Apples are 6 for $1.50 and oranges are 5 for $3.00. How much does it cost to buy 2 apples and 2 oranges Help me solve show me the steps

Answer:

2nd option

Step-by-step explanation:

[tex]\frac{7\pi }{12}[/tex] is an angle in the second quadrant

Thus to find the reference angle, subtract from π , that is

r = π - θ

Answer:

the answer is rotation hope it helps ahhaha

Answer:

h(x) = 3^(x + 1)

Step-by-step explanation:

The exponential function is;

g(x) = 3^(x)

Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;

g(x) = c•b^(x)

In this question, we are told it is stretched by a factor of 3 along the y-axis.

Thus, new function h is;

h(x) = 3 × 3^(x)

Using law of indices, we have;

h(x) = 3^(x + 1)

Answer:

B.

Step-by-step explanation:

Since the numbers in the root is all the same, lets say [tex]\sqrt{2}[/tex] is a variable.

7x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex]

Group with like terms:

7x[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

Combine like terms:

8x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

There you have it! Since all the square roots are the same thing, we can treat them like variables.

the answer is B..................

Answer:

36π mm²

Step-by-step explanation:

Formula: πr²

r=radius

r=6

π6²=36π

Answer:

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

Step-by-step explanation:

Given

[tex]\{(5, -9), (6, -6), (-3, 8), (9, -6)\}[/tex]

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

[tex]\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}[/tex]

[tex]\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}[/tex]

Required

Which is not a function

An ordered pair is represented as:

[tex]\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}[/tex]

However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)

From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.

Answer:

B

Step-by-step explanation:

B was missed. You have to convert this from hours into minutes before you can deal with seconds.

Answer:

2.5 years

Step-by-step explanation:

The given amount invested, which is the principal, P = $16,800

The simple interest rate, R = 5% per annum

The intended total value of the investment, A = $18,900

The simple interest on the principal, I = A - P

∴ I = $18,900 - $16,800 = $2,100

The formula for the simple interest, I, is given as follows;

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Therefore, we have;

[tex]T = \dfrac{I \times 100}{P \times R}[/tex]

Plugging in the values, gives;

[tex]T = \dfrac{2,100 \times 100}{16,800 \times 5} =2.5[/tex]

The time it will take the investment to grow to $18,900 is T = 2.5 years

Answer:

answer will be the integer only which was added to zero

Answer:

160=130+x

x=160-130

x=30

Answer:

2√10 km

Step-by-step explanation:

By Pythagoras theorem,

x^2 + 9^2 = 11^2

x^2 + 81 = 121

x^2 = 121 - 81

x^2 = 40

= 4 x 10

x^2 = 2^2 x 10

x = 2√10 km

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

x - 2y + 8 = 0

Step-by-step explanation:

that is the procedure above

Answer:

You can't answer these questons

sorry

Hope This Helps!!!

Answer:

(A)

Step-by-step explanation:

The bottom arrow goes to 5 1/2, and then because adding -3 is the same as subtracting 3, the top arrow correctly goes back 3, resulting in an answer of 2 1/2.

Hope it helps (●'◡'●)

Answer:

[tex]10x - \frac{1}{x} = 3 \\ 10x = 3 + \frac{1}{x} \\ 10x = \frac{3x + 1}{x} \\ 10x \times x = 3x + 1 \\ 10 {x}^{2} = 3x + 1 \\ 10 {x}^{2} - 3x - 1 = 0 \\ 10 {x}^{2} - 5x + 2x - 1 = 0 \\ 5x(2x - 1) + 1(2x - 1) = 0 \\ (5x + 1)(2x - 1) = 0 \\ \\ 5x + 1 = 0 \\ 5x = - 1 \\ x = \frac{ - 1}{5} \\ \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} [/tex]

hope this helps you.

Have a nice day!

Hello!

8 × 3 + 10 - 13 × 2 =

= 24 + 10 - 13 × 2 =

= 24 + 10 - 26 =

= 34 - 26 =

= 8

Good luck! :)

Answer:

8

Step-by-step explanation:

According to bdmas rule

First multiply 8 and 3 or 13 and 2

Then, there will be 24 + 10 - 26

Then add 24 + 10, there will be 34

and again minus by 26

Then finally answer will be 8

Answer:

D.

Step-by-step explanation:

She cannot buy a negative number of notebooks. She can buy 0 notebooks, or 1 notebook, or 2, or 3, etc. The number of notebooks she buys must be a non-negative integer.

Answer: D.

Answer:

The number of FM listereners are 24000.

Step-by-step explanation:

Let the listeners of FM are p and thus the istereners of AM are 5p.

According to the question,

p + 5 p = 144000

6 p = 144000

p = 24000

The number of FM listereners are 24000.

Answer:

3ft and 24 ft.

Step-by-step explanation:

The longer piece is 8 times as long as shorter piece

therefore,

Total length of the wooden board = 27 ft.

27 = longer length + shorter length

27 = x + 8x

27 = 9x

dividing both sided by 9

3 = x

since x was the length of the shorter piece

shorter piece is 3 ft. long

and the longer piece was equal to 8x

longer piece is 24 ft. long

Answer:

See below

Step-by-step explanation:

Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:

AB^2 - BD^2 = AD^2

We have the values of AB and BD, so we can substitute them and solve for AD:

x^2 - (x/2)^2 = AD^2

x^2 - x^2 / 4 = AD^2

AD^2 = 3x^2 / 4

AD = x√3 / 2

DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:

AD^2 + DE^2 = AE^2

(x√3 / 2)^2 + x^2 = AE^2

3x^2 / 4 + x^2 = AE^2

AE^2 = 7x^2 / 4

AE = x√7 / 2

Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4

Therefore, we can come to the conclusion AE^2 = 7 EC^2

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

[tex]$^9C_4$[/tex]

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

[tex]$^9C_4=\frac{9!}{4!(9-4)!}$[/tex]

      [tex]$=\frac{9!}{5! \ 4!}$[/tex]

     [tex]$=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$[/tex]

    = 126

Answer:

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Step-by-step explanation:

The given expression to us is ,

[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]

Now take the LCM as ( x - 1 ) and Simplify , we have ,

[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]

Simplifying further , we get ,

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Hence the second option is correct .

Step-by-step explanation:

[tex] \frac{ \frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1) - 2}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2 - 2} \\ = \frac{7 - 4x}{2x - 4} = \frac{ - 4x - 7}{2(x - 2)} \\ thank \: you[/tex]

[tex]option \: b \\ thank \: you[/tex]

Answer:

Step-by-step explanation:

z = (k*x*y) / w²

Where,

k = constant of proportionality

z = 72 when x = 80, y = 30 and w = 5

z = (k*x*y) / w²

72 = (k * 80 * 30) / 5²

72 = 2400k / 25

Cross product

72 * 25 = 2400k

1800 = 2,400k

k = 2,400/1800

k = 24/18

= 4/3

k = 1 1/3

k = 1.33

find z when x = 20, y = 60 and w=9

z = (k*x*y) / w²

z = (1.33 * 20 * 60) / 9²

z = (1596) / 81

Cross product

81z = 1596

z = 1596/81

z = 19.703703703703

Approximately,

z = 19.7

Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

Step-by-step explanation:

Here's what we know about Fernando's fees:

$10 is the initial fee

$4 is the hourly fee (h)

Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)

Here's what we know about Brenna's fees:

No initial fee

$6 is the hourly fee (h)

Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)

We want to find which hour Fernando and Brenna will have saved the same amount of money.

To do this, let's first set up an equation for Fernando and Brenna separately:

Fernando's equation:

0.3(10 + 4h) = how much money he saves from the total cost

Brenna's equation:

0.25(6h) = how much money she saves from the total cost

Now we set them equal to each other:

0.3(10 + 4h) = 0.25(6h)

There's your answer!

Hope it helps (●'◡'●)

Subtract the amount Kelsey got more than Jake from the total:

1250 - 200 = 1050

Divide by 2:

1050/2 = 525

Jake got 525

Kelsey got 525 + 200 = 725

Answer:

Step-by-step explanation:

Six liters of paint will cover 50 square meters.

  6L ⇒ 50m²

then,

  1L ⇒ 50/6 m²

  9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²

       ⇒ 75 m²

Answer:

[tex]\rm\displaystyle 0,\pm\pi [/tex]

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

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

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]

factor out tanγ:

[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]

divide both sides by tanαtanβ-1 and that yields:

[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]

multiply both numerator and denominator by-1 which yields:

[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]

recall angle sum indentity of tan:

[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]

let α+β be t and transform:

[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]

remember that tan(t)=tan(t±kπ) so

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]

therefore when k is 1 we obtain:

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]

isolate -α-β to left hand side and change its sign:

[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]

when is 0:

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]

likewise by Opposite Angle Identity we obtain:

[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]

isolate -α-β to left hand side and change its sign:

[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]

and we're done!

Answer:

-π, 0, and π

Step-by-step explanation:

You can solve for tan y :

tan y (tan a + tan B - 1) = tan a + tan y

Assuming tan a + tan B ≠ 1, we obtain

[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]

which implies that

y = -a - B + kπ

for some integer k. Thus

a + B + y = kπ

With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.

It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so

[tex]B=\frac{\pi }{2} - a + k\pi[/tex]

but with the given limitation we must have k = 0, because 0 < π/2 - a < π.

On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again

k = 0, so we obtain

[tex]\frac{\pi }{2} - a=-a[/tex]

a contradiction.

Observe that

5/12 = 1/4 + 1/6

so that

tan(5π/12) = tan(π/4 + π/6)

Then

tan(5π/12) = sin(π/4 + π/6) / cos(π/4 + π/6)

… = (sin(π/4) cos(π/6) + cos(π/4) sin(π/6)) / (cos(π/4) cos(π/6) - sin(π/4) sin(π/6))

… = (cos(π/6) + sin(π/6)) / (cos(π/6) - sin(π/6))

(since sin(π/4) = cos(π/4) = 1/√2)

… = (√3/2 + 1/2) / (√3/2 - 1/2)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1) / (√3 - 1) × (√3 + 1) / (√3 + 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3 … … … (C)

If you insist on using the half-angle identity, recall that

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

==>   tan²(x) = (1 - cos(2x)) / (1 + cos(2x))

Let x = 5π/12. The angle x lies in the first quadrant, so we know tan(x) is positive.

==>   tan(x) = +√[(1 - cos(2x)) / (1 + cos(2x))]

We also know

cos(2x) = cos(5π/6) = -√3/2

which means

tan(x) = tan(5π/12) = √[(1 - (-√3/2)) / (1 + (-√3/2))]

… = √[(1 + √3/2) / (1 - √3/2)]

… = √[(2 + √3) / (2 - √3)]

… = √[(2 + √3) / (2 - √3) × (2 + √3) / (2 + √3)]

… = √[(2 + √3)² / (2² - (√3)²)]

… = √[(2 + √3)² / (4 - 3)]

… = √[(2 + √3)²]

… = 2 + √3