Question
Use the Quotient Rule of Logarithms to write log3 (10x) - log3 (2) as a single logarithm.

The true statements are

The side length of the transparent cube is given as

Length = 10 millimetres

The volume of the cube is calculated as

Volume = Length³

Substitute the known values in the above equation, so, we have the following representation

Volume =10³

Evaluate

Volume = 1000 cubic millimetres

1000 cubic millimetres and 30 cubic millimetres do not have the same value

So, the co-worker is incorrect.

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Answer: y=x−2 y = x − 2

Step-by-step explanation:

The transformed equation of  is  y = x³ is y =-1/7(x+8)³

Given that :

The equation of y=x^3 and Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis

Applying the given transformations, we have:

To have a vertical compression by a factor of 1/7, we need to multiply the function by 1/7. So, we have:

y=1/7x³

We must add 8 to x in order to have a horizontal shift of 8 units to the left. We thus have:

y=1/7(x+8)³

A reflection over the x-axis would be the final step, we need to multiply the function by −1. So, we have:

y= -1/7(x+8)³

Therefore, the transformed equation is y= -1/7(x+8)³

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The inverse function of the function f(x) = 2x - 4 will be x/2 +2.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

f(x) = 2x - 4

y = 2x - 4

So x = y +4 /2

x = y/2 +2

Now to get the inverse of the function  put the x value in y

So [tex]f^{-1}[/tex](x) = x/2 +2

Hence, inverse function will be x/2 +2.

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Answer:

The integers could be 8 and 4, just checked with a calculator

Reflection then translation are rigid transformation can map triangle ABC onto triangle Fed.

What is congruent?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.

Main body:

It has been given in the question that Δ ABC and ΔFED are congruent by SSS congruence theorem.

ΔFED is the picture image of ΔABC and slightly shifted towards left.

Therefore, we can tell about the transformations that if ΔABC is reflected on x-axis and translated towards left, it can map ΔFED.

Hence ,Option B is the answer.

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Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

Given that,

We have to find the missing reasons in the two column.

Given

AC bisects ∠DAB and CA bisects ∠DCB

Prove

ΔDAC≅ΔABC

Statement                                                          Reasons

1. AC bisects ∠DAB                                           Given

2. ∠DAC≅∠BAC                                              definition of angle bisects

3.AC≅AC                                                         reflexive property
4.CA bisects ∠DCB                                           given

5. ∠DCA≅∠BCA                                              definition of angle bisects

6. ΔDAC≅ΔABC                                               ASA postulate

Therefore, Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

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The total number of cartons needed more to pack small 15 cartons than 35 large cartons is108 cartons.

Division is defined as one of the four basic operations of arithmetic in mathematics.

The parameters for this question are:

Total number of cartons =2835

Number of small cartons needed = 15 cartons

Number of large cartons needed = 35 cartons

To package the orange juice in large cartons we need [tex]\frac{2835}{35} =81 cartons[/tex]

Also, to package 15 small cartons we need [tex]\frac{2835}{15} =189 cartons[/tex]

Number of more small cartons than large cartons is

Small cartons -large cartons

=189-81=108 more cartons.

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The greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1 is 2.

The given number are 96 and 120.

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

The factors of given number are

The factors for the number 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.

Therefore, the greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1 is 2.

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Answer:

156 cm³

Step-by-step explanation:

The solid is a prism with a trapezoid base.

volume = (area of base) × height

V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm

V = 156 cm³

Answer:

2x - 9

Step-by-step explanation:

x = unknown number

2 * x -9

2x - 9

Answer:

it depends im pretty sure that you mean y and x cord  so answer is 0 x 6 y

Step-by-step explanation:

or 0 X so width or y height 6 Y

Using the graph of the relationship, the missing values are:

x   | y    

2     6

4     12

6     18

Given the graph attached below where:

The graph shows the relationship between the number of gallons (x) and the cost in dollars (y).

For example, if an ordered pair on the graph is (2, 8), it means it would cost $8 for 2 gallons.

Thus, to find the respective values for each missing pair of values, trace the corresponding value on the graph that is given.

The complete table is therefore:

x   | y    

2     6

4     12

6     18

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=================================================

Work Shown:

[tex]A = P*e^{rt}\\\\A = 4000*e^{0.07*7}\\\\A \approx 6529.26487982264\\\\A \approx 6529.26[/tex]

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Explanation:

Let your calculator handle the constant 'e's value, rather than typing in the numbers 2.718... so you can get the most accuracy possible. It's like how many calculators have a [tex]\pi[/tex] button for similar reasoning. If your calculator doesn't have an 'e' button, then this should be sufficient

e = 2.71828182846

By the way, it's a bit odd how your teacher didn't require you to round to the nearest cent. Something like 6423.12590591 should round to 6423.13

The area of the path is 456 square feet

The formula for determining area of a rectangle is given as;

A = lw

Where;

Now, substitute the values into the formula, we have;

Area of the rectangle  = 40 × 70

Area of the rectangle = 2800 square feet    (1)

Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft

Area of rectangular garden with Path = 44 × 74

= 3256 square feet       (2)

Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet

Hence, the value is 456 square feet

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The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let the no. of nickels be N and no. of dimes be D.

∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)

Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)

Now multiply (i) by 5 we get 5N + 5D = 85...(iv)

Now subtracting (iv) from (iii) we get,

5D = 60.

D = 12 hence N = 5.

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Answer:

A trapezoid is isosceles if and only if its diagonals are congruent. So if we can prove that the bases are parallel and the diagonals are congruent, then we know the quadrilateral is an isosceles trapezoid, as Cool Math accurately states.

Step-by-step explanation:

Answer:

11 pizza rolls

6 chicken wings

Answer:

11 pizza Rolls and 6

Step-by-step explanation:

Answer:3/2

Step-by-step explanation:

3/8 divided by 1/4 is the same as multiplying 3/8 by 4/1

= 12/8

=3/2

The number in standard form will be 16 thousand 6 hundred.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (9 × 10) + (4 × 100) + (6 × 1,000) + (1 × 100) + (2 × 10) + (9 × (1,000 + 100 + 10)

Simplify the expression, then we have

⇒ (9 × 10) + (4 × 100) + (6 × 1,000) + (1 × 100) + (2 × 10) + (9 × (1,000 + 100 + 10)

⇒ [(9 + 2 + 9) × 10] + [(4 + 1 + 9) × 100] + [(6 + 9) × 1,000]

⇒ 15 × 1,000 + 14 × 100 + 20 × 10

⇒ 16 × 1,000 + 6 × 100

The number in standard form will be 16 thousand 6 hundred.

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Answer:

0.80

Step-by-step explanation:

The hundredth is 2 digits after the decimal.

Rounding 0.799, we want 0.xx

Look at the third digit, 9, meaning we round up.

However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.

We get 0.80

Answer:

I'm not sure but based on my work I would say option 2.

Hope this helps!

Step-by-step explanation:

The polynomial that is in standard form is: B. [tex]x^4 - 8x^2 - 16[/tex].

A polynomial that is expressed in standard form is given in such a way that the terms of the expression are written in ordered from from the term with the highest degree, to the term with the lowest degree. The constant comes last in a polynomial that is expressed in standard form.

5 - 2x is not expressed in standard form because it is not properly ordered. The constant needs to come last.

[tex]x^4 - 8x^2 - 16[/tex] is well ordered, therefore, it is a polynomial that is expressed in standard form.

[tex]5x^3 + 4x^4 - 3x + 1[/tex] is not well ordered. It is not in standard form.

The answer is therefore: B. [tex]x^4 - 8x^2 - 16[/tex].

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The equations are: line 2:- y = 4x-4, line 3:- y = -2x+3 and line 4:- y = 2x+1

The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Given are 4 lines,

For line 1:-

Since, we have only one point of this line and no information about slope, so we can not find its equation.

For line 2:-

Points are - (0, -4) and (1, 0)

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

Slope = 4/1 = 4

Solving for c,

-4 = 4*0 + c

c = -4

Equation will be,

y = 4x-4

Similarly,

For line 3:-

y = -2x+3

For line 4:-

y = 2x+1

Hence, The equations are: line 2:- y = 4x-4, line 3:- y = -2x+3 and line 4:- y = 2x+1

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1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].

We are given that polynomial [tex]$3 x^2+x-4$[/tex] is being divided by factor [tex]$(\mathrm{x}-1)$[/tex]

It is also said that when David perform the mathematical operation it gives remainder 0 .

Remainder 0 represents that divisor [tex]$(\mathrm{x}-1)$[/tex] is a factor polynomial [tex]$3 x^2+x-4$[/tex].

As x-1 is a factor of the given ploynomial, we can get one of the root of by setting it equal to 0 and solve for x.

Therefore,

x-1=0

Adding 1 on both sides, we get

[tex]$$\begin{aligned}& x-1+1=0+1 \\& x=1 .\end{aligned}$$[/tex]

Therefore, 1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

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Answer:

x = 4

y = 1

Step-by-step explanation:

x + 3y = 7 --> Eq1

4x - y = 15 --> Eq2

Find x in term of y using Eq1

x = 7 - 3y

Substitute x in Eq2

4(7-3y) -y = 15

28 - 12y - y = 15

-12y-y = 15 - 28

-13y = -13

y = -13/-13

y = 1

Find x

x = 7-3(1) = 4

If you have to solve for x first

Find y in term of x using Eq 2

y = 4x - 15

Substitute y in Eq 1

x + 3(4x -15) = 7

x + 12x - 45 = 7

x + 12x = 7 + 45

13x = 52

x = 52/13

x = 4

Find y

y = 4(4) -15 = 16 - 15 = 1

We prooved the paragraph proof of Theorem 3.8 that if two lines are perpendicular to the same line, then they are parallel to each other.

In the given question we have to explain the a paragraph proof of Theorem 3.8.

Let the lines that cross line a be m and n. Let m be parallel to a. As a result, the intersection of m and a produces four 90° angles.

Let n be parallel to a. This indicates that each of the four angles created by the intersection of n and an is 90 degrees.

The same-side internal angles (between lines m and n) are also congruent because all of the angles are congruent. The lines are parallel if two internal angles on the same side are congruent.

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The right question is:

Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

The cost of the car is 500000 and by selling it with an 8% gain he earned 40000.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A car dealer gained 40,000 on a sale which is 8% profit.

Assuming the cost of the car to be x.

∴ (108/100)x - x = 40000.

1.08x - x = 40000.

0.08x = 40000.

x = 40000/0.08.

x = 500000

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The amount of paper required to make the model is 94.2 square cm

The given parameters in the question are

Slant height = 7 cm

Diameter = 6 cm

This means that

Radius = Diameter/2 = 6 cm/2

So, we have

Radius = 3 cm

The amount of paper required to make the model is then calculated as

A = πr(r + l)

So, we have

A = 3.14 * 3 * (3 + 7)

Evaluate

A = 94.2

Hence, the amount needed is 94.2 square cm

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Answer:

change 5 weeks to days(5*7)-35days

then convert the days to seconds

35*86400/10*86400

answer 7/2