Translate the given phrase into an algebraic expression and simplify if possible: the quotient of 12 and the product of 3 and 4.

Note: Enter only the simplified result.

Answer:

1) 5
2) 0.8
3)  -1.3

4) -[tex]\frac{4}{9}[/tex]

5) ±10

6) ±[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

Answer:

Hi,

Step-by-step explanation:

sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)

a=45° and b=30°

[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]

The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

Scaling is the way of enlarging or reducing the image of an object.

Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;

Convert both measures to same units

Since 1 feet. = 12 in

90 feet = 90/12 in = 7.5 in

Take the ratio

3 : 7.5 = 30: 75

Reduce to lowest term

30: 75 = 2 : 5

Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

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Answer:

a negative linear association (C)

Re-Written Problem [Formatted]

Teams with varying numbers of players are playing a group card game. the time taken by each team to complete one game is given in the table. What is the relationship between the two variables?

Numbers of players on team are going to be 1, 2 , 3, 4, 5.

time taken to complete game (in minutes) 32, 26, 20, 14, 8

(Select the correct answer)

A. Positive linear association

B. Exponential relationship

C. Negative linear association

D. No relationship

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

Step-by-step explanation:

Lower x values (numbers of players on team) are correlated with higher y values (time taken to complete game)

[note: I know which values are x and y because of a cause-and-effect relationship. x causes y. number of players causes a change in minutes {it wouldn't make sense for the number of time it took to cause the number of players} ]

So, if we were to graph this relationship, we would see a downward-slope / negative slope of a line, because greater x-values are associated with lower y-values.

So, you would see a negative line, showing a negative linear association.

Answer:

The angle Sita here is called Amplitude

Answer:

Solution: Here, the given equations are,

[tex]: \implies8x+5y=2...(i)\:and\:y-2=0...(ii)[/tex]

From equation,(ii); y-2=0

[tex] \therefore \: y = 2.........(iii)[/tex]

Substituting the value of y from equation (iii) to equation (i),we get

[tex]: \implies{8x + 5y = 2}[/tex]

[tex]: \implies{8x + 5(2) = 2}[/tex]

[tex]: \implies{8x = 2 - 10}[/tex]

[tex]: \implies{8x = - 8}[/tex]

[tex]: \implies{x = - 1}[/tex]

[tex] \therefore \: x = - 1[/tex]

Thus, x= -1 and y= 2 is the solution.

8x+5y=2...(i) y-2=0...(ii)

8(-1)+5(2)=2 2-2=0

2=2(True) 0=0(True)

Answer: 0.5 or - 0.834

Step-by-step explanation: Here is the explanation!

Answer:

67m²

Step-by-step explanation:

12m + 6m + 4m + 36 m 8m = 67m²

For the first image, I would recommend using Desmos; it is an online graphing calculator. You can find it on online and it is free; I use it all the time for my school work

I would input each function and sees which one matches the image on the test.

As for the second image, I believe the answer is C; x is greater than or equal to -1.

For the third and last image, I believe the answer is A; x is less than -1.

I hope this helps .

[tex]35 - 12 + \frac{6 - 36}{4 } \\ 35 - 12 + \frac{216}{4} [/tex]

[tex] 35 - 12 + \frac{216}{4} \\ 35 - 12 + 54[/tex]

[tex]35 - 12 + 54 \\ 77[/tex]

Answer: x=15, y=3

Step-by-step explanation:

Subtracting the two equations, we get -3y=-9, meaning y=3.

Substituting this into the first equation, we get that x-3=12, and thus, x=15.

Answer:

The answer is D = 9/57

Step-by-step explanation:

Get the variable D by itself as stated to solve for D.

I got the other numbers to the other side.

70D + 6 - 9D = 35 + 4D - 20.

(70D - 9D - 4D) = (35 - 20 - 6)

57D = 9

D = 9/57

Answer:

11.25

Step-by-step explanation:

6 3/4 + 4 1/2

Answer:

[tex]1.25332[/tex]

Step-by-step explanation:

[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]

Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .

Usually, simplification involves proceeding with the pending operations in the expression.

Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

Given the following formula,

w=x-y/2 -z

We need to solve for y.

[tex]w = \dfrac{x-y}{2 -z}[/tex]

By cross multiplication

[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]

subtract x both side

2w - wz -x = x - y -x

y = x - 2w + wz

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Answer:

[tex]x=\frac{3}{4},\:x=-1[/tex]

Keys:

For this problem, you need the quadratic formula(listed below).

When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.

Step-by-step explanation:

solving for x₁ and x₂

[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]

[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]

[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]

solve for x₁

[tex]\frac{-1+7}{2\cdot \:4}[/tex]

[tex]=\frac{6}{2\cdot \:4}[/tex]

[tex]=\frac{6}{8}[/tex]

[tex]= \frac{6\div2}{8\div2}[/tex]

[tex]=\frac{3}{4}[/tex]

solve for x₂

[tex]\frac{-1-7}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{8}[/tex]

[tex]=-\frac{8}{8}[/tex]

[tex]=-1[/tex]

Hope this helps!

Answer:

i believe the answer is A

Step-by-step explanation:

Answer:

In terms of Pi: [tex]3\pi + 6[/tex] km

Exact value (rounded): 15.42477 km

Approximated (3.14): 15.42 km

Step-by-step explanation:

Hello!

A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]

We can plug in the values to solve for the perimeter.

In terms of Pi, it is [tex]3\pi + 6[/tex],

Exact value of Pi, it is 15.42477

Approximation of Pi (3.14), it is = 15.42

All the numbers follow a pattern of division by 2

Therefore the next number is 3/2 which is equal to 1.5

the exact value of sin A  to the nearest ten- thousandth is 0. 6625

a² + b² = c²

The opposite side is unknown, so use the pythagorean theorem to find it

c = hypotenuse = 4

a= opposite site = ?

b= adjacent side = 3

Substitute into the formula

4² = a² + 3²

16 = a² + 9

a² = 16 -9 = 7

Find the square root

a =√7 = 2. 65

To find Sin A, use

Sin A = opposite side ÷ hypotenuse

Sin A = 2. 65 ÷ 4 = 0. 6625

Thus,  the value of sin A is 0. 6625

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Let's replace every copy of x with 7 and simplify.

[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5*7+1}+9 = 3\\\\\sqrt{35+1}+9 = 3\\\\\sqrt{36}+9 = 3\\\\6+9 = 3 \ \text{ .... note the 6 on the left isn't negative}\\\\15 = 3\\\\[/tex]

Which is clearly false. This is probably the set of steps you followed to get "no solution".

Why is there no solution? Well let's subtract 9 from both sides to isolate the square root

[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5x+1}+9-9 = 3-9\\\\\sqrt{5x+1} = -6\\\\[/tex]

Recall that the result of a square root operation is never negative. The range of [tex]y = \sqrt{x}[/tex] and [tex]y = \sqrt{5x+1}[/tex] is the set of nonnegative numbers. There is no way we can have the left hand side result in -6

If there was a negative sign out front the square root and we have this instead

[tex]-\sqrt{5x+1}+9 = 3\\\\[/tex]

then the answer would be x = 7

Unfortunately, there isn't such a negative sign, so we stick with "no solutions".

Answer:

[tex] - \infty < x < \infty [/tex]

Step-by-step explanation:

Answer:

r = - 18/5

I hope this helps! ^^

( This problem has 13 steps, so it would take a lot of time to type them in ^^)

Answer:

(2,0)

Step-by-step explanation:

The intersecting points of the two lines is the solution for the two equations.

(2,0) is the solution.

The value of this equation is x = 0

The representation of an equation of the first degree - is given by:

[tex] \boxed{ \large \sf ax + b = 0}[/tex]

This representation is also defined in a first degree function.

— To solve this expression, let's: add or subtract the real terms. Then we will do the division.

⚘ Resolution

[tex] \large \sf{-3+8x-5=-8}[/tex]

[tex] \large \sf{-8+8x=-8}[/tex]

[tex] \large \sf{8x=0}[/tex]

[tex] \large \sf{x=0 \div 8}[/tex]

[tex] \green{ \boxed{ \boxed{ \blue{ \large \sf{x=0}}}}} \\ [/tex]

Therefore, the value of this equation will be x = 0

Answer: even

Step-by-step explanation:

A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.

[tex]f(x)_=-6x^{2}-5x^{2}-2=-11x^{2}-2\\\\f(-x)=-11(-x)^{2}-2=-11x^{2}-2\\\\\therefore f(x)=f(-x)[/tex]

Therefore, the function is even.

Answer:

hope you can understand

Answer:

3m²n⁴

Step-by-step explanation:

Given :

⇒ [tex]\sqrt[4]{81m^{8}n^{16} }[/tex]

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

Solving :

⇒ [tex]\sqrt[4]{81}[/tex] × [tex]\sqrt[4]{m^{8} }[/tex] × [tex]\sqrt[4]{n^{16} }[/tex]

⇒ [tex]\sqrt[4]{3^{4} }[/tex] × [tex]\sqrt[4]{(m^{2})^{4} }[/tex] × [tex]\sqrt[4]{(n^{4})^{4} }[/tex]

⇒ 3 × m² × n⁴

⇒ 3m²n⁴