Solve the equation 2(3x + 7) + 5 = 49.

Answer:

-16

Step-by-step explanation:

start with brackets

-5-3 = -8

2(-8)

= -16

In regression analysis, the independent variable is the variable that is being manipulated or controlled to observe its effect on the dependent variable.

If the independent variable is measured in kilograms, it means that it represents a measure of weight. The dependent variable, on the other hand.

For example, if the independent variable is the weight of a person in kilograms, the dependent variable can be their body mass index (BMI), blood pressure, or any other health-related measure.

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The unit of measurement for the independent variable in regression analysis does not determine the unit of measurement for the dependent variable. The relationship between the two variables is expressed through the regression equation, irrespective of their units of measurement.

In regression analysis, the independent variable is not dependent on the unit of measurement. Therefore, the statement "if the independent variable is measured in kilograms, the dependent variable" is neither true nor false. The unit of measurement for the independent variable does not determine the unit of measurement for the dependent variable.

In regression analysis, the independent variable is the variable that is believed to have an effect on the dependent variable. The dependent variable is the variable that is being predicted or explained by the independent variable. The relationship between the two variables is expressed through a regression equation.

For example, let's say we are conducting a regression analysis to understand the relationship between a person's weight (independent variable) and their blood pressure (dependent variable). The weight can be measured in kilograms, pounds, or any other unit, while the blood pressure can be measured in millimeters of mercury (mmHg). The unit of measurement for the independent variable does not determine the unit of measurement for the dependent variable.

Therefore, the unit of measurement for the independent variable in regression analysis does not determine the unit of measurement for the dependent variable. The relationship between the two variables is expressed through the regression equation, irrespective of their units of measurement.

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The absolute maximum value of the function f(t) is 2 and the absolute minimum value of the function f(t) is -10 at t = -1 and t = 5 respectively.

Given function: The given capability can be communicated as: f(t) = t  3t, [1, 5]. f(t) = t (1 - 3) = - 2tWe must determine the given capability's greatest and absolute smallest benefits. To determine the maximum and minimum values of the given function, the following steps must be taken: Step 1: Step 2: Within the allotted time, identify the function's critical numbers or points. Step 3: At the critical numbers and the ends of the interval, evaluate the function. To decide the capability's outright most extreme and outright least qualities inside the given interval1, analyze these numbers. Assuming we partition f(t) by t, we get f′(t) = - 2.

The basic focuses are those places where the subsidiary is either unclear or equivalent to nothing. Because the subordinate is characterized throughout the situation, there are no fundamental focuses within the allotted time.2. How about we find the worth of the capability toward the finish of the span, which is f(- 1) and f(5): f(-1) = -2(-1) = 2f(5) = -2(5) = -10. This implies that irrefutably the greatest worth of the capability f(t) is 2 and unquestionably the base worth of the capability f(t) is - 10 at t = - 1 and t = 5, individually. " The response that is required is "The absolute maximum value of the function f(t) is 2 and the absolute minimum value of the function f(t) is -10 at t = -1 and t = 5 respectively."

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Answer:

Olivia has 240.

Step-by-step explanation:

Amelia took 36 and there were 288 left over. A ratio of 1:5 with 288 would be 48 and 240 so therefore, Olivia has 240.

Answer:

$105

Step-by-step explanation:

I used a proportion to solve this:

\(\frac{63}{3} = \frac{x}5}\)

Cross multiply:

3x = 315

Divide both sides by 3

x = 105

Answer:$105

Step-by-step explanation:

Salary for 3 hrs=$63

Salary for 5hrs= salary for one hour×5 hrs,

Salary for one hour= 63/3=$21

Salary for 5 hours= 21×5: $105

Considering the definition of an equation and the way to solve it, the cost of one hot wing is $0.6.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality must be true.

To solve an equation, keep in mind:

Being "x" the cost of one hot wing, and knowing that:

the equation in this case is:

First customer payment= Second customer payment

8x +4= 10x +2.80

Solving:

4 - 2.80= 10x - 8x

1.2= 2x

x= 1.2 ÷ 2

x=0.6

Finally, the cost of one hot wing is $0.6.

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9514 1404 393

Answer:

  B.  4

Step-by-step explanation:

Equating exponents, we have ...

  2x +7 = 15

  2x = 8 . . . . . subtract 7

  x = 4 . . . . . . divide by 2

The equation is true when the value of x is 4.

hope this helps enjoy.

Answer:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be \(x\) and \(y\) the amounts of nickels and dimes that Carrie and Joan have, as \(c\) the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

Carrie's amount of money:

\(0.05\cdot x = c\) (Eq. 1)

Joan's amount of money:

\(0.10\cdot y = c\) (Eq. 2)

Relation between amounts of coins:

\(x = y+40\) (Eq. 3)

First we eliminate \(c\) by equalizing (Eq. 1) and (Eq. 2):

\(0.05\cdot x = 0.10\cdot y\)

Then, we reduce the resulting formula by (Eq. 3):

\(0.05\cdot (y+40) = 0.10\cdot y\)

\(y+40 = 2\cdot y\)

\(y = 40\)

And rest of variable are now determined:

\(x = 40+40\)

\(x = 80\)

\(c = 0.05\cdot (80)\)

\(c = 4\)

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Answer:

739,266

Step-by-step explanation:

Answer:

the answer is |x-15.3|_<_0.4

14.8 and 15.6 in that order

Step-by-step explanation:

With an allowance of 0.4 the length of the straw will be x > 14.8 and x < 15.6.

The absolute value of equality is expressed as |a| is a = ±a.

The absolute value of inequality can be expressed as |a| < 2 is a<2 and a > -2 in the later case we have multiplied a with negative sign and this switches the inequality after simplification.

According to the given question

The length of a manufactured plastic straw is 15.2cm with an acceptable allowance of 0.4cm.

Here allowance of 0.4cm means ±0.4cm allowance on the specific size that plastic straw manufacturer have fixed.

∴ The equation of this will of two forms

(i) x - 15.2 > -0.4.

(ii) x - 15.2 < 0.4.

Now solving these two equations

 x - 15.2 > - 0.4

 x > 15.2 - 0.4

 x > 14.8.

AND

 x - 15.2 < 0.4

 x < 15.2 + 0.4

x < 15.6.

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Using Hypothesis testing,

a) Two samples are independent.

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ : an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Null hypothesis is accepted.

so, an expectant mother's cigarette smoking has no effect on the bone mineral.

We have given that,

A study which is conducted for check an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

For new-born whose mother's cigarette smoking

sample size , n₁= 77

X-bar, x₁-bar = 0.098 g/cm

standard deviations, s₁ = 0.026 g/cm

For new-born whose mother did not cigarette smoking

sample size , n₂ = 161

standard deviations, s₂ = 0.025 g/cm.

mean (X-bar) , x₂-bar = 0.095 g/cm

a) the two samples are independent since they are different types of mothers, smoking mothers and non smoking mothers

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ: an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Test statistic:

t = (x₁-bar - x₂-bar )/S (√1/n₁+1/n₂)

where , S = √(s₁²(n₁ - 1) + s₂²(n₂ -1))/n₁+n₂ - 2

S = √((0.026)²(76) +(0.025 )²(160))/236

= 0.0253

then, t = (0.098 - 0.095 )/0.0253(√1/77 +1/161 )

=> t = 0.859

Using the critacal table critical t is

Critical t = ±1.970065

Degrees of freedom =236.0000

P-Value=0.3935 which is greater than α(0.05),

So , we accept H₀

Thus, an expectant mother's cigarette smoking has not effect on the bone mineral content of her otherwise healthy child.

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Answer:

b. m∠KML + m∠MLK = m∠JKM

Step-by-step explanation:

right on edge

The statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a triangle shown in the picture:

As we know, triangle is a polygon with three sides and three interior angles.

From the definition of the triangle, The triangle's interior angles add up to 180°

m∠MKL + m∠MLK + m∠KML = 180

Also, the sum of the two interior angles is equal to the exterior angle.

m∠KML + m∠MLK = m∠JKM

Thus, the statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.

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The 0.00133 in scientific notation is 1.33 x 10^(-3).

Scientific notation is in form of a x 10^b, where b is integer & a is non-zero real number between 1 and 10.

There are 3 stages to convert 0.00133 in scientific notation :

Therefore, 0.00133 in scientific notation is 1.33 × 10^(-3) and It has 3 significant figures.

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Answer:

Step by step explanation

1. \( \frac{1}{1 - x} + \frac{x}{ {x}^{2} - 1} \)

Use \( \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} \) to rewrite the fractions

\( - \frac{1}{x - 1} + \frac{x}{(x - 1)(x + 1)} \)

Write all numerators above the Least Common Denominator ( X - 1 ) ( X + 1 )

\( \frac{ - (x + 1) + x}{(x - 1)(x + 1)} \)

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

\( \frac{ - x - 1 + x}{(x - 1)(x + 1)} \)

Using \((a - b)(a + b) = {a}^{2} - {b}^{2} \) , simplify the product

\( \frac{ - x - 1 + x}{ {x}^{2} - 1 } \)

Since two opposites add up to zero, remove them from the expression

\( \frac{ - 1}{ {x}^{2} - 1} \)

So, Option A is the right option.

___________________________________

2.

\( \frac{ {x}^{2} - x - 12}{ {x}^{2} - 16} - \frac{1 - 2x}{x + 4} \)

Write - X as a difference

\( \frac{ {x}^{2} + 3x - 4x - 12 }{ {x}^{2} - 16 } - \frac{1 - 2x}{x + 4} \)

Using \( {a}^{2} - {b}^{2} = (a - b)(a + b)\) , factor the expression

\( \frac{ {x}^{2} + 3x - 4x - 12 }{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} \)

Factor the expression

\( \frac{x(x + 3) - 4(x + 3)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} \)

Factor out X+3 from the expression

\( \frac{(x + 3)(x - 4)}{(x - 4)(x + 4)} - \frac{1 - 2x}{x + 4} \)

Reduce the fraction with x-4

\( \frac{x + 3}{x + 4} - \frac{1 - 2x}{x + 4} \)

Write all the numerators above the common denominator

\( \frac{x + 3 - ( 1- 2x)}{x + 4} \)

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

\( \frac{x + 3 - 1 + 2x}{x + 4} \)

Collect like terms

\( \frac{3x + 3 - 1}{x + 4} \)

Subtract the numbers

\( \frac{3x + 2}{x + 4} \)

Undefined at,

X + 4 = 0

Move constant to R.H.S and change its sign

\(x = 0 - 4\)

Calculate

\(x = - 4\)

So, the answer is :

\( \frac{3x + 2}{x + 4} \) , undefined at X = -4 and 4

Hope this helps..

Best regards!!

Answer: 58.33%

Step-by-step explanation:

So, Liz flipped the coin a total of 60 times

Let this be the denominator.

Probability of coin landing up: 35/60

Probability of coin landing down: 24/60

We need the probability of the coin landing up.

So, convert 35/60 into a percentage

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1003560 × 100100= (35 × 10060) × 1100 = 58.33/100

So, the probability is 58.33%

Answer:

80 in^2 or 80 square inches

Step-by-step explanation:

Area of the top triangle=

1/2*4*4

8 square inches,

Area of the square=

4*4

16 square inches

Area of the rectangle=

4*8

32 square inches

Area of both bottom triangles=

2(1/2*3*8)

24 square inches

add them up and you get

Suppose that the joint probability density of two random variables X1 and X2 is given by F(x1,X2) = {6e^-2x1-3x2 for x1 > 0 and x2 > 0, otherwise.

Find the probability P(I2).

Solution: The joint probability density of two random variables X1 and X2 is given by F(x1, x2) = {6e^(−2x1 − 3x2) for x1 > 0 and x2 > 0, otherwise. Find the probability P(I2).It is known that, for any joint probability density function f(x, y) and any real number a,b,c, and d such that a ≤ b and c ≤ d, we have: P(a ≤ X ≤ b, c ≤ Y ≤ d) = ∫(c to d) ∫(a to b) f(x,y)dxdy.

We use this formula to calculate the required probability. We have:I2 = {X2 > 2X1}. Hence, we want to find the probability that X2 > 2X1. This probability can be written as: P(I2) = P(X2 > 2X1) = ∫(0 to ∞) ∫(2x1 to ∞) f(x1,x2)dx2dx1= ∫(0 to ∞) ∫(2x1 to ∞) 6e^(−2x1 − 3x2) dx2dx1= 6 ∫(0 to ∞) e^(−2x1) ∫(2x1 to ∞) e^(−3x2) dx2dx1Now, let's solve the inner integral first. We get:∫(2x1 to ∞) e^(−3x2) dx2= (-1/3) e^(−3x2)|2x1 to ∞= (-1/3) e^(−6x1)Now we substitute this value of the integral back into the outer integral. We get: P(I2) = 6 ∫(0 to ∞) e^(−2x1) (-1/3) e^(−6x1) dx1= (-2) ∫(0 to ∞) e^(−8x1) dx1= (-2) (1/8)= -1/4. Hence, the required probability P(I2) is equal to -1/4.

Therefore, the correct option is (D) -1/4.

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Answer:

Multiplication Property of Equality

Step-by-step explanation:

Answer:

Division Property of Equality..

Step-by-step explanation:

To estimate the maximum possible error in computing the resistance R, we can use the error propagation formula. Let ΔR₁ and ΔR₂ represent the maximum errors in the measurements of R₁ and R₂, respectively.

The formula for the parallel combination of resistors is given by 1/R = 1/R₁ + 1/R₂. Taking the derivative with respect to R₁ and R₂, we have dR/dR₁ = -1/R₁² and dR/dR₂ = -1/R₂². Applying the error propagation formula, ΔR = sqrt((dR/dR₁ * ΔR₁)² + (dR/dR₂ * ΔR₂)²).

Substituting the given values, R₁ = 6 ohms, R₂ = 5 ohms, ΔR₁ = ΔR₂ = 0.05 ohms, and using the derivative values, we can calculate ΔR. Evaluating the expression, we find ΔR ≈ 0.030 ohms.Therefore, the maximum possible error in computing R is approximately 0.030 ohms. Hence, the correct option is a. 0.030.

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Step-by-step explanation:

T3=8

8=a+2d

where a is first term ,d is common ratio

8=a+2(2)

8=a+4

a=8-4

a=4

first term T1 is 4

T2=a+d

T2=4+2

T2=6

T4=a+3d

T4=4+3(2)

T4=4+6

T4=10

T5=a+4d

T5=2+4(2)

T5=4+8

T5=12

4,6,8,10,12

As the input values (n) increase, the value of the sequence term a_n = (n^2 - 3) / (n + 1) alternates between positive and negative values, indicating that the sequence is not monotonic.

To see this, consider the first few terms of the sequence:

a_1 = -2

a_2 = 1

a_3 = -4/2 = -2

a_4 = 7/3

As we can see, the sequence does not consistently increase or decrease as n increases.

To determine if the sequence is bounded, we can look at the limit of the sequence as n approaches infinity. We have:

lim (n -> infinity) (n^2 - 3) / (n + 1)

= lim (n -> infinity) (1 - 3/n^2) / (1 + 1/n)

= 1/1 = 1

Since the limit exists and is finite, the sequence is bounded. Specifically, we have:

-2 <= a_n <= 1

for all n.

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Answer:

Line y = -x + 2 intersects line y = 3x + 1

Step-by-step explanation:

The solution to a system of equations is the point at which the two lines intersect.  To find this point, first equate the equations and solve for x:

\(\begin{aligned}y & = y\\-x + 2 & = 3x + 1\\-x+2+x & = 3x+1+x\\2 & = 4x + 1\\2-1 & =4x+1-1\\1 &=4x\\x & =\dfrac14\end{aligned}\)

Substitute the found value of x into one of the equations, and solve for y:

\(y=3\left(\dfrac14\right)+1=\dfrac74\)

Therefore, the solution to the system of equations (the point at which the two lines intersect) is:

\(\left(\dfrac14,\dfrac74\right)\)

So the description that best describes the solution to the system of equations is:

Line y = -x + 2 intersects line y = 3x + 1

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the industry's output is Y = 3, and the profit of each firm  = -2.

a) Supply curve of an individual firm

The price received by the individual firm will be P. Its demand curve is given by

D(p) = 20 - p.

Each firm chooses output to maximize its profit. Profit maximization occurs when the price is equal to the marginal cost. Mathematically,

P = MC(y)

4y = P

y = P/4

Thus the supply curve of the firm is y = P/4

b) The smallest price at which the product can be sold. The product can be sold at the minimum of the supply curve, which is y = 0, given P ≥ 0. Therefore the smallest price is P = 0.

c) Equilibrium price and output

Equilibrium occurs when each firm is producing at its profit-maximizing output given the output of other firms. Let the number of firms in the industry be n. The output of the industry is Y = ny. The industry supply curve is given by

S(P) = nP/4

The equilibrium price intersects the industry supply curve with the demand curve. Thus the equilibrium price satisfies

S(P) = Y

nP/4 = 20 - P

=> P = 80/(4 + n).

The equilibrium number of firms is the number that makes the industry supply curve equal to the demand curve. Thus

20 - P = nP/4

=> P = 80/(4 + n)

=> n = (80 - 20P)/P

= 20/P - 4.

Thus the equilibrium number of firms is a function of P and can range between 1 and infinity, but it must be an integer. The equilibrium output of each firm is given by

y = P/4 = 20/(4n + n²)

The equilibrium output of the industry is given by

Y = n

y = 5/P = (n² + 4n)/80.

d) Equilibrium number of firms with new demand curve D(p) = 21 - p.

The intersection of this curve with the marginal cost curve is at p = 21/5. This is greater than the minimum possible price of 0. Thus there is a positive profit to be earned in this industry, and new firms can enter the market.

e) Equilibrium price and output with new demand curve with the new demand curve D(p) = 21 - p, the industry supply curve and the equilibrium price are as given in part (d). The equilibrium output of each firm is given by y = P/4 = 21/20, and the equilibrium output of the industry is given by Y = 21/4.

f) Equilibrium number of firms, price, output, and profit with demand curve D(p) = 24 - p. This demand curve intersects the marginal cost curve at p = 6. The minimum possible price is P = 0. Thus there is a range of prices from 0 to 6 where firms can profit positively.

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the output of the industry is Y = 3, and the profit of each firm is (6)(3/2) - (2)(2(3/2)² + 8) = -2.

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Answer:

Unit price 12.16 for 4.07 pounds is $2.99 per pound

Unit price 14.99 for 5.11 pounds is $2.93 per pound

The best deal is the 14.99 per 4.11 pounds

Step-by-step explanation:

Unit price 12.16/4.07 = 2.99 rounded to the nearest cent

Unit price 14.99/5.11 = 2.93 rounded to the nearest cent.

Answer:

1) $2.99

2)$2.93

The better buy is the 4.07 pound bag

Step-by-step explanation:

To find the unit price you find the cost per pound

$12.16 : 4.07

? : 1

4.07x = 12.16

x = 2.98771499

$2.99

$14.99 : 5.11

? : 1

5.11x = 14.99

x= 2.9334638

The expected value E[(1-x)(1-x)] is 1/4. This represents the average value of the function (1-x)(1-x) for the given probability distribution of x values.

We are given an indicator variable x with values 0 and 1. The probability of x = 0 is 1/4 and x = 1 is 3/4. We need to find the expected value E[(1-x)(1-x)].

Step 1: Determine the function we are working with.
We have the function (1-x)(1-x), which simplifies to (1-2x+x^2).

Step 2: Find the probabilities for each value of x.
For x = 0, the probability is 1/4.
For x = 1, the probability is 3/4.

Step 3: Compute the function values for each x value.
For x = 0, (1-2(0)+0^2) = 1.
For x = 1, (1-2(1)+1^2) = 0.

Step 4: Calculate the expected value.
E[(1-x)(1-x)] = (1)(1/4) + (0)(3/4) = 1/4.

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Answer:

The value of w is 63°.

Step-by-step explanation:

All the sides of triangle sum up to 180°.

so

w+71+46=180

or w+117=180

or w=180-117

=63

∠ XYQ is 122 degrees.

Angles are an important concept in mathematics and geometry. They are formed when two rays or line segments intersect at a common endpoint, known as the vertex. Angles can be measured in degrees, which is a unit of angular measure. A full circle is 360 degrees, and angles can be classified based on their measure relative to this standard. For example, an angle measuring less than 90 degrees is called an acute angle, while an angle measuring exactly 90 degrees is a right angle. An angle measuring between 90 and 180 degrees is an obtuse angle, and an angle measuring exactly 180 degrees is a straight angle. Angles are used in many applications, such as trigonometry, physics, and engineering. They are also important in everyday life, such as determining the direction of travel or the position of objects.

We can start by using the fact that angles XYQ and ZYQ are co-interior angles (also known as consecutive interior angles) and that they lie on a straight line, which means they add up to 180 degrees. So we have:

∠XYQ + ∠ZYQ = 180

Substituting the given values for ∠ZYQ and ∠XYQ, we get:

(10a + 2) + (5a - 2) = 180

Simplifying and solving for a, we get:

15a = 180

a = 12

Now we can substitute this value back into the expression for angle ∠XYQ to find its value:

∠XYQ = 10a + 2 = 10(12) + 2 = 122

Therefore, angle ∠XYQ is 122 degrees.

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Answer:

x + 10 = 24

Step-by-step explanation:

In the figure attached,

There are two external points A and B.

Fro point A two tangents AD and AE have been drawn and From point B tangents BE and BC have been drawn.

Since AD = 10 units,

Therefore, AE = 10 units

(Since tangents drawn from a point to a circle are same in measure, therefore, AD = AE)

Therefore,

BE = AB - AE

Since BE = BC

So BC = AB - AE

       x = 24 - 10

x + 10 = 24

Therefore, (x + 10) = 24 will be the equation to be used to solve for x.