a) Rotation, then reflectionb) Reflection, then rotation c) Reflection, then translationd) Rotation, then translation

Answer:

294 grams

Explanation:

The amount of radioactive material left after t hours given that the half-life is to hours is

Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives

which is our answer!

Hence, the amount of radioactive copper left after 9 hours is 294 grams.

Answer:

B. Emergency fund.

Step-by-step explanation:

d) n + (n +1) = 67

1) Let's call the first number as n, and its consecutive as n +1

Then we can write:

n + (n +1) = 67

n +n +1 = 67

2n +1 = 67

2n = 66

n= 33

and n+1 = 34

2) Hence, the answer is n + (n +1) = 67

Given:

The triangle ADC is formed by reflecting the triangle ABC across the line segment AC

So, the triangles ABC and ADC are congruent

The area of the triangle ADC = Area of the triangle ABC

The area of the triangle = 1/2 * base * height

Base = AC = 4 units

Height = BE = 3 units

So, the area will be as follows:

So, the answer will be:

Area of the triangle ADC is 6 square units

Whereas working with laws of exponents, when splitting the exponential equations with the same base, the exponents ought to be subtracted.

Basically, the Quotient of Powers rules is used to decrease the number of terms when parts like terms with exponents. In order to get the solution, just remove the exponents while dividing the terms with the same base, it is applicable to exponents with the same bases. when powers are multiplied,  for two whole numbers of the same bases the exponents are added, whereas when powers are divided for two whole numbers of the same bases,  exponents are subtracted. The zero exponent rule basically states that when any number is raised to the power of zero it results in 1.

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We will determine the final price as follows:

So, the final price is approximately $12.74.

Hello!

So, we are given the following to solve:

                      [tex]7\frac{1}{5} -6\frac{2}{5}[/tex]

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form of Solution:

               [tex]\frac{4}{5}[/tex]

Hence, the correct choice is B. Hope this helps!

Answer:

B. 4/5

Step-by-step explanation:

7 1/5= to 36/5

6 2/5= to 32/5

subtract both numbers on top and keep the bottom, which equals to 4/5

Using the elimination method,  the value of A and B must 3 and 4 respectively to eliminate x in the equation. The value of A and B must be 3 and 7 respectively to eliminate y.

System of equation can be solved using elimination method, substitution method of graphical method.

But we are asked to use elimination method.

Therefore, the system of equation are as follows:

Equation 1: A [-4x + 7y = 4]

Equation 2: B [3x - 3y = 6]

Therefore,

If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 4.

If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 7.

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Answer:

17/8 or 2 and 1/8 cups

Step-by-step explanation:

turn the 8 and 1/2 into one fraction :

17/2

then divide that by 4:

17/8

Solution

The formula for arc length is;

The solution of the given equation w.r.t m is m = 3 ,i.e., option A

With one exception, algebraic equations are essentially algebraic expressions.

An = sign is required in all algebraic equations.

No matter what kind of equation it is, all equations use the = sign.

The next topic is algebraic expression, which lacks the operators =,,, >, and.

To put it simply, there is no comparison between two terms in an algebraic statement.

Algebraic expressions frequently use terms like polynomial and square root.

So you now recognize the distinction between the two?

1) An algebraic equation has the symbol =, and 2) an algebraic expression lacks any comparison symbols (such as > and =).

As per the question:

[tex]6\frac{1}{9} + 3\frac{1}{3} =28\frac{1}{3}[/tex]

55/9 + 10/3 = 85/3

(55m+30m)/9 = 85/3

85m/9 = 85/3

85m = (85*9)/3

85m = 85*3

m = (85*3)/85

∴ m = 3

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Answer: 695.30

Step-by-step explanation: We know that 634.8 is what the monthly mortgage is, then we use the value of $726 and divide it by 12 which represents the 12 months in a year. So 726 ÷ 12 = 60.5 therefore monthly he will additionally need to pay that amount. I don't think the annual real estate taxes are going to be used for this problem. So after this, we do the following equation. 634.8 + 60.5 = 695.3. We round this value to the nearest cent and we get 695.30. When the digit to the right is less than 5 we round toward 0... 695.3 was rounded down toward zero to 695.30

The slope is defined as rise/run - in other words, for every step you take horizontally, how many steps you should take vertically to get to a point on the same line.

In our case, the ladder rises 20 feet for every horizontal change of 4 feet; therefore, the slope is

dividing 30 ft by 4 ft gives 5; therefore,

Hence, the correct answer to choose is A. 5.

The diameter of the Earth is 11.3 times less than the diameter of the Jupiter

Fractions are written as a ratio of two integers. Given the following parameters;

Diameter of Jupiter = 1.43•10^5km

Diameter of Earth = 1.27 * 10^4km

Find the ratio

Ratio = Jupiter/Earth

Ratio = 1.43•10^5/1.27*10^4

Ratio = 1.13 * 10^1

Ratio = 11.3

Jupiter = 11.3 of Earth

This shows that the diameter of Jupiter if 11.3 times greater than Earth.

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Answer:

D

Step-by-step explanation:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since line has slope of 2, equation is y = 2x + c.

Substitute (-8, 1) into the equation to find c

1 = 2(-8) + c

c = 17

Hence, equation of line is y = 2x + 17.

The correct answer is [D]

Hence, the equation of line is y = 2x + 17.

Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.

The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical.

Y = mx + c, where m is the slope and c is the y-intercept, is the equation for a line.

Since the line has slope of 2, equation is y = 2x + c.

Substitute (-8, 1) into equation to find c

1 = 2(-8) + c

c = 17

Hence, the equation of line is y = 2x + 17.

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Answer:

The total surface area is;

Explanation:

Given the square pyramid as show in the attached image.

The total surface area is the sum of the area of the base square and the area of the four triangles.

Given;

substituting the given values;

Therefore, the total surface area is;

To find out the unit rate

Divide cups of sugar by the teaspoon of vanilla

so

The answer is 1/3

Option A

Since the scaling factor of the dilation (0.5) is fewer than 1, it shrinks (make smaller) the triangle around the origin (zero). Intuitively, the dilation is getting the points of the triangle closer to zero (in a way that preserves the shape of the triangle).

Formally, to know the coordinates of a point of the triangle after the dilation, we just need to multiply the original coordinates of the point by the scaling factor (this works for the dilation is around zero).

The original coordinates of D are

Multiplying them by the scale factor, we get

The coordinates of D after the given dilation is

The expression we have is:

We need to compare this equation of our parabola, with the general equation of a parabola in vertex form:

Where (h,k) is the vertex of the parabola, and a indicates if the parabola opens up or opens down (if a is positive the parabola opens up, and if a is negative the parabola opens down).

We take our equation:

And we arrange the terms so that it looks like the vertex form:

And we can find the values of a, h, and k:

We only need h and k for the vertex:

Answer: the vertex is at (0,-7)

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.

Exponent rules include: Rule of the product of powers: When multiplying like bases, add the powers together. Rule of the quotient of powers: When splitting like bases, take the powers out. Power of powers rule: When increasing a power by another exponent, multiply all the powers together.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Let the value be 2048

[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex]

simplifying the above expression we get

[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3=512 \\[/tex]

[tex]$&=512\left(\frac{1}{2^{-1}}\right)^2[/tex]

By using exponent rule, we get

[tex]$&\left(\frac{1}{2^{-1}}\right)^2=\frac{1^2}{\left(2^{-1}\right)^2} \\[/tex]

[tex]$&=512 \cdot \frac{1^2}{\left(2^{-1}\right)^2}[/tex]

1² = 1

[tex]$&=512 \cdot \frac{1}{\left(2^{-1}\right)^2}[/tex]

[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]

[tex]$=512 \cdot \frac{1}{\frac{1}{4}}$$[/tex]

[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]

[tex]$=512 \cdot \frac{1}{\frac{1}{4}}[/tex]

[tex]$&\frac{1}{\frac{1}{4}}=4 \\\pi[/tex]

= 512 × 4

= 2048

By simplifying the expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.

Therefore, the correct answer is option (b).

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The probability a single event A occurs is:

The probability P two consecutive events A and B occurs is:

So, let's consider the probability of the first event: getting tails.

Favorable outcomes: Tail

Number of favorable outcomes: 1

Total outcomes: Tail, Head

Number of total outcomes: 2

So, the probability of getting a tail is:

So, let's consider the probability of the second event: getting tails in the second time.

Favorable outcomes: Tail

Number of favorable outcomes: 1

Total outcomes: Tail, Head

Number of total outcomes: 2

So, the probability of getting a tail is:

Finally, let's calculate the probability of getting a tail twice.

Answer: The probability is 1/4.

The width of the border will be 8 inches.

In the given question, it is stated that a rectangular board has dimensions of 18*14 around which a person has to put a border of shells. If there are enough shells for the border of an area of 320 square inches, we need to find out the Width of the border.

Firstly, we know the Area of Rectangle is l*b => Length*Breadth

So, now we calculate the area of the board with dimensions l = 18 and b = 14

=> A₁ = l*b

=> A₁ = 18*14

=> A₁ = 252 square inches

We get the Area of the Board as 252 Square inches.

Now, there are shells enough to cover a border area of 320 square inches.

So, the Board and Border area will be A₁ + A, where A₁ and A are the areas of the Board and border respectively.

So, Total Area = 252 + 320

Total = 572 Square inches.

Now, let 'w' be the width of the border. Then the dimensions for the board will be

l = (18 + w)

b = (14 + w)

Using the formula for the Area of the rectangle, we get

=> Total = l * b

=> Total = (18 + w)*(14 + w)

=> 572 = w² + 32m + 252

=> w² + 32m - 320 = 0

=> w² + 40w -8w -320

=> w(w + 40) -8(w + 40)

=> (w+40) (w-8)

We get factors as w = -40 and 8

Since Width can not be negative quantity, width w will be 8 inches.

Hence, the width will be 8 inches for the border.

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The given equation is

We will solve it in this way

For the 1st equation

Subtract 7 from each side

Subtract 4x from both sides

For the 2nd equation

Subtract 3x from both sides

Divide both sides by -7

The solutions are

7, -1

The answer should be B

We get that the distance is

so the answer is 5

Answer:

80,200

Step-by-step explanation:

There is a formula for the sum of a series of numbers from a_1 to a_n.

S = (a_n * a_n+1)/2

This formula means: multiply the last number of the series by what would be the next number, and divide by 2.

The last number you have is 400. The next number would be 401.

Multiply 400 by 401 and divide by 2. That is the sum of the 400 numbers.

S = (401 * 402)/2

S = 160400/2

S = 80200

Answer: The sum is 80,200

Here's a way to understand the formula.

You are adding 400 numbers, from 1 to 400.

Write the first 200 numbers on a line:

1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   ...   198   199   200

Now write the next 200 numbers, from 201 to 400 under these numbers, but start from 400 and go down 1 each number to the right.

You end up with these two lines:

1        2       3        4       5       6        7        8      9        ...     198   199   200

400  399   398   397   396   395   394   393  392    ...    203  202   201

Now add every two numbers in the same column.

1        2       3        4       5       6        7        8      9        ...     198   199   200

400  399   398   397   396   395   394   393  392    ...    203  202   201

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

401   401   401    401    401    401    401    401   401     ...    401   401   401

Now you have 200 times the number 401.

200 * 401 = 80,200

Writing the given trigonometry expression: cos(2 tan inverse (x)) as algebraic expression gives

Data given in the question are as follows:

cos(2 tan inverse (x))

Using trigonometry (double angle formula)

cos 2x = 1 - 2sin² x

when x = tan inverse (x)

cos(2 tan inverse (x))  = 1 - 2sin² tan inverse (x)        (1)

cos² x + sin² x = 1

cos² x = 1 - sin² x

cos x = √(1 - sin x)

tan x = sin x / cos x

[tex]tan x = \frac{sinx }{\sqrt{1-sin^{2}x } }[/tex]

squaring all parts of the trigonometry expression and clearing the fraction

[tex]tan^{2}x = \frac{sin^{2} x }{1-sin^{2}x }[/tex]

[tex](tan^{2}x) (1-sin^2x) = sin^2x[/tex]

[tex]tan^{2}x-tan^{2}xsin^2x = sin^2x[/tex]

[tex]tan^{2}x = sin^2x+tan^{2}xsin^2x[/tex]

[tex]tan^{2}x = sin^2x(1+tan^{2}x)[/tex]

[tex]sin^2x = \frac{tan^{2}x}{(1+tan^{2}x)}[/tex]

since tan (tan inverse) (x) = x

[tex]1 - 2sin^2 tan^{-1} (x) = 1 - 2x^2 / (1 + x^2)[/tex]

[tex]=\frac{ 1 + x^2 -2x^2}{1+x^2}[/tex]

[tex]=\frac{ 1 -x^2}{1+x^2}[/tex]

Therefore trigonometry expression cos(2 tan inverse (x)) gives an algebraic expression in the form (1-x²) / (1+x²)

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Given the functions

The graph of the given functions

From the graph of the functions above, it can be seen that each of the functions have the same domain

The answer is the first option.

solve each of the expressions

the correct operator is =.

The most appropriate choice for the similarity of figures will be given by:

So,

(A) HIJK∼WXYZ [Given].

(B) The two triangles are similar [Given].

(C) 5cm on the drawing represented 2 miles on the ground.

Let 22.5 cm on the drawing represent x miles on the ground.

The problem:

x = 9 miles22.5 cm on the drawing represented 9 miles on the ground.

Therefore, the most appropriate choice for the similarity of figures will be given by:

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