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Answer: The given triangles have an area [tex]1/2[/tex] × [tex]base[/tex] × [tex]height[/tex]

Step-by-step explanation:

The moving principle states that if you move a shape rigidly without stretching it the area does not change whereas the additivity principle states that if you combine different shapes without overlapping them then the area is the cumulative sum of each of the figures.

Since both, the principle will give out the same answers. the arrangement for the expression can be manipulated also.

For the first triangle applying the moving principle gives,

Area  [tex]=[/tex] [tex]b[/tex] × [tex](\frac{1}{2}[/tex] · [tex]h)[/tex]

For the second triangle applying the additivity principle,

Area [tex]=\frac{1}{2}[/tex] ([tex]b[/tex] · [tex]h[/tex])

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Answer: (10, ∞)

Step-by-step explanation:

See the graph in the attached image.

Answer:

[tex]\mathsf {A. x = -5}[/tex]

Step-by-step explanation:

[tex]\implies \mathsf {-3 + x = -8}[/tex]

[tex]\implies \mathsf {x = -8 + 3}[/tex]

[tex]\implies \mathsf {x = -5}[/tex]

The total distance travelled is 1075.91 km.

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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Answer: -120

Step-by-step explanation:

[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]

Answer:

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Let the initial price be x.

After the first sales quarter the price is reduced by 10% and became:

After the second sales quarter the price is reduced by 20% and became:

The decrease over the two quarters is:

This is equivalent of 28%, hence the correct answer choice is B.

If the number of multiple-choice questions is x and the number of short answer questions is y, then:

[tex]x+y=28\\\\3x+5y=100[/tex]

Answer: 2

Step-by-step explanation:

When x = 3, y = -2.

When x = 6, y = 4.

The average rate of change over the interval is:

[tex]\frac{-2-4}{3-6}=\frac{-6}{-3}=\boxed{2}[/tex]

Answer:

x = 2

y = 4

Step-by-step explanation:

Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.

Add the 3 on its lower left to get 10.

so, 3 - x = 1. x = 2

17 - y = 13. y = 4

Step-by-step explanation:

You need to attach the table in order to get an answer.

Answer:

44.70 US dollars

Step-by-step explanation:

euro left=(250/1.3687)-150=32.66(rounded to nearest cents

US dollars=32.66x1.3687

                =44.70US dollars

Answer:

Step-by-step explanation:

The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.

__

Let x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...

  0.15x +0.07(70000-x) = 9000

__

Simplifying the equation gives a 2-step linear equation.

  0.08x +4900 = 9000 . . . . simplified

  0.08x = 4100 . . . . . . . . . . subtract 4900

  x = 51,250 . . . . . . . . . . . .divide by 0.08

  70000 -x = 18,750

The woman should invest $51,250 at 15% and $18,750 at 7%.

Answer:

The answer will be 63%.

Step-by-step explanation:

they have all ready mentioned that.

Answer:2

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Answer:

The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)

Step-by-step explanation:

Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

apply row operations:

R₂= R₂ - 2 R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

R₃= R₃ -  R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right][/tex]

R₄ = R₄ +R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right][/tex]

R₄ = R₄ +R₃

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right][/tex]

we can clearly see that after performing row operations there are 3 non zero rows,

therefore the Rank of the given matrix is 3

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Car averages x miles per gallon means that 1 gallon is enough to drive 36 miles.

We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).

Total miles driven is 10+50=60.

As a car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons

A data set, the arithmetic mean, also known as arithmetic average, is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.

As a car averages 40 miles per gallon on the highway for 50 miles on the highway it will use

50/40=1.25 gallons;

So average miles per gallon equals to

[tex]=\frac{10+50}{0.4+1.25}\\=36[/tex]

Therefore option D is correct.

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Answer: Each child gets 1/3

Step-by-step explanation: x/3

Answer: C

Step-by-step explanation:

An equation is formed of two equal expressions. The correct option is C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved for x as shown below, Therefore,

[tex]\dfrac{rx+t}{s} = w\\\\[/tex]

Using the multiplication property of equality, multiply s on both the sides of the equation,

rx + t = ws

using the subtraction property of equality, subtract t on both the sides of the equation,

rx = ws - t

[tex]x = \dfrac{sw-t+t}{r}[/tex]

Hence, the correct option is C.

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Answer:

power of a power

Step-by-step explanation:

the power of a power law says that, "if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same."

for example, for this problem, you would do:

[tex](x^4)^9\\= x^4^*^9\\= x^3^6[/tex]

Answer:

Option B :39 degrees is the correct.

The nearest degree is 39°

Step-by-step explanation:

Laws of cosines relates each side with its opposite angle.

Formula for this is :

[tex]c^{2} =a^{2} +b^{2} - 2abcosC[/tex]

[tex]a^{2} = b^{2}+c^{2} - 2bccosA[/tex]

[tex]b^{2} =a^{2}+c^{2} -2accosB[/tex]

in figure a=28

              b=18

              c=25

Here we have to find angle between a and c that is B

So [tex]18^{2} = 25^{2} +28^{2} -2*25*28cosB[/tex]

324 = 625 + 784 - 1400cosB

1400cosB =  625 + 784 - 324

1400cosB = 1085

cosB = 0.775

∠B = 39.195° ≈ 39°

The boat change 39°  when it made its first turn.

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Answer:

B 39 degrees

Step-by-step explanation:

The person above me is correct and I got proof for the people with trust issues. :  )

Adding 2x to both sides, we get [tex]\boxed{2x+y=5}[/tex]

[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].

We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).

This set is {3, 4, 11, 13, 14, 15, 17, 24}

Answer:

CI = $182.25

Step-by-step explanation:

Compound interest formula:

[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex]  ,

where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).

Using formula:

CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]

CI = $182.25

The numeral preceding and succeeding each of the following numerals.

Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.

Adding adds 1 to the unit digit.

Subtracting 1 gives 99 because 9 is the largest digit in base 10.

So A. 100 base 8

The largest digit in base 8 is 7, so

..., 77, 100, 101,...

B. 10000 base 7

The largest digit in base 7 is 6, so

..., 6666, 10000, 10001, ...

Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:

509 + 1 = 510.

C. 305 base 6

5 is the largest digit in base 6, so

..., 304, 305, 310, ...

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Answer:

127 degrees = x

Step-by-step explanation:

A six sided polygon has interior angles that sum to

(n-2)(180) =  (6-2)(180 = 720

so all of the angles in the question add to 720

 98 + 133 + x + x + 155 + 80 = 720

  solve for x = 127 degrees

Answer:

x = 127

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6 , then

sum = 180° × 4 = 720°

sum the interior angles and equate to 720

x + x + 155 + 80 + 98 + 133 = 720 , that is

2x + 466 = 720 ( subtract 466 from both sides )

2x = 254 ( divide both sides by 2 )

x = 127

Answer:

Blank 1 = SAS

Blank 2 = HL

Black 3 = ASA

Blank 4 = SSS

This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.

Answer:

D

Step-by-step explanation:

In functions like this, its best to pay attention to the end points of the rays.

On the lower line:

it ends at x -1

because it is a closed circle, that means x can also equal -1.

x≤-1

On the upper line:

it starts at -1

it is an open circle, meaning x cannot be -1

x>-1

Answer:

144, 196, 256

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