There are 6 cans of juice of the same weight and a box. If the 6 cans
are put in the box, the total weight of the cans and the box is 1620 g.
If only 2 cans are put in the box, the total weight is 660g. How many
grams does this box weigh?

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

Flip the equation:

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

Add -3 to both sides:

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

[tex]\fbox{x = y - 3}[/tex]

__________________________________________________________

[tex]x-2y=-1[/tex] for y

Add -x to both sides:

[tex]x-2y+-x=-1+-x[/tex]

[tex]-2y=-x-1[/tex]

Divide both sides by -2:

[tex]\dfrac{-2y}{-2} =\dfrac{-x-1}{-2}[/tex]

[tex]\fbox{y = $\dfrac{1}{2}x+ \dfrac{1}{2} $}[/tex]

The solution of the compound inequality are

-2x ≤ 4   and  10 ≥ -2x

10 < 3x - 2 OR -3x - 2 > 14

A sentence or equation having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality.

To solve the compound inequality each of them is solved individually

-2x ≤ 4   and  10 ≥ -2x

-2x ≤ 4           10 ≥ -2x

dividing by a negative sign reverses the inequality    

x ≥ -2              -5 ≤ x

plot attached

The solution of the inequality is x ≥ -2  and -5 ≤ x

10 < 3x - 2 OR -3x - 2 > 14

10 + 2 < 3x       -3x > 14 + 2

12 < 3x              -3x > 16

3 < x                 x < -5.333

3 < x                 x < -5

plot attached

The solution of the inequality is 3 < x  OR   x < -5

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The required vertices of the triangle C'D'E' are (-8, 1), (-6, 5), and (-2, 4) respectively.

Given that,
Triangle CDE is reflected over the x-axis. What are the vertices of triangleC'D'E' is to be determined.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,

The coordinates of vertices  C, D, and E are (-8, -1), (-6, -5), and (-2, -4) respectively.

For the reflection across the x-axis is given as,

(x , y) = (x  -y)

Now,

C(-8, -1) across the x-axis C'(-8 , 1)

D(-6, -5) across the x-axis D'(-6 , 5)

E(-2, -4) across the x-axis E'(-2 , 4)

Thus the required vertices of the triangle C'D'E' are (-8, 1), (-6, 5), and (-2, 4) respectively.

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Answer:

Step-by-step explanation:

2. Subtraction property of equality

3. Simplification

4. Subtraction property of equality

5. Simplification

Using system of linear equations, the law firm employed  7 associate and 9 partners

The system of linear equations can be defined as a set of two or more linear equations that have the same variables. Linear equations can be said as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

In this question, we have to write out two equations and solve for the unknown variable.

let;

x + y = 16 ...eq(i)

400x + 1000y = 11800 ...eq(ii)

From equation 1

x = 16 - y ...eq(iii)

Put eq(iii) into equation (ii)

400(16 - y) + 1000y = 11800

6400 - 400y + 1000y = 11800

6400 + 600y = 11800

600y = 11800 - 6400

600y = 5400

y = 5400 / 600

y = 9

Put y = 9 in equation (i)

x + 9 = 16

x = 16 - 9

x = 7

The firm has 7 associate and 9 partners

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Answer:

Try Doing Like this.

If u still need to understand, watch organic chemistry tutor guide or ask tr until u understand.

Inequality                                                 classifications

x + 5y = −2 and x + 5y = 4                       Inconsistent

y = 3x + 4 and −2x + y = 4                       consistent and independent

3x + y = 4 and −6x − 2y = −8                   consistent and dependent

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

x + 5y = −2

x + 5y = 4  

subtracting gives

0 = -6 no solution  

A system is deemed consistent if it has at least one solution.

A consistent system is independent if it only has one solution.

-3x + y = 4

−2x + y = 4  

subtracting gives

-x = 0

x = 0

substituting x to get y

-3 * 0 + y = 4

y = 4

A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.

3x + y = 4

−6x − 2y = −8

subtracting gives

9x + 3y = 12 - none cancels out meaning infinite number of possible solutions

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The function representing the given situation will be f(x) = x², where x is the number of week.

A function is defined as a relation between a set of inputs having one output each.

Given that, Cate started with $0 in her account. After one week, Cate saved $1; after two weeks she saved $4; after three weeks she saved $9; and after four weeks she saved $16.

As we see,

In 1 week the amount is $1

In 2 week the amount is $4

In 3 week the amount is $9

Which is showing that the amount is square of the week.

Hence, we can write the function as f(x) = x², where x is the number of week.

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The number of pizzas there now will be 3 ¹⁷/₂₀. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Eli brings 6 3/5 pizzas to a party. His companions eat 5 7/10 pizzas. Peng appears with 2 3/4 pizzas.

⇒ (6 + 3/5) - (2 + 3/4)

⇒ (33 / 5) - (11 / 4)

⇒ (132 - 55) / 20

⇒ 77 / 20

⇒ 3 ¹⁷/₂₀

The number of pizzas there now will be 3 ¹⁷/₂₀. Then the correct option is D.

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Option D in the correct form is given below.

D. 3 17/20

Answer:

2nd Option

Step-by-step explanation:

m=6

y=-3

so from equation

y=mx+c

y=6x-3

is the req ...... equation..

Answer: 2nd Option is the answer for this

Step-by-step explanation:

Answer:

u = 112

Step-by-step explanation:

u/4-8=20

u/4 - 8 + 8 = 20 + 8  ==> add 8 on both sides to isolate u

u/4 = 28

4 * u/4 = 4 * 28  ==> multiply by 4 on both sides to isolate u

u = 112

The probability of the card being an ace, given that it is a non-face card will be 0.1 or 10%

There are total 52 cards.

Out of 52, 26 are red and 26 are black.

Each of the four French suits—clubs (♣), diamonds (♦), hearts (♥) and spades (♠).—has 13 ranks in a regular 52-card deck. King, Queen, and Jack are the three court cards (face cards) in each suit, and their pictures are reversed (double-headed). The ten numerical cards, or pip cards, in each suit range in value from one to 10.

Out of 52 cards, (Kings, Queen, Ace) are faced card.

And each set of cards have 4 different colour and shades.

So, total number of faced card will be = 4*3 = 12

So, total number of not a faced card = 52-12 = 40

So, the value of P (It is an ace and it is not a face card) =4/52

So, the value of P(It is not a face card)=40/50

[tex]P\left(\frac{\text { It is a ace }}{\text { It is not a face curd }}\right) =\frac{P(\text { It is an ace and it is not aface carl) }}{P(\text { It is not a face card) }} \\\\ =\frac{\frac{4}{52}}{\frac{40}{52}}\\\\=\frac{4}{40}\\\\=0.1=10\% }[/tex]

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Montag serves as a metaphor for free thought in Fahrenheit 451. Guy doesn't fit in with society as Beatty or Mildred do.

Although the parallels are subtle, there are some similarities between the modern world and the setting of "Harrison Bergeron" in the narrative. Egality is a topic that both of them address and that has issues and effects. Another resemblance is the conflict that results from competition and attempts to stop it from happening, both of which cause issues.

The manipulative and desensitizing impact of the mass media is one political practice in American culture that the short story "Harrison Bergeron" might be seen as an oblique indictment of. overregulation of some human actions. restricting freedom of speech

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The measure of the third angle = 105°.

What is angles?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The sum of the angles in a triangle is :

A° + B° + C° = 180°

Where A, B and C are the three angles in a triangle.

Hence, if two of the angles are given as : 55° and 20°

The measure of the third angle will be :

Let the measure of the third angle = C

(55 + 25 + C) = 180°

180° - (55° + 20°)

180° - 75° = 105°

The measure of the third angle = 105°

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Answer:

160/3

Step-by-step explanation:

[tex]\frac{2^{2010}+2^{2008}}{2^{2005}-2^{2003}} \\ \\ =\frac{2^7 + 2^5}{2^2 - 1} \\ \\ =\frac{128+32}{4-1} \\ \\ =\frac{160}{3}[/tex]

You will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.

What is continuous compound interest?

In theory, continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

The formula for continuously compounded interest is:

              [tex]A = P * e^{rt}[/tex]

where:

A is the ending balance (the amount you will have after 4 years)

P is the principal (the initial amount you deposited, in this case $3,000)

r is the interest rate (2.5% per year, or 0.025)

t is the time in years (4 years)

Plugging these values into the formula, we get:

            [tex]A = $3,000 * e^{(0.025 * 4)}[/tex]

Calculating this gives us an ending balance of $3,276.44.

Hence, you will have $3276.44 after 4 years if you deposit $3,000 at an annual interest rate of 2.5%, compounded continuously.

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The number of dark chocolate AJ sold is 75

Simultaneous equations are two or more algebraic equations that share variables e.g. m and d . They are called simultaneous equations because the equations are solved at the same time.

If the number of Milk chocolate candy is m and the number of dark chocolate candy is d, then

m+d= 200 equation 1

3m+4d= 675 equation 2

to eliminate m we multiply both equations by 3

3m+3d= 600 equation 3

3m+ 4d=675 equation 4

subtract equation 3 from 4

d = 675-600

d= 75

Therefore the number of dark chocolate candy AJ sold is 75.

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The area of the composite figure is 242in² as per the given information in the figure.

Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).

A crossed rectangle is a crossed (self-intersecting) quadrilateral made up of two opposing sides and the two diagonals of a rectangle[4] (therefore only two sides are parallel). It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic,  with opposite sides of equal length and equal angles that are not right angles.

Area =Area of the down rectangle+ Area of the up rectangle+2×Area of the triangle

Area= (7×24)+(4×13)+2×(1/2)×b×4

Let, 13+2x=24

Here, x=b

So, 2b=11

b=11/2

Area= 168+52+4(11/2)

Area=168+52+22

Area=242in²

Therefore, the area of the composite figure is 242in².

So, option C is correct.

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There are no equations that 's suitable.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

823÷418=2

1112÷834=1.333333333

Hence, There are no equations that 's suitable.

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The value of the expression divide negative 3 and one-sixth ÷ negative 8 and two-fifths is 95 over 252. Option B

A fraction can be defined as the part of a whole item, number or element.

The several types of fractions are;

From the information given, we have that;

-3 1/ 6 ÷ - 8 2/ 5

Turn into improper fractions

-19/ 6 ÷ 42/ 5

Take the inverse of the divisor and multiply

- 19/ 6 × 5/ 42

95/252

Hence, the value is 95/252

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Amy is considering visiting her new friend at one of his beach houses she chooses to visit  Destin and 85.

Amy is considering visiting her new friend at one of his beach houses in Florida.

She really loves the warm weather,

So she would like to choose to go somewhere with a high median temperature, and a small interquartile range.

We have to determine the place should she choose to visit.

Interquartile range :

The interquartile range is a measure of where the middle fifty is in a data set.

Destin HI 70 75 80 85.

Here She can choose the 4th position and which is 85.

The only one that passes 85.

Amy is considering visiting her new friend at one of his beach houses she chooses to visit Destin and 85.

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Answer:

  (B) 146 feet

Step-by-step explanation:

You want to know the maximum height of a pebble whose height is described by p(t) = -16t² + 48t + 110.

We can write the equation in vertex form as follows:

  p(t) = -16(t² -3t) +110

  p(t) = -16(t² -3t +2.25) +110 +16(2.25)

  p(t) = -16(t -1.5)² +146

This shows the vertex of the quadratic curve to be (1.5, 146).

The maximum height of the pebble is 146 feet.

Step-by-step explanation:

then we do the multiplications and compare :

(x - p)² = q

x² - 2px + p² = q

x² - 2px + p² - q = 0

our target is

x² + 4x - 20 = -8

x² + 4x - 12 = 0

now we compare the variable expression with the target.

x² = x² check

4x = -2px

4 = -2p

p = -2

-12 = p² - q = 4 - q

-16 = -q

q = 16

so, we have

(x - -2)² = 16

(x + 2)² = 16

The value of the a is 2.

What is the fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when used in conversational English.

We have,

8⁻¹ / 4⁻¹ - a⁻¹ = 1

By simplifying the given equation we get,

8⁻¹ - a⁻¹ = 1 * 4⁻¹

By further calculating the equation,

1/8 - 1/a = 1/4

4(1/8 - 1/a) = 1

4/8 - 4/a = 1

1/2 - 4/a = 1

4/a = 1/2

1/a = 4/2

a = 2/4

a = 2

Hence, the value of the a is 2.

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It is growing exponentially so this is non linear function of squares of given negative numbers.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element. A relation between a domain and range is called a function when each value in the domain only has one value in the range.

Here,

0²=0

-1²=1

-2²=4

-3²=9

Hence, It is a nonlinear function of the squares of the given negative numbers because it is growing exponentially.

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Answer: 10

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]6^2 + 8^2=x^2\\\\36+64=x^2\\\\100=x^2\\ \\ x=10[/tex]

a ball is dropped from a height of 20 feet. each time it drops h feet, it rebounds 0.89h feet, 343.63 feet the total distance traveled by the ball.

The length of the line connecting any two places is known as their distance from one another. Subtracting the different coordinates will reveal the distance if the two locations are on the same horizontal or vertical line.

h₁ = 20 feet = h

h₂ = 0.89h

h₃ = 0.89²h

h₄ = 0.89³h

...........................

h(n) = 0.89ⁿh

Therefore, total distance travelled = 20 + 2 (0.89h + 0.89²h + 0.89³h +.....)

                                                        = 20 + 2h (0.89 + 0.89² + 0.89³ +.....)

Sum of (h.p)∞ = a/ (1-r)

Where, a = first term = 0.89

r = common ratio = 0.89

total distance travelled = 20 + 2 × 20 ×(0.89) × [1/(1 - 0.89)]

                                      = 343.63 ft.

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Answer:

Step-by-step explanation:

im not 100% sure but probly 135

Answer:

angle c and b are 137 degrees both

Step-by-step explanation:

given angle is 43° and when subtracted from 180°

we have 137°.

using the alternative angle property the angle b is also 137°.

Answer:

x=21

y=9/15 or 15/9

Step-by-step explanation

scale factor is either 15/9 or 9/15 - can't tell which way by the question

9/15x35=21

x=21