Linear Law Additional Mathematics F4​

Answer:

So if PT=TQ and TQ=7x-9

PT=5x+3=TQ=7x-9

5x+3=7x-9

minus 5x both sides

3=2x-9

add 9 both sides

12=2x

divide 2

6=x

PT=5x+3

PT=5(6)+3

PT=30+3

PT=33

PT=QT=33

x=6

Answer:

x^2+3x+3

Step-by-step explanation:

f(x) = 3x - 1

g(x) = x^2 + 4

f(x) + g(x) = 3x-1+ x^2 +4

                 Combine like terms

                   = x^2+3x+3

Answer:

what can i help u with

Step-by-step explanation:

No; the relation passes the vertical-line test. Yes; only one range value exists for each domain value

Yes; two domain values exist for range

yes; only one range value exists for each domain.

Answer:

k = 5/6

Step-by-step explanation:

First, we can make this have the form of a quadratic function, or ax²+bx+c=0. To do this, we can first subtract 10x from both sides to get

(2k+1)x²-8x=-6

Next, we can add 6 to both sides, resulting in

(2k+1)x²-8x+6 = 0

For a quadratic function of form ax²+bx+c=0, we can see that a=2k+1, b=-8, and c=6. We can then apply the quadratic equation, or

x= (-b ± √(b²-4ac))/(2a) to get our roots to be

x= (8 ± √(64-4(6)(2k+1)))/(2*(2k+1))

=  (8 ± √(64-(48k+24)))/(4k+2)

=  (8 ± √(40-48k))/(4k+2)

For the roots to be equal, we must have the two roots equal to each other. We can write this as

(8 + √(40-48k))/(4k+2) = (8 - √(40-48k))/(4k+2)

multiply both sides by (4k+2) to remove the denominator

8+√(40-48k) = 8 - √(40-48k)

subtract 8 from both sides to isolate the square roots

√(40-48k) = - √(40-48k)

The only number that is equal to its negative self (and is real) is 0. Therefore, √(40-48k) = - √(40-48k) = 0, so we have

√(40-48k) = 0

square both sides to remove the square root

40-48k = 0

add 48k to both sides to isolate the k and its coefficient

40 = 48k

divide both sides by 48 to isolate k

k = 40/48 = 5/6

Answer:

r = 10.72 cm

Step-by-step explanation:

h = 6 cm

Volume of cone = 722 cubic cm

[tex]\frac{1}{3}\pi r^{2}h=722\\\\\frac{1}{3}*3.14*r^{2}*6=722\\\\r^{2}=\frac{722*3}{3.14*6}\\\\r^{2}=114.97\\\\r = \sqrt{114.97}\\\\r = 10.72[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{9x + 3 + 7x + 4}}\\\huge\boxed{\rm \star COMBINE\ the \ LIKE\ TERMS\star}\\\huge\boxed{\rightarrow\mathsf{(9x + 7x) + (3 + 4)}}\\\huge\boxed{\rightarrow\mathsf{16x + 7}}\\\huge\boxed{\star{\textsf{Answer: 16x + 7}}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

Step-by-step explanation:

Remark

The cos(60) = 1/2

The radii marked 6 is the adjacent side. You have to solve for the hypotenuse.

Why?

Because the hypotenuse is the distance from the center of the circle to the point of intersection of the angle. Once you have the hypotenuse, you can find the length of the tangent, which will lead to the area of the kite. Then take away 1/3 the area of the circle.

Hypotenuse

Cos(60) = 1/2

cos(60) = adjacent / hypotenuse        Multiply both sides by the hypotenuse

hypotenuse * cos(60) = adjacent       Divide by Cos(60)

hypotenuse = adjacent / cos(60)  

adjacent = 6

hypotenuse = 6/0.5

hypotenuse = 12

Tangent

tangent^2 = 12^2 - 6^2

tangent^2 = 144 - 36

tangent^2 = 108

tangent = sqrt(108)

tangent = 6sqrt(3)

Triangles

The area of the triangle = 1/2 6sqrt(3) * 6

The area of the triangle = 18 sqrt(3)

There are two triangles so the area = 36 sqrt(3) That's the area of the kite.

Circle sector.

Area of the circle sector = 1/3 * pi * r^2

r = 6

Leave pi as it is.

Area of the circle sector = 1/3 * pi * 6^2

area of the circle sector = 12 pi

Answer

Area of the red part = area of the triangles - the area of circle sector

Area of the red part = 36*sqrt(3) - 12* pi            

Answer:

a = 56.3°

Step-by-step explanation:

tan(a) = 9/6 = 1.5

atan(1.5) = 56.31°

Answer:

[tex]\boxed {\boxed {\sf 56.3 \textdegree}}[/tex]

Step-by-step explanation:

We are asked to find the measure of angle a.

This triangle is a right triangle because of the small triangle in the corner representing a 90 degree or right angle. Therefore, we can use trigonometric functions. The three main functions are:

The side measuring 6 is adjacent or next to angle a. The side measuring 9 is opposite angle a. Therefore, we will use the tangent function.

[tex]tan \theta= \frac{ opposite}{adjacent}[/tex]

[tex]tan \ a = \frac{ 9}{6}[/tex]

Since we are solving for an angle measure, we use the inverse trigonometric function.

[tex]tan ^{-1} * tan \ a = tan ^{-1} * \frac{9}6}[/tex]

[tex]a= tan ^{-1} * \frac{9}6}[/tex]

[tex]a= 56.30993247[/tex]

Round to the nearest tenth. The 0 in the hundredth place tells us to leave the 3 in the tenth place.

[tex]a \approx 56.3[/tex]

The measure of angle a is approximately 56.3 degrees.

Answer:

your answer is 50 I hope it's helps you t

Answer:

50

Step-by-step explanation:

(5)(6+4)

5(6)+5(4)

30+20

50

THANK YOU

Answer:

Step-by-step explanation:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boxed{ \boxed{\boldsymbol{Rule : a^{-1}=\frac{1}{a} }}} \\\\\\\\ (2+3)^{-1} \times (2^{-1}+2^{-1}) = \\\\1)\ (2+3)^{-1}=5^{-1}=\frac{1}{5} \\\\2)\ 2^{-1}+2^{-1}=\frac{1}{2} +\frac{1}{2} } =1 \\\\3)\ \frac{1}{5} \cdot 1=\boxed{\frac{1}{5} }[/tex]

The question is incomplete. The complete question is :

Let [tex]p(t) = -0.0375t^2 + 0.225t[/tex]  be the density function for the shelf life of a brand of banana which lasts up to 4 weeks. Time, t, is measured in weeks and [tex]$0 \leq t \leq 4$[/tex]. Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place.

Answer:

2.4

Step-by-step explanation:

 Given :

[tex]p(t) = -0.0375t^2 + 0.225t[/tex]

Mean :

[tex]$=\int_0^4 tp (t) \ dt$[/tex]

[tex]$=\int_0^4 t (0.0375 t^2 + 0.225t) \ dt$[/tex]

[tex]$=-0.0375 \int_0^4 t^3 \ dt + 0.225 \int_0^4 t^2 \ dt$[/tex]

[tex]$=-0.0375 \left[ \frac{t^4}{4} \right]^4_0 + 0.225 \left[ \frac{t^3}{3} \right]^4_0$[/tex]

[tex]$=-0.0375 (64) + 0.225 \left( \frac{64}{3} \right)$[/tex]

[tex]$=-2.5 + 4.8$[/tex]

= 2.4

Therefore, the mean is 2.4

Answer:

x=2.24

Step-by-step explanation:

To do this problem, you must find the scale factor. Using two corresponding sides you can find it.

Using 2.4 and 3:

2.4 / 3 = 0.8

Scale factor: 0.8

Now find x:

2.8 × 0.8 = 2.24

x = 2.24

Hope this helped.

Answer:

3

Step-by-step explanation:

3 would be the degree of the polynomial since it has the highest degree.

Answer:

3 loaves 2 bananas left.

Step-by-step explanation:

The answer is asking how many loaves of three bananas Seth can make. 11 can be divided by 3 a total of 3 times, leaving a remainder of 2 bananas that would not be enough to make another loaf.

Answer:

64.

Step-by-step explanation:

The digits used are 1 , 2, 7 and 8

To make a number of three digits, the digits are repeated.

To make the three digit number

The ones place is filled by 4 ways.

The tens place is filled by 4 ways.

The hundred place is filled by 4 ways.

So, the total number of ways to make a three digit number is 4 x 4 x 4 = 64.

Answer:

$532

Step-by-step explanation:

We do 51,072 / 96 which is 532.

Each employee received $532.

Answer:

the answer will be

1.2x10⁴

hope it helps

Answer:

We have been provided the number, 3430000. Therefore, the standard form is, 3430000=3.43×106, here, we have moved 6 places to the left. Hence, the standard form of 3430000 is 3.43×106. Note: It is important to note that the standard form of representing numbers is also called scientific form or standard index form.

Answer:

[tex]\displaystyle x = \frac{\pi}{4} + k\, \pi[/tex] for integer [tex]k[/tex] (including negative numbers.)

Step-by-step explanation:

Pythagorean Identity: [tex]\sin^{2}(x) + \cos^{2}(x) = 1[/tex]. Equivalently, [tex]\cos^{2}(x) = 1 - \sin^{2}(x)[/tex].

Rewrite the original equation and apply this substitution to eliminate [tex]\cos(x)[/tex]:

[tex]\displaystyle \sin^{6}(x) + \cos^{6}(x) = \frac{1}{4}[/tex].

[tex]\displaystyle (\sin^{2}(x))^{3} + (\cos^{2}(x))^{3} = \frac{1}{4}[/tex].

[tex]\displaystyle (\sin^{2}(x))^{3} + (1 - \sin^{2}(x))^{3} = \frac{1}{4}[/tex].

Let [tex]y = \sin(x)[/tex] ([tex]-1 \le y \le 1[/tex].) The original equation is equivalent to the following equation about [tex]y[/tex]:

[tex]\displaystyle y^{6} + (1 - y^{2})^{3} = \frac{1}{4}[/tex].

Expand the cubic binomial in the equation:

[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, (y^{2})^{2} - (y^{2})^{3} = \frac{1}{4}[/tex].

[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, y^{4} - y^{6} = \frac{1}{4}[/tex].

Simplify to obtain:

[tex]\displaystyle 1 - 3\, y^{2} + 3\, y^{4} = \frac{1}{4}[/tex].

Rearrange and simplify:

[tex]12\, y^{4} - 12\, y^{2} + 3 = 0[/tex].

[tex]3\, (2\, y^{2} - 1)^{2} = 0[/tex].

[tex]2\, y^{2} - 1 = 0[/tex].

[tex]\displaystyle y^{2} - \frac{1}{2} = 0[/tex].

Solve for [tex]y[/tex]:

Either [tex]\displaystyle y = \frac{1}{\sqrt{2}}[/tex] or [tex]\displaystyle y = -\frac{1}{\sqrt{2}}[/tex].

If [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{\pi}{4} + 2\, k\,\pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].

On the other hand, if [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{3\, \pi}{4} + 2\, k\,\pi = \frac{\pi}{4} + (2\, k + 1) \, \pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].

Combine both situations to obtain:

[tex]\displaystyle x = \frac{\pi}{4} + 2\, k\, \pi[/tex] for all [tex]k \in \mathbb{Z}[/tex].

Answer:

the answer is d 6 tickets are 30$

Answer:

2552cm^2

Step-by-step explanation:

C.S.A=1320cm^2 ;r=?

h=15cm.

[C.S.A. = 2πrh]

(r=1320×7/660=14cm)

Now,

TSA of cylinder = 2πr (h + r) sq

TSA=2×22/7(15+14)=2552cm^2

Answer:

Step-by-step explanation:

x+1=0

then f(x)=2

x=-1

vertex is (-1,2)

Answer:

-1,2

Step-by-step explanation:

Plato

Answer:

X=0

Step-by-step explanation:

Answer:

[tex]\frac{16}{81}[/tex]

Step-by-step explanation:

[tex](\frac{27}{8} )^{-\frac{4}{3} }[/tex]

[tex]=((\frac{3}{2} )^3)^{-4/3}[/tex]

[tex]=(\frac{3}{2} )^{-4}[/tex]

[tex]=(\frac{2}{3} )^{4}[/tex]

[tex]=\frac{16}{81}[/tex]

Answer:

16/81

Step-by-step explanation:

a negative exponent means 1/...

the number in the numerator means "to the power of".

the number in the denominator means take the root of that power.

so, we have to take the third root of the expression, or this then to the power of 4, and finally build 1/... if the whole result.

and the sequence is not making a difference.

the third root of of 27/8 = 3/2

this to the power of 4 = 81/16

this 1/... = 16/81

Answer:

The choose (C)

F(x)=x/ (x+1)(x-2)

Answer: -46

Step-by-step explanation:

[tex]u_1=50=50-(1-1)*4\\u_2=46=50-(2-1)*4\\u_3=42=50-(3-1)*4\\...\\\\u_n=50-(n-1)*4\\\\\\u_{25}=50-(25-1)*4=-46\\\\\\Answer\ -46\\[/tex]

Answer:

Side length ≈ 12.04

Step-by-step explanation:

145 = x²

144 is the closest  square, with the root 12

The square root of 145 is approximately 12.04

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

The approximate side length is 12.0 in

Step-by-step explanation:

The area of a square is given by

A = s^2  where s is the side length

145 = s^2

Taking the square root of each side

sqrt(145) = sqrt(s^2)

12.04159458 = s

The approximate side length is 12.0 in

Answer:

Step-by-step explanation:

0.9*2b = 1.8b

0.9*-1 = -0.9

So far we have 1.8b-0.9. It can't be simplified further.

Then, we add the 2nd part, -0.5b+1.

We have:

1.8b-0.9-0.5b+1. Next we combine like terms.

1.8b-0.5b = 1.3b.

-0.9+1 = 0.1

Then we put it together.

1.3b+0.1 is our answer.

Hope this helped! Have a nice day :D

Hi there!  

»»————-　★　————-««

I believe your answer is:

1.3b + 0.1

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\0.9(2b-1)-0.5b+1\\--------------\\\rightarrow 1.8b - 0.9 - 0.5b + 1\\\\\rightarrow 1.8b - 0.5b - 0.9 + 1\\\\\rightarrow \boxed{1.3b +0.1}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

C

Step-by-step explanation:

Let the coordinates be (m, n) then by using the section formula we have

m=(5*8+3*(-8))/(5+3)=2

n=(5*(-1)+3*(7))/(5+3)=2

The point is (2,2)

Solving expression

[tex]\\ \rm\Rrightarrow (62-42)3[/tex]

[tex]\\ \rm\Rrightarrow 3(20)[/tex]

[tex]\\ \rm\Rrightarrow 60[/tex]

Answer:

3 times the difference of 62 and 42

Step-by-step explanation:

(62−42)×3

The difference of 62 and 42 times 3

Answer:

22/5

Step-by-step explanation:

3m+18+2m=40

5m=40-18

5m=22

m=22/5

[tex] \bf \large \longrightarrow \: 3m \: + \: 18 \: + \: 2m \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: + \: 18 \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 40 \: - \: 18[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 22[/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \frac{22}{5} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \cancel\frac{22}{5} \: \: ^{4.4} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: 4.4[/tex]