Need step-by-step explanation. Will mark the brainliest. Basically explained this equation as if i am a 5 year old child. (with step of course)

Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex]  => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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With her 5 3/5 gallons of paint, Latanya can paint up to 11 full bookcases.

Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is a solution to the problem. Solving an equation is locating its solution or solutions.

Let's first translate 5 3/5 gallons of paint into an incorrect fraction:

5 3/5 = (5 x 5 + 3)/5 = 28/5

Next, we can find the number of bookcases she can paint by dividing the total amount of paint by the amount needed for each bookcase:

28/5 ÷ 1/2

= 28/5 x 2/1

= 56/5

=11 1/5.

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To double, the population must increase by a factor of 2, which would take ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.

To solve for the time it took for the bacterial population to double, we need to use the exponential growth formula:

[tex]N(t) = N_0 * e^{(kt)[/tex]

where N0 is the initial population, N(t) is the population at time t, k is the growth rate, and e is the base of the natural logarithm (approximately 2.71828).

Since the population is increased sixfold in 10 hours, we can set up the equation as:

[tex]N_0 * e^{(kt)} = 6 * N_0[/tex]

Taking the natural logarithm of both sides gives:

kt = ln(6).

Dividing both sides by k and using the fact that the natural logarithm of 2 is approximately 0.693,

ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.

So it took approximately 2.817 hours for the population to double.

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On solving the provided question, we can say that Amount of commission = Total sales value x Rate of commission = 3,200

aggregate attempting to calculate the time required, total number or quantity. The quantity at hand or under consideration is incredibly energetic. the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.

[tex]Amount of commission = 3,200\\Total sales value = 80,000//[/tex]

Rate of commission = 4% on sales

Amount of commission = Total sales value x Rate of commission

Amount of commission = 80,000 x 4%

Amount of commission = 3,200

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Answer:

its b

Step-by-step explanation:

Answer:

the domain is: {−3,0,1,6}

the range is:{2,3,4,−6,4}

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Explanation:

In the relation:

{(−3,2),(0,3),(1,4),(1,−6),(6,4)}:

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is:

{−3,0,1,6}

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is:

{2,3,4,−6,4}

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

The solution of units problem is   Suzy has 5 toy trucks by using the equation 15 = 3 * Suzy's number of toy trucks

According to the given information:

If Patricia has 3 times as many toy trucks as Suzy, we can set up an equation where:

Patricia's number of toy trucks = 3 * Suzy's number of toy trucks

We know that Patricia has 15 toy trucks, so we can substitute that value into the equation:

15 = 3 * Suzy's number of toy trucks

Now we can solve for Suzy's number of toy trucks:

Suzy's number of toy trucks = 15 / 3

Suzy's number of toy trucks = 5

Therefore, Suzy has 5 toy trucks.

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Answer: equation: 3/5 * 5/8 = 38 = 0.375

Spelled result in numbers/words is three eighths/ 3/8.

Step-by-step explanation:

the basketball field takes up 3/8 of the playground

3/5 * 5/8 = 38 = 0.375 = 3/8

then (simplify) 0.375 into a fraction.

3/5 * 5/8 = 38 = 3/8

Answer:

Equation: 3/8 * 5/8

Answer:3/8

Step-by-step explanation:

Equation: 3/5 * 5/8. Since it is 5/8 of 3/5, you can do 3/5 * 5/8.

Answer: 3/8. Since 3/5 * 5/8 = 3/8, the answer will be 3/8

The values of x for each equation is given below:

To find the value(s) of x, you will need to solve each equation for x.

1. -1/2 - 4x/5 = 1/2 - 2x

Add 1/2 to both sides:

-1/2 - 4x/5 + 1/2 = 1/2 - 2x + 1/2

Combine like terms on the left side:

0 - 4x/5 = 1 - 2x

Multiply both sides by 5:

0 - 4x = 5 - 10x

Add 4x and 10x to both sides:

4x + 10x = 5

Combine like terms:

14x = 5

Divide both sides by 14:

x = 5/14

2. 2x - 3x/2 = -x + 1/3

Multiply both sides by 2:

4x - 3x = -2x + 2/3

Combine like terms:

x = 2/3

3. 5/3 - x/5 = -1

Add x/5 to both sides:

5/3 - x/5 + x/5 = -1 + x/5

Combine like terms on the left side:

5/3 = -1 + x/5

Add 1 to both sides:

5/3 + 1 = -1 + x/5 + 1

Combine like terms:

6/3 = x/5

Multiply both sides by 5:

30/3 = x

Divide both sides by 3:

10 = x

4. -2x - 4 = -1/5 + 3x/4

Add 2x to both sides:

-4 = 2x - 1/5 + 3x/4

Add 1/5 to both sides:

-4 + 1/5 = 2x + 3x/4 + 1/5

Combine like terms:

-39/5 = 5x/4

Multiply both sides by 4/5:

-39/5 * 4/5 = 5x/4 * 4/5

Combine like terms:

-39/5 = 5x/4

Multiply both sides by 4:

-39 = 20x/4

Divide both sides by 20:

-39/20 = x

5. -6x + 1 = x - 1

Add 6x to both sides:

-6x + 6x + 1 = x - 1 + 6x

Combine like terms:

0 = 7x

Divide both sides by 7:

0/7 = 7x/7

Combine like terms:

0 = x

The values of x are: 5/14, 2/3, 10, -39/20, and 0.

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Answer:

Step-by-step explanation:

$3120 and $3888

width of the road=2m

outer Rectangle, I = 40m, b = 16m

Inner Rectangle, I = 36m, b = 12m

Area of Outer rectangle = 40x16= 640m2

Area of inner Rectangle = 36x12= 432m2

Area of the road=640-432 =208m2

cost of paving bricks  $15

=208x15 = $3120. Ans

Area of inner Rectangle 432m2

cost of covering with grass  $9

= 432x9= $3888.

Answer: brick cost= 3120 grass cost =3888

Step-by-step explanation:

Calculate area of the road by subtracting the area of the inner plot (36x12) from the area of the whole plot (40x16). Multiply the individual costs by the area of their respective places.

(40x16) - (36x12) = 208

208x16 = 3120

36x12 = 432

432x9 = 3888

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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slope found by rise over run or m = (y2 - y1) / (x2 - x1)

orientation is important to not mix either values order.

( 9 - 21) / ( -1 - 5) => ( -12 ) / ( - 6 )

negatives cancel and simplify to find

m = 2

Answer:

Therefore, the simplified expression with the given values is √e^16.

Step-by-step explanation:

Given the values of the variables m = 4, n = -3, and p = -3, we can simplify the expression √e^(m + n^2 - p) as follows:

m + n^2 - p = 4 + (-3)^2 - (-3) = 4 + 9 + 3 = 16

So the expression becomes: √e^16 = √e^(m + n^2 - p) = √e^16

Therefore, the simplified expression with the given values is √e^16.

The value of x is 14

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

To find the mean, add up all the numbers and then divide by the number of numbers

(9+ 8+10+ x+14)/5 = 11

Multiply each side by 5

9+ 8+10+ x+14 = 55

Combine like terms

41 +x = 55

Subtract 41 from each side

x =14

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Answer:

5894 seconds

Step-by-step explanation:

Convert  1 hour 38 min 14 seconds to seconds​

1 hour = 3600 seconds

1 min = 60 seconds

38 mins = 60 x 38 = 2280 seconds

Now add all numbers together

3600 + 2280 + 14 = 5894 seconds

So, 1 hour 38 minutes 14 seconds is 5894 seconds.

The statements that MUST be true based on the given information are:

For Quadrilateral C, if all four sides are congruent, then opposite sides are parallel and opposite angles are congruent. This can be proven using the fact that in an isosceles trapezoid (which is a special case of Quadrilateral C), opposite angles are congruent.

For Quadrilateral L, having two pairs of parallel sides and congruent diagonals means that it is a parallelogram with congruent diagonals. This type of parallelogram is known as a rhombus, and its opposite angles are congruent. Additionally, in a rhombus, consecutive angles are not necessarily supplementary or congruent.

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Answer:

[tex]p(3and7)andq(1and9)[/tex]

The minimum number of hours life guarding that Daniel must work to meet his requirements = 12 hours

To the nearest whole number approximately:

If the digit following the decimal is less than 5, only the number preceding the decimal should remain unchanged.

Add one to the number before the decimal and eliminate the decimal part if the digit following the decimal is five or greater.

Given the information,

Babysitting pays Daniel $8 per hour, and life guarding pays him $15 per hour.

Daniel can only work a total of 18 hours per week and must make at least $200.

Daniel has been babysitting for three hours.

Daniel thus makes 3 x 8 = 24 dollars.

He has earned $200 - 24 = 176 dollars from the original $200.

Let's say Daniel was a lifeguard for m hours.

He therefore made m x 15 = 176.

15 × m = 176

m = 11.73

m ≈ 12 hours

So, the minimum number of whole hours = 12

This means, Daniel must work 12 hours lifeguarding to meet his requirements.

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a)  the number of sides = 24 sides (b) interior angle= 158.75° (c) sum of interior angles = 4080° (d) lines of symmetry = 12 (e) rotational symmetry of order  = 24.

a) To find the number of sides of a regular polygon given the value of its exterior angle, we use the formula:

360°/exterior angle = number of sides

So, for an exterior angle of 15°, we have:

360°/15° = 24 sides

b) To find the value of one interior angle, we use the formula:

interior angle = (number of sides - 2) * 180°/number of sides

So, for a polygon with 24 sides, we have:

interior angle = (24 - 2) * 180°/24

interior angle= 158.75°

c) The sum of the interior angles of a polygon with n sides is given by the formula:

sum of interior angles = (n - 2) * 180°

So, for a polygon with 24 sides, we have:

sum of interior angles = (24 - 2) * 180° = 4080°

d) To find the number of lines of symmetry of a regular polygon, we find the highest number of rotations that will produce the same figure. A regular polygon has n lines of symmetry if it can be divided into n equal parts by rotations of 360°/n.

So, for a regular polygon with 24 sides, we have:

lines of symmetry = 360°/interior angle = 360°/158.75° = 24/2 = 12

e) To find the order of rotational symmetry of a regular polygon, we find the number of rotations that will produce the same figure.

A regular polygon has rotational symmetry of order n if it can be divided into n equal parts by rotations of 360°/n.

So, for a regular polygon with 24 sides, we have:

rotational symmetry of order = 360°/exterior angle = 360°/15° = 24.

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Were using the following formula to determine a line's equation using two points: Assuming (x1, y1) & (x2, y2) represent two important points on the line, y2 - y1 Equals m(x2 - x1).

A point in mathematics is symbolized by such a dot (.) and utilized to indicate an accurate location in space. It lacks all three dimensions—length, breadth, and height. It has no size, in other terms. A point's name is often written in all caps.

A straight line is mathematically represented by the equation y=mx+b. The y-intercept, or point at which line crosses the y-axis, is denoted by the letters "b," whereas the letters "m" denote the slope of the line.

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Answer:

y= 1/2x + 5/2

Step-by-step explanation:

................

Answer:

slope (m) is 4, y-intercept (m) is -3

Step-by-step explanation:

y=4x-3

use y¹-y² over x¹-x² to find slope, then use one of the points to fill in for x and y to find y-intercept

The transformation that maps △UVW onto △U'V'W' is (d) 270 degrees counterclockwise

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

The figure

From the figure, we can see that

Triangle △UVW has the same side length as the triangle △U'V'W'

This means that

(x, y) = (x, y)

The orientations are 270 degrees apart in the counterclockwise direction

So, we have

(x, y) = (y, -x)

Hence, the transformation is (d)

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Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.

In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.

Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:

x + y = 120

The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:

4.17(120) = 501.6

We can also find the cost of the high-quality and cheaper beans in terms of x and y:

5.25x is the cost of the high-quality beans

2.00y is the cost of the cheaper beans

The total cost of the two types of beans is the sum of their individual costs:

5.25x + 2.00y

Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:

5.25x + 2.00y = 501.6

Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:

x = 120 - y (from the first equation)

5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)

Simplifying and solving for y, we get:

630 - 5.25y + 2.00y = 501.6

3.25y = 128.4

y ≈ 39.5

Now we can use this value of y to find x:

x = 120 - y

x = 120 - 39.5

x ≈ 80.5

Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.

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Answer:

angle a = 122°

Step-by-step explanation:

since the opposite angles in a parallelogram are equal, therefore,

Angle a = angle c

therefore,

14x -4 = 15x - 13

-4 +13 = 15x - 14x

x = 9

therefore angle a = 14 x 9 - 4 = 122°

Let's call the width of the rectangle "w".

According to the problem, the length of the rectangle is 12 meters more than 5 times the width, so we can write that as:

L = 5w + 12

And the area is given as 32 square meters, so we can write that as:

A = L * w = 32

Now we have two equations:

5w + 12 = L

L * w = 32

We can use the first equation to substitute the value of L in the second equation:

L = 5w + 12

32 = (5w + 12) * w = 5w^2 + 12w

Expanding the right side of the equation, we get:

32 = 5w^2 + 12w

Now we have a quadratic equation that we can solve for w. To do this, we can use the quadratic formula:

w = (-b ± √(b^2 - 4ac)) / 2a

where a = 5, b = 12, and c = -32. Plugging in these values, we get:

w = (-12 ± √(12^2 - 4 * 5 * -32)) / (2 * 5)

w = (-12 ± √(144 + 640)) / 10

w = (-12 ± √(784)) / 10

w = (-12 ± 28) / 10

w = (16 / 10) or ( -40 / 10)

w = 1.6 or -4

Since the width cannot be negative, the width must be 1.6 meters.

The expression for the number of paid vacation days for x years is

2 + 3x.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of paid vacation days = 2

Now,

She will receive an additional three days per year of paid vacation for each year she remains with the company.

This means,

For x years,

Number of paid vacation days = 2 + 3x

Now,

The expression for x years.

= 2 + 3x

Thus,

2 + 3x is the expression for the number of paid vacation days for x years.

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The complete question.

A)

Write an expression for the number of paid vacation days for x years.