4 Solve these inequalities. Show the solutions on the number lines.
a 4v-2 > 16
b 6 ≥ 2(w-7)
0
5 a Write as a recurring decimal.
b Convert 0.45 to a fraction.
(5 marks)

Erika is working on solving the exponential equation 50^x = 17; The solution is x = 0.7242.

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Erika is working on solving the exponential equation 50^x = 17;

however, she is not quite sure where to start.

The equation is

[tex]50^x = 17\\[/tex]

By taking the log both sides

[tex]log_a b = x\\\\a_x = b[/tex]

By using the base formula

[tex]log_0 y = \dfrac{logy}{log b}[/tex]

So, [tex]log_{50} 17= x\\\\[/tex]

[tex]x = \dfrac{log17}{log 50}[/tex]

x = 0.7242

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Answer:

do u still need help with this

Answer:

(7,-5)

Step-by-step explanation:

See attached graph.

Answer:

a bunch

Step-by-step explanation:

Answer:

it is probably 9 or 12 I apologize apologise in advance if I'm wrong

Step-by-step explanation:

Point L is the midpoint

The midpoint is halfway between the two points. In this case, Point F and Point B are 10 units away from each other. The midpoint is the distance between the points (10) divided by 2.

Step-by-step explanation:

please mark me as brainlest

Answer:

102

Step-by-step explanation:

Answer:

a=1

b=-1

c=1

value of discriminant =-3

quadratic function will intersect x-axis 0 times

Step-by-step explanation:

The orthocenter is the point of intersection of the three altitudes.

An orthocenter can be defined as the point of intersection of altitudes which are perpendicular from the vertex to the opposite sides of a triangle.

Therefore, the orthocenter is the point of intersection of the three altitudes.

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Some ways through which the value of a thing be estimated are:

Given: 11.51 * 12.95, an estimated value of the individual numbers can be made out to be 12 * 13 respectively.

This refers to the rough calculation of the approximate value of a thing, usually a number.

In mathematical calculations, estimates are important as they are used to round off the value of numbers either to the nearest tenth, hundredth, thousandth, etc.

Hence, we can see that your question is incomplete, so I gave you a general overview of estimates to give you a better understanding of the concept.

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Answer:

(1,-4)

Step-by-step explanation:

Answer:

 (-7/9)^4 = 2401/6561

Step-by-step explanation:

The rules of exponents apply.

  (a^b)/(a^c) = a^(b-c) . . . . . quotient rule

  (a^b)^c = a^(bc) . . . . . . . . power rule

__

The first rule of exponents shown above helps us find the value of a/b.

  [tex]\dfrac{a}{b}=\dfrac{\left(\dfrac{-7}{9}\right)^8}{\left(\dfrac{-7}{9}\right)^6}=\left(\dfrac{-7}{9}\right)^{8-6}=\left(\dfrac{-7}{9}\right)^2[/tex]

The second rule of exponents shown above tells us how to find the square.

  [tex]\left(\dfrac{a}{b}\right)^2=\left(\left(\dfrac{-7}{9}\right)^2\right)^2=\left(\dfrac{-7}{9}\right)^{2\times2}\\\\\boxed{\left(\dfrac{a}{b}\right)^2=\left(\dfrac{-7}{9}\right)^4=\dfrac{2401}{6561}}[/tex]

_____

Additional comment

Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.

Answer:

Slope:  1/4

y - int: (0,-6)

Step-by-step explanation:

-x+4y=-24

4y = -24+x

y=1/4 * x - 6

The direction of the force is given as = 38.21⁰ while the magnitude is given as 7N

Fr = [tex]\sqrt{F1^2+F2^2+2F1F2CosO}[/tex]

∅ = 60 degrees

= √3² + 5² + 2*3*5cos60

= √49

FR = 7N

7cos∅ = 3 + 5cos∅

7cos ∅ = 3 + 2.5

cos∅ = 5.5/7

∅ = cos⁻¹0.7857

= 38.21⁰

Hence the direction of the force is = 38.21⁰

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Division problem 6/0 as a multiplication problem = 6×1/0

Simplified solution of the problem = ∞

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation.

Given division problem,

6/0

Division is inverse of the multiplication

∴ 6/0 = 6×1/0

Now, simplifying

6 × 1/0 = 6 × ∞ = ∞

Hence, ∞ is the solution of the division problem 6/0 after converting it into multiplication problem 6 × 1/0.

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Answer:

The correct answer is b.

Step-by-step explanation:

[tex]16 {x}^{2} = - 16[/tex]

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

No real solutions.

Answer:

12.0 ft

Step-by-step explanation:

The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%

The given parameters are:

Cards = 52

Face card = 12

Ace = 4

The probability of selecting a face card is:

P(Face card) = 12/52

Now, there are 51 cards.

The probability of selecting an ace is:

P(Ace) = 4/51

The required probability is:

P = 12/52 * 4/51

Evaluate

P = 0.0181

Express as percentage

P = 1.81%

Approximate

P = 2%

Hence, the probability is 2%

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The answer to the drop down menu are:

Congruent angles are known to be two or more angles that are said to be similar or identical to one another. Thus, one can say that their measure of their angles is the same to each other.

Based on the above, the angles given able are congruent to the other angles because they are known to have the same angle (in terms of  degrees and radians).

Therefore, The answer to the drop down menu are:

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Answer:

Hope this helps

Step-by-step explanation:

Answer: 7 apples

Step-by-step explanation:

Considering it's the same person and you only had a typo?

There are 230 highway signs during road trip.

Length is defined as the act of measuring the length of objects in some specified units which can be standard or non-standard.

Here, The total length of a road trip = 18.4 hours.

Highway signs are posted = after every 0.08 hours.

To find: Number of highway signs.

The number of highway signs is found = 18.4 / 0.08 = 230.

Thus there are 220 highway signs available during the road trip.

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Answer: its 218

Step-by-step explanation: you just have to subtract 250 minus 32

The sequence which shows arithmetic sequence is -3, -10, -17, -24, -31, ....... so the correct option is Option D.

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.

Here, out of the given option option D follows the definition.

Difference between two consecutive term is equal.

-10 - (-3) = -10 + 3 = -7

-17 - (-10) = -17 + 10 = -7

-24 - (-17) = -24 + 17 = -7

-31 - (-24) = -31 + 24 = -7

Thus, the sequence which shows arithmetic sequence is -3, -10, -17, -24, -31, ....... so the correct option is Option D.

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Answer:

Translation as Triangle A has been translated by vector (3,-1) to now being (-2,-3)

Translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

The process of changing the location of the image on the coordinate system will be known as the translation.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have merely changed their direction or directions.

Given that Translate Triangle A by a vector (3, -1) to give triangle B. Then, rotate your triangle B 180° around the origin to give triangle C.

Triangle A translation ⇒ (3,-1)

The second translation = (-2,-3).

Therefore, the translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

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Answer:

171

Step-by-step explanation:

180×95/100

180×95=17100

17100/100=171.

That is how I got my answer.

Answer:

B

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses it

the line crosses the y - axis at (0, - 4 ) ← y- intercept

Answer:

-4

Step-by-step explanation:

if you graph it, we can find out two points are 0,17 and 1,13

we can find the slope from rise/run

-4 is the  slope of the line represented by the equation y + 3 = -4(x-5)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The equation of the line is y + 3 = -4(x-5)

We have to find slope

Let us simplify the equation to slope intercept form to find slope

y+3=-4x+20

y=-4x+17

Hence, -4 is the  slope of the line represented by the equation y + 3 = -4(x-5)

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