The two triangles are congruent. Solve for x. Then find all missing angles.

(I found x but I don’t know how to figure out y)

Part 1: If Mary doubles the area of her original square garden, the expression that represents the area of Mary's new garden is 2x^2.

Part 2: If the side length of Mary's original garden is 9 feet, the area of Mary's new garden is 162 square feet.

Part 1: If Mary doubles the area of her original square garden, the new area of her garden will be 2 times the area of her original garden.

If the area of her original garden is x^2, then the area of her new garden will be:

2(x^2) = 2x^2

So, the expression that represents the area of Mary's new garden is 2x^2.

Part 2: If the side length of Mary's original garden is 9 feet, then the area of her original garden is:

x^2 = (9 feet)^2 = 81 square feet

To find the area of Mary's new garden, we can substitute 81 for x^2 in the expression we found in Part 1:

2x^2 = 2(81 square feet) = 162 square feet

So, the area of Mary's new garden is 162 square feet.

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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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The length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the length c by application of the trigonometric ratio of sine for the angle 50°.

sin 50° = 5/c {opposite/hypotenuse}

by cross multiplication

c = 5/sin 50°

c = 6.5270

Therefore, the length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.

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Dinner would cost $123 at either restaurant if Betty's lobster weighed 36 pounds.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In the context of this problem, the slope and the intercept are defined as follows:

Hence the functions for each restaurant are given as follows:

The costs are the same when:

y1(x) = y2(x)

51 + 2x = 15 + 3x

x = 36.

The cost is of:

y = 15 + 3 x 36

y = $123.

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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 required Venn diagram is given in the picture.

The graphic representation of the differences and affinity between the two concepts is a Venn diagram.

In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship among sets and their contents.

Note: "The set of natural numbers starts from 1, hence '0' is not included in the set of natural numbers."

Here we have

A spinner is split into eight wedges numbered 0-7

The set of numbers = 0, 1, 2, 3, 4, 5, 6 and 7  

The set of numbers that is less than 5 = {0, 1, 2, 3, 4 }

The set of numbers that are natural numbers = {0, 1, 2, 3, 4, 5, 6, 7 }

The set number that natural number and less than 5 = {1, 2, 3, 4 }  

Hence,

The required Venn diagram is given in the picture.

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[ Complet Question is given in picture ]

Answer:

I don't understand French

Step-by-step explanation:

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.

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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Answer:

y= 1/2x + 5/2

Step-by-step explanation:

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

Answer:

38 yards of ribbon

Step-by-step explanation:

23.92 +.16x = 30

30-23.92 = 6.08

.16x =6.08

6.08/.16 = x

x =38 yards

Answer:

you cannot cancel (5-5) because it is multiplied to 5 and 4 if the question was 5+(5-5)=4+(5-5) you can cancel 5-5

The reason that we can't cancel out the (5 - 5) is because it is attached to different numbers and as such they must be multiplied first with distributive property.

According to the distributive property of algebra, multiplying the sum of two or more addends by a number will give us the same result as when each addend is multiplied individually by the number and the products are added together.

This also applies to addition as well.

We are given;

5(5 - 5) = 4(5 - 5)

Now, according to the distributive property, we will have to first multiply out the bracket to get a solution. Thus, we can't cancel out the (5 - 5) because it is attached to different numbers and as such they must be multiplied first with distributive property in mind.

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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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There were 297 children and 185 adults who swam that day. Let x be the number of children and y be the number of adults who swam that day.

According to the problem, we know that:

x + y = 482 ---(1) (total number of people who swam)
1.5x + 2y = 815.5 ---(2) (total revenue generated)

To solve for x and y, we can use any method of solving a system of linear equations, such as substitution or elimination. Here's how to solve using the substitution method:

From equation (1), we can write:

x = 482 - y

Substituting this into equation (2), we get:

1.5(482 - y) + 2y = 815.5

Simplifying and solving for y, we find:

723 - 1.5y + 2y = 815.5

0.5y = 92.5

y = 185

Substituting this value of y back into equation (1), we find:

x + 185 = 482

x = 297

Therefore, there were 297 children and 185 adults who swam that day.

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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.

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:

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

Answer:

the equation: 251+D=468

the answer: 217 miles

Step-by-step explanation:

Samantha drove a total of 468 miles, and she drove 251 miles on the first day. D would represent the distance traveled on the second day. The added distance traveled on both days will equal the total amount driven.

So, our equation will be 251 + D = 468.

To solve the equation,  we can use the inverse operations method in order to isolate D(the variable) To do that, we have to subtract 251 from both sides(both sides so that the equation still has the same value).

D=468-251.

Now we can simplify the equation to:

D=217.

The answer is: 217 miles will be traveled on the second day.

A sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%

To estimate the sample size, we can use the following formula:

n = (Z^2 * p * (1-p)) / E^2

where:

n = sample size

Z = the Z-score for a given confidence level (for 97% confidence, Z = 2.33)

p = the proportion in the pilot sample (0.641)

E = the maximum allowed error of estimation (0.047)

Plugging in the values, we get:

n = (2.33^2 * 0.641 * (1 - 0.641)) / 0.047^2

n = (5.3929 * 0.359) / 0.00222009

n = 1.928 / 0.00222009

n = 869.75

Since the sample size must be a whole number, we round up to the nearest whole number.

n = 870

Therefore, a sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%

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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.

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

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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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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y=6, x=16

you create a system with the two variables and manipulate an equation so that you can substitute in the other to make it a single-variable equation. you then solve for that variable by isolating it and you can solve for the second variable afterwards. hope this helps!

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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The size of angle BCA is 45 degrees

A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.

Where the two uneven sides meet, the two angles are equal. It can be thought of as two congruent triangles sharing a base. It has two diagonals that right-angle intersect with one another.

Given:

From the Figure we can see that

AB = BC and AD = DC = AC

and, ABC = 90 degrees

Now, In triangle ABC using Angle sum Property

A + B + C = 180

So,  A + 90 + C = 180

A + C = 90

As, AB = BC

Then, 2C = 90

C = 45

Hence, the angle is 45 degrees

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The Question attached here seems to be incomplete/ inappropriate. The complete Question is:

ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle  BCA

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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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 number of ways to choose 2 toppings from a menu of 18 toppings is a classic example of a combinatorial problem.

We have a set of 18 items (toppings), and we want to know how many ways there are to choose 2 of these items. The answer is given by the binomial coefficient C(18, 2), which is the number of ways to choose 2 items from a set of 18 items, where order does not matter and repetition is not allowed.

The formula for a binomial coefficient is:

C(n, k) = n! / (k! * (n - k)!)

where n! means n factorial, which is the product of all positive integers from 1 to n. So, for example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

Using this formula, we can calculate the number of ways to choose 2 toppings from a menu of 18 toppings:

C(18, 2) = 18! / (2! * (18 - 2)!) = 18 * 17 / (2 * 1) = 153 ways

So there are 153 different ways to choose 2 toppings from a menu of 18 toppings.

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