Write (3+4 i)+(8+2 i)as a complex number in standard form

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3 ⇒ 2nd and 4th

Step-by-step explanation:

Let us revise some fact about the product of two numbers

We need to select all the expressions with a product less than 2/3

∵ 4 and 1/8 × 2/3

- 4 and 1/8 means mixed number [tex]4\frac{1}{8}[/tex]

∵ [tex]4\frac{1}{8}[/tex] > 1

- That means the product of it and 2/3 will be greater than 2/3

   as the first fact above

∴ [tex]4\frac{1}{8}[/tex] × [tex]\frac{2}{3}[/tex] > [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{2}{3}[/tex] is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

   as the second fact above

∴ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{2}{3}[/tex] × 2

∵ 2 > 1

- That means the product of it and 2/3 will be greater than 2/3

   as the first fact above

∴ [tex]\frac{2}{3}[/tex] × 2 > [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{5}{6}[/tex] is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

   as the second fact above

∴ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3

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Only the expressions 2/3 x 2/3 and 5/6 x 2/3 have products less than 2/3, with products of 4/9 and 5/9 respectively.

To determine which expressions have a product less than 2/3, each expression must be evaluated separately:

4 and 1/8 x 2/3 = 33/8 x 2/3

2/3 x 2/3 = 4/9

2/3 x 2 = 4/3

5/6 x 2/3 = 10/18 or 5/9

After simplifying, the expressions that yield a product less than 2/3 are:

2/3 x 2/3 = 4/9, as 4/9 is less than 6/9 (2/3)

5/6 x 2/3 = 5/9, which is also less than 6/9 (2/3)

The expressions 4 and 1/8 x 2/3 and 2/3 x 2 are both greater than 2/3.

Answer:

52.33 inches

Step-by-step explanation:

Multiply the length of one side by the square root of 2.

In this case: 37, you would divide that by the square root of 2.

Hope this helps!

Answer:

Question 3:  [tex]4x^3+x^2-12x-3[/tex]

Question 4:  [tex]\frac{1}{2x}, x\neq 0[/tex]

Step-by-step explanation:

Question 3

g(x) * h(x) means to multiply both the functions given.

Also note the distributive property:

[tex](a+b)(n+p)=an+ap+bn+bp[/tex]

Now, lets multiply:

[tex]g(x)*h(x)=(4x+1)(x^2-3)\\=(4x)(x^2)-3(4x)+1(x^2)-1(3)\\=4x^3-12x+x^2-3\\=4x^3+x^2-12x-3[/tex]

The 2nd answer choice is right

Question 4

[tex](\frac{f}{g})(x)[/tex]  means to divide both the functions and simplify, if possible. Lets do this:

[tex](\frac{f}{g})(x)=\frac{6x-3}{12x^2-6x}=\frac{3(2x-1)}{6x(2x-1)}=\frac{3}{6x}=\frac{1}{2x}[/tex]

This is the correct answer.

The restriction on the domain is any x value that we CANNOT PUT IN THE FUNCTION.

We know we cannot divide by 0, so what makes this fraction division by 0??

If we put x = 0, the function is undefined. So x CANNOT be 0.

Third answer choice is right.

Votes received by Wayne is 112

Solution:

To find: votes received by Wayne

Let the vote received by Wayne be "x"

Juan received 4 times as many votes as Wayne

Therefore,

Juan votes = 4 times as many votes as Wayne

Juan votes = 4x  ---- eqn 1

Neal received twenty less votes than Juan

Neal votes = twenty less votes than Juan

Neal votes = Juan votes - 20

Neal votes = 4x - 20 ---- eqn 2

Kerry got half as many votes as Neal

Kerry votes = half of neal votes

Kerry votes = [tex]\frac{4x - 20}{2}[/tex]  ---- eqn 3

The total votes cast in the election was 1,202

Wayne votes + Juan votes + Neal votes + Kerry votes = 1202

Plug in eqn 1 , eqn 2, eqn 3

[tex]x + 4x + 4x - 20 + \frac{(4x - 20)}{2} = 1202\\\\2x + 8x + 8x - 40 + 4x - 20 = 1202 \times 2\\\\22x - 60 = 2404\\\\22x = 2404 + 60\\\\22x = 2464\\\\x = 112[/tex]

Therefore votes received by Wayne is 112

Answer:

10

Step-by-step explanation:

n is the number of selections and k the number selected, that is

n = 5 and k = 2

note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1, thus

[tex]\frac{5(4)(3)(2)(1)}{2!(5-2)!}[/tex]

= [tex]\frac{120}{2(1)3(2)(1)}[/tex]

= [tex]\frac{120}{2(6)}[/tex]

= [tex]\frac{120}{12}[/tex]

= 10

Answer:

7/10

Step-by-step explanation:

you got 7 out of 10 dollars

Answer:

70%

Step-by-step explanation:

Because the fraction would be 7/10 when you make it to precent form it would be 70/100 which is 70%

Answer:

[tex]0.333 - 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.251[/tex]

[tex]0.333 + 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.416[/tex]

The 99% confidence interval would be given (0.251;0.416).

(25.0 ,41.6)

Step-by-step explanation:

1) Data given and notation  

n=219 represent the random sample taken    

X=73 represent the students that reported that they have at least $1000 of credit card debt.

[tex]\hat p=\frac{73}{219}=0.333[/tex] estimated proportion of students that reported that they have at least $1000 of credit card debt.

[tex]\alpha=0.01[/tex] represent the significance level

z would represent the statistic (variable of interest)    

p= population proportion of students that reported that they have at least $1000 of credit card debt.

2) Confidence interval

The confidence interval would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 99% confidence interval the value of [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2=0.005[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.

[tex]z_{\alpha/2}=2.58[/tex]

And replacing into the confidence interval formula we got:

[tex]0.333 - 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.251[/tex]

[tex]0.333 + 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.416[/tex]

And the 99% confidence interval would be given (0.251;0.416).

We are confident that about 25.1% to 41.6% of students have at least $1000 of credit card debt.

And for this case the most accurate option is:

(25.0 ,41.6)

The ounces of chocolate chips used by Mrs Jacob is 70 ounce

Solution:

Given that Jacob is making several batches of cookies and is using 84 total ounces of chips

Let "c" be the ounces of chocolate chips

Let "p" be the ounces of peanut butter chips

To find: ounces of chocolate chips used by Mrs Jacob

Given that There are 5 times as many ounces of chocolate chips as peanut butter chips

Thus we can frame a equation as:

ounces of chocolate chips = 5 x ounces of peanut butter chips

c = 5p -------- eqn 1

Jacob used 84 total ounces of chip. Therefore,

ounces of chocolate chips + ounces of peanut butter chips = 84

c + p = 84 ---- eqn 2

Substitute eqn 1 in eqn 2

5p + p = 84

6p = 84

Substitute p = 14 in eqn 1

c = 5(14) = 70

Thus the ounces of chocolate chips used by Mrs Jacob is 70 ounce

Answer:

D. 384

Step-by-step explanation:

Sorry for the very late response. But if anyone wasn't sure if 384 is correct, it is. I can confirm this because I just took the test. I hope I could help! (:

Answer:

B

Step-by-step explanation:

The 2 part of the ratio represents 39 instructors.

Dividing 39 by 2 gives the value of one part of the ratio, that is

39 ÷ 2 = 19.5 ← value of 1 part of the ratio, thus

number of employees = 12 × 19.5 = 234 → B

Answer:always

Step-by-step explanation:

Answer:

The unit rate of pages per hour is 36 pages per hour .

Step-by-step explanation:

Given as :

Penny reads 12 pages in one-third of an hour.

∵ 1 hour = 60 minutes

So , one-third of an hour = [tex]\dfrac{1}{3}[/tex] × 60 min

Or, one-third of an hour = 20 min

Now, According to question

∵ In 20 min , the number of pages read by Penny = 12

So, In 1 min , the number of pages read by Penny = [tex]\dfrac{12}{20}[/tex]

∴ In 60 min , the number of pages read by Penny = [tex]\dfrac{12}{20}[/tex] × 60 min

i.e In 1 hour ,the number of pages read by Penny = 12 × 3 = 36 pages

Hence,The unit rate of pages per hour is 36 pages per hour . Answer

A negative exponent means to move the decimal point to the left.

5 x 10^-2 = 0.05

Answer:

5 x 10^-2 = 0.05

Explanation:

A negative exponent means to move the decimal point to the left.

Hope this helped!

Have a wonderful day!

~Lola

Answer:

The inequality is [tex]l\times (3.25)\leq 107.25[/tex]

Step-by-step explanation:

Given: Area of volleyball net= [tex]107.25 ft^{2}[/tex]

          Width of Volleyball net= [tex]3.25 \ ft[/tex]

Considering the volleyball net is in rectangular shape and l and w is length and width respectively.

Area of rectangle= [tex]l\times w[/tex]

Now, using formula to form inequality

⇒ [tex]l\times (3.25)\leq 107.25[/tex]

Next, using the inequality to find length of Volleyball net.

∴  [tex]l\times (3.25)\leq 107.25[/tex]

Dividing both side by 3.25

⇒ [tex]l= \frac{107.25}{3.25} = 33\ ft[/tex]

∴ l= 33 ft

The possible length of Volleyball net is 33 ft.

Answer:

b

Step-by-step explanation:

Positive coterminal angle = 688 degrees

Negative coterminal angle = -392 degrees

Solution:

Coterminal Angles are angles who share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians

Positive coterminal angle:

The positive coterminal angle of [tex]-32^{\circ}[/tex] is given as:

We have to find positive coterminal angle between 500° and 1000°

Between 500° and 1000° there is an angle which is coterminal to 0°:

2 x 360° = 720°

positive coterminal angle = [tex]-32^{\circ} + 720^{\circ} = 688^{\circ}[/tex]

Negative coterminal angle:

We have to find negative coterminal angle between – 500° and -50°

Negative coterminal angle = [tex]-32^{\circ} - 360^{\circ} = -392^{\circ}[/tex]

Answer:

So the correct option is D

{-2 , 0 , 4}

Step-by-step explanation:

Given:

A Graph

To Find:

Zeroes of the function graph = ?

Solution:

Zeroes of Graph:

Wherever the function graphs line cuts the x-axis are called ZEROES of the function graphs.

Here there are three different points were the function graphs  cuts on x-axis. Therefore three zeroes,which are -2 , 0 , 4

i.e x = - 2 , x = 0 (origin),and x = 4

So the correct option is D

{-2 , 0 , 4}

Answer:

x = 26

Step-by-step explanation:

The parallel lines are Line l and Line m. The other line shown is the transversal.

When 2 parallel lines are cut by a trasversal it creates 4 euqual angles and another 4 equal angles of different measure.

The angle "5x + 7" is equal to the angle "8x - 71" since they are alternate exterior angles.

So, we can equate both expressions and use algebra to solve for "x". The process is shown below:

[tex]5x+7=8x-71\\8x-5x=71+7\\3x=78\\x=\frac{78}{3}\\x=26[/tex]

Hence,

the value of x is 26

Answer: 40:8 and 20:4

Step-by-step explanation :It matches up if you multiply both top and bottom with 8 to get 40:8 and multiply with 4 to get 20:4 .

Answer:

A and E

Step-by-step explanation:

Answer:

2x - 4

Step-by-step explanation:

Write out the equation:

(2 * x) - 4

Simplify

2x - 4

:)

Answer:

-16n-41

Step-by-step explanation:

2(-n-3)-7(5+2n)

First begin by expanding the bracket.  That is, multiplyingthe brackets by 2 and -7 appropriately.

In  doing so we have,

2(-n) x 2(-3) -7(5) x -7 (+2n)

simplifying becomes:

-2n-6-35-14n

collwct like terms becomes -2n-14n-6-35

Final answer becomes Thus: -16n-41

Answer:

Area =  [tex]2w^2+12w+16[/tex]

Step-by-step explanation:

We let the width of the pool be "w"

We know the length is twice as long as width, so the length is:

2w

So,

Width = w

Length = 2w

Since a sidewalk with 2 feet width goes around the pool completely, the area enclosed by pool + sidewalk would have 2 feet around it, so its length and width would be:

Width = w + 2 + 2 = w + 4

Length = 2w + 2 + 2 = 2w + 4

The area of a rectangular region is always length * width, so the expression for area of pool and sidewalk would be:

[tex](w+4)(2w+4)\\=2w^2+4w+8w+16\\=2w^2+12w+16[/tex]

If we let the width of the swimming pool be "w", the expression for the area of pool and sidewalk is:

Area =  [tex]2w^2+12w+16[/tex]

The number that satisfies the condition that, when added to five and then doubled, is one less than the number itself is -11. We found this number by setting up an equation and solving for the variable.

Let's define x to be the number we're trying to find. According to the question, if the sum of this number and five is doubled, the result is one less than the number.

The equation based on the given information is 2(x + 5) = x - 1. To solve for x, let's distribute the 2 to both terms in the parentheses: 2x + 10 = x - 1.

Next, we need to get all the x terms on one side and the constant terms on the other side. We can do this by subtracting x from both sides, giving us: x + 10 = -1. Then, subtract 10 from both sides to isolate x: x = -11. So, the number we're looking for is -11.

The equation of line in point slope form is y - 4 = 7x - 56

Solution:

Given that m = 7 and point is (8, 4)

We have to find the equation of line in point slope form

It emphasizes the slope of the line and a point on the line

The point slope form is given as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where "m" is the slope of line

Substitute m = 7 and (x, y) = (8, 4) in above point slope form

[tex]y - 4 = 7(x - 8)[/tex]

[tex]y - 4 = 7x - 56[/tex]

Thus equation of line in point slope form is found

We can write the equation in standard form

The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.

[tex]y - 4 = 7x - 56\\\\7x - y -52 = 0[/tex]

Answer:

D

Step-by-step explanation:

We need to find 2 roots of the quadratic function given and find the greater of the two roots.

We factorize the quadratic and find the two solutions first:

[tex]x^2-6x+5=0\\(x-5)(x-1)=0\\x=1,5[/tex]

So,

x = 1

and

x= 5

Out of the two, x = 5 is the greater root.

D is the correct answer.

Answer:

8a+5

Step-by-step explanation:

Like terms and yea

Answer: 8a + 5

Step-by-step explanation:

Combining like terms makes you add 5a + 3a and +7 - 2

With 4.5 rolls of wire, the electrician can wire up to 6 rooms, assuming a constant wire requirement per room and no additional factors like wastage or special installations.

If an electrician requires 3/4 of a roll of electrical wire to wire one room, then to wire multiple rooms, you can multiply this amount by the number of rooms. In this case, we're dealing with 4 and 1/2 rolls of wire, which is equivalent to 4.5 rolls.

To find out how many rooms can be wired, divide the total amount of wire available by the amount needed for one room:

4.5 rolls ÷ 3/4 roll per room = 4.5 ÷ 3/4 = 6.

So, with 4 and 1/2 rolls of wire, the electrician can wire up to 6 rooms in the house. Keep in mind that this calculation assumes a constant amount of wire is needed for each room and that there are no extra factors like wastage or additional requirements for special installations.

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The question is incomplete. Here is the complete question:

During ski season,the owner of ski shop has determined that the number of customers in a day is greater than or equal to 50 more then the temperature(Fahrenheit) . Write an inequality for the problem and determine the constraints on the variables.

Answer:

[tex]N\geq T+50[/tex]

Step-by-step explanation:

Let the number of customers be 'N' and the temperature in Fahrenheit be 'T'.

Given:

Number of customers is related to temperature in Fahrenheit as:

Number of customers is greater than or equal to 50 more than the temperature in Fahrenheit. This means,

[tex]N\geq T+50[/tex]

Now, since 'N' represents number of customers and number can never be a negative quantity. So, the only constraint for this inequality is that the number of customers must be greater than or equal to 0.

So, [tex]N\geq 0[/tex]

Answer:

m∠1 = 50°

m∠2 = 88°

Step-by-step explanation:

Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.

Answer:

2.) m/_1 = 50

3. )m/_2=88

Step-by-step explanation:

2.) the line that the exterior angle 140 is on is a straight line. this means it is 180 degrees. 180 - 140 = 40. the box in the left corner means it is a right angle or 90 degrees. evey triangle is 180 degrees so add 40 and 90 to get 130 and then subtract 130 from 180 to get 50 which is the angle number 1.

3.)the line 120 is on is a straight line so we do 180 minus 120 to get the angle inside. it is 60. 60 +32 = 92. 180 - 92 is 88 degrees.

The solution is x = 4

Step-by-step explanation:

The given equation is a linear equation so it will have only one equation

Given equation is:

[tex]5x+3=2x+15​[/tex]

Subtraction property of equality:

[tex]5x+3-3 = 2x+15-3\\5x = 2x+12[/tex]

Subtraction property of equality:

[tex]5x-2x = 2x-2x+12\\3x = 12[/tex]

Division Property of Equality:

[tex]\frac{3x}{3} = \frac{12}{3}\\x = 4[/tex]

Hence,

The solution is x = 4

Keywords: Linear equation, variables

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Using the distributive property...

2(x+3) = 2x+6

answer: 2x+6