3
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.

Calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations.

When the equations are solved simultaneously, they are known as simultaneous equations.

Jogging be considered as x

Cycling be considered as y

Shelly spent 40 minutes jogging and 22 minutes cycling, and burned 620 calories to write this in equation we get,

40x + 22y = 620

Shelly swapped times,

22 minutes of jogging and 40 minutes of cycling and burned the same number of calories,

22x + 40y = 620

By multiplying two equation we get,

multiply equation 1 by 22 and equation 2 by 40 we get,

880x + 484y = 13640

880x + 1600y = 24800

Now subtracting equation 1 from 2 we get,

1116y = 11160

y = 11160/1116

y = 10

Therefore, putting value of y in equation 1 we get,

880x + 484(10) = 13640

880x = 13640 - 4840

x = 8800/880

x = 10

Therefore, calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

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The radius of the circle is √17.

The center of the circle is (4, 2).

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle with radius r and center (h, k) is

(x - h)² + (y - k)² = r²

Now,

x² + y² - 4 y - 8x + 3 = 0

x² - 8x + y² - 4y + 3 = 0

x² - 8x + 4² - 4² + y² - 4y + 2² - 2² + 3 = 0

(x - 4)² + (y - 2)² - 16 - 4 + 3 = 0

(x - 4)² + (y - 2)² = 16 + 4 - 3

(x - 4)² + (y - 2)² = √17

This means,

radius = √17 and center = (4, 2)

Thus,

The radius and center of the circle are √17 and (4, 2).

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The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The length of the ladder is 10 feet. And the inclination angle is 65°. Then the distance from the bottom of ladder to the wall is given as,

cos 65° = x / 10

x = 4.23 feet

If the ladder reaches a window 9.6 feet above the ground, then the angle is given as,

sin θ = 9.6 / 10

sin θ = sin 73.74°

     θ = 73.74°

The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.

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Answer:

y = (2/3)x + 3

Step-by-step explanation:

first we need to find the y-intercept

we can do this by using what is given, the point (-3,1) and the slope (2/3)

using the slope-intercept formula: y = mx + b.

m = slope

b = y intercept

we can plug in the x and y values we were given

so,

1 = (2/3)(-3) + b

we can now easily solve for b

1 = (2/3)(-3) = b

first multiply

1 = -2 + b

then add 2 to both sides, this way we isolate b

3 = b

now that we have the y intercept we can write the equation of the line

y = (2/3)x + 3

if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.

1 = (2/3)(-3) + 3

multiply first

1 = -2 + 3

add the like terms

1 = 1

Answer:

Step-by-step explanation: 22/7 is a rational number because it can be expressed as a ratio or fraction of two integers. The numerator (22) and denominator (7) are both integers, and the denominator is not equal to zero, so 22/7 is a well-defined fraction. Since every fraction represents a rational number, 22/7 is also a rational number

Step-by-step explanation:

1000ml=1 litre

800 divided by(1000 multiplied by 5)=16%

Answer:

Step-by-step explanation:

is A

The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

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Answer:

24 cans of soda for $8.89 is the better deal.

Step-by-step explanation:

Divide 24 cans of soda for $8.89 by 2. That way, with the same amount of cans, you can determine which one is more expensive.

1) 12 cans of soda: $4.75

2) 12 cans of soda: $4.445

The second one is cheaper.

Answer:

nth term = n²-6

Step-by-step explanation:

we know our nth-term formula is going to be of the form an² + bn + c. We just have to find a, b, and c.

In this series,

-5, -2, 3, 10, 19....

a=1, b=0, c=-6

nth term = n²-6

if n=1 then,

nth term=1²-6

⇒nth term=-5

The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).

In general, a system of linear equations can have one of three possible outcomes:

One unique solution (as in this case)

No solution (if the equations are inconsistent)

Infinitely many solutions (if the equations are dependent)

To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.

First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:

-10x - 4y = 14

5x + 2y = -7

-5x = 7

Now we can solve for x:

-5x = 7

x = -7/5

We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:

5x + 2y = -7

5(-7/5) + 2y = -7

-7 + 2y = -7

2y = 0

y = 0

Therefore, the solution to the system of equations is (x,y) = (-7/5,0).

This is called a unique solution, meaning there is only one possible solution for the system of equations.

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Complete Question:

Solve

5x + 2y = -7

10x + 4y = -14

And find the number of solutions for the equation

The lemon are limiting ingredient  in lemonade recipe.

Here the limiting ingredient is lemon because here for 1 cup of sugar we have 1 lemon it's clearly seems that the juice of 1 lemon never melt the 1 cup of sugar that's why here limiting ingredient   is lemon.

A limiting reagent is a substance that is completely consumed upon completion of a chemical reaction. They are also called limiting agents or limiting reactants. According to the stoichiometry of a chemical reaction, a certain amount of reactants is required for the reaction to go to completion. Consider the following reactions involving the formation of ammonia.

[tex]3H_{2} +N_{2} - > 2NH_{3}[/tex]

In the above reaction, 3 moles of hydrogen gas are required to react with 1 mole of nitrogen gas to produce 2 moles of ammonia. But what if only 2 moles of hydrogen gas and 1 mole of nitrogen were available during the reaction? Not all nitrogen can be used in this case (because 3 moles of hydrogen gas are required to react all the nitrogen). Hydrogen gas is therefore called the limiting reagent for this reaction as it limits the reaction.

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For given circle, Area of shaded region is 52π cm².

What exactly is a circle?

A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.

The equation for a circle in the plane is:

(x-h)^²+ (y-k)² = r²

When the coordinate points are (x, y)

(h, k) is the coordinate of a circle's center.

where r is the circumference of a circle.

where circle area = πr²

Circle circumference=2πr

Now,

Radius of biggest circle = 8cm

radius of unshaded circle= 4cm and

radius of smaller shaded circle= 2cm

Then,

Area of shaded region= Area of biggest circle - area of white circle + area of smaller shaded circle

=π*8² - π*4² + π*2²

=64π-16π+4π

=52π cm²

hence,

           Area of shaded region is 52π cm².

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Answer:

              The greatest possible five-digit number you can create with the numbers 6, 0, 3, 2, and 4 is 64,320.

Step-by-step explanation:

               When it comes to creating the biggest number with a given set of digits, the one and only rule is to organize the digits from greatest to least, this way it ensures that you have the maximum possible values that aren't mitigated by having a small number before a larger one. Based on this, we can organize 6, 0, 3, 2, and 4 from greatest to least, which will be 64,320. Hence, the greatest possible five-digit number you can create with those given numbers is 64,320.

Have a great day! Feel free to let me know if you have any more questions :)

The current age of Rita is 17 years and Cheryl is 7 years respectively, according to mentioned data.

Let us assume Rita's present age be x and Cheryl's age be y.

Rita's age two years ago = 3 × Cheryl's age two years ago

x - 2 = 3 (y - 2) - equation 1

Rita's age after three years = 3 × Cheryl's age after three years

x + 3 = 2 (y + 3) - equation 2

Solving equation 1

x - 2 = 3y - 6

x = 3y - 6 + 2

x = 3y - 4

Solving equation 2

x + 3 = 2y + 6

x = 2y + 6 - 3

x = 2y + 3

Keep the value of x from equation 2 in equation 1

2y + 3 = 3y - 4

Rearranging the equation

3y - 2y = 3 + 4

y = 7

Keep the value of y in equation x = 2y + 3

x = 2×7 + 3

x = 14 + 3

x = 17

So, Cheryl's and Rita's age is 7 and 17 years respectively.

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Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

What are points, lines, and planes?

Point: A point is a basic geometric object that represents a specific location in space.

Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.

Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.

Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.

Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.

Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.

Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.

Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

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The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.

What is the definition of a function?

A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).

There are several types of functions in mathematics. Here are a few examples:

An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.

Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.

A polynomial function is a function composed of polynomials.

Functions that may be used to inverse another function are known as inverse functions.

Now,

Given function is F(x)=4(x+6)2+5

=(4x+24)2+5

=8x+48+5

=8x+53

hence,

          The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.

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Answer:

Below

Step-by-step explanation:

Since the center (h,k) is (4,1)   and the circle passes through (4,-4) the radius is 5    ( from y = 1 to -4 ...a distance of 5 )

the equation for a circle is of the form  (x-h)^2 + (y-k)^2 = r^2

  becomes   (x-4)^2 + ( y-1)^2 = 5^2   < ==== graph this equation

radius = 5   then the diameter = 10  then     circumference = pi * d = 10 pi

Step-by-step explanation:

inscribed angles subtended by the same arc are equal.

the angle FGH is "based" on the same arc (FH) as the angle FJH.

so, FGH = FJH = 56°.

The required measure of angle m∠Q is 42 degrees, as of the given condition.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,

m∠O + m∠P + m∠Q = 180°

Using the given information,

m∠O = (6x - 14)°

m∠P = (2x + 16)°

m∠Q = (2x + 8)°

(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°

10x + 10 = 180°

10x = 170

x = 17

Substituting the value of x back into the expression for m∠Q,

m∠Q = (2x + 8)°

m∠Q = (2 * 17 + 8)°

m∠Q = 42°

So the value of m∠Q is 42 degrees.

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The estimate for the number of the paintings that are over 70 years old is given as follows:

68 paintings.

The histogram shows the number of observations that appear in each range of the data-set.

24 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:

24/(3 x 4) = 2 units.

Then the estimate of those over 70 years old is given as follows:

Then the total amount is of:

2 x 22 + 24 = 68.

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Joan paid with $19.00, she should receive $19.00 - $12.00, which equals $11.30 in change.So Joan should receive 11.30 in change.

Joan should receive $11.30 in change. To calculate this, we must start with the total cost of her items, which comes to $10.20 ($1.20 for the milk, $4.70 for the sandwich, and $3.30 for the sherbet). To this we must add the tax, which was $1.80. This brings the total cost to $12.00. Joan should receive $11.30 in change. To get this answer, we can use the following formula: Change = Total Payment - (Cost of Items + Tax). In this case, the formula would look like this: Change = 19.00 - (1.20 + 4.70 + 3.30 + 1.80). After calculating, the answer is 11.30. So Joan should receive 11.30 in change.

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Answer:

The equation of the line of symmetry of triangle ABC is:

Step-by-step explanation:

The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.

As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.

If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).

Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:

[tex]\implies y=\dfrac{2}{3}x+4[/tex]

Perpendicular lines have slopes that are negative reciprocals of one another.  Therefore, the slope of the perpendicular line is -³/₂.

Substitute the found slope and point A (4, 37) into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]

Rearrange the equation to standard form:

[tex]\implies 2y-74=-3(x-4)[/tex]

[tex]\implies 2y-74=-3x+12[/tex]

[tex]\implies 3x+2y-74=12[/tex]

[tex]\implies 3x+2y=86[/tex]

Therefore, the equation of the line of symmetry of triangle ABC is:

The average of the three hidden prime numbers is 5, as the sum of any two of the numbers is equal to 10, and since all three numbers are prime, the only possible values are 3, 5, and 7.

3 + 5 + 7 = 15

15/3 = 5

The average of the three hidden prime numbers is 5. This means that the sum of any two of the numbers on the cards must be equal to 10. Since all three numbers are prime,as the sum of any two of the numbers is equal to 10 the only possible values are 3, 5, and 7. Therefore, the three numbers on the hidden sides of the cards are 3, 5, and 7. To calculate the average, we add the three values together and divide by three. 3 + 5 + 7 = 15, and 15 divided by 3 is 5. Therefore, the average of the hidden prime numbers is 5.

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The only option that represents an object with volume is; Option D: Water Bottle

An object that will have volume is a 3-D object which means that it has length, width and height. Thus, 2D objects cannot have a volume.

Let us access the given options;

A) Baseball diamond: This refers to the baseball field because of the shape of the infield. Thus, it has only length and width and is a 2D shape which doesn't have a volume.

B) Floor Rug: A floor rug, is a plane shape which means it s a 2D shape which doesn't have a volume.

C) A piece of paper: This is a plane shape which means it s a 2D shape which doesn't have a volume.

D) Water Bottle: This is a 3D shape that has length, width and height and as such it has volume.

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Answer:

J(t) = 230,600(1.009)^t

Step-by-step explanation:

J(t) = 230,600(1 + 0.009)^t, or

J(t) = 230,600(1.009)^t                                                                                                                                                                                                              If this is Wrong ill do. it again!!

Answer:

216 in^3

Step-by-step explanation:

Volume = 6 in. * 4 in. * 9 in. = 216 in^3

If the array includes just the positive integers [tex]{\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}[/tex], the magic square is said to be normal. Some authors take magic square to mean normal magic square.

A magic square is a square grid of numbers that has the same sum for every row, column, and diagonal. It is a mathematical puzzle that has been known and studied for thousands of years. Magic squares can be of different sizes, but the most common are those with odd numbers of rows and columns.

The concept of magic squares dates back to ancient China, where they were believed to have mystical properties. In India, they were used for divination and as part of religious rituals. In Europe, magic squares were popularized in the 16th century, where they were used as a form of mathematical entertainment. Magic squares are not only interesting mathematical puzzles but also have practical applications.

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Complete Question: -

Fill the given squre with numbers from 0 to 8 ( using each of them exactly once) in such a way that the sum of the numbers in the first second and third rows are third rows are in the ratio 1 : 2 : 3. At the same time the sum of the numbers in the first second and third columns also have to be in the same ratio.​