find two positive real numbers such that the sum of the first number and the second number is 48 and their product is a maximum

Answer:

We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.

Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.

So, the last digit of the first number is 3. And the answer is (A) 3

The length of each side of the regular pentagon is 10 units

Let's use the fact that the floor is a regular pentagon to set up an equation involving the side lengths.

A regular pentagon has five sides of equal length, so we can set the two expressions for the side lengths equal to each other:

2× + 4 = 4 × - 2

Solving for x, we get:

2x = 6

x = 3

Now that we have the value of x, we can substitute it back into either expression for the side length to find the length of each side. Let's use the expression (2× + 4) inches:

2× + 4 = 2(3) + 4

= 6 + 4

= 10 units

Learn more about pentagon here

brainly.com/question/24275169

#SPJ4

Step-by-step explanation:volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length

Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.

To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.

One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.

If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.

If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.

If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.

Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.

To learn more 'quadrilaterals':

https://brainly.com/question/23935806

#SPJ11

Answer:

The answer is $31.20

Step-by-step explanation:

do 20% of 26 and add it to the $26

Answer: 54 square in

Step-by-step explanation:

I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation

Answer:

Step-by-step explanation:

we have perimeter 16

for perimeter 4+4+4+4 we add together it's 16

for area we have 4 times 16

Answer:

C.

Step-by-step explanation:

x² - 36 = 0

x = 6

6² = 6 x 6 = 36

So..

36 - 36 = 0

As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.

To solve the equation [tex]x² - 36 = 0[/tex]  , we can use the difference of squares formula:

A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.

[tex]a² - b² = (a + b)(a - b)[/tex]

In this case, a² = x² and b² = 36, so we can write:

[tex]x² - 36 = (x + 6)(x - 6)[/tex]

Setting this expression equal to 0 and solving for x, we get:

[tex](x + 6)(x - 6) = 0[/tex]

[tex]x + 6 = 0 or x - 6 = 0[/tex]

[tex]x = -6 or x = 6[/tex]

Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are  [tex]x = -6[/tex] and [tex]x = 6.[/tex]

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ1

Answer:

Step-by-step explanation:

150

The associative characteristic of multiplication is what the equation  (n · p) · q = n · (p · q) represents.

A mathematical assertion that establishes the equality of two expressions is known as an equation. It usually consists of two sides, divided by an equal sign (=), with one or more terms on each side, which could be variables, constants, or both. The objective of equation solving is to identify the value(s) of the variable(s) necessary to make the equation correct. There are many mathematical methods for solving equations, including factoring, simplification, substitution, and the quadratic formula.

given

The associative characteristic of multiplication is what the equation  (n · p) · q = n · (p · q) represents.

According to this characteristic, a multiplication expression's outcome is unaffected by the way its factors are organized.

In other words, you can arrange the variables however you like and still arrive at the same conclusion.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

Learn more about Interval

brainly.com/question/4184136

#SPJ11

The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.

For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.

For the given quadrilateral we have:

2y - 16 = y - 6

2y - y = -6 + 16

y = 10

Also,

2x + 2 = y + 6

Substitute the value of y = 10:

2x + 2 = 10 + 6

2x = 16- 2

2x = 14

x = 7

Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.

Learn more about parallelogram here:

https://brainly.com/question/11220936

#SPJ1

To work out the mean cost of a present in pounds (£), we need to divide the total cost of the presents (£80.52) by the number of presents (4).

The calculation will look like this:

£80.52 ÷ 4 = £20.13

Therefore, the mean cost of a present in pounds (£) is £20.13.

Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

Answer:

x = 45.

Step-by-step explanation:

Given a straight line with the equation.

First collect like terms:

2x + x = 180 - 45

Then calculate:

3x = 135

Finally after dividing both sides by 3:

x = 45

Answer:

Step-by-step explanation:

To find the product of (7-8x)(3x^3-2x^2+x), we need to use the distributive property of multiplication over addition/subtraction.

First, let's distribute the 7 across the second factor:

(7)(3x^3) - (7)(2x^2) + (7)(x)

This simplifies to:

21x^3 - 14x^2 + 7x

Next, we need to distribute the -8x across the second factor:

(-8x)(3x^3) + (-8x)(-2x^2) + (-8x)(x)

This simplifies to:

-24x^4 + 16x^3 - 8x^2

Now, we can combine the two simplifications:

(7-8x)(3x^3-2x^2+x) = 21x^3 - 14x^2 + 7x - 24x^4 + 16x^3 - 8x^2

Finally, we can combine like terms to simplify the expression:

-24x^4 + 37x^3 - 22x^2 + 7x

Therefore, the product of (7-8x)(3x^3-2x^2+x) is -24x^4 + 37x^3 - 22x^2 + 7x.

Answer:

53 miles per hour

Step-by-step explanation:

To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:

average speed = total distance / total time

In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:

average speed = 265 miles / 5 hours

Simplifying the expression, we get:

average speed = 53 miles per hour

Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.

Answer: 53 miles per hour

Step-by-step explanation:

To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:

Average speed = distance ÷ time

Average speed = 265 miles ÷ 5 hours

Average speed = 53 miles per hour

Therefore, Jennifer's average rate of speed was 53 miles per hour.

Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

The triangle is right-angled

In a right-angled triangle, the following equality holds

[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]

[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]

Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]

(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

To learn more about sample and population refer :

https://brainly.com/question/9295991

#SPJ11

The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards

The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).

Sample space S in probability theory denotes the set of all possible outcomes of an experiment.

In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,

These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).

Learn more about Outcomes

brainly.com/question/27292589

#SPJ11

The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection

The probability of choosing a red card or a king from a deck of 52 cards is 8/52 or 2/13. To calculate this, we first need to determine the number of cards that are either red or a king. There are 26 red cards in a deck of 52 cards, so the probability of choosing a red card is 26/52 or 1/2. There are four kings in a deck of 52 cards, so the probability of choosing a king is 4/52 or 1/13.

However, we need to be careful to avoid counting the red kings (two of which exist in a deck of 52 cards) twice. To account for this, we subtract the probability of choosing a red king from the sum of the probabilities of choosing a red card and a king. The probability of choosing a red king is 2/52 or 1/26, so the probability of choosing a red card or a king is:

P(red card or king) = P(red card) + P(king) - P(red king)
P(red card or king) = 26/52 + 4/52 - 2/52
P(red card or king) = 28/52
P(red card or king) = 2/13

The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection (i.e., the probability that they occur jointly).

See more about probability at: https://brainly.com/question/24756209

#SPJ11

The given conditional statements are false, true, false, True.

They are determined by following:

(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.

Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.

The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.

If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.

To learn more about the 'conditional statement':

https://brainly.com/question/11073037

#SPJ11

Answer: 300 minuets

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

60 miles is 1 hr. all it is, is a ratio.  multiply 60 by 5 to get your answer; 350

As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.

Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.

Now, let's create another linear function using points B and C:

slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1

y-intercept (b) = y - mx = 4 - 1 * 3 = 1

Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:

2 = 1 + 1

This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.

In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.

To know more about equation here

https://brainly.com/question/10413253

#SPJ4

The crοss-sectiοn in the image  shοwn appears tο be a trapezοid.

A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is  trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.

The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.

To know more about quadrilateral visit:

brainly.com/question/14552

#SPJ1

Answer:

Step-by-step explanation:

120

Answer:

10 is the answer of q u estion

The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).

To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.

Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation  c(t) = 45 + 45(t-2)  correctly represents this situation.

To know more about derivation, click here:

https://brainly.com/question/23847661

#SPJ11

There are 169 outcomes in the complement of the given event.

To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.

Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.

Learn more about Complement

brainly.com/question/13058328

#SPJ11