Solve the equation below by factorising. 12 − 8w + w² = 0​

Answer:

∠ 10 = 86°

Step-by-step explanation:

∠ 7 and ∠ 10 are same- side interior angles and sum to 180° , that is

∠ 7 + ∠ 10 = 180°

94° + ∠ 10 = 180° ( subtract 94° from both sides )

∠ 10 = 86°

In the sentence 52 = 15∙3 + 7, 7 is equal to 36.7

In mathematics, equality is a relationship that states that two quantities have the same value or that two mathematical expressions represent the same mathematical object.

Someone or something that is equal to another has the same quantity, value, or rights as that other thing. One cup and eight ounces are equivalent, for instance. Equal pay for equal work performed by men and women is an illustration of equality.

If both operands have the same value, the equal-to operator (==) returns true; otherwise, it returns false. If the operands do not have the same value, the not-equal-to operator (!=) returns true; otherwise, it returns false.

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Answer:

4x + 5y - 2

Step-by-step explanation:

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

The probability that a randomly selection of 20 toasters for testing, no more than one is defective is: 0.9401

To solve this exercise the formula and the procedure that we have to use for binomial distribution is:

Where:

Information about the problem:

Applying the binomial distribution formula, we get:

P(x) = n! /[x! *(n-x)!] * pˣ * (1 - p)ⁿ⁻ˣ

P(x) = 20! /[x! *(20-x)!] * 0.02ˣ * (1 - 0.02)²⁰⁻ˣ

Using the P formula to calculate the probability that no more than one of these toasters is defective, we have:

P = P(0) + P(1)

P(0) = 20! /[0! *(20-0)!] * 0.02⁰ * (1 - 0.02)²⁰⁻⁰

P(0) = 20! /(0!*20!) * 0.02⁰ * (0.98)²⁰

P(0) = 1/0! * 1 * 0.6676

P(0) = 1/1 * 1 * 0.6676

P(0) = 0.6676

P(1) = 20! /[1! *(20-1)!] * 0.02¹ * (1 - 0.02)²⁰⁻¹

P(1) = 20! /(1!*19!) * 0.02¹ * (0.98)¹⁹

P(1) = (20*19!) / (1!*19!) * 0.02¹ * (0.98)¹⁹

P(1) = 20/1! * 0.02 * 0.6812

P(1) = 20 * 0.02 * 0.6812

P(1) = 0.2725

P = P(0) + P(1)

P =  0.6676 + 0.2725

P =  0.9401

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

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-1 is the extraneous solution

To know the value of x first we need to remove the square root of the equation

[tex]\sqrt \sqrt{x +25}[/tex]  = [tex]\sqrt{x + 5}[/tex]

So to get the value we have to square both sides of the equation

[tex](\sqrt\sqrt{x +25})^{2}[/tex] = [tex](\sqrt{x + 5} )^{2}[/tex]

We get

[tex]\sqrt{x +25}[/tex]= x + 5

Now again we have to square both sides of the equation

x + 25 = [tex](x + 5)^{2}[/tex]

x + 25 =[tex]x^{2}[/tex] + 10x + 25( As we know [tex](a + b)^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] + 2ab )

[tex]x^{2}[/tex] + 9x = 0

x( x + 9) = 0

Therefore x = 0, -9

1 = [tex]\sqrt{-1}[/tex]

9 = [tex]\sqrt{81}[/tex]

The square root of 81 is 9 but the square root of -1 is an imaginary number

so the correct choice is " 9 is the solution of the equation " and -1 is the extraneous solution

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The value of given expression for x=0 is 1, x=-2 is 0.44 and x=2 is 2.25.

Given the expression is (3/2)ˣ.

Firstly, we will simplify the given expression (3/2)ˣ for x=0.

Substitute the value x=0 in given expression, we get

(3/2)ˣ =(3/2)⁰

As we know that something raise to power zero is 1.

So, we get

(3/2)ˣ =1

Now, we will simplify the given expression (3/2)ˣ for x=-2.

Substitute the value x=2 in given expression, we get

(3/2)ˣ =(3/2)²

Now, we will square the expression to simplify it, we get

(3/2)ˣ =9/4

(3/2)ˣ =2.25

Furthermore, we will simplify the given expression for x=-2.

Substitute the value x=-2 in given expression, we get

(3/2)ˣ =(3/2)⁻²

Now, we will square the given expression, we get

(3/2)ˣ =(9/4)⁻¹

Further, we will divide it above expression by 1 to remove negative sign, w eget

(3/2)ˣ =1/(9/4)

(3/2)ˣ =4/9

(3/2)ˣ =0.44

Hence, the value of expression (3/2)ˣ  for x=0, 2 and -2 is 1, 2.25 and 0.44.

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Since lines a and b have the same slope, then: the lines are parallel.

The slope of a line is the rise/run or change in y / change in x. When two lines lie parallel to each other, they will have equal slope value.

On the other hand, when two lines lie perpendicularly to each other, their slopes will be negative reciprocal.

For example, if a line has a slope of 2/3, the slope of the line that is parallel to it will be 2/3 also, while the slope of the line that is perpendicular to it will be -3/2.

Thus:

The slope of line a = 2/3

The slope of line b = 2/3

Therefore, since lines a and b have the same slope, then: the lines are parallel.

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Answer: the lines are parallel.

The amount the PTA at Greenville High School raised this year is $30,023.

The percentages are also called the centesimal ratio, and are usually accompanied by the symbol “%”, which reads “percent”.

The fact that the PTA at Greenville High School raises 30% less funds this year compared to last year means that the amount raised this year is 70% of last year's funds, in essence, 70% multiplied by last year's:

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Answer: (A) -24x1/4  (B) Negative multiplied by a positive equals a negative

Step-by-step explanation:

The question says below sea level, so the whole number is negative. we don't need city A its a distraction so city C is multiple by city D. why do we multiply because the word of means multiple there for the expression is

write the product into one single fraction

-24x1

   4        canceled the 4 in the fraction -24x1

                                                                      4

-6x1    any expression divided by one remains the same -6x1

  1

solution

x1=0

The simplified form of trigonometric expression, cosec θ / sin θ + cos θ cot θ is 1.

Given,

The trigonometric expression = cosec θ / sin θ + cos θ cot θ

We have  to simplify this expression.

For that we can use trigonometric identities.

cosec θ = 1 / sin θ

cot θ = cos θ / sin θ

We can substitute the above given identities in the expression.

Then we get,

cosec θ / sin θ + cos θ cot θ = (1 / sin θ) / (sin θ + cos θ x (cos θ/sin θ))

= (1 / sin θ) / ((sin²θ + cos²θ) / sin θ)

Cancel sin θ from both numerator and denominator.

= 1 / sin² θ + cos² θ

We know that sin² θ + cos² θ = 1

So, we get,

1 / sin² θ + cos² θ = 1 / 1 = 1

Therefore, the simplified form of  cosec θ / sin θ + cos θ cot θ is 1.

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Answer:

Hello,

Step-by-step explanation:

[tex]n=\overline{EDCBA}\\\\A=3*B\ My\ ones\ digit\ is\ three\ times\ greater\ than\ my\ tens\ digit.\\E=3+B\ My\ ten\ thousands\ digit\ is\ 3\ more\ than\ my\ tens\ digit.\\C=2*E\ My\ hundreds\ digit\ is\ twice\ my\ ten\ thousands\ digit. \\D=C-1\ My\ thousand\ digit\ is\ one\ less\ than\ my\ hundreds\ digit.\\\\A=3*B\\E=3+B\\C=2*E\\D=C-1\\\\\begin{array}{|c|c|c|c|c|}A&B&C&D&E\\--&--&--&--&--\\0&0&6&5&3\\3&1&8&7&4\\6&2&X&X&5\\9&3&X&X&6\\X&4&X&X&X\\--&--&--&--&--\\\end{array}\\[/tex]

[tex]\\\\Numbers\ are\ 35600\ or\ 47813.[/tex]

Answer: yes, because you can't score negative numbers in a game and the absolute value is really just making all numbers positive unless there is a negative variable outside of the absolute value symbols

Step-by-step explanation: brainliest?

Answer:

45°

Step-by-step explanation:

AB and BC are congruent which mean ∠BAC and ∠BCA are congruent.

We already know ∠ABC is 90°.

We cans set up the equation with what is given.

180 = 90 + 2c

Subtract 90 from both sides.

90 = 2c

Divide both sides by 2

45 = C

So angle C is 45°

We need to know about logarithm to solve this problem. The value of the given logarithm is 1.

Logarithm is an exponent that the base is raised to inorder to get a certain number. There are few rules of logarithm, log a +log b can be written as log ab, log a -log b can be written as log a/b, when the number whose logarithm is calculated has been raised to a power then the power can be multiplied to the log itself. When logarithm is written as log with no mentioned base then the base is 10. The log of a number same as the base is always 1 and the log of 1 is always zero because a nonzero number raised to zero is always 1. We will be using these rules to find the value of the given logarithm.

[tex]log_{9}9[/tex]=1 since [tex]9^{1} =9[/tex]

Therefore we found the value of the given logarithm to be 1.

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For the given statement conclusion it was drawn using the law of syllogism.

Option A is our correct answer

The Law of Syllogism states that,

If the following two statements are true:

- If p, then q.

- If q, then r.

Then the third statement is true:

- If p, then r.

We have,

p - If you do the unit review, q - you will do well on the test.

q - If you do well on the test, r - then you will do well in the course.

Therefore, p - if you do the unit review, r - then you will do well in the course.

This is in the form of:

- If p, then q.

- If q, then r.

Then the third statement is true:

- If p, then r.

Thus this conclusion was drawn using the law of syllogism.

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An elevator descends at a constant speed, the change in elevation after 19 seconds will be an elevation of distance

d= 19v where acceleration remains constant

Generally, An angle is created when a horizontal line and a line of sight are placed side by side.

In conclusion, This angle is known as the angle of elevation. If the line of sight rises above the horizontal line, the angle that is generated is known as an angle of elevation.

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Answer:

Box of oat:

24*5*25(all in cm)=3000 cm3

cereal:

26*4*2.8=291.2 cm3

oat is grater by 2708.8

Step-by-step explanation:

28mm was changed to 2.8 cm

Answer:

B/a

Step-by-step explanation:

Because 1/a is still the same as a to power negative one and so 1/b. 1/a divided by 1/b is b/a

In 12144 ways the students can get first, second, or third place.

The permutation system is used to locate the special range of preparations that may be shaped through taking r matters from the n to be had matters. Permutations are beneficial to shape distinctive words, quantity preparations, seating preparations, and for al. of the conditions related to special preparations. As consistent with the permutation formula, the permutation of 'r' items taken from 'n' items is identical to the factorial of n divided through the factorial of distinction of n and r.

The formula for permutations is

nPr= n!/(n-r)!

From the given question let us consider,

n= 24    r=3

Now let us solve using formula

24P3= 24!/(24-3)!

=24*23*22*21......*2*1

=12144

Therefore there are 12144 ways.

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The lower and upper bounds for the following to the given degrees of accuracy are: a- 64 mins (63.5 ≤ 64 < 64.5) c- 30m/s (27.5 ≤ 30 < 32.5) b- 20g (15 ≤ 20 < 25) d-7500mm (7450 ≤ 7500 < 7550)

The upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.

For a- 64 mins (nearest 1 min)

As the degree of accuracy is to the nearest 1 min;

1 min ÷ 2 = 0.5 min

Upper bound = 64 + 0.5 = 64.5 min

Lower bound = 64 - 0.5 = 63.5 min

For c- 30m/s (nearest 5m/s)

5m/s ÷ 2 = 2.5 m/s

Upper bound = 30 + 2.5 = 32.5 m/s

Lower bound = 30 - 2.5 = 27.5 m/s

For b- 20g (nearest 10g)

10g ÷ 2 = 5

Upper bound = 20 + 5 = 25g

Lower bound = 20 - 5 = 20g

For d- 7500(nearest 100mm)

100mm ÷ 2 = 50mm

Upper bound = 7500 + 50 = 7550mm

Lower bound = 7500 - 50 = 7450mm

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The mean of of −26,39,−10,−16,12,31 is 5 which is determined by summing up the numbers and dividing by 6

What is the mean?

The mean is the sum of the integers divided by the number of integers therein, in other words, the mean is determined sum , having computed the sum we divide by 6 since there are six numbers in the distribution

sum=-26+39-10-16+12+31

sum=30

mean=sum/n

n=6(there are six numbers)

mean=30/6

mean=5

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[tex]\displaystyle\\Answer:\ C. \ f=\sqrt{\frac{B}{4} }[/tex]

Step-by-step explanation:

After evaluating the expression x³ . x⁵, we get the result as 256.

We are given an expression:

x³ . x⁵

We can use the properties of exponents that if the base is same and two numbers are multiplied, then the powers get added.

So, the expression will become:

= x ³⁺⁵

Simplifying the expression, we get that:

= x⁸

Now, we need to evaluate the expression at x = 2

Put x = 2 in the expression, we get that:

= 2⁸

Evaluating it, we get that:

= 256

Therefore, after evaluating the expression x³ . x⁵, we get the result as 256.

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The possible two-course meals that could be ordered assuming diners must order one meal from each category are;

It follows from the task content that the categories are as indicated below;

Starters Mains

Garlic Bread

Prawns Soup

Chicken Risotto

The condition that diners must order one meal from each category simply leaves the diners with;

Consequently, the expected number of possible two-course meal combination is; 3 × 3 = 9.

Ultimately, the possible two-course meals that could be ordered assuming diners must order one meal from each category are as listed above.

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Answer: A and B

-3^4 = -3 × -3 × -3 × -3 = 81

When dealing with multiplying all negative numbers, the result is going to be positive.

-3^2 = -3 × -3 = 9

Step-by-step explanation:

Divide

81/9 = 9

Find an equivalent expression whose product is |+9|

(-3)^2 = -3 × -3 = 9

(-3)^4 = -3 × -3 × -3 × -3 = 81

81/9 = 9

A is correct, so we must find the next correct answer.

(-3)^6 = -3 × -3 × -3 × -3 × -3 × -3 = 729

(-3)^4 = -3 × -3 × -3 × -3 = 81

729/81 = 9

B is correct. Thus,

[tex]\frac{(-3)^4}{(-3)^2} = B)\frac{(-3)^6}{(-3)^4} = A)\frac{(-3)^2}{(-3)^4}[/tex]

Hope this helps, and have a great day.

Answer:

(2)(6)+3

?

=

15

15=15

True

Step-by-step explanation:

help

The percentage of scores will fall between 85 and 115 is 68.26%

Given,

Scores on the Wechsler Adult Intelligence Scale (WAIS) are normally distributed with,

Mean = 100

Standard deviation = 15

We have to find the percentage of scores fall between 85 and 115.

That is,

P(85 < X < 115) = \ [tex]P[/tex] [tex](\frac{85-100}{15}[/tex]  <  [tex]\frac{x-mean}{standard deviation}[/tex]  < [tex]\frac{115-100}{15}[/tex][tex])[/tex]

= P(-1 < Z < 1)

= \P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

\P(85 < X < 115) = 0.6826

The probability that a person would score between 85 and 115 is 0.6826

And, the percentage of scores will fall between 85 and 115 is 68.26%

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