Express 8^-4 using a positive exponents

Answer:

3. 4 cm apart

4. 12 feet

Step-by-step explanation:

3. since the scale is every 1cm is 14 miles than to find 56 miles on a map you should divide 56/14 which would equal 4cm.

4. since the scale is every 1 inch is 6 feet and you have to find how long a motorcycle is if it was 2 in on a diagram, then you should multiple 6 by 2 which would equal 12 feet

hope this helps

Answer:

Step-by-step explanation:

Whole numbers are numbers such as 0, 1, 2, 3, 4. Irrational numbers are numbers that cannot be represented as a ratio, such as \(\sqrt{2}\). The first one would be false.

Rational numbers are numbers that can be represented as a ratio, like \(\frac{4}{5}\) or \(\frac{2}{1}\). Because 4/5 is not a whole number but is a rational number, the second one would be true.

Irrational numbers are numbers that cannot be represented as a ratio. Because integers can be represented as a ratio, since integers are numbers like -2, -1, 0, 1, 2, etc, all irrational numbers are not integers and, therefore, the third one is false.

Using the definition of rational numbers and integers from responses two and three, respectively, this fourth one is false.  

By using the concept of number line, it can be calculated that

a) g is a function

b) g(5) = 3 means after 5 flips, the person is at '3' on the number line

c) Probability that g(3) = 0 is zero

What is a number line?

All the real numbers, integers, fractions can be pictorially represented with the help of a line. The line is known as number line.

a) Here, g represents the position after the nth flip

After n flips, a person stands at only one position on the number line, not more than one. So every point on the domain has unique image. So g is a function.

b) g(5) = 3 means after 5 flips, the person is at '3' on the number line

c) The person is initially standing at zero. To move to zero position, even number of flips have to be made. But 3 is not an even number. So probability that g(3) = 0 is zero

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By definition, a Perfect square trinomial has the following form:

Perfect square trinomials can be expressed in Squared-binomial form, as following:

In this case, you know that the first term of the Perfect square trinomial Tia wrote on the board, is:

And the last term is:

Then you can identify that:

Solving for "a", you get:

Notice that:

Solving for "b", you get:

Knowing "a" and "b", you can write the following Squared-binomial:

And determine that the missing term is:

Therefore, the missing value is not a Perfect square, because it is not obtained by multiplying two equal Integers.

The answer is: Option B.

The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.\) Option A

The vertex form of a quadratic function is given by\(f(x) = a(x - h)^2 + k\) where (h, k) represents the coordinates of the vertex.

In the given quadratic function \(f(x) = x^2 - 8x - 4\), we can rewrite it in the vertex form by completing the square:

\(f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20\)

From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).

The term\((x - 4)^2\) tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.

The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4\) is  \((x - 4)^2 - 20.\)

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42 1/2 ( aka 85/2) as a percent is 4250%.

To convert a percentage to a fraction, we can write the percentage as a fraction with a denominator of 100 and then simplify.

42 1/2 % can be written as:

42 1/2 % = 42.5/100

To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2.

42.5/100 = (42.5 ÷ 2) / (100 ÷ 2) = 21.25/50

Next, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25.

21.25/50 = (21.25 ÷ 25) / (50 ÷ 25) = 17/40

Therefore, 42 1/2 % is equal to 17/40 as a fraction in its simplest form.

Brainliest?

Answer:

60

Step-by-step explanation:

The computation of the third quartile is given below:

The third quartile Q3 is

= 3(n + 1)÷ 4

= 3 (24 + 1) ÷ 4

= 75 ÷ 4

= 18.75th term

Now the 18.75th term is

= 18th term + 0.75 term

= 57 +  (19 term - 18term)

= 57 +  0.75 (61 - 57)

= 57 + 0.75 (4)

= 60

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

it's 30

Step-by-step explanation:

30+4_2= dakukabilat

Answer:

-2x + 4

Step-by-step explanation:

-7x + 7 - (-5x + 3)

-7x + 7 + 5x - 3

-2x + 4

Answer:

\(-2x+4\)

Step-by-step explanation:

Let's write this mathematical operation:

\((-7x+7)-(-5x+3)\\\\-7x+7+5x-3\\\\\)

Group similar terms:

\(-7x+5x+7-3\)

Simplify:

\(-2x+4\)

Answer:

1157

Step-by-step explanation:

1. x must be 4 digits long

2. 1155<x<1165

3. 1157 is the only number that has a 7 as one of its digits and is between 1155 and 1165 (117_, 17__, 7___ > 1165)

Step-by-step explanation:

F(x) =x^2

G(x) =x-3

G(f(x))

= (x^2) -3

F(f(x))

= (x-3)^2

(x-3)(x-3)

x^2 -6x+9

For the second one

1/(x-3)

x-3 ≠ 0

x ≠ 3

So the domain restriction = 3

Answer:

i agrey with other guy

Step-by-step explanation:

Answer:

1/256

Step-by-step explanation:

\(4^{-4}\)

\((1/4)^{4}\)

=> 1/256

the value of variable x in the rhombus is Option (c) 25.

A parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.

Let O be the intersection point of the line AC and the line BD in the rhombus.

This two lines intersect at a 90° angle in the center. ( Property of Rhombus)

∠AOD=90°

∠AOD+∠OAD+∠ODA=180° (triangle sum property)

90°+x+x+40°=180°

2x=180°-130°

x=25

Hence the value of x=25.

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Answer:

C

Step-by-step explanation:

the angle opposite of it is 30

1) f(x) =x² (x -1)⁴ (x + 5)

= x. x (x -1)(x-1)(x-1)(x-1) (x+5)

The zeros are the values of x that makes the polynomials zero

From the expression above, the zeros are: 0, 0, 1, 1, 1, 1, -5

Hence, 0 = 2 mutiplicity

1 = 4 multiplicity

-5 = 1 multiplicity

Effect

The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis

In summary

Zero Multiplicity Effect

0 2 The graph will touch the x-axis at the root but will not cross the x-axis

1 4 The graph will touch the x-axis at the root but will not cross the x-axis

-5 1 The graph will cross the x-axis at the root.

Answer: 70%

Step-by-step explanation:

0.7
----- x 100% = 70%

 1

Answer:

70%

Step-by-step explanation:

When turning a decimal into a percent always bring the decimal point two places to the right.

0.7.0.

070%

70%

a. The integral converges and its value is 3.

b. The integral converges and its value is -1.

c. The integral diverges.

d. The integral converges and its value is 1/5 ln(5/2).

e. The integral converges and its value is 1/9 ln 2.

f.  Integral diverges because 1/0 is undefined.

a.

\(\int_0^ \infty (1 + 2x) e^{(-x)} dx\)

Applying limit

= limₐ→∞ \(\int _0^a (1 + 2x) e^{(-x)} dx\)

= limₐ→∞ \((-e^{(-a)}(a+3) - 2e^{(-a)} + 3)\)

= 3

b.

\(\int_-\infty^1 (1 + 2x) e^{(-x)} dx\)

= limₐ→-∞ \(\int_a^1 (1 + 2x) e^{(-x)} dx\)

= limₐ→-∞ \((e^{(-a)}(2a+3) - 2e^{(-a)} - 1)\)

= -1

c.

\(\int _{-\infty}^4\sqrt{(6 + y)} dy\)

= limₐ→-∞ ∫a⁴ √(6 + y) dy

= limₐ→-∞ \([2/3 (6 + y)^(3/2)]_a^4\)

= ∞

d.

\(\int_2^\infty 1/(x^2 + x - 6) dx\)

= limₐ→∞ \(\int_2^a 1/(x^2 + x - 6) dx\)

= limₐ→∞ \([1/5 ln|a-3| - 1/5 ln|a+2|]\)

Using natural log

= 1/5 ln(5/2)

e.

\(\int_3^\infty e^{-3x} / (9 + e^{-3x}) dx\)

= limₐ→∞ \(\int_3^a e^{(-3x)} / (9 + e^{(-3x)}) dx\)

= limₐ→∞ \([-1/3 \:ln|a^3 - 27| - 1/9 \:ln|9 + e^{(-3a)}| + 1/9\: ln\: 18]\)

= 1/9 ln 2

f.

∫₀¹ 1/√(x - x) dx

= ∫₀¹ 1/0 dx

Hence it is undefined.

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Question :-

determine if the following integrals converge or diverge. if the integral converges, determine its value. show your work carefully, writing the improper integral as a limit of an intermediate ordinary integral. you must evaluate the intermediate integral, and you must use proper limit notation, to obtain credit here.

a.

\(\int_0^ \infty (1 + 2x) e^{(-x)} dx\)

b.

\(\int_-\infty^1 (1 + 2x) e^{(-x)} dx\)

c.

\(\int _{-\infty}^4\sqrt{(6 + y)} dy\)

d.

\(\int_2^\infty 1/(x^2 + x - 6) dx\)

e.

\(\int_3^\infty e^{-3x} / (9 + e^{-3x}) dx\)

f.

∫₀¹ 1/√(x - x) dx

The maximum home value that can be financed is approximately $35,365.85.

Let's represent the maximum home value that can be financed by H.

If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.

Therefore, we have:

H × 82% = $29,000

Multiplying both sides by (1/82%), we get:

H = $29,000 / 82%

= $35,365.85

Hence, the maximum home value that can be financed is approximately $35,365.85.

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Answer:

sh. 24,000

Step-by-step explanation:

Given that the hire purchase price for a flat screen TV is 25% more than the cash price. If kamuyu bought the TV on hire purchase terms by paying a deposit of sh.14,000 and the remaining amount in 8 equal installment of sh.2,000 then the total amount paid by Kamuyu on hire purchase

= 14000 + 8(2000)

= 14000 + 16000

= sh. 30,000

Recall that the hire purchase price is 25% more than the cash price. Let the cash price be  C then,

1.25C = 30,000

Divide both sides by 1.25

C = 30000/1.25

= sh. 24,000

The cash price for the TV is sh. 24,000

Measure of bottom interior angle of the drawn right angle is θ.

The shape formed by two rays or two lines that have a common end is called an angle. The word "angle" is derived from the Latin word "angulus", which means "angle". The two rays are called the sides of an angle and the common end is called the vertex.

Given,

In the figure

θ is the measure of exterior alternate angles

and, 90 + θ is the measure of exterior angle in the drawn right triangle

sum of two opposite interior angles is equal to the exterior angles

90 + x = 90 + θ

x = θ

Hence,θ is the measure of the bottom interior angle of the drawn right triangle.

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Answer:

1- 0.123

2- 0.0745

3- 0.9706

Answer:

2000 meters

Step-by-step explanation:

400 * 5

Answer:

no

Step-by-step explanation:

No, it is not a random sample of the students in school.

Answer:

No

Step-by-step explanation:

A random sample is a sample that is taken from a larger set. Molly specifically chose to interview the youngest students, so the sample is not random.

Answer:

4.8

Step-by-step explanation:

When you multiply two negative number you get a positive number.

Answer: Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid. The period of both the sine function and the cosine function is \displaystyle 2\pi2π. In other words, every \displaystyle 2\pi2π units, the y-values repeat. If we need to find all possible solutions, then we must add \displaystyle 2\pi k2πk, where \displaystyle kk is an integer, to the initial solution. Recall the rule that gives the format for stating all possible solutions for a function where the period is \displaystyle 2\pi :2π:

\displaystyle \sin \theta =\sin \left(\theta \pm 2k\pi \right)sinθ=sin(θ±2kπ)

There are similar rules for indicating all possible solutions for the other trigonometric functions. Solving trigonometric equations requires the same techniques as solving algebraic equations. We read the equation from left to right, horizontally, like a sentence. We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process. However, with trigonometric equations, we also have the advantage of using the identities we developed in the previous sections.

The rectangular painting is 3 feet shorter in length than in height.

Let "x" represent the painting height, then its length can be expressed as "x-3"

12.

The area of the rectangular painting can be calculated by multiplying its length by its height.

For the painting

h=x

l=x-3

-Replace the formula with the expressions for both measurements:

-Distribute the multiplication on the parentheses term:

The polynomial that represents the area of the painting is:

13.

The perimeter of a rectangle is calculated by adding all of its sides, or two times its length and two times its height. You can calculate the perimeter of the painting as follows:

We know that

h=x

l=x-3

Then the perimeter can be expressed as follows:

-Distribute the multiplication on the parentheses term:

-Order the like terms together and simplify them to reach the polynomial:

14.

The painting has the unique quality of having an area that is equal to the value of the perimeter, then we can say that:

-Replace this expression with the polynomials that represent both measures:

To solve the expression for x, first, you have to zero the equation, which means that you have to pass all therm to the left side of the equation. Do so by applying the opposite operation to both sides of the equal sign.

We have determined the following quadratic equation:

Using the quadratic formula we can calculate the possible values for x. The formula is:

Where

a is the coefficient that multiplies the quadratic term

b is the coefficient that multiplies the x term

c is the constant of the quadratic equation

For our equation the coefficients have the following values:

a=1

b=-7

c=6

Replace these values in the formula and simplify:

Next is to calculate the addition and subtraction separately:

-Addition

-Subtraction

The possible values of x, i.e., the possible heights of the painting are:

x= 6ft

x=1 ft

15.

To determine the extraneous solution created when the area was set equal to the perimeter you have to calculate the corresponding length for both possible values of the height:

For the height x= 1ft, the corresponding length of the painting would be -2ft. This value, although mathematically correct, is not a possible measurement for the painting's length since these types of measures cannot be negative.