What is a two step problem with variables on each side equal 19? (Please help)

Answer:

[tex]a_{14}=\dfrac{52}{3}[/tex]

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

where:

Given terms of an arithmetic sequence:

Substitute the values into the general formula to create two equations:

[tex]\sf\underline{Equation \:1}\\\begin{aligned}a_4 & = 14\\\implies a+(4-1)d & = 14\\a + 3d & = 14\end{aligned}[/tex]

[tex]\sf\underline{Equation \:2}\\\begin{aligned}a_{10} & = 16\\\implies a+(10-1)d & = 16\\a + 9d & = 16\end{aligned}[/tex]

Subtract Equation 1 from Equation 2 to eliminate a:

[tex]\begin{array}{l r l}& a+9d & = 16\\- & a+3d & = 14\\\cline{2-3}&6d & = \:\:2\end{array}[/tex]

Solve for d:

[tex]\begin{aligned}\implies 6d & = 2\\\dfrac{6d}{6} & = \dfrac{2}{6}\\d & = \dfrac{1}{3} \end{aligned}[/tex]

Substitute the found value of d into one of the equations and solve for a:

[tex]\begin{aligned}a + 3d & = 14\\ \implies a+3 \left(\dfrac{1}{3}\right)&=14\\a+1&=14\\a+1-1&=14-1\\a&=13\end{aligned}[/tex]

Substitute the found values of a and d into the general formula to create an equation for the nth term of the arithmetic sequence.

[tex]\implies a_n=13+(n-1)\dfrac{1}{3}[/tex]

[tex]\implies a_n=13+\dfrac{1}{3}(n-1)[/tex]

To find the 14th term, simply substitute n = 14 into the equation:

[tex]\begin{aligned}a_n & = 13+\dfrac{1}{3}(n-1)\\\implies a_{14}& = 13+\dfrac{1}{3}(14-1)\\&=13+\dfrac{1}{3}(13)\\ & = \dfrac{39}{3}+\dfrac{13}{3}\\&=\dfrac{52}{3}\end{aligned}[/tex]

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Answer:

x<0; x>0

Step-by-step explanation:

Basically, anything but zero, depending on what a is.

Answer:

x = ± [tex]\sqrt{a}[/tex]

Step-by-step explanation:

x² = a ( take square root of both sides )

x = ± [tex]\sqrt{a}[/tex]

Answer:

$560.33

Step-by-step explanation:

Hotel: 79.95*2*2=$319.8

Dinner: 182-50=$132

Breakfast:

Rental:

Hotel+dinner+breakfast+rental: 319.8+132+35.09+73.44=$560.33

The distance covered by the falling freely body from rest will be 48 feet.

The study of motion without considering the mass and the cause of the motion.

When a body falls freely from rest, the distance it travels straight changes as the square of the time (air resistance excluded). If something is dropped 192 feet from the summit of a tower, it lands on the ground in 8 seconds.

We know that the acceleration is due to gravity (g = 32 ft/s²).

d ∝ t²

d/t² = constant

Then the distance covered by the falling freely body from rest will be given as,

d / 4² = 192 / 8²

d / 16 = 192 / 64

d = 16 x 192 / 64

d = 48 feet

The distance covered by the falling freely body from rest will be 48 feet.

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Solution:

Substitute the value of the variable into the expression, then simplify.

             Answer: -8

_________________________________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer:

2x/y = -8

Step-by-step explanation:

The values are,

→ x = 12

→ y = -3

Given expression,

→ 2x/y

Simplifying the expression,

→ 2x/y

→ (2 × 12)/(-3)

→ (24)/(-3)

→ -(24/3) = -8

Hence, the answer is -8.

The interval where the function is negative is:

(-5 - √19 , -5 + √19)

That is the solution set of the inequality.

Here we have the following inequality:

x^2 + 10x + 5 < 0

So we want to find the values of x for which the quadratic function is negative.

To do so, we can solve:

x^2 + 10x + 5 = 0

The solutions are given by the quadratic formula:

x = (-10 ± √(10^2 - 4*6))/(2*1)

x = (-5 ± √19)

notice that the quadratic has positive leading coefficient, so it open upwards, then the function is below zero between the two roots, on the interval:

-5 - √19 < x < -5 + √19

Then the correct option is D.

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Answer:

C. ME ZH

B. IG LM

F. TH= NM

Step-by-step explanation:

The correct congruence statements are A, B, and C such that ∠N = ∠I, GH = LM, and ∠M= ∠H are true for similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

To determine which congruence statements are correct, we need to identify the corresponding sides and angles of the triangles.

The corresponding sides and angles are those that are in the same position in each triangle.

Using this information, we can check each statement:

A. ∠N = ∠I: This statement is true because ∠N and ∠I are corresponding angles in the congruent triangles.

B. GH = LM: This statement is true because GH and LM are corresponding sides in the congruent triangles.

C. ∠M= ∠H: This statement is true because ∠M and ∠H are corresponding angles in the congruent triangles.

D. IG = LM: This statement is false because IG and LM are not corresponding sides in the congruent triangles.

E. IH = NM: This statement is false because IH and NM are not corresponding sides in the congruent triangles.

F. ∠L = ∠I: This statement is false because ∠L and ∠I are not corresponding angles in the congruent triangles.

Therefore, the correct congruence statements are A, B, and C.

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Answer:

  31/45 lb

Step-by-step explanation:

You want to know the weight of a 5/9 lb bag after 2/15 lb of fruit are added to it.

Fractions can be added when they have a common denominator. Here, the denominator will need to have factors of 3² = 9 and 3·5 = 15. It can be ...

   3·3·9 = 45

Using this denominator, the fractions are ...

  bag weight = 5/9 lb = 25/45 lb

  fruit weight = 2/15 lb = 6/45 lb

The total weight of the fruit and the bag is ...

  total weight = 25/45 lb + 6/45 lb = 31/45 lb

With the fruit, the bag weighs 31/45 pounds.

The mass of the tow chain will be equal to 12.96 kg.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m.

The mass of 1 m chain = 2.16 kg

Mass of 6-meter chain = 2.16 x 6

Mass of 6-meter chain = 12.96 kg

Therefore, the mass of the tow chain will be equal to 12.96 kg.

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Answer:

5y + 3 is the sum of the three ages

Step-by-step explanation:

Let y=Mark, d=Daniel j=Jack, and s=The sum

Mark is y years old. In five years jack will be twice as old as Mark

j + 5 = 2(y+5)

j + 5 = 2y + 10

j = 2y + 10 - 5

j = 2y + 5

Daniel will be two years younger than jack is now

d + 5 = j - 2

d = j - 2 - 5

d = j - 7

Replace j with (2y+5)

d = (2y+5) - 7

d = 2y - 2

Expression in terms of y for the sum of the 3 ages now

s = y + j + d

replace j and d with expressions we came up with above

s = y + (2y+5) + (2y-2)

s = y + 4y + 3

s = 5y + 3 is the sum of the three ages

2:3=5

Ali=2÷5×£68000

Ali=£40800

Hassan=3÷5×£68000

Hassan=£27200

Answer:

the answer is 3.456 × 108

Answer:

The answer is B

Step-by-step explanation:

Just look at the numbers, that is the only one with the correct range.

The scores on the test are centered around 66 and vary from 43 to 85. Therefore, the correct option  is option B.

Distributions are objects that generalise the traditional idea of functions used for mathematical analysis. They are often referred to as Schwartz distributions or generalised functions. Functions with no classically defined derivatives can be distinguished using distributions.

In the theory of partial differential equations, distributions are frequently utilised because it may be simpler to prove the existence of distributional solutions (weak solutions) rather classical solutions or because there may not be any suitable classical solutions. The scores on the test are centered around 66 and vary from 43 to 85.

Therefore, the correct option is option B.

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Option 2. The description of the rigid motion transformation would be the dilation of the figure by the scale factor of 1/2.

The term rigid motion transformation has to do with the fact that when an object is moved the size and the shape of the object would still have to stay the same. This is different for the non rigid motion. This because the size and the shape would have to increase in this case.

When the object is moved from one area to the other and it remains the same then we would have to say that the rigid transformation has occurred.

Hence we would have to say that Option 2. The description of the rigid motion transformation would be the dilation of the figure by the scale factor of 1/2.

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The weight of the trout is 6.17 pounds.

We know that the weight of a trout varies jointly as its length and the square of its girth.

If W is the weight, x is the length and y is the girth, then:

W = k*x*y^2

Where k is a constant.

We know that one trout with:

x = 26 in

y = 18in

Has a weight of 10.5, then we can write:

10.5 = k*(26)*(18)^2 = k*8,424

Solving for k we get:

10.5/8,424 = k

Then the equation is:

W = (10.5/8,424)*x*y^2

Now, our trout has:

x = 22 in

y = 15 in

Then the weight is:

W =  (10.5/8,424)*22*15^2 = 6.17

The weight of the trout is 6.17 pounds.

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Answer:

x=3 and her is right

Answer whyyyy

Step-by-step explanation:

the correct option is the second one:

"No, because she should have rounded 63 down to 60"

In that case, her estimation would have been 24.

First, we need to understand how rounding works. When we want to round to a given digit, we need to look at the digit that its located at its right.

In this case, LaVonne estimated 38% of 63, and the roundings that she did are:

38% up to 40%. This is correct, because the second digit is 8, so we round up here.

63 to 70. This is incorrect, because the second digit is 3 (smaller than 4) then here she should have round down to 60 instead of up to 70.

So what she should have gotten is:

0.4*60 = 24

That is a better estimation, were the actual value of the 38% of 63 is:

0.38*63 = 23.94

You can see that when rounding down, the estimation is much closer to the actual value.

So, the correct option is the second one:

"No, because she should have rounded 63 down to 60"

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Answer:

d

Step-by-step explanation:

Let the number be 'x'.

First find x and then find 130% of x.

30% of  x = 25

   [tex]\sf \dfrac{30}{100}*x = 25[/tex]

            [tex]\sf x = 25*\dfrac{100}{30}\\\\ x = \dfrac{250}{3}\\\\[/tex]

Now, find 130% of x

   130% of x = [tex]\sf \dfrac{130}{100}*\dfrac{250}{3}\\\\[/tex]

                    [tex]\sf = \dfrac{325}{3}\\\\ = 108.3[/tex]

Answer:

hello! it's all explained in the photo :)

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

m(<BCD) = 2x alternative Z

c=2x d=8x

m(<CD) =180 U

180/10x

x=18

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06[/tex]

Number of bags of sand needed to cover the area of circular pool is 51 bags.

A circle is a round-shaped figure that has no corners or edges.

Now it is given that,

Diameter of pool, D = 14 feet

So, Area of pool = π(D/2)²

⇒  Area of pool = π(14/2)²

⇒  Area of pool = π(7)²

⇒  Area of pool = 153.86 square feet

Now given Area of 1 bag = 3 square feet

So, number of bags required = Area of pool / Area of 1 bag

⇒ number of bags required = 153.86/ 3

⇒ number of bags required = 51.28

⇒ number of bags required ≈ 51

Thus, Number of bags of sand needed to cover the area of circular pool is 51 bags.

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Answer:

Expression for f(x) = [tex]\frac{\sqrt{x + 1} - 4}{7}[/tex]

Domain in interval notation: [tex]\:[-1,\:\infty \:)[/tex]

Step-by-step explanation:

[tex]\textrm{Let }f(x)\text{ represent the function}[/tex]

Step 1: Add 1 to [tex]x[/tex]  ==>   x + 1

Step 2: Take square root ==> [tex]\sqrt{x+1}[/tex]

Step 3: Subtract 4: ==>  [tex]\sqrt{x+1} - 4[/tex]

Step 4: Divide by 7 ==> [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]

The expression for f(x) is [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]

The domain of a function is the set of all inputs  for which the function is real and defined

[tex]\sqrt{x+1}[/tex] is real only for positive values of the square root

This means

[tex]\sqrt{x+1} \ge 0[/tex]

Squaring both sides we get

[tex]x + 1 \ge 0[/tex]

Subtracting 1 from both sides we get

[tex]x \ge -1[/tex]

This is the lower limit for [tex]x.[/tex] There is no upper limit

The domain of[tex]f(x)[/tex] is therefore

[tex]x \ge -1[/tex]

In interval notation it is expressed as

[tex][-1,\infty)[/tex]

Note the square bracket on the left and parenthesis on the right. This notation means that -1 is part of the domain but [tex]\infty[/tex]  is not included since at [tex]\infty[/tex]  the function is not defined

From the given table, we can see that the value of f(2) is 4

The input values in a function table are the dependent variables while the output values in a function table are the dependent variables.

Let the function of the table be represented as y = f(x), this shows that the variable x is independent while f(x) is dependent.

In order to determine the value of f(2), we need the output value, when the input value is 2. From the given table, we can see that the value of f(2) is 4

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Answer:

me not soluesan match huiudresst