Rotation: 180° about the origin

Answer: 10,000 or 10^4

Step-by-step explanation: I will assume in the problem that the logarithm is of base-10. We can therefore rewrite the equation in words as 10^4=x. The general form of a logarithm is log base y of x=z. This can be rewritten as y^z=x. We are doing the same thing here. We know that 10^4 is 10,000 so that is our answer.

Hope this helps!

For practice here are some problems (assume all logarithms are our base 10): log x = 3, log x = 1.

The total area is given as 160 sq feet. The total yard that is to be purchased is 18 yards

To get the area of the room we would first have to find the area of the sides.

We can call 1 of the areas S1.

The length l1 = 13

The width w1 = 16

area =

s1 = 13 * 16

We have

s2 with

l2 = 6

w2 = 8

then the area

s2 = 6 * 8

S1 - s2

= 208 - 48 =

160

1 square yard = 9 square foot

17.7778 = 160 square feet

Juan has to purchase approximately 18 yards

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I like big black oliy men

The graph that models the situation is on the image at the end, we can see that she scored 8 2-pointers and 1 3-pointer.

Let's define the variables:

x = number of 2-points that she scored.

y = number of 3-points that she scored.

We know that she scored 19 points, then we have the equation:

2x + 3y = 19

And we also know that she scored a total of9 baskets, so we have other equation:

x + y  =9

Then we have a system of equations:

2x + 3y = 19

x + y = 9

The graph of that system is the graph that models the situation, it is shown at the end of the answer.

There you can see that the solution is (8, 1)

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The solution is,  Chun is correct.

The angle bisector divides the sides of the triangle proportionally. Any proportion that is written should equate ratios of corresponding sides.

here, we have,

Chun's proportion correctly relates the top-side measures to their corresponding bottom-side measures:

 top short : bottom short = top long : bottom long

 5 / 8 = 15 / x

Traci's error is that she mixes top-side and bottom-side measures. Her incorrect relation is ...

 top short : bottom long = bottom short : top long

She has used top:bottom for short measures and bottom:top for long measures. This mixing will give Traci an incorrect solution.

Chun's proportion correctly gives x=24.

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The inequality represented by the given number line is expressed as;

-3 ≤ x < 1

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Now, a square bracket at one end of an interval indicates that the interval is closed at that end (i.e., the number adjacent to the opening or closing square bracket is included in the interval).

Thus, the inequality here is expressed as;

-3 ≤ x < 1

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Answer:

Step-by-step explanation:

Let's use the following variables:

Let F be the number of sections of Finite Math

Let A be the number of sections of Applied Calculus

Let C be the number of sections of Computer Methods

We can create a system of equations based on the given information:

F + A + C = 7 (the college wishes to offer a total of seven sections)

40F + 60A + 290C = 298000 (the college wishes to bring in $298,000 in revenues)

40F + 40A + 10C = 220 (the college wishes to accommodate 220 students)

We can solve this system of equations using any method we prefer. Here's one possible way:

Multiply the third equation by 10 to get:

400F + 400A + 100C = 2200

Subtract the third equation from the second equation to eliminate C:

20A + 280C = 76000

Multiply the first equation by 40 and subtract it from the previous equation to eliminate A:

240C = 76000 - 1600

Solve for C:

C = 290

Substitute C = 290 into the third equation to solve for F:

40F + 40A + 10(290) = 220

40F + 40A = -2680

F + A = -67

Substitute C = 290 and F + A = -67 into the first equation to solve for A:

A = 10

Substitute A = 10 and C = 290 into the first equation to solve for F:

F = -3

We have a problem here: we obtained a negative number of sections for Finite Math, which is impossible. This means that the original system of equations is inconsistent, and there is no solution that satisfies all the requirements.

Therefore, the college cannot offer the desired number of sections while accommodating the desired number of students and revenue. Some adjustments need to be made, such as changing the number of students per section or the tuition fees.

Answer: 168

Step-by-step explanation:  

The equation would be C = 1.25w, where c is the total cost of w pounds of oranges do not include units or a dollar sign.

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

The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

We are given that oranges are being sold for $ 1.25 per pound.

The equation would be as;

C = 1.25w

where c is the total cost of w pounds of oranges and does not include units or a dollar sign.

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Correct order of steps for constructing an angle bisector of ∠DEF using only a straightedge and compass is option C.

A angle bisector is a line that bisects an angle into two equal angles. A bisector means dividing a shape or object into two equal parts. When we draw a ray that bisects an angle into two equal parts of equal magnitude, it is called a bisector.

Given,

Compass and straightedge to draw angle bisector of ∠DEF

Steps to draw angle bisector are:

1. Draw a circle with a radius less than DE and center E, and label

the points of intersection G and H.

2. Draw a line from point G to point H.

3. Draw a circle with radius GH and center G and another circle

with radius GH and center H, and then draw an equilateral triangle.

4. Use a straightedge to connect E to the rightmost vertex of the

equilateral triangle.

Hence, option C describes correct order of constructing an angle bisector of ∠DEF using only a straightedge and compass.

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The angles of the triangle will be 5 °, 45 °, and 130 °.

The triangle is a two-dimensional geometric object with three straight sides and three angles. The lengths of the triangle's three sides can differ from the third side (isosceles triangle), be equal (equilateral triangle), or be any combination of the three (scalene triangle).

The sum of the angles in a triangle is always 180 degrees; the opposite angle of the longest side is the largest, and the opposite angle of the shortest side is the smallest.

Now,

Let x be the common factor that multiplies the ratio of 1:9:26. Then, the measures of the angles can be expressed as x, 9x, and 26x.

Since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:

x + 9x + 26x = 180°

Simplifying the equation, we get:

36x = 180

Dividing both sides by 36, we get:

x = 5

Therefore, the measures of the angles are:

x = 5 degrees (the smallest angle)

9x = 45 degrees

26x = 130 degrees (the largest angle)

So the angles of the triangle are 5 degrees, 45 degrees, and 130 degrees.

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Using the roots of the given equation, x²+x-6=0, the value of the expression, 2β²-3α², is -19

From the question, we are to evaluate the given expression.

In order, to evaluate the expression, we will solve the given quadratic equation

To solve x²+x-6=0, we can use factoring method

Solving the equation

x² + x - 6 = 0

(x + 3)(x - 2) = 0

Setting each factor equal to zero, we get:

x + 3 = 0 or x - 2 = 0

Solving for x in each case, we get:

x = -3 or x = 2

So the solutions to the equation are x=-3 and x=2.

Since α<β

Thus,

α = -3 and β = 2

Then,

2β²-3α²

= 2(2)² -3(-3)²

= 2(4) -3(9)

= 8 - 27

= -19

Hence, the value is -9

Here is the correct question:

If α and β are the roots of the equation x²+x-6=0, where α<β, evaluate 2β²-3α²

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Answer:

Step-by-step explanation:

triangle-

b+h/2=a

5x6/2=30

rectangle-

2.5x12=30

area of drawing-

30+30=60

answer:60cm^2

For the value the functions F(x)=G(x) is here no solution.

In mathematics, function is an expression that defines a relationship between one independent variable and another dependent variable.

Given that F(x)= abs(3x+2)-6 =| 3x+2|-6

                 G(x)= 3x-5

for F(x)=G(x)

  |3x+2|-6=3x-5

  3x+2-6=3x-5

    3x-4=3x-5

Hence no solution.

The graph is given below.

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For the value the functions F(x)=G(x) is here no solution.

In mathematics, function is an expression that defines a relationship between one independent variable and another dependent variable.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one other object f if the object x is present in the set of inputs (referred to as the domain) (x) among the range of potential outcomes (called the codomain).

Given that F(x)= abs(3x+2)-6 =| 3x+2|-6

                G(x)= 3x-5

for F(x)=G(x)

 |3x+2|-6=3x-5

 3x+2-6=3x-5

   3x-4=3x-5

Hence no solution.

The graph is given below.

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Answer: Krysti's mistake was ordering only 12 small T-shirts when she should have ordered more. To figure out how many small T-shirts she should have ordered, we can start by finding out how many classmates wanted small T-shirts:

60% of 25 classmates = 0.60 x 25 = 15 classmates

So, 15 classmates wanted small T-shirts. If Krysti had ordered one small T-shirt for each of these classmates, she would have needed 15 small T-shirts. However, Krysti only ordered 12 small T-shirts, which means she is short by 3 shirts.

To avoid this mistake, Krysti should have double-checked her calculations and made sure that the number of small T-shirts she ordered matched the number of classmates who wanted small T-shirts.

Step-by-step explanation:

X = 5 is the other zeros of polynomial.

What is a polynomial, simply put?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).  

                                       The different types of polynomial equations are - linear equations, quadratic equations, cubic equations, and biquadratic equations. The equations formed with variables, exponents and coefficients are called as polynomial equations.

   g(x) = x³ - x² - 34x + 70

       x = 5

 g(5) = 5³ - 5² - 34 * 5 + 70

         = 125 - 25 -  170 + 70

          = 195  - 195

          = 0

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Answer:

2n^2

Step-by-step explanation:
The is a Quadratic sequence:

First difference is 6 10 14 18
Second difference is 4 4 4 4
Divide the second term by 2 which is 2n^2

Aaron running speed is 2 3/4 miles per hour

What is Speed?

Speed is the ratio of distance to the time in which the distance was covered. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s, km/hr, miles/hr and so on. It is also a measurement of how fast an object is moving through a path.

Where the formula is Speed = Distance/Time

Where Distance covered = 1/8 miles

Time taken = 1/22 of an hour

Speed = (1/8)/(1/22)

Speed = 1/8 *22/1

Speed = 22/8

Speed = 11/4

Spees = 2 3/4 miles per hour

Therefore, Aaron running speed is 2 3/4 miles per hour

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Therefore, the scale factor used in the drawing is 4000/3.

In mathematics, a factor refers to a number or algebraic expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers can be multiplied by another whole number to produce 12 (1 × 12, 2 × 6, 3 × 4). Factors play an important role in many areas of mathematics, including algebra, number theory, and geometry, and are used to simplify expressions, solve equations, and factorize polynomials.

Given by the question.

The scale factor is the ratio of the length of an object on the drawing to the actual length of the object.

Since 6 millimeters on the drawing represents 8 meters in reality, the scale factor can be expressed as:

Scale factor = Actual length / Length on drawing

Scale factor = 8 meters / (6 millimeters)

To simplify this fraction, we need to convert meters to millimeters by multiplying by 1000:

Scale factor = (8 meters * 1000) / 6 millimeters

Scale factor = 8000 / 6

The fraction cannot be simplified further, so the scale factor is:

Scale factor = 4000/3

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Therefore, the combined volume of the two rectangular prisms is 132 cubic units.

2-D enclosed shapes with four sides, four corners, and four right angles are called rectangles. A rectangle has two equal and parallel opposite sides.

To determine the combined volume of the two rectangular prisms shown in the diagram, we need to find the sum of their individual volumes. The volume of a rectangular prism is given by the formula:

Volume = length x width x height

In the diagram, we can see that the first rectangular prism has a length of 5 units, a width of 3 units, and a height of 4 units. The second rectangular prism has a length of 6 units, a width of 4 units, and a height of 3 units.

To find the volume of the first rectangular prism, we can use the formula:

Volume of first prism = length x width x height

Volume of first prism = 5 units x 3 units x 4 units

Volume of first prism = 60 cubic units

To find the volume of the second rectangular prism, we can use the same formula:

Volume of second prism = length x width x height

Volume of second prism = 6 units x 4 units x 3 units

Volume of second prism = 72 cubic units

Finally, to find the combined volume of the two prisms, we just need to add their individual volumes:

Combined volume = Volume of first prism + Volume of second prism

Combined volume = 60 cubic units + 72 cubic units

Combined volume = 132 cubic units

Therefore, the combined volume of the two rectangular prisms is 132 cubic units.

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Answer:333

Step-by-step explanation:53533535

In answering the question above, the solution is If a/b = 1/4 and c/d = 1/3, fraction then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are stated in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You may assess it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a whole number or object.

Let's start by decomposing { into two fractions:

[tex]{ = a/b + c/d\\\\{ = (ad + bc)/bd[/tex]

If [tex]a/b = 1/2 and c/d = 1/3, then ad + bc = (1/2)(bd/2) + (1/3)(bd/3) = bd/3 + bd/6 = 3bd/6 + bd/6 = 4bd/6 = 2/3,[/tex] which works.

If [tex]a/b = 1/2 and c/d = 1/4, then ad + bc = (1/2)(bd/2) + (1/4)(bd/4) = bd/4 + bd/8 = 2bd/8 + bd/8 = 3bd/8,[/tex] which doesn't work.

If [tex]a/b = 1/2 and c/d = 1/5, then ad + bc = (1/2)(bd/2) + (1/5)(bd/5) = bd/4 + bd/25 = 25bd/100 + 4bd/100 = 29bd/100[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/4, then ad + bc = (1/3)(bd/3) + (1/4)(bd/4) = bd/9 + bd/16[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/5, then ad + bc = (1/3)(bd/3) + (1/5)(bd/5) = bd/9 + bd/25,[/tex] which doesn't work.

If a/b = 1/4 and c/d = 1/3, then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

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Answer:

Step-by-step explanation:

Mark decompose 5/6 into three fractions using fractions : 1/3, 5/18, 2/9

What is fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given, fraction

5/6

Multiplying 3 with both numerator and denominator

15/18

= (6 + 5 + 4)/18

= 6/18 + 5/18 + 4/18

= 1/3 + 5/18 + 2/9

Hence, 1/3, 5/18, 2/9 are fractions Mark used to decompose 5/6.

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Answer:

x = ± √((y + 2)/4)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y.

Steps to find the inverse of y = 4x^2 - 2:

Replace y with x and x with y:

x = 4y^2 - 2

Solve for y:

x + 2 = 4y^2

(x + 2)/4 = y^2

± √((x + 2)/4) = y

Note that we have a ± sign because the square root of a positive number can have two values, one positive and one negative.

Therefore, the inverse of y = 4x^2 - 2 is:

x = ± √((y + 2)/4)

Answer:

y=±([tex]\sqrt{x+2}/2[/tex])

Step-by-step explanation:

The missing length the right triangle to the nearest tenth is 8.8 units.

The figure in the image is a right traingle.

To solve for the second leg of the right triangle given the first leg and hypotenuse, we can use the Pythagorean theorem.

It states that the sum of the squares of the two legs is equal to the square of the hypotenuse.

a² + b² = c²

Let's denote the second leg by 'b'. Then we have:

2² + b² = 9³

Simplifying the equation:

4 + b² = 81

Subtracting 4 from both sides:

4 - 4 + b² = 81 - 4

b² = 77

Taking the square root of both sides:

b = √77

b = 8.8 units

Therefore, the second leg of the right triangle is 8.8 unit.

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The value of the function at x = -10, x = 2, and x = 5 will be 20,201, 17, and 1,226, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 2x⁴ + x² - 10x + 1

At x = - 10, the value of the function is given as,

f(-10) = 2(-10)⁴ + (-10)² - 10(-10) + 1

f(-10) = 20,201

At x = 2, the value of the function is given as,

f(2) = 2(2)⁴ + (2)² - 10(2) + 1

f(2) = 17

At x = 5, the value of the function is given as,

f(5) = 2(5)⁴ + (5)² - 10(5) + 1

f(5) = 1,226

The value of the function at x = -10, x = 2, and x = 5 will be 20,201, 17, and 1,226, respectively.

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Answer:

74

Step-by-step explanation:

-6 (-5 - 4) - 4(-3 - 2)

30 + 24 + 12 + 8 = 74

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money accumulated, P is the principal (initial) amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this problem, we want to find the principal amount P that will accumulate to $12,000 in 3 years at an annual interest rate of 6% compounded monthly. First, we need to convert the annual interest rate to a monthly rate:

r = 0.06/12 = 0.005

Next, we can substitute the given values into the formula and solve for P:

12,000 = P(1 + 0.005/12)^(12*3)

12,000 = P(1.005)^36

P = 12,000/(1.005)^36

P ≈ $9,883.86

Therefore, the amount of money that should be deposited today is approximately $9,883.86.

Step-by-step explanation:

The answer for the given polynomial function are given below:

Real zero of the polynomial : x= -7

                                           x= 7/2

                                           x= 7

Not a real zero of the polynomial : x= -49

                                                    x= -7/2

                                                    x= 49

It is a function of a single independent variable involving only non - negative integer powers. For example 5x+7.

What is zero of polynomial?

Zero of polynomial  are the points for which the polynomial becomes zero as a whole.

Given polynomial function is P(x)= (2x-7)(x²- 49)

For the zeros of the polynomial we need to take P(x)=0

                      (2x-7)(x² -49)=0

              Either (2x-7)=0 or (x² -49)=0

                   If, 2x-7=0            

                      2x=7

                       x=7/2

         If, x² -49=0

             x² =49

             x=±√49

             x=± 7

Hence, x= -7, 7/2, 7

so the real zeros of the polynomial are -7, 7/2, 7.

rest of the numbers are not the real zeros of the polynomial.

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No, -(p « › q) and p «> -q are not logically equivalent.

When two logical assertions have the same truth value for all conceivable truth value assignments to their constituent propositions, the two statements are said to be logically equivalent. In other words, two assertions are comparable logically if and only if all feasible permutations of the truth values of their component propositions are equal.

First, let's rewrite the statements using the standard logical operators of negation, conjunction, and implication:

-(p « › q) is equivalent to ¬(p ∧ ¬q)

p «> -q is equivalent to ¬p → ¬¬q, which simplifies to p → q

Now, we can construct a truth table with columns for p, q, ¬(p ∧ ¬q), and p → q:

p |      q |   ¬(p ∧ ¬q)    |    p → q

--|----------|------------------|-----

T        T          F               T

T        F          T               F

F       T           T               T

F       F           T               T

We can see that the truth values of the two statements are not always the same.

For example, when p is true and q is false, ¬(p ∧ ¬q) is true and p → q is false.

Therefore, -(p « › q) and p «> -q are not logically equivalent.

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