(-8)-(6+30i) Express your answer in the form (a+bi)

Answer: 2/3

Step-by-step explanation:

7/9 - 2/8 =x 4/9

= 48/72

However, they are asking for the answer in SIMPLEST FORM.

48/72 in simplest form is 2/3.

Answer:

67

Step-by-step explanation:

9*7=63

13*5=65

23*3=69

Answer:

67

Step-by-step explanation:

Only number whose factors are 67 and 1

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The y-coordinate of point A is -22

Step-by-step explanation:

Given

B = (24,16)

P = (4,-3)

The formula for mid-point of AB will be given by:

[tex]P = (\frac{x_A+x_B}{2} , \frac{y_A+y_B}{2})[/tex]

As we already know the y-coordinate of midpoint

We can put the formula's y coordinate equal to the given value

[tex]\frac{y_A+y_B}{2} = -3\\\frac{y_A + 16}{2 } = -3\\y_A+16 = -3 * 2\\y_A +16 = -6\\y_A = -6-16\\y_A = -22[/tex]

Hence,

The y-coordinate of point A is -22

Keywords: Mid-point, coordinate geometry

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Answer:

27k-20n

Step-by-step explanation:

3(9k-4)-4(5n-3)

27k-12-20n+12

27k-20n-12+12

27k-20n

Answer:

The x-coordinate gives the solution of the original equation.

Step-by-step explanation:

Let us assume that the original equation is 2x = x + 5 ........... (1) and the solution that this equation has will be x = 5.

But, if we solve the equation by graphing each side as a separate line i.e. y = 2x and y = x + 5, then solving those two equations we get the solution x = 5 and y = 10.

Therefore, the x-coordinate i.e. x = 5 gives the solution of the original equation (1). (Answer)

Answer:

D

Step-by-step explanation:

edge

Answer:

The area would be 111.41 unit² ( approx )

Step-by-step explanation:

Given,

KLMN is a trapezoid,

In which KL=MN, KM=15, m∠MKN=49°,

Suppose O and P are point in the segment LM, ( shown below )

Such that,

KN = OP,

In triangle MKO,

m∠KMO = 49° ( ∵ KM ║ LM, using alternative interior angle theorem ),

KM = 15 unit ( given )

[tex]\sin 49^{\circ} = \frac{KO}{KM}[/tex]

[tex]\implies KO = KM \sin 49^{\circ}=15 \sin 49^{\circ}[/tex]

i.e. height of the trapezoid KLMN is 15 sin 49°,

Again,

[tex]\cos 49^{\circ} = \frac{OM}{KM}[/tex]

[tex]\implies OM = KM \cos 49^{\circ}=15 \cos 49^{\circ}[/tex]

[tex]OP + PM = 15 \cos 49^{\circ}[/tex]

[tex]\implies KN + PM = 15 \cos 49^{\circ}----(1)[/tex]

Now, in right triangles KOL and NPM,

KL = MN,

OK = NP

By HL postulate of congruence,

Δ KOL ≅ Δ NPM

By CPCTC,

LO = PM,

⇒ LM = LO + OP + PM = PM + OP + PM = OP + 2PM = KN + 2PM-----(2),

Thus, the area of the trapezoid KLMN,

= 1/2 × height × sum of opposite parallel sides

[tex]=\frac{1}{2}\times KO\times (KN+LM)[/tex]

[tex]=\frac{1}{2}\times KO\times (KN+KN + 2PM)[/tex]

[tex]=\frac{1}{2}\times KO\times (2KN+2PM)[/tex]

[tex]=KO\times (KN+PM)[/tex]

[tex]=15 \sin 49^{\circ}\times 15 \cos 49^{\circ}[/tex]

[tex]=111.405157734[/tex]

[tex]\approx 111.41\text{ square unit }[/tex]

The area of a triangle can be found using the formula 1/2 x base x height. For a base of 166 mm and height of 930 mm, the area is 77.19 cm². However, for trapezoid KLMN, additional information is needed to calculate its area.

To find the area of a trapezoid, especially when it has special properties like equal non-parallel sides (as trapezoid KLMN does with KL equal to MN), we often need to break it down into simpler shapes such as triangles and rectangles. However, with the information given, it's not straightforward to calculate the area of the trapezoid without additional height or angle information. The area of a triangle can be calculated using the formula ½ × base × height. For example, if you have a triangle with a base of 166 mm and height of 930.0 mm, the area is calculated as ½ × 166 mm × 930.0 mm which equals 77190 mm² or 77.19 cm² when converted to square centimeters, maintaining the proper number of significant figures.

Answer:

B or D ( answer = 5 => Two options is one! One of the options should be 5)

Note: The width of a rectangle will never be negative.

Answer:

its d. 5

Step-by-step explanation:

Answer:

5184

Step-by-step explanation:

first of all we sove multiplication of terms then addition

2592+1296+1296

5184 ans

Answer:

The equivalent equation is correctly matched with a key feature of the graph is

y = 3(x + 2) highlights that the x-intercept is at -2.

Step-by-step explanation:

Given:

[tex]y=3x+6[/tex]

Solution:

The Given Equation is in Slope - Point Form i.e

[tex]y=mx+c[/tex]

Where,

[tex]m=slope\\\\c=y-intercept[/tex]

On Comparing the given equation with above we get

[tex]slope=m=3\\\\y-intercept =6[/tex]

Now we Know that

Intercepts:

The line which intersect on x-axis and y-axis are called intercepts.

There are two intercepts:

y-intercept: The line which intersect at y-axis. So when the line intersect at y-axis X coordinate is zero.

x-intercept: The line which intersect at x-axis. So when the line intersect at x-axis Y coordinate is zero.

For x-intercept

Put y = 0 in

[tex]y=3(x+2)[/tex]

[tex]0=3x+6\\\\3x=-6\\\\\therefore x=\dfrac{-6}{3}=-2[/tex]

∴ x-intercept of

[tex]y=3x+6[/tex]

x-intercept = -2

The equivalent equation is correctly matched with a key feature of the graph is

y = 3(x + 2) highlights that the x-intercept is at -2.

Final answer:

Each apple costs 41 cents when a dozen apples are bought for $4.92, determined by dividing the total cost by the number of apples.

Explanation:

The question asks to find the cost per apple when a dozen apples are purchased for $4.92. To find the cost per individual apple, you divide the total cost by the number of apples. There are 12 apples in a dozen, so:

$4.92 ÷ 12 apples = $0.41 per apple

So, each apple costs 41 cents. This exercise of finding the individual cost from a total is an example of a ratio used in basic arithmetic, often taught in middle school mathematics.

s>7

So, all values greater than 7 are included in the number line.

Step-by-step explanation:

We need to use number line to show numbers in the solution set of the inequality 2s+ 36 greater than 50

Solving and finding value of s:

2s+36>50

Adding -36 on both sides

2s+36-36>50-36

2s>14

Divide both sides by 2

s>7

So, all values greater than 7 are included in the number line.

The number line is shown in figure attached below

Keywords: Solving inequalities

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Answer:

A

Step-by-step explanation:

Took the test in edge

Answer:

Step-by-step explanation:

If 2 pounds costs $4, then 1 pound costs $2.  That's why the equation is y = 2x and x is the number of pounds you buy.  If you buy 2.5 pounds, then the cost is y = 2(2.5) so

y = $5

Answer:

22

Step-by-step explanation:

21.6 would round up because 6 is closer to 10 than it is 0

The number 21.6 rounded to the nearest whole number is 22.

Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.

Rounding can be done for whole numbers as well as decimals.

Given a number 21.6.

We have to round the number.

Here the first digit after the decimal place is 6, which is greater than 5.

So we have to add 1 to the last digit in the whole part.

So 21.6 is rounded to 22 to the nearest whole number.

Hence the correct number is 22.

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Answer:

$768

Step-by-step explanation:

Let x bet the cost of 124 training session.

Given:

Maria finds a local gym that advertises 101 training sessions for $626.

Find the cost of 124 training sessions.

Solution:

cost for each training sessions [tex]=\frac{626}{101}[/tex]

cost for each training session = $6.19

So, we get cost of 124 training sessions by multiplication of cost of each training sessions and number of training sessions.

[tex]x=cost\ of\ each\ training\ session\times number\ of\ training\ session[/tex]

[tex]x=6.19\times 124[/tex]

[tex]x=767.56[/tex]

round 767.56≅768

[tex]x=768[/tex]

Therefore, the cost of 124 training sessions is $768

Step-by-step explanation:

Solve the bracket first. starting with multiplication and then subtraction

0.00035 + (4.2 x 10-5)

0.00035 + (42-5)

0.00035 + 37

0.01295

Answer:

Step-by-step explanation:

9×3 = 27

9×4 = 36

9×5 = 45

HOPE IT HELPS

Answer : 9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,162,171,180,189,198,207,216,225,234,243,252,261,270,279,288,297,306,315,324,333,342,351,360,369,378,387,396,405,414,423,432,441

Answer:

The equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.

Step-by-step explanation:

As the sentence statement is

"Two more than 1/3 of number is eight".

Lets decode this sentence and write the corresponding mathematical expression.

Hence, the equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.

Keywords: equation, algebraic expression

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Complete Question with table is attached

Answer:

Miguel will save money of $90 if he earns $120.00

Step-by-step explanation:

The figure attached clearly shows the ratio of his earnings and savings. We have to find what would be the savings amount if he earn $120.00. So, first we have to calculate the percentage of ratio of his earnings and savings. As per the data given in the figure,

If he earns $10.00, he saves $7.50, calculate %amount he saves as below,

           [tex]\frac{\$ 7.50}{\$ 10.00} \times 100=0.075 \times 100=75 \%[/tex]

Likewise, calculate for all given data. If he earns $50.00 then he saves $37.50

           [tex]\frac{\$ 37.50}{\$ 50.00} \times 100=0.75 \times 100=75 \%[/tex]

If he earns  $150.00 and save $112.50,

           [tex]\frac{\$ 112.50}{\$ 150.00} \times 100=0.75 \times 100=75 \%[/tex]

So, from all above, it clearly tells that Miguel saves 75% of amount from his earnings. Now, given earnings as $120.00. By finding 75% of $120.00, we can find his savings in that amount. So,

             [tex]\frac{75}{100} \times \$ 120=0.75 \times 120=\$ 90[/tex]

Answer:

D. $90.00

Step-by-step explanation:

Answer:

The length of A'B' is 15 units

Step-by-step explanation:

As line segment AB has end points

The distance formula to calculate the distance between two points is given by:

[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]

[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]

[tex]d=\sqrt{16^2+(-12)^2}[/tex]

[tex]d=\sqrt{256+144}[/tex]

[tex]d=\sqrt{400}[/tex]

[tex]d=20[/tex]

[tex]d=20[/tex] is also the length of the line segment AB.

As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.

So,

The length of A'B' can be obtained by multiplying the length of AB by 3/4

Therefore,

The length of A'B' = 3/4 × 20 = 15

So, the length of A'B' is 15 units.

Keywords: dilation, distance formula, length, line segment

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Answer:

  The slopes of the lines are different.

Step-by-step explanation:

If you do convert the standard form equation to slope-intercept form, you get ...

  y = -x +5

You see that the slope of this line is -1, whereas the slope of the other line is +1. Both lines have a y-intercept of 5. It is the slopes that are different.

_____

You can determine this to be the case without converting the form of the equation if you have some practice with the various forms of the equation of a line.

In standard form, if the variable signs are the same, the slope is negative. Of course, in slope-intercept form, the sign of the slope is the sign of the coefficient of x.

Answer:

C,D,A

Step-by-step explanation:

Answer:
Was it factory or dealer-installed?
Are there charges for documents like taxes and tags?

Is there a dealer advertising fee?

Step-by-step explanation:

''Step two involves preparing a list of suitable questions for the dealers you wish to visit. For example, if you want rustproofing, was it factory-installed or dealer-installed? Are there charges for documents like taxes and tags? Is there a dealer advertising fee? These charges won't appear on a factory invoice, but you will pay for them.''

Answer:

93 h

Step-by-step explanation:

P = 4300eᵏᵗ

1. Calculate the value of k

lnP = ln4300 + kt

ln5800 = ln4300 + k(40 h)

8.666 = 8.366 + 40k h

8.666 - 8.366 = 40k h

0.299 = 40 k h

k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹

2. Calculate the time for the population to double

2 × 4300 = 4300eᵏᵗ

2 = eᵏᵗ

ln2 = kt

t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h

It takes 93 h for the population to double.

Answer:

11/10

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10

Answer: 105.26

Step-by-step explanation: 9263/88=105.26

Do you have or own a calculator?

Final answer:

The resulting solid will have four edges.

Explanation:

To find the number of edges in the resulting solid, let's first determine the dimensions of the solid after the wedges are cut off.

The original wooden block measures 2 inches by 2 inches by 3 inches. After cutting off the wedges, each side will be reduced by 2 inches (1 inch from each corner), resulting in a solid with dimensions of 2 - 2(1) = 0 inches by 2 - 2(1) = 0 inches by 3 - 2(1) = 1 inch.

A solid with dimensions of 0 inches by 0 inches by 1 inch is essentially a rectangular prism with one dimension equal to zero. Such a solid has six faces, eight vertices, and four edges.

Therefore, the resulting solid will have four edges.

Answer: Yes, it does, because each input value has an unique output value.

Step-by-step explanation:

First, you need to know when a relation is considered a function.

By definition, a relation is a function if an only if each input value has one and only one output value.

It is important to remember that the input values are the values of "x" and the output values are the values of "y".

Then, in this case, you can observe in the graph attached ( which shows the data for Camille’s puppy), that each x-value (Weeks) has an unique y-value (Weight in pounds).

Therefore, based on this and keeping on mind the explained before, you can conclude that the data for Camille’s puppy shows a function.

Answer:

Yes it does

Step-by-step explanation:

Because it passes the vertical line test and it only touches 1 unit point in the line no need for big explanations you cant understand

Answer:

[tex]\frac{1}{20}[/tex]

Step-by-step explanation:

First, we need to look at the # of chips. There are a total of 25, 6 of which are blue.

This means that the chance of getting the first blue chip would be [tex]\frac{6}{25}[/tex]

As there is no replacement, the total number of chips is 24 and there are only 5 blue left. This gives us the chance of [tex]\frac{5}{24}[/tex]

Now all we need to do is mulitply these two and then simplify

[tex]\frac{6}{25} *\frac{5}{24} =\frac{30}{600} =\frac{1}{20}[/tex]

Answer:

1/20

Step-by-step explanatio

pick without replacement must mean pick it two times without put back the first chip

6/25 x 5/24 = 1/20

Answer:

option C. and D.

Step-by-step explanation:

For two quantities with inverse variation, as one quantity increases, the other quantity decreases. For example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases.An inverse variation can be represented by the equation xy=k or y=kx .

The best use of a sign chart when graphing rational functions involves identifying critical points, determining function values within each interval, and using this information to sketch the graph. The sign chart is a valuable tool for analyzing the behavior of a rational function on the x-axis.

The sign chart is a useful tool when graphing rational functions because it helps identify the intervals where the function is positive, negative, or undefined. This information is crucial for accurately sketching the graph of a rational function. Here is how to use a sign chart:

Identify the critical points of the function by setting the numerator and denominator equal to zero and solving for the variables.

Choose a value from each interval determined by the critical points and evaluate whether the function is positive or negative at that value.

Record the signs in a table or chart to visualize the pattern.

Use the sign chart to determine the intervals on the x-axis where the function is positive, negative, or undefined.

Plot any vertical asymptotes, holes, and x-intercepts on the graph.

Sketch the graph by using the information from the sign chart and locating the appropriate points.

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Answer:

A) [tex]\frac{x+y+z}{3}[/tex]

Step-by-step explanation:

the formula for average is the sum of the digits, then divide that sum by the number of digits.

for example: let x = 1, let y = 2, let z = 3

so 1+2+3 is 6

then divided by the number of digits: 3

6/3=2

the average is 2