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The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

The equation is given as:

[tex](\frac18)^{-3a} = 512^{3a}[/tex]

Express the equation as a base of 2

[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]

Evaluate the products

[tex]2^{9a} = 2^{27a}[/tex]

Cancel out the common base

9a = 27a

The above equation is not true because [tex]9a \ne 27a[/tex]

Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

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The value of x is 10√3 .

The missing figure is attached with the answer

A triangle is a polygon with three sides , three angles and three vertices.

A right angle is a triangle in which one of the sides of a triangle is equal to 90 degree.

As it is a right angled triangle therefore the trigonometric ratios are applicable

From the given figure sin 60 needs to be determine to find the value of x

sin x = Perpendicular / Hypotenuse

sin 60 = 5 / x

[tex]\rm \dfrac{\sqrt{3}}{2} = \dfrac{5}{x}[/tex]

x = 10√3

Therefore the value of x is 10√3

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Answer:

x-4y = 8

Step-by-step explanation:

The standard form for the equation of a line is Ax+By=C  where A is a positive integer and B and C are integers

First we need to find the slope

m = ( y2-y1)/(x2-x1)

m = (-3-1) / (-4-12)

     =-4/-16

    = 1/4

The point slope form is

y-1 = 1/4(x-12)

Multiply each side by 4

4(y-1 )= 4*1/4(x-12)

4(y-1) = x-12

4y -4 = x-12

Subtract 4y from each side

4y-4-4y = x-4y -12

-4 = x-4y -12

Add 12 to each side

-4+12 = x-4y -12+12

8 = x-4y

x-4y = 8

The standard form is x-4y = 8

Answer:

x-intercept: -4

Step-by-step explanation:

It's where the slope intercepts with the x-axis

Answer:

Step-by-step explanation:

x-intercept:  the x-value is that when y = 0:  (-4, 0).

y-intercept:  the y-value when x = 0: (0, 5)

Answer:

x =  -12

y = 3

Step-by-step explanation:

[tex]1/2x + 6(x+15) = 12\\1/2x + 6x + 90 = 12\\6\frac{1}{2} x + 90 = 12\\6\frac{1}{2} x= -78\\x = -12[/tex]

[tex]y = x + 15\\y = -12 + 15\\y = 3[/tex]

Answer:

a) The third term is 19
b) The new term-to-term rule is subtract 13 and then divide by 6.

Step-by-step explanation:

First term: -2
Second term: 1 (-2 * 6 = -12 + 13 = 1)
Third term: 19 (1 * 6 = 6 + 13 = 19)

Our reversed sequence is now 19, 1, -2

First term: 19

Second term: 1 (19 - 13 = 6 / 6 = 1)

Third term: -2 (1 - 13 = -12 / 6 = -2)

It's term is -3 it can be divided into 6 points +79

The input values for each of the given functions are as outlined below.

Input values are also defined as domain which is the set of input values for which the function is defined. Thus, let us look at each of the given functions;

1) g(f) = 2f. The input value here is f

2) f(h) = h - 7. The input value here is h.

3) h(g) = -4 + g. The input value here is g

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Answer:

x = 10

Step-by-step explanation:

5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side

10x - 60 + 21 = 2x + 41

10x - 39 = 2x + 41 ( subtract 2x from both sides )

8x - 39 = 41 ( add 39 to both sides )

8x = 80 ( divide both sides by 8 )

x = 10

The decision when the z value is within the rejection region is that we'll have to reject the null hypothesis.

It should be noted that the rejection region is also known as the critical region. It is the set of values where the null hypothesis is rejected.

When the observed test statistic is in the rejection region, we'll have to reject the null hypothesis and then accept rte alternative hypothesis.

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Divya should not check her answers for extraneous solution as it's not required in this case.

It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.

Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.

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Answer:

No, she shouldn't.

Answer:

[tex]IK = IJ\sqrt{2}[/tex]

Step-by-step explanation:

First, it's an isosceles right triangle, which means there is a 90 degree angle and the two other angles are equal.

To find what the two other angles are, you can set up a quick equation:

let x be angle

90 + 2x = 180, since the sum of the interior angles in a triangle is always 180.

then,

[tex]2x = 90\\x = 45[/tex]

Therefore, the triangle is a 45-45-90 triangle.

You have the measure of IJ, which is one of the legs of the triangle. The way you can find the length of the hypotenuse of a 45-45-90 triangle is by multiplying the length of one of the legs by [tex]\sqrt{2}[/tex].

This means the equation is [tex]IK = IJ\sqrt{2}[/tex]

Answer:

[tex]\sf IK=IJ\sqrt{2}[/tex]

Step-by-step explanation:

The interior angles of a triangle sum to 180°.  Therefore, if ΔIJK is an isosceles right triangle where m∠J = 90°:

To calculate the base angles:

⇒ m∠K + m∠I + m∠J = 180°

⇒ m∠K + m∠I + 90° = 180°

⇒ m∠K + m∠I = 90°

⇒ m∠K = m∠I = 45°

Therefore, IJ and JK are the legs of the right triangle and IK is the hypotenuse.

To find the length of the hypotenuse, use Pythagoras' Theorem.

Pythagoras’ Theorem:  [tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for IK:

[tex]\sf \implies IJ^2+JK^2=IK^2[/tex]

[tex]\sf \implies 4^2+4^2=IK^2[/tex]

[tex]\sf \implies IK^2=32[/tex]

[tex]\implies \sf IK=\sqrt{32}[/tex]

[tex]\implies \sf IK=\sqrt{16 \cdot 2}[/tex]

[tex]\implies \sf IK=\sqrt{16}\sqrt{2}[/tex]

[tex]\implies \sf IK=4\sqrt{2}[/tex]

As IJ = 4 then:

[tex]\implies \sf IK=IJ\sqrt{2}[/tex]

Answer:

y = 38 + 12x

Step-by-step explanation:

38is fixed cost per month and since the charge is $12 per GB, the variable cost is 12x where x is the GB used

Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]

Step-by-step explanation:

Setting the equations equal to each other.

[tex]x-3=-2x+1\\\\3x=4\\\\x=\frac{4}{3}\\\\\implies y=\frac{4}{3}-3=-\frac{5}{3}[/tex]

Answer:

the graph of f(x)= -2-10x+16

Answer:

the vertex would be (-5,41)

Step-by-step explanation:

You just plug the -5 back into the equation to get 41

[tex]\log_290=\log_2(3^2\cdot10)=\log_23^2+\log_210=2\log_23+b=2a+b[/tex]

Step-by-step explanation:

Did you mean.

[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]

[tex] \: [/tex]

[tex] = \sin( - \frac{4\pi}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]

[tex] = \sin( - 4 \times 60 \degree) [/tex]

[tex] = \sin( - 240 \degree) [/tex]

[tex] = \sin(0 - 240 \degree) [/tex]

[tex] = \sin(360 \degree - 240 \degree) [/tex]

[tex] = \sin(120 \degree) [/tex]

[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]

Answer:

[tex]-4^{15}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left[(-4)^5\right]^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies (-4)^{(5 \times 3)}[/tex]

[tex]\implies (-4)^{15}[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:[/tex]

[tex]\implies -4^{15}[/tex]

The equation representing the value of the collection after 7 years is  value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4

An equation is a mathematical statement , where the algebraic expression is equated to another algebraic expression.

It is given that

Ella has a collection of vintage action figures that is worth $430.

collection

appreciates at a rate of 4% per year

equation representing the value of the collection after 7 years is

value of collection = 430 + (0.04 * 430 )* t

value of collection = 430 + (0.04 * 430 )* 7

= $550.4

Therefore the equation representing the value of the collection after 7 years is  value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4

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The resulting reflected image would be congruent to image 1, i.e. have congruent corresponding sides.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.

Reflection is a rigid transformation, hence it does not affect the size and shape of the object or pre-image.

The resulting reflected image would be congruent to image 1, i.e. have congruent corresponding sides.

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Step-by-step explanation:

[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]

Hope it helps

Z – 6 < 3

Z < 3 + 6

Z < 9

Answer:

Conclusion : it lives in the water

Step-by-step explanation:

Concept :The conclusion of a conditional statement is the result of the hypothesis. The “then” part of an if-then statement is called the conclusion.

therefore, for the given statement,

the 'then' part is 'it lives in the water'

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Answer:

one solution

(second option listed)

Step-by-step explanation:

We can that these two lines, each representing one equation/function, only meet at one specific value.

In a system of equations, we are essentially looking for a solution that works for both equations.

So, if both lines share a point/value (meaning they intersect), that point is a solution to the system of equations.

Because these lines only overlap at one point, this system of equations has one solution.

Answer:

1 solution (C)

Explanation:

They have one point of intersection.

Answer:

[tex]2*2^1^/^4[/tex]

(≈2.378)

Step-by-step explanation:

we know that:

[tex]a^x*a^y=a^x^+^y[/tex]

[this is the same as multiplying any exponents]

3/4 + 1/2 = 1 + 1/4

if [[tex]a^x*a^y=a^x^+^y[/tex]], then [[tex]a^x^+^y=a^x*a^y[/tex]] must also be true

so,

[tex]2^1^+^1^/^4=2^1*2^1^/^4\\[/tex]

= [tex]2*2^1^/^4[/tex]

([tex]2^1^/^4 = 1.189207115[/tex])

1.189207115 · 2 = 2.37841423001

(rounded to 2.378)

Answer:

[tex]2*2^1^/^4[/tex]

(2.37841)

Explanation:

3/4 + 1/2 = 1 + 1/4

= [tex]2*2^1^/^4[/tex]

([tex]2^1^/^4 = 1.189207115[/tex])

(2)(1.189207115) = 2.37841423001

At first, he made [tex]2\frac{5}{8}[/tex] kg of tuna filling.

Mr Abdul made tuna and curry potato filling for some puffs.

3/5 of the filling he made was tuna and the rest was curry potato.

So, amount of curry potato = 1- 3/5 = 2/5

Ratio of tuna & curry potato = tuna : curry potato

                                               = 3/5 : 2/5  = 3 : 2

Let amount of tuna = 3x & amount of curry potato = 2x

After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.

According to the question, he then had equal amounts of tuna filling and curry potato filling left.

So, 3x - 1/8 = 2x + 3/4

Multiplying 8 in both sides we get,

⇒ 24x - 1 = 16x +6

⇒ 24x - 16x = 7

⇒ 8x = 7

⇒ x = 7/8

So, 3x = (3×7/8) = 21/8 kg = [tex]2\frac{5}{8}[/tex] tuna filling at first.

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Answer:

“The slope is Negative three-fourths, and the y-intercept is 3.”

Step-by-step explanation:

the graph passes through the points (0 , 3) and (4 , 0)

Then

The slope is :

[tex]=\frac{0-3}{4-0}[/tex]

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

Since , the graph passes through (0 , 3)

THen the y-intercept is 3.

The provided equation has no solution because the square of any number cannon is negative.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is:

Find a solution to the given equation

Please refer to the attached picture for the expression.

We have an expression:

[tex]\rm \dfrac{3}{\left(m+3\right)}-\dfrac{3}{\left(m-3\right)}=\dfrac{m^2+9}{\left(m^2-9\right)}[/tex]

3(m - 3) - 3(m + 3) = m² + 9

3m - 9 - 3m - 9 = m² + 9

m²  ≠ -27

As the square of any number cannot is negative, so no solution to the provided equation.

Thus, the provided equation has no solution because the square of any number cannon is negative.

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Answer:

D = No Solution

Step-by-step explanation:

Answer:

What is the common ratio between successive terms in the sequence?

27, 9, 9, 1,

3,

of

Answer:

The boy earned $773 in the fourth month.

Step-by-step explanation:

1) First, we need to find the total amount of money he needs so that the average of the 4 months would be 500. We can do this by multiplying 500 and 4 (essentially, we are working backward when trying to find the average) [tex]500*4=2000[/tex] So, we know that the boy needs $2000 total by the end of the fourth month to make the 4-month average $500.

2) Now, we know how much the boy made for the first 3 consecutive months, so add those numbers up. [tex]435+230+562=1227[/tex] So within the first 3 months, the boy made $1227.

3) Finally, we know how much money the boy needs by the end of the fourth month and how much he made by the third, so to figure out how much he earned in the fourth month, we can simply subtract $1227 from $2000. [tex]2000-1227=773[/tex]

There 6840 ways  can first, second, and third place be assigned.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

We will use the concept of permutation

[tex]^{20}P_3[/tex]= 20!/ (20-3)!

     = 20*19*18*17!/ 17!

    = 6840 ways.

Hence, there are 6840 ways.

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