What is the solution to the system of equations?A. The solution is (2, 7) because the solution to the system must satisfy both equations simultaneously.B. The solution is (1, 6) because the solution to the system must satisfy one equation or the other equation.C. The solution is (3, 5) because the solution to the system must represent the y-intercepts of both equations.D. The solution is (-1.5, -5) because the solution to the system must represent the x-intercepts of both equations.

The sum of the weight of the empty box and the 940 feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kg.

A number is expressed using scientific notation when it contains a number larger than 1 but less than 10, that multiplies a power of 10

The empty weight of the box = 56.7 grams

The number of feathers added = 940 feathers

Mass of one feather (unit weight) = 0.000567 kilogram

The total weight of the box with the 940 feathers is found as follows;

56.7 grams = 0.0567 kilograms

Mass of the empty box in kilograms = 0.0567 kilograms

Total mass of the 940 feathers 0.000567 × 940 = 0.53298 kilograms

The total weight of the box with the 940 feathers inside is; 0.0567 kilograms + 0.53298 kilograms = 0.58968 kilograms

The total weight of the box and the feathers = 0.58968 kilograms =

[tex]5.8968 \times {10}^{ - 1} [/tex]

kilograms

Rounding the coefficient to the nearest tenth gives;

The total weight of the box and the feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kilograms

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

function G(x)

Step 02:

discrete finite function:

range:

we must analyze the function to find the solution.

range:

{ 3 , 5 , 8 }

The answer is:

range:

{ 3 , 5 , 8 }

15, 0, -8, -9

Negatives go backwards

The measures of the internal angles of the triangle are given as follows:

A triangle is composed by three internal angles, and the sum of it's measures is of 180º.

In the context of this problem, the measures are given as follows:

Considering that the sum is of 180º, we can build an equation to solve for x as follows:

3x + 10 + 6x + 2x + 5 = 180

11x + 15 = 180

11x = 165

x = 165/11

x = 15

Hence the measures of the angles are given as follows:

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The measure of the angles are;

It is important to note that the sum of angles in a triangle is supplementary.

Also, supplementary angles are defined as pair of angles that sum up to 180 degrees.

Two angles are termed supplementary when they add up to give 180 degrees.

Since, we have that the sum of the interior angles of a triangle are supplementary, then,

Angle A + Angle B + Angle C = 180 degrees

Given the values as;

Now, put or substitute the values into the formula

3x + 10 + 6x + 2x + 5 = 180

collect like terms

3x + 6x + 2x = 180 - 15

Add or subtract like terms

11x = 165

Make 'x' the subject by dividing both sides by the coefficient of x, we have;

11x/11 = 165/11

Find the quotient

x = 15

But we have to find the angles by substituting the value of x

m∠ A = 3x + 10 = 3(15) + 10 = 55 degrees

m∠ B = 6x = 6(15) = 90 degrees

m∠ C = 2x + 5 = 2(15) + 5 = 35 degrees

Hence, the angles are 55 degrees,  90 degrees and 35 degrees respectively.

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Using the subtraction between integers, it is found that the distance between -17 and 9 is given by:

B. -26.

When we subtract a positive by a negative, the result is always positive.

This is because the result will take the negative makes the signal of the negative number being inverted, then the negative becomes a positive and is added to the first amount.

For this problem, the numbers are given by:

-17 and 9.

The distance between two points on a number line is given by the subtraction between them, hence:

9 - (-17) = 9 + 17 = 26.

The negative meant that the signal of the -17 was inverted and the number became 17, then it was added with 9 resulting in 26.

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The cost of 11 inches of wire will be 44 cents

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

The 15 inches of wire costs 60 cents, so the cost of 1 inch of wire is;

Rate = 60/15 =4 cents

So the cost of 1 inch of wire which is the rate of 4 cents.

Now we have to find the cost (in cents) of 11 inches wire.

We know the cost of 1 inch of wire cost 4 cents so the cost of 11 inches of wire is;

= Total inches of wire x Price of 1 inch of wire

= 4 x 11

= 44

Tehrefore, The cost of 11 inches of wire is 44 cents

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Answer: The answer is -4.37u-11

Step-by-step explanation: Just do math.

When Janet has $50 in a savings account that earns 10% annually, the interest is $15.

It should be noted that the interest is the extra amount that's given for keeping money for a specified period of time. Interest is the payment of a sum over and above the original amount owed by a lender or deposit-taking financial institution to a depositor or lender, at a set rate.

The formula for calculating interest is given as:

Interest = PRT / 100

where P = Principal. = $50

R = rate = 10%

T = Time = 3

Interest = PRT / 100

Interest = (50 × 10 × 3) / 100.

Interest = 1500 / 100

Interest = $15

The interest is $15.

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The angle 4 is an alternate angle to 80° and this tells us that; ∠4 = 80°

Alternate angles are defined as the angles that occur on opposite sides of the transversal line and have the same size. Thus, Alternate angles are always equal.

These interior alternate angles can be gotten by drawing a Z shape which produces two different types of alternate angles namely alternate interior angles and alternate exterior angles.

Now, we are given that only one known angle in the image which is 80°. However, we see that the angle we want to find which is angle 4 is an alternate angle to the known angle.

Thus, by definition of alternate angles, we can say that ∠4 = 80°

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[tex] {x}^{2} - x - 1 = x + 2 \\ {x }^{2} - x - 1 - x - 2 = 0 \\ {x}^{2} - x - x - 1 - 2 = 0 \\ {x}^{2} - 2x - 3 = 0 \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ \\ or \\ x + 1 = 0 \\ \\ x = 3 \\ \\ or \\ \\ x = - 1[/tex]

WHEN x=3

[tex]y = 3 + 2 \\ y = 5[/tex]

When x=-1

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

NOW WE HAVE A PAIR OF SOLUTIONS AS

( 1 ) If p varies directly as q, for p = 4.5 when q = 12, then the relationship between p and q is p = kq represented as 4.5 = (8/3)12

( 2 ) If p and q is 16 then the direct variation is 1

Any time one quantity directly affects the other, such as when one quantity rises relative to the other and vice versa, there is a direct variation between the two variables. It is the relationship between two variables where one of the variables is a fixed multiple of the other. Since the two variables are directly correlated, they are also known as directly proportional.

There are two kinds of proportionalities: direct variation and inverse variation. When two quantities are multiplicatively connected by a constant, the relationship is said to be proportional. In a direct variation, the ratio of the two quantities stays the same, whereas in an inverse variation, the product of the two quantities stays the same.

If p varies directly as q

for p = 4.5

when q = 12

Then p = kq

4.5 = 12k

k = 12/4.5

k = 8/3

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The algebraic expression for the statement the product 7 and the square of a number is 7x²

Algebraic expressions are described as mathematical expressions that consist of arithmetic terms, factors, constants, variables and coefficients.

These expressions are also composed of arithmetic operations which may include;

From the information given, we have that;

The product 7 and the square of a number

Now, let the number be x

The square of x is x²

This statement is expressed as;

7x²

Thus, the expression is 7x²

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The complete question:

The product 7 and the square of a number. Write the algebraic expression

Answer:

8 ( x + 3y + 2z) we can take 8 common in the whole expression

1) Alternate interior angles

2) Corresponding angles

3) Alternate exterior angles

4) Same-side interior angles

5) Vertical angles (angles opposite of each other)

The slope of the line through (-10, 1) and (0, -4) is  [tex]\frac{-1}{2}[/tex].

The slope of the line is m=   [tex]\frac{y_{2}-y_{1} }{x_{2-x_{1} } }[/tex]

                                          =  [tex]\frac{ (-4)- (1)}{0- (-10)}[/tex]

                                          = [tex]\frac{-5}{10}[/tex]

                                          = [tex]\frac{-1}{2}[/tex]

Slope is a measure of the steepness of a line or part of it connecting two points.

The slope of a line is the ratio of the amount by which y increases when x increases by some amount. The slope shows how steep the line is, or how much y increases as x increases.

Types of slopes

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The value of n is 0.06.

Given:

The mass of Earth is 5.97 × 10²⁴ kg.

The mass of Mercury is 3.29 × 10²³ kg.

The ratio of the mass of Earth to the mass of Mercury is represented as 1: n.

The ratio of the mass of Earth to the mass of Mercury can be calculated as,

= mass of Earth/mass of Mercury

⇒  [tex]\frac{5,97*10^{24} }{3.29*10^{23} } = \frac{1}{n}[/tex]

⇒ n = 0.0551

⇒ n ≅ 0.06 ( 2 significant figures)

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we can use the formula

where F is the force, m the mass and a the acceleration

now, replacing

then solve for m

the mass is 19.05Kg

a. The elements are in this sample space = 8.

b.  "there are more heads than tails" = 1.

c. Probability that there are more heads than tails = 1/8.

d. Probability for equal number of heads and tails = 0.

The formula for calculation the probability is;

P(E) = number of times E occurs/ number of times experiment is performed

The sample space of flipping three coins.

S = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

a. The elements are in this sample space.

The total element present on the sample space is 8.

b.  "there are more heads than tails"

Sample space for more heads than tails is only HHH.

S = 1

c. The probability that there are more heads than tails.

Probability = number of heads than tails/total outcome

Probability = 1/8

d. The probability that there are an equal number of heads and tails

S = 0; Non outcome has equal number of head ans tail.

Probability = 0.

Thus, the probabilities of different situations are obtained.

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Distance using absolute value for each example are given below:

As given in the question,

Distance Using Absolute Value

Difference between each set of points on the number line and also confirming it by writing an absolute value statement for each.

1) –15 and 35

Distance Using Number Line     –15 – (–35) = –15 + 35 = 20

Absolute Value Statement    |–15 – (–35)| = 20

2) 47 and –12

Distance Using Number Line    47 – (–12) = 47 + 12 = 59

Absolute Value Statement     |47 – (–12)| = 59

3) –43 and 27

Distance Using Number Line     –43 – (–27) = –43+27 = – 16

Absolute Value Statement      |–43 – (–27)| = 16

4) –10 and 4

Distance Using Number Line     –10 – 4 = –14

Absolute Value Statement     |–10 – 4| = 14

5) 50 and –25

Distance Using Number Line     50 – (–25) = 50 + 25 = 75

Absolute Value Statement     |50 – (–25)| = 75

6) 36 and –19

Distance Using Number Line     36 – (–19) = 36+19 = 55

Absolute Value Statement    |36 – (–19)| = 55

7) –30 and –40

Distance Using Number Line    –30 – (–40) = –30 + 40 = 10

Absolute Value Statement    |–30 – (–40)| = 10

8) –2 and –45

Distance Using Number Line     –2 – (–45) = –2 + 45 = 43

Absolute Value Statement    |–2 – (–45)| = 43

9) 18 and 46

Distance Using Number Line     18 – 46 = –28

Absolute Value Statement    |18 – 46| = 28

10) –10 and –44

Distance Using Number Line      –10 – (–44) = –10 + 44 = 34

Absolute Value Statement    |–10 – (–44)| = 34

11) –28 and 41

Distance Using Number Line       –28 – 41 = –69

Absolute Value Statement     |–28 – 41| = 69

12) 7 and –9

Distance Using Number Line       7 – (–9) = 7+9 = 16

Absolute Value Statement      |7 – (–9)| = 16

13) –52 and 28

Distance Using Number Line       –52 – 28 = –80

Absolute Value Statement      |–52 – 28| = 80

14) 22 and –50

Distance Using Number Line       22 – (–50) = 22 + 50 = 72

Absolute Value Statement       |22 – (–50)| = 72

15) –4 and –31

Distance Using Number Line       –4 – (–31) = –4 + 31 = 27

Absolute Value Statement       |–4 – (–31)| = 27

16) 19 and 51

Distance Using Number Line       19 – 51 = –32

Absolute Value Statement     |19 – 51| = 32

17) 0 and –38

Distance Using Number Line       0 – (–38) = 0+ 38 = 38

Absolute Value Statement      |0 – (–38)| = 38

18) 2 and –14

Distance Using Number Line       2 – (–14) = 2+14 = 16

Absolute Value Statement       |2 – (–14)| = 16

Therefore, distance using absolute value for each example are given below:

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First:

1 divided 1/10:

1 divided 1/10= 10.

2. 4 divided 1/10:

Using the same procedure:

4 divided 1/10= 40.

Using the ruler:

this implies counting each millimeter contained in 1 centimeter, when it is 1 centimeter, there are ten centimeters, and when it is 4 cm there are 40 mm.

Answer:

1 divided 1/10= 10

4 divided 1/10= 40

We have the relation:

y = 4x + 3

Since the slope (4) and the y-intercept (3) were already found, we need now to graph this line.

In order to do so, we can find two points belonging to this line and then draw a line that passes through those points.

The first point can be (0, 3), since we know that the y-intercept is 3, i.e., y = 3 for x = 0.

Now, to find a second point we can choose a value for x, let's say x = 1, and use it in the equation of the line to find the corresponding value of y:

y = 4x + 3 , x = 1

y = 4 * 1 + 3

y = 4 + 3

y = 7

So, (1, 7) is another point we can use.

Now, we can select the second button on the toolbox to draw a line through the points (0, 3) and (1, 7):

Answer:

Josie can by 4 dish sets.

Step-by-step explanation:

Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?

can be represented by equation:

35d + 10 = 150

subtract 10 from both sides:

35d + 10 - 10 = 150 - 10

35d = 140

divide both sides by 35:

35d/35 = 140/35

d = 4

Josie can by 4 dish sets.

check:

35(4) + 10 = 150

The mean of the number of shoes according to the obtained results is; 8.49.

The median of the number of pairs of shoes obtained is; 9.

It follows from the complete task content that the mean and median of the data set are to be evaluated;

Since the mean is the average of all obtained data values, it follows from the mean formula;

Mean = Sum Total/Total Frequency

Mean = { ( 8 × 4 ) + ( 4 × 5 ) + .......+ (13 × 4) } / 65

Mean = 552/65

Mean = 8.49.

Also, the median of the set of 65 data values can be guessed to be the 33rd term.

On this note, the data value which corresponds to a cumulative frequency of 33 upon orderly arrangement is the median term.

Hence, since; 8 + 5 + 4 + 4 + 7 = 28; Hence, upon addition of 14, we have; 42.

Therefore, the median of the number of pairs of shoes is; 9 pairs of shoes.

Remark; The complete task requires that the mean and median be determined.

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Based on the given ratio, the total number of chocolate chip and oatmeal raisin cookies in the cookie box is 10.

The ratio refers to the numerical relationship that one value or number bears to another.

Ratios are fractional values, showing how much a value is contained in another, or in relation to another.

Ratios are depicted using the ratio sign (:), fractions, decimals, or percentages, like proportions.

The ratio of chocolate chip cookies to oatmeal raisin cookies = 1:4

The sum of ratios = 5 (1 + 4)

The number of chocolate chip cookies in the cookie box = 2

Using the above ratio, there will be 8 oatmeal raisin cookies, that is 2/1 x 4

The total number of cookies (both types) in the cookie box = 10 (2/1 x 5).

Thus, we can conclude that based on the relative sizes of both cookies, the total number in the box is 10.

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The missing value for which there is one solution of the equation are 13, -11 and 11.

For the given question,

The expression is given as;

(4/3)(-9x + 12) - x = _x - 9

Putting, 13, -11 and 11 will given the one solution of the equation.

Except -13 as expression is not defined for it.

Put -13 at the blank space and solve it,

-12x + 48 - x = - 13 x - 9

- 13x + 48 = -13x - 9

-13x will get cancelled.

Thus,

48 = -9

But,

48 ≠ -9

Thus, -13 is not a solution of the expression.

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Step 1:

Draw the rectangle with the given dimensions

Step 2:

Next, apply the Pythagoras theorem

Opposite = 12

Adjacent = 18

Hypotenuse = L the side facing right angle

Step 3:

Final answer

The length of the diagonal is 21.6

Answer:14 becuase

Step-by-step explanation:so your dad left you because he $H!T hates you and he want to divorces your mom and he told me to say $H!T you to you

The final answer to the function given as here can be answered as 15 when formulated properly with the formulas substituted to it.

Any kind of mathematical phrase, rule, or law that can be used to establish the link between an independent variable and a dependent variable.

This function can be solved as

Given f(x) = 4x – 1,

as in here f (4) = 4 x 4 – 1

f (4) = 15

A function is a kind of rule that has the ability to produce one output for a single input. This is illustrated by the equation y=x2. Any kind of input present for x results in an absolute single output for y. Considering that x is the input value, we would state that y is a function of x.

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 the output.

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Notice that s stands for the slant height of the pyramid, and this height is the height of each one of the lateral triangular faces.

We will need to use the next formulas

Therefore, the surface area is

Lateral Area=116.1 m^2

As for the volume, the volume of a regular pyramid is

In our case,

Therefore,

Volume= 77.9 m^3