Please give a step to step explanation

In similar  triangles, 15.07 miles  is the measure of the missing length h .

What does "similarity" for triangles mean?

Triangles are said to be comparable if two of their angles have measurements that are the same as those of two other triangles' angles. In proportion, and with the same measure, are the equivalent sides and angles of identical polygons.

                            To test whether two triangles are similar, use one of the three triangle similarity theorems, Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS).

    35/65 = 28/h

      h = 35 * 28/65

      h = 15.07 miles

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- 8/9 - (-2/9)

The answer I have gotten is -6/9

The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

We have,

In an equilateral triangle,

- all three sides are of equal length

- the altitude drawn from any vertex bisects the opposite side into two equal segments, forming a right triangle.

Let's denote the side length of the equilateral triangle as "s."

When an altitude is drawn, it bisects the base into two equal segments, each measuring "s/2."

The altitude forms a right triangle with the base, where one leg is the altitude (15 m) and the other leg is half of the base (s/2).

So,

Using the Pythagorean theorem, the value of "s":

s² = (s/2)² + 15²

s² = s²/4 + 225

4s² = s² + 900

3s² = 900

s² = 300

s = √300 = 10√3

Now,

Perimeter = 3 * side length

Perimeter = 3 * 10√3

Perimeter = 30√3 meters

Thus,

The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

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The coordinates of point P are (12, 12.5).

to put different elements or individuals in a coordinated effort.

To find the coordinates of point P, we can use the fact that P divides NO into two segments in the ratio of 4:3.

First, we can find the distance between points N and O using the distance formula:

d(NO) = sqrt((19-5)^2 + (9-16)^2) = sqrt(196 + 49) = sqrt(245)

Next, we can use the ratio of 4:3 to determine the distance between P and O:

d(OP) = (3/7) * d(NO) = (3/7) * sqrt(245)

Similarly, we can find the distance between P and N:

d(NP) = (4/7) * d(NO) = (4/7) * sqrt(245)

Now, we can use the midpoint formula to find the coordinates of P:

x-coordinate of P = (x-coordinate of N + x-coordinate of O) / 2 = (5 + 19) / 2 = 12

y-coordinate of P = (y-coordinate of N + y-coordinate of O) / 2 = (16 + 9) / 2 = 12.5

So the coordinates of point P are (12, 12.5).

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Answer: The simple interest will be 20%.

Step-by-step explanation:

we know the simple interest of borrowed amount is:

S.I.= (P x R x T)/100 ..... (i)

where P⇒ Principal amount

R⇒ rate of interest

T⇒ time

and

total Pays Back amount = Principal amount + S.I.

Hence S.I. = Pays Back amount - Principal amount

Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means

if Principal amount = P

then Pays Back amount = 2P ⇒ S.I.= P

Rate of Interest = R

and Time = 5 years

P= (P x R x 5)/100

R= 100/5

R = 20%

Therefore, the simple interest is 20% annually.

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The surcharge weight should be set at 12.25 lb, since 99% of all packages are at least 1.0 lb under this weight.

In this problem, we are given that the weight distribution of packages sent in a certain manner is normal, with a mean value of 12 lb and a standard deviation of 3.5 lb. The standard deviation is a measure of how much the data varies from the mean.

Now, the package service wishes to establish a weight value c, beyond which there will be a surcharge. We want to find the value of c such that 99% of all packages are at least 1.0 lb under the surcharge weight. This means that we are looking for a weight value that is exceeded by only 1% of all packages.

To find this weight value, we can use the properties of the normal distribution. We know that the area under the normal curve represents the probability of an event occurring. In this case, we want to find the weight value c that corresponds to the 1% probability.

To do this, we first need to standardize our normal distribution by converting it to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by subtracting the mean (12 lb) from our target weight value c, and then dividing by the standard deviation (3.5 lb). This gives us a z-score, which represents the number of standard deviations away from the mean our target weight value is.

Next, we can use a standard normal distribution table or calculator to find the z-score that corresponds to the 1% probability. This is approximately -2.33.

Finally, we can solve for c by reversing the standardization process. We multiply the z-score (-2.33) by the standard deviation (3.5 lb) and add the mean (12 lb) to get our target weight value c.

Therefore, c = -2.33 x 3.5 + 12 ≈ 0.25 lb.

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The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is -

10 - 1/2x < -18

Solve the inequality to get the value for x.

First collect all the like terms -

-1/2x < -18 + (-10)

Then use arithmetic operation of addition -

-1/2x < -28

Multiply (-1) to both the sides -

-1/2x × (-1) < -28 × (-1)

1/2x < 28

Then move the coefficient of variable to right hand side of the equation -

x < -1 / (2 × (-28))

Then use arithmetic operation of multiplication and division-

x < 1/56

Therefore, the inequality is 0 < x < 1/56.

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The dimension of rectangular piece of land is 17 x 12 square units in size.

The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.

The space occupied by a flat shape or an object's surface can be referred to as the area.

What is the rectangular area formula?

Rectangle area equals length x width

Let the rectangle plot's length and breadth be x and y, respectively.

Juliet has a 58-meter fence.

The rectangular piece of land's perimeter is 58 meters.

2(length + width) = 58

x + y = 58\2

⇒ x + y = 29

Moreover, the plot's total area is 204 square units.

x × y = 204

⇒ x × (29 - x) = 204

[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]

(x-12) (x-17) = 0

x = 12, x = 17

When, x= 17

y = 29 - 17 = 12m

when x = 12

y = 29 - 12 = 17m

As a result, the rectangular land parcel has dimensions of 17 x 12 square units.

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The complete question:

A carpet is laid on a rectangular floor of length 12m and breadth 8m. This leaves a margin of width 1m round the carpet. What is the area of the carpet?

Solution:

The area of the carpet laid on a rectangular floor of length 12m and breadth 8m is, 56 meter²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The area of the carpet can be calculated by subtracting the area of the margin from the total area of the rectangular floor.

The total area of the floor is:

= 12m x 8m

= 96 square meters.

The area of the margin is:

= 2 x (12m + 8m) x 1m

= 40m.

Therefore, the area of the carpet is:

= 96m² - 40m²

= 56 meter²

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A car traveling at 60 miles per hour will travel distance of 66 feet before the driver reacts to an obstacle.

To convert miles per hour to feet per second, we need to multiply by the conversion factor of 1.4667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds, 5280/3600 = 1.4667).

Therefore, a car traveling at 60 miles per hour is traveling at 88 feet per second.

Using the given reaction time of 3/4 of a second, the distance traveled before the driver reacts is:

distance = rate x time = 88 feet/second x 3/4 second = 66 feet

Hence,

A car traveling at 60 miles per hour will travel a distance of 66 feet before the driver reacts to an obstacle.

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The postal cost  is $26

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

twice the weight = 2(40) = 80 kg

volume = 50cm x 50cm x 20cm = 50,000 cm³  = 50 litres

80 + 50  = 130

distance = 200 km

one thousandth = 0.001

one thousandth of the distance = 0.001 * 200 = 0.2

Multiply 130 by 0.2 as given

130*0.2 = 26

The postal cost  is $26

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The values of x which have a mean time no greater than 120 seconds is 1

The mean (means the arithmetic mean, different from the geometric mean) of a data value is the sum of all values divided by the total number of values.

The most commonly used measure of central tendency and referred to as the “average.”

We are given that;

Time =120sec

Table

118 129 120 114 x

Now,

The mean value of the table entry;

Mean=(118+ 129+ 120+ 114+ x)/5

Mean= 481+x/5

481+x/5<120

481+x<600

x<119

Therefore, the values by the mean will not be grater than 120 will be 1

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Answer:

[tex]the \: formula \: for \: v = \frac{s}{t} [/tex]

[tex]when \: t = 2.5 \: \: s = 225 \: \: v = 90[/tex]

The consecutive even integers are 4,6 and 8.

An even number is a number that can be perfectly divided by 2. An example of an even number is 10. A consecutive even number is an even number that follows each other on the number line.

Let the first even number be represented with x

The second even number : x + 2

The third even number : x + 4

x + 2(x + 4) = 20

x + 2x + 8 = 20

3x = 20 - 8

3x = 12

x = 12 / 3

x = 4

The second even number : 4 + 2 = 6

The third even number : 4 + 4 = 8

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The domain and the range of the piecewise function for this problem are given as follows:

For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.

The range is obtained as follows:

Hence the range is given as follows:

[-2, ∞).

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Answer: 80/3 months

Step-by-step explanation:

Let x be the number of months until Zera reaches her limit.

Then on month x, her charges are 200x, and her payments are 125x.

This leaves her with 200x - 125x = 75x dollars owed.

we need to see when this equals 2000, so she hits her limit:

2000 = 75x

.: x = 2000/75 = 80/3

She can continue her pattern for 80/3 months, (≈26.666667)

The equivalent expression is (10x - 7y)²

They are defined as expressions that are composed of variables, terms, coefficients, factors and constants.

They are also made up of arithmetic operations.

It is important to note that equivalent expressions are defined as expressions having the same solution but usually differ in the mood of their arrangement.

From the information given, we have that;'

100x^2-49y^2

Find the perfect squares of the values, we have;

(10x - 7y)²

Hence, the expression is (10x - 7y)²

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The quadratic expression 100x² - 49y² is equivalent to (10x - 7y)(10x + 7y)

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Given the quadratic equation:

100x² - 49y²

Factorizing the polynomial:

100x² + 70xy - 70xy - 49y²

= 10x(10x + 7y) - 7y(10x + 7y)

= (10x - 7y)(10x + 7y)

The expression is equivalent to (10x - 7y)(10x + 7y)

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Answer:

$90

Step-by-step explanation:

180 - 50% or 180 x .50 = $90

Answer:

Your score as a percent is **92%**. Here is how I calculated it:

To convert a fraction to a percent, you need to divide the numerator by the denominator, multiply the result by 100, and add a "%" sign

In your case, the fraction is 23/25, so you need to divide 23 by 25, multiply by 100, and add a "%".

23 ÷ 25 = 0.92

0.92 × 100 = 92

92 + "%" = 92%

Therefore, your score as a percent is 92%.

Step-by-step explanation:

The points A(-4,3) ; B(-3,4) ; C(4,3) ; D(4,-3) are plotted on the graph.

What is meant by a coordinate plane?

Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line which is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.

The given points are

A is 4 units to the left and 3 units up which means  A is (-4,3).

B is 3 units to the left and 4 units up which means B is (-3,4).

C is 4 units to the right and 3 units up which means C is (4,3).

D is 4 units to the right and 3 units down which means D is (4,-3).

All these 4 points are plotted on the coordinate plane and the graph is attached below.

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the value of the variable x that makes these two solids similar is 12mm. and explained as

Let's assume that the sides x, 24 belong to one of the solids and the sides 4, 8 belong to the other similar solid. To find the value of the variable x that makes these two solids similar, we can set up a proportion using the corresponding sides:

x/24 = 4/8

We can simplify this proportion by cross-multiplying:

8x = 24 x 4

Simplifying the right-hand side of the equation, we get:

8x = 96

Dividing both sides of the equation by 8, we get:

x = 12

Therefore, the value of the variable x that makes these two solids similar is 12. We can also use this value to find the missing side of the first solid:

x/24 = 4/8

Substituting x = 12, we get:

12/24 = 4/8

Simplifying both sides of the equation, we get:

1/2 = 1/2

This confirms that the two solids are indeed similar. We can also use the ratio of corresponding sides to find the missing side of the second solid:

x/4 = 24/8

Substituting x = 12, we get:

12/4 = 24/8

Simplifying both sides of the equation, we get:

3 = 3

This confirms that the two solids are similar and that the corresponding sides are in the same ratio. Therefore, the missing side of the second solid is 3 times its corresponding side, which is 8. Therefore, the missing side is 24.

In conclusion, the value of the variable x that makes these two solids similar is 12. The missing side of the first solid is 4 and the missing side of the second solid is 24.

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The sum Given it can seen that according to the closure property of Rational numbers  the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x.

What is Closure Property of Integers ?

Closure Property of Integers states the sum or subtraction of two integers always gives an integer.

Rational number is defined as a number that can be made by dividing two integers.

Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number.

using the closure property and based on the sum given, the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x

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Answer: 1583.90

In June it’s 1583.90$

the average daily balance of Elliott's account for the month of June is $902.

calculate the average daily balance for Elliott's account in June. To calculate the average daily balance, we need to determine the balance at the end of each day in June. Starting with a balance of $1223 on June 1st, we can calculate the balance at the end of each day by adding or subtracting the amount of each transaction. The table below shows the daily balances: Day of June - Transaction type - Transaction amount -Balance

1 - Starting balance - 1223 - 1223

5 - Deposit - 615 - 1838

8 - Withdrawal - -632 - 1206

9 - Withdrawal - -120- 1086

10 - 30 - No transactions - 0 1086

The sum of the daily balances is: 01086 × 30 = 32580

The average daily balance is the sum of the daily balances divided by the number of days in June:

average daily balance = 32580 / 30 = 902

Therefore, the average daily balance of Elliott's account for the month of June is $902.

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you forgot to put the question

Answer:

40%/100×20=8

the answer is $8

When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.

To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.

If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.

Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.

In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.

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Both slope are equal so we can say that both lines are parallel

slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").

Line a: 2x + y = 10

Line b:

- 6x – 3y = 3

and line

Line a: 2x + y = 10

= slope of line A is

2x + y = 10

y = -2x+10

slope = -2

- 6x – 3y = 3

-3y = 6x +3

x = -2y -1

slope  = -2

in  this case both slope are equal so we can say that both lines are parallel

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Answer:

135 markers

Step-by-step explanation:

Let's call the number of markers in each large box "x."

After giving away 15 markers to each of 3 teachers, there were 90 markers left, so:

x - (15 * 3) = 90

Expanding the expression on the right side:

x - 45 = 90

Adding 45 to both sides:

x = 135

So, each large box originally contained 135 markers.