Combine the like terms to simplify the expression 10x+8-3x+6

Answer:

\(27 \frac{2}{3} \)

Step-by-step explanation:

Ok, so first substitute x for 4 in

"g(x) = 5x + 1", and x for 3 in

"k(x) = 2/x + 2x". Now you got:

g(4) = 5(4) + 1

k(3) = 2/(3) + 2(3)

Now you can solve each individually.

g(4) = 5 × 4 = 20

20 + 1 = 21

g(4) = 21

k(3) = 2 × 3 = 6

6 + 2/3 = 6 2/3

k(3) = 6 2/3

g(4) + k(3) = 21 + 6 2/3 = 27 2/3

Hope this helps :)

Answer:

Step-by-step explanation:

by definition : The inverse of a relation consisting of points of the form (x,y) is the set of points (y,x)

if (1,7) is a point belong to f(x), then the inverse has to be (7,1) not (8,1)

Ordered pair\((8, 1)\) cannot belong to the inverse of the given function because ordered pair \((7,1).\)belong to the inverse function of the given function.

" Inverse  function is defined as when the domain and range of a function interchange with each other of the given function. It is represented by\(y = g(x)\)then its inverse is \(x = f(y)\)"

According to the question,

Given function,

Function\(f(x)\) with ordered pair \((1,7)\)

Domain of a function\(= 1\)

Range of a function \(= 7\)

As per the definition of inverse function,

Domain of inverse function \(= 7\)

Range of a inverse function \(= 1\)

Ordered pair\((7, 1)\) belongs to inverse of the given function.

Hence, ordered pair\((8, 1)\) cannot belong to the inverse of the given function.

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The required answers ar(a)P = $2,000,r = 4.5%,n = 2 (b)$ 2985.17, (c) 4.45%

(A) Using the given information, we can identify the following values:

P = $2,000 (the present value or initial deposit)

r = 4.5% (the annual percentage rate)

n = 2 (the number of times per year that interest is compounded, since it is compounded semi-annually)

(B) To find the future value of the account balance after 9 years, we can use the formula:

\(S(t) = P(1 + r/n)^{nt}\)

where t is the time in years. Substituting the given values:

\(S(9) = $2,000(1 + 0.045/2)^{2*9}= $2,000(1.0225)^{18}\)

= $2,000(1.505016)

= $2985.17

Therefore, Monique will have $$2985.17 in the account in 9 years.

(C) The annual percentage yield (APY) takes into account the effect of compounding on the effective interest rate. It is calculated as:

\(APY = (1 + \frac{r}{n})^n - 1\)

Substituting the given values:

\(APY = (1 + 0.045/2)^2 - 1\)

= 0.0445 or 4.45%

Therefore, the annual percentage yield for the savings account is 4.45% rounded to 3 decimal places.

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Answer:

20,34

Step-by-step explanation:

Let the two numbers bw a,b

Their sum is 54

a+b=54⋯(1)

Their difference is 14

a−b=14⋯(2)

(1)+(2)

2a=68

a=34⟹34+b=54

b=54−34=20

Answer
34 and 20.

Step-by-step explanation:

34+20 is equal to 54.
34-20 is equal to 14.
I hope this helps! :)

Answer:

the equation is true

Step-by-step explanation:

solve the equation 4x + 6 = 4 + 2(2x + 1). Which choice describes the meaning of his result, 6 = 6?

4x + 6 = 4 + 2(2x + 1)

4x + 6 = 4 + 4x + 2

6 = 4 + 2

6 = 6

There are 48 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

Explanation: We are given that a standard deck of 52 cards. (a) The first card is an Ace and (b) the second card is not a Queen. In a standard deck of 52 cards, there are four aces. If the first card drawn is an ace, then there are 51 cards left in the deck and 12 cards that are queens. Hence, there are 51 − 12 = 39 cards that are not queens. So, we can say that, There are 4 aces × 39 cards that are not queens = 156 ways to choose two different cards from a standard 52-card deck such that the first card is an Ace and the second card is not a Queen.

However, we have to remove the case where both cards are aces and the second card is a queen. So, we subtract 1 from the previous answer to get, 156 − 1 = 155 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

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Answer:

15.23

Step-by-step explanation:

Using  cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).

To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.

In cylindrical coordinates, the solid e can be defined as follows:

Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).

Angle: θ ranges from 0 to 2π (full revolution around the z-axis).

Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.

To convert the integral, we need to express x^2 in terms of cylindrical coordinates:

x^2 = (rcosθ)^2 = r^2cos^2θ

The integral in cylindrical coordinates becomes:

∫∫∫ (r^2cos^2θ) r dz dr dθ

Now we can determine the bounds for the variables:

r ranges from 0 to 2.

θ ranges from 0 to 2π.

z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.

Substituting the bounds and integrating, we can evaluate the integral to find the desired result.

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Answer:

98 degrees

Step-by-step explanation:

Angle JKG and angle LKO are vertical angles, which are equal.

The formula for a line segment is:

segment = √((x2 - x1)^2 + (y2 - y1)^2)

1. Calculate the difference between the x-coordinates: x2 - x1

2. Square the result of step 1: (x2 - x1)^2

3. Calculate the difference between the y-coordinates: y2 - y1

4. Square the result of step 3: (y2 - y1)^2

5. Add the results of step 2 and step 4: (x2 - x1)^2 + (y2 - y1)^2

6. Calculate the square root of the result of step 5: √((x2 - x1)^2 + (y2 - y1)^2)

This final result is the length of the line segment.

The formula for a line segment is relatively straightforward. Begin by calculating the difference between the x-coordinates (x2 - x1) and square the result. Then find the difference between the y-coordinates (y2 - y1) and square the result. Add the two results together and take the square root of the sum. This final result is the length of the line segment. This formula can be used to calculate the length of any line segment, regardless of its size or shape.

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Answer:

667 pizzas

Step-by-step explanation:

5-2=3 Unit CM

2000/3=666.6

Can't have .6 of a pizza, so round up

667

Answer:

b

Step-by-step explanation:

There is an estimated rise of 3.58 hatched eggs for every one degree Fahrenheit increment every day. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A scientist is interested in the relationship between the number of eggs hatched per day for frogs (y) and temperature.

Based on the collected data, the least-squares regression line is y = 15.66 +3.58x, where x is the number of degrees by which temperature exceeds 60 degrees Fahrenheit.

For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs.

Thus, the correct option is B.

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Answer: For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs

Step-by-step explanation:

took the test :)

The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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Given:

The inequality is \(y \leq |3x - 6| + 2\).

Alisha solved the given inequality and got

\(y \leq 3x -4\) for \(x \geq 2\) and \(y \leq -3x - 4\) for \(x < 2\).

To find:

The Alisha's error, and  the correct answer.

Solution:

We have,

\(y\leq |3x-6|+2\)

For \(x \geq 2, |3x-6|=3x-6\). So,

\(y\leq 3x-6+2\)

\(y\leq 3x-4\)

For \(x < 2, |3x-6|=-(3x-6)\). So,

\(y\leq -(3x-6)+2\)

\(y\leq -3x+6+2\)

\(y\leq -3x+8\)

Alisha's second inequality is wrong because she did not distribute the negative with 6.

Therefore, the correct answer is

\(y \leq 3x -4\) for \(x \geq 2\) and \(y \leq -3x +8\) for \(x < 2\).

The correct answer is B. Dilating a figure by a scale factor of 1 does not describe a rigid motion transformation.

Rigid motion transforms, also known as isometrics, preserve the character's shape and size.

This means that the transformed shape is the same as the original shape. Rigid motion includes rotation, translation, and reflection.

Rigid Motion transformation preserves character shape and size.

This includes rotation, translation and reflection.

However, dilation changes the size of the shape.

Enlarging a picture by a factor of 1 does not change the size of the picture. This is not a rigid motion transform as the character will not be preserved exactly as it was before the transform.

For expansion with a scale factor of 1, the number is simply multiplied by 1 to get the same number.

The picture remains the same size after being scaled by a scale factor of 1, so no transformation is needed to change the shape or size of the picture.

Therefore, it does not apply to rigid body motion transformations.

In summary, enlarging a figure by a scale factor of 1 is not a rigid body motion transformation because it does not change the size of the figure, making it identical to the original figure.

Option B enlarges the figure by a scale factor of 1, so rigid body motion transformations are not described.

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From the  X coordinate is -0.45 centimeter and Y coordinate is -2.0 cm of the center of mass for the uniform plate.

According to the Question:

Since the plate is uniform, we can divide it into three rectangles, each with a mass proportional to its area and with its barycenter at its geometric center. We will refer to the large piece of 35cm x 10cm; it occupies 63.6% of the total surface and its barycenter is at

(x₁, y₁) = (−5.0cm,−2.5cm).

Now,

The top 20cm× 5cm piece has 18.2 % of the total area; its center of mass is at (x₂, y₂) = (10cm,12.5cm).  

Now,

The bottom 10cm× 10cm piece (section 3) also has 18.2 % of the total area; its center of mass is at (x₃, y₃)​ = (5cm,−15cm).

(a) The x coordinate of the center of mass for the plate is

   \(X_{com} = (0.636)X_1 + (0.182)X_2 + (0.182)X_3\)

            = -0.45 cm

(b) The y coordinate of the center of mass for the plate is

    \(Y_{com} = (0.636)Y_1 + (0.182)Y_2 + (0.182)Y_3\)

             = -2.0 cm.

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The probability that between 12 and 20 people are home when the UPS delivery man makes his deliveries is 0.909

We have the following data; Number of stops = 50 Probability that someone is home when delivery is made = 0.35We are to find the probability that between 12 and 20 people are home when he makes his deliveries.The problem can be modelled by the binomial distribution model with;

Number of trials (n) = 50Probability of success (p) = 0.35Probability of failure (q) = 0.65We are to find the probability of having between 12 and 20 people home when the delivery is made, that is P(12 ≤ X ≤ 20). Using a binomial distribution table or a calculator, we can determine this probability as;

P(12 ≤ X ≤ 20) = P(X ≤ 20) - P(X ≤ 11)We can then use the binomial probability formula to find P(X ≤ 20) and P(X ≤ 11) as follows;

P(X ≤ 20) = ∑(nCr pᵢq⁽ⁿ⁻ⁱ⁾), where i = 0 to 20P(X ≤ 11) = ∑(nCr pᵢq⁽ⁿ⁻ⁱ⁾), where i = 0 to 11

We can obtain these probabilities by using a binomial distribution table or by using a calculator.

First, we modelled the problem using the binomial distribution. We found the probability of having someone at home for any particular stop as P(success) = 0.35 and the probability of not having someone at home as P(failure) = 1 - P(success) = 0.65. The UPS delivery man makes 50 stops along his daily route, and we want to find the probability that between 12 and 20 people are home when he makes his deliveries. This problem can be solved by using the binomial distribution formula.

The probability mass function for the binomial distribution is P(X = k) = (nCk) * p^k * q^(n-k), where n is the number of trials, p is the probability of success, q is the probability of failure, k is the number of successes we want to find, and (nCk) is the number of ways to choose k successes from n trials. Using a binomial distribution calculator or a binomial distribution table, we can find that:

P(X ≤ 20) = 0.989 (to 3 decimal places)P(X ≤ 11) = 0.080 (to 3 decimal places)Therefore, P(12 ≤ X ≤ 20) = P(X ≤ 20) - P(X ≤ 11) = 0.989 - 0.080 = 0.909 (to 3 decimal places).

The probability that between 12 and 20 people are home when the UPS delivery man makes his deliveries is 0.909 (to 3 decimal places).

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Answer:

bust stop #2 6.5 minutes

Step-by-step explanation:

Answer:

bust stop #2 6.5 minutes

Step-by-step explanation:

The pair (3, 36) means 3 dozens required 36 cookies

And the unit rate is 12

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

x = dozen

y = cookies

This means that

(3, 36) means 3 dozens required 36 cookies

Using the ordered pair in (a):

The unit rate of the pair (3, 36) is 36/3 = 12.

This means that for every 1 dozen change, there is a corresponding 12 cookies change

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a. The PMF (Probability Mass Function) for X is:

PMF(X) = {}

0.1, for X = 0

0.2, for X = 1

0.25, for X = 2

0.2, for X = 3

0.15, for X = 4

0.06, for X = 5

0.03, for X = 6

0.01, for X = 7

b. The mean (μ) is 2.54; the Variance (σ²) is 1.6484

c. The CDF is a valid CDF because it is a non-decreasing function and it approaches 1 as x approaches infinity.

a) The PMF (Probability Mass Function) for X, the number of goals scored in a World Cup soccer match, is given by the following:

PMF(X) = {}

0.1, for X = 0

0.2, for X = 1

0.25, for X = 2

0.2, for X = 3

0.15, for X = 4

0.06, for X = 5

0.03, for X = 6

0.01, for X = 7

This PMF is valid because it assigns probabilities to each possible value of X (0 to 7) and the probabilities sum up to 1. The probabilities are non-negative, and for any value of X outside the range of 0 to 7, the probability is zero.

b) To compute the mean and variance of X, we can use the following formulas:

Mean (μ) = Σ(X * PMF(X))

Variance (σ^2) = Σ((X - μ)² * PMF(X))

Using the PMF values given above, we can calculate:

Mean (μ) = (0 * 0.1) + (1 * 0.2) + (2 * 0.25) + (3 * 0.2) + (4 * 0.15) + (5 * 0.06) + (6 * 0.03) + (7 * 0.01) = 2.54

Variance (σ²) = [(0 - 2.54)² * 0.1] + [(1 - 2.54)² * 0.2] + [(2 - 2.54)² * 0.25] + [(3 - 2.54)² * 0.2] + [(4 - 2.54)² * 0.15] + [(5 - 2.54)² * 0.06] + [(6 - 2.54)² * 0.03] + [(7 - 2.54)² * 0.01] ≈ 1.6484

c) The CDF (Cumulative Distribution Function) of X is a function that gives the probability that X takes on a value less than or equal to a given value x.

The CDF can be obtained by summing up the probabilities of X for all values less than or equal to x.

CDF(x) = Σ(PMF(X)), for all values of X ≤ x

For example, the CDF for x = 3 would be:

CDF(3) = PMF(0) + PMF(1) + PMF(2) + PMF(3)

CDF(3) = 0.1 + 0.2 + 0.25 + 0.2

CDF(3) = 0.75

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a) The PMF for X is valid because it assigns non-negative probabilities to each possible value of X and the sum of all probabilities is equal to 1.

b) The mean of X is 2.55 and the variance is 2.1925.

c) The CDF of X is a valid cumulative distribution function as it is a non-decreasing function ranging from 0 to 1, inclusive.

a) The PMF (Probability Mass Function) for X, the number of goals scored in a randomly selected World Cup soccer match, can be represented as follows,

PMF(X) = {

 0.1, if X = 0,

 0.2, if X = 1,

 0.25, if X = 2,

 0.2, if X = 3,

 0.15, if X = 4,

 0.06, if X = 5,

 0.03, if X = 6,

 0.01, if X = 7,

 0, otherwise

}

This PMF is valid because it satisfies the properties of a valid probability distribution. The probabilities assigned to each value of X are non-negative, and the sum of all probabilities is equal to 1. Additionally, the PMF assigns a probability to every possible value of X within the given distribution.

b) To compute the mean (expected value) and variance of X, we can use the formulas,

Mean (μ) = Σ (x * p(x)), where x represents the possible values of X and p(x) represents the corresponding probabilities.

Variance (σ^2) = Σ [(x - μ)^2 * p(x)]

Calculating the mean,

μ = (0 * 0.1) + (1 * 0.2) + (2 * 0.25) + (3 * 0.2) + (4 * 0.15) + (5 * 0.06) + (6 * 0.03) + (7 * 0.01)

  = 0 + 0.2 + 0.5 + 0.6 + 0.6 + 0.3 + 0.18 + 0.07

  = 2.55

The mean number of goals scored in a World Cup soccer match is 2.55.

Calculating the variance,

σ^2 = [(0 - 2.55)^2 * 0.1] + [(1 - 2.55)^2 * 0.2] + [(2 - 2.55)^2 * 0.25] + [(3 - 2.55)^2 * 0.2]

      + [(4 - 2.55)^2 * 0.15] + [(5 - 2.55)^2 * 0.06] + [(6 - 2.55)^2 * 0.03] + [(7 - 2.55)^2 * 0.01]

    = [(-2.55)^2 * 0.1] + [(-1.55)^2 * 0.2] + [(-0.55)^2 * 0.25] + [(-0.55)^2 * 0.2]

      + [(-1.55)^2 * 0.15] + [(2.45)^2 * 0.06] + [(3.45)^2 * 0.03] + [(4.45)^2 * 0.01]

    = 3.0025 * 0.1 + 2.4025 * 0.2 + 0.3025 * 0.25 + 0.3025 * 0.2

      + 2.4025 * 0.15 + 6.0025 * 0.06 + 11.9025 * 0.03 + 19.8025 * 0.01

    = 0.30025 + 0.4805 + 0.075625 + 0.0605 + 0.360375 + 0.36015 +          0.357075 + 0.198025

    = 2.1925

The variance of the number of goals scored in a World Cup soccer match is 2.1925.

c) The CDF (Cumulative Distribution Function) of X can be calculated by summing up the probabilities of X for all values less than or equal to a given x,

CDF(X) = {

 0, if x < 0,

 0.1, if 0 ≤ x < 1,

 0.3, if 1 ≤ x < 2,

 0.55, if 2 ≤ x < 3,

 0.75, if 3 ≤ x < 4,

 0.9, if 4 ≤ x < 5,

 0.96, if 5 ≤ x < 6,

 0.99, if 6 ≤ x < 7,

 1, if x ≥ 7

}

The CDF is valid because it satisfies the properties of a valid cumulative distribution function. It is a non-decreasing function with a range between 0 and 1, inclusive. At x = 0, the CDF is 0, and at x = 7, the CDF is 1. The CDF is right-continuous, meaning that the probability assigned to a specific value of x is the probability of x being less than or equal to that value.

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The percentage of nurses holding a BSN (Bachelor of Science in Nursing) degree would be an example of descriptive statistics. Descriptive statistics involve summarizing and describing data in a meaningful way, such as through percentages, averages, or frequencies.

In this case, the percentage of nurses with a BSN degree provides information about the proportion of nurses who have completed a four-year bachelor's degree program in nursing.

This statistic can be used to understand the educational background of the nursing workforce and to assess the level of academic preparation among nurses.

By examining the percentage of nurses with a BSN degree, policymakers, healthcare organizations, and researchers can gain insights into the educational composition of the nursing workforce. This information can be valuable for making decisions related to workforce planning, policy development, and resource allocation in healthcare settings.

It is important to note that the percentage of nurses holding a BSN degree may vary across different regions or countries due to variations in educational requirements and healthcare systems. Some countries may have a higher proportion of nurses with a BSN degree compared to others.

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Answer:

P = P (1 + r / n) ^ rt

Step-by-step explanation:

Answer:

y = 1/2x - 6

Step-by-step explanation:

y2 - y1 / x2 - x1

-2 - (-5) / 8 - 2

3 / 6

= 1/2

y = 1/2x + b

-5 = 1/2(2) + b

-5 = 1 + b

-6 = b

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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Step-by-step explanation:

3^-5= 1/3^5

9^-3=1/9^3

3^-4=1/3^4

Answer:

Step-by-step explanation:

3^-5 = 1/ 3 ^5 = 1/243

9^-3 = 1/9^3    = 1 /729

3^-4 = 1/3^4

For any number which has a negative power there will be a 1 as the numerator and the number with its power as the denominator

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

\(x \times 0.25 = y\)

have an amazing day <3

Answer:

x*.25=y?

Step-by-step explanation: