Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?

A polynomial with a degree of two is referred to as a quadratic polynomial.

When the highest power of a variable term in a polynomial expression equals 2, the term is considered a quadratic polynomial. The exponent of a polynomial is all that is considered when determining its degree. It does not account for the power of a coefficient or constant term.

When a quadratic polynomial is equated to 0, it generates a quadratic equation or a quadratic function. The solutions to a quadratic equation are known as its roots or zeros.

A quadratic polynomial is a second-degree polynomial with the highest degree term having the value 2 as its coefficient. A quadratic equation is written in its general form as ax² + bx + c = 0.

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In the circle below the  suppose m WXU=102° and mL XWV=68° then the following is m ZXUV = 88°.

Four-sided shapes with all four corners on the same circle are known as cyclic quadrilaterals. A cyclic quadrilateral's internal angles are always added up to 360 degrees.

(a) m / WXU = 102° (Given)

(b) To find m ZXUV, we can use the property that the angles in a cyclic quadrilateral add up to 360°. Since WXU, XWV, and XLV are all inscribed angles that intercept the same arc, they are congruent. Therefore, m WXU = m XWV = m XLV = 102°. Adding these angles together, we have:

102° + 102° + 68° + m ZXUV = 360°

Solving for m ZXUV, we get:

m ZXUV = 360° - (102° + 102° + 68°)

m ZXUV = 88°

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Answer:

A = 18π units²

Step-by-step explanation:

The area (A) of the semicircle is calculated as

A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then

A = [tex]\frac{1}{2}[/tex]π × 6² = [tex]\frac{1}{2}[/tex]π × 36 = 18π ← exact answer

Answer:

= 2700

Step-by-step explanation:

1300+700+700

The given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
Given expression,
an=19-7(n-1)

The above-given expression is an explicit formula for the arithmetic progression,

Comparing the given expression with general expression an = a + d[n-1]

From the above comparison, we
first term,a = 19 and
the common difference, d = -7

Thus, the given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.

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Answer:

c Calculate the product of the length and width, height and width and height and length then

multiply by 2.

Step-by-step explanation:

it will look like this 2lw+2hw+2hl

The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.

And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.

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Answer:

j = 2m-3

Step-by-step explanation:

Breakdown:

2m = Twice Michael's age

-3 = Three years younger

Answer:

a) 64.37m^2   b) 15.71 meters

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex]

Rectangle: quadrilateral, parallelogram, all angles are 90 degrees

a) The area of the park not covered by the wading pool is equivalent to the area of the wading pool subtracted from the total area:

because the radius of the pool is 2.5

Area of wading pool = [tex]\pi 2.5^2=6.25\pi m^2[/tex]

The total area of the park is length x width because it is a rectangle

Area of park = [tex]14*6=84m^2[/tex]

Area of the park not covered by the wading pool = [tex]84-6.25\pi[/tex] ≈ 64.37m^2

b) The meters of fence needed to surround the circular pool is the circumference of the circle

Circumference: [tex]2.5*2\pi=5\pi[/tex] ≈ [tex]15.71[/tex]

Answer:

x = 25

Step-by-step explanation:

First we need to show that these two triangles are similar.  Add up the angles 68 and 38 degrees in the first triangle, and then subtract this sum from 180 degrees.  This results in 74 degrees, which matches 74 degrees in the second triangle.

Next we write and solve an equation of ratios:

 6        10

----- = -------

15         x

Cross multiplying returns 6x = 150, so that x = 25.

Note that 6/15 is the ratio of the shortest sides, and 10/x is the ratio of the longest sides.

Answer: D

Step-by-step explanation:

v=4/3*3.14*13^2

Answer:

the answer is 52 because all angels are equal

Step-by-step explanation:

Math joke: Tell Algebra to stop finding his X She dont want him anymore!!!!

lol hope this helps!

Answer:

128 is your answer

Step-by-step explanation:

Triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle

180-52=128

52+128=180

Respuesta:

6200

Explicación paso a paso:

Dado que :

Cantidad total que tiene Elena:

Su dinero + cantidad dada por su madre = (7500 + 1500) = 9000

Gastos de Elena:

Admisión = 6500

Almuerzo = 4750

Recuerdos = 3950

Gastos totales = (6500 + 4750 + 3950) = 15200

Cantidad restante:

Gastos totales - Cantidad que Elena tiene

(15200 - 9000) = 6200

The time that it will take for the object to reach maximum height is given as follows:

3 seconds.

The maximum height is given as follows:

304 feet.

The object's height is modeled by a quadratic function in the following format:

h = -16t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 96, h(0) = 160.

Hence the function is defined as follows:

h(t) = -16t² + 96t + 160.

Meaning that the coefficients of the quadratic function are given as follows:

a = -16, b = 96, c = 160.

The coefficient a is negative, meaning that this is a concave down quadratic function, thus the vertex of the quadratic function represents the maximum height.

The t-coordinate of the vertex is given as follows:

t = -b/2a = -96/-32 = 3 seconds.

Then the maximum height is of:

h(3) = -16(3)² + 96(3) + 160

h(3) = 304 feet.

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Answer:

(x-5)2+(y+7)2=4    

Step-by-step explanation:

Yes, a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm is possible.

As we know if these sides form a triangle, then

the sum of two sides > the third side

Now, the sum of 10.2 cm and 5.8 cm = 16 cm > 4.5 cm

The sum of 5.8 cm and 4.5 cm = 10.3 cm > 10.2 cm

The sum of 10.2 cm and 4.5 cm = 14.7 cm > 5.8 cm

Here the sum of the two sides is greater than the third side in all three cases.

Therefore a triangle whose sides are 10.2 cm, 5.8 cm and 4.5 cm is possible.

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Answer:

(k+5)(k−1)=k2+4k−5

Step-by-step explanation

Answer:

Job 2

Step-by-step explanation:

Find how much job 1 pays for 1 hour:

(150 - 30) ÷ 8 = 15

Job 1 pays $15 per hour.

Assuming variable x stands for number of hours worked, job 2 pays $17 an hour.

Put job 1 into a similarly formatted equation:

Variable y = total pay

y = 15x + 30

Compare job 1 and 2:

Job 1: 15x + 30

Job 2: 17x + 25

Just by looking at the two expressions, there is no obvious higher paying job so let's try plugging in 8 hours for x:

15(8) + 30 = 150

17(8) + 25 = 161

$161 is more than $150 so job 2 pays more.

Step-by-step explanation: it will be c because 45 divided by 15 = 3

Answer:

one interior angle of octagon is 135 degree because the sum of interior angles of octagon is 1080 degree and when we divide it with the no of sides of octagon i.e. 8 the value of one internal angle should come 135 degree

Step-by-step explanation:

Hope this helps u!!

Answer:

x=-315

Step-by-step explanation:

I'm assuming the equation was x=(2-5)105.

If its not, please let me know. I will change my answer.

Answer:

x= -315

Step-by-step explanation:

Answer: do it the idea

Step-by-step explanation:easy

The equation is x + 0.3 = 9.124 and the value of x is 8.824.

The following is a linear equation in one variable. It can be expressed in the form of ax+b=0. Here a and b are integers and x is a variable that has only one solution. In these type of equations only one variable is present.

We can write an equation to find the score without the penalty by using the information provided. Let x be the score without the penalty. We know that the final score (with the penalty) is 9.124 and that the penalty is 0.3 points. Therefore, we can set up the equation:

x + 0.3 = 9.124

To find the score without the penalty, we need to subtract 0.3 from both sides of the equation:

x = 9.124 - 0.3

x = 8.824

So, the score without the penalty is 8.824

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Supposing a band of 20 members, we have that the probabilities are given as follows:

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

The probability that all members have different birthdays is of P(X = 0), hence:

P(X = 0) = (1 - 1/365)^20 = 0.9466.

Hence the probability that there is a birthday coincidence is of:

P(X > 0) = 1 - P(X = 0) = 1 - 0.9466 = 0.0534.

This problem is incomplete, hence we suppose a band of 20 members.

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Answer:

488 adults and 276 children

Step-by-step explanation:

So, we need two linear equations here to start, and we do have them.

Our first linear equation tells us how we get the number of forks:

2c + 5a = 2992

And the second tells us the number of people there:

c + a = 764

I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:

c = 764 - a

Then, we will substitute this into our first equation, giving us:

2(764 - a) + 5a = 2992

Then, we will open the parentheses, giving us:

1528 - 2a + 5a = 2992

Combining like terms and subtracting 1528 from both sides gives us:

3a = 1464

Dividing by 3:

a = 488

So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:

488 + c = 764

Minus 488 from both sides gives us:

c = 276

So, there were 276 children. In total, we had 488 adults and 276 children.

Hope this helped!

The answer is 90 times to expect picking an apple or banana.

If the fruit is chosen 300 times, then it would be a 1:3 ratio of apple or banana to the other fruits. This means that 100 times out of the 300 times, you would expect to pick an apple or banana.

Predicting the outcome using the experiment results because 300 times is a sizable number.

8+4 is either an apple or a banana in 40 times.

Therefore, the solution would be x in 300 times.

[tex]x = \frac{300}{40}[/tex] x12

x = 90

Therefore, the probability of picking an apple or banana is 90 times.

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Answer:

B

Step-by-step explanation:

Apply the Pythagorean Theorem to determine whether or not the given triplets represent right triangles or not:

I. 5 feet and 13 feet:  5^2 + 12^2 = 13^2 is TRUE

II.  9 ft and √63 ft:  9^2, 63, 12^2:  63 + 81 do add up to 144  TRUE

III.  2, 10, 12^2:  2 + 10 do NOT add up to 144.  FALSE

Answer B is correct

Answer:

The answer is 12V3 60°

Hope I help you