x-5\\=x(x-5)+1(x-5)\\=(x+1)(x-5)[/tex]

Factorizing  x^2 – 3x – 10

[tex]x^2 -3x -10\\=x^2-5x+2x-10\\=x(x-5)+2(x-5)\\=(x+2)(x-5)[/tex]

Looking at the fators of both polynomials we can see:

The LCM will be the combination of all factors of polynomials. The factor that occurs in both factorization will be written only once

Hence,

LCM is 3 (x + 1)(x - 5)(x + 2)

Keywords: Polynomials, LCM

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Answer:

95 nickels 19 dimes

Step-by-step explanation:

d=dimes

5d=nickels

0.05(5d) + 0.10(d) = 6.65

0.25d + 0.10d = 6.65

0.35d=6.65

Divide by 0.35

d= 19 (19 coins)

19 dimes =$1.9

6.65-1.9= $4.75

Nickels=$4.75

4.75/0.05 = 95 coins

19*5=95

  114 coins in total

19*0.10 = 1.9

95*0.05=4.74

4.75+1.9= 6.65

Answer:

There are 19 dimes and 95 nickels

Step-by-step explanation:

Represent the numbers of nickels and dimes by n and d.  Then n = 5d.

The value of the nickels is $0.05n and that of the dimes is $0.10d.  Together these two amounts come to $6.65:

$0.05n + $0.10d = $6.65.

But n = 5d.

Substituting 5d for n, we get:

$0.05(5d) + $0.10d = $6.65

Combining the two terms on the left, we get:

0.25d + 0.10d = 6.65, or

0.35d = 6.65.

Solving for d, we get d = 6.65/0.35, or d = 19.  Since n = 5d, n = 5(19) = 95.

There are 19 dimes and 95 nickels.

Answer:

B. y - 35 = 2(x - 10)

Step-by-step explanation:

The height of the plant, y, after x days could be modeled by the equation

Answer:

the answer is B

Step-by-step explanation:

Using the Pythagorean theorem:

L = √(15^2 - 9^2)

L = √(225 - 81)

L = √144

L = 12

The answer is 12'

Answer:0.0009

Step-by-step explanation:

Answer:

1/6+−2/9=−1/18

Step-by-step explanation:

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(16×33)+(−29×22)=?

Complete the multiplication and the equation becomes

318+−418=?

The two fractions now have like denominators so you can add the numerators.

Then:

3+−418=−118

This fraction cannot be reduced.

Therefore:

16+−29=−118

Answer:

Spending will be more than $59 billion more than 4 years after 2000.

Step-by-step explanation:

Given:

[tex]y=11.3x + 13.8[/tex]

x is the number of years.

Business spending is $59 billion.

Hence we can say that y = $59.

Now Substituting the value of y in above equation we will find the value of x in number of years.

[tex]11.3x+13.8=59\\11.3x=59-13.8\\ 11.3x= 45.2\\\\x=\frac{45.2}{11.3} = 4 years.[/tex]

Hence we can say that,

After 4 years after 2000 the spending will be more than $59 billion.

or

Spending will be more than $59 billion more than 4 years after 2000.

The equation demonstrates that the spending will exceed $59 billion more than 4 years after 2000.

To solve the problem, we first need to set the equation y = 11.3x + 13.8 to greater than 59, as we are trying to find out when the spending will be more than $59 billion. The equation will therefore be, 11.3x + 13.8 > 59.

Then, we subtract 13.8 from both sides of the equation to isolate the term with x, resulting in 11.3x > 45.2.

Finally, we divide each side by 11.3 to solve for x, which will give us x > 4. Consequently, the spending will be more than $59 billion more than 4 years after 2000.

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Answer:

s=-4.1

Step-by-step explanation:

you just need to divide by -5 of each item

so we have -5s/-5=21.5/-5

s=-4.1

Answer:

6(3 + v)

Step-by-step explanation:

Given

18 + 6v ← factor out 6 from each term

= 6(3 + v) ← in factored form

Answer:

Step-by-step explanation:

The Waist to Hip Ratio (WHR) is a ratio commonly expressed as a decimal that has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Jonia has a WHR greater than 1, she is at “high risk” for cardiovascular problems.

Answer:

£120:£30

Step-by-step explanation:

A ratio of 4:1 is also a ratio of 4x:x, as long as x is not equal to 0.

4x + x = 150

5x = 150

x = 30

4x = 4(30) = 120

4:1 = 120:30

Answer: £120:£30

Answer:

1 2/3

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact Form:

5/3

Decimal Form:

1.6

Mixed Number Form:

1 2/3

Answer:

-4 1/3 divided by -2 3/5 equals 5/3

Answer:

Step-by-step explanation:

47x+12y

Answer:

7/15 de la tablilla de chocolate le va a quedar.

Step-by-step explanation:

2/3 se converte en 10/15

y 1/5 se converte en 3/15

Entonces le va a quedar 10/15-3/15 = 7/15 de la tablilla de chocolate.

Answer:

2/3 - 1/5 = 7/15

Step-by-step explanation:

tienes que obtener denominadores iguales para restar las fracciones para obtener una respuesta. El denominador que tiene 3 y 5 igual es 15. así que tienes que multiplicar 3 por 5 y 5 por 3 y todo lo que hagas abajo deberías hacerlo al number de arriba.

Answer:

SAS Theorem

Step-by-step explanation:

It would be the SAS theorem because you know 2 sides that have an angle in common on both triangles.

Answer:

m∠ADC=55°

Step-by-step explanation:

step 1

Find the value of x

we know that

m∠CDE+m∠EDF=180° ----> by supplementary angles (form a linear pair)

substitute the given values

[tex](2x+1)\°+(x-7)\°=180\°[/tex]

solve for x

[tex]2x+x=180+6[/tex]

[tex]3x=186[/tex]

[tex]x=62[/tex]

step 2

Find the measure of angle ∠ADC

we know that

m∠ADC=m∠EDF ----> by vertical angles

m∠EDF=(x-7)°

substitute the value of x

m∠EDF=(62-7)°=55°

therefore

m∠ADC=55°

Answer:

C. because you would multiply each of the 6 cars by the amount of people it can hold which is 6

Answer:

Option B) minimum value at −10

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -10x+15[/tex]

This function represent a vertical parabola open upward (because the leading coefficient is positive)

The vertex represent a minimum

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)-15=x^{2} -10x[/tex]

Divide the coefficient of term x by 2

10/2=5

squared the term and add to the right side of equation

[tex]f(x)-15=(x^{2} -10x+5^2)[/tex]

Remember to balance the equation by adding the same constants to the other side

[tex]f(x)-15+5^2=(x^{2} -10x+5^2)[/tex]

[tex]f(x)+10=(x^{2} -10x+25)[/tex]

rewrite as perfect squares

[tex]f(x)+10=(x-5)^{2}[/tex]

[tex]f(x)=(x-5)^{2}-10[/tex] ----> function in vertex form

The vertex of the quadratic function is the point (5,-10)

therefore

The minimum value of the function is -10

Answer:

12   girls   18 boys Total 30 students

Step-by-step explanation

x=number of girls

18/3 = x/2

3x=18*2

3x=36

x=12

  Other proof

x= number of groups

3x +2x = 30

5x=30

x=6

3*(6) + 2*(6) = 30

18+12=30

Answer:

-116

Step-by-step explanation:

Answer:

-116

Step-by-step explanation:

2^-2=1/2^2=1/4

5^3=5*5*5=125

12*3=36

-------------------------

1/4(36)-125

9-125=-116

Answer:

A. y=3/2x

B. y=3/2x

C. 18

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

You just multiply 16 by 4.

There are 16 ounces in one pound.

So, 64 ounces in 4 pounds.

The correct option is E.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

There are 16 ounces in one pound.

In 4 pounds,

= 16 x 4 ounces.

= 64 ounces.

Therefore, 64 ounces in 4 pounds.

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