Consider the system of linear equations.

To use the linear combination method and addition to eliminate the x-terms, by which number should the first equation be multiplied?
–2
-1/2
1/2
2

Well,

Given that [tex]x=\sin(\theta)[/tex],

We can rewrite the equation like,

[tex]\dfrac{\sin(\theta)}{\sqrt{1-\sin(\theta)^2}}[/tex]

Now use, [tex]\cos(\theta)^2+\sin(\theta)^2=1[/tex] which implies that [tex]1-\sin(\theta)^2=\cos(\theta)^2[/tex]

That means that,

[tex]\dfrac{\sin(\theta)}{\sqrt{1-\sin(\theta)^2}}\Longleftrightarrow\dfrac{\sin(\theta)}{\sqrt{\cos(\theta)^2}}[/tex]

By def [tex]\sqrt{x^2}=x[/tex] therefore [tex]\sqrt{\cos(\theta)^2}=\cos(\theta)[/tex]

So the fraction now looks like,

[tex]\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

Which is equal to the identity,

[tex]\boxed{\tan(\theta)}=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

Hope this helps.

r3t40

[tex]\bf x^2-x-6\div x^2-4\implies \cfrac{x^2-x-6}{x^2-4}\implies \cfrac{(x-3)(x+2)}{\underset{\textit{difference of squares}}{x^2-2^2}} \\\\\\ \cfrac{(x-3)~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-2)~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x-3}{x-2}[/tex]

Answer:

kerri's speed is 50 MPH (miles per hour)

Step-by-step explanation:

You look at the one, and follow the line upward until it stops, and that shows the speed, per hour. I know thats correct so i hope this helps you and good luck on the rest of the test :)

Answer:

50 miles per hour.

Step-by-step explanation:

In this graph, distance covered by Kerri has been shown on y-axis and time on x-axis.

Speed of Kerri will be defined by the rate of change in distance which is slope of the line.

Speed = [tex]\frac{\text{change in distance}}{\text{change in time}}[/tex]

           = [tex]\frac{300-0}{6-0}[/tex] = 50 miles per hour.

Answer:

B) 46.67°

Step-by-step explanation:

Step 1 : Write the cosine formula to find the angle C

c² = a² + b² - 2ab cos C

Step 2 : Substitute the values in the formula

6² = 7² + 8² - 2(8)(7) cos C

cos C = 0.6875

C = cos^-1 (0.6875)

C = 46.567 °

Step 3 : Round off to 2 decimal places

Angle C = 46.57°

!!

Answer:

See below.

Step-by-step explanation:

The y-coordinate , giving the value of the function at this point. It is a part of the range of the function.

Answer:

It is the y-value

Step-by-step explanation:

Took the test on edg.

On a plotted graph, 'm' commonly represents the slope indicating how much the line rises or falls for each step across. On the other hand, 'n' usually demonstrates the y-intercept - the point where the line crosses the y-axis.

The relationship between the values of m and n plotted on a number line depends on the mathematic law or concept being applied. But in many cases, such as on a graph, 'm' typically represents the slope while the 'n' value shows the y-intercept.

Slope (m) shows how much a line moves up or down along the y-axis for each step across the x-axis ('run'). The equation for this is ∆y/∆x meaning the change in y over the change in x. For example, if the slope (m) is three, each time the x value increases by one, the y value will rise by three.

The y-intercept (n) is the point where the line crosses the y-axis. This is the value of y when x = 0.

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Answer:

[tex]\boxed{\text{0.675 h}}[/tex]

Step-by-step explanation:

18 min = 0.3 h

Car 1 started 0.3 h before Car 2.

  Let t = time of Car 2. Then

t + 0.3 = time of Car 1

Distance = speed × time, and both cars travel the same distance. Then

[tex]\begin{array}{rcl}45(t + 0.3) & = & 65t\\45t + 13.5 & = & 65t\\20t & = & 13.5\\t & = & \textbf{0.675 h}\\\end{array}\\\text{Car will overtake Car 1 in } \boxed{\textbf{0.675 h}}[/tex]

Check:

[tex]\begin{array}{rcl}45(0.675 + 0.3) & = & 65 \times 0.675\\45 \times 0.975 & = & 43.875\\43.875 & = & 43.875\\\end{array}[/tex]

OK.

Answer:

Car2 overtakes Car1 after 0.675 hours

Step-by-step explanation:

To solve this question, we must know that

Speed = distance / time

Speed_car1 = 45 mph = distance_car1/ time_1

Speed_car2= 65 mph = distance_car2/ time_2

We know that

time1 - time2 = 18 minutes = 0.3 h

And, at the time of the overtake, both cars will have traveled the same distance.

So,

distance_car1 = 45 mph * time1 = distance_car2 = 65 mph * time2

time1 / time2 = 65/45

time1 = 1.444*time2

Then,

1.444*time2- time2 =  0.3 h

time2 = 0.675 h

time1 = 0.975 h

Car2 overtakes Car1 after 0.675 hours

Answer:

Tangent of 45º When a square is divided by a diagonal into two equal right triangles, the angles measure 90º, 45º and 45º. The diagonal (hypotenuse of the triangle) is then obtained by applying the Pythagorean theorem: Trigonometric Ratios. Trig.

Step-by-step explanation:

Answer:

Answer is m∠4=40

Step-by-step explanation:

According to the image which i have posted below,we first want to take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.

m∠6 = m∠7 (vertical angles)

11x + 8 = 12x – 4

12x - 11x = 8 + 4

x = 12

so

m∠6 = 11x + 8  

m∠6 = 11(12) + 8

m∠6 = 132 + 8

m∠6 = 140

m∠4 = 180 - m<6

m∠4 = 180 - 140

m∠4 = 40

Answer is m∠4=40....

Answer:

W'(-3,3) V'(-4,3) U'(-4,5)

Step-by-step explanation:

The mapping for 90 degrees counterclockwise rotation is;

[tex](x,y)\to (-y,x)[/tex]

The given points have coordinates: W(3,3) V(3,4) U(5,4)

[tex](x,y)\to (-y,x)[/tex]

This implies that:

[tex]W(3,3)\to W'(-3,3)[/tex]

[tex]V(3,4)\to V'(-4,3)[/tex]

[tex]U(5,4)\to U'(-4,5)[/tex]

The required points of the image are:

W'(-3,3) V'(-4,3) U'(-4,5)

Answer:

8

Step-by-step explanation

First you have to plug in 3 for x:

5(3-1)-2

Then using PEMDAS you would simplify that:

5(2)-2

10-2

8

Answer:

C(x) =24+6(z-1) where z is the total of units sold.

Therefore if z=10 units, the answer is: C(x)=24+6(10-1)

Or 24+6(9)

Or $78

Step-by-step explanation:

Answer:

10 Units would cost $78

Step-by-step explanation:

We will be using the following equation to solve this problem

[tex]C(x) = 24+6(x-1)[/tex]

Where x will be the amount of units of coverage that are sold. The equation subtracts 1 from the amount of units sold (since the first unit costs $24) and multiplies that by $6 which is the cost per unit. Then it adds $24 to that, which gives us the total cost.

Since we sold 10 units of coverage we plug that into the equation

[tex]C(10) = 24+6(10-1)[/tex]

[tex]C(10) = 24+6(9)[/tex]

[tex]C(10) = 24+54[/tex]

[tex]C(10) = 78[/tex]

So 10 units of coverage sold would cost $78

Answer:

9.13 cm^2.

Step-by-step explanation:

The diagonal of the square = the diameter of the circle.

The length of the diagonal = 4√2 cm (because we have a 45-45-90 triangle), so the radius of the circle is half of this = 2√2 cm.

The area of the shaded part = area of the circle - area of the square

= π (2√2)^2 - 4^2

=  25.13 - 16

= 9.13 cm^2.

Answer:

A.   y = 9(x +1/2)^2 - 13/4.

Step-by-step explanation:

y = 9x^2 + 9x - 1

y = 9(x^2 + x) - 1

y = 9 [ (x + 1/2)^2 - 1/4] - 1

y = 9 (x + 1/2)^2  - 9/4 - 1

y = 9(x +1/2)^2 - 13/4.

Answer: First Option

[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]

Step-by-step explanation:

For a quadratic function of the form:

[tex]y = ax ^ 2 + bx + c[/tex]

The vertex form of the equation is:

[tex]y = (x-h) ^ 2 + k[/tex]

Where the vertex is the point (h, k) and [tex]h =-\frac{b}{2a}[/tex]

In this case the equation is: [tex]y=9x^2+9x-1[/tex]

So:

[tex]a=9\\b=9\\c=-1[/tex]

Therefore:

[tex]h =-\frac{9}{2*(9)}[/tex]

[tex]h =-\frac{1}{2}[/tex]

[tex]k=9(-\frac{1}{2})^2+9(-\frac{1}{2})-1\\\\k=-\frac{13}{4}[/tex]

Finally the equation in vertex form is:

[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]

Answer:

x=2, y=7 -------> y=11-2x  and 4x-3y=-13

x=5, y=2 ------> 2x+y=12 and x=9-2y

x=3, y=5  -----> 2x+y=11 and x-2y=-7

x=7, y=3 ------> x+3y=16  and  2x-y=11

Step-by-step explanation:

Part 1) we have

2x+y=12 -----> equation A

x=9-2y -----> equation B

Solve by substitution

Substitute equation B in equation A and solve for y

2(9-2y)+y=12

18-4y+y=12

4y-y=18-12

3y=6

y=2

Find the value of x

x=9-2(2)=5

therefore

The solution is

x=5, y=2

Part 2) we have

x+2y=9 -----> equation A

2x+4y=20 ---> equation B

Multiply equation A by 2 both sides

2(x+2y)=9*2

2x+4y=18 -----> equation C

Compare equation C with equation B

Both equations have the same slope with different y-intercept

therefore

The lines are parallel and the system has no solution

Part 3) we have

x+3y=16 ------> equation A

2x-y=11 -----> equation B

Solve the system by elimination

Multiply equation B by 3 both sides

3(2x-y)=11*3

6x-3y=33 -----> equation C

Adds equation A and equation C

x+3y=16

6x-3y=33

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

x+6x=16+33

7x=49

x=7

Find the value of y

x+3y=16

7+3y=16

3y=16-7

3y=9

y=3

therefore

The solution is

x=7, y=3

Part 4) we have

y=11-2x -----> equation A

4x-3y=-13 ---> equation B

Solve by substitution

Substitute equation A in equation B and solve for x

4x-3(11-2x)=-13

4x-33+6x=-13

10x=-13+33

10x=20

x=2

Find the value of y

y=11-2(2)=7

therefore

The solution is

x=2, y=7

Part 5) we have

y=10+x -----> equation A

-3x+3y=30 ---> equation B

Multiply equation A by 3 both sides

3*y=3*(10+x)

3y=30+3x

Rewrite

-3x+3y=30 ----> equation C

equation B and equation C are identical

therefore

The system has infinitely solutions

Part 6) we have

2x+y=11 -----> equation A

x-2y=-7 ----> equation B

Solve by elimination

Multiply equation A by 2 both sides

2(2x+y)=11*2

4x+2y=22 ----> equation C

Adds equation B and equation C and solve for x

x-2y=-7

4x+2y=22

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

x+4x=-7+22

5x=15

x=3

Find the value of y

x-2y=-7

3-2y=-7

2y=3+7

2y=10

y=5

therefore

The solution is

x=3, y=5  

Answer:

2/9

Step-by-step explanation:

We have [tex]f(x)=2 \cdot 3^x[/tex] and are asked to find [tex]f(-2)[/tex].

[tex]f(-2)[/tex] means to replace x with -2 and evaluate the expression named f.

Let's do that:

[tex]f(x)=2 \cdot 3^x[/tex]

[tex]f(-2)=2 \cdot 3^{-2}[/tex]

[tex]f(-2)=2 \cdot \frac{1}{3^2}[/tex]

[tex]f(-2)=2 \cdot \frac{1}{9}[/tex]

[tex]f(-2)=\frac{2}{9}[/tex]

Answer:

2/9

Step-by-step explanation:

Given:

We'd substitute x with -2:

[tex]2 *3^{-2}[/tex]

Using order of operations, we'd solve the exponent first:

[tex]3^{-2}=.111[/tex](repeating)

Multiply by 2:

.111(repeating) * 2 = 2/9

Our answer is 2/9

Answer: 1 1/6 cups of sugar

Step-by-step explanation:

First let’s convert 3 1/2 into an improper fraction: 7/2

Then we multiply 7/2 by 1/3: 7/2*1/3=7/6

Then finally we convert 7/6 into a mixed number, so your answer will be 1 1/6

Answer:

$895.09

Step-by-step explanation:

Applying the given formula:

A = $600e^(0.04*10), or

   = $895.09

We find that the answer is  $895.09.

Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from the previous.

How to find how much would $600 be worth after 10 years, if it were invested at 4% interest compounded continuously?

Hint: Use the formula below and round your answer to the nearest cent.)

A(t)=P•e^rt.

Applying the given formula:

A = $600e^(0.04*10),

or

= $895.09.

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Answer:

C. x + 9 = 11

Step-by-step explanation:

We are trying to identify which of the equations does not match with the others. In this case, solve for x in each equation:

Option A):

6 + x = 9

Subtract 6 from both sides:

6 (-6) + x = 9 (-6)

x = 9 - 6

x = 3

Option B):

15 = x + 12

Subtract 12 from both sides:

15 (-12) = x + 12 (-12)

15 - 12 =  x

x = 3

Option C):

x + 9 = 11

Subtract 9 from both sides:

x + 9 (-9) = 11 (-9)

x = 11 - 9

x = 2

Option D):

7 + x = 10

Subtract 7 from both sides:

x + 7 (-7) = 10 (-7)

x = 10 - 7

x = 3

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

As you can tell, all the equations end with x = 3 as there answers except C. x+9=11, making (C) your answer.

~

Answer:

[tex]P(A\cap B)=0.12[/tex]

Step-by-step explanation:

If two events, A and B are independent, then [tex]P(A\cap B)=P(A)\times P(B)[/tex], otherwise the two events are dependent.

If P(A)=0.60 and P(B) =0.20, then A and B are independent events, if

[tex]P(A\cap B)=0.60\times 0.20[/tex]

[tex]\implies P(A\cap B)=0.12[/tex]

Therefore the best complete is:

If P(A) = 0.60 and P(B) = 0.20, then A and B are independent events if [tex]P(A\cap B)=0.12[/tex]

Answer:

Step-by-step explanation:

p(a and b) = 0.12

Answer:

We know that the formula to mix chemical solutions is: C1V1 = C2V2

where C represents the concentration of the solute, and V represents volume in milliliters or ml.

In this case, we have:

0.06V1 = 0.15×350

Solving for 'V1' we have:

V1 = (0.15×350)/0.06 = 52.5/0.06 = 875

Therefre I can make 875 mL of a 6% solution by diluting 350 mL of a 15% solution.

Answer:

The person on top is wrong the answer is 14,400 in.² or D

Step-by-step explanation:

The correct option is B. 720in squared. The area of the rectangle, when enlarged by a factor of 6, scales by the square of 6, resulting in an enlarged area of 720 square inches.

To determine the area of a rectangle after it has been enlarged by a factor, we need to understand how area scales with respect to the linear dimensions. When a shape is enlarged by a factor, the area scales by the square of that factor.

Given:

→ Original area = 20 square inches

→ Enlargement factor = 6

Steps to Find the Enlarged Area:

→ Calculate the scaling factor for the area:

= 6²

= 36.

→ Multiply the original area by this scaling factor:

= 20 in² * 36

= 720 in².

Therefore, the area of the enlarged rectangle is 720 square inches, which corresponds to answer choice B.

Answer:

1.Intersecting segments theorem

In this scenario, two secant segments intersect each other inside the circle.The relationship is that the product of the segment pieces of one segment is equal to the product of the segment piece of the other.

Hint⇒identify the corresponding segment pieces for multiplication

2.Two secant segments that intersect outside circle

In this scenario the product of the whole secant with its external part is equal to the product of the other whole secant segment with its external part.

Hint ⇒identify the segment pieces outside the circle and the whole segments that include the external parts

3.One secant and one Tangent

In this case, the relation is that the product of whole segment with its external part is equal to square of the tangent segment.

Hint⇒ Identify the tangent segment and the whole secant segment that has an external part.

Hope this Helps.

Answer:

$394.5

Step-by-step explanation:

40 x 6 = 240

6.5 x 9 = 58.5

(6 x 2) x 8 = 96

240 + 58.5 + 96

Answer:

[tex]\large\boxed{(f+g)(x)=x^2+2x-6}[/tex]

Step-by-step explanation:

[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\(f+g)(x)=(2x+1)+(x^2-7)=2x+1+x^2-7=x^2+2x-6[/tex]

1 and 3 I believe are the correct answers

Answer:

Option 1 , Option 3 and Option 4 are correct.

Step-by-step explanation:

Number of customers using landlines decreases 10% per year.

Let x be the umber of customers using landlines in 2002.

⇒ Number of customer using landlines in 2003 = [tex]x-\frac{10}{100}\times x[/tex]

                                                                               = [tex]x-0.1x[/tex]

                                                                               = 0.9x

Number of customers using landlines in 2004 =  [tex]0.9x-\frac{10}{100}\times 0.9x[/tex]

                                                                              = [tex]0.9x-0.1\times0.9x[/tex]

                                                                              = [tex]0.9x-0.09x[/tex]

                                                                              = [tex]0.81x[/tex]

Therefore, from this Option 1 , Option 3 and Option 4 are correct.

Answer: (AoPS)

125

Step-by-step explanation:

A distance of 1 meter is 50 times 2 cm, so the actual distance between the two cities is 50 times 2.5 km, which is 125 km.

To find the actual distance between two cities on a map given a scale, convert the map distance to real-world distance using the scale ratio.

The actual distance between two cities on the map can be calculated as follows:

So, the actual distance between the two cities is 1.25 kilometers.

Answer:

The answer is 12a^3+2a²+23a+18 ....

Step-by-step explanation:

The given terms are:

(3a + 2)(4a² - 2a + 9)

Now multiply each value of second bracket with the first bracket:

=4a²(3a+2) -2a(3a+2)+9(3a+2)

=12a^3+8a²-6a²-4a+27a+18

Solve the like terms:

=12a^3+2a²+23a+18

Therefore the answer is 12a^3+2a²+23a+18 ....

Answer:

He needs to get 1 right

Step-by-step explanation:

1/40 is equal to .025. This means the other 39/40 incorrect ones are worth .975(97.5%). If we multiply the .975 by the 15 percent of his overall grade, we get 14.625. When you subtract this from the overall grade, you get 70.075, which is just above a 70%.

For this case we have that the general qualification is 70, of it Evan has accumulated 84.7%. Making a rule of three:

70 ----------> 100%

x -------------> 84.7%

Where "x" represents the rating that Evan has accumulated:

[tex]x = \frac {84.7 * 70} {100}\\x = 59.29\\70-59.29 = 10.71[/tex]

Evan is missing 10.71 to get 70.

In percentage, we have to:

100% -84.7% = 15.3%

Now we have that the exam represents 15% of the grade, this is divided into 40 questions.

It is observed that Evan must correctly answer the 40 questions of the exam, so he would get 15%. Even so, it would lack a 0.3% note to reach 70.

Answer:

He must answer the 40 questions correctly.

Answer:

5.9

Step-by-step explanation:

The mean means arithmetic average (some people just say average here).

The average of 4 numbers is the sum of those 4 numbers divided by the number of numbers which is 4 in this case.

So we have this formula:

[tex]\frac{3.8+4.2+5.3+x}{4}=4.8[/tex]

Multiply both sides by 4:

[tex]3.8+4.2+5.3+x=4(4.8)[/tex]

Simplify:

[tex]13.3+x=19.2[/tex]

Subtract 13.3 on both sides:

[tex]x=19.2-13.3[/tex]

Simplify:

[tex]x=5.9[/tex]