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Answer:

22 - 34i

Step-by-step explanation:

note that i² = - 1

Given

(5 - 4i)(6 - 2i) ← expand factors using FOIL

= 30 - 10i - 24i + 8i²

= 30 - 10i - 24i - 8 ← collect like terms

22 - 34i

Answer:

22 - 34i

Step-by-step explanation:

Answer:

Noun. (plural simplified expressions) (mathematics) an expression that has been condensed and shortened, so that all the like terms have been combined.

Step-by-step explanation:

you are welcome!

Answer:

i answered all of them!

Step-by-step explanation:

Answer:

13 th and 14 th

Step-by-step explanation:

Since the line divides the cup into one - eighth

Thus a measurement of 1 3/4

The number of 1/8th's obtainable from 1 3/4 :

1 3/4 = 7/4

7/4 divided by 1/8th

7/4 ÷ 1/8

7/4 × 8/1

= 56/4 = 14

14 gives the upper limit of the line starting from the bottom, Therefore, a measurement of 1 3/4 should be between the 13 th and 14 th line. Since the bottom of the cup will have no line.

Answer:

the answer for 58-(14)2=

its = 30

Step-by-step explanation:

58-(14)2. It can also be written as 58-2(14)

58-28

= 30

Answer:

x = - 5, x = 2

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

note that log x = [tex]log_{10}[/tex] x

Given

log (x² + 3x) - log10 = 0, then

log([tex]\frac{x^2+3x}{10}[/tex] ) = 0, thus

[tex]\frac{x^2+3x}{10}[/tex] = [tex]10^{0}[/tex] = 1 ( multiply both sides by 10 )

x² + 3x = 10 ( subtract 10 from both sides )

x² + 3x - 10 = 0 ← in standard form

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

Solution is x = - 5, x = 2

Answer:

The equation has the solution(s) x = - 5, and x = 2

Step-by-step explanation:

Let's start by adding log(10) to either side of the equation --- (1)

[tex]\log _{10}\left(x^2+3x\right)-\log _{10}\left(10\right)+\log _{10}\left(10\right)=0+\log _{10}\left(10\right)[/tex]

= [tex]\log _{10}\left(x^2+3x\right)=\log _{10}\left(10\right)[/tex]

If you recall, one property proves that [tex]\log _{10}\left(10\right):\qu 1[/tex]. We can substitute this value back into the simplified equation --- (2)

[tex]\log _{10}\left(x^2+3x\right)=1[/tex]

We can also apply the logarithmic definition, If logₐ(b) = c then b = aᶜ. Using this definition we receive a further simplified equation --- (3)

[tex]x^2+3x=10^1[/tex]

[tex]x^2+3x=10[/tex]

Solving for the expression we receive the solution(s) x = 2, and x = - 5, our first option.

Note : The first solution is correct, but I wanted to take a slightly different approach

Answer:

it will be A. good buddy

Step-by-step explanation:

The data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123. The correct option is B.

A stem-and-leaf display, also known as a stem-and-leaf plot, is a technique used to visualize the shape of distribution by displaying data in a graphical fashion, similar to a histogram.

The data represented by the different rows of stem-and-leaf display is,

First row → 25, 26, 27

Second row → 53, 58

Third row → 62, 67, 69

Fourth Row → 96, 96

Fifth Row → 123

Hence, the data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123.

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Answer:

Total income = 27 [tex]\times[/tex] 25 + 14% of $1000= $815

Step-by-step explanation:

Number of hours for which Johnathan worked = 25

Salary for each hour = $27

So, income for 25 hours = 25 [tex]\times[/tex] 27 = $675

Now, it is given that he has sold 25 items.

Sales made beyond the 20 items = $1000

Additional income for additional sales = 14% on each set of 5 items

He has sold exactly 5 additional items that means 1 set of 5 additional items.

So, Additional income for additional sales = 14% [tex]\times[/tex] 1000 = $140

Therefore, total income of this week = Income for 25 hours + Income due to additional sales of 5 items

Therefore Total income = 27 [tex]\times[/tex] 25 + 14% of $1000= $815

Answer:

a^2-9

Step-by-step explanation:

Answer:

1:4

Step-by-step explanation:

Find the ratio of corresponding sides

[tex]\frac{10}{40}=\frac{1}{4}\\\\\\\frac{11}{44}=\frac{1}{4}\\\\\\\frac{18}{72}=\frac{1}{4}\\\\\[/tex]

Scale factor:

1:4

Answer:

4
To find the scale factor, we need to know what number we multiply each side length in Figure AAA by to get the corresponding side length in Figure BBB.

Let's see how the corresponding sides relate:

10×4

11×4

18×4

​

=40

=44

=72

​

===============================================

Explanation:

Add the equations by adding the terms straight down.

The x terms add to x+x = 2x.

The y terms add to y+(-y) = y-y = 0y = 0, so the y terms go away

The constants add to 5+7 = 12

The z terms add to -z+z = 0z = 0 and those go away as well

After all that adding, we have 2x = 12 which solves to x = 6 after dividing both sides by 2.

Answer:

C. 65

Step-by-step explanation:

By the property of intersecting chords inside a circle.

[tex] TW\times WU = CW\times WV[/tex]

[tex] 14\times (2x + 2)= 12\times (2x + 5)[/tex]

[tex] 28x + 28= 24x + 60[/tex]

[tex] 28x - 24x =60-28[/tex]

[tex] 4x =32[/tex]

[tex] x =\frac{32}{4}[/tex]

[tex] x =8[/tex]

UT = 14+ 2x + 2

CV = 12+2x+5

UT + CV = 14 + 2x + 2 + 12 + 2x + 5

UT + CV = 4x + 33

UT + CV = 4*8+ 33 = 32 + 33 = 65

UT + CV = 65

Answer:

Hey there!

Angle x would be 62 degrees because angles in a triangle add to 180 degrees.

Let me know if this helps :)

Answer:

x = 62 degrees

Step-by-step explanation:

Total degrees of a triangle = 180

=> 68.5 + 49.5 + x = 180

=> 118 + x = 180

=> 118 - 118 + x = 180 - 118

=> x = 62

Answer:

3h+7/h

Step-by-step explanation:

the parenthesis in g(4+h) is saying that is x. plug in 4+h in the x and evaluate.

so you would get 3(4+h)-5. distribute the 3 and get 12+3h-5. combine like terms to get 3h+7!

then it's just over h because you can't simplify anymore. so the real answer is 3h+7/h!!

Answer:

y ≥ 2

Step-by-step explanation:

The range is all of the values that f(x) can have. In order to find the range, let's first find the vertex. That's pretty easy to do since f(x) is already written in vertex notation (vertex notation is f(x) = a(x - c)² + d where (c, d) is the vertex). Since c = -5 and d = 2, the vertex is (-5, 2). Because the value of a is positive (a = 3 in this case, which is positive) we know that the parabola opens upward, therefore the vertex is the minimum. This means that the y-coordinate of the vertex is the smallest possible y-value of the function, therefore, since the y-coordinate of the vertex is 2, the range is y ≥ 2. Note that we use ≥ and not >, this is because y can be 2, therefore, it is included in the solution set.

Answer:

Hey there!

First, we must understand what range is. Range is just another word for all the possible y values of the equation.

This equation, f(x) = 3(x+5)² +2 is in vertex form. We see that this creates a parabola with a vertex at (-5, 2) and opens up.

Thus, the range of this graph would be: [2,∞) in interval notation. Note, the [ is used for greater than or equal to, or less than or equal to, and the ")" is used for less than or greater than.

We use ) for ∞, because ∞ is just a concept, not a real number.

Finally, all functions are defined for all values of x means that this is an f(x) function, and the f(x) is equal to something that can be written in terms of x.

Let me know if this helps :)

Answer: p= 1/7

Step-by-step explanation:

5/7=p+4/7

-p=4/7-5/7

-p=-1/7

P=1/7

Answer:

35 minutes

Step-by-step explanation:

From 2:42 to 3:00, there are 18 minutes and from 3:00 to 3:17, there are 17 minutes so the answer is 18 + 17 = 35 minutes.

Answer:

The correct option is;

d. 130·(60·h)+2000 = 43000

Step-by-step explanation:

The volume of water held by a pool at Sapphire island = 43,000 gallons

The volume of water the pool currently holds = 20,000 gallons

The rate at which the pool is being filled = 130 gallons/minute

The equation to find h, the number of hours it will take to fill the pool from its current level can be written as follows;

The rate at which the pool is being filled in gallons per hour = 130 × 60 gallons/hour = 7800 gallons/hour

We have;

The volume of water pumped in h hours = (130×60) gallon/hour × h hour =  130×60×h gallons

Whereby we want the total volume of water in the pool to be 43,000 gallons, we add the volume of water obtained from pumping for hours to the volume of water already in the pool, to get 43,000 gallons as follows;

130×60×h gallons + 20,000 gallons = 43,000 gallons

Therefore, the correct option is 130·(60·h)+2000 = 43000.

Answer:

10.05 units

Step-by-step explanation:

We can find the distance between these points using the distance formula. The distance formula is:

[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

We know that x1 is 3, x2 is 4, y1 is 4, and y2 is -6, so we can substitute inside the equation.

[tex]\sqrt{(4 - 3)^2 + (-6 - 4)^2} \\\\\sqrt{1^2 + -10^2} \\\\\sqrt{1 + 100} \\\\\sqrt{101} \\\\\approx10.05[/tex]

Hope this helped!

Answer:

no solution

Step-by-step explanation:

|4x + 8| + 12= 4

Subtract 12

|4x + 8| = -8

An absolute value must be non negative

Since ours is negative, there is no solution

Answer:

10 times

Step-by-step explanation:

Since the leftmost value is called ones place.

the second leftmost value is called tens place.

the third leftmost value is called a hundred place.

the fourth leftmost value is called a thousand place and so on.

So, The value of 4 in 4,735 is 4 thousand = 4,000

and the value of 4 in 6,412 is 4 hundred = 400.

Hence, the value of the 4 in 4,735 is 10 times the value of the 4 in 6,412.

Answer:

10 times greater.

Step-by-step explanation:

4 in 4735 has a values of 4000.

In 6412 it has a values of 400.

Answer:

Step-by-step explanation:

let l be the length of the rectangle

let w be the width of the rectangle

The statement

The length of a rectangle is 6 feet more than three times the width of the

rectangle is written as

l = 6 + 3w

From the question

l = 24 feet

Substitute the value into the above formula and solve for the width

That's

24 = 6 + 3w

3w = 24 - 6

3w = 18

Divide both sides by 3

w = 6

Therefore

Hope this helps you

Answer:

A kite

Step-by-step explanation:

The coordinates of the vertices of the quadrilateral are;

A(2, 3), B(4, 6), C(8, 9), and D(5, 5), therefore,  the length of the sides of the quadrilateral can be found using the following formula;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

(x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints on the side

For side AB, we have;

[tex]l_{AB} = \sqrt{\left (6 - 3 \right )^{2}+\left (4-2 \right )^{2}} = \sqrt{13}[/tex]

The slope = 1.5

For side BC, we have;

[tex]l_{BC} = \sqrt{\left (9 - 6 \right )^{2}+\left (8-4 \right )^{2}} = 5[/tex]

The slope = 3/4

For side CD, we have;

[tex]l_{CD} = \sqrt{\left (5 - 9 \right )^{2}+\left (5-8 \right )^{2}} = 5[/tex]

The slope = 4/3

For side DA, we have;

[tex]l_{DA} = \sqrt{\left (3 - 5 \right )^{2}+\left (2-5 \right )^{2}} = \sqrt{13}[/tex]

The slope = 2/3

Angle ADC = Actan (2/3 - 4/3)/(1 + 2/3*4/3) = -19.44 = 180-19.44 = 160.55°

Angle ABC = Actan (0.75 - 1.5)/(1 + 0.75*1.5) = -19.44 = 180-19.44 = 160.55°

Therefore, given that the quadrilateral has two pairs of equal adjacent sides and the angles are equal at the meeting point of the two squares, it is best described as a kite.

Answer:

no solution

Step-by-step explanation:

|m|/2 -1=-3

step 1= |m|/2=-3+1

step 2=|m|/2=-2

Step 3: Solve Absolute Value.

  |m|=−4

No solutions. (Absolute value cannot be less than 0.)

Greetings,

I hope you and your family are staying safe and healthy!

Answer: No Solution

Step-by-step explanation:

[tex]\frac{|m|}{2} - 1 = -3\\\\\frac{|m|-2}{2} = -3\\\\[/tex]

Alternate forms assuming m > 0

[tex]\frac{m}{2} -1 = -3\\\\\frac{m-2}{2} = -2[/tex]

[tex]\frac{\sqrt{m^2} }{2} - 1 = -3[/tex]

Therefore,

No solutions exist.

I guaranteed correct answers only. Please kindly rate my answer and press the heart. Thanks!

Answer:

72

Step-by-step explanation:

Consecutive even integers have a difference of 2 between them

let n be the first integer, then

n + 2, n + 4, n + 6 are the second, third and fourth, then

n + 2 + n + 6 = 76 ( sum of second and fourth )

2n + 8 = 76 ( subtract 8 from both sides )

2n = 68 ( divide both sides by 2 )

n = 34

Thus the 4 even integers are

34, 36, 38, 40

sum of first and third = 34 + 38 = 72

Answer:

0.4 l of purple sand

Step-by-step explanation:

Volume to be filled in:

Red sand

Blue sand

Yellow sand

Total volume filled:

Purple sand needed:

Answer is 0.4 l of purple sand required

5 / 4 =1.25PER LB

1.25 x 6 =7.5

Answer:

Hey there!

3x-9=12

3x=21

x=7

Let me know if this helps :)

Answer:

Step-by-step explanation:

[tex]3x - 9 = 12 \\ collect \: like \: terms \\ 3x = 12 + 9 \\ 3x = 21 \\ divide \: both \: sides \: by \: 3[/tex]

[tex] \frac{3x}{3} = \frac{21}{7} \\ x = 7[/tex]