What is the solution to the following system of equations?
infinite solutions no solution (0, 1) (4, –1)

Answer:

She ran 5 miles

Step-by-step explanation:

To solve this, we can easily use proportion.

The question state that there are 5,280 feet in a mile, We are ask to find the number of miles Rily run, if she ran 26,400 feet.

Using proportion;

Let x = the number of miles Rily  can run

5,280 feet     = 1 mile

26,400 feet    = x

Cross-multiply

5280x = 26,400

To get the value of x, we will divide both-side of the equation by 5280

5280x/5280 = 26400/5280

(On the left-hand side of the equation, 5280 will cancel-out 5280 leaving us with x and on the right-hand side of the equation 26400 will divide 5280)

x = 26400 / 5280

x=5 mile

Therefore, If Rily ran 26400 feet, then she has ran 5 miles.

Answer:

B. {-4,3,5,8}

Step-by-step explanation:

We are given,

The set representing the function is {(-1,5),(2,8),(5,3),(13,-4)}.

It is required to find the range set of the function.

Now, as we know,

In the ordered pair [tex](x,y)[/tex], the y co-ordinate 'y' represents the range values of a function.

So, we see that,

The range values of the given function are 5, 8, 3 and -4.

Thus, the set representing the range of the function is {-4,3,5,8}.

Answer:

(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]

Upon solving the given expression, we get

=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)

=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]

=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]

which is the required simplified form of the given equation.

Hence, option A is correct.

Answer:

Close to 240 times but probably not exactly 240 times

Step-by-step explanation:

The scale ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.

The ratio you're referring to is called the scale factor. The scale factor is the ratio of the length of one side of a polygon to the length of the corresponding side of a similar polygon. Let's denote this scale factor as ( k ).

To calculate the scale factor, you need to choose corresponding sides from the two similar polygons. Once you've chosen a pair of corresponding sides, divide the length of one side by the length of the corresponding side from the other polygon.

Let's say we have two similar polygons, Polygon A and Polygon B, and we want to find the scale factor between them. Let's denote the length of a side of Polygon A as [tex]\( L_A \)[/tex] and the length of the corresponding side of Polygon B as [tex]\( L_B \)[/tex]. Then, the scale factor, ( k ), is given by:

[tex]\[ k = \frac{L_A}{L_B} \][/tex]

This ratio will give you the scale factor between the two polygons.

The image of point (5, -1) under the same translation that maps point P to P' is (1, -8). This translation vector is obtained by subtracting the coordinates of P from P'.

To find the image of point (5, -1) under the same translation T that maps point P to P', we can calculate the vector that represents the translation from P to P' and then apply the same translation to point (5, -1).

The translation vector is given by:

Translation vector = P' - P = (-6, -4) - (-2, 3) = (-4, -7)

Now, to find the image of point (5, -1) under the same translation, we simply add this translation vector to (5, -1):

Image of (5, -1) = (5, -1) + (-4, -7) = (5 - 4, -1 - 7) = (1, -8)

So, the image of point (5, -1) under the translation T is (1, -8). Therefore, the correct answer is B. (1, -8).

Learn more about image of point here:

https://brainly.com/question/32018278

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The simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

As we know, the expression can be defined as the combination of constants and variables with mathematical operators.

To begin, either multiply or divide the value in parentheses (32-4), which equals 5.

Add the number in the parentheses once more: 90/[10+5 (always do the parenthesis first) [10+5]= 15.

Finally, divide 90/15 by 6, always keeping that in mind (PEMDAS)

Thus, the simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.

Learn more about the arithmetic operation here:

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To construct an angle with a side on line l that is congruent to ∠ABC, follow these steps: Draw line l, measure ∠ABC, draw a ray from line l with the same angle, label the intersection point as B, and segment AB is congruent to side AC.

To construct an angle with a side on line l that is congruent to ∠ABC, you can follow these steps:

Draw line l.

Use a protractor to measure ∠ABC.

Draw a ray from line l, starting at point A and making the same angle as ∠ABC.

Label the point where the ray intersects line l as B.

Now, segment AB is congruent to side AC of ∠ABC.

2x +4 =14

2x =10

x =5

 the number is 5

Answer:

Step-by-step explanation:

The answer is actually B. $160,000; $320,000

The reason for this is because -

$10,000 is the constant, so let a= 10,000.

The investment doubles every 13 years, so let b=2.

Let x= the number of 13-year periods.

The value of a $10,000 investment doubling every 13 years will be $160,000 after 52 years and $320,000 after 65 years.

To calculate the value of an investment that doubles every 13 years, you can determine the number of times the investment will double over a given period. In this case, after 52 years, the investment will have doubled 4 times (since 52 divided by 13 is 4), and after 65 years, it will have doubled 5 times (since 65 divided by 13 is 5).

The formula for the future value of an investment that doubles is: Future Value = Present Value × (2^number of doublings).

After 52 years, the investment's worth would be calculated as follows:

$10,000 × (2^4) = $10,000 × 16 = $160,000

After 65 years, the investment's worth would be:

$10,000 × (2^5) = $10,000 × 32 = $320,000

Therefore, the correct answers are $160,000 after 52 years and $320,000 after 65 years, which corresponds to choice B.

We are given a function H(t) that represents the height of a cannon ball after t seconds as:

                  [tex]H(t)=-16t^2+48t+12[/tex]

and a second cannon ball is represented by the function g(t) as:

                       [tex]g(t)=10+15.2t[/tex]

PART A:

  t           0            1             2            3

H(t)        12          44          44           12

g(t)         15.2       25.2      40.4       55.6

Hence, between t= 2 seconds and t=3 seconds the ball will meet

     such that H(t)=g(t)

Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.

and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.

Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.

and the time at which they meet is calculated by solving:

[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]

As t can't be negative.

Hence, we get:

t=2.109 seconds

PART B:

The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.

Answer:

The value of [tex]m\angle 3-m\angle 1[/tex] = [tex]50^{\circ}[/tex]

Step-by-step explanation:

Vertical Angle theorem: It is about the angles that are opposite to each other.

Also, vertical angle are congruent that means vertical angles are equal.

In the given figure; [tex]m\angle 3[/tex] and [tex]70^{\circ}[/tex] are vertical angle

then, by vertical angle theorem,  [tex]m\angle3 =70^{\circ}[/tex].

Supplementary angle: the sum of the angles whose measure on the straight line is 180 degree.

From the figure, [tex]70^{\circ}[/tex] , [tex]\angle 1[/tex] and [tex]m\angle 2 =90^{\circ}[/tex] forms a straight line.

then, by the definition of Supplementary angle;

[tex]70^{\circ}+m\angle 1 +m\angle 2=180^{\circ}[/tex]

Substituting the value of  [tex]m\angle 2 =90^{\circ}[/tex] in above equation:

[tex]70^{\circ}+m\angle 1 + 90^{\circ} =180^{\circ}[/tex] or

[tex]160^{\circ}+m\angle 1=180^{\circ}[/tex]

Simplify:

[tex]m\angle 1=180^{\circ}-160^{\circ} =20^{\circ}[/tex]

therefore,  [tex]m\angle 1= 20^{\circ}[/tex] and [tex]m\angle 3=70^{\circ}[/tex],

the value of [tex]m\angle3-m\angle1= 70^{\circ}-20^{\circ} =50^{\circ}[/tex].

Answer:

[tex]10x^4+65x^3-25x^2[/tex]

Step-by-step explanation:

Multiply 5x^2(2x^2 + 13x − 5)

[tex]5x^2(2x^2 + 13x - 5)[/tex]

Multiply 5x^2 inside the parenthesis

[tex]5x^2 * 2x^2 = 10x^4[/tex]

[tex]5x^2 * 13x = 65x^3[/tex]

[tex]5x^2 * (-5) = -25x^2[/tex]

Collect all the terms together

[tex]10x^4+65x^3-25x^2[/tex]

Assembly Line A will produce 24975 units during the same time that Line B produces 555 units.

Let's assume that the time it takes for Assembly Line A to produce 45 units is equal to the time it takes for Assembly Line B to produce 37 units. This means that the time it takes for Line A to produce 1 unit is equal to the time it takes for Line B to produce 1 unit.

Now, we can set up a proportion to find how many units Line A will produce during the same time that Line B produces 555 units:

45 units / 1 unit = x units / 555 units

Cross-multiplying, we get:

45 * 555 = x units * 1

x units = 24975 units

Therefore, Line A will produce 24975 units during the same time that Line B produces 555 units.

Answer:

The museum is 4 blocks east and 10 blocks south from her hotel.

Step-by-step explanation:

It is given that ruby is visiting San Francisco. From her hotel she walks:

(a) 1 block west and 4 blocks south to a coffee shop.

(b) Then she walks 5 blocks east and 6 blocks south to a museum.

First she moves 1 block west and 4 blocks south and reached at point B. After that she walks 5 blocks east and 6 blocks south and reached at point D.

From the below figure it is noticed that point D is 4 blocks east and 10 blocks south from the origin because

[tex]South=4+6=10[/tex]

[tex]East=5-1=4[/tex]

Therefore the museum is 4 blocks east and 10 blocks south from her hotel.