If Jon runs 35 miles a week, and Jacky runs 57 miles a week, how much more does Jacky run than Jon?

The y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.

In the given question, we have to solve the y-value of the solution to the system of equations.

3x + 5y = 1..................(1)

7x + 4y = -13...............(2)

Multiply equation 1 by 4 and equation 2 by 5, we get

12x + 20y = 4................(3)

35x + 20y = -65................(4)

Subtract equation 4 by 3, we get

23x = -69

Divide by 23 on both side, we get

x = -3

Now putting the value of x in the equation 1, we get

3(-3) + 5y = 1

-9 + 5y = 1

Add 9 on both side, we get

5y = 10

Divide by 5 on both side, we get

y = 2

Hence, the y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.

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The complete question is:

What is the y-value of the solution to the system of equations?

3x + 5y = 1; 7x + 4y = - 13

They sell 21 pizzas for $321 in one evening.

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation. It is a mathematical problem expressed entirely in words typically used as an educational tool.

Word problems are regarded as an important aspect of the basic curriculum because they require students to apply their understanding of various concepts to real-life settings.

Let us assume that,

small size pizza =x

medium size pizza =y

large size pizza =z

so, x+y+z=21

6x+9y+10z= 321

y=z+1

x+y+z=21

6x+9y+10z= 321

y-z=1

6x+9y+10z= 321

y+4z=31

5z=30

z=6

y=z+1

y=7

x+y+z=21, x=8

{8,7,6}

8*$6=$48

7*$9=$56

6*$10=$60

Thus, they sell 21 pizzas for $321 in one evening.

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The value of x would be 1496 m.

What is trigonometry?

Trigonometry is based on the study of the six basic trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are defined in terms of the ratios of the sides of a right triangle. For example, the sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we can apply the trigonometric ratio, we get

sin22 = x/4000

0.374 = x/ 4000

x = 0.374 * 4000

x = 1496m

Hence, the value of x would be 1496 m.

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Answer:f=56 I hope this helps

Step-by-step explanation:

f divide (-7) =-8

Dividing a positive and a negative equals a negative: (+) divided sign (-) =( -) and then

Write the division as a fraction

-1/7f=-8

Multiply both sides of the equation by -7

f=56

Answer:

f = 56

Step-by-step explanation:

Given statement,

→ f divided by -7 is -8.

Forming the equation,

→ f/-7 = -8

Now the value of f will be,

→ f/-7 = -8

→ f = -8 × -7

→ f = 8 × 7

→ [ f = 56 ]

Hence, the value of f is 56.

1260

Just as 12 is to 72. 210 is to x

setup ratio, cross multiply, and solve for x:

Answer is 1260

The length of the unknown side of this right angled triangle is 12cm.

This is a question about the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as c^2 = a^2 + b^2, where c is the hypotenuse, and a and b are the other two sides.

In this case, we know that the base of the triangle is 8cm and the length is 9cm.

So we can use the formula c = √(a^2 + b^2)

c = √(8^2 + 9^2)

c = √(64 + 81)

c = √(145)

c = 12cm

Therefore, the length of the unknown side of this right angled triangle is 12cm.

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Yes, the function f(x)=2x-3 is a one-to-one function.

The Inverse of a Function:

The inverse of a function can be computed if the function can be proven to be one-to-one. Take the one-to-one function and compute its inverse by interchanging x and y in the expression and solving for y.

Graphically, then, the graphs of the function and its inverse are the reflections of each other about the line y=x.

Use the definition to test the one-to-one of f.

Let x and x be the elements in the domain off and assume f(x₁)=f(x₂)

2x₁-3=2x₂-3

2x₁=2x₂

x₁=x₂

since f(x₁)=f(x₂) implied x the function f is one-to-one.

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Explanation:

When going from A(-2,-3) to A '(-6,-9), we multiplied both coordinates by the scale factor 3. In other words, we tripled the coordinates.

Do the same thing to the coordinates of point B.

Therefore we arrive at (12, 0) as the final answer. This is choice C.

Total charge that Tom has to pay is $142.2, and the express function for the monthly charge is c(x) = 105 + (x -4) * 12

As per data given, monthly value given is $105 = free text + free call + 4gb  and extra gigabyte x $12. Tom that use 7.1 of data will be charge as follow:

Tom charge = normal use + extra use

To charge = 105 + extra gigabyte x12

Extra gigabyte = tom use - normal use

Extra gigabyte = 7.1 - 4

Extra gigabyte = 3.1

Tom charge = 105 + 3.1 x 12

Tom charge = 105 + 37.2

Tom charge = 142.2

The expression of monthly charge, since we have already define that value is $105 = free text + free call + 4gb and extra gigabyte x $12. We can see that text is not charge and call is not charge. So the formula will be:

Monthly charge = 105 + (extra gigabyte - 4) x 12

As per question said the variable for extra gigabyte is x and monthly charge is c(x) then

c(x) = 105 + (x - 4) * 12



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Answer:

comparing (x+2) with (x-a) we get a=-2

Using factor theorem

p(x)=0

p(-2)=0

(-2)⁴-(-2)³+c×(-2)²+3×-2-2=0

-16+8+4c+12=0

4+4c=0

4c=-4

c=-4/4

c=-1

Answer:

Step-by-step explanation:

To prove that sinA/(1-cosA) = 1/cosA, we will start with the left-hand side and simplify it using trigonometric identities.

sinA/(1-cosA) = sinA/(1-cosA) * (sin^2A + cos^2A) / (sin^2A + cos^2A)

= (sinAsin^2A + sinAcos^2A) / (sin^2A + cos^2A - sin^2AcosA - cos^2AcosA)

= (sinAsinAcosA + sinAcosAcosA) / (sinAcosA - cosAcosA)

= sinA/cosA / (sinA/cosA - 1)

= 1/cosA

Therefore, sinA/(1-cosA) = 1/cosA, which is true.

Their taxable income  $9,250.

Single-tax-return filing status with the IRS. For unmarried individuals who are not eligible to file as the head of household, single is the default filing status.

When submitting your tax return, you must choose the single filing status if you were not married on the last day of the tax year and you are not eligible to utilize any other filing status.

The amounts for the 2022 standard deduction are as follows: Married Jointly Filing or Qualifying Widow(er) - $25,900 (an increase of $800) $19,400 (an rise of $600) for the head of the household Married Filing Separately or Single: $12,950 (an increase of $400).

An individual making $50,000 will pay $9,250, according to the exhibit that is attached.

People who make $50,000 fall into the $42,001-$100,000 category and pay $7,250 plus 25% of any amount over $42,000.

The tax burden is as follows:

= 7,250 + ( 25% x (50,000 - 42,000))

= 7,250 + (25% x 8,000)

= $9,250.

The complete question is,

Using Exhibit 11-4 as a guide, calculate the tax due on a person with a $50,000 taxable income.

$9,250 \s$10,110 \sO $15,000 \sO $12,500.

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Answer:

9876567890

Step-by-step explanation:

Both Elena and Lin are right , in my opinion. According to Elena, length BC is 16.5 units. Lin estimates that BC is 17.1 units long.

The remainder of the query is included in the attachment. The figure shows that ED is parallel to A B and B C is parallel to A B. In light of the Pythagoras theorem,

[tex]$\mathrm{AC}^ 2=\mathrm{AB}^ 2+\mathrm{BC}^ 2$[/tex]

[tex]$\mathrm{BC}^ 2=196-36=160$[/tex]

[tex]$\mathrm{BC}=12.649$[/tex] or [tex]$12.65$[/tex]

Both Elena and Lin are right .A visual that conveys information rather than just representing it. particularly : a diagram demonstrating the relationships and arrangements (as between parts): a dotted line drawing used in science or math .

A diagram is a picture that shows how something works, how it's organised, or how it's related to something else. Even when they go by the names "map," "chart," or "graph," several diagram kinds are still considered to be diagrams. as flowcharts, organisational charts, and mind maps. An illustration that depicts an object's component elements and their relationships to one another is called a diagram.

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The data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.

A relation is a function if it has only One y-value for each x-value.

We have to check whether the data (36, 6); (18, 5); (0, 4); (-18, 3)

is an example of function.

The ordered pairs are thirty six comma six comma eighteen comma five comma zero comma four comma minus eighteen comma three.

As we observe there is only one y value for each x value.

and the x values are not repeated.

Hence, the data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.

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The relationship of the degree x - [[- b+v(b2 - 4ac)V2a] = 0 describes the relationship between a quadratic equation's factors and its solutions. A quadratic equation's general equation is f(x) = ax*+ bx +. function:

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and respectively.

expression: Terms (constants and variables) are separated by mathematical operators to form a mathematical expression. equation: Two expressions are equated using a mathematical equation. The quadratic equation f(x) = axe + bx + c is given.

The quadratic equation (ax2 + bx + c= 0) can be expressed as a product of its linear factors as (x - k)(x - h), where h, k are the quadratic equation's roots. This process is known as factoring a quadratic equation.

We may write [h] =- b + v(b2 - 4ac)y2a [K]=(-b- V(b2 - 4ac))/2a using the quadratic formula. The link between the elements of a quadratic equation and its solutions can be expressed as - x- [[-b+v(b- 4ac)y2a] =0

X=[(b' - 4AC)y2A] = 0.

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Answer:

I. x = -4 and II. x = 12

Step-by-step explanation:

For this problem, you would simply need to plug in the values and see if the inequality is true, and if it is, it is a solution, so let's go through the options.

Plugging in x = -4 gives us: -4 < 12 which is true since negative four is less than positive twelve, so this is a solution.

Plugging in x = 0 gives us: 0 < 12 which is true since zero is less than twelve, so this is a solution.

Plugging in x = 12 gives us: 12 < 12 which is false since twelve is not less than twelve but is rather equal to it. if the less than symbol had a line under it, it would also include values equal to it in which case x = 12 would be a solution but since it doesn't, this is not a solution.

Plugging in x = 13 gives us: 13 < 12 which is false since thirteen is not less than twelve but is rather greater than it, so this is not a solution.

By utilizing the Quadratic Equations' formula for the roots, we can solve the most complex quadratic equations.

For example,

then the equation's roots

Now

The equation's roots are -2 and —3.

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

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Answer:

you take rows multiplied by row

such that 5rows × 3 rows = 15 squares in total

The shrink-wrapped carton of 64 juice boxes contained 2 gallons of juice.

To find out how many gallons of juice were in the shrink-wrapped carton, we first need to convert the number of juice boxes to cups and then convert that amount to gallons.

Each juice box contains 1/2 cup of juice, so 64 boxes contain 64 * (1/2) = 32 cups.

There are 16 cups in 1 gallon, so to convert 32 cups to gallons, we divide 32 cups by 16 cups/gallon.

32 cups / 16 cups/gallon = 2 gallons

So, the shrink-wrapped carton of 64 juice boxes contained 2 gallons of juice.

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The quotient is the quantity we arrive at when dividing two numbers.

When a number is divided, the result is the quotient. The mathematical symbol (÷) stands for division, which is a technique for allocating items equally among groups. In mathematics, the quotient is the outcome of dividing an integer by any divisor. It is the quantity of times the dividend contains the divisor.

An integer or a decimal number can be the quotient.

A whole number is the quotient when a number is entirely divisible by another integer. The quotient is a decimal number when a number cannot be divided by another number entirely.

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If you are worried about your future in math and want to improve your mathematical abilities, the best way to do so is to practice regularly and seek out additional resources to help you understand the material.

Here are some specific things you can do:

Practice problems: Work through a variety of different types of problems to build your skills and confidence.

Find a study group: Join a study group with other students who are also taking the same math class. This can be a great way to get extra help and support.

Use online resources: There are many online resources, such as videos and tutorials, that can help you understand mathematical concepts.

Seek extra help: Don't be afraid to ask your teacher or a tutor for extra help if you are struggling with a particular topic.

Stay motivated: Keep in mind the importance of math in many fields and how it will be useful in future, and set realistic and challenging goals for yourself.

Make connections between different topics: Try to understand how different mathematical concepts are related and how they can be applied in real-world situations.

Remember, learning math takes time and practice, so be patient and persistent.

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If the x coordinate is positive and the y coordinate is zero, the location of the point is in positive x- axis.

The position of a point or a shape in a specific space is determined by coordinates, which are numbers (a map or a graph).

Cartesian coordinates are introduced to students in Year 4 and are taught in primary school. The x axis, which is the horizontal axis, and the y axis, which is the vertical axis, are used to identify points (the vertical axis).

Coordinates are always written with two numbers separated by commas and enclosed in brackets. Coordinates are ordered pairs of numbers, where the first number represents the point on the x axis and the second, the point on the y axis.

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The height of the TV would be 61.27 inches.

What is Pythagoras theorem?

The hypotenuse's square length is equal to the sum of the squares of the lengths of the other two sides of the right-angled triangle, according to the Pythagorean theorem, commonly known as the Pythagoras theorem.

Here, The 75 inches represents the length of diagonal of the TV because the length of TV is always measured diagonally. So, the diagonal's length is 75 inches.

We've width as 43.25 inches.

Since TV is of the shape of rectangle, we can calculate the height by applying Pythagoras theorem.

So, we've   hypotenuse² = (side 1)² + (side 2)²

It can be written as,

                   diagonal² = height² + width²

                   (75)² = height² + (43.25)²

                  height² =  (75)² -  (43.25)²

                               = 5625 - 1870.5625

                               = 3754.4375

                   height = √3754.4375 = 61.27 inches.

Hence, height will be 61.27 inches.

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Answer:

16,080

Explanation:

The answer will be 76, using a gradient.

What is the gradient of the slope?

To find the gradient of the given data, horizontal as well as the vertical distance between two points in parallel is necessary to find.

532/7=76

Hence the answer is 76

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Any alternative for the variable in a function that results in a zero answer is said to as the zero of a function.

The x-intercept(s) of the function's graph, or the real zero of a function, is where the function's graph hits the x-axis graphically.

The values of the variable in a function that allow the function to equal zero are termed the zeros of the function. The places on the x-axis where the graph crosses the x-axis are referred to as a function's zeros graphically. In other respects, we can say that the zeros of something like a function are the x-intercepts of the graph.

Finding the values of the variable that correspond to the function's zeros can be achieved by equating the function to 0. By calculating the polynomial and then equating it to 0, we can discover the zeros for polynomials.

Example:

Find the zeros of the function f(x) = ex - 1. Answer: Zero of function f(x) = ex - 1 is x = 0.

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The equation, Y = - 2x + 3 has infinitely many solutions.

Here we are given the equation y = 2x + 3. Now since this equation has 2 variables, it can be easily plotted on a graph. After plotting this equation, we can see that it makes a never-ending line, hence, this equation will have infinitely many solutions.

For any equation to have a solution, there must be an intersecting point or a common value for x or y.

Here for every value of x, we get a different value of y, which can be easily seen in the graph.

Furthermore, when an equation has 2 variables, there must be at least 2 equations for the system to have a unique solution, hence the given equation has infinitely many solutions.

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Correct Question

How many solutions does Y = - 2x + 3 have?

The degree and maximum possible number of terms for the product is 4 and 9 respectively

An algebraic expression can be described as a mathematical expression consisting of variables, factors, coefficients, terms and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

A trinomial can be defined as an algebraic expression having three non-zero terms with more than one variable in the expression

Given the expressions;

(x² + x + 2)(x² - 2x + 3)

expand the bracket

x⁴ -2x³ + 3x² + x³ -2x² + 3x + 2x² -4x + 6

collect like terms

x⁴ -2x³ + x³ + 3x² - 2x²+ 3x - 4x + 6

Add or subtract like terms

x⁴ - x³ + x² -x + 6

Hence, the degree is 4

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Answer:

3p-g-10

Step-by-step explanation:

3(p-3)-g-1

3p-9-g-1

3p-g-9-1

3p-g-10