Give your answer in terms of [tex]\pi \\[/tex]

Answer:

x = 200

Step-by-step explanation:

Given equation:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]

Steps:

1. Substitute 15 as the value of y in the equation:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]

2. Add 10 to both sides:

[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]

3. Multiply both sides by 5 to isolate x:

[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]

4. Check your work:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]

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Hey there!

[tex] \boxed{\bold{\green{ x = 200}}} [/tex]

[tex] \\ [/tex]

Given expression :

[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]

1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :

[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]

[tex] \\ [/tex]

2) Solve for x :

[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]

⇢Add 10 to both sides of the equation :

[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

⇢Multiply both sides of the equation by 5:

[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]

[tex] \\ [/tex]

3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :

[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]

[tex] \\ \\ [/tex]

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well that's Economics not Mathematics

1. 20,000×10%=2,000

2. 20,000×14%=2,800

3. 20,000×5%=1,000

4. Business Marketing

5. 20,000×30%=6,000

What completes the proof are:

1. LC ≅ CU; CU ≅ UK

2. Given

3. Unequal angle theorem (Aa → Ss)

The unequal angle theorem states that the longer side of a triangle will always be directly opposite the largest angle measure. This implies that, if an angle that is opposite a side is greater than another another, the side it is opposite will also be longer than the side opposite the other angle (Aa → Ss).

From the image given, statement 1 was given as well as statement 2.

Statement 1 would be: LC ≅ CU; CU ≅ UK.

The reason for statement 2 will also be "given".

Then, UL > CK using the unequal angle theorem (Aa → Ss).

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Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.

In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:

[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]

2 · r² = (9-r)²

2 · r² = 81 - 18 · r + r²

r² + 18 · r - 81 = 0

The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).

Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.

The image is missing and is thus included in the figure attached below.

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Answer:

6.5

Step-by-step explanation:

Median is always the middle number of the set of data, so lets re order the numbers least to greatest

1,2,4,5,6,7,8,8,9,12

Since there's an even amount there wont be an exact middle number, however we know its in-between 6 and 7. So we can do 6+7 = 13 and then 13/2 = 6.5 to get the middle number or median.

Answer:

see explanation

Step-by-step explanation:

the centroid is where the medians intersect.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

(3)

GF = [tex]\frac{1}{2}[/tex] CG = [tex]\frac{1}{2}[/tex] × 14 = 7

CF = CG + GF = 14 + 7 = 21

(4)

GD = [tex]\frac{1}{3}[/tex]  AD = [tex]\frac{1}{3}[/tex] × 45 = 15

AG = 2 × GD = 2 × 15 = 30

(5)

GE = 2 × BG , that is

9x = 2(3x + 6) = 6x + 12 ( subtract 6x from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Answer:

2x^3 - 3x^2 + 7x - 3

Step-by-step explanation:

Area = length * width

= (2x - 1)(x^2 - x + 3)

= 2x(x^2 - x + 3) - 1(x^2 - x + 3)

= 2x^3 - 2x^2 + 6x - x^2 + x - 3

= 2x^3 - 3x^2 + 7x - 3

Answer:

30.34 degree

Step-by-step explanation:

Apply sine formula

[tex]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}[/tex]

[tex]\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}[/tex]

->simplify

[tex]\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}[/tex]

you will get

[tex]\sin \left(b\right)=\frac{5\sqrt{2}}{14}[/tex]

which
sin b is about 0.50507

[tex]sin^{-1}\left(0.50507\right)[/tex]

->arc sine in degree mode

the answer is 30.34

Answer:

h=8.0

Step-by-step explanation:

law of sines

sinA/a=sinB/b

b/a=sinB/sinA

b = a times sinB/sinA

b = 10 times sin53/sin90

on a calculator type sin53 in degrees

b = 10 times 0.7986/1

b = 7.986

Answer:

x4 = 8

Step-by-step explanation:

To find the mean, add the values and divide by the number of values.

mean = (x1 + x2 + x3 + x4)/4

(3 + 12 + 7 + x4)/4 = 8

x4 + 22 = 32

x4 = 10

Answer:

x4 = 8

Step-by-step explanation:

Answer:

the term that best describes 3 is a coefficient because a

Step-by-step explanation:

Coefficient is a number that is being multiplied by the variable.

Answer:

60:31

Step-by-step explanation:

Answer:

Answer:11

Step-by-Step Answer:

When we multiply 11 with 1\2 then thier answer will be 11\2

assuming is simple interest

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if  you have $1000 and need to buy 10 chairs worth $5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:

x + 10(5) ≤ 1000

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.

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Answer:

The answer is (0.5, 0)

Step-by-step explanation:

[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]

Using a calculator, it is found that the equation of linear regression that fits the data is given by:

C. y=-0.295x+20.667

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are given as follows: (1, 20.71), (2, 19.69), (3, 19.61), (4, 19.64), (5, 19.26). Hence the equation is:

Doing this, the equation is:

y = -0.295x + 20.667.

Hence option C is correct.

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Answer:

Rational numbers is a ratio (i.e., P/Q and Q≠0)

Irrational numbers cannot be expressed as a fraction.

so a

Rational numbers can show a Fraction

Irrational numbers can not show a Fraction

Hope This Helped

Answer:

Rational numbers are any infinite number or ratio that goes on and on and represents such mathematical values, e.g five-over-twelve is a rational number because it is a fraction.

Irrational numbers are squares of a number or any number that does not include a comparison(e.g division, fraction, ratio, etcetera) of a value. For instance, the square root of 2 is an irrational number because it does not go on indefinitely.

Unit conversion is a way of converting some common units into another without changing their real value. The value of (3π/4) radian converted to a degree is 135°.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

Since π radian is equal to 180°. Therefore, the value of (3π/4) radian is equal to,

1 radian = 180°/π

(3π/4) radian = (3π/4) × (180°/π) = 135°

Hence, the value of (3π/4) radian converted to a degree is 135°.

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Answer:

option 2

Step-by-step explanation:

The valid solution for the positive demand is (6,3)

The equation of the function is given as:

[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]

Next, we test the options::

Option (a): (t, C(t)) = (2,3)

This gives

[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]

Evaluate the radicand

[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)

Option (b): (t, C(t)) = (6,3)

This gives

[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]

Evaluate the radicand

[tex]-\sqrt{0} + 3 = 3[/tex]

Evaluate the root

0 + 3 = 3

Evaluate the sum

3 = 3 ---- this is true

Hence, the valid solution for the positive demand is (6,3)

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Answer:

the answer is in picture

Step-by-step explanation:

hope it will help you

Answer:

(-4, -6)

Step-by-step explanation:

(x,y) = ((x1+x2)/2 , (y1+y2)/2)

[substitute the values given]

(x,y) = ((-4+-4)/2 , (-4+-8)/2)

[solve]

(x,y) = (-8/2 , -12/2)

[simplify]

(x,y) = (-4, -6)

THE ANSWER IS (-4, -6) HOPE IT HALP'S MARK IT AS BRAILY.

Answer:

X = 7 and -35.6666

Step-by-step explanation:

The correct true statement is: b.  The swimmer comes back up 9 seconds after the timer was started.

Given:

h(t)=t^2−12t+27

Let velocity of the function= 0

h(t) = 2t - 12

0 = 2t - 12

2t = 12

Divide both side by 2t

t=12/2

t = 6secs

Substitution

h(6) = 6²-12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

The correct statement is b.

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The range that is appropriate to use to represent the numerical data is 0.0 to 26.0.

A line graph is a graph that is used to represent numerical data. It shows the changes in the data with the passage of time. There are two axes on a line graph, the vertical axis and the horizontal axis. The range of the vertical axis should start from 0 and end at the largest number of data set.

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The number that produces a rational answer when added to 0.85 is; 193/180

A rational number is an algebraic term expressed as a fraction. The fraction can also be in decimals but only if the decimal places are not repeating or not infinitely long. If they aren't, then these are called irrational numbers.

Now, let us convert 0.85 to a fraction. Thus;

0.85 = 85/100 = 17/20

From the given options, the only one that when added to 0.85 will yield a rational number is 2/9. This is because;

17/20 + 2/9 = 193/180

193/180 is a rational number.

The missing options are;

A. 2/9

B. 0.2645751311...

C. √2

D.

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Answer:

A. A reflection over the y-axis and then a rotation 90 degree clockwise about the origin.

Step-by-step explanation:

Given information: Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.

A sequence of transformations to produce the same results could be the opposite of this, wherein Figure H undergoes a series of transformations to form Figure G.