Jackie runs and dances for a total of 55 minutes every day. She dances for 25 minutes longer than she runs. Part A: Write a pair of linear equations to show the relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day. (5 points) Part B: How much time does Jackie spend running every day

Step-by-step explanation:

y = 2x + 1 -------- (I)

y = 4x + 6 --------(ii)

from eqn (I)

y = 2x + 1

sub y = 2x + 1 in eqn (ii)

2x + 1 = 4x + 6

2x - 4x = 6 - 1

-2x = 5

x = -5/2

sub x = -5/2 in eqn (I)

y = 2(-5/2) + 1

y = -5 + 1

y = -4

Therefore, (x, y) = (-5/2, -4)

To add a function in FG, open the functions. php file in your theme folder, add the code for the function at the bottom of the file, save the file, and add the code for the function in the template files where you want it to appear.

To add a function in FG, you first need to open the functions. php file in your theme folder. This is where all the functions for your theme will be stored. Once you have the file open, you can add the code for the function that you want to create. This code should go at the bottom of the file. After you have added the code, save the file. Now, you need to add the code for the function in the template files where you want it to appear. To do this, add the following code: <?php your_function_name(); ?>. This code will call the function that you created in the functions.php file. Once you have added this code, save the file and the function should now appear in your theme.

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-9/7 is the inverse of 9/7.

-9/-7 = 9/7

9/7 + (-9/7) = 0

-9/7 is consequently the additive opposite of -9/-7.

By merely switching the integer's sign, you can add the original number and the additive inverse to produce a result equal to 0. The value that, when added to the original number, results in zero is known as a number's additive inverse. It is what we add to a number to make it equal to zero. Considering that an is the starting number, its additive inverse will be a minus one, or -a, such that;

a+(-a) = a – a = 0

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Answer:

Step-by-step explanation:

1. What are the x-intercepts of the graph representing f?  They are the points on the horizontal axis where the graph touches or crosses the axis.  Note that on this axis, y = 0.

2. What are the x- and y-coordinates of the vertex of the graph?  Since the function is written as the product of two binomials, we can take these coordinates directly from the binomials:  (x - 2) yields x = 2 and (x + 4) yields x = -4.

3. What is the y-intercept?   Multiply out these binomials.  We get:

f(x) = x^2 + 2 - 8.   When x = 0, y = -8.  The y-intercept is (0, -8).

1) The x-intercepts of the graph representing f are; 2 and 4

2) The x- and y-coordinates of the vertex of the graph are; (1, -5)

3) The y-intercept is at; (0, -8)

We are given the function; f(x) = (x - 2)(x + 4)

1) The x-intercepts of a graph are the points where the graph crosses the x-axis. The x-intercepts are the value of x when f(x) = 0. Thus, the x-intercepts here are 2 and 4.

2) The vertex is the lowest point of the graph in this case as the parabola opens upwards.

Let us expand the function to get;

f(x) = x² - 2x + 4x - 8

f(x) = x² + 2x - 8

where;  a = 1, b = 2, c = -8

Formula for the x-coordinate of the vertex is;

x = -b/2a

x = -2/2(1)

x = 1

Thus;

y =  (1 - 2)(1 + 4)

y = -5

x- and y-coordinates of the vertex of the graph are; (1, -5)

3) The y-intercept is the point at which x = 0. Thus;

y = 0² + 2(0) - 8

y = -8

The y-intercept is (0, -8).

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Answer:

80 mph

Step-by-step explanation:

Answer: 12 and 0.972

Step-by-step explanation: am doing it

All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.

A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.

All Quadrant I points have two positive coordinates.

Quadrant II points all have a negative x-coordinate and a positive y-coordinate.

All Quadrant III locations have two negative coordinates.

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343200 fts distance travelled in an hour

5720 ft was travelled in 1 minute and,

95.33 ft distance was travelled in 1 second.

The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles.

The British imperial and American customary systems of measurement both use the foot as a unit of length, denoted by the standard symbol: ft. An other sign that is frequently used is the prime symbol, ′. One foot is precisely equal to 0.3048 meters as of the International Yard and Pound Agreement of 1959.

5,280 feet per mile, sometimes known as a statute mile, is a unit of measurement (1.609 km). It derives from the mille passus, or "thousand paces," of the Romans, which was equivalent to 5,000 Roman feet.

65 miles per hour

so 65 * 5280 = 343200 ft travelled in 1 hr

in one minute distance travelled = 343200/60 = 5720  fts

and in one second distance travelled = 5720/60 = 95.33 fts.

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Given :

Mr. Ford's 2002 Focus would get 36 miles/gallon.

He starts with 13.2 gallons of gas in his gas tank.

To Find :

Write a slope-intercept equation that models how much gas remains in his tank after each mile of of travel(hint: g/mi).

Solution :

Let, required equation is :

y = mx + c

Here, y is gas remains in gallons.

Here, m is slope i.e. miles travelled per gallon.

So, m = -36  ( since gas is decreasing )

Initially distance travelled is 0 i.e. putting x = 0

y = c = 13.2

Therefore, y = -36x + 13.2 this is the required equation.

Answer:

y > 14/3

Step-by-step explanation:

-3y<-14

Divided both sides by -3. Because divided by a negative number, the < will switch to the >

y > 14/3

Answer:

q+7=61

soln

Step-by-step explanation:

q=61-7=54answer

Answer: 636.28

Step-by-step explanation:

first calculate the area of the square and the semicircle after u find the area of semicircle, multiply by four and add it to the area of the square. formula for area of semicircle = [tex]\frac{\pi r^2 }2\\[/tex]

formula of area of square  [tex]side^2[/tex]

Answer:

x= 69°

Step-by-step explanation:

First find the inner angle of the 159°

so you would do 180-159=21

next you add 21 ° to the 90° from the right angle

that gives you 111°

last you do 180-111 and you get 69

Answer:

x = 69

Step-by-step explanation:

180 - 159 = 21

The sum of the three angles of any triangle is equal to 180 degrees, so:

21 + 90 + x = 180

111 + x = 180

180 - 111 = x

x = 69

Have a nice day!

Therefore a quadratic function can be written in vertex form as

y = a(x - h)^2 + k.

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

A quadratic function can be written in vertex form as y = a(x - h)^2 + k

Where (h, k) is the vertex, and a is the leading coefficient.

y = ax^2 + bx + c (standard form)

y = a(x + b/2a)^2 + c - b^2/4a

y = a(x - h)^2 + k where h = -b/2a and k = c - b^2/4a

For example,when y = 3x^2 - 6x - 5

y = 3x^2 - 6x - 5

y = 3(x^2 - 2x) - 5

y = 3(x^2 - 2x + 1 - 1) - 5 = 3(x - 1)^2 - 8

So, the equation is in vertex form y = 3(x - 1)^2 - 8

Note that this only works for parabolas that opens upwards or downwards, if the parabola opens to the sides, the vertex form is y = a(x-h)^2 +k

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Answer:

-2x + 10

Step-by-step explanation:

Apply the distributive law:  a(b - c) = ab - ac

-2(x - 5 ) = -2x - ( -2) x 5

= - 2x - ( - 2 ) x 5

- ( -2 ) x 5 = 10

= -2x + 10

Answer:63,761,876,784

Step-by-step explanation:

Since an isosceles triangle has two equal sides, it has two equal angles and two equal heights. Therefore, if you know the length of two sides, you can use the formula A = (1/2)bh to calculate the area, where b is the length of the base and h is the length of the two equal heights.

An isosceles triangle is a triangle with two equal sides and two equal angles. Since the two equal sides also have two equal heights, we can use the formula A = (1/2)bh to calculate the area of the triangle without the height. The formula A = (1/2)bh requires the length of the base (b) and the length of the equal heights (h). Therefore, if you know the length of two sides, you can use the formula to calculate the area of the isosceles triangle without the height.

1. Determine the length of two sides of the triangle.

2. Calculate the area of the triangle using the formula A = (1/2)bh, where b is the length of the base and h is the length of the two equal heights.

3. Plug the known values into the formula and solve for the area.

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The expression x3 3x2 12x 19 is a polynomial expression in standard form.

To add 24 to this expression, we need to add 24 to each of the terms. This means that the answer is x3 + 3x2 + 12x + 43. To check our work, we can use theFOIL  method to expand the expression and make sure that the coefficients of each of the terms are correct. The FOIL method stands for First, Outer, Inner, Last. The first and last terms are the x3 and 43, the outer terms are 3x2 and 12x, and the inner terms are 3x2 and 12x. When we multiply these terms, we get x3 + 3x2 + 12x + 43, which is our final answer.

Calculation

x3 + 3x2 + 12x + (19 + 24)

= x3 + 3x2 + 12x + 43

The expression x3 3x2 12x 19 is a polynomial expression in standard form.

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The correct solutions for "x" after factorizing the cubic equation are:

x1 = -4

x2 = 0.5

x3 = 3

Cubic Equation:

A cubic polynomial in mathematics is a polynomial whose highest degree is three. A cubic equation is one that contains a cubic polynomial.

Either one real root or three real roots are present in every cubic equation. The cubic equation is written as ax^3+bx^2+cx+d=0.

Therefore, standard form of the cubic equation is: ax^3 + bx^2 + cx + d = 0

Given: 2x³ +x² -25x +12

On comparing with the standard form of the cubic equation, we get;

a=2

b=1

c=-25

d=12

After factorizing the cubic equation, we have three roots.

x1 = -4

x2 = 0.5

x3 = 3

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Answer:

y=-26.7x+14.1

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

y=−26.7x+14.1

Step-by-step explanation:

y=−17.5x+2.7x+14.1−11.9x

y=−26.7x+14.1

Solve for x:

Step 1: Flip the equation.

−26.7x+14.1=y

Step 2: Add -14.1 to both sides.

−26.7x+14.1+−14.1=y+−14.1

−26.7x=y−14.1

Step 3: Divide both sides by -26.7.

x=−0.037453y+0.52809

Solve for y:

y=−26.7x+14.1

Answer:

20  C 13 = 77520

Step-by-step explanation:

That's the answer that it told me on delta math.

Answer:

152°

Step-by-step explanation:

2x + 48 = 3x - 4 (the measure of an exterior angle of a triangle = the sum of the measures of the two non-adjacent interior angles of the triangle)
=> 4 + 48 = 3x - 2x (on transposing)
=> 52 = x
Substituting the vale of x in the m∠JKM,
m∠JKM = 3x - 4 = 3(52) - 4 = 152°

Hope you understood!!

Answer:

The formula is [tex]a_n = 3n-2[/tex]

The 14th term is 40, in other words, [tex]a_{14} = 40[/tex]

========================================================

Explanation:

The given sequence is 1, 4, 7, 10, ...

Subtract each adjacent term:

This shows that each term is increasing by 3. This is the common difference, so d = 3.

The first term is [tex]a_1 = 1[/tex]

The nth term of the arithmetic sequence is...

[tex]a_n = a_1 + d(n-1)\\\\a_n = 1 + 3(n-1)\\\\a_n = 1 + 3n-3\\\\a_n = 3n-2\\\\[/tex]

As a check, let's plug in say n = 3 to find that:

[tex]a_n = 3n-2\\\\a_3 = 3(3)-2\\\\a_3 = 9-2\\\\a_3 = 7\\\\[/tex]

The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.

-----------

We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.

[tex]a_n = 3n-2\\\\a_{14} = 3(14)-2\\\\a_{14} = 42-2\\\\a_{14} = 40\\\\[/tex]

The 14th term is 40.

You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.

Step-by-step explanation:

y = 2x + b ---> 3 = 2(1) + b ---> b = 1

Therefore, y = 2x + 1

Answer:

The box must be 2.4 in deep.

Step-by-step explanation:

Front dimensions are 9 in by 7.5 in.  Find the area of the front:  it is

A = (9 in)(7.5 in) = 67.5 in^2.  One way to complete this work would be to divide the given volume by this area, 67.5 in^2.  

A slightly different approach follows:

The volume must be 162 in^2.  Given V = (width)(height)(depth),

                                   V

(depth) must be -----------------------

                            (width)(height)

In this particular case,

                                162 in^3

(depth) must be ----------------------- = 2.4 in

                              (7.5 in)(9 in)

The box must be 2.4 in deep.

nope. bc...

0 ≠ 72 + 9.

yw!

Answer:

no.

Step-by-step explanation:

y (0) = 8(9) + 9

0 = 72 + 9

0 = 81

0 does not equal 81

that usually means that word has a definition that will be given at the bottom of the page or in the glossary depending on what type of book or excerpt of text you have.

hope this helps!