2(3) 3 as an exponent + 5

The value of logarithmic expression log s√7/t² is log (7/t²)^1/s.

By considering the given  logarithmic expression

log s√7/t²

=log (7/t²)^1/s

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:

(-2.5 , 0.5)

Step-by-step explanation:

You can use the midpoint formula.

x(sub1) + x(sub2) / 2  ,  y(sub1) + y(sub2) / 2

For example:

-5 + 0 / 2  ,  -2 + 3 / 2

-5 / 2  ,  1 / 2

-2.5 , 0.5

midpoint = (-2.5 , 0.5)

Answer:

692

Step-by-step explanation:

600 + (16,700 - 7,500) x 1%

600 + 16,700 - 7,500/100

600 + 9,200/100

600 + 92 = 692

I hope this helped.

Please correct me if I am wrong.

The answer is

7x-1/8x

Answer:

$125

Step-by-step explanation:

I = Prt

I = ($500)(.05)(5) = $2,500(.05) = $125

The change received by Chloe after paying a $20 bill for ribbons is $3.2.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given is the table that represents the cost per yards of the ribbons.

From the question, we can write -

Ribbon       Cost per Yard ($)

Chiffon                 5.88

Satin                     1.50

Lace                     3.29

Tulle                     2.25

Cost of one yard of satin ribbon → $1.50.

Then, the cost of 5.5 yards of satin ribbon [A1] → 5.5 x 1.50 = $8.25.

Cost of one yard of tulle ribbon → $2.25.

Then, the cost of 3.8 yards of tulle ribbon [A2] → 3.8 x 2.25 = $8.55.

Total cost of both the Ribbons → A1 + A2 = 8.25 + 8.55 = $16.8.

Money paid by Chloe → $20

Change received by Chloe → 20 - 16.8 = $3.2

Therefore, the change received by Chloe after paying a $20 bill for ribbons is $3.2.

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Answer:

There are no like terms

Step-by-step explanation:

x+26

There are no like terms

Answer: x+26 is 26

Step-by-step explanation:

In linear equation, there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.

What are a definition and an example of a linear equation?

Let the number of 250g=0.25  kg jars be x and that of 500g=0.5 kg jams be y;

therefore:

total number of jars was

x+y=511

x=511-y..........i

total amount kg was:

0.25x+0.5y=186.5....ii

substituting i in ii

0.25(511-y)+0.5y=186.5

127.75-0.25y+0.5y=186.5

solving for y we get:

0.25y=186.5-127.75

0.25y=58.75

y=58.75/0.25

y=235 jars

and

x=511-x

=511-235

=276

hence , there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.

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By applying the Alternate Interior Angles Theorem, the measure of angle x is: C. 60 degrees.

The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Since the two lines are parallel lines, angles 3 and 4 are alternate interior angles. Therefore, by applying the supplementary angle theorem, the measure of angle 3 is given by:

Q + R = 180°

85° + m<3 = 180°

Angle 3 = 180° - 85°

Angle 3 = 95°

Also, the sum of the angles formed on a straight line is supplementary and equal to 180°. Therefore, we have:

x + 25° + 95° = 180°

x + 120° = 180°

x = 180° - 120°

x = 60°

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86°  is the measure of each angle when its supplementary angle.

What does math's supplementary angle mean?

Let the larger angle be x.

Smaller angle = x - 8

As both angles are supplementary,

x + (x - 8) = 180°

2x - 8 = 180°

2x = 188°

x = 94°

Therefore, larger angle = 94°

Smaller angle = 94° - 8° = 86°

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The slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.

Given the following data:

Points on x-axis = (-3, 2).

Points on y-axis = (5, -1).

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope, m = (-1 - 5)/2 + 3)

Slope, m = -6/5

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

At point (2, -1), we have:

-1 = -6/5(2) + c

-1 = -12/5 + c

c = 12/5 - 1

c = 7/5

In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.

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The early pay will always be $60 no matter the number of days, the deposit plus will be $35, $50, $65, $80, and the daily pay would be $0, $30, $60 $90, $120.

Based on the information, if you choose the option early pay, you will pay only $60 and you can swim as many days as you want, due to this, the total paid will always be $60.

Day 0: $20 (deposit)

Day 5: $20 (deposit) + $15 = $35

Day 10: $20 (deposit) + $30 = $50

Day 15: $20 (deposit) + $45 = $65

Day 20: $20 (deposit) + $60 =$80

Day 0: $0

Day 5: $30 (6x5)

Day 10: $60 (6x10)

Day 15: $90 (6x15)

Day 20: $120 (6x20)

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The midpoint of the given numbers (1.29 and 1.3) is 1.295

From the question, we are to calculate the midpoint of the given numbers

The given numbers are 1.29 and 1.3

To determine the midpoint of two numbers on a number line, we will add the two numbers together, and then divide value of their sum by 2

Adding up the numbers

1.29 + 1.3

= 2.59

Now, divide the result by 2

Dividing

2.59/2

= 1.295

∴ On the number line, the midpoint of the given numbers is 1.295

Hence, the midpoint of the given numbers (1.29 and 1.3) is 1.295

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Answer:

x=5526

Step-by-step explanation:

8597-x=7429-4358

Combine like terms

8597-x=3071

Group all constants on the right side of the equation

8597-x=3071

Subtract 8597 from both sides

(8597- x )-8597=3071-8597

Group like terms

-x+(8597-8597)=3071-8597

Simplify the arithmetic

-x=3071-8597

Simplify the arithmetic

-x=-5526

Isolate the x

-x=-5526

Multiply both sides by-1

-X x -1=-5526 x -1               the small x is for multiplication

Remove the one(s)

X=-5526 x -1

Simplify the arithmetic

x=5526

The degree of the polynomial 3x^6 - 4x^4 + 5x - 6 degree of polynomial is 6

Definition of degree of polynomial

The degree of polynomials in one variable is the highest power of the variable in the algebraic expression.

Here the algebraic expression is 3x^6 - 4x^4 + 5x - 6

Polynomials appear in lots of regions of arithmetic and technological know-how. for instance, they're used to form polynomial equations, which encode a extensive variety of issues, from essential word issues to complex medical troubles;

they are used to outline polynomial features, which seem in settings ranging from fundamental chemistry and physics to economics and social technological know-how; they're utilized in calculus and numerical analysis to approximate other features.

In advanced mathematics, polynomials are used to assemble polynomial jewelry and algebraic sorts, which are imperative ideas in algebra and algebraic geometry.

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Step-by-step explanation:

yes, this is a reflection across the y-axis.

the points near to the mirror appear also near in the reflection. and the points far from the mirror appear also far in the reflection.

Answer:

good less to the worl then

24.67 liters of the 4.5% solution are added.

As per the known fact, the relation between concentration and volume of solution is -

[tex] C_{1} V_{1} + C_{2} V_{2} = C_{final}V_{final}[/tex]

Let the [tex] V_{2}[/tex] be x. So, final volume will be (18 + x).

Keep the values in formula to find the value of volume of solution required for dilution -

8%×18 + 4.5%×x = 6%×(18 + x)

Rewriting the equation -

0.08×18 + 0.045×x = 0.06(18 + x)

Performing multiplication to find the value of x -

1.44 + 0.045x = 1.08 + 0.06x

Rewriting the equation -

1.44 - 1.08 = 0.06x - 0.045x

Performing subtraction on both sides of the equation -

0.37 = 0.015x

Shifting 0.015 to other side fo equation and performing division

x = 0.37 ÷ 0.015

x = 24.67 liters

Hence, 24.67 liters of 4.5% solution should be added to make a 6% solution.

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50 would be the largest count of fishes that would be in the tanker.

This is because of divide rule.

If the owner wants to keep the equal number of fishes in the tanker, he have to divide the total number of fishes by total number of tankers.

so,

= [tex]\frac{1423}{29}[/tex]

= 49.

It implies that 27 tankers would have 49 fishes in each of them and rest 2 tankers will adjust the remaining extra 2 fishes in themselves , so they would accommodate 50 fishes in each of them.

As the name implies, division rules in mathematics allow one to determine if a number may be divided by another number without using the actual division procedure. When two numbers can be divided evenly, the quotient is always a whole number and the remainder is always zero.

In accordance with the rule of seven divisibility, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining portion of the given number should be a multiple of seven or it should be equal to zero." 798, for instance, may be divided by 7.

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The product or multiplication of the polynomials is given as

x² +11x + 24.

A result or product is produced by multiplication or a statement that lists the factors to be multiplied.

Given (x+8) (x+3)

let us find the product :

= x² + 8x + 3x + 24

= x² +11x + 24

Let us now test the equivalency .

(x+8) (x+3) = (1+8)(1+3) = (9)(4) = 36

x² +11x + 24 = (1)² + 11(1) + 24 = 36

Hence we can see that the product is same in both the cases.

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The number of candies that Augustus will spend on the 30th day will be 536870912 candies.

It should be noted that from the information, Augustus is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework.

Therefore, the amount that he will get on the 30th day will be:

= 1 × 2^29

= 1 × 536870912

= 536870912

Therefore, the number of candies that Augustus will spend on the 30th day will be 536870912 candies.

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Answer:

x= 7

Step-by-step explanation:

3x= 13+8

3x= 21

x= 21/3

x= 7

The time it will take to cover another distance of 145 miles is; 2.5 hours

We are given;

First distance driven = 348 miles

Time taken for first distance = 6 hours

Formula for speed is;

Speed = Distance/Time taken

Thus;

Speed for fist distance = 348/6

Speed = 58 mph

Now, at the same speed she wants to cover another distance 0f 145 miles. Thus;

Time taken = distance/speed

Time taken = 145/58

Time taken = 2.5 hours

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Answer:

The dimensions are 10 inches and 24 inches.

Step-by-step explanation:

Since the quadrilateral is a rectangle, the diagonal divides the rectangle into two right triangles. That means we can use the Pythagorean Theorem, which applies only to right triangles.

On the bottom left triangle, the sides forming the right angle are the legs. They measure x and 2x + 4. The are a and b in the Pythagorean Theorem equation. The side of the triangle measuring 2x + 6 is the hypotenuse of the right triangle, the side opposite the right angle and the longest side in a right triangle. The hypotenuse is c in the Pythagorean Theorem equation.

Start with the equation of the Pythagorean theorem.

[tex] a^2 + b^2 = c^2 [/tex]

Now substitute the values we have for a, b, and c.

[tex] (x)^2 + (2x + 4)^2 = (2x + 6)^2 [/tex]

Square the two binomials. You an use the pattern:

[tex] (a + b)^2 = a^2 + 2ab + b^2 [/tex]

which I will use, or you can use FOIL and collect like terms.

[tex] x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]

Collect like terms, and move all terms to the left side equaling zero.

[tex] 5x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]

[tex] x^2 - 8x - 20 = 0 [/tex]

Try to factor the left side. We need two numbers whose product is -20 and whose sum is -8. -10 and 2 work.

[tex] (x - 10)(x + 2) = 0 [/tex]

Set each factor equal to zero, and solve for x.

x - 10 = 0  or  x + 2 = 0

x = 10  or  x = -2

Since one side of the rectangle measures x, x = -2 cannot be a solution since you cannot have a negative side length.

x = 10 is acceptable.

2x + 4 = 2(10) + 4 = 24

Answer: The dimensions are 10 inches and 24 inches.

Answer: 1/3

Step-by-step explanation:

Answe3/9

Step-by-step explanation: You just subtract the 2 from the 5 because the denominators are the same. You subtract because there is one subtraction sign and one addition sign.

The x-intercept of the function are (√2-1,0) and(-√2-1,0). and the y-intercept of the function is  (0,-1) and the inverse of the function is f⁻¹(x)=±√(x+2)-1.

The x and y intercepts of a function is defined as the points on the cartesian plane where the graph of the function intersects  the co-ordinate axes.

The intercepts are calculated by substituting the value of x and y to zero to calculate the corresponding variable.

The inverse of a function y=g(x) is calculated by finding the value of x from the equation.

At x=0 , we get the y intercept.

f(0)=(0+1)²-2

or, f(0)=-1

So the y-intercept is at (0,-1) .

At y=0 we get the x-intercept.

f(x)=0

or,(x+1)²-2=0

or,(x+1)²=2

or, x+1= ±√2

or, x=±√2-1

Therefore the x-intercepts are (√2-1,0) and(-√2-1,0).

Now let us calculate the inverse of the function.

y=(x+1)²-2

or,y+2=(x+1)²

or, x+1=±√(y+2)

or, x=±√(y+2)-1

Hence the inverse of the function is written as

f⁻¹(x)=±√(x+2)-1

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