Solve the system of linear equations. - 3x + 5y = 13 x + 4y = -10 ​

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

Learn more on age word problems here;

https://brainly.com/question/17043336

#SPJ1

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

Read more on parallel lines here: https://brainly.com/question/12783631

#SPJ1

Answer:

The point at f(-3) is at (-3,1).

Step-by-step explanation:

To find the y-value of a function at a specific point by using the graph, keep in mind that the x-axis is the axis that lies horizontally on the graph.

So, look along the horizontal line through the center until you find where x = -3. Now find the corresponding y-value to that x-value by looking above or below that point until you find where it intersects the graph. When you find that point, look to see what number the point corresponds with on the y-axis. In this case, it corresponds to y = 1.

Remember that ordered pairs are formatted as (x,y).

Hope this helps.

The length of DE is approximately 7.71 cm which finds by the use of the law of sines to solve for the length of DE.

The law of sines is a theorem in trigonometry that relates the sides and angles of any triangle. Specifically, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle. Mathematically, the law of sines can be written as:

a/sin(A) = b/sin(B) = c/sin(C)

Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function represents a different ratio of two sides of a right triangle and can be used to solve problems in geometry, physics, engineering, and other fields that involve angles and triangles. Trigonometric functions are also used to model periodic phenomena, such as sound waves and electromagnetic radiation. They are a fundamental part of mathematics and have numerous applications in science and technology.

According to the given information

We can use the law of sines to solve for the length of DE. Let's start by finding angle BAC:

angle BAC = 180 - angle ABC - angle ACB = 180 - 64 - 90 = 26 degrees

Now we can use the law of sines:

DE/sin(90) = CD/sin(26)

DE = CD * sin(26)

Substituting in the given values, we have:

DE = 16 * sin(26)

DE ≈ 7.71 cm (rounded to 3 significant figures)

Therefore, the length of DE is approximately 7.71 cm.

To know more about law of sines :

https://brainly.com/question/17289163

#SPJ1

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

For more such questions on future value

https://brainly.com/question/24703884

#SPJ8

3x+5x+12z+15z+8y+7y

8x+17z+15y

Answer:

\(3x + 8y - 12 z + 5x - 7y + 15z \\ 8x + y + 3z\)

Step-by-step explanation:

I hope this helps you

The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate \(= (1 + r/m)^m - 1\)

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate \(= (1 + 0.145/2)^2 - 1\)  

Simplifying the expression inside the parentheses:

Nominal rate \(= (1 + 0.0725)^2 - 1\)

Calculating the exponent:

Nominal rate \(= (1.0725)^2-1\)

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

For similar question on nominal rate.

https://brainly.com/question/28971185  

#SPJ8

Answer:

C. 16 days

Step-by-step explanation:

Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.

If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.

2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.

4 more workers join to complete the job, so we now do 12 work each day.

150 - 54 = 96

96 work is left to do, which would be done in 8 days by 12 workers.

8 days + 8 days = 16 days

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

adjective of colloquial is words used in conversation but not formal speeck and the adj quantity expresses an approximate amount rather than the exact number

Answer:

I think it's B but I'm not 100% sure

The number of roots the polynomial equation 2x⁴ + 5x³ -3x² - 5 have is 4

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

2x^4+5x^3-3x^2-5

Express the polynomial expression properly using proper superscripts

So, we have the following representation

2x⁴ + 5x³ -3x² - 5

The degree of a polynomial is the number of roots in it

This means that

Degree = 4

So, we can conclude that the polynomial equation 2x⁴ + 5x³ -3x² - 5 has 4 roots

Read more about polynomial at

https://brainly.com/question/17517586

#SPJ1

Answer:

2,748.5

Step-by-step explanation:

Answer:

thank uuu

Step-by-step explanation:

The cost of packaging the box of chocolates per weight unit is;  ¹/₄x²/(x + 2)

We are given the cost of packing the box as;

C(x) = ¹/₄x²

where;

x is the number of chocolates

We are told that a box can never have fewer than 3 chocolates.

Now, the weight of a box of chocolates is given by; W(x) = x + 2

Thus, cost per unit weight is;

C(x)/W(x) = ¹/₄x²/(x + 2)

Read more about Algebra Problems at; https://brainly.com/question/723406

#SPJ1

Answer:16

Step-by-step explanation:

Answer:

monday

Step-by-step explanation:

Answer:

= −21/4 x−21

Step-by-step explanation:

Answer:

f(-3) = -2

f( 1 ) = - 1

If f(x) = -2, then x = 3

If f(x) = 2, then x = -5

Step-by-step explanation:

Looking at the graph, we can easily determine the value of the given functions.

f(-3) = -2 (This function basically asks, if x = -3, what is the value of y? In the graph, it shows that the value of y is -2).

f( 1 ) = - 1  (Similarly, this function  asks, if x = 1, what is the value of y? In the graph, it shows that the value of y is -1).

If f(x) = -2, then x = ?  ←← For this particular question, you're given the value of y = -2. All you need to do is look at the graph to see what is the value of x  given that y = -2. Even though it is not clearly labeled on the graph, it shows the value of x = 3 (it is right where the end arrow is located).

Therefore, If f(x) = -2, then x = 3.

If f(x) = 2, then x = ?  ←← Similar to the previous question, you're given the value of y = 2.  In the graph, one of the given points has the coordinates of (-5, 2). This gives you the value of x = -5.

Therefore, If f(x) = 2, then x = -5.

Please mark my answers as the Brainliest if you find my explanations helpful :)

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

Learn more about amplitude click;

https://brainly.com/question/9525052

#SPJ1

a) The probability that the test comes back negative for all six people is  95.8%,

b)  The probability that the test comes back positive for at least one of the six people is 4.2%.

(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.

Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:

P(negative for all 6) = (0.993)^6 ≈ 0.958

Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.

(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.

The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.

The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:

P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042

Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.

In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.

Know more about Probability here:

https://brainly.com/question/13604758

#SPJ8

There 9% represent babies born with a birth defect, and 09-99(9%) to represents babies without birth defects.

The percentage is defined as a ratio expressed as a fraction of 100.

According to one study, 45 out of every 500 babies born in the world have a serious birth defect.

Use two-digit numbers 00-99; let 00- represent babies born with some kind of major birth defect.

p = x/n

p = 45/500

p = 0.9 = 9%

So, the simplest way to assign random numbers to conduct a simulation based on this statistic, it can use 00-99(9%) to represent babies born with a birth defect, and 09-99(9%) to represent babies without birth defects.

Hence, the correct answer would be an option (B).

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ1

The numbers arranged in the ascending order is A = 2/5 , 2/3 , 5/7 , 3/4

Given data ,

Let the numbers be represented as A

Now , the value of A is

A = { 2/3 , 3/4 , 5/7 , 2/5 }

On simplifying , we get

The value of 2/3 = 0.67

The value of 3/4 = 0.75

The value of 5/7 = 0.71

The value of 2/5 = 0.4

And , 0.4 < 0.67 < 0.71 < 0.75

Hence , the ascending order is  2/5 , 2/3 , 5/7 , 3/4

To learn more about ascending order click :

https://brainly.com/question/20681445

#SPJ1

When the population standard deviation, is unknown, a hypothesis test for the population mean is conducted the same way as if the population standard deviation were known. The t-distribution is used instead of the conventional normal distribution, which is the only distinction (z-distribution).

Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

To learn more about the surface area of a cylinder from the given link

https://brainly.com/question/27440983

#SPJ4

Answer:

X=10,503

Step-by-step explanation:

x+9=16×657

X+9=10,512

X=10,512-9

X=10,503