Solve for 2. Write the smaller solution first, and the larger solution s
4x2 + 40 + 84 = 0
smaller x =
larger x =​

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sec x = [tex]\frac{1}{cosx}[/tex] , sin²x + cos²x = 1

Consider the left side

tan²y × cos²y + [tex]\frac{1}{sec^2y}[/tex]

= [tex]\frac{sin^2y}{cos^2y}[/tex] × cos²y + [tex]\frac{1}{\frac{1}{cos^2y} }[/tex] ← cancel cos²y in the product

= sin²y + cos²y

= 1

= right side ⇒ proven

Step-by-step explanation:

[tex] (\tan^2y) (\cos^2y) +\frac{1}{\sec^2y} = 1\\

LHS

= (\tan^2y) (\cos^2y) +\frac{1}{\sec^2y} \\\\

\frac{\sin^2y}{\cos^2y}\times \cos^2 y + \cos^2 y \\\\

= \sin^2y + \cos^2 y \\\\

= 1\\\\

= RHS\\\\

\purple {\boxed {\bold {\therefore (\tan^2y) (\cos^2y) +\frac{1}{\sec^2y} = 1}}} \\[/tex]

Hence Proved

Answer:

A, B, C all have one solution.

Step-by-step explanation:

1) Each equation in this question has one variable (x). This means that only one solution will be there.

2) Solve for x, you can cross out option D. When you subtract 52x from both sides, you're left with 52 = -78

Which is not true

3) Option A, if solved x = -65/68

4) Option B, x = 13/2

5) Option C, x = 5

All except D, have one solution, I don't know if it's a multiple choice answer but this is how I can help.

Answer:

The answer is A, B, and C.

Step-by-step explanation:

I got this answer on Khan Academy.

Hope this helps! :)

Answer:

x = -8

Step-by-step explanation:

3x + 2 = 2x - 6

Answer:x = -8

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

In the picture attached it can be seen that if the plane cuts a right rectangular prism through five of the six faces, a pentagon is created. The picture is just an example, any five faces are possible to create a pentagon

Answer:

Answer:45

6 x 5+15=45

Step-by-step explanation:

Hope this helped!

Answer:

Look at explanation

Step-by-step explanation:

First, plug in x=5 into the equation y=6x+15 for x.

[tex]y=6(5)+15[/tex]

Solve.

[tex]y=6(5)+15\\=30+15\\=45\\y=45[/tex]

Answer:

-4n - 40 > -120

<=> -4n > -80

<=> 4n < 80

<=> n < 20

=> Option B is correct.

q/(-7) + 1 > 5

<=> q/(-7) > 4

<=> q < 4 x (-7)

<=> q < -28

=> Option C is correct.

Hope this helps!

:)

Answer:

Perimeter = 28 ft

n = 11

Step-by-step explanation:

Area = length x width

33 = n * 3

n = 11 = length

then the perimeter is 2Length + 2Width

= 2*11 + 2*3 =

22 + 6 = 28

Answer:

Step-by-step explanation:

Area = 33 sq ft

length * width = 33

n * 3 = 33

Divide both sides by 3

n = 33/3

n = 11 ft

Perimeter = 2*(length + width)

                = 2*(11 + 3)

                = 2* 14

                = 28 ft

Answer:

x+y

Z2

1/2xy

Step-by-step explanation:

(x+y)^2 finds the area of the outer square by squaring its side length.

z^2 + 4 (1/2xy) finds the area of the outer square by adding the area of the inner square and the four triangles.

Answer:

x = 0

Step-by-step explanation:

when you plug in x as 0, you would have

0 + 3y = 12

0 = 8 - 2y

3y = 12

3y divided by 3 is y

12 divided by 3 is 4

y = 4

plug y in for the second equation

0 = 8 - 2(4)

0 = 8 - 8

this is why x = 0

hope that made sense, sorry if it didn't, i don't know how to explain it online

Step-by-step explanation:

Reflection mean bouncing light of a shining surface.

Answer:

When a student tells her a number, she uses a rule to determ

Step-by-step explanation:

Get the answers ... When a student tells her a number, she uses a rule to determine the new number. Ms. Augustine always uses the same rule. The table below shows some of the results. What would the number be when the student says 8? A. 58. B. 56. C. 54

Answer:

58

Step-by-step explanation:

Answer:

(0,-21)

Step-by-step explanation:

The x value of a y intercept is always 0

So we can plug in 0 to the equation to solve for the y intercept

(2*0-3)(3*0+7)

-3*7= -21

y intercept: (0,-21)

Answer:

-21

Step-by-step explanation:

f(x)=(2x-3)(3x+7)

The y intercept is when x=0

f(0) = (0-3) (0+7)

     -3*7

    -21

The y intercept is -21

Answer:

5/9 of a chance

Step-by-step explanation:

or a 55.55- chance

Answer:

3.02 miles

Step-by-step explanation:

Look at the attached picture

Hope it will be helpful to you..

Answer:

A. 40 Miles

Step-by-step explanation:

To find the answer I'd use a proportion. To do this you would set it up like this: [tex]\frac{1 inches}{5 miles} = \frac{8 inches}{x miles}[/tex]

Then you could either cross multiply or do it the way I'm going to explain. 1 time 8 equals 8, and when you multiply the top number you have to multiply the bottom number by the same number. So 5 time 8 equals 40. The real distance between the cities is 40 miles.

Answer:

just 100% because it is only that alone. You could have 1.0 as a decimal or 100/100 as a fraction, or 5/5, 18/18 and so on

Step-by-step explanation:

Answer:

100% is equal to 100%.

Step-by-step explanation:

Think about it in fractions, for a precentage to be 100% it need to be the same number of the top and bottom

20/20 = 100%

Answer:

(y-3)=(1/4)(x-5) or (y-1)=(1/4)(x+3)

Step-by-step explanation:

point slope formula: (y-y1)=m(x-x1)

slope formula: (y2-y1)/(x2-x1)

slope = m

Answer:

the first one

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The y axis or interval (0,Infinity) is forever going more lower and the x is forever going to the negatives

Answer:

45 goals

Step-by-step explanation:

You have the fraction 24/8

After you simplify it you get 3/1 (that’s the percentage of goals/games)

Supposing goals = x,

x/15 = 3/1

x= 45 goals

Answer:

see below

Step-by-step explanation:

Let w = width

L = length = w+5

The area is l*w

A = (w+5)*w

A = w^2 +5w

Answer:

1

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

if you add the value if f(x) to t

Answer: The answer is B. Mean :)

Answer:

[tex](1)7n^2\\(2)3n^2\\(3) 1[/tex]

Step-by-step explanation:

(1) [tex]14n^2, 35n^4[/tex]

[tex]14n^2=2 X 7 X n^2\\35n^4=5 X 7 Xn^2Xn^2\\$Therefore, the GCF of 14n^2$ and 35n^4$ is 7Xn^2=7n^2[/tex]

(2)[tex]21n^3, 18n^2[/tex]

[tex]21n^3=3 X 7 X n^2 X n\\18n^2 =3 X 6 X n^2\\$Therefore, the GCF of 21n^3$ and 18n^2$ is 3Xn^2=3n^2[/tex]

(3) [tex]7n^2, 9[/tex]

The two terms are co-prime. Therefore their GCF is 1.

Answer:

yes, 10

Step-by-step explanation:

Take the second term and subtract the first term

20-10 = 10

Take the third term and subtract the second term

30-20 = 10

Take the fourth term and subtract the third term

40-30 =10

Each time the difference is 10, so it is an arithmetic sequence

This is an arithmetic sequence and the common difference is 10

Answer:

y = 90°

Step-by-step explanation:

y + x = 110° because the sum of two interior angles is equal to an interior angle

x + 70° = y ➡ y - x = 70°

y + x = 110°

y - x = 70° add two equations

2y = 180° (x eliminated -x)

y = 90°

Answer:

4 m

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

12 pi  = 1/3 pi  (3)^2 x

12 pi = 1/3 pi 9 x

12 pi = 3pi x

Divide each side by 3 pi

12 pi / 3pi = 3pix/ 3pi

4 =x

Answer:

F, y-axis

Step-by-step explanation:

If point E's y-coordinate is 0, it is located somewhere on the y-axis (meaning F is correct). If point E's x-coordinate is 0, it cannot be on the x-axis (meaning E is incorrect). When a point is on the y-axis, it does not fall into any quadrant (meaning A, B, C, and D are incorrect).

Answer:

x = 2,  y=3

Step-by-step explanation:

3x + y = 9

5x + 4y = 22

Multiply the first equation by -4

-4(3x + y) = 9*-4

-12x -4y = -36

Add this to the second equation to eliminate y

-12x -4y = -36

5x + 4y = 22

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

-7x    = -14

Divide each side by -7

-7x/-7 = -14/-7

x = 2

Now find y

3x+y = 9

3(2) +y = 9

6+y = 9

Subtract 6 from each side

-6+6 +y = 9-6

y = 3

Answer:

x = 2, y = 3

Step-by-step explanation:

3x + y = 9 (1)

5x + 4y = 22 (2)

Multiply equation (1) by -4 and add to equation (2)

-12x - 4y = -36

5x + 4y = 22

-7x = -14

x = 2

Using any equation, solve for y

5(2) + 4y = 22

4y = 12

y = 3