Big Money Bank has an offer for new customers: if you deposit $5,000 in a savings account, you will earn 6. 5% simple interest over the first 10 years

Part A) Solve for x because it has a coefficient of 1 in both equations.

Part B)  The solution is,

⇒ (x, y) = (57/8, 16/3)

Part C) The slope is,

⇒ m = 128/171

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ x + y = 10

⇒ 2y = x + 6

Now, We can solve the equation as,

⇒ x + y = 10

⇒ 2y - x = 6

Add both equation,

⇒ 3y = 16

⇒ y = 16/3

⇒ x + y = 10

⇒ x + 16/13 = 10

⇒ x = 10 - 16/13

⇒ x = 57/8

Hence, The solution is,

⇒ (x, y) = (57/8, 16/3)

Thus, The slope is,

⇒ m = (16/3) / (57/8)

       = 16×8 / 3×57

       = 128/171

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The slope of the perpendicular to the line of slope -10/3 is 3/10.

What is meant by the perpendicular of a line?

A straight line that forms a right angle (90 degrees) with another line is referred to as being perpendicular. Two lines are perpendicular to one another if they cross one other at a straight angle. The term "perpendicular to all points in the plane" or "perpendicular to each line it intersects" is used to describe a line that is perpendicular to the plane. Two lines will always be parallel to one another if they are perpendicular to the same line. If and only if the slope product of the two lines equals minus one, two lines are perpendicular to one another.

Given a straight line with a slope of -10/3.

We are asked to find the slope of the perpendicular to this line.

The perpendicular of a line has a slope which is reciprocal and negative to the slope of the line.

Therefore the slope of the perpendicular to the line of slope -10/3 is 3/10.

To learn more about the perpendicular, follow the link.

https://brainly.com/question/17565270

#SPJ1

Answer:

64 divided by 8 =8 is your answer

The sum formula for geometric sequence is Sn = a(1 - r^n) / (1 - r)

A unique kind of sequence is a geometric sequence. It is a sequence in which each term aside from the first term and is multiplied by a fixed number to obtain its subsequent term. To obtain the following term in the geometric sequence, one must multiply with a fixed term known as the common ratio, and one need only divide the term by the same common ratio to determine the previous term in the sequence.

There are infinite and finite geometric sequences. The formula for the same is Sn = a(1 - r^n) / (1 - r). Here Sn is the sum of the first n terms of the geometric sequence,  a is the first term of the sequence,  r is the common ratio between consecutive terms in the sequence and n is the number of terms in the sequence

Read more about geometric sequence on:

https://brainly.com/question/24643676

#SPJ4

The value of weight 74kg after converting to lbs is 163.14288 lbs

Converting between units of measurement is a common practice, especially when dealing with international systems or different industries. To convert 74kg to lbs, you need to use the conversion factor of 2.20462.

Knowing how to convert between units can help you in your day-to-day life or in your work. Here, we're using the formula 1 kilogram is equivalent to 2.20462 pounds.

To convert 74kg to lbs, you can simply multiply 74 by 2.20462.

74kg x 2.20462 = 163.14288 lbs

Therefore, weight of 74kg is equivalent to 163.14288 lbs.

To know more about weight:

brainly.com/question/30176113

#SPJ4

Let A be a symmetric matrix, which means that A is equal to its own transpose, i.e., A = Aᵀ. We want to prove that if A is invertible, then its inverse A⁻¹ is also symmetric.

To show that A⁻¹ is symmetric, we need to show that (A⁻¹)ᵀ = A⁻¹.

We know that A is invertible, so A⁻¹ exists. Taking the transpose of both sides of the equation A = Aᵀ, we get:

(Aᵀ)ᵀ = A

which simplifies to:

A = Aᵀ

Multiplying both sides of this equation by A⁻¹, we get:

A⁻¹ A = A⁻¹ Aᵀ

Using the property of transpose (i.e., (AB)ᵀ = Bᵀ Aᵀ), we can rewrite the right-hand side of the equation as:

A⁻¹ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

where I is the identity matrix.

Substituting this back into the original equation, we get:

A⁻¹ A = I

Taking the transpose of both sides of this equation, we get:

(A⁻¹ A)ᵀ = Iᵀ

which simplifies to:

Aᵀ (A⁻¹)ᵀ = I

Using the property of transpose again, we can rewrite the left-hand side of the equation as:

(A⁻¹)ᵀ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

Substituting this back into the equation, we get:

(A⁻¹)ᵀ Aᵀ = I

which can be rearranged as:

(A⁻¹)ᵀ = (Aᵀ)⁻¹

Since we know that A = Aᵀ, we can substitute this into the equation to get:

(A⁻¹)ᵀ = A⁻¹

which shows that A⁻¹ is symmetric. Therefore, if a symmetric matrix is invertible, then its inverse is symmetric also.

Learn more about symmetric matrix here: brainly.com/question/30711997

#SPJ4

Solving an equation, the number of textbooks sold by the textbook store, which sold a combined total of 236 in a week is as follows:

An equation is a mathematical statement that two or more algebraic expressions are equal or equivalent.

Equations are differentiated from mathematical expressions by the use of the equal sign (=).

The total number of math and physics textbooks sold in a week = 236

Let the number of physics textbooks sold = x

Let the number of math textbooks sold = x + 52

2x + 52 = 236

2x = 236 - 52

2x = 184

x =92

The number of textbooks sold for the week:

Physics textbooks sold = 92

Math textbooks sold = 144 (92 + 52)

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

Answer:

35 degrees

Step-by-step explanation:

The direction "North" is parallel to itself, because of the reflexive property of parallel lines. Using the alternate interior angles theorem, the measure of x + 25 must be equal to 60 degrees. 60 - 25 = 35

Answer:

x = 35°

Step-by-step explanation:

The angle made by the directional line from wharf to Shell Cove relative to North is 60° at the point of departure from the wharf

The angle that this same line makes at the point of arrival at Shell Cove must be 60° relative to North since the two North directions are perpendicular and the line connecting the wharf and shell cove is a transversal intersecting these lines

This is because of the property that when two parallel lines are intersected by a transversal, the alternate interior angles must be the same

The angle made by this transversal at Shell Cove = x + 25 degrees

Since (x + 25)° = 60°

x = 60° - 25°

x = 35°

From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.

To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.

The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.

The prime factorization of 2 is 2, and the prime factorization of 3 is 3.

The common factors are 3, so the LCM of 9 and 3 is 9.

Therefore, the common denominator of 7/9 and 2/3 is 9.

To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.

The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.

The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.

Learn more about prime factorization here: brainly.com/question/1081523

#SPJ4

Answer:

4x=>-74

Step-by-step explanation:

x+23=>18

4(x+23)=>18

4x+92=>18

collect like terms

4x=>18-92

4x=>-74

Answer is 4 (x + 23 ) ≥ 18

Step by step

4 times the sum of a number and 23

4(x + 23)

Is at least 18

≥ 18

Your inequality

4 (x + 23 ) ≥ 18

to solve, distribute

4x + 92 ≥ 18

subtract 92 from both sides

4x + 92 - 92 ≥ 18 - 92

simplify

4x ≥ -74

divide both sides by 4 to solve for x

4/4 x ≥ -74/4

x ≥ 18.5

18.5 is equal to or greater than 18 so problem solved

** We used ≥ in this inequality which means at least (equal to) this number or greater

The addition of the polynomials 2x² + 6x + 5  and   3x² - 2x - 1 will be 5x²  +   4x   +   4.

Sums of terms of the form k × x^n, where k is any number and n is a positive integer, make up polynomials.

A polynomial is a mathematical equation made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division.

Start with: 2x² + 6x + 5   +   3x² − 2x − 1

Place like terms together: 2x² +3x² +   6x−2x + 5−1

Which is: (2+3)x²  +   (6−2)x  +  L(5−1)

Add the like terms: 5x²  +   4x   +   4

Learn more about polynomial on:

https://brainly.com/question/4142886

#SPJ1

add the polynomials 2x² + 6x + 5   and   3x² - 2x - 1

The prime factorization of 105 is 3 × 5 × 7. We can also write this as 3 × [tex]5^1[/tex] × [tex]7^1[/tex], where the exponents indicate the number of times each prime factor appears in the factorization.

To find the prime factorization of 105, we can use the following steps:

Find a factor of 105. One way to do this is to try dividing 105 by prime numbers (2, 3, 5, 7, 11, ...) until we find a factor. We can also notice that 105 is divisible by 3 since the sum of its digits (1 + 0 + 5) is a multiple of 3.

Divide 105 by the factor we found in step 1 to get a smaller number.

Repeat steps 1 and 2 with the smaller number until we get a prime number.

Using this method, we can find the prime factorization of 105 as follows:

105 ÷ 3 = 35

35 ÷ 5 = 7

Since 7 is a prime number.

Learn more about prime factors at

https://brainly.com/question/29775157

#SPJ4

The distribution is roughly symmetric and unimodal, and the median and IQR best represent the data set.

If you plot a histogram of the data;

the distribution appears to be roughly symmetric and unimodal.

We can also calculate some summary statistics to better understand the center and spread of the data:

The range is a simple measure of spread, but it can be heavily influenced by outliers.

The IQR is a more robust measure of spread that is less affected by outliers.

Finally, the standard deviation is a commonly used measure of spread that takes into account how far each data point is from the mean.

Read more about set of data here:

https://brainly.com/question/19243813

#SPJ1

Step-by-step explanation:

They can be found by considering where the second derivative changes signs. In similar to critical points in the first derivative, inflection points will occur when the second derivative is either zero or undefined.

make me brainlist

Answer:

The answer to your question is, 2 meters.

Step-by-step explanation:

We know that a median is the middle number in a sorted, ascending or descending list of numbers.

How to caluclate it:

Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2

Rearreange the date in accending order:

1/3, 1/2, 2/3, 1, 2, 3, 4, 4, 6

Next we should always pick the middle of the number in the arranged data..:

Media would = 2 meters

Thus, your answer is, 2 meters

The probability of finding oil (to 1 decimal) is 0.7.

Probability is a statistic that is used to show the possibility or chance that a certain event will occur. Probabilities can be expressed as fractions from 0 to 1, in contrast to percentages from 0% to 100%. The four main types of probability that mathematicians study are axiomatic, classic, empirical, and subjective. Given that the terms potential and probability are interchangeable, you could define probability as the probability that a particular event will take place.

To determine probability the  Preliminary geologic  , we obtain,

P(oil)=0.3+0.4

P(oil)=0.7.

To know more about probabilities visit:

https://brainly.com/question/30034780

#SPJ1

The function that satisfies the differential equation y′ = -2 with initial condition y(0) = -8 is y = -2x - 8.

To solve the differential equation y′ = -2 with initial condition y(0) = -8, we need to find the function y(x) that satisfies both the differential equation and the initial condition.

We can start by integrating both sides of the differential equation with respect to x:

∫y′ dx = ∫(-2) dx

y = -2x + C

where C is a constant of integration.

To find the value of C, we can use the initial condition y(0) = -8:

y(0) = -2(0) + C = C = -8

So the solution to the differential equation with initial condition is:

y = -2x - 8

Therefore, the function that satisfies the differential equation y′ = -2 with initial condition y(0) = -8 is y = -2x - 8.

For such more question on equation:

https://brainly.com/question/29283461

#SPJ4

The equation of the line that's vertical to the given line and passes through the point(,6) is y = (-2/3) x28/3.

To find the equation of a line vertical to a given line, we need to use the fact that the pitches of two vertical lines are negative reciprocals of each other.

Let's start by chancing the pitch of the given line. The equation of a line in pitch- intercept form is y = mx b, where m is the pitch and b is the y- intercept. We can rewrite the given line 3x- 2y = 5 in pitch- intercept form by working for y

3x- 2y = 5

- 2y = -3 x 5

y = (3/2) x-5/2

So the pitch of the given line is3/2.

The pitch of a line vertical to this line is the negative complementary of3/2, which is-2/ 3.

Now we can use the point- pitch form of the equation of a line to find the equation of the line that passes through the point(,6) and has pitch-2/ 3. The point- pitch form is

y- y1 = m( x- x1)

where( x1, y1) is the point the line passes through and m is the pitch.

Substituting in the values we know, we get

y- 6 = (-2/3)( x- 5)

Expanding the right side, we get

y- 6 = (-2/3) x10/3

Adding 6 to both sides, we get

y = (-2/3) x28/3

So the equation of the line that's vertical to the given line and passes through the point(,6) is y = (-2/3) x28/3.

To further about vertical :

https//brainly.com/question/29268451

#SPJ1

Answer:

$14,498.1

Step-by-step explanation:

To find the amount Rob will have in 5 years with compound interest, we can use the formula:

A = P (1 + r/n)^(nt)

where:

A = the future value of the investment

P = the principal amount invested

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $7,869 (the principal amount)

r = 13% or 0.13 (the annual interest rate)

n = 1 (the interest is compounded annually)

t = 5 (the number of years)

Substituting these values into the formula, we get:

A = $7,869 (1 + 0.13/1)^(1*5)

A = $7,869 (1.13)^5

A = $14,964.92

Therefore, to the nearest cent, Rob will have $14,964.92 in 5 years.

Option A. In observational studies, the variable of interest can be either numerical or categorical, so it does not have to be numerical.

Observational studies are a type of study in which researchers observe and record data on variables of interest without manipulating them directly. These studies are often used in fields such as epidemiology, social sciences, and psychology to investigate relationships between variables and identify potential risk factors for diseases or other outcomes.

The variable of interest in an observational study can be either numerical or categorical. Numerical variables are those that can be measured and expressed as a numerical value, such as age, height, weight, or blood pressure. Categorical variables are those that are qualitative or nominal in nature, such as gender, race, or smoking status.

To learn more about observational studies please click on below link.

https://brainly.com/question/17593565

#SPJ4

In observational studies, the variable of interest ____

A. cannot be numerical.

B. must be numerical.

C. is controlled.

D is not controlled.

The choice that represents the quotient of the radicals is given as follows:

D. [tex]x\sqrt{2}[/tex]

The quotient of the radicals for this problem is defined as follows:

[tex]\frac{\sqrt{18x^3}}{\sqrt{9x}}[/tex]

As both the numerator and the denominator have the same root(square root), we can apply the quotient and then take the square root, thus:

[tex]\sqrt{\frac{18x^3}{9x}}[/tex]

Then we can simplify the expression inside the square root as follows:

Hence the square root is taken as follows:

[tex]\sqrt{2x^2} = x\sqrt{2}[/tex]

Meaning that option D is the correct option.

More can be learned about quotient of radicals at https://brainly.com/question/30305238

#SPJ1

Using the theorem of angle around a point, the value of GHJ is 237 degrees

When we talk about the "angle around a point," we are usually referring to the total angle formed by two or more lines or line segments that intersect at a common point, known as the vertex.

Specifically, the "angle around a point" is equal to 360 degrees or 2π radians. This is because, when two or more lines intersect at a point, they form multiple angles, and the sum of these angles is always equal to 360 degrees or 2π radians.

Since we know that FPJ and JPI are congruent, this implies that they're equal to one another. We can find the value by setting them as x

x + x + 51 + 66 + 99 = 360

Reason: The sum of angles around a point is equal to 360 degrees

2x + 216 = 360

2x = 360 - 216

2x = 144

x = 72

The value of FPJ and JPI is 72.

The value of GHJ is is equal to 66 + 99 + 72 = 237°

Learn more on angle around a point here;

https://brainly.com/question/24375372

#SPJ1

a. To find the angle QCP, we can start by finding the coordinates of the points P, Q, and C. Since P and Q are midpoints of the edges FG and GH, respectively, we can find their coordinates as follows:

P = (0, y, z) where y = (3+4)/2 = 3.5 and z = (0+4)/2 = 2

Q = (x, y, 0) where x = (3+4)/2 = 3.5 and y and z are the same as before.

Since C is the center of the cube, we can find its coordinates as:

C = (2, 2, 2)

Now we can use the dot product formula to find the angle QCP:

cos(QCP) = (PC · QC) / (|PC| · |QC|)

where PC and QC are the vectors from P to C and from Q to C, respectively.

PC = C - P = (2, 2 - 3.5, 2 - 2) = (2, -1.5, 0)

QC = C - Q = (2 - 3.5, 2 - 3.5, 0) = (-1.5, -1.5, 0)

|PC| = sqrt(2² + (-1.5)² + 0²) = sqrt(5.25)

|QC| = sqrt((-1.5)² + (-1.5)² + 0²) = sqrt(4.5)

PC · QC = 2(-1.5) + (-1.5)(-1.5) + 0 = -3 + 2.25 = -0.75

cos(QCP) = (-0.75) / (sqrt(5.25) * sqrt(4.5)) = -0.166666...

Therefore, the angle QCP is cos⁻¹(-0.166666...) ≈ 100.53° (rounded to two decimal places).

b. To find the total surface area of the solid remaining after pyramid PGQC is removed, we need to find the area of the four triangular faces and the square base of the pyramid and subtract them from the total surface area of the cube.

The square base of the pyramid has side length PQ = sqrt((3.5 - 3)² + (3.5 - 4)² + 2²) = sqrt(2.5) and area PQ² = 2.5 cm².

Each of the triangular faces has base PQ and height equal to the distance from P or Q to the plane containing the opposite vertex and the center of the cube. This distance is equal to the length of the perpendicular from the vertex to the opposite face, which is half the length of the diagonal of the cube.

The diagonal of the cube is sqrt(3² + 4² + 4²) = sqrt(41), so the height of each triangular face is sqrt(41)/2.

Therefore, the area of each triangular face is (1/2)PQ(sqrt(41)/2) = (sqrt(41)/4) cm².

The total surface area of the cube is 6s², where s is the length of a side of the cube. Since the volume of the cube is 1728 cm³, we have s³ = 1728, or s = 12 cm.

Therefore, the total surface area of the cube is 6(12²) = 864 cm².

The total surface area of the solid remaining after the pyramid is removed is:

864 - 4(sqrt

When comparing two numbers, there are a few different things you might be interested in: which is larger, which is smaller, or whether they are equal.

In this case, we can see that both numbers are negative, which means they are to the left of zero on the number line. In general, the further left a number is on the number line, the smaller it is. Therefore, we can say that:

-2.25 > -3

In other words, -2.25 is larger (closer to zero) than -3.

The solution to the system of inequalities is (80, 50).

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given:

To raise money for the show,

the drama club is selling tickets.

Let x be the number of student tickets sold and y represents the number of adult tickets sold.

According to the question,

x + y ≤ 130

5x + 10y ≥ 900.

We have drawn a graph of the system of inequalities.

And the graph is given in the attached image.

Therefore, the solution is (80, 50).

To learn more about the systems of inequalities;

https://brainly.com/question/19526736

#SPJ9

Answer:

ED = 57 , AB = 19

Step-by-step explanation:

the midsegment FC is half the sum of the parallel bases , that is

[tex]\frac{AB+ED}{2}[/tex] = FC

[tex]\frac{4x+3+18x-15}{2}[/tex] = 38 ( multiply both sides by 2 )

22x - 12 = 76 ( add 12 to both sides )

22x = 88 ( divide both side by 22 )

x = 4

then

ED = 18x - 15 = 18(4) - 15 = 72 - 15 = 57

AB = 4x + 3 = 4(4) + 3 = 16 + 3 = 19

Answer:

Below

Step-by-step explanation:

Radians =  degrees * pi /180

Radians * 180/pi   =  degrees

Answer:

0 triangles can be formed

Step-by-step explanation:

In order to determine the number of distinct triangles that can be formed with the given information, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's start by drawing a rough sketch of the triangle:

     Z

     |\

     | \

     |   \ x

     |     \

     |       \

     X-----Y

      y=2

We know that mZX = 51°, so we can label that angle on our diagram:

     Z

     |\

     | \

     |   \ x

     |     \

     |51°  \

     X-----Y

      y=2

We can use the sine law to find the length of side XY:

sin(51°) = XY / 5

XY = 5 * sin(51°)

XY ≈ 3.95

Now we need to check whether XY is less than the sum of the other two sides, XZ and YZ:

XZ + YZ > XY

2 + √(x² - XY²) > XY

2 + √(5² - 3.95²) > 3.95

2.86 > 3.95 (false)

Since XY is greater than the sum of the other two sides, it is not possible to form a triangle with the given measurements. Therefore, the number of distinct triangles that can be formed is 0.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

The perimeter of the square is 12 units.

Let's call the side length of the square "s". We can use the Pythagorean theorem to relate the side length of the square to its diagonal:

s² + s² = (3√2)²

2s² = 18

s² = 9

s = √9 = 3

So the side length of the square is 3. Since all sides of a square are equal, the perimeter of the square is 4 times the side length:

Perimeter = 4s = 4(3) = 12

Therefore, the perimeter of the square is 12 units.

To Learn More About perimeter click

https://brainly.com/question/6465134

#SPJ4

Answer: the third and 5th option but I'm not sure if its right