Using a numberline, find both the intersection and the union of the following intervals:
(-∞,6) and (-∞,9)

Hi :)

I'd start by adding 5 to both sides of the equation. That would make the equation easier.

[tex]\boldsymbol{\sqrt{2x}-5=3}}[/tex]

[tex]\boldsymbol{\sqrt{2x}=2}[/tex]

The next step is to get rid of the radical sign.

Which operation will undo the square root? Squaring.

So that's why we square both sides:

[tex]\boldsymbol{2x=4}[/tex]

And Now we just divide both sides by 2

[tex]\boldsymbol{x=2}[/tex]

~[tex]\textit{\textbf{Learn More; Work Harder}}[/tex]~

:)

The domain of the functions are:

The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?

Function 1

The function is given as:

f(x) = √4x + 6

Set the radicand greater than 0

4x + 6 > 0

Subtract 6 from both sides

4x > -6

Divide by 4

x > -3/2

Express as interval notation

[-3/2, ∞)

Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2

Function 2

The function is given as:

g(x) = -4√-20x - 6

Set the radicand greater than 0

-20x - 6 > 0

Add 6 to both sides

-20x > 6

Divide by -20

x < -6/20

Simplify

x < -3/10

Express as interval notation

(-∞, -3/10]

Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10

Function 3

The function is given as:

f(x) = 15 + √5x - 16

Set the radicand greater than 0

5x - 16 > 0

Add 16 to both sides

5x > 16

Divide by 5

x > 16/5

Express as interval notation

[16/5, ∞)

Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5

Function 4

The function is given as:

p(x) = √20x + 6

Set the radicand greater than 0

20x + 6 > 0

Subtract 6 from both sides

20x > -6

Divide by 20

x > -6/20

Simplify

x > -3/10

Express as interval notation

(-3/10, ∞]

Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10

Read more about domain at:

https://brainly.com/question/10197594

#SPJ1

The chances of it happening more than once in 4 trials is 13%

From the information given, we have can deduce that;

Probability of 1 trial = 55%

= 55/ 100

Find the ratio

= 0. 55

We are to find the probability of it happening more than once in 4 different trials

If the probability of it happening in one trial is 555 which equals 0. 55

Then the probability of it happening in 1 in 4 trials is given as;

P(1/4 trials) = 1/ 4 × 55%

P(1/4 trials) = 1/ 4 × 0. 55

Put in decimal form

P(1/4 trials) = 0. 25 × 0. 55

P(1/4 trials) = 0. 138

But we have to know the percentage

= 0. 138 × 100

Multiply the values, we have

= 13. 8 %

Thus, the chances of it happening more than once in 4 trials is 13%

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

  order: 2, 3, 1

Step-by-step explanation:

Reasonableness checks and your knowledge of integers and fractions will help you solve this. The offered questions are intended to help you think this through.

For an output of -31, the machine (x -2)² cannot possibly be last. Its output can only be positive.

  machine 2, (x-2)², cannot be last

Also, machine 3 cannot be last. For the output to be -31, the input to machine 3 must be -1/31. Neither of the other machines can produce a fraction with the inputs they might receive.

For an input of x=0, the machine 1/x cannot possibly be first. 1/0 is undefined.

The other two machines will give the following outputs for an input of 0:

  machine 1: 4(0) -32 = -32

  machine 2: (0 -2)² = 4

It is unlikely that machine 1 will be first, because the other two machines cannot do anything useful with -32 as an input.

  machine 3, 1/x, cannot be first

The reasoning of part (a) tells you the last machine must be machine 1. The reasoning of part (b) tells you the first machine cannot be 3, so must be 2. The order of the machines must be ...

The number of bars which can be cut for the 1" X 1" and 2" X 2" square bars are; 117 and 29 units respectively.

The total area of the given pan can be evaluated as follows;

Area = length × width

= 9 × 13

= 117 square units.

Hence, the number of 1" X 1" bars can be cut which can be cut from the pan;

= 117/(1×1)

= 117 1" X 1" bars.

For the 2" X 2" square bars, we have;

= 117/(2×2);

29 remainder 1 square unit.

Ultimately, one square unit of the pan is wasted for the 2" X 2" square bars.

Read more on area;

https://brainly.com/question/8294080

#SPJ1

Answer:

Step-by-step explanation:

8 adults means 48 children

11 adults means 66 children

15 adults means 120 children

Answer:

See Below

Step-by-step explanation:

y = a (x-7)^2 -3       where 'a'  is any number except 0

Answer:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=2x^2-x-10[/tex]

The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.

To find these points, factor the quadratic equation, set it to zero, then solve for x.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=2 \cdot -10 = -20[/tex]

[tex]\implies b=-1[/tex]

Therefore, the two numbers are -5 and 4.

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 2x^2-5x+4x-10[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-5)+2(2x-5)[/tex]

Factor out the common term (2x - 5):

[tex]\implies (x+2)(2x-5)[/tex]

Set the factored function to zero:

[tex]\implies (x+2)(2x-5)=0[/tex]

Apply the zero-product property:

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts of the graph are:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Learn more about quadratic equations here:

https://brainly.com/question/27956741

https://brainly.com/question/27947331

The solution to the inequality x-13<=7+4x is x >= -20/3

The inequality expression is given as:

x-13<=7+4x

Add 13 to both sides of the inequality

x <= 20 + 4x

Subtract 4x from both sides of the inequality

-3x <= 20

Divide both sides of the inequality by -3

x >= -20/3

Hence, the solution to the inequality x-13<=7+4x is x >= -20/3

Read more about inequality at:

https://brainly.com/question/25275758

#SPJ1

Complete question

Solve the inequality for x

x-13<=7+4x

Answer:

210

Step-by-step explanation:

[tex]512=2^9 \\[/tex] has 9 prime factors

Now, if you want to maximize the number of different prime factor, apply the following method: let [tex]p(n)[/tex]  be the nth prime number, in increasing order. Let [tex]v[/tex]  define as follow :  [tex]v(0)=1,v(n+1)=v(n)p(n+1)[/tex] , and find n  such that [tex]v(n) < 1000,v(n+1) > 1000[/tex]. n will be the number of factors and v(n) your integer.

[tex]v(1)=2v(0)=2v(2)=3v(1)=6v(3)=5v(2)=30v(4)=7v(3)=210v(5)=11v(4)=2310[/tex]

There you are,  210 , with only 4 different prime factors.

→Credits: Xavier Dectot←

The cost of manufacturing the article bin 2004 will be 1875.

Percentage increase is the ratio of increase to the initial value in percentage.

Given that In 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled, labor cost increased by 30% and transport costs increased by 20%

Given that in 2001, the cost of manufacturing = 1250

If this cost was divided between the Material, labor, and transportation equally, then, cost for each sector will 1250/3 = 416.67

The cost of manufacturing = 833.33 + 541.67 + 500

The cost of manufacturing = 1875

Therefore, the cost of manufacturing the article bin 2004 will be 1875.

Learn more about Percentage Increase here: https://brainly.com/question/9513317

#SPJ1

Answer:

1.6 and 9.6

Step-by-step explanation:

The interest due on financing option is $307.50

What is interest on financing?

Interest on financing is the extra amount paid by the couple when their total payments are compared to the cash price of $6,230.

The total payments would be the 25% down payment plus the sum of the twelve monthly payments of $415 each

Down payment=cash price*25%

Down payment=$6230*25%

Down payment=$1,557.50

Total monthly payments=amount of each monthly payment*number of monthly payments

monthly payment=$415

number of monthly payments=12

Total monthly payments=$415*12

Total monthly payments=$4,980

Total payment under financing=Down payment +Total monthly payments

Total payment under financing=$1,557.50+$4,980

Total payment under financing=$6,537.50

Interest=$6,537.50-$6,230

Interest on financing=$307.50

Find out more on down payment on: brainly.com/question/1698287.

#SPJ1

Complete question:

Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415. How much interest did they pay due to financing?

Answer:

event

An event can be described as an individual or set of outcomes of an experiment.

Events are a subset of the experiment's sample space.

The sample space of an experiment is the complete set of possible outcomes of that experiment.

Answer: Plant B produced 4000 panels

Step-by-step explanation: Let the number of panels produced by plant A = a and the number of panels produced by plant B = x. In total, we have 3000 + x.  Now for the defective panels. 10% of plant a + 3% of plant b = 6% of both a and b. 300 + 3/100(x) = 6/100(3000 + x). 300 + 0.03x = 180 + 0.06x. Now, we simplify. 300 - 180 = 0.06x = 0.03x. So, 120 = 0.03x and 40 = 1% of x. This means x = 4000. So, therefore, Plant B produced 4000 panels. We can check our work by using the value of x we got. 4000 + 3000 = 7000. 6% of 7000 = 420. 120 = 3% of 4000. 120 + 300 = 420 so the answer we got is correct. Hope this helped

Answer:

c subtract 5 from both sides

Answer:

3

Step-by-step explanation:

6.01 has 3 sig fig

I think that's how I do it

The five-number summary is:

Minimum: 4

Quartile Q1: 11.25

Median: 12.5

Quartile Q3: 16.5

Maximum: 20

The box plot is attached below.

The five-number summary of a data that is displayed on a box plot include: minimum and maximum values, lower and upper quartiles, and the median.

Given the data, 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19, the five-number summary is:

Minimum: 4

Quartile Q1: 11.25

Median: 12.5

Quartile Q3: 16.5

Maximum: 20

There are no outliers. Thus, the box plot that represents the five-number summary is shown in the image attached below.

Learn more about five-number summary on:

https://brainly.com/question/1742240

#SPJ1

Answer: it is correct i got it from edmentum

Step-by-step explanation:

The excluded values are x = 4 and x - 1

The complete question is added as an attachment

The function is given as:

(2x^2 - 7x - 4)/(x^2 - 5x + 4)

Set the denominator to 0

x^2 - 5x + 4 = 0

Expand

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

Factorize the equation

x(x -1) - 4(x - 1) = 0

This gives

(x - 4)(x - 1) = 0

Solve for x

x = 4 and x - 1

Hence, the excluded values are x = 4 and x - 1

Read more about excluded values at

https://brainly.com/question/1418453

#SPJ1

Answer: Its D 1 and 4

Step-by-step explanation:

I took the assignment

Answer: A

Step-by-step explanation:

The points are (-5, 8) and (4, 6).

The distance is [tex]\sqrt{(-5-4)^2 + (8-6)^2}=\sqrt{85}[/tex]

Answer:

x=25 and y=-10

Step-by-step explanation:

x+2y=5 ..........(1)

4x+12y=-20.........(2)

using elimination method.

multiply equ(1) by 4 and equ(2) by 1

so we have

x+2y=5..........*4

4x+12y=-20.........*1

4x+8y=20................(3)

4x+12y=-20.............(4)

subtract eq(4) from (3) we have

-4y=40

y=-10

substitute y=-10 in equation (1)

we have:

x+2(-10)=5

x-20=5

x=25

Answer:

converges

Step-by-step explanation:

the individual fraction terms go against 0 with larger and larger n.

and therefore the sum converges.

the numerator of the fractions stays constant (4) but the denominator (bottom) of the fraction increases more and more with investing n (it does not matter that it uses roots, compared to the constant 4 they too grow immensely large with large n).

the limit of a/infinity is defined as 0.

The forecasted capital expenditure related to the information below exists at 4,900.

Therefore, the correct answer is option b) 4,900.

Capital exists directed as the lifeblood of any business. It exists the group of assets of the business that contains their financial value to create the production of goods and services.

For calculating the forecasted capital-

Net PP&E beginning of period = 15,000

Net PP&E end of period = 17,500

Depreciation expenses = 2,400

Forecasted capital expenditure = Net PP&E end of period + Depreciation expenses - Net PP&E beginning of the period

= 17500 + 2400 - 15,000

Forecasted capital expenditure = 4,900

Therefore, the correct answer is option b) 4,900.

To learn more about Capital, refer to:

brainly.com/question/16179329

#SPJ9

The complete question is:

What’s the forecasted capital expenditure based on the information below?

Net PP&E beginning of period: 15,000

Net PP&E end of period: 17,500

Depreciation expenses: 2,400

Review Later

a) 2,500

b) 4,900

c) 100

d) -100

Answer:

  (x, y) = (-√3/2, 1/2)

Step-by-step explanation:

The terminal point for that angle can be read from a unit circle chart.

On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...

  (x, y) = (-√3/2, 1/2)

Answer: 1:52 PM

Step-by-step explanation:

PAULA: 2:14PM FINISHED THE RACE

BEATRICE: FINISHED 22 MINUTES EARLIER THEN PAULA

YOU TAKE 2:14PM AND SUBTRACT THE 22 MINS BEATRICE RAN TO GET YOU ANSWER.

SO 2:14 -14 MINS=2:00PM 14+8=22 (THE MINS BETRICE FINISHED)

2:00-8 MINS ( REMAINING FROM THE 22 ) THEN 2:00-8 MINS =1:52

ANSWER:1:52PM

The value of 'x' from the expression is 9/ 11

Given the expression;

3 x +14 (3x-4) +3 x ( 6) +3 (х+2 )=4

First, we expand the bracket

3x + 42x - 56 + 18x + 3x + 6 = 4

collect like terms

3x + 42x + 18x + 3x - 56 + 6 = 4

Add up like terms

66x - 50 = 4

66x = 4 + 50

66x = 54

Make 'x' the subject of formula

x = 54/ 66

x = 9/ 11

Thus, the value of 'x' from the expression is 9/ 11

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

Using the normal distribution, there is a 0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching this problem on the internet, the parameters are given as follows:

[tex]\mu = 150, \sigma = 9, n = 10, s = \frac{9}{\sqrt{10}} = 2.85[/tex]

The probability is one subtracted by the p-value of Z when X = 157, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (157 - 150)/2.85

Z = 2.46

Z = 2.46 has a p-value of 0.993.

1 - 0.993 = 0.007.

0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

More can be learned about the normal distribution at https://brainly.com/question/15181104

#SPJ1

Answer:

Step-by-step explanation:

yes

The gross pay, taxable income, withholding taxes, and net pay can be computed as follows:

a) The gross pay per pay period = $500

b) Taxable income per pay period = $425

c) Federal tax withholding per pay period = $46.75

d) FICA withholding per pay period = $26.35

e) Medicare withholding per pay period = $6.16

f) State tax wtihholding per pay period = $10

g) Net pay per pay period = $335.74

The number of hours per pay period = 40 hours

The number of pay periods in a month = 2

The total number of hours worked per month = 80 hours (40 x 2)

Earnings per hour = $12.50

a) The gross pay per pay period = $500 (40 x $12.50)

Deductions per pay period:

Health care = $25

401k = $50

The gross pay per pay period  = $500

Total deductions per pay period = $75

b) Taxable income per pay period = $425 ($500 - $75)

c) Federal tax withholding per pay period = $46.75 ($425 x 11%)

d) FICA withholding per pay period = $26.35 ($425 x 6.2%)

e) Medicare withholding per pay period = $6.16 ($425 x 1.45%)

f) State tax wtihholding per pay period = $10 ($500 x 2%)

Total withholding taxes = $89.26

g) Net pay per pay period = $335.74 ($425 - $89.26)

Learn more about the gross and net pay and taxable income at https://brainly.com/question/4356180.

#SPJ2

The vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5

The quadratic function is given as:

f(x) = x^2 - 3x

Differentiate the function

f'(x) = 2x - 3

Set the function to 0

2x - 3 = 0

Add 3 to both sides

2x = 3

Divide by 2

x = 3/2

Set x = 3/2 in f(x) = x^2 - 3x

f(x) = 3/2^2 - 3 * 3/2

Evaluate

f(x) = -9/5

So, we have:

(x, f(x)) = (3/2, -9/5)

The above represents the vertex of the quadratic function.

This is properly written as:

(h, k) = (3/2, -9/5)

The vertex form of a quadratic function is

f(x) = a(x - h)^2 + k

So, we have:

f(x) = a(x - 3/2)^2 - 9/5

In f(x) = x^2 - 3x,

a = 1

So, we have:

f(x) = (x - 3/2)^2 - 9/5

Hence, the vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5

Read more about vertex form at

https://brainly.com/question/24850937

#SPJ1