Need help with Systems of 2 Equations Word Problems . Problem 3.

Answer:

138 grams of zinc

Step-by-step explanation:

Zinc : copper = 3 : 19

Let amount of zinc = 138 grams

3 : 19 :: x : 874

Product of means  = product of extremes

19 * x = 3 * 874

      x = \(\frac{3*874}{19}\)

      x = 3 * 46

Zinc = 138 grams

\(\underline{\underline{\sf \bigstar \qquad Solution \qquad \: \bigstar}} \\ \)

Let weight of copper be 3x and weight of zinc be 19x.

☯ \(\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\\)

\(:\implies \textsf {Total weight = weight of copper + weight of zinc} \\ \\ \\ \)

\(:\implies \textsf {Total weight = 3x +19x} \\ \\ \\ \)

\(:\implies \underline{ \boxed{ \textsf {Total weight = 22x}}} \\ \\ \\ \)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━

\(\dashrightarrow\:\:\textsf{ Weight of chemical = weight of zinc + weight of copper} \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x = 3x + 19x \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x = 3x + 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 22x - 3x = 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf 19x = 874 \\ \\ \\ \)

\(\dashrightarrow \: \: \sf x = \dfrac{874}{19} \\ \\ \\ \)

\(\dashrightarrow \: \: \underline{\boxed{ \sf x = 46}} \\ \\ \\\)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

\(\bigstar\:\underline{\frak{Finding \: the \: weight \: of \: the \: zinc \: in \: a \: chemical : }}\)

\(\longrightarrow\:\:\sf weight \: of \: zinc = 3x \\ \\ \\ \)

\(\longrightarrow\:\:\sf weight \: of \: zinc = 3 \times 46 \\ \\ \\ \)

\(\longrightarrow\:\: \underline{ \boxed{\sf weight \: of \: zinc =138 \: grams}} \\ \\ \\ \)

\(\therefore\:\underline{\textsf{The chemical contains \textbf{138 grams}} \textsf{ of zinc}}. \\ \)

Answer:

That day Jiao spent $CNY 514.29.

Step-by-step explanation:

Given that Jiao is a Chinese student visiting family in the United States, and she spent $ 79 on dinner for her family one evening, if the exchange rate that day is UDS to CNY = 6.51, to determine approximately how much money did she spend in CNY the following calculation must be performed:

79 x 6.51 = X

514.29 = X

Therefore, that day Jiao spent $ CNY 514.29.

Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

Answer:

In the notation t(x):

t = name of the function

x = domain or input value

t(x) = is a range (or output) value y for a given x.

The symbol "t(x)" is read as the value of t at x, or simply t of x.

The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

2) Yes

3) No

4) Yes

5) 2x + 8

6) 5(x - 8)

7) 3x + 21

Hope this helps :)

Answer:

2000

Step-by-step explanation:

3x450=1350

1350+650=2000

=2000

Answer:

BODMAS

3 x 450 = 1350

1350 + 650 = 2000

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

A = 30-2x

Step-by-step explanation:

Answer:

the answer is 4 with a square root of 2

Hello

To solve this question, it would be easier if we draw the triangle.

To solve for this, we would use Cosine rule. This is because, we have the values of two sides and one angle.

from the calculations above, the value of G is equal to 651cm

The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Given that:

y = total cost

x = miles

We are also given the system of linear equations that models the scenario given as:

y = 0.27x + 27 --> equation 1

y = 0.21x + 45 --> equation 2

To find the value of x, make both equations equal to each other and solve:

0.27x + 27 = 0.21x + 45

Combine like terms

0.27x - 0.21x = -27 + 45

0.06x = 18

Divide both sides by 0.06

0.06x/0.06 = 18/0.06

x = 300

To find the value of y, plug in the value of x into equation 1, and find y:

y = 0.27(300) + 27

y = 81 + 27

y = 108

Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

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Answer:

see below

Step-by-step explanation:

x+y = 0 so x= -y

2x+4y =1 so -2y+4y = 1 so 2y = 1

so y = 0.5

x = -0.5

Answer:

C = 8π m

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

use the given area (A) and solve for r

A = πr² = 16π ( divide both sides by π )

r² = 16 ( take square root of both sides )

r = \(\sqrt{16}\) = 4

then

C = 2π × 4 = 8π m

Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

Answer:

50 i think if im wrong sorry

For the given expression √25 = ∛125. As, 5 is equal to 5.

For the given question;

Square root of 25 i.e, √25

To identify the square root of 25, determine the number because when multiplied by itself yields 25. The square root of 25 is thus 5.

To find the cube root of 125, determine the number that when multiplied on its own twice yields 125.

The cube root of 125 is thus 5, because 5×5×5 = 125.

The radical sign with such a small three (named the index) above and on the left is the symbol for cube root.

Thus, both the values are equal.

√25 = ∛125.

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Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

The value of side length c is 13.55 units.

The length of side c is calculated by applying sine rule as shown below;

The formula for sine rule is given as;

a/sinC = b/sinA

For the given question, we will have the following equation,

c/sin (34) = 11 / sin (27)

The value of c in the triangle is calculated as follows;

c = (sin 34 / sin 27 ) x 11

c = 13.55 units

Thus, the value of side length c is determined by applying sine rules.

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To answer this question we will construct the factor tree.

Computing the subtraction we get:

Dividing the above result by 5 we get:

Dividing by 7 we get:

Dividing by 19 we get:

Dividing by 577 we get:

Notice that 1009 is a prime number.

Therefore the factor tree is as follows:

Answer: The prime factors of (3^18 - 2^18) are 5, 7, 19, 577, and 1009.

1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Answer:

Missing Angle = 26⁰ ( corresponding angles )

The angle of elevation of the ladder is 59.0 degrees

We can use trigonometry to solve this problem. Let x be the angle of elevation of the ladder. Then, we have:

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

In this case, the opposite side is 12 ft (the height of the ladder), and the hypotenuse is 14 ft (the length of the ladder).

We want to find the angle x, so we can use the inverse sine function:

So, we have

sin(x) = 12/14

sin(x) = 0.8571

Take the arc sin of both sides

x = 59.0 degrees

Hence, the angle is 59.0 degrees

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The cost of the carpet will be $2,335.5.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The dimensions of the carpet are;

⇒ 15 feet by 18 feet

Now,

The area of the carpet = 15 x 18

                                   = 279 feet²

                                   = 270 / 3 yards²

                                   = 90 yards²

Since, The carpet costs = $25.95 per square yard.

Hence, The carpet cost for 90 yards² = 90 x $25.95

                                                          = $2,335.5

Thus, The cost of the carpet will be $2,335.5.

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Answer:

13 correct me if i am wrong

Step-by-step explanation:

The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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Answer:

it is option C

hope it helps

97 And 83

Answer:

$18.28

Step-by-step explanation:

To complete this problem is a straightforward answer:

First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!