Israel started to solve a radical equation in this way:

square root of x plus 6 − 4 = x
square root of x plus 6 − 4 + 4 = x + 4
square root of x plus 6 = x + 4
(square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)

x + 2 = 0 x + 5 = 0
x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5
x = −2 x = −5

Solutions = −2, −5

What error did Israel make?

He subtracted 6 before subtracting x.
He added 4 before squaring both sides.
He factored x2 + 7x + 10 incorrectly.
He did not check for extraneous solutions.

Answer: c) 91.68 < μ < 98.32

Step-by-step explanation:

Let μ  be the mean score of all students.

Let [tex]\overline{x}[/tex] represents the sample mean score.

As per given , we have

Sample size : n= 30

Sample mean : [tex]\overline{x}=95[/tex]

Sample standard deviation: [tex]s=6.6[/tex]

Significance level [tex]\alpha=0.01[/tex]

Now, Confidence interval of mean when population standard deviation is unknown is given by :-

[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]

Degree of freedom = n-1 = 29

Critical two-tailed t-value : [tex]t_{0.01/2,29}=t_{0.005,29}=2.756[/tex] [By students' t distribution table]

Confidence interval of mean will be:

[tex]95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)[/tex]

i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32

So correct option is c) .

Answer:

[tex] x = 18 [/tex]

Step-by-step explanation:

Given:

Angle ABC = 2x

Angle CDE = 8x

Required:

Value of x

SOLUTION:

Line AB is parallel to line CD, therefore, angle ABC and angle BCD are alternate interior angles. Alternate interior angles are equal. Thus:

Angle ABC = Angle BCD = 2x

Since, line BC is parallel to line DE, angle BCD and angle CDE are consecutive interior angles.

Consecutive interior angles are supplementary, therefore:

Angle BCD + Angle CDE = 180°

[tex] 2x + 8x = 180 [/tex]

Use this equation to solve for x

[tex] 10x = 180 [/tex]

Divide both sides by 10

[tex] \frac{10x}{10} = \frac{180}{10} [/tex]

[tex] x = 18 [/tex]

Answer:106.

Step-by-step explanation:

Answer:

The overall group of sciences that study numbers, shapes and their relationships. An example of math is arithmetic, the study of addition, subtraction, multiplication and division.

Answer:

Step-by-step explanation:

6 + 8 + p = 14 + p

Answer: 14+p

Step-by-step explanation:  We have to add these numbers-

6 + 8 + p

14+p

(Since we don't know the value of p this is how far we can simplify )

Answer:

  14

Step-by-step explanation:

The objective function C=x+3y is the same as one of the constraining boundaries, x+3y≥14. Hence the minimum value of C is constrained to be 14.

Answer:

Step-by-step explanation:

A complex number is a number that has both real and imaginary part. An example of a complex number is z = x+iy where x is the real part and y is the imaginary part.

If z = x+iy, the conjugate of z₁ will be x-iy

adding the complex number to its conjugate will give;

P = z+z₁

P = x+iy +(x-iy)

open the parenthesis

P = x+iy+x-iy

collect like terms

P = x+x+iy-iy

P = 2x

We can see that the resulting value does not contain the imaginary number i, hence the result is a real number.

Hence the result of adding a complex number to its conjugate is a REAL NUMBER

Taking the difference;

P =  = z-z₁

P = x+iy -(x-iy)

open the parenthesis

P = x+iy-x+iy

collect like terms

P = x-x+iy+iy

P = 0+2iy

P = 2iy

We can see that the resulting value contains the imaginary number i, hence the of taking their difference is a complex number.

Hence the result of subtracting a complex number from its conjugate is an IMAGINARY NUMBER

Answer:

3x^2 - 48 = 0

Step-by-step explanation:

The roots of a quadratic equation whose roots are -4 and 4, means that valid solutions for the quadratic equation are -4 and 4.

The two forms we know for the quadratic equation are the factored binomials:

(ax + cy)(bx + dz) = 0

and the full equation

ax^2 + bx + c = 0

We will start with the factored form:

(x + 4) ( x - 4) = 0

Note that if we solve this, we get the roots:  x + 4 = 0  ==> -4 && x - 4 = 0 ==> 4

Now we apply foil to get the unfactored form:

(x + 4) (x - 4) = 0

x * x + x * -4 + 4 * x + 4 * -4 = 0

x^2 + -4x + 4x + -16 = 0

x^2 - 16 = 0

And now we want the leading coefficient to be 3.

3x^2 - 16  = 0

This looks like what we want; however, now with the leading 3, our solutions are no long +4 and -4.  So, we need to re-evaluate.

Going back to the binomials with the idea of a leading 3, let's rewrite them to still give us the solutions 4 and -4, but with the 3 included:

(3x + 12) (x - 4) = 0

Note, we simply multipled one binomial by 3 to maintain the roots of the original, but also incorporate the leading 3.

3x + 12 = 0              x - 4 = 0

3x = -12                        x = 4

x = -4

So now, we simply apply foil to this new equation of binomials to get our final quadratic equation:

(3x + 12) (x - 4) = 0

3x * x + 3x * -4 + 12 * x + 12 * -4 = 0

3x^2 + -12x + 12x + -48 = 0

3x^2 - 48 = 0

This is our quadratic equation we wish to use.

Note, we could have gotten this same equation by simply multiplying the original (x^2 - 16) = 0 by 3.

Cheers.

Answer:

n=-24

Step-by-step explanation:

Answer:

n =-24

Step-by-step explanation:

[tex]n-29=-53[/tex]

Collect like terms and simplify

[tex]n =-53+29\\\\n =-24[/tex]

Answer:

89

Step-by-step explanation:

Given that

2 O, 2 T and 1 M

Now based on this, the following ways are there  

1

Three ways i.e. {M,T,O}

2

XX or XY

XX in 2C1 = two ways i.e. {OO or TT}

XY in 3C2 × 2! = six ways

3

XXY or XYZ

XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve ways

XYZ in 3C3 × 3! = six ways

4

XXYY or XXYZ

XXYY = 4! ÷ (2! × 2!) = six ways

XXYZ in 2C1 ×  4! ÷ 2! = twenty four ways

5

= 5! ÷ (2! ×2!)

= 120 ÷ 4

= 30

Therefore, the total is

= 3 + (2 +6)+ (12 +6) + (6 +24) + 30

= 89

There are 30 different letter permutations.

The word is given as:
MOTTO

From the given word, we have the following parameters:

The number of different (d) letter permutation is then calculated as:

[tex]d = \frac{n!}{T!O!}[/tex]

This gives

[tex]d = \frac{5!}{2!2!}[/tex]

Evaluate each factorial

[tex]d = \frac{120}{2 \times 2}[/tex]

Evaluate the product of 2 and 2

[tex]d = \frac{120}{4}[/tex]

Divide 120 by 4

[tex]d = 30[/tex]

Hence, there are 30 different letter permutations.

Read more about permutations at:

https://brainly.com/question/11732255

Answer:

3

Step-by-step explanation:

30 hundreds = 30*100 which = 3000 and 3000/1000 = 3

Answer:

3

Step-by-step explanation:

30x100=3000 is the answer to solving your problem

Step-by-step explanation:

75+54

129°

the answer is 129°

Answer:

m ≈ 3

Step-by-step explanation:

3.53631284916 x 10^3 ≈ 3 x 10^3

Answer:

ok

Step-by-step explanation:

quadrant 4

.................

Answer:

Quadrant 4

Step-by-step explanation:

In Quadrant 4 the x-axis is positive (+) and the y-axis is negative (-). Here is the point plotted on a coordinate grid to help you understand better.

Hope this helps :)

The domain is the set of possible x values or inputs. We list each unique x value once (ignoring any repeats)

The range is the set of possible y outputs. Convention is to sort the values from smallest to largest.

This relation is not a function because the x value x = 5 corresponds to multiple y values.

Answer:

0.16

Step-by-step explanation:

Answer:

x + 3.5

Step-by-step explanation:

You are adding

hopefully this helps you:)

Answer: D. The data are discrete because the data can only take on specific values.

Step-by-step explanation:

Discrete data refers to data that has a specific value in a specific period and so can be counted as opposed to continuous data that cannot be counted as it goes on to infinity. An example of continuous data would be the height of students in a class. This is continuous because a person's height could be 1.02325845...... metres.

The number of car accidents on a particular stretch of highway can be counted and the data can only take on a specific value thereby making it discrete data.

In this exercise we have to use the knowledge of distance to understand which the best alternative corresponds to car accidents, in this way we find that:

Letter D. The data are discrete because the data can only take on specific values.

Discrete information in visible form refers to data that bear a distinguishing value fashionable a distinguishing period accordingly can be check in order as opposite to continuous information in visible form that cannot be deem as it continue to infinity.

An instance of constant data hopeful the height of person actively learning fashionable a class. This is constant cause a person's crest could be 1.02325845 metres.

The number of vehicle driven on streets accidents in contact a particular stretch of heavily traveled maybe have importance and the data can only oppose a particular financial worth by that making it discrete information in visible form.

See more about distance at brainly.com/question/989117

Answer:

the answer is zero

Step-by-step explanation:

-9+9=0

Answer:

1y - 5

Step-by-step explanation:

Remember to follow PEMDAS. Simplify the expression.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, distribute -5 to all terms within the parenthesis:

-5(y) = -5y

-5(1) = -5

Next, combine like terms:

-5y + 6y - 5

(-5y + 6y) - 5

1y - 5

1y - 5 is your answer.

~

Answer:

Step-by-step explanation:

4x^2(x^2 - 5x + 6)

4x^2(x - 3)(x - 2)

Answer:

Dhshshshhshsjehsjsjjsjssjsjsjsjsjsjjshhdhddhhdjdjddjdjjhdhdkdhjsdfggdhjjjjd

Step-by-step explanation:

Complete Question

The  complete question is shown on the first uploaded image

Answer:

Interval                Slope  of secant lines

 [1,2]                            113.000

 [1, 1.5]                          75.000

 [1, 1.1 ]                           51.960

  [1, 1.01]                       47.482

 [1, 1.001]                       47.048

Step-by-step explanation:

From the question we are told that

   The  function is  [tex]f(x) =  16x^3 -x[/tex]

Now considering the intervals

  For  [1, 2]

The  slopes of secant lines is mathematically represented as

     [tex]\frac{ f(2) - f(1)}{2-1}  =  \frac{16(2)^3 - 2 - [16(1)^3 -1] }{2-1 }  =  113.000[/tex]

  For  [1, 1.5]

The  slopes of secant lines is mathematically represented as

     [tex]\frac{ f(1.5) - f(1)}{1.5-1}  =  \frac{16(1.5)^3 - 1.5 - [16(1)^3 -1] }{1.5-1 }  = 75.000[/tex]

  For  [1, 1.1]

The  slopes of secant lines is mathematically represented as

     [tex]\frac{ f(1.1) - f(1)}{1.1-1}  =  \frac{16(1.1)^3 - 1.1 - [16(1)^3 -1] }{1.1-1 }  = 51.960[/tex]

   For  [1, 1.01]

The  slopes of secant lines is mathematically represented as

     [tex]\frac{ f(1.01) - f(1)}{1.01-1}  =  \frac{16(1.01)^3 - 1.01 - [16(1)^3 -1] }{1.01-1 }  =47.482[/tex]

   For  [1, 1.001]

The  slopes of secant lines is mathematically represented as

     [tex]\frac{ f(1.001) - f(1)}{1.001-1}  =  \frac{16(1.01)^3 - 1.001 - [16(1)^3 -1] }{1.001-1 }  =47.048[/tex]

Answer:

Decomposers in a food web are organisms that break down dead or decaying organisms and turn them into simpler, inorganic materials, making nutrients available for primary producers. A rotten fruit is not completely wasted because it will go back into the dirt for a producer to use, and the food chain continues.

Hope this helps!

Answer:

10.8 meters

Step-by-step explanation:

1.2 times 9 minutes= 10.8

Answer:

10.8 meters

Step-by-step explanation:

9 * 1.2 = 10.8