Find the surface area of the prism.
4 in.
2 in.
7 in.

Answer:

5.5

Step-by-step explanation:

2x+7=16

   -7   -7

2x=11

2x/2=11/2

x=5.5

The value of m∠SRT as shown in the circle below is 46.5°.

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

To calculate the value of m∠SRT, use the formula below

Formula:

But,

From the diagram,

Given:

Substitute these values into equation 2

Finally we substitute the value m∠SUT into equation 1

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To make the sum of 6x - 5 equal to zero, a polynomial of -6x + 5 should be added, which cancels out the x term and the constant term of the original expression. This addition ensures that both the x term and the constant term cancel each other, resulting in a sum of zero.

The polynomial that should be added to 6x - 5 so that the sum is zero, we need to determine the polynomial that cancels out the existing terms.

Since the given expression is 6x - 5, we want to add a polynomial of the form -6x + 5 to it.

By adding this polynomial, the x term from the original expression will cancel out with the -6x term we are adding, and the constant term -5 will cancel out with the +5 term we are adding.

When we add 6x - 5 to -6x + 5, the x terms cancel each other out, resulting in 0x or simply 0. Similarly, the constant terms cancel each other out, resulting in 0.

Therefore, the sum of 6x - 5 and -6x + 5 is indeed zero.

In conclusion, to make the sum of 6x - 5 and the added polynomial equal to zero, we should add -6x + 5 to it.

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The 12.7 moles of a compound contain 7.65 x 10 24 particles.

Avogadro's number is the number of units, which could be atoms, particles, electrons, molecules, or even ions, per mole of a substance. The value of Avogadro's number is 6.02214076 x 10 23.

To answer this question, we will multiply the given moles of the compound to Avogadro's number, which will have a unit of particles/mol.

Number of particles of given compound = number of moles * Avogadro's number in particles/mol = 12.7 moles * 6.02214076 x 10 23 particles/moles

Number of particles of given compound = 7.65 x 10 24 particles

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Answer:

V=1/3πSh=72π

Step-by-step explanation:

Need to find S(area):

S(triangle)=1/2x6x8=24(ft)

h=9(ft)

=> V=1/3πSh=72π

Answer:

x=-2

Step-by-step explanation:

Answer:

x² = \(\frac{256}{9}\)

Step-by-step explanation:

\(\frac{3x}{4}\) - 13 = - 9 ( add 13 to both sides )

\(\frac{3x}{4}\) = 4 ( multiply both sides by 4 to clear the fraction )

3x = 16 ( divide both sides by 3 )

x = \(\frac{16}{3}\)

Then

x² = ( \(\frac{16}{3}\) )² = \(\frac{16^2}{3^2}\) = \(\frac{256}{9}\)

Answer:

Y= 5/3x -7

Step-by-step explanation:

To find the slope with the given points you find the distance between the y values and the x values. (Rise/Run = Y/X). Once you find the pattern you can use it until you find the y intercept if you're using graph paper!

Hope this helps! :)

(Side Note: The distance for the y values from -2 and 3 is +5. The distance for the x values is +3 )

Answer:

Inverse of 11(x-3) : x/11+3

Slope of 11(x-3) : m=11

Step-by-step explanation:

= 11(x-3)

= x intercepts (3,0), y intercepts (0,-33)

= Inverse of 11(x-3) : X/11+3

= slope of 11(x-3) : m=11

Answer:

Rs 12,500

Step-by-step explanation:

the price before VAT = 100/10 × Rs 5000 =

Rs 50,000

the price before discount = 50,000 / 80%

= 50,000/0.8 = 62,500

so the discount amount = 62,500-50,000

= Rs 12,500

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

The 30 pound bag of bird food

Step-by-step explanation:

19.50 divided by 25 = 0.78 cents a pound

22.80 divided by 30 = 0.76 cents a pound

Therefore, 0.76 cents is cheaper :)

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer:

B

Step-by-step explanation:

Answer:

0.05n + 0.10 d =24.40

Step-by-step explanation:

Nickel is worth 0.05 of a dollar(1)

The system of equations below would be the best to use to find the number of nickels and dimes Anthony had at the end of the first week is:

n + d = 368

0.05n + 0.10d = 24.40

The number of nickels and dimes Anthony saved at the end of the first week can be determined using two equations. This is known as simultaneous equations.

The total number of nickels and dimes in the jar is 368. This can be represented with the equation:

nickels + dimes = 368

n + d = 368. This would be the first equation.

A nickel is equal to 0.05 of a dollar and a dime is equal to 0.1 of a dollar. The total sum of money in the jar is $24.40. This means that the value of dimes and nickels in the jar is $24.40. This can be represented with the equation: 0.05n + 0.10d = 24.40. This is the second equation.

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Answer:

Right angle is an angle of 90°

Obtuse angles is an angle greater than 90°

Answer:

A right angle is an angle of 90°

An Obtuse angles is an angle greater than 90°

The surface area of a triangular prism is 288 square inches. If the triangle base is 8 inches, each rectangular face will be 8 inches broad and 10 inches long. The height of the triangular prism is 16 inches.

To find the height of the triangular prism, we need to use the formula for the surface area of a triangular prism:

Surface Area = 2(Area of the rectangular face) + (Perimeter of the base) x (Height)

We know that the rectangular face has a width of 8 inches and a length of 10 inches, so its area is:

Area of the rectangular face = 8 x 10 = 80 square inches

We also know that the surface area of the triangular prism is 288 square inches. Substituting these values into the formula, we get:

288 = 2(80) + (Perimeter of the base) x (Height)

Simplifying this equation, we get:

288 = 160 + 8(Height)

128 = 8(Height)

Height = 16 inches

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Answer:

115:345:460

Step-by-step explanation:

The probability that student chosen at random is 16 years is 0.28.

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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Answer:

(x-2)(x+2)

Step-by-step explanation:

use the difference of squares

x²-4 = x²-2² = (x-2)(x+2)

Answer:

$45-$2.50xx

Step-by-step explanation:

Let first of all determine the original amount on the gift card as follows

amount utilized=$2.50*16=$40

balance left after utilizing $40=$5

original amount on the gift card=amount utilized+balance left=$40+$5=$45

if xx cups of coffee is purchased ,the amount utilized would be xx*$2.50

i.e $2.50xx

The equation for the amount left would total amount on the gift card minus the $2.50xx

equation for amount remaining =$45-$2.50xx

If the questioner has duplicated x,which means he or she meant just x

equation of the amount remaining would=$45-$2.50x

The probability of rolling a 6 on a 6-sided die is 1/6.

Rolling a 6-sided die gives us six possible outcomes: 1, 2, 3, 4, 5, or 6. Since we're interested in the event of rolling a 6, there is only one favorable outcome, which is rolling a 6. The total number of outcomes is six (one for each face of the die). Therefore, the probability of rolling a 6 is calculated by dividing the number of favorable outcomes (1) by the total number of outcomes (6), resulting in 1/6.

Probability is a measure of how likely an event is to occur. In this case, we have a fair 6-sided die, which means each face has an equal chance of landing face-up. The probability of rolling a specific number, such as 6, is determined by dividing the number of ways that event can occur (1 in this case) by the total number of equally likely outcomes (6 in this case). So, in a single roll of the die, there is a 1/6 chance of rolling a 6.

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Answer:

31.5 (rounded)

Step-by-step explanation:

Answer:

5 ∛249

≈ 31.45597 (In decimal form)

Step-by-step explanation:

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

To find the divergence and curl of the vector field F(x, y, z) = x²yi - (2²-3x) 5+uy³k, we can use vector calculus operations.

The divergence of a vector field measures the rate of outward flow from an infinitesimally small region surrounding a point. It is calculated using the divergence operator (∇·F), which is the dot product of the gradient (∇) with the vector field F. In this case, the divergence of F can be found as follows:

∇·F = (∂/∂x)(x²yi) + (∂/∂y)(- (2²-3x) 5+uy³k) + (∂/∂z)(0)

      = 2xyi - 15(2²-3x) 4+uy³k

The curl of a vector field measures the rotation or circulation of the field around a point. It is calculated using the curl operator (∇×F), which is the cross product of the gradient (∇) with the vector field F. In this case, the curl of F can be found as follows:

∇×F = (∂/∂x)(0) - (∂/∂y)(x²yi) + (∂/∂z)(- (2²-3x) 5+uy³k)

      = 0 - x²yi - 15u³k

Therefore, the divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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