What is the value of log?.

Answer:

R875

Step-by-step explanation:

We know

R35 = 1kg of breakfast cereal

? = 25kg of breakfast cereal

35 times 25 = R875

So, 25kg of breakfast cereal will cost R875.

Examples of perfect trinomials are-

x 2 + y 2 + XY,

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Answer:

complementary property

Step-by-step explanation:

©Thank You

Answered By Solution 49

The derivative of log₇(x) is 1/(xln(7))

To find the derivative of log₇(x), we can use the chain rule and the properties of logarithms.

The chain rule states that if we have a composite function, such as y = f(g(x)), then the derivative of y with respect to x is given by

dy/dx = dy/dg * dg/dx.

In this case, y = log_7(x) and g(x) = x, so

dy/dx = d/dx (log_7(x))

As by logarithmic property log₇x = ln(x)/ ln(7)

dy/dx = d/dx (ln(x)/ln(7))

To find the derivative of ln(x), we can use the property that the derivative of ln(x) is 1/x. This is because the natural logarithm function is the inverse of the exponential function eˣ, and the derivative of eˣ is eˣ. Therefore, the derivative of ln(x) is the reciprocal of x, or 1/x.

The differentiation of log₇(x) is given by:

d/dx (log₇(x)) = (1/x) * (d/dx (x)) * (1/ln(7))

= (1/x) * 1 * (1/ln(7))

= 1/(x ln(7))

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3x° - 3° = 2x° + 13°

They are vertically opposite angle...

3x° - 2x° = 13° + 3°

1x = 16°

x = 16°

hence...the value of x is 16°

Answer:

length= 8x

width= x

perimeter of a rectangle= 2L+2W

=2(8x) + 2(x)

=16x + 2x

perimeter=18x

The zeroes of the polynomial f(x) are 7, 6 and -1. The solution is obtained by the method of polynomial long division.

What is polynomial long division?

A long division polynomial is a formula for dividing one polynomial by another of the same degree or lower. The divisor, quotient, dividend, and remainder are all components of the long division of polynomials, just like they are for long division of numbers.

We are given f(7) = 0.

This means that (x-7) is one factor of f(x).

Using Polynomial Long Division,

Dividing :  x^3 -12x^2 + 29x + 42 ("Dividend")

By         :    x-7    ("Divisor")

Dividend     x^3  -  12x^2  +  29x  +  42

- divisor  * x2   x^3  -  7x^2        

Remainder      -  5x^2  +  29x  +  42

- divisor  * 5x     -  5x^2  +  35x    

Remainder             -       6x           +  42

- divisor  * (-6)            -       6x           +  42

Remainder                                  0

Quotient :  x^2-5x-6  

Remainder:  0

Now, factoring x^2-5x-6 , we get

⇒x^2-6x+x-6

⇒x(x-6)+1(x-6)

⇒(x+1)(x-6)

Thus, the factors are (x+1), (x-6) and (x-7).

Hence, the zeroes of the polynomial f(x) are 7, 6 and -1.

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The two bikers are 11.18 miles apart from each other according o the coordinate plane.

A surface with two dimensions made of two number lines is referred to as a coordinate plane. When the origin, the place where the X- and Y-axes intersect, is reached, it is produced. A coordinate grid's numbers are used to find points. For graphing points, lines, and many other things, a coordinate plane is helpful. It functions as a map and gives precise directions on how to get from one place to another.

Distance between two coordinates is given by

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, (x₁, y₁) is (5, 4) and (x₂, y₂) is (3,-7)

Putting the values in formula

d = [tex]\sqrt{(3-5)^2+(-7-4)^2}[/tex]

d = [tex]5\sqrt{5}[/tex]

d = 11.18 miles

Thus, The two bikers are 11.18 miles apart from each other according o the coordinate plane.

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There are 60 pupils who don't read novels but read comic books, since there are twice as many students who do.

When two algebraic expressions have at least one unknown or variable, they are equal.

If they are novels and comic books:

           novels

                   yes                no

comics

         yes     30                 2x

         no       x                  10

Since there are no other alternatives, the matrix's total number of digits must be 130.

30 + 2x + x + 10 = 130

Since x = 30 and 3x + 40 = 130,

The percentage of students that don't read comic books is x.

There are 60 pupils who don't read novels but read comic books, since there are twice as many students who do.

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Answer:

it's a little blurry but i think the slope is 2/3 and the y-intercept is -2

Step-by-step explanation:

The equation y=3x+5 depicts a straight line with a slope of -3 and a y-intercept of 5, and it is written in slope intercept form. Replace x with any number and solve for y to find ordered pairings that can be graphed.

Write the equation in the form y = mx + b to determine the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept (0, b). Plot the y-intercept next. 3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.

You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.

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Full Question = What kind of line does the linear inequality y=3x+5 represent?

The area of the shaded region is  h² +6h, 3x²- 3x  and r².

•The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper.

•The surface area of a specific 2-D shape is measured as the number of unit squares needed to cover its whole surface area.

•Area measurements are frequently expressed in square cm², square feet, square inches, square meters, etc. Draw unit squares with sides of 1 centimeter to determine the area of the square figures shown below. In order to measure the shape, we shall use the unit cm² or square centimeters.

1st figure

area of shaded region = outer rectangle - inner rectangle

= 3h(h+2) - 2h(h)

= 3h² +6h- 2h²

= h² +6h

area of shaded region = outer rectangle - inner rectangle

= 3x²- 3x

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Each phrase has a value, Lola is right. Because each equation has a value of 1, Lola is right.

These two phrases, according to Lola, have the same value.

Equivalent expressions are those that have the same value. In mathematics, equivalent numbers and statements frequently appear. Let's think about a few instances. Since the decimal numbers 0.5 and the fraction 1/2 have the same value, they are comparable numbers.

[a/b -] Expression A Expression B

0 [ a/b 0]-4 Which clarifies if Lola is right.

Because each phrase has a value, Lola is right. Because each equation has a value of 1, Lola is right.

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Complete question

Lola says these two expressions have the same value.

Expression A

Expression B

Left-bracket (StartFraction an Over b EndFraction) Superscript negative 4 Baseline Right-bracket Superscript 0

Left-bracket (StartFraction a Over b EndFraction) Superscript 0 Baseline Right-bracket Superscript negative 4

Which explains whether Lola is correct?

Lola is correct because each expression has a value of 0.

Lola is correct because each expression has a value of 1.

Lola is not correct because the value of expression A is 1 and the value of expression B is (StartFraction b Over a EndFraction) Superscript 4.

Lola is not correct because the value of expression A is (StartFraction b Over a EndFraction) Superscript 4 and the value of expression B is 1.

Answer:

hey

Step-by-step explanation:

The expression that best represents maria's age if she is 13 of her father's age is y = x/3

Given that,

The age of Maria's father is x.

To find: Which equation best describes Maria's age if she is 13 years older than her father?

Father of Maria is x years old. We have to find the expression best represents Maria's age.

Let age of Maria = y years

If Maria is 1/3 of her father's age then we can write the expression as below.

Age of Maria y = x/3.

Therefore answer is " y = x/3 "

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The test had 30 number of problem worth 2 points and 8 number of problem worth 5 points

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let x represent the number of 2 points and y represent the number of 5 points.

The number of 5 point problems is 22 less than the number of 2 point, hence:

y = x - 22

x - y = 22    (1)

Also, the test is worth 100 points, hence:

2x + 5y = 100    (2)

From both equations:

x = 30, y = 8

30 number of problem worth 2 points and 8 number of problem worth 5 points

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The number of bags of pink beads that can be made from today's shipment is given as follows:

5 bags.

The number of bags is obtained applying the proportions in the context of this problem.

We have that each bag weights 1/10 of a pound.

The shipment was of 4/7 pounds of pink beads, hence the total number of bags of pink beads that can be made from today's shipment is calculated as follows:

4/7/(1/10) = 4 x 10/7 = 40/7 = 5.

(rounded down, as the number of bags is a countable amount).

The problem is given by the image presented at the end of the answer.

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Answer:

x=32°.

Step-by-step explanation:

Exterior angle add up to 360°

85°+71°+2x°+3x°+44°=360°

=2x°+3x°+200°=360°

=5x°=360°-200°

=5x°=160°

=5x/5=160/5

x =32°.

The measure of ∠V of the parallelogram is = 150.5°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the measure of the angle ∠Y = 10x + 27

Let the measure of the angle ∠W = 2x + 29

Now , for a parallelogram the opposite sides are congruent and opposite angles are congruent

Substituting the values in the equation , we get

10x + 27 = 2x + 29

Subtracting 2x on both sides of the equation , we get

8x + 27 = 29

Subtracting 27 on both sides of the equation , we get

8x = 2

Divide by 8 on both sides of the equation , we get

x = 1/4

Let the measure of the angle ∠Y = 10 ( 1/4 ) + 27

Let the measure of the angle ∠Y = 2.5 + 27

Let the measure of the angle ∠Y = 29.5°

Now , same-side interior angles (consecutive angles) are supplementary

Substituting the values in the equation , we get

angle ∠Y + angle ∠V = 180°

29.5° + m∠V = 180°

Subtracting 29.5 on both sides of the equation , we get

m∠V = 150.5°

Hence , the measure of m∠V = 150.5°

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Answer:wach the vido

Step-by-step explanation:

Answer:

Nick is 6 years old.

Erica is 18 years old.

Step-by-step explanation:

Hello!

We know that Erica is 12 years older than Nick, which also means she is 3 times older than Nick. We can represent this situation as two equations.

Let E be Erica's age, and x be Nick's age.

E = x + 12, and E = x* 3

Since E is equal to E, we can say that x + 12 = 3x.

The value of x is 6. Nick is 6 years old, and Erica is 18 years old.

The solution for this equation is x = -36

3/4 ( x + 8 ) = 1/2 ( x - 6)

(Opening the brackets)

(3x + 24)/4  = ( x - 6)/ 2

By cross multiplication,

2(3x + 24) = 4( x - 6 )

6x + 48 = 4x - 24

(Taking the Variable to  one side)

6x - 4x = - 24 - 48

2x = - 72

x= - 72/2

x = -36

Hence, the solution for this equation is x = -36

Answer:

a.   [tex]62^{\frac{1}{3}} = \sqrt[3]{62}[/tex]

b.   [tex]220^{\frac{1}{2} = \sqrt{220}[/tex]

a. [tex]\sqrt[3]{240} = 240^{\frac{1}{3}}[/tex]

b. [tex]\sqrt{5} = 5^{\frac{1}{2}}[/tex]

Step-by-step explanation:

Y = [tex]4^{x}[/tex] + 64 = 5y - 1, x = (5y - 65)/16, and x = (20*[tex]4^{x}[/tex] - 260). Take the logarithm of both sides, apply the laws of logarithms, and solve for x.

A logarithm is a mathematical function for expressing the relationship between two integers. It is the exponent to which a base number must be increased in order to equal a particular number. The base-10 logarithm of 100, for example, is 2, because 10 to the power of 2 equals 100.

Let y = [tex]4^{x}[/tex]

[tex]16^{x}[/tex] + 64 = 5y - 1

[tex]16^{x}[/tex] = 5y - 65

Dividing both sides by 16

x = (5y - 65)/16

x = (5*[tex]4^{x}[/tex] - 65)/16

Substituting y = [tex]4^{x}[/tex]

x = (5*([tex]4^{x}[/tex]) - 65)/16

Simplifying,

x = (5*[tex]4^{x}[/tex] - 65)/16

x = (20*[tex]4^{x}[/tex] - 260)/16

Divide both sides by 20

x = ([tex]4^{x}[/tex] - 13)/2

Take the logarithm of both sides:

log(x) = log([tex]4^{x}[/tex] - 13)/2

Apply the laws of logarithms:

log(x) = x*log(4) - log(13)/2

Solve for x:

x = (log(13)/2)/log(4) - log(x)/log(4)

x = (log(13)/2 - log(x))/log(4)

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The 3-Systems of Equations Calculator is an online tool that provides the answer for the unknown variables after solving three equations with three different variables each utilizing a different approach.

To resolve equations involving the three variables x, y, and z, use the 3 systems of equations calculator. A group of three equations with three variables make up the three systems of equations. Three equations are entered, the equations are rearranged, and the values of x, y, and z are solved for.

This calculator can also calculate equations of the second and third degree, which result in complex solutions for the variables x, y, and z. Three actual solutions are provided by the calculator if the equation system is linear.

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Answer:

y = -4x + 2

Step-by-step explanation:

y-6=-4x+4

y = -4x - 4 + 6

y = -4x + 2

Answer:

The required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.

Step-by-step explanation:

Given that,

An oven is turned on and set to reach the desired temperature of 350 degrees Fahrenheit. The oven warms up at a constant rate. The oven’s temperature is 134 degrees Fahrenheit at 1 minute and it reaches its desired temperature at 5 minutes.

What are functions?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Here,

At time m = 1 min, temperature T = 134 °F

At time m = 5 min. temperature T = 450 °F

Slope of the equation M = 450 - 134 / 5 - 1

                                        = 216 / 4

                                        = 54

Linat relationship can be given as,

T - 134 = 54 (m - 1)

T = 54m -54 + 134

T = 54m + 80

Thus, the required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.

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Hope it helps :)

The coordinate of the intersection is (k, m*k + b).

A parallelogram is a four-sided shape with opposite sides that are parallel. The diagonal of a parallelogram cuts the shape into two congruent triangles. The coordinates of the intersection of the diagonal of a parallelogram with the vertical line of the parallelogram can be found by solving the equation of the line that forms the diagonal and the equation of the vertical line.

If the diagonal of the parallelogram is given by the equation y = mx + b, where m is the slope of the diagonal and b is the y-intercept, and the vertical line is given by the equation x = k, where k is the x-coordinate of the vertical line.

To find the x-coordinate of the intersection point, we can substitute x = k into the equation of the diagonal:

x = k

Then, we can substitute this value of x into the equation of the diagonal:

y = mx + b

This will give us the y-coordinate of the intersection point.

So, the coordinate of the intersection is (k, m*k + b)

Note: You need the equation of the diagonal and the equation of the vertical line to find the intersection point.

Therefore, The coordinate of the intersection is (k, m*k + b).

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x = k

Then, we can substitute this value of x into the equation of the diagonal:

y = mx + b

This will give us the y-coordinate of the intersection point.

So, the coordinate of the intersection is (k, m*k + b)

You need the equation of the diagonal and the equation of the vertical line to find the intersection point.

Therefore, The coordinate of the intersection is (k, m*k + b).

The mass when L = 0.6 is given as follows:

M = 68.57 kg.

The mass of the cube is modeled according to a proportional relationship, as follows:

M = kL.

In which k is the constant of proportionality.

The mass the cube is 40 kg when the length of its edge is 35 cm = 0.35 m, hence the constant is obtained as follows:

0.35k = 40

k = 40/0.35

k = 114.28.

Hence the mass when L is of 0.6 m is given as follows:

M = 114.28 x 0.6

M = 68.57 kg.

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