Rahquez and Francesca both leave the coffee shop at the same time, but in opposite directions. If
Francesca travels 5 mph faster than Rahquez and after 3 hours they are 105 miles apart, how fast is each
traveling?

to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]

Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.

The study of relationships among triangle angles and angles is known as trigonometry. Mathematical modeling is a fundamental idea in all of geometry because it can be used to reduce any straight-sided form to a collection of triangles. Amazingly complex connections exist between trigonometry and other areas of mathematics, particularly mathematics, real or complicated, infinite series, logarithms, and infinite series.

Here,

Given : Cosx = 9/26 (First quadrant)

To find : Cos2x

We use the formula:

=>Cos2x = 2Cos²x -1

=> Cos2x  = 2(9/26)² - 1

=> Cos 2x = -0.760355

Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.

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Answer:

QS = 12

Step-by-step explanation:

Hello!

We can see that QS is the sum of QR and RS, which is equal to 6x.

We can substitute the given values to solve for x, and then use that to find QS.

The value of x is 2. We can now find QS by substituting 2 for x in 6x.

QS = 12.

Answer:

15

Step-by-step explanation:

Opposite angles in a parallelogram are equal. (this is a parallelogram because it has 2 pairs of parallel sides.)

So

3x+2=47

3x=45

x=45/3

x= 15

1. The length of the altitude is 15 units.

2. The perimeter of trapezoid ABCD is 132 units.

An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.

The perimeter of a trapezoid is the sum of all its sides.

From the question;

1. To determine AE,

DE = (DG - EF)/ 2

     = (22 - 6)/ 2          (since AB = EF = 6)

     = 8

DE = 8 units

The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;

/hyp/^2 = /opp/^2 + /adj/^2

AD^2 = DE^" + AE^2

17^2 = 8^2 + AE^2

289 = 64 + AE^2

AE^2 = 225

AE = 15

Thus the length of the altitude is 15 units.

2. To determine the perimeter of the trapezoid, we have;

AE = (AD - EF)/ 2

     = (58 - 16)/ 2           (since BC = EF = 16)

     = 21

AE = 21 units

So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;

/hyp/^2 = /opp/^2 + /adj/^2

AB^2 = BE^2 + AE^2

         = 20^2 + 21^2

AB = 841^1/2

AB = 29

Perimeter of the trapezoid = 29 + 16 + 29 + 58

                       = 132 units

Thus, the perimeter of the trapezoid is 132 units.

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Distributive property is illustrated by the statement given as 4[3+2]=4[3]+4[2]

The distributive property is defined as an expression of the form A(B + C). This property is known by distributive law and applies to subtraction also. This can be solved by a multiplication over addition operation that is written as:

A(B + C) = AB + AC

Distributive property is the sum of two numbers times a third number is equal to the sum of each add end times the third number.

Since the general rule is that:

a(b + c) = ab + ac

Then, 4[3+2]=4[3]+4[2]

Therefore, the given statement elaborates the Distributive property.

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You can sand 14.4 yd² of wood in 3.2 hours.

A ratio is used to compare two or more like quantities or numbers with the same units. It is often written with a colon, and when used in words, we say the ratio of one quantity "to" the second quantity. A rate is a ratio that compares two different quantities which have different units.

9:2

x:3.2

therefore;

x = (3.2 x 9)/2

x = 28.8/2

x = 14.4 yd² of wood

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The decimal value of the ratio for A is greater than for B. Then mixture A is redder.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Two red dye and water combinations are created by a science teacher. For every 20 mL of water in Mixture A, 3 mL of red dye is present. For every 30 mL of water in Mixture B, 4 mL of red dye is present.

The ratio of the red dye to water for A is given as,

⇒ 3 / 20

⇒ 0.15

The ratio of the red dye to water for B is given as,

⇒ 4 / 30

⇒ 0.133

The decimal value of the ratio for A is greater than for B. Then mixture A is redder.

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The exponential expression is (√4×√2)².

Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.

The given number is √8.

Now, 8=(√4×√2)²

=(2×√2)²

= 4×2

= 8

Therefore, the exponential expression is (√4×√2)².

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"Your question is incomplete, probably the complete question/missing part is:"

Rewrite the exponential expression using factors of √8 so that the base of the equation is a product of two factors, with one factor being a perfect square.

The transformation in the graph is 1 units vertically downwards.

The correct option is A: The graph of g(x) is the graph of f(x) shifted down 1 unit.

Let the function f(x) and g(x) are two real functions.

And  g (x) = f (x) + k, where k is real numbers.

Function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given:

The function f(x) = eˣ,

and the function g(x):

g(x) = f(x)-1= eˣ-1.

The graph of both the functions are given in the attached images.

For the base function f (x) and a constant k, the function given by

The transformations in the graph is defined by:

g (x) = f (x) + k, where k is real numbers.

Function can be sketched by shifting f (x), k units vertically.

The value of k determines the direction of the shift. Specifically,

if k > 0, the base graph shifts k units upward, and

if k < 0, the base graph shifts k units downward.

Here, k = -1

And the graph of g(x) is the graph of f(x) is shifted down 1 unit.

Therefore, the f(x) is shifted to 1 unit downward.

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Answer:

8.5

Step-by-step explanation:

there's a rule to get the distance between 2 points

√((1st x- 2nd x)²+(1st y- 2nd y)²)

√((-6-(-6))²+(5-(-3.5))²)

=√((-6+6))²+(5+3.5))²)

you can just type that on your calculator and you'll get the result

√((-6+6))²+(5+3.5))²)

=√((5+3.5))²)

= √((8.5))²)

the root goes away with the power (exponent)

so it equals 8.5

Answer:

Step-by-step explanation:

[tex]N^{2} =49[/tex]

To solve take the square root of 49.

[tex]\sqrt{49}[/tex] = 7

Option c which is 7

Answer:

Step-by-step explanation:

Well it would be funchen because as you see it just makes sence

Answer:

not a function

Step-by-step explanation:

In a function, an input gives only one output. As you can see from the graph, the input which is 4 produces 3 different outputs which are 2, 3 and 4, thus it cannot be a function.

Answer:

The solution is the point (-3,2)

Step-by-step explanation:

x + 2y = 1  Subtract 2y from both sides

x + 2y - 2y = 1 - 2y

x = 1 - 2y  Substitute 1 - 2y in for x in the second equation and solve for y.

5x -4y = -23

5(1 - 2y)  -4y = -23  Distribute the 5

5(1) - 5(2y) - 4y = -23

5 -10y - 4y = -23  Combine like terms

5 -14y = -23  Subtract 5 from both sides

5 -5  - 14y = -23 -5

-14y = -28  Divide both sides by -14

[tex]\frac{-14y}{-14}[/tex] =  [tex]\frac{-28}{-14}[/tex]

y = 2

Solve for y

x + 2y = 1  Substitute in 2 for y and solve for x

x + 2(2) = 1

x + 4 = 1   Subtract 4 from both sides

x + 4 - 4 = 1 - 4

x = -3

The solution is the point (-3,2)

Check:

2 + 2y = 1

-3 + 2(2) = 1

-3 + 4 = 1

1 - 1  checks

5x - 4y = -23

5(-3) - 4(2) -23

-15 - 8 = -23

-23 = -23

Answer:

Step-by-step explanation:

9.0 × 10-10 I think.....

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.

given

Table 1:  

x 0 -4 3 -2 9 3

y 5 8 7 8 5 -2

No, Table 1 is not a function.

Since there are two images of element '3'.

i.e. 3 is mapped to 7 and -2.

Table 2:

x 2 -7 5 1 -6 3

y 5 8 -6 8 5 7

Yes, this relation is a function.

Because corresponding to each x there is a single image.

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

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The coordinates of Point D are (2.5, 8).

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

Given:

Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0).

We have to find the coordinates of Point D.

Let its fourth vertex be D(a, b).

Join AC and BD. Let AC and BD intersect at point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint of AC as well as that of BD.

Using the midpoint formula,

Midpoint = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Here, ([tex](x_1, y_1) = (-3, 6.5), (x_2, y_2) = (4.5, 0)[/tex]

⇒  Midpoint of AC = [tex](\frac{-3 + 4.5}{2}, \frac{6.5 +0}{2}) = (\frac{1.5}{2}, \frac{6.5}{2}) = (0.75, 3.25)[/tex]

Now,

Midpoint of BD is = [tex](\frac{-1+a)}{2}, \frac{-1.5+b}{2})[/tex]

⇒

[tex]\frac{-1+a}{2} = 0.75, \frac{-1.5+b}{2} = 3.25 \\ -1 + a = 1.5, -1.5 + b = 6.50\\a = 2.5, b = 8[/tex]

Hence, the coordinates of Point D are (2.5, 8).

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Answer:

14 bags.

Step-by-step explanation:

20 equal slices, so 20/20.

You eat 3/10 of it. 3/10 is equivalent to 6/20.

20/20 - 6/20 is 14/20.

You need 14 bags.

An example of limit in polynomial will be the polynomial function f(x) = x³ + 2x² - 5. As x approaches 2, the value of the function approaches 11. So, the limit of f(x) as x approaches 2 is 11.

A polynomial simply means an expression which is composed of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division

In mathematical notation, we can write it as: Here, lim x->2 (x³ + 2x² - 5)

= x³ + 2x² - 5

= 2³ + 2(2²) - 5

= 8 + 8 - 5

= 11

This means that as x gets arbitrarily close to 2, the values of the function gets arbitrarily close to 11.

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The standard deviation of 83 million eggs and 2,655 millions eggs represent that of 3% of the farmers, of the production that is normally distributed, indicates that the mean egg production by Queensland farmers is about 2498.1 million eggs.

A normal distribution is a probability distribution such that the values of the distribution are symmetrical around the mean value of the distribution.

The standard deviation, σ = 83 million eggs

The percentage of farmers that produce more than 2,655 million eggs, x = 3%

The formula for the z-score is; [tex]Z = \dfrac{x - \mu}{\sigma}[/tex]

Therefore, we get;

[tex]Z = \dfrac{2655 - \mu}{83}[/tex]

From the z-score table for P(Z > Z₁), where Z₁ is the z-score corresponding to Φ(1 - 0.03) = Φ(0.97)

The z-value corresponding to Φ(0.97) is about 1.89

Therefore;

[tex]Z = \dfrac{2655 - \mu}{83} \approx 1.89[/tex]

83 × 1.89 ≈ 2655 - μ

μ ≈ 2655 - 83 × 1.89 = 2498.1

The mean egg production by Queensland farmers is about 2498.1 million eggs per year

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Answer:

perimeter = 70 yards

Step-by-step explanation:

⭐What is the area of a rectangle?

⭐What is the perimeter of a rectangle?

1. Make the equation for the area of the given rectangle and solve for x

2. Substitute x into the expressions of the length and width and solve for the perimeter

1. Define the expressions of the length and width of the rectangle

width: x

length: 4x

2. Make the equation for the area of the rectangle

[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]

3. Solve for x

[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4

[tex]49 = x^2[/tex]

[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x

∴ [tex]7 = x[/tex]

4. Substitute x into the expressions of the length and the width

width: x

width = 7

height: 4x

height = 4(7) = 28

5. Solve for the perimeter

[tex]perimeter = 2(length) + 2(width)[/tex]

[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]

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Choices that is equivalent to the expression √5. √20 is 5.2

In mathematics, the word "equivalent" designates two quantities, numbers, or meanings that are the same. A bar across an equivalent sign or Equivalent Sign shall be used to indicate the equivalence of two such quantities. Additionally, it denotes the logical equivalent of two values or a group of quantities.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

x= (5)^1/2*(20)^1/2

x= (5)^1/2*(2.2.5)^1/2

x=5.2

So B is the correct option.

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Based on the principles of kinetic theory, the speed of sound in matter is determined by the mean free paths of the molecules that make up the matter and the properties of the material itself.

Velocity is the speed at which an object moves or changes position over a period of time. It is usually measured in units such as meters/second, miles/hour, kilometers/hour. It is an important factor in the movement of objects and the movement of sound, light and other forms of energy. Speed ​​is also an important factor in transport safety, as it affects how long it takes a vehicle to stop and how far it must travel to stop safely.

Predict the ranking of sound speeds for four different materials.

Steel, 25°C air, 50°C air and water. Use the theory of motion of matter to protect your predictions.

Therefore, the speed of sound varies greatly depending on the material. Below is the ranking of the speed of sound for the four substances listed. From fastest to slowest:

1. 25°C Air: The speed of sound in warm air at 25°C is the fastest of the four substances, and because air is made up of both light and heavy molecules, it can travel quickly. The speed of sound in warm air at 25 °C is about 343 m/s.

2. 50°C air: The speed of sound in air at 50°C is slower than in air at 25°C. This is because molecules in warm air spread out more and move more slowly. The speed of sound in air at 50 °C is approximately 331 m/s.

3. Water: Water molecules are denser and move slower, so the speed of sound in water is slower than in air. The speed of sound in water is approximately 1,482 m/s.

4. Steel: The speed of sound in steel is the slowest of the four substances. This is because steel is composed of heavier molecules that move slower than those in air and water.

Overall, the order of sound velocities for the four materials is air at 25°C, air at 50°C, water, and steel. This classification is based on the principle of kinetics that the speed of sound in a material is determined by the mean free paths of the molecules that make up the material and the properties of the material itself.

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When the cross-section of a wall is 7/16 of an inch thick and the drywall is 1/4 inches thick, the thickness of the texturing on wall is A. 3/16

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, the cross-section of a wall is 7/16 of an inch thick. If the drywall is 1/4 inches thick. The thickness of the texturing on the wall is the total thickness of the wall minus the thickness of the drywall. The total thickness of the wall is 7/16 inches, and the thickness of the drywall is 1/4 inches, so the thickness of the texturing is:

= 7/16 inches - 1/4 inches

= 3/16 inches.

Therefore, the answer is A. 3/16 inches.

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The population of US is 330 million approx.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.

Given

population of new york = 2.727272% population of US

population of new york = 9 million

population of US = 1/2.727272% of new york

population of US =  36.6666 x 90,00,000

population of US = 33,00,00,087.9 = 330 million approx

Hence population of US is approx 330 million.

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On solving the provided question, we can say that - the value of the percentage = 1/10; 12/100

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

10%; 12%; 22% and 24%

1/10; 12/100; 11/50 and 6/25

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The new transformation coordinates are B""(6, 15), C""(-3, 12), and Dilate k=3 by multiplying both x and y by 3.

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

For point B,

B(1,2) → B'(1 , -2) → B"( 2, -5) → B""( 6 ,-15)

For point C,

C(-2,1) → C'( -2 , -1) → C"( -1 , -4 )→ C"" ( -3 , -12)

In order to reflect a point across the x-axis, keep the x coordinate constant while changing the y coordinate to its opposite.

<1, -3> the following translations: Add 1 to x, take 3 away from y.

Add 3 to both x and y to dilate k=3.

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The  largest amount of money they can borrow is $$276.268.65

The main formula used in this problem is the Present Value of an annuity Formula:

P = R[1-(1+i)⁻ⁿ]/i

Where;

The maximal monthly payment that Bethany and Samuel can afford is $1,500.

The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.

This implies that

R=1,500

t=30

r=%5.1 = 5.1 /100 = 0.051

m=12, because they make the payments monthly

i=r/m=0.051/12=0.00425

n=mt = 12*30=360

That is,

i) they will make 360 monthly payments,

ii) the largest amount of money they can borrow can be found using the formula:

P = R[1-(1+i)⁻ⁿ]/i

Substituting the known values:

P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425

Therefore, $276.268.65 is the largest possible principal for the situation

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