Which step contains a mistake in solving for the system of equations?

x + 2y = 5
y = 3x - 8

1. x + 2(3x) - 8 = 5
2. x + 6x - 8 = 5
3. 7x = 13
4. x = 13/7
5. 7x 8 5

Answer:

9/34

Step-by-step explanation:

I find when multiplying fractions, its easier to separate them into the numerator and denominator.

So we have 12 x 3, and 17 x 8

12 x 3 = 36

17 x 8 = 136

So we have 36/136

Simplified, that is 9/34

Answer:

488

Step-by-step explanation:

2(20x8) + 2(20x3)+2(8x3)

Assuming the "x" is not a variable.

The answer is 488

However, if "x" is a variable. The equation would be

40x^8 + 56x^3

Answer:

488

Step-by-step explanation:

using BODMAS

METHOD 1.

[tex]2(20 \times 8) + 2(20 \times 3 + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) = \\ = 320 + 120 + 48 \\ = 448[/tex]

METHOD 2.

[tex]2(20 \times 8) + 2(2 \times 3) + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) \\ = 2(160 + 60 + 24) \\ = 2 \times 244 \\ =488[/tex]

The total number of miles for the four trips is 25 miles.

Given that;

Linda traveled for one hour each day for four days at a speed that made her cover one mile in an even number of minutes. After the first day, she started to lose speed, and it took her 5 minutes longer to complete a mile than the day before. Her journey distance was also an integer amount of miles throughout the four days.

We know that,

Distance is a product of speed and time. We need to find the distance here with the use of the given conditions, time is 1 hour.

Speed = Distance / Time

Hence, speed is 1 mile per x minutes because we want to distance by multiplying the time and speed together yielding 60 min * 1 mile / x mins.

Minutes cancel out, so now we have 60/x as our distance for the first day.

The distance for the given case;

⇒ [tex]\frac{60}{x},\frac{60}{x+5},\frac{60}{x+10},\frac{60}{x+15}[/tex]

It is given that x = 5;

⇒ [tex]\frac{60}{5},\frac{60}{10},\frac{60}{15},\frac{60}{20}[/tex]

= 12 + 6 + 4 + 3

= 25

The total number of miles for the four trips is 25 miles.

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Answer:

the bakery sold 1468 blueberry buns sooooo yeah

Step-by-step explanation:

To select the community, there are 20 ways available.

What is Combination?

A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant.

Solution:

Since 2 particular students are to be included,

we have to arrange 3 students from 6 students.

nCr = n! / (n-r)!*r!

6C2 = 6!/ (6-3)! 3!

6C2 = 6*5*4*3!/ 3! * 3*2

6C2 = 5*4 = 20

Thereofre, there exists 20 ways of doing the above mentioned.

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Answer:

h=2

h= -7/5

hope this helped :)

The expression for the cost of each scarf is s/4.

According to the question,

We have the following information:

Let s be the total amount Heidi spent for scarves. each of the 4 scarves that she bought cost the same.

Now, the cost of 1 scarf can be easily found by dividing the total cost of the scarves by the number of scarves.

(If we would have to find the cost of 15 scarves then first we would have used division and then multiplication.)

So, we have the following expression:

4 scarves = s

Cost of one scarf = s/4

Hence, the expression for the cost of each scarf is s/4.

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Answer:

length is 20 yards, width is 15 yards

Step-by-step explanation:

Length = width + 5

2(W + 5) + 2(W) = 70

2W + 10 + 2W = 70

4W + 10 = 70

4W = 60

W = 60 ÷ 4

W = 15 yards

L = 15 + 5

L = 20 yards

Answer:

[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]

Step-by-step explanation:

When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator.  To do this, find the lowest common multiple (LCM) of the denominators.

The given subtraction is:

[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}[/tex]

The LCM of the denominators 2 and 8 is 8.  Therefore, we need to rewrite the first fraction as an equivalent fraction with 8 as its denominator.  To do this, multiply its numerator and denominator by 4:

[tex]\implies \sf \dfrac{1}{2} \times\dfrac{4}{4}=\dfrac{4}{8}[/tex]

Therefore:

[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}[/tex]

To subtract fractions with the same denominator, simply subtract the numerators. (The denominator stays the same).

[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}=\dfrac{4-1}{8}=\dfrac{3}{8}[/tex]

Final solution

[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]

Answer:

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

Step-by-step explanation:

66.6% = 0.6666... = [tex]\frac{2}{3}[/tex]

Answer:

Fraction = 2/3

Step-by-step explanation:

Given information,

→ Percentage = 66.6%

→ Decimal = 0.6

→ Fraction = ??

Then the required fraction is,

→ Percentage ÷ 100

→ 66.6/100

→ 2/3

Hence, the fraction is 2/3.

The first four terms of the sequence would be -

9, 12, 15, 18

Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -

3, 6, 9, 12, 15

x, x + 2, x + 4, x + 6

We have the following sequence -

f(n) = 3n + 6

We can write the first four terms as -

f(1) = 3 x 1 + 6 = 9

f(2) = 3 x 2 + 6 = 12

f(3) = 3 x 3 + 6 = 15

f(4) = 3 x 4 + 6 = 18

Therefore, the first four terms of the sequence would be -

9, 12, 15, 18

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The area of hexagon is found to be 18 square units by using the giving conditions.

P = 6a, where an is the length of one of its sides, is the formula for a regular hexagon's perimeter. Here, the hexagon's interior angles are all 120 degrees.

Given: The perimeters of an equilateral triangle and a regular hexagon are equal.

We need to find the area of the hexagon.

Let,

x = side of trainagle

a = side of hexagon

3x = 6a

x = 2a

Area of equilateral triangle = ([tex]\sqrt{3}[/tex]/4)x² = 12 square units

Area of hexagon is given as follows:

= 6([tex]\sqrt{3}[/tex]/4)a²

= (6[tex]\sqrt{3}[/tex]/4)(x²/4)

= 12(6)/4

= 18 square units

Therefore, the area of hexagon is found to be 18 square units by using the giving conditions.

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Answer:

a = 5 cm

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (13)² = a² + (12)²

→ 169 = a² + 144

→ a² = 169 - 144

→ a = √25

→ [ a = 5 cm ]

Hence, value of a is 5 cm.

80°,20° or 50°,50° are possible for the other two angles.

Given:

One angle of an isosceles triangle measures 80°.

we assumed that the 80° is one of the equal angles, then there is another 80° angle.That makes 160°.

Since a triangle always totals 180°,

180° - 160° = 20°.

if the 80° was the only different angle instead,the two remaining angles total:

180 - 80 = 100

Since we have two identical angles remaining, we need only divide the 100° in half to get the final answer:

100/2 = 50°.

Therefore 80°,20° or 50°,50° are possible for the other two angles.

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Darryl receive $579.44  in dividends every year .

In the question ,
it is given that

Darryl's portfolio

number of shares of Essentia Inc. = 66

dividend received from each share in a year = $1.79 per share

So , amount of dividend received from Essentia Inc. = 66 × 1.79

= $118.14

number of shares of SFT Legal = 95

dividend received from each share in a year = $2.62 per share

So , amount of dividend received from SFT Legal = 95 × 2.62

= $248.9

number of shares of Grath Oil = 180

dividend received from each share in a year = $1.18 per share

So , amount of dividend received from Essentia Inc. = 180 × 1.18

= $212.4

So , total dividend Darryl receives = $118.14 + $248.9 + $212.4

= $579.44

Therefore , amount of dividend received by Darryl each year is $579.44  .

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Answer: $58.50

Step-by-step explanation:

    We will set up a proportion to help us solve.

[tex]\displaystyle \frac{15\; \text{boxed lunches}}{\$175.50} =\frac{5\; \text{boxed lunches}}{\$x}[/tex]

     Next, we will cross-multiply.

15 * x = 175.5 * 5

15x = 877.5

x = $58.50

0.001828 (option b) is the probability that the hand contains 4 jacks .

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Number of ways to pick the four jacks = 4C4

Number of ways to pick the other 8 cards from 48= 48C8

Number of ways to pick a hand of 12 from the full deck = 52C12

P(4 J's and 8 others)= [4C4*48C8]/52C12 = 377348994/2.06379...x10^11

=0.001828...

------------

This is the same as the probability of picking 8 cards that are not

jacks in a hand of 12 cards or 48C8/52C12.

-----------

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Answer:

9

Step-by-step explanation:

Pythagorean triples. 3, 4, 5. Multiply by 3 and get 9.

The surface area of the triangular prism is  936 cm².

In geometry, a triangular prism is a three-sided prism.

Therefore, the surface area of the triangular prism can be calculated as follows:

surface area of triangular prism = bh + L(x + y + z)

where

Therefore,

surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)

surface area of triangular prism = 432 + 7(72)

surface area of triangular prism = 432 + 504

surface area of triangular prism = 936 cm²

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Answer:

Step-by-step explanation:

A and D are the answers that I would pick

Answer:

B and C

Step-by-step explanation:

- 1 / -3 = 1/3, we know negative divide by a negative number = positive

- -1/3 = 1/3, we know negative times negative = positive

Answer:

1/28 kilo

Step-by-step explanation:

sb help me on my recent please

Answer:

x = 12

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

This means that 6x - 19 + 3x + 7 + 84 = 180

6x - 19 + 3x + 7 + 84 = 180

==> combine like terms

9x + 72 = 180

==> subtract 72 from both sides

9x = 108

==> divide both sides by 9

x = 12

If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.

What is a measure of angle?

An angle is measured in degrees, thus the term "degree measure." Because one complete revolution equals 360 degrees, it is divided into 360 parts. Each stage of the revolution represents a degree.

The given data:

A measure of EOF = 26 and a measure of FOG = 38.

Then we can say that OF is an angle bisector of angle EOG.

Then the measure of BOG = EOF + FOG

                                            = 26 + 38

                                            =  64 degrees.

Hence, If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.

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Answer:

No solution (0 = 1)

Step-by-step explanation:

Given equation,

→ 5 + 2x = 2x + 6

Then the value of x will be,

→ 5 + 2x = 2x + 6

→ 2x = 2x + 6 - 5

→ 2x - 2x = 1

→ 0 = 1

Hence, there is no solution.

[tex]\boxed{\begin{array}r \large{ \tt solution \: : } \: \: \: \: \: \\ \\ { \longrightarrow5 + 2x = 2x + 6}  \\ \\ \\ ( \sf 2x \: \: present \: \: on \sf\: \: both \: \: \\ \sf sides \: \: of \: \: equality \: \: \: \\ \sf \: \: gets \: \: \sf canceled\: \: out) \\ \\ \sf \longrightarrow5 \neq6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \: \: therefore \: \: there \: \: is \\ \tt no \: \:solution \: \: for \: \: x \: \: \\ \\ \tt that \: \: is \: \: no \: \: value \: \: \: \: \\ \tt \: of \: \: x \: \: that \: \: satisfies \\ \tt the \: \: given \: \: equation\end{array} }[/tex]

The missing side lengths are (m = 4[tex]\sqrt{6}[/tex] , n =  6[tex]\sqrt{2}[/tex]).

According to given triangle, Using triangular formula;

tan 30 = [tex]\frac{2\sqrt{6} }{n}[/tex]

⇒[tex]\frac{1}{\sqrt{3} }[/tex]  = [tex]\frac{2\sqrt{6} }{n}[/tex]

⇒ n = [tex]6\sqrt{2}[/tex]

  n = [tex]6\sqrt{2}[/tex]

Similarly,

sin 30 = [tex]\frac{2\sqrt{6} }{m}[/tex]

⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{2\sqrt{6} }{m}[/tex]

⇒ m = [tex]4\sqrt{6}[/tex]

   m = [tex]4\sqrt{6}[/tex]

so,

    m = [tex]4\sqrt{6}[/tex] and n = [tex]6\sqrt{2}[/tex]

So, the correct option is D.

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The most likely problem with the sample they gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".

Thus, the most likely problem with the sample lycos web site gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".

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The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).

A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

For a dilation with a scale factor of 2, we have:

Point A (-8, 1)   →   (-8 × 2, 1 × 2)  = Point A' = (-16, 2)

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A' = (-16, 2)   →  Points A' = (-(-16), -(1)) = (16, -1).

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Complete Question:

What is the image point of (-8, 1) after the transformation D₂ о R180°?

As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.

What is directrix?

A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:

Directrix - conic section

Directrix - generatrix

Directrix - rational normal scroll

The equation of a quadratic function, with vertex (h,k), is:

y = (a)(x - h)² + k

In which, a is the leading coefficient.

The directrix is: y = k + 4a.

In this problem, the equation of parabola is given as:

y = (1/8)(x-2)² - 3

The coefficients in the given equation are a = 1/8 = 0.125,

h = 2, k = -3,

Hence the directrix is given by:

y = -3 + 4 x 0.125

y = -3 + 0.5

y = -2.5.

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