Find the solution(s) of the system of equations:
y = –x2 + 4x + 5
y = x2 + 2x + 1

a. (–1,2) and (2,17)
b. (1,0) and (–2,9)
c. (1,4) and (2,9)
d. (–1,0) and (2,9)

[tex]2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\[/tex]

[tex]\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\[/tex]

[tex]x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\[/tex]

[tex]\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right][/tex]

Answer:

z = 2.25xy

Step-by-step explanation:

Given z varies jointly as x and y then the equation relating them is

z = kxy ← k is the constant of variation

To find k use the condition x = 3, y = 8 and z = 54 , then

54 = k × 3 × 8 = 24k ( divide both sides by 24 )

[tex]\frac{54}{24}[/tex] = k = 2.25

z = 2.25xy ← equation of variation

Answer:

The total cost for two packets of Fig rolls is £1.62

Step-by-step explanation:

Answer:

(x,y) =(7/2,4)

The economic output is rising and is expected to continue rising in the coming months, the economy is currently in the expansion stage of the business cycle.

The business cycle consists of the following stages which changes with time;

Thus, when the economic output is rising and is expected to continue rising in the coming months, the economy is currently in the expansion stage of the business cycle.

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Answer:

Step-by-step explanation:

9h + 24 = 60

The correct option is  D. 136.1 cubic inches.

Given, Radius of cone is 5.1 inches.

Height of cone is 5 inches.

We know that, volume of cone,

[tex]V=\frac{1}{3} \pi r^{2} h[/tex]

Here r is the radius of cone and h is its height.

on putting the value of r and h, we get

[tex]V=\frac{1}{3} \times3.14\times(5.1)^{2} \times5[/tex]

[tex]V=\frac{1}{3} \times3.14\times26.01\times5[/tex]

Or, [tex]V=136.119 \ cubic \ inches[/tex].

The volume of cone to the nearest tenth is 136.1 cubic inches.

Hence the correct option is  D. 136.1 cubic inches.

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Answer:

hope it helps have a great day

Answer is option C

Answer:

[tex]\sqrt{29}[/tex]

Step-by-step explanation:

The line has a horizontal length of 2 units and a vertical length of 5 units

The line is then the hypotenuse h of a right triangle.

Using Pythagoras' identity

h² = 2² + 5² = 4 + 25 = 29 ( take square root of both sides )

h = [tex]\sqrt{29}[/tex]

The length of the line given is √29 units.

Hence, the correct option is C.

Given is line on the cartesian plain we need to calculate its length.

Refer to the figure attached.

The figure can be converted into a right triangle with perpendicular = 5 units and the base = 2 units.

The line asked will act as the hypotenuse, so, to find its length we will use the Pythagorean theorem,

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the perpendicular side of the right triangle is given as 5 units, and the base is given as 2 units.

Let's denote the length of the hypotenuse as 'x'.

According to the Pythagorean theorem, we have:

x = 5² + 2²

Simplifying this equation:

x² = 25 + 4

x² = 29

To find the length of the hypotenuse, we take the square root of both sides:

x = √29

So, the length of the hypotenuse, in this case, is approximately √29 units.

Learn more about Pythagorean theorem, click;

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#SPJ6

Step-by-step explanation:

please mark me as brainlest

Answer:

hi

Step-by-step explanation:

Answer:

She reads one page in 1.40

Answer:

angle 4 is 47 degrees....

Answer: usually I’d answer the question but when it comes to really long questions especially in edmentum…

Step-by-step explanation:

I hit the submit button and go on myassignmenthelp.com or something like that and it’ll paraphrase the answer… I’d do it a couple times

A because the > symbol means greater so if n is on the open side that means its greater

~Shoto Todoroki here~

its option A

i figured this out by trial and error :/

have a good day!

Answer:

23/99 or 0.22222222222222.

Step-by-step explanation:

Answer:

23/99

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

(x + 13) ft = 24 ft

or, x ft = 24 ft - 13 ft

or, x ft = 11 ft

or, x = 11

Hope it helps.

Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.

Answer:

Step-by-step explanation:

Isosceles Triangle: A triangle with two equal sides. The angles opposite the equal sides are also equal.

so

(x + 13) = 24

x + 13 = 24

x = 24 - 13

x = 11

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

check

11 + 13 = 24

24 = 24

the answer is good

Answer:

The answer is 0

Step-by-step explanation:

Based on the given conditions, formulate: 3 ÷ 5

Evaluate the equation/expression: 0.6

Find the largest integer less than or equal to : 0.6 : 0

Answer: 0

====================================================

Explanation:

3/13 = 15/65 after multiplying top and bottom by 5

2/5 = 26/65 after multiplying top and bottom by 13

Let's say there are 65 marbles in the bowl. That would mean 15 of them are red (since 15/65 reduces to 3/13) and 26 are blue. That gives 15+26 = 41 so far. Leaving 65-41 = 24 marbles that must be green.

The probability of selecting a green marble is 24/65. Once that first green marble is taken out, it is not replaced. We have 65-1 = 64 marbles left, 15 of which are red. The probability of picking red on the second selection is 15/64.

Multiply the fractions mentioned:

(24/65)*(15/64)

(24*15)/(65*64)

360/4160

9/104

Answer: x= -2, y= 3

Step-by-step explanation:

3x+5y=9

X-y=-5

Multiply bottom equation by 5

3x+5y=9

5x-5y=-25

3x + 5x=8x

5y-5y cancels out

9-25= -16

8x= -16

X= -2

Plug -2 back into equation of choice to find y

3(-2)+5y=9

-6+5y=9

Add -6 to both sides

-6+6 cancels

9+6=15

5y=15

Y=3

Method used:-

Completing the square method.

Steps :-

[tex]( x - 1 ) ( x + 2 ) = - 2\\x^{2}+x-2=-2 \\x^{2}+x=-2+2 \\x^{2}+x=0[/tex]

Now, make the left hand side of the equation by adding the square of ½ to both sides of the equation.

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

Simplify the equation. You'll get a +ve & -ve value.

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

Simplify it further.

[tex]\boxed{\sf\:x=0}\\ \boxed{\sf\:x=-1 }[/tex]

The solutions are :-

x = 0 & x = -1

______

Hope it helps ⚜

if u reduced the price by 10% first it would go from 100% to 90%

20% of 90 is 18

at the end the price is 72% of the original price.

Bodil is correct. The reduction is less than 30%.

Answer:

KNOW PAIN FEEL PAIN ACCEPT PAIN

Answer:

One liter of water.

A Pineapple.

A Bunch of Bananas.

A 1 liter bottle of water

Answer:

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line

Step-by-step explanation:

u single?