state which theorem you can use to show that the quadrilateral is a parallelogram​

Using exponents rule the missing term in the equation 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____ is found to be 7^(-29).

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The given expression is - 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____

Let the missing term be x.

Then the equation is -

7^(-147) × 7^(98) = 7^(18) × 7^(-38) × x

Since, the base of the exponents is same, so apply the operations on the powers of the base.

The exponent rule is - a^(b) × a^(c) = a^(b + c)

Write the equation according to the rule -

7^(-147 + 98) = 7^(18 - 38) × x

Now perform the arithmetic operation of addition and subtraction -

7^(-147 + 98) = 7^(18 - 38) × x

7^(-49) = 7^(-20) × x

The exponent rule is - a^(b) / a^(c) = a^(b - c)

Write the equation according to the rule -

x = [7^(-49)] / [7^(-20)]

x = 7^[-49 - (-20)]

x = 7^(-49 + 20)

x = 7^(-29)

Therefore, the missing term is x = 7^(-29).

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Select the correct answer from the drop-down menu. Find the missing term. 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____

The given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.

(1) 0.4 is a rational number because it can be written as 4/10 which is a fraction with a denominator that is not zero.

(2) 0.21 is a rational number because it can be written as 21/100 which is a fraction with a denominator that is not zero.

(3) 0.14 is a rational number because it can be written as 14/100 which is a fraction with a denominator that is not zero.

(4) 0.124 is a rational number because it can be written as 124/1000 which is a fraction with a denominator that is not zero.

(5) -1.124 is a rational number because it can be written as -1124/1000 which is a fraction with a denominator that is not zero.

(6) 19.45 is a rational number because it can be written as 1945/100 which is a fraction with a denominator that is not zero.

(7) -2.35 is a rational number because it can be written as -235/100 which is a fraction with a denominator that is not zero.

In conclusion, all the given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.

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Answer:

3x (1 - 3)

Explanation in detail:

= 3x - 9x²

= 3x (1 - 3x) (1 - 3x)

The balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

Let t be the number of seconds since the balloons took off, and Hp(t) and Hg(t) be the altitude of the purple and gold balloons respectively at time t.

We know that:

Hp(t) = 0 + 2.5t (the purple balloon starts at sea level and climbs at a rate of 2.5 m/s)

Hg(t) = 1515 + 222t (the gold balloon starts 1515 m above sea level and climbs at a rate of 2*22 m/s)

We want to find the time t when the balloons are at the same altitude, so we can set Hp(t) = Hg(t) and solve for t:

0 + 2.5t = 1515 + 222t

2.5t = 1515 + 222t

2.5t - 222t = 1515

0.5t = 1515 - 1515

t = 0

So the balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

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The length of every median in an equilateral triangle whose side length is 5 is; 4.33

In geometry, a median of a triangle is defined as a line segment joining a vertex to the midpoint of the opposite side which therefore bisects that side.

This tells us that every single triangle has exactly three medians, with one from each vertex, and as a result they all intersect each other at the centroid of the triangle.

The median joins a vertex and the opposite side's midpoint. Thus;

side = 5

half side = 5/2 = 2.5

Using Pythagoras theorem;

a² + b² = c²

Thus;

2.5² + b² = 5²

b² = 18.75

b = √18.75

b ≈ 4.33

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The required function that represent the given situation is y = 10x + 350.

In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.

Rental fee is $350 for the first week and $10 for each additional day or any portion of a day.

So, The equation that represent this problem is;

Let cost y (in dollars) to rent the dumpster for x days.

y = 350 + 10x (y in dollar)

y = 10x + 350

Here, slope of function is 10 and y- intersect is 350.

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Where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.

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Elizabeth would travel a distance of [tex]11\frac{2}{5}[/tex] miles.

The distance between Elizabeth's house and Carson's house = Sum of (the distance between Elizabeth's house and the Library + the distance between the library and Millo's house + the distance between Millo's House and Carson's House). That is:

Total Miles = [tex]6\frac{1}{2}[/tex] + [tex]2\frac{2}{5}[/tex] + [tex]2\frac{1}{2}[/tex]

To calculate the total miles, we need to transform the mixed numbers into fractions. We can do that as:

[tex]6\frac{1}{2}[/tex] = [(6 × 2) + (1)]/2 = 13/2

[tex]2\frac{2}{5}[/tex] = [(2 × 5) + (2)]/5 = 12/5

[tex]2\frac{1}{2}[/tex] = [(2 × 2) + (1)]/2 = 5/2

So, the distance from Elizabeth's house to Carson's House has 57/5 miles, and it is calculated as:

13/2 + 12/5 + 5/2 = 57/5

Then, convert 57/5 into a mixed number, and we get:

57/5 = [tex]11\frac{2}{5}[/tex]

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Answer:

5:38 am

Step-by-step explanation:

Since the train arrived at it's final destination at 12:28 pm and it took two hours to get there. Subtract two hours from the final destination time and it's 10:28 am. Then it took 4 hours and 50 minutes to arrive to Wildgrove, so subtract four hours of the time when the train arrived. It is now 6:28 am. Subtract fifty minutes from that and you would get 5:38 am.

p.s. There are time calculators online if you need an answer if this is kinda hard to understand

The fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.

Divide implies to distribute anything evenly. After learning about whole number division, let's move on to fraction division. The numerator and the denominator are the two components of a fraction. Fractional division is roughly the same as fractional multiplication. When dividing fractions, we multiply the smaller of the two fractions by their reciprocals.

Given that George builds the fence at a rate of 1/3 section per 1/2 hour.

The fraction of fence that George build per hour can be obtained as:

1/3 = 1/2 hour

x = 1 hour

Using the butterfly method for multiplication we have:

x = (1/3) ÷ (1/2)

x = (1/3) × (2)

x = 2/3

Hence, the fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.

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The member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

What is Equation of a straight line ?

The equation of a straight line as follows : y = mx+c where m is slope of a straight line and c is y-intercept.

Given that the equation of the line of best fit is given by

Let x represents the amount of time in minutes.

Let y represents the temperature in degrees Fahrenheit.

From the equation of line of best fit, it is obvious that the temperature that a person can tolerate is 173 degrees Fahrenheit at 0 minutes.

Because the y - intercept represents the temperature when the x - value is zero.

So,  the member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

Therefore, The member can tolerate a temperature of 173° Fahrenheit for 0 minutes

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The calculator short hand notations are;

a) -4E3

b) -3E4

c) 3E4

d) 4E3

We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.

It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.

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She left the 1/6 yards pipes.

Now, According to the question:

Rose bought a length of 4/6 copper pipe.

She used 1/2 yard to repair a water line in her house.

To find how much pipe does she have left?

Pipes available = 4/6 yards

Pipes used = 1/2 yards

Pipes left = total pipes bought - she doesn't suit that way

Pipes left = Total pipes available - pipes used

= 4/6 yards - 1/2 Yards

= 4-3/6

= 1/6 yards

Pipes left = 1/6 yards

Hence,  She left the 1/6 yards pipes.

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The given question is incomplete, complete question is:

Rose bought a length of 4/6 copper pipe. She used 1/2 yard to repair a water line in her house. How much pipe does she have left? Solve this problem any way.

The ascending order of the given data is-

80g < 12254g < 0. 845kg <  1. 2kg.

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a. More than 3,000 people are killed yearly in crashes involving large trucks or buses.

The stopping distance of a large truck or bus is determined by calculating the kinetic energy (K) of the vehicle, the coefficient of friction (μ) between the road and the tires, and the weight (W) of the vehicle. The formula for calculating the stopping distance is K = (μ * W2) / 2g, where g is the acceleration due to gravity. This means that the heavier the vehicle and the lower the coefficient of friction, the longer the stopping distance. Since large trucks and buses are heavier than cars, they have a longer stopping distance and are more likely to be involved in fatal crashes.

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The simplify of given equation 11k/ (55k^2+ 22k) is 1/(5k+2).

Given,

[tex]\frac{11x}{55^{2}+22k }[/tex]  We have to simplify in rational expression

The common factor is 11. So, we have to pick the common factor from the equation.

= [tex]\frac{11x}{55^{2}+22k }[/tex]

= [tex]\frac{1}{5x + 2}[/tex]

Therefore the simplification of given equation is 1/(5k+2).

Reasonable expressions resemble fractions with variable denominators (and often numerators too). An example of a rational expression is x 2 x + 3 dfracx2x+3 x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction.

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In a scenario when X is replaced with (x-3) then it means that the value of x will be reduced by 3 units.

This is referred to as the process which involves the replacement of a word , number or phrase with another when performing different types of operations.

During an arithmetic operation and X is replaced with (x-3), then it means that the value of X will be reduced by 3 units and an example is given below:

Let's assume X is 5 and we substitute it with (x-3) will therefore become (5-3) = 2. This depicts that there has been a reduction by 3 units thereby making it the correct choice.

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The length of GH is about 7.3 units. The solution has been obtained by using the formula of distance between two points.

What is distance between two points?

The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation

[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]  is used to calculate the distance between two points. One can use this formula to get the separation between any two points on an x-y plane or coordinate plane.

We are given two points as G(-9,-4) and H(-2,-6)

Using the distance formula,

[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]

[tex]d=\sqrt{(-2 +9)^{2} + (-6 +4)^{2} }[/tex]

[tex]d=\sqrt{(7)^{2} + (-2)^{2} }[/tex]

[tex]d=\sqrt{49 + 4 }[/tex]

[tex]d=\sqrt{53 }[/tex]

d = 7.3 units

Hence, the length of GH is about 7.3 units.

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The speed required to obtain this decrease in travel time is 360 mph.

Formula between speed, distance, and travel time

v = d/t

The formula to calculate distance is

d = v × t

In the first condition

d₁ = v₁ × t₁

720 = v × t₁

t₁ = 720/v

In the second condition

d₂ = v₂ × t₂

720 = (v + 40) (t₁ - 0.2)

720 = (v + 40) (720/v - 0.2)

720 = v (720/v - 0.2) + 40 (720/v - 0.2)

720 = 720 - 0.2v + 28,800/v - 8

0.2v + 8 - 28,800/v + 720 - 720 = 0

0.2v + 8 - 28,800/v = 0

0.2v² + 8v - 28,800 = 0

v² + 40v - 144,000 = 0

Factorize quadratic equations

v² + 40v - 144,000 = 0

v² + 400v - 360v - 144,000 = 0

v (v + 400) - 360 (v + 400) = 0

(v + 400) (v - 360) = 0

v + 400 = 0   or   v - 360 = 0

v = - 400              v = 360 mph

(negative speed is impossible)

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The required value of side q is  117. 05 cm for the triangle ΔQRS.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle  ΔQRS, r = 83 cm, mm∠R=161° and mm∠S=5°

To find the length of the side q,

The third angle can be calculated using the angle sum property as;

angle Q + angle R + angle S = 180 degrees

angle Q + 161 degrees + 5 = 180 degrees

angle Q = 180 - (166) degrees

angle Q = 14 degrees

To find the length of q we shall apply the Sine rule.

q / Sin Q = r / Sin R

q / Sin 14 = 83 / Sin 161

Now  cross multiplication we will get;

q = (83 x Sin 14 ) / Sin 161

q = 117. 05 cm (approximately)

So,  the length of q is  117. 05 cm.

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It has a diameter of about 60,000 light-years (18,400 parsecs).

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The two processes that caused the puddle to form and then disappear were evaporation and infiltration.

Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.

Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.

The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.

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Answer: you can solve for x using the Pythagorean theorem:

Step-by-step explanation. let's say your questing in sides are 12 and 40 what is x. you have side x, y, and h. y=12 h=40. now you solve using the Pythagorean theorem x2 + y2 = h2. (The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).)

a. The length of x is 4 cm.

b. The area of the shaded face in the triangle prism is 36 cm².

The net of the triangular prism shows that the shaded face is a rectangle.

The side labelled x is the same as the side of the triangular face with a side of 4 cm, when the net of the triangular prism is folded.

Therefore:

a. Length of x = 4 cm

b. Area of shaded face = area of rectangle = length × width

= 9 × 4

= 36 cm²

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A) The system of equations that you can use to find the number of five-dollar bills and ten-dollar bills are;

x + y = 125

5x + 10y = 990  

B) The number of five-dollar bills are 52 and ten-dollar bills are 73.

The parameters are that the total number of five and ten-dollar bills equals 125 dollars.

Let x denote the number of five dollar bills and let y denote the number of ten dollars bills. Thus;

Total number of bills is;

x + y = 125      --- (1)  

The total value of all bills is $990  

Thus, we have;

5x + 10y = 990  

Divided by 5 into both sides  to get;

x + 2y = 198  ----- (2)

Now solve (1) and (2) for x and y values

Subtract eq (1) from eq (2) to get;

x + 2y - x - y = 198 - 125

y = 73

Substitute y = 73 in (1)

x + 73 = 125

x = 52

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The diagonal V2 of the square will be √2 feet.

What are squares?

A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Area of square=(side)²

Perimeter of square=4*side

Now,

as side=1 foot

By applying Pythagorean theorem,

Diagonal²=side²+side²

therefore,

V2²=1²+1²

=2

V2= √2 feet

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The value of x in the figure is 20

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Given;

Ratio of first line segment = 4.4/6.3

Ratio of other line segment= 14.08/x

Now, to find the value of x

4.4/6.3 = 14.08/x

4.4x= 14.08x6.3

x=14.08x6.3/4.4

x=20.16

Therefore, according to ratio x will be equal to 20

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Answer:

30 ft

Step-by-step explanation:

h/(40 + 8) = 5/8

h = 30

The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.

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The number of students who do not buy lunch is 624 students - 420 students = 204 students.

The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.

Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:

(255° / 360°) x 624 students = 420 students

Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.

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