The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of x.

Answer:

Prime numbes

Step-by-step explanation:

Numbers whose only factors are 1 and itself are called prime numbers.

Such numbers have only two factors.

Examples are: 2, 3, 5, 7 ,9... etc.

Answer:

Prime numbers

Step-by-step explanation:

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.

Step-by-step explanation:

To solve the equation:

6(sin(x))^2 + 7cos(x) - 3 = 0

We can use the identity:

sin^2(x) + cos^2(x) = 1

Rearranging the equation, we get:

6(1-cos^2(x)) + 7cos(x) - 3 = 0

Expanding and rearranging, we get:

6cos^2(x) + 7cos(x) - 9 = 0

This is now a quadratic equation in terms of cos(x).

Using the quadratic formula, we get:

cos(x) = [-7 ± √(7^2 - 4(6)(-9))]/(2(6))

cos(x) = [-7 ± 13]/12

cos(x) = 1/2 or -3/2

Now we use the inverse cosine function to find x for each solution for cos(x).

When cos(x) = 1/2, we get:

x = π/3 + 2πk or x = 5π/3 + 2πk

When cos(x) = -3/2, we get:

there are no solutions for this case.

Therefore, the general solution to the equation is:

x = π/3 + 2πk or x = 5π/3 + 2πk where k is an integer.

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The 12th mortgage payment is 23,998.11 pesos, which is calculated based on the loan amount, 2 years of accrued interest, and the monthly mortgage payment formula.

To calculate the amount of the 12th mortgage payment, we need to break down the steps involved:

1. Calculate the loan amount after 2 years of accruing interest:

The loan amount after 2 years will be the sum of the initial loan amount and the accrued interest. Since the interest is compounded semi-annually at a rate of 15%, the formula for calculating the future value (FV) of the loan after 2 years is:

FV = PV * (1 + r/2)²ⁿ

Where PV is the present value (loan amount), r is the interest rate, and n is the number of compounding periods.

In this case:

PV = 2,000,000 pesos

r = 15% = 0.15

n = 2 years

FV = 2,000,000 * (1 + 0.15/2)²²

FV = 2,000,000 * (1 + 0.075)⁴

FV ≈ 2,479,095.31 pesos

2. Calculate the monthly mortgage payment for the first 5 years:

The monthly mortgage payment during the first 5 years is half of the payments from the 6th to the 30th year. Since the mortgage is for 30 years, there are 360 monthly payments.

The formula for calculating the monthly mortgage payment is:

PMT = PV * (r/12) / (1 - (1 + r/12)⁽⁻ⁿ⁾)

Where PMT is the monthly payment, PV is the loan amount, r is the monthly interest rate, and n is the number of months.

In this case:

PV = 2,479,095.31 pesos (calculated in step 1)

r = 12% = 0.12

n = 360 months (30 years)

PMT = 2,479,095.31 * (0.12/12) / (1 - (1 + 0.12/12)⁽⁻³⁶⁰⁾)

PMT ≈ 23,998.11 pesos

3. Calculate the amount of the 12th mortgage payment:

Since the first monthly mortgage payment is made exactly 2 years after the loan is requested, the 12th mortgage payment corresponds to the payment made in the 13th month.

Therefore, the amount of the 12th mortgage payment is approximately 23,998.11 pesos.

In conclusion, the amount of the 12th mortgage payment is approximately 23,998.11 pesos. This calculation takes into account the initial loan amount, accrued interest over 2 years, and the monthly mortgage payment formula. It is important to note that the calculations provided are based on the information and assumptions given in the question.

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Answer:many

Step-by-step explanation:manymulti- a combining form meaning “many,” “much,” “multiple,” “many times,” “more than one,” “more than two,” “composed of many like parts,” “in many respects,” used in the formation of compound words: multiply; multivitamin.

Answer:

The number next to 1 is 2.5.

It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)

Step-by-step explanation:

The value next to 1 in the table above = number of dimes we have in 1 quarter.

Let the value next to 1 be "x".

That is:

1 quarter = x dimes

If 4 quarters = 10 dimes, then,

Cross multiply to find, how many dimes, x is equal to.

Thus:

1*10 = 4*x (cross multiplication)

10/4 = 4x/4 (dividing both sides by 4)

2.5 = x

The number next to 1 is 2.5.

It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)

Answer:

Isosceles trapezoid has congruent base angles:

∠A ≅ ∠D and ∠B ≅ ∠C

Answer:

x = 16 degrees

y = 28 degrees

Step-by-step explanation:

1.) ∠A ≈ ∠D since they are base angles: so;

5x = 80

=> divide 5 on both sides:

x = 16 degrees

2.) Now Substitute 16 in for the x-value

5x ⇒ 5(16) = 80,

3.) Since we know the measure of the sum of interior angles is 360° we can say that:

(4y - 12) + 100 + 5(16) + 80 = 360

=> 4y - 12 + 100 + 80 + 80 = 360

=> 4y + 248 = 360

Subtract 248 on both sides of "="

=> 4y = 112

Divide 4 on both sides of "="

=> y = 28

Hope this helps!

The divergence is y\(e^{-y\) + \(e^{-y\) - xy\(e^{-y\).

The Divergence Theorem states that the flux of a vector field D across a closed surface S is equal to the triple integral of the divergence of D over the volume enclosed by S.

Mathematically, the Divergence Theorem can be written as:

∬S D · dS = ∭V ∇ · D dV

where S is the closed surface, D is the vector field, dS is the outward-pointing differential surface area vector, ∇ · D is the divergence of D, V is the volume enclosed by S, and dV is the differential volume element.

Now, let's evaluate both sides of the Divergence Theorem for the given vector field D = xy * \(e^{-y\) * ay + z * \((xy)^2\) * az + (-\(y^2\) + z) * x * ax, passing through the surfaces of the parallelepiped.

First, we need to find the divergence of D, ∇ · D. The divergence is given by:

∇ · D = (∂(Dx)/∂x) + (∂(Dy)/∂y) + (∂(Dz)/∂z)

Let's calculate each component separately:

∂(Dx)/∂x = ∂(xy * \(e^{-y\))/∂x = y\(e^{-y\)

∂(Dy)/∂y = ∂(xy * \(e^{-y\))/∂y = xy * (-\(e^{-y\)) + \(e^{-y\) = \(e^{-y\) * (1 - xy)

∂(Dz)/∂z = ∂(\((xy)^2\))/∂z = 0 (since there is no z dependence in this component)

Therefore, the divergence of D is:

∇ · D = y\(e^{-y\) + \(e^{-y\) * (1 - xy) + 0 = y\(e^{-y\) + \(e^{-y\) - xy\(e^{-y\)

Next, we need to evaluate the flux of D across the surfaces of the parallelepiped. Since the parallelepiped is a closed surface, we can evaluate the flux by calculating the integral of D · dS over each surface.

The parallelepiped has six faces: front, back, top, bottom, left, and right.

To evaluate the flux, we need to find the outward-pointing normal vectors and the differential surface area elements for each face.

For example, let's consider the front face. The outward-pointing normal vector is -ax (negative x-direction), and the differential surface area element is dy * dz.

The flux across the front face is given by:

∬front D · dS = ∬front (D · (-ax)) dy dz

Similarly, we can set up the integrals for the other faces and calculate the flux for each face.

Finally, we sum up the flux across all the faces to obtain the total flux.

If you provide the dimensions of the parallelepiped or any additional information, I can assist you further in evaluating both sides of the Divergence Theorem.

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Answer:

The answer is 3 11/21

Step-by-step explanation:

Answer:

              \(\underlie{\bold{\ 3\frac{11}{21}\ }}\)

Step-by-step explanation:

\(2\frac7{15}\cdot1\frac37=\frac{2\cdot15+7}{15}\cdot\frac{1\cdot7+3}{7}=\frac{37}{15}\cdot\frac{10}{7}=\frac{37}{3}\cdot\frac{2}{7}=\frac{37\cdot2}{3\cdot7}=\frac{74}{21}=\frac{3\cdot21+11}{21}=3\frac{11}{21}\)

Answer:

The area of the circle is 314 inches

Step-by-step explanation:

Area if a circle = πr²

r = radius

r= d/2

r=20 /2

r=10 inches

Area =3.14×10²

= 3.14×100

=314 inches

Answer:

314 in. cubed

Step-by-step explanation:

The formula to find the area of a circle is:

A= πr²

Pi is 3.14 so substitute that in

A= 3.14(r)²

The radius is 10 because the radius is half of the diameter.  Half of 20 is 10.  So substitute that in the radius symbol.

A= 3.14(10)²

Square 10, which is 10 times 10.  10 times 10 equals 100.

A= 3.14(100)

100 times 3.14 is 314 because 100 has two zeroes which means you move the decimal point in 3.14 two places to the right.  It gets you 314.0 which is just 314.

A= 314

The probability density function is defined as the derivative of the cumulative distribution function. It represents the relative likelihood of a continuous random variable taking on a specific value. The total area under the probability density curve is always equal to 1.

For a continuous random variable X, the probability density function f(x) satisfies the following properties:

1. Non-negativity: f(x) ≥ 0 for all x.

2. Integrates to 1: The integral of the probability density function over the entire range of X is equal to 1:

  ∫[−∞, ∞] f(x) dx = 1

This integral represents the total area under the probability density curve, which must be equal to 1.

To calculate the probability of X falling within a certain interval [a, b], we can use the probability density function as follows:

P(a ≤ X ≤ b) = ∫[a, b] f(x) dx

This integral gives the probability that X takes on a value between a and b.

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Answer:

the slope of parallel lines are - the same

i.e,m1=m2

the slope of perpendicular lines are- negative reciprocals

i.e,m1*m2= -1

where, m1 and m2 slopes of two lines

A. The slope of parallel lines are: the same/equal

B. The slope of perpendicular lines are negative reciprocals.

If two lines are parallel to each other, they will have the same slope. If the slope of one is 4, the slope of the other line that is parallel to it would also be 4.

On the other hand, the slope of perpendicular lines are negative reciprocal of each other. That is, if the slope of one is, -1, the slope of the other line would be 1.

Therefore, parallel lines have the same slope, while perpendicular lines have slope values that are negative reciprocal to each other.

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Step-by-step explanation:

I hope this answer is helpful ):

Answer:

A

Step-by-step explanation:

There is a 50% chance of this correct

This is the number 27 thousand

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Explanation:

There are three slots and 30 choices per slot. Repeats are allowed.

So there are 30*30*30 = 27,000 different locker combos.

Answer:

a1 3/2

a2 -2

b none of these are technically correct but the closest would be b4

Step-by-step explanation:

y2 - y1 / x2 - x1

7 - 1 / 4 - 0

6/4 ~ 3/2

y = 3/2x + 1

y2 - y1 / x2 - x1

-5 + 1 / 1 + 1

-4/2 ~ -2

y = -2x - 3

Hello!

Five times x increased by three times y is  5x + 3y

Answer:

t=36

Step-by-step explanation:

54-18 = 36

Answer:

t + 18 = 54

Step-by-step explanation:

t + 18 = 54

subtract 18 from both sides

t = 36

The temperature during the night was 36 degrees

Hope that helps

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

We can be 90% certain that the interval contains the population mean,, if the level of confidence is 90%. The associated z-scores are 1.645. We can be 95% certain that the interval contains the population mean, if the level of confidence is 95%.

In other words, the difference in effect estimates between the two subgroups is deemed to be statistically unimportant if the confidence intervals overlap.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.

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Answer:

#565 is the best answer I can give you

Answer:

X= -1

Step-by-step explanation:

2x+5=1(x+4)

2x+5=1x+4

2x-1x=-5+4

x=-1

True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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Answer:

y=4

Step-by-step explanation:

hello :

Y-3 (4-2Y) = 16​

y-12+6y = 16​

7y-12=16

so :7y =12+16

7y=28

y=28/7 =4

Answer: the width of the rectangle is 14 units

Let's denote the length of the rectangle to be x and the width to be y.

The first sentence tells us that the length, x , is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. x = 2y - 4.

In the question given that the perimeter of the rectangle is 76 units

Perimeter of a rectangle is 2( length + breadth )

According to the question :

76 = 2(x + y)

76 = 2(2y – 4 + y)

76 = 2(3y – 4 )

76 = 6y – 8

84 = 6y

y = 14 units

putting the value of in x = 2y – 4

x = 2(14) – 4

x = 24 units

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Answer:14

Step-by-step explanation

The answer is PROBABLY a whole number.

(2) 10^3 = 1000; 20^3 = 8000. So the number is between 10 and 20; and closer to 10.

(3) Of the possible answers 11, 12, 13, and 14, only one of them has units digit 4 when raised to the 3rd power.

Answer:

L=14m

Step-by-step explanation:

volume of a cube =L×L×L

V=L³

2744=L³

L=³√2744

L=14m

To determine the equation that best describe the data in the table, let us substitute the value of x given on the table into each equation and check for the equation that gives us the corresponding values of y;

for x = -2, y=-4; substituting x= -2 into each equation, we have;

From the first substitution, only equation a and c gave us the corresponding value of y.

Secondly, let's substitute another value of x into the two right right equaabove to confirm the best;

At x=1, y= -7; substituting x=1 into equation a and c we have;

From the above only equation c gave us the corresponding value of y at x=1.

Since only equation c gave us the corresponding values of y for both substituttions. The equation that best describe the data on the table is equation cequatio

The divergence theorem is used to compute the net outward flux of the vector field across the boundary of a region in the first octant.

The divergence theorem, also known as Gauss's theorem, relates the flux of a vector field across a closed surface to the divergence of the field within the enclosed region.

In this case, we are given a region "d" in the first octant between the planes z = xy and z = xy. To compute the net outward flux of the vector field "f" across the boundary of region "d", we can apply the divergence theorem.

The divergence theorem states that the flux across the boundary is equal to the triple integral of the divergence of the vector field over the volume enclosed by the boundary.

By evaluating this triple integral, we can determine the net outward flux.

The net outward flux represents the total flow of the vector field through the surface boundary, taking into account both the magnitude and direction of the field.

It provides valuable information about the behavior and characteristics of the vector field within the given region.

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Explanation:

The given equation y = -3x+1/2 is in slope intercept form y = mx+b

We match the terms to find that m = -3 is the slope and b = 1/2 is the y intercept.

The y intercept is where the graph crosses the vertical y axis.