When solving this system of equations by elimination, which could be the resulting equation when the variable y has been eliminated?

9x + 3y = 12

2x + y = 5

answers:

A) 3x = -3

B) 11x = 17

C) 15x = 27

D) 7x = 7

Answer:

2x + (x + 2)

Step-by-step explanation:

Let the number = x

"twice a number" means 2x

"increased by the sum of the same number and five" means to add x + 5, so the expression is

2x + (x + 2)

Answer:

83 m

Step-by-step explanation:

23.6 x 3.5 = 82.6 ≈ 83 m

The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable takes a value less than or equal to z.

In order to model continuous phenomena or quantities that depend on chance, such as time, length, and mass, continuous random variables are utilized.

The likelihood that the random variable takes a value inside that interval is defined as the area under the density function over an interval. Therefore, the probability that the random variable will have a value less than or equal to z is given by the area under the normal curve from negative infinity to z.

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When possible, it is often easier and more convenient to use radians to calculate arc length.

We have,

When calculating the length of a given arc, using radians is generally considered easier and more straightforward than using degrees.

This is because the formula for arc length in radians is simpler and involves fewer conversion factors.

The formula for arc length in radians is given by:

Arc length = rθ

where r is the radius of the circle, and θ is the central angle of the arc measured in radians.

On the other hand, the formula for arc length in degrees is given by:

Arc length = (πr/180)θ

where π is the mathematical constant pi, r is the radius of the circle, and θ is the central angle of the arc measured in degrees.

As you can see, the formula for arc length in degrees requires the additional conversion factor of π/180, which can make the calculations more complex and prone to errors.

Therefore,

When possible, it is often easier and more convenient to use radians to calculate arc length.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}\)

Step-by-step explanation:

\( \sf{ - 4 - ( - 9)}\)

When there is a ( - ) in front of an expression in Parentheses, change the sign of each term

⇒\( \sf{ - 4 + 9}\)

Calculate

⇒\( \sf{5}\)

Hope I helped!

Best regards!!

Answer:

5

Step-by-step explanation:

- 4 - ( -9 )

Two negatives multiplied  = positive

Therefore,

-4 + 9 = 5

The coordinates of midpoint D from the given triangle ABC is (-4x, 0).

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]

From the given figure, the coordinates are A(-6x, 4y) and B(-2x, -4y) and C(8x, -2y)

D(x, y)=[(-6x-2x)/2, (4y-4y)/2]

= (-4x, 0)

Therefore, the coordinates of midpoint D is (-4x, 0).

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Answer:

6+1.25t

Step-by-step explanation:

W(in the 1st month)=6+1.25

W(in the 2nd month)=6+1.25+1.25

W(in the 3rd month)=6+1.25+1.25+1.25

W(in the t months)=6+t(1.25)

Answer:

1

Step-by-step explanation:

"exceeds"= greater than

d is greater than 7 hours

d > 7

Answer:

20.5

Step-by-step explanation:

(20+21)/2 = 20.5

:) Hope this helps, please mark as brainliest!

Answer:

probability that 2 cards drawn from a deck of 52 cards are both kings.

is probability that first card is a king times probability that second card is a king

with replacement 4/52*4/52 =0.592%

without replacement 4/52*3/51=0.452%

Step-by-step explanation:

Answer:

1. Using spread sheet software to complete business taxes

A. Enter check and amend data in accordance with organizational and task requirement

B. Import and export data b/n compatible spread sheet based on software & system procedures

C. Use manual user documentation and online help to overcome spread sheet design problems

D. Preview adjust and print spread sheet in accordance with organizational and production

Answer:

The specific heat of the brass can be calculated using the formula:

Q = mcΔT

where Q is the heat transferred, m is the mass of the brass, c is the specific heat of the brass, and ΔT is the change in temperature.

First, calculate the heat transferred from the brass to the water:

Qbrass = mcΔT = (125 g)(c)(100 °C - 35 °C) = 9375c J

Next, calculate the heat transferred from the water to the brass:

Qwater = mcΔT = (76 g)(4.184 J/g. °C)(35 °C - 25 °C) = 3191.84 J

Since the heat lost by the brass is equal to the heat gained by the water:

Qbrass = Qwater

9375c J = 3191.84 J

c = 0.34 J/g. °C

Therefore, the specific heat of the brass is 0.34 J/g. °C.

Step-by-step explanation:

Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

We set the division result equal to 4 bottles since each care package should contain 4 bottles, and then we solve for "s".

The following equation represents the issue:

s ÷ 12 = 4

where "s" denotes the overall quantity of tiny sunscreen bottles Jordan had to work with, "" stands for division, and "4" denotes the quantity of bottles contained in each care package.

We can determine how many bottles should go into each care box by dividing the total number of bottles by the entire number of care packages. As there should be 4 bottles in each care package in this instance, we set that amount to the outcome of the division and use the formula to find "s".

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Answer: 2010.6 m²

Step-by-step explanation: formula for a cylinder is π×r²×h

8/2=4

π×4²×10=2010.6

Answer:

\(\sf y =\dfrac{-1}{3}x + 7\)

Step-by-step explanation:

Equation of line: y =mx +b

 Here, m is the slope and b is the y-intercept.

Parallel lines have same slope.

            \(\sf y =\dfrac{-1}{3}x + 4\)

     So, the slope of the required line = -1/3

Equation of the required line:  

                \(\sf y =\dfrac{-1}{3}x + b\)

Point(6,5) goes through the line. substitute x = 6 and y =5 in the above equation and then we can find the value of y-intercept 'b'

    \(\sf 5 =\dfrac{-1}{3}*6 +b\\\\ 5 = -2 + b\\\\5+2 = b\\\\\boxed{b = 7}\)

Equation of the require line:

           \(\sf \boxed{\bf y =\dfrac{-1}{3}x+7}\)

Answer:

100

Step-by-step explanation:

"Percent" or "%" means "out of 100" or "per 100".

Therefore 20% can be written as  20 /100

Therefore, 20 is 20% of  100

Answer:

-4

Step-by-step explanation:

plug in 3 for x

2(3)-10

6-10

=-4

The expression that is an element of AxBxB is (1,2,3)

The given data is A= (a, b}, B = {1,2,3}

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.

\(& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\\)

\(& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\\)

\(& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}\)

The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.

The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.

Therefore, the expression that is an element of AxBxB is (1,2,3).

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An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.

In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;

h + 178 = T

Substituting the given parameters into the algebraic equation, we have the following;

h + 178 = 214

Solving for h, we have the following;

h = 214 - 178

h = 36 hours.

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Answer:

A

Step-by-step explanation:

Answer:

A. 3x/10

Step-by-step explanation:

\(\frac{x}{5}+\frac{x}{10}\)

Find a common denominator. The lowest common denominator is 10, so match the equations to fit that denominator.

\((\frac{x*2}{5*2})+\frac{x}{10}\\\frac{2x}{10}+\frac{x}{10}\)

Now that the denominators are the same, combine the fractions by adding the numerators.

\(\frac{3x}{10}\)

Your answer is a.

As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.

This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.

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The approximated value of f(1.09) using the given data, the absolute error, and the relative error is 0.28782, 0.005177086, and 1.83% respectively.

Given data Xi

F(x) 1.050.24141.100.29331.150.3492

To approximate f(1.09) we will use the Divided difference (DD) polynomial method.

The first divided difference is:

\(f[x_1,x_2]=\frac{f(x_2)-f(x_1)}{x_2-x_1}\)

Substituting the values from the table we get,

\(f[x_1,x_2]=\frac{0.2933-0.2414}{1.10-1.05}\)

\(=1.18\)

The second divided difference is:

\(f[x_1,x_2,x_3]=\frac{f[x_2,x_3]-f[x_1,x_2]}{x_3-x_1}\)

Substituting the values from the table we get,

\(f[x_1,x_2,x_3]=\frac{0.3492-0.2933}{1.15-1.05}\)

=0.5599999999999998

Now, we can construct the DD polynomial as:

\(P_2(x)=f(x_1)+f[x_1,x_2](x-x_1)+f[x_1,x_2,x_3](x-x_1)(x-x_2)\)

Substituting the values we get,

\($$P_2(x)=0.2414+1.18(x-1.05)+0.56(x-1.05)(x-1.10)$$\)

\(P_2(x)=0.2414+1.18(x-1.05)+0.56(x^2-2.15x+1.155)\)

\(P_2(x)=0.28204+1.3808(x-1.05)+0.56x^2-1.2464x+0.68\)

Now to find f(1.09) we will substitute x=1.09,

\(P_2(1.09)=0.28204+1.3808(1.09-1.05)+0.56(1.09)^21.2464(1.09)+0.68\)

\(P_2(1.09)=0.28781999999999997\)

To find the absolute error, we will subtract the exact value from the approximated value,

$$Absolute error=|0.28782-0.282642914|=0.005177086$$

The exact value is given to be 0.282642914.

To find the relative error, we will divide the absolute error by the exact value and multiply by 100,

Relative error=\(\frac{0.005177086}{0.282642914}×100\)

=\(1.83\%$$\)

Therefore, the approximated value of f(1.09) using the given data, the absolute error, and the relative error are 0.28782, 0.005177086, and 1.83% respectively.

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Answer:

18.6inches

Step-by-step explanation:

Given the length of a side of a pentagon to be 6 inches.

If this length is dilated by a factor of 3.1, the new length will be;

New length = Old length * dilation factor

New length = 6 * 3.1

New length = 18.6inches

Hence the length of each side of the dilated pentagon is 18.6inches