Is 2352 a perfect square? If not, find the smallest number by
which 2352 must be multiplied so that the product is a perfect
square. Find the square root of new number.

To find the values of a and b, we need to ensure that the function is differentiable at x = 1. Thus, the function defined by f(x) = x^2 + 3x + a, x <= 1 and bx + 2, x >= 1 differentiable at x = 1 are a = 3 and b = 5.

First, we need to check that the function is continuous at x = 1. Since the function has different definitions for x <= 1 and x >= 1, we need to check that the limit of the function as x approaches 1 from both sides is the same.

Limit as x approaches 1 from the left (x <= 1):

f(x) = x^2 + 3x + a

lim x->1- f(x) = lim x->1- (x^2 + 3x + a) = 1^2 + 3(1) + a = 4 + a

Limit as x approaches 1 from the right (x >= 1):

f(x) = bx + 2

lim x->1+ f(x) = lim x->1+ (bx + 2) = b + 2

For the function to be continuous at x = 1, these two limits must be equal.

4 + a = b + 2

a = b - 2

Now we need to check that the derivative of the function at x = 1 exists and is equal from both sides.

Derivative of the function for x <= 1:

f(x) = x^2 + 3x + a

f'(x) = 2x + 3

f'(1) = 2(1) + 3 = 5

Derivative of the function for x >= 1:

f(x) = bx + 2

f'(x) = b

f'(1) = b

For the function to be differentiable at x = 1, these two derivatives must be equal.

5 = b

Substituting b = 5 into the equation we found earlier for a, we get:

a = 5 - 2 = 3

Therefore, the values of a and b that make the function defined by f(x) = x^2 + 3x + a, x <= 1 and bx + 2, x >= 1 differentiable at x = 1 are a = 3 and b = 5.
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Answer:

im gooder like that

Step-by-step explanation:

3z*5=15z

15z+4z-7

19z-7  

The measure of the angle x in the circle is 65 degrees

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

The circle

On the circle, we have the angle at the vertex of the triangle to be

Angle = 100/2

Angle = 50

The sum of angles in a triangle is 180

So, we have

x + x + 50 = 180

Evaluate the like terms,

2x = 130

So, we have

x = 65

Hence, the angle is 65 degrees

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The parabola has an axis of symmetry x=22, vertex at (22, 2), and opens downward.

Given the focus (22, 3) and directrix y=1, we can determine the following:

a. Axis of symmetry: Since the parabola is vertical (directrix is horizontal), the axis of symmetry will be a vertical line passing through the focus. So, x=22 is the axis of symmetry.

b. Vertex: The vertex is the midpoint between the focus and the directrix. To find the vertex, average the y-coordinates of the focus and the directrix. Vertex = (22, (3+1)/2) = (22, 2).

c. Direction: If the focus is above the directrix, the parabola opens upward. If the focus is below the directrix, the parabola opens downward. In this case, the focus (22, 3) is above the directrix y=1, so the parabola opens downward.

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The current number of classrooms is 24, and the number of students per class is 70 if there were a total of 1200 students.

Let us assume that the number of classes = x

Number of students per class = 1200/x

Number of classrooms planned = x - 4

Number of students planned per class = 1200/ x+10

Total number of students = 1200

By using the above data, the equations will be written as:

(1200 / x-4) = (1200/x) +10

By multiplying the equation 2 we get:

1200x = 1200x + [tex]x^{2}[/tex] - 4800 - 40x

[tex]x^{2}[/tex] - 480- 4x = 0

(x-24) (x+20) = 0

x = 24

Number of rooms built = x =24

Number of students per class = (1200/24-10) = 60 students

Therefore, we can conclude that the current number of classrooms is 24, and the number of students per class is 60 + 10 =70.

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The correct answer is e. 2/7.

To evaluate this line integral, we need to parameterize the curve given by the parabola y = x from (1, 1) to (-1, 1).

Let's let x = t and y = t, where t goes from 1 to -1. Then we can rewrite the integral as follows:

[tex]\int\ C (x - y)\dx + (y \sin y)\dy[/tex]

[tex]= \int\limits^1_{-1} {[(t - t)dt + (t sin t)}\,dt}[/tex]

[tex]= \int\limits^1_{-1} { (t \sin t)} \, dt[/tex]

We can evaluate this integral using integration by parts:

Let u = t and [tex]dv = sin t\ dt[/tex]. Then [tex]du/dt = 1[/tex] and v = -cos t.

Using the formula for integration by parts, we have:

[tex]\int\limits^1_{-1} { (t \sin t)}\, dt = -t \cos t |_{-1}^{1} + \int\limits^1_{-1} { cos t}\, dt[/tex]

= -cos(-1) + cos(1) + sin(-1) - sin(1)

= 2sin(1) - 2cos(1)

Therefore, the value of the line integral is:

[tex]S_c(x - y)dx + (y \sin y)dy = 2\sin(1) - 2\cos(1)[/tex]

Hence, the correct answer is e. 2/7.

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To find the limit of (7x3)/(4x2-2x+10) as x approaches infinity, we need to divide the highest power of x in the numerator and denominator, which is x3, by the highest power of x in the denominator, which is x2. This gives us: (7x3)/(4x2-2x+10) = (7/4)x

As x approaches infinity, the value of (7/4)x also approaches infinity. Therefore, the limit of (7x3)/(4x2-2x+10) as x approaches infinity is infinity.

To find the limit of (7x^3)/(4x^2-2x+10) as x approaches infinity, we'll first look at the highest powers of x in the numerator and denominator.

In this case, the highest power of x in the numerator is x^3, and in the denominator, it's x^2. Since the highest power of x in the numerator is greater than that in the denominator, the limit will go to infinity (or -infinity) depending on the coefficients of the highest powers.

For this function, the coefficients are positive (7 for x^3 and 4 for x^2), so the limit as x approaches infinity will be positive infinity.

Your answer: The limit of (7x^3)/(4x^2-2x+10) as x approaches infinity is positive infinity.

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Area of sector NPQ ≈ 127.23 square units

To find the area of the sector NPQ, we first need to find the measure of the central angle that defines the sector. We know that the measure of the angle NPQ is 104 degrees, but we need to find the measure of the central angle that includes this arc.

Since NP is a radius of the circle, we know that triangle NQP is an isosceles triangle, with angles NQP and PNQ each measuring (180 - 104)/2 = 38 degrees. Therefore, the measure of the central angle that includes arc NPQ is 2 * 38 + 104 = 180 degrees.

The area of the sector NPQ is then a fraction of the total area of the circle, where the fraction is equal to the ratio of the central angle to the total angle around the circle. Since the total angle around a circle is 360 degrees, the fraction of the circle's area covered by the sector is:

180 degrees / 360 degrees = 1/2

Therefore, the area of the sector NPQ is equal to half the area of the circle with radius 9 units:

Area of sector NPQ = (1/2) * π * 9^2 = 40.5π

Rounding to the nearest hundredth, the area of the sector NPQ is approximately:

Area of sector NPQ ≈ 127.23 square units

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The numerical value of Oz is approximately -1819.86.

Using the chain rule, we have:

[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt\\dz/ds = dz/dy * dy/ds[/tex]

We can calculate each term using the given equations:

dz/dx = 1

dx/dt = 2

dy/dt = 0

dz/dy = cos(y)

dy/ds = 6t

Substituting these values, we get:

[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt = 1 * 2 + cos(y) * 0 = 2\\dz/ds = dz/dy * dy/ds = cos(y) * 6t = 6t * cos(6st)[/tex]

To find дz as/Əz, we need to solve for as in terms of z and s:

z = x + sin(y) = 2t + sin(6st)

x = 2t

y = 6st - 1

Solving for s in terms of t, we get:

s = (y + 1)/(6t)

Substituting this into the equation for z, we get:

z = 2t + [tex]sin(6t(y+1)/(6t)) = 2t + sin(y+1)[/tex]

Taking the partial derivative of z with respect to as, we get:

[tex]дz/Əz = 1[/tex]

B. To find the numerical values of дz and Oz, we need to plug in the given values of x, y, s, and t into our equations. Using the given values, we get:

x = 2t = -964

y = 6st - 1 = -3617

z = x + sin(y) = -964 + sin(-3617) ≈ -964.73

Using the values of s and t, we can find:

s = (y + 1)/(6t) ≈ -0.9985

t = x/2 ≈ -482

Substituting these values into our equation for дz as/Əz, we get:

дz/Əz = 1

Therefore, the numerical value of дz is 1.

Substituting these values into our equation for dz/ds, we get:

dz/ds = 6t * cos(6st) ≈ -1819.86

Therefore, the numerical value of Oz is approximately -1819.86.

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The coordinates of transforming image of the vertices of the triangle ABC are A' (1, -1) ,B' (3, 1) , and C' (1, 4).

In triangle ABC,

Coordinates of the vertices of triangle ABC are,

A(-1,1), B(1,3) and C(4,1)

The transformation T y=x reflects the points across the line y=x.

The image of each point, we simply swap the x and y coordinates of each point.

So, applying the transformation T y=x to the vertices of triangle ABC, we get,

A' = (-1, 1) → (1, -1)

B' = (1, 3) → (3, 1)

C' = (4, 1) → (1, 4)

This implies,

The image of triangle ABC under the transformation T y=x is triangle A'B'C', where,

A' is located at (1, -1)

B' is located at (3, 1)

C' is located at (1, 4)

Therefore, in triangle ABC labeling the coordinates of the vertices of A'B'C'  after transformation are as follows,

A' (1, -1)

B' (3, 1)

C' (1, 4)

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The above question is incomplete, the complete question is:

Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation T y=x is A’ B’ C’. State and label the coordinates of A’ B’ C’.

1 hour =60 minutes

Step-by-step explanation:

Let M be the time in minutes . T be temperature in Farhenheit. From 45th min to end of the hour there remains a steady temperature. after that gyms starts to cools down . For time 45≤M≤60, Temperature T=77oF.To find a) Is M a function of T ? we know that Temperature changes with respect to time . So M is independent variable and T is dependent variable . so M cannot be a function of T .

When rt is a diameter of circle p, it divides the circle into two equal halves. Since the sum of angles in a circle is 360 degrees, each half of circle p measures 180 degrees.

Thus, each arc of circle p that is intersected by diameter rt measures half of the circle or 90 degrees.

Therefore, each arc of circle p measures 90 degrees when rt is a diameter.

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Answer: We can check whether the expression (x + 18) is a factor of x² - 324 by dividing x² - 324 by (x + 18) using polynomial long division or synthetic division.

Using polynomial long division:

x + 18 │x² + 0x - 324

       -x² - 18x

       ----------

        18x - 324

        18x + 324

        ----------

            0

Since there is no remainder, we can see that (x + 18) is indeed a factor of
x² - 324.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

The experimental probabilities are obtained considering the trials, hence:

The more trials, the closer the experimental probability should be to the theoretical probability.

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The amount for the fencing cost  is $903. 36

From the information given, we have that the shape of the garden is  semi -circle.

Now, the formula that is used for calculating the circumference of a semicircle is expressed as;

C = πr + 2r

Given that the parameters of the equation are;

From the information given,

Substitute the values, we have;

Circumference = 3.14(19) + 2(19)

expand the bracket

Circumference = 59. 66 + 38

Add the values

Circumference = 97. 66 feet

Then,

if 1 feet = $9.25

Then, 97. 66 feet = x

x = $903. 36

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The expression that represents the length (in feet) of the world's longest glass-bottom bridge is 4.3x+550.4.

Let's denote the length of the Coiling Dragon Cliff Skywalk as y (in feet). According to the given information, we have:

y = x + 128

The length of the world's longest glass-bottom bridge is 4.3 times longer than the Coiling Dragon Cliff Skywalk, so we can write an expression for it as:

Length of the longest glass-bottom bridge = 4.3 * y

Now, we can substitute the expression for y from the first equation:

Length of the longest glass-bottom bridge = 4.3 * (x + 128)

To simplify, distribute the 4.3:

Length of the longest glass-bottom bridge = 4.3x + 550.4

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The missing number for box a transaction amount account balance are a = 10, b = 210, c = 210.

Using the information provided in the table, we can fill in the missing numbers as follows:

For transaction 3: The account balance after transaction 2 was $100, and transaction 3 had an amount of $90. Therefore, the account balance after transaction 3 is $190. Hence, the missing number in box a is 190.

For transaction 4: The account balance after transaction 3 was $190, and transaction 4 had an amount of -$200. Therefore, the account balance after transaction 4 is -$10. Hence, the missing number in box b is -10.

For transaction 5: The account balance after transaction 4 was -$10, and transaction 5 had an amount of $c. Therefore, the account balance after transaction 5 is 0. Hence, the missing number in box c is 10.

Therefore, the completed table is:

transaction amount account balance

1 150 150

2 50 100

3 90 190

4     -200-10

5 10 0

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The projected stock price of Ghost Rider Co. in 4 years is $45.24.

First, we need to calculate the future EPS of Ghost Rider Co. in 4 years. We can do this using the formula for the future value of an annuity:

[tex]FV = PV x (1 + r)^n[/tex]

where FV is the future value, PV is the present value, r is the growth rate, and n is the number of years.

Using this formula, we get:

[tex]FV = $1.65 x (1 + 0.085)^4 = $2.36[/tex]

Next, we can use the following formula to determine the anticipated stock price:

Estimated stock price = EPS x PE ratio

When we enter the values we have, we obtain:

Projected stock price = $2.36 x 19.15 = $45.24

Therefore, the projected stock price of Ghost Rider Co. in 4 years is $45.24.

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Answer:

6, 9, 10, 10, 11, 11, 12, 13, 15, 15, 18

Q1 (the first quartile) represents the data point that separates the lowest 25% of the data from the rest of the data. To find Q1, we can use the formula:

Q1 = (n + 1) / 4

where n is the total number of data points.

In this case, n = 11, so:

Q1 = (11 + 1) / 4 = 3rd data point

So, Q1 is 10.

Q3 (the third quartile) represents the data point that separates the highest 25% of the data from the rest of the data. To find Q3, we can use the formula:

Q3 = 3(n + 1) / 4

In this case:

Q3 = 3(11 + 1) / 4 = 9th data point

So, Q3 is 15.

D4 represents the fourth decile, which is the data point that separates the lowest 40% of the data from the rest of the data. To find D4, we can use the formula:

D4 = (n + 1) / 10 * 4

In this case:

D4 = (11 + 1) / 10 * 4 = 5th data point

So, D4 is 11.

D Assimilation represents the data point that is closest to the mean (average) of the data. To find D Assimilation, we first need to find the mean of the data:

Mean = (6 + 9 + 10 + 10 + 11 + 11 + 12 + 13 + 15 + 15 + 18) / 11 = 12

The data point closest to the mean is 12, so:

D Assimilation = 12

Pss (the range) represents the difference between the largest and smallest data points. In this case:

Pss = 18 - 6 = 12
6  9  10 10 11 11 12 13 15 15 18

                             Dss=12

   Q1=10       Q3=15

       D4=11

Step-by-step explanation:

31.8 kilograms is equivalent to 31,800 grams.

The correct answer is (D) 31,800 grams.

To convert kilograms to grams, we multiply the number of kilograms by 1000. So, to convert 31.8 kilograms to grams, we can use the following formula:

31.8 kilograms x 1000 grams/kilogram = 31,800 grams

Therefore, 31.8 kilograms is equivalent to 31,800 grams.

To convert kilograms to grams, we need to multiply the number of kilograms by 1000 because there are 1000 grams in one kilogram. In this case, Eddie's dog weighs 31.8 kilograms. To find out how many grams this is, we simply multiply 31.8 by 1000, which gives us 31,800 grams. Therefore, 31.8 kilograms is equivalent to 31,800 grams. It's important to understand the basic metric system conversions, like kilograms to grams, as they are commonly used in everyday life, particularly when it comes to measuring weight. Knowing how to make these conversions can be helpful in many different situations, from cooking and baking to medical and scientific contexts.  

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The explicit formula for the given sequence is An = 256 * (0.25)ⁿ⁻¹, where n is the term number. Using this formula, we can generate the first five terms of the sequence as follows:

A1 = 256 * (0.25)¹⁻¹ = 256 * 1 = 256
A2 = 256 * (0.25)²⁻¹ = 256 * 0.25 = 64
A3 = 256 * (0.25)³⁻¹ = 256 * 0.0625 = 16
A4 = 256 * (0.25)⁴⁻¹ = 256 * 0.015625 = 4
A5 = 256 * (0.25)⁵⁻¹ = 256 * 0.00390625 = 1

In simpler terms, the explicit formula for the given sequence is found by multiplying the first term by the common ratio raised to the power of n-1, where n is the term number. This results in a decreasing sequence as the common ratio is less than 1. The first five terms of the sequence are 256, 64, 16, 4, and 1, respectively.

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The answer is option B: 1.116%.

To find the APR(Annual Percentage Rate) for Jason's loan, we first need to calculate the total amount of interest he paid.

The finance charge of $55 is the interest paid for the 360-day term.

To find the total interest, we can use the formula:

Total interest = (finance charge / loan amount) x (days in a year / loan term in days)

Plugging in the values, we get:

Total interest = (55 / 5000) x (365 / 360)

Total interest = 0.011 x 1.01389

Total interest = 0.01116 or 1.116%

Therefore, the APR for Jason's loan is 1.116%.

The answer is option B: 1.116%.

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2/9 as a percentage is approximately 22.2%.

To convert the fraction 2/9 to a percentage, you simply need to divide the numerator (2) by the denominator (9) and then multiply the result by 100.

1. Divide the numerator by the denominator: 2 ÷ 9 ≈ 0.2222
2. Multiply the result by 100: 0.2222 × 100 = 22.22%

Now, to round the answer to one decimal place, we consider the second digit after the decimal point. In this case, it's 2. Since it's less than 5, we can round down.

So, 2/9 as a percentage rounded to one decimal place is approximately 22.2%.

In summary, converting a fraction to a percentage involves dividing the numerator by the denominator and then multiplying the result by 100. Rounding to a specific decimal place helps in presenting the result in a more easily understandable form, especially when dealing with non-integer values.

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Answer:

Rate: 36:3

Unit Rate: 12:1

Step-by-step explanation:

The evaluation of the triple integral ∫∫∫E 4[tex]x^{2}[/tex] + 3dV is  (38/15)ππ

To evaluate the triple integral ∫∫∫E 4x^2 + 3dV in spherical coordinates, we need to express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.

The volume element dV in spherical coordinates is given by:
dV =  sin φ dρ dθ dφ
where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.
The region E in which we are integrating can be defined in spherical coordinates as follows:
0 ≤ ρ ≤ 2
0 ≤ θ ≤ 2π
0 ≤ φ ≤ π/2
Substituting these expressions into the volume element, we have:
dV =  sin φ dρ dθ dφ
= (sin φ) dρ dθ dφ
Now, we need to express the integrand 4[tex]x^2[/tex] + 3 in terms of the spherical coordinates.

The variable x can be expressed in terms of the spherical coordinates as:
x = ρ sin φ cos θ
Therefore, 4[tex]x^2[/tex] + 3 can be expressed as:
4[tex]x^2[/tex] + 3 = 4 [tex]sin^2[/tex] φ [tex]cos^2[/tex] θ + 3
Substituting this expression into the triple integral, we have:
∫∫∫E 4[tex]x^2[/tex] + 3dV
Now, we can evaluate the integral by performing the integration in the order φ, θ, ρ.
= (8/15)π + 2π
= (38/15)ππ

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From the given graph, the roots of the quadratic equation, 0 = x² - 6x + 5, is 1 and 5. The correct option is the last option x= 1, 5

From the question, we are to determine the roots of the quadratic equation from the provided graph.

From the given information,

The given quadratic equation is

0 = x² - 6x + 5

The roots of a quadratic function are the values of x where the function equals zero. On a graph, this corresponds to the points where the graph intersects the x-axis.

From the graph, we will read the x-coordinates of the points where the graph intersects the x-axis.

From the given graph, the x-coordinates of the points where the graph intersects the x-axis are 1 and 5

Hence, the roots of the quadratic equation is 1 and 5

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The largest box of soup will hold about 120 ounces or 221 cubic inches of soup.

Since the scale factor is 2, the volume of the largest box will be 2^3 = 8 times the volume of the smallest box. Therefore, the volume of the largest box will be 8 x 15 cubic inches = 120 cubic inches. To find the dimensions of the largest box, we need to find the cube root of 120 cubic inches, which is approximately 5.87 inches.

Since the smallest box has no shape restrictions, we can assume that the largest box will also have a rectangular shape. Therefore, a set of dimensions for the largest box could be 5.87 inches x 5.87 inches x 5.87 inches, or rounded to the nearest tenth, 5.9 inches x 5.9 inches x 5.9 inches.

This would result in a volume of approximately 221 cubic inches, which is about 120 ounces of soup.

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Answer:

a = 16

b = 8z

Step-by-step explanation:

Expanding the given expression, we get:

(4y + z)^2 = (4y + z) × (4y + z)

= 16y^2 + 8yz + z^2

Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:

a = 16

b = 8z

Therefore, the value of a is 16 and the value of b is 8z.

The difference in measures of center as a multiple of the measure of variation can be expressed using the coefficient of variation.

To express the difference in measures of center as a multiple of the measure of variation, you can use the coefficient of variation (CV).

The CV is calculated by dividing the standard deviation (measure of variation) by the mean (measure of center), and then multiplying by 100 to express the result as a percentage.

For example, if the standard deviation of one dataset is 5 and the mean is 10, the CV would be 50%. If the standard deviation of another dataset is 2 and the mean is 8, the CV would be 25%.

To express the difference in measures of center as a multiple of the measure of variation between these two datasets, you would calculate the difference in their means (10-8=2) and divide it by the CV of the combined dataset ((5/10 + 2/8)/2 = 47.5%).

Therefore, the difference in measures of center is approximately 0.042 times the measure of variation (2/47.5%).

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[tex]\sf Let \ d_1 \ and \ d_2 \ be \ the \ lengths \ of \ the \ sides \ of \ diagonals.[/tex]

[tex]\sf Given \ that \ d_1=8 \ cm[/tex]

[tex]\sf And \ d_2=10 \ cm[/tex]

[tex]\therefore\sf Area \ of \ rhombus=\dfrac{1}{2} (d_1)(d_2)=\dfrac{1}{2}(8)(10)=40 \ cm^2[/tex]

[tex]\rightarrow\boxed{\sf Area \ of \ rhombus=40 \ cm^2}[/tex]