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The simplified expression of (x¹² ÷  x⁴). x³ is x¹¹

The expression can be solved as follows:

(x¹² ÷  x⁴). x³

The law of indices can be used to solve the expression.

Therefore,

[tex]\frac{x^{a} }{x^{b} } = x^{a - b}[/tex]  and [tex](x^{a} )^{b} = x^{ab}[/tex] and [tex]x^{a} .x^{b} = x^{a+b}[/tex]

Hence,

(x¹² ÷  x⁴) = x¹² / x⁴ = x¹²⁻⁴ = x⁸

Therefore,

(x⁸). x³ = x⁸⁺³

Finally,

x⁸⁺³ = x¹¹

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We need to find the values of "x" and "y" from two triangles that are congruent. If the triangles are congruent it means that the corresponding angles are equal. This means that angle R and angle N are the same, and from the angle sum theorem w know that the interior angles of triangle QPR sum 180, that is mathematically:

Since angle N is 3x+y, we replace that in the equation:

Simplifying we get:

That gives us equation (1), but we need another equation since we have two variables. The other equation we get it from angles L and P, since this two angles must be equal. So we get the following equation:

Solving for "x", we get:

The value of "x" is 7. Now we input this value in equation (1), like this:

Solving for "y", we get:

therefore, the value of "y" is 30.

2x² - x²

Factor:

x²(2 - 1)

x²(1)

x²

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

(3x² + x + 8) + (x² - 9)

Add like terms:

(3x² + x²) + x +(8 - 9)

4x² + x - 1

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

-3x² - 7x + 9 - 5x² + 6x - 4

Add like terms:

(-3x² - 5x²) + (-7x + 6x) + (9 - 4)

-8x² - x + 5

olution:

iven;

Applyin the power property of logarithm given as;

Thus;

Simplify further, we have;

ivide both sides by 2;

NSWER:

Answer:

YOU MUST SOLVE   ---> |3x + 2|

Step-by-step explanation:

|3x + 2| = 4

-2          -2

3x = 4

x = 0.75

HOPE this HELPED

EXPLANATION

Given two points of a line, we can find the the equation of that line using the steps below:

• Step 1

Determine the slope of the line, using the formula below:

The points given are (-4, 1) and (5, -3). This implies that the coordinates are

x₁= -4 y₁=1 x₂=5 y₂=-3

Substitute the values into the formula and simplify.

• Step 2

Determine the y-intercept(b) of the line.

Substitute x₁= -4 y₁=1 and m=-4/9 into y=mx + b and solve for intercept(b).

1 = (-4/9)(-4) + b

Subtract 16/9 from both-side of the equation.

The intercept (b) = -7/9

• Step 3

Form the equation by substituting the value of the slope and intercept into y=mx + b.

Hence, the equation of the line is:

Answer:

Each bag of lemons cost $3.30

Step-by-step explanation:

The equation will be

6x = 26.10 - 6.306x=26.10−6.30

Solve for x to get,

6x = 19.86x=19.8

x = 3.3x=3.3

Answer:

$3.30 for each bag of lemons

Step-by-step explanation:

We know that Omar only bought both lemons and eggs. We also know that the total amount of money he spent on groceries is $26.30 and that the eggs are worth $6.30 out of the total.

So, if we can subtract the cost of the eggs from his total cost of groceries to find how much the lemons cost. After that we can divide the cost of all the lemons, which is $19.80, by the number of bags, which is 6, to find how much each bag costs.

(26.10 - 6.30) / 6 = ?

19.8/6 = 3.30

Answer:

25 child tickets and 50 adult tickets

Step-by-step explanation:

Let c be the number of child tickets and a be the number of adult tickets. We have this system of equations:

6.00c + 9.60a = 630.00

a = 2c

Substitute 2c for a in the top equation:

6.00c + 9.60(2c) = 630.00

6.00c + 19.20c = 630.00

25.20c = 630.00

c = 25, a = 50

Answer:

5

Step-by-step explanation:

according to my own understanding since her flag to the drawing is 20. each colour is 4,then u divide 20 by 4. The answer is 5

The answer is a) 27/6 b) 1/2 c) 0.6 = 6/10 = 3/5 and their sum is 5.6

The four basic arithmetic operations in Maths, for all real numbers, are:

→ Addition (Finding the Sum; ‘+’)

→ Subtraction (Finding the difference;  ‘-’)

→ Multiplication (Finding the product; ‘×’ )

→ Division (Finding the quotient; ‘÷’)

In this given question ;

a) [tex]\frac{3}{4}[/tex] + 6

first take LCM so we will get : [tex]\frac{3+24}{6}[/tex] = [tex]\frac{27}{6}[/tex]

b) [tex]\frac{2}{4}[/tex]÷ 1

this implies [tex]\frac{1}{2}[/tex] ÷ 1 = [tex]\frac{1}{2}[/tex]× 1 = [tex]\frac{1}{2}[/tex]

c) [tex]\frac{3}{5}[/tex] = 0.6

If we were to solve a + b + c we get : 27/6 = 4.5

b= 1/2 = 0.5

so 4.5+ 0.5 + 0.6 = 5.6

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Answer: 8, 16, 24, 32, 40, 48

Step-by-step explanation:

because if you add all of those numbers up, that's what you get.

Answer:

8 - 16 - 24 - 32 - 40 - 48

Step-by-step explanation:

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

Answer: 1.75

Step-by-step explanation:

13/4 = 3.25

5.00-3.25

1.75

When the population has a mean of 30, if 3 points are added to each score, the mean for the new distribution is 33.

It should be noted that mean simply means the average of a given set of numbers that are given. The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.

In this case, the population has a mean of 30 a and 3 points are added to each score.

In this case, the new mean will be the addition of the numbers. This will be illustrated as:

= 30 + 3

= 33

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Answer:

$50

Step-by-step explanation:

We will call x the original price of the sunglasses.

We can create the equation below using the information given.

[tex]x*\frac{30}{100} =15[/tex]

Now solve for x.

[tex]x = 15*\frac{100}{30}[/tex]

[tex]x = \frac{100}{2}[/tex]

[tex]x=50[/tex]

Drop Down 1

(2 in)(10 ft/1 in) = 20 ft

Drop Down 2

This means the scale factor is 1:2, and thus the new length will be 3 inches.

The given points are located in the 1st quadrant.

Refer to the attachment.

Since the two points x or abscissa = 8.7 and ordinate or y axis = 2.3 and  both the numbers are positive thus they belong to the First quadrant.

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nswer:

Explanation:

ere, we want to solve the syastem of linear equations simultaneously by elimination

We have this as:

We start by multiplying the first equation by 6 and the second by 4. We have this as:

Add both equations as follows:

To get x, we multiply the first equation by 5 and the second by 3

We have this as:

We proceed to add both equations:

The amount of power used when Sanjay applied a force of 225N to move a wheelbarrow over the given distance at a velocity of 1.8m/s is 405 watts.

Power is the quantity of energy transferred per unit time. The relationship between force, velocity and power is expressed aa;

P = F × v

Given the data in the question;

To find the amount of power used, plug the given values into the above formula and solve for P.

P = F × v

P = 225kgm/s² × 1.8m/s

P = 225kgm²/s³ × 1.8

P = 405kgm²/s³

Power P = 405W

Therefore, the amount of power used by Sanjay is 405 watts.

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He will cover 301.875 miles in 7.5 hours at a unit speed of 40.25 miles per hour.

A ratio that compares two amounts of different types of units is called a rate. When a unit rate is expressed as a fraction, the denominator is 1 unit.

Rate = Distance/Time

If Mr.Salcedo was driving at 120 3/4 miles in 3 hours, his unit rate will be calculated as:

Unit rate =[120 3/4]/3

Unit rate = 483/12

Unit rate = 40 1/4 miles/hr

This shows that he  drove 40 1/4 miles/hr.

The miles he drove in 7 1/2 hour is expressed as;

Miles driven = 161/4 * 15/2
Miles driven = 301.875 miles

Hence the miles that he will drive in 7.5 hours is 301.875miles and the unit rate is 40.25 miles/hr

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If the rectangle shown is dilated by a scale factor of 1.5 with the origin as the center of dilation , then the resulting rectangle is shown below .

In the question ,

From the figure given below , we can see that the coordinates of the rectangle are (4,2) , (4,4) , (-2,2) , (-2,4)  .

let us name the coordinates of the rectangle  as A(4,2) , B(4,4) , C(-2,4) , D(-2,2)  .

and to dilate the rectangle by a scale factor of 1.5 with center of dilation at the origin , we multiply coordinates of the original shape with the dilation factor

so the rule to describe the dilation will be

(x,y)→(1.5x,1.5y)

Using this rule to find the new coordinates of the rectangle A'B'C'D'  .

When A = (4,2)

A' = (1.5*4,1.5*2)

A' = (6,3)

When B = (4,4)

B' = (15*4,1.5*4)

B' = (6,6)

When C = (-2,4)

C' = (1.5*(-2),1.5*4)

C' = (-3,6)

When D = (-2,2)

D'  = (1.5*(-2),1.5*2)

D' = (-3,3)

So the coordinates of the rectangle A'B'C'D' is A' = (6,3) , B' = (6,6) , C' = (-3,6) , D' = (-3,3) .

the new resulting rectangle is drawn below

Therefore , if the rectangle shown is dilated by a scale factor of 1.5 with the origin as the center of dilation , then the resulting rectangle is shown below .

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Slope is [tex]\frac{-2}{3}[/tex] of coordinates (6,5) and (9,-7).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; however, there is no obvious reason for this. The slope of a curve at a point in differential calculus is defined as the slope of the tangent line at that point as a generalization of this practical definition. The slope can be determined between any two locations when the curve is represented by a series of points in a diagram or list of point coordinates. Maybe when the curve is represented as a continuous function.

Given Data

coordinates - (6,-5) and (9,-7)

slope of the line denoted as m

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

m = [tex]\frac{-7-(-5)}{9-6}[/tex]

m = [tex]\frac{-2}{3}[/tex]

Slope is [tex]\frac{-2}{3}[/tex]

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An equation to represent this situation is |x - 102| = 10.

The greatest and least guesses that can be made without Houston winning a prize are 112 pounds and 92 pounds.

Given:

Actual Weight of Houston = 102 pounds

Now, if the guess is not within 10 pounds of his actual weight, Houston wins a prize.

An equation to represent this situation can be written as,

|x - 102| = 10

As we know a modulus function always generates a positive value.

We need the difference between the guessed weight and the actual weight to be exactly 10 pounds so we have applied modulus in the equation.

Now we utilize the above equation to determine the greatest and least guesses that can be made without Houston winning a prize.

The greatest guessed weight will be,

x - 102 = 10 ⇒ x = 102 + 10 ⇒ x = 112 pounds

The least guessed weight will be (the modulus value will be negative in this case)

-x + 102 = 10 ⇒ x = 102 - 10 ⇒ x = 92 pounds

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Answer:

he must make sure he gets up to 49 and higher to obtain an average of 76 or greater

Step-by-step explanation:

logically from 49 - 100 :)

The place value of the underlined digit (6) is tens of thousands and should be rounded to 70,000.

A place value simply refers to a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

In this scenario, the place value of the underlined digit (6) is tens of thousands and 9 is the next digit to six (6). Therefore, we would add one (1) to the underlined digit (6) and then change all of the other digits to zero (0) as follows:

69,807 = 70,000

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the answer is definitely 9

If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm

The width of a rectangle is 15 cm less than the length

Consider the length of the rectangle as x

The the width of the rectangle = x-15

The perimeter of the rectangle = 150 cm

The perimeter of the rectangle = 2(l+w)

Where l is the length and w is the width

Substitute the values in the equation

2(x+(x-15))=150

2(2x-15)=150

4x-30 = 150

4x = 180

x = 45 cm

The width of the rectangle = x-15

= 45-15

= 30 cm

Hence, If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm

The complete question is

The width of a rectangle is 15 cm less than the length. The perimeter is

150 cm. Find the rectangle's dimensions.

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The smallest number of signs that he can sell to have an income of $300 in one week is 12.

The price of one sign is x

Number of signs he sells per week = 37-x

The total earning from selling these is  x(37-x)  which is given as $300

(37- x) x = 300

37x - x² = 300

x² - 37x + 300 = 0

As per formula to find base in a quadratic equation

[tex]x =\frac{37 - \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 - \sqrt{1369-1200 } }{2} \\x =\frac{37 - \sqrt{169 } }{2} \\x = \frac{37-13}{2}\\ x = \frac{24}{2}\\ x = 12[/tex]

The other base can be

[tex]x =\frac{37 + \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 + \sqrt{1369-1200 } }{2} \\x =\frac{37 + \sqrt{169 } }{2} \\x = \frac{37+13}{2}\\ x = \frac{50}{2}\\ x = 25[/tex]

Therefore  the smallest number of signs that he can sell to have an income of $300 in one week is 12.

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