Shen and Linda are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.

Answer:

If a shirt is on sale for 25% off and the original price was $120, then the sale price is $90. This is because 25% of $120 is $30, and when we subtract this amount from the original price, we get $120 - $30 = $90.

In general, if an item is on sale for x% off and the original price was y dollars, then the sale price is y - (x/100) * y dollars. For example, if the discount is 25% and the original price is $120, then the sale price would be $120 - (25/100) * $120 = $90.

Step-by-step explanation:

Answer:

The sale price is $90

Step-by-step explanation:

Now,

(120 × 25) ÷ 100 = $30

Here, we get 25% of $120 is $30

So,

$120 - $30 = $90

Thus, The sale price is $90

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Answer:

25

Step-by-step explanation:

Let x be the mystery number.

The minimum number of factors a number can have is two:

(These numbers are called prime numbers).

If a number has exactly 3 factors, it must be an perfect square number since every perfect square has an odd number of factors and any number that is not a perfect square will have an even number factors..

Odd square numbers between 20 and 30:

Factors of 25:  1, 5 and 25.

Therefore, Grey's mystery number is 25.

Proof:

Answer:

To solve this equation, we can first rewrite it in a form that is easier to work with. We can do this by dividing both sides by 9^2, which gives us:

(9^2x+1)/9^2 = 27^x-3

We can then simplify the left side of the equation by taking the square root of both sides, which gives us:

3x+1/3 = 3^x-3

We can then rearrange the terms on the left side of the equation to get:

3x = 3^x-6

We can then subtract 3^x from both sides of the equation, which gives us:

3x-3^x = -6

We can then divide both sides of the equation by 3-3^x, which gives us the final solution:

x = -6 / (3-3^x)

This is the value of x that satisfies the original equation.

Step-by-step explanation:

Note that this line is in form y = mx + b, where b is the y intercept and m is the slope.

Y intercept is the value of y at x = 0

The function starts at y = 6

Slope is 1/4, meaning that for every 4 x the line travels, it goes up 1.

This is what the graph would look like:

(see image)

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The length of a rectangle is found to be 18 cm.

An enclosed 2-D shape plane called a rectangle has four sides, four corners, and four right angles (90°). It has equal and parallel opposite sides. Because a rectangle is a two-dimensional form, it has length and width as its two dimensions. The length of a rectangle is considered as its longer side; its breadth is considered as its shorter side.

The perimeter of the rectangle is given as 54 cm. Let's consider the length of the rectangle as x and the width as y.

The formula to calculate the perimeter is 2(x+y).

The length is given as 2y.

Then, the perimeter is,

[tex]\begin{aligned}\text{Perimeter}&=2(2y+y)\\&=4y+2y\\&=6y\\54&=6y\\y&=\frac{54}{6}\\&=9\end{aligned}[/tex]

Then, the length is 2y=2×9=18.

The answer is 18 cm. Therefore, the correct option is option a.

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The best and most correct answer is 2x greater then zero which satisfy the condition.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

If x ≥ 0, then we need to find x+|x|

Since {x | x < 0} and {x | x > 0} there is no number that is less than zero and greater than zero at the same time.

WE need to add here;

x+|x|  = 2x

Therefore, we can see that 2x is greater then zero which satisfy the condition.

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Answer:

Butane Gas

Step-by-step explanation:

When you add butane gas to soapy water, it reacts with a lighter/fire and will burst into flames. An example video should show up if you search for burning hand fire experiment online.

The corresponding angle to angle 4 is angle 8.

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The condition under which someone becomes more rational is when someone provided probability information.

Probability gives information about the likelihood that something will occur. For instance, weather patterns are used by meteorologists to predict the possibility of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

Everyday existence heavily relies on probability. In the analysis of political strategies, the determination of blood types, sports and gaming strategies, purchasing or selling insurance, online shopping, and online games.

Thus, having knowledge about probability makes someone more rational.

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Answer: A :)

Step-by-step explanation:

The first rider the displacement is, 17 km.

And the 2nd river the displacement is 20.22 km.

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.

Here we have two triangle with two arm know for both.

So we have to find the 3rd arm for both triangle.

Now we have for a right triangle

a^2 + b^2 = c^2

For other triangle we know the cosine law of triangle is,

a^2 + b^2 - 2ab cosθ = c^2

θ is the opposite angle of c

For the first rider the displacement is,

[tex]c = \sqrt{a^2 +b^2} = \sqrt{8^2 + 15^2} = 17 km[/tex]

For the 2nd river the displacement is

[tex]c = \sqrt{a^2 + b^2 - 2abcostheta}[/tex]   θ = 120°

[tex]c = \sqrt{a^2 - b^2 - 2ab cos(120)} \\c = \sqrt{(8^2 + 15^2 - (2*8*15cos(120))} \\c = \sqrt{289 - 240 cos(120)} \\c = \sqrt{289- (-120)} \\c = \sqrt{409}\\ c = 20.22 km[/tex]

Hence, the first rider the displacement is, 17 km.

And  the 2nd river the displacement is 20.22 km.

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The expression that is equivalent to the given expression is 4√5.

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: √80

We have to find which expressions are equivalent to the given expression.

For this, we first evaluate all options and see which option is suitable for the given expression.

160 ≠ √80

4√10 = 16 ×10 = 160 ≠ √80

4√5 = 16 × 5 = √80

8√5 = 64 × 5 ≠ √80

Hence, the expression that is equivalent to the given expression is 4√5.

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Medical institution 64 grams of bismuth-214 must be prepared.

A medical institution is a facility in which medical care is provided. It can be a hospital, clinic, nursing home, or other type of health care facility. Medical institutions provide a wide range of services including diagnosis, treatment, and preventive care. In addition to providing direct patient care, they also provide educational opportunities, research, and administrative services. Medical institutions are staffed by a variety of healthcare professionals such as doctors, nurses, allied health professionals, and administrative staff. They are responsible for providing quality care to their patients and ensuring the safety and wellbeing of their staff and visitors.

Given: 2 hours = 20 minutes

If each half life is 20 minutes, and 2 hours (120 minutes) go by,

then n = 6 ( [tex]\frac{120}{20}[/tex] )

The setup is as follows:

[tex]1g=m_{i}(\frac{1}{2}) ^{\frac{120}{20} }[/tex]

[tex]1g=m_{i}(0.015625)[/tex]

[tex]\frac{1}{0.015625} =64g[/tex]

Hence, 64 grams of bismuth-214 must be prepared if the shipping time is 2 hours.

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The required amount that Ethan have to pay is $32.

A sales discount is a marked down cost presented by a business on an item or administration. Figure out how to remember limits for solicitations. A deals rebate, likewise usually known as only a 'markdown' furnishes clients of a business with a diminished rate on at least one of the items or administrations being advertised.

We have,

Selling price = $39.99

Discount = 20%

20% of $39.99 = 20×$39.99/100

⇒ $7.99

So the payable amount for video game = $39.99 - $7.99

⇒ $32

Thus, required price is $32.

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Therefore the directional derivative of f at a in the direction of the vector ad is grad F( x, y ) ×ad(u)  =64/10

Any function's rate of change at a given location in a fixed direction is known as its directional derivative. Any derivative is thought of in this way: as a vector form. It provides information on the function's immediate rate of variation.

Here,

The terms "directional derivative" and "gradient of a function" must be used in order to respond to this question.

Grad F(x, Y) = 64/10 ad(u)

A function's gradient is a vector with the following definitions:

Grad f(x,y) is equal to f(x,y)/x I + f(x,y)/y j.

where the definition of the directional derivative in the direction of ab is

Grad f(x,y) = Uab(u), where Uab is a unitary vector pointing in the direction of ab.

Consequently, Uab (u) = Uab/|ab|

If f (x,ydirectional )'s derivative in the direction of vector ab is 5, then.

A (7, 3), B (12, 3), and vector ab is then:

ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] as well as |ab| = (5)2 (0)2 |ab| = 5

a unitary vector in the direction of ab is:

ab(u) = 5×i/ 5 and according to equation (1)

δf(x,y) / δx × i  × 5 × i / |5| = 5

δf(x,y) / δx × i  × 5 × i = 25

δf(x,y) / δx = 5       then   f( x,y ) = 5 × x  + ????

We go on to calculate the component on j of f(x,y)

Following the same procedure

ac = ( 7 , 7 ) - ( 7 , 3 )     ⇒   ac = [ 0 ,  4 ]      |ac| = √(4)² + (0)²

|ac| = 4

In the direction of ac(u), the unitary vector is:

ac/|ac| = 4 × j / 4

Then :

j / 4 + f(x,y) / y = 4

16 is equal to f(x,y) / y j + 4 j.

both f(x,y) = -4y & f(x,y) / y = - 4

f(x,y) = 5 × I + 4 × j

Finally:

((15 - 7, 9 - 3)) as the vector ad ⇒ ad = ( 8 , 6 ) ( 8 , 6 )

a unitary vector in the direction of

ad(u) = (8 ×i + 6 ×j) / √ (8)² Plus (6)

² ⇒ ad(u) = (8 ×i + 6 ×j) /√ (8)² + (6) ²

ad(u) = (8 ×i + 6 ×j) /10

Currently, we have f (x, y) = 5 I + 4 j and ad(u) = 8 I + 6 j /10.

We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)

grad F( x, y ) ×ad(u)  = ( 5 × i + 4 × j ) × ( 8 ×i  + 6 ×j ) /10

grad F( x, y ) ×ad(u)  = 4 + ( 24/10)

grad F( x, y ) ×ad(u)  =64/10

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The inverse function [tex]f^{-1}[/tex](8) = 3/2

A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) produces y, then introducing y into the inverse of f produces x. An invertible function has an inverse, which is represented by the symbol.[tex]f^{-1}[/tex]

The function given is

f(x) = 2x + 5

We have to find the inverse

Let us consider f(x) as y

y = 2x + 5

Now by replacing x to y and y to x

x = 2y + 5

By solving for y and replacing f-1(x)

2y = x - 5

y = (x - 5)/2

[tex]f^{-1}[/tex](x) = (x - 5)/2

We have to find [tex]f^{-1}[/tex](8)

[tex]f^{-1}[/tex](8) = (8 - 5)/2 = 3/2

So

The inverse function [tex]f^{-1}[/tex](8) = 3/2

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The SSS( Side-Side-Side) Congruance theorem can be used to prove that

△MLQ ≅ △NPQ.

So, The correct option is option (B).

We have given that,

The above figure shows three triangles .

Also, MQ = NQ

Q is mid point of Side LP .

or LM~= PN => LM = PN

we have to show that △MLQ ≅ △NPQ

Mid point is defined as a point which divide the side into to equal parts i.e if P is mid point of AB then AP = BP.

Using this fact , we have

LQ = QP --(1) ( because Q is mid point)

MQ = NQ (given)

LM = PN ( given)

That's we see that all three sides of triangle are

equivalents to corresponding sides of second triangle.

Therefore, these two triangles are congruent by SSS rule of congruance, i. e △MLQ ≅ △NPQ.

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Complete Question

Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN

Which congruence theorem can be used to prove △MLQ ≅ △NPQ?

a) AAS

b) SSS

c) ASA

c) SAS

the 165 different committees are possible in combination.

What is combination?

If the order of the selections is unimportant, a combination is a mathematical choice made from a collection of various elements (unlike permutations). An apple and a pear are just one of three conceivable combinations if three fruits, such as an orange, an apple, and a pear, are provided. A k-combination of a set S is, technically speaking, a subset of the k distinctive elements of S. Alternatively said, two combinations are identical if and only if they have the same members. (How each set's members are ordered is not crucial.) the number of k-combinations given a set of n elements

That would be equal to the Combinations of 11 items taken 3 at a time.

C(n , k) = n!/[k!(n - k)!]

= 11!/[3!*(11 - 3)!]

= 11!/(3!*8!)

= 11*10*9/3*2

= 15*11

=165

Hence the 165 different committees are possible in combination.

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The flux of the vector-field F = 1i + 1j + 3k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.

Flux form of Green's Theorem for the given vector-field

φ = ∫ F.n ds

= ∫∫ F. divG.dA

Here G is equivalent to the part of the plane = 2x + 1y + z = 2.

and given F = 1i + 1j + 2k

div G = div(2x + 1y + z = 2) = 2i + 4j + k

Flux = ∫(1i + 1j + 3k) (2x + 1y + z) dA

φ = ∫ (2 + 4 + 2 ) dA

= 8∫dA

A = 1/2 XY (on the given x-y plane)

2x+4y =2

at x = 0, y = 1/2

y = 0, x = 1

1/2 (1*1/2) = 1/4

Therefore flux = 8*1/4 = 2

φ = 2.

Green's theorem has numerous applications. One method is to solve two-dimensional flow integrals, which state that the sum of fluid outflows from a volume equals the total outflow summed around an enclosing area.

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Answer:

2.7x +2y

Step-by-step explanation:

Why because  u distribute the 2 to get  1.2x + 1.5x + 2y. CBL and get

2.7x +2y

The method to find the domain and range of the line graph is shown below .

In the question ,

we have to explain how we can find the domain and range of a line graph that is linear function .

we know that ,

Domain is the set of all possible input values , which produce a valid output from a particular function. It is set of all values for which the function is mathematically defined.

For Example ,

let the linear function be ⇒ f(x) = 2x + 1 ,

for the function every real number is a possible input .

thus ,  function's domain is all real numbers .

A line graph (shown below) , will extend forever in either y direction.

The range of linear function is all real numbers .

Therefore , the method to find the domain and range is explained above .

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There are 4 ways are there to color the five squares

Given that

Reds cannot be placed close to one another per the regulations, so the three reds must be placed in squares 1, 3, and 5.

We can use either yellow or blue in Square 2. There is only one color remaining for square 4 after each of those decisions.

There are 4 ways.  

Red  Yellow  Red  Blue  Red  

Red  Blue  Red  Yellow  Red  

Red  Yellow  Red  Yellow  Red  

Red  Blue  Red  Blue  Red  

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The slope percentage of the given ratio i.e. 1:12 is 83.33%.

You can determine the slope percentage by dividing the elevation change by the horizontal distance covered (sometimes called "the rise divided by the run") and multiplying the result by 100. The "run" assumes a flat surface - it doesn't account for elevation change when factoring in the actual distance traveled.

Example: let’s assume a mountaineer climbs 1,000 feet in altitude (the rise) and the horizontal distance measured on the map is 2,000 feet (the run).

thus, 1,000/2,000 = 0.5

Multiply 0.5 by 100 to derive the percent of the slope, which is 50%.

Hence, the slope percentage of 1:12 is = (1/12) x 100

                                                                  = 8.33 x 100

                                                                = 83.33 %.

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The complete question is -

What is the slope percentage of 1:12?

Answer:

84%

Step-by-step explanation:

To find the mean, you use a formula.

You add up all the numbers, then divide that by how many numbers you have:

80 + 92 + 80 + 84

336 / 4 = 84

thus 84 is the answer

After six years, the population will grow to 586,455 if compounded annually at a rate of 7.5%.

This is exactly like a compound interest problem where the interest rate is 7.5% compounded annually for 6 years.

If we use the compound interest formula A = P(1+r/n)nt where A is the end amount to be found, p = initial amount (p= 380,000), n = number of times the interest is compounded annually (n= 1) and t is the time in years (t=6)

A = 380,000(1 + .075/1)1(6)

A = 380,000(1.075)6

A = 586,454.58 people

Rounded to the nearest whole number

the population after 6 years should be

586,455 people

Hence we get the required answer.

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Your question is incomplete. Please find the missing content below.

A city has a population of 380,000 people. suppost that each year the population grows by 7.5%. what will be the population after 6 years.

Answer: 24 cm

Step-by-step explanation:

51cm is the hypotenuse, so that it will be C in the equation!

45^2 + b^2 = 51^2

2025 + b^2 = 2601

b^2 = 576

b = 24 cm

Answer:

Step-by-step explanation:

Line 1: -3y = 2x + 6 Line 2: (2/9)y - 4 = (1/3)(x - 18)