Function rules from equations
For a given input value q, the function f outputs a value r to satisfy the following equation.
11g 4= 3r6
Write a formula for f(g) in terms of q.
f(q) =
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Answer:

65

Step-by-step explanation:

We are given f(x) = 9

Substitute 9 for x in f(x) = 8x - 7

f(x) = 8 (9) - 7

f(x) = 72 - 7

f(x) = 65

Answer:

B. Yes, the constant of proportionality is 2.

Step-by-step explanation:

Given:

A linear relationship is shown in the table.

Time (hours) 2 4 6 8

Distance (miles) 4 8 12 16

Is the linear relationship also proportional? Explain.

A. No, the constant of proportionality is 2.

B. Yes, the constant of proportionality is 2.

C. No, there is no constant of proportionality.

D. Yes, there is no constant of proportionality.

Solve:

To know if a linear relationship is proportional, all we have to find out is if after we divide distance by time and if all equal the same. Ex: 4/4=1,3/3=1. As we can see all are equal to 1.

Let's see the table:

Time (hours)                    Distance (miles)

2                                                  4

4                                                  8

6                                                  12

8                                                  16

The formula for it is 'k=y/x'

where;

k: constant of proportionality  

y and x are two quantities that are directly proportional to each other.

Also means;

y = Distance

x = Time(Hours)

Time (hours)                    Distance (miles)

2                                                  4                                                4/2=2

4                                                  8                                                8/4=2

6                                                  12                                               12/6=2

8                                                  16                                                16/8=2

As you see all equal to 2. It a constant. Also means that;

Yes, the linear relationship is proportional and the constant of proportionality is 2.

Answer: B. Yes, the constant of proportionality is 2.

RevyBreeze

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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The length of the spine will be;

⇒ 48.2 cm

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A kite is shaped like an isosceles triangle.

Now,

Since, A kite is shaped like an isosceles triangle.

Hence, Two sides of a triangle is equal to each other.

Let the length of the spine = x

So, We can formulate by the Pythagoras theorem,

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ 62² = (78/2)² + x²

⇒ 3844 = 39² + x²

⇒ 3844 = 1521 + x²

⇒ 3844 - 1521 = x²

⇒ 2323 = x²

⇒ x = √2323

⇒ x = 48.2 cm

Thus, The length of the spine = 48.2 cm.

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The relationship between altitude and boiling point is given below.

What is altitude?
Altitude is the height above sea level. It is usually measured with a barometer or GPS satellite. Altitude can be used to describe the height of an airplane, a mountain, or even the position of a satellite in space. Altitude can also be used to measure how high a person is standing on Earth. Altitude can also be used to compare the relative heights of two different points on Earth. Altitude is an important factor when flying, as it can determine air pressure, air temperature, and wind speed.

Sea Level 212°F
1,000 ft. 211°F
2,000 ft. 210°F
3,000 ft. 209°F
4,000 ft. 208°F
5,000 ft. 207°F
6,000 ft. 206°F
7,000 ft. 205°F
8,000 ft. 204°F
9,000 ft. 203°F
10,000 ft. 202°F

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The length of the triangle ΔABC will be √7 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

In triangle ΔABC, AC = BC, the CD is perpendicular to AB with D belonging to AB, AB = 4 inches, and CD = √(3) inches.

The CD is half of the length AB. Then we have

CD = AB / 2

CD = 4 / 2

CD = 2 inches

Then the length of AC is calculated as,

h² = (√3)² + (2)²

h² = 3 + 4

h= √7 inches

The length of the triangle ΔABC will be √7 inches.

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Logarithmic Functions

In mathematics, the logarithmic function is an inverse function to exponentiation

Domain and range of logarithmic functions

We know that is defined only when >0. So the domain is the set of all positive real numbers. We can see that can be either a positive or negative real number (or) it can be zero as well. Thus,  can take the value of any real number.

Note:

The domain of function = is >0 (or) (0,∞).

The range of any log function is the set of all real numbers ().

Logarithmic graph

We know that exponentials and functions are inversely proportional to each other, and so their graphs are symmetric concerning the line =. Also, note that =0 when =0 as =(1)=0 for any . Thus, all such functions have an -intercept of (1,0).  A logarithmic function doesn’t have a -intercept as 0 is not defined.

Properties of logarithmic graph

>0 and ≠1.

The logarithmic graph increases when >1 and decreases when 0<<1.

The domain is obtained by setting the argument of the function greater than 0.

The range is the set of all real numbers.

Graphing logarithmic functions

Before plotting the log function, just have an idea of whether you get an increasing curve or decreasing curve as the answer. If the >1 then the curve is increasing, and if 0<<1, then the curve is decreasing.

Here are the steps for graphing logarithmic functions:

Find the domain and range.

Find the vertical asymptote by setting the argument equal to 0. Note that a  function doesn’t have any horizontal asymptote.

Substitute some value that makes the argument equal to 1 and use the property (1)=0. This gives us the -intercept.

Substitute some value that makes the argument equal to the base and use the property ()=1 This would give us a point on the graph.

Connect the two points (from the last two steps) and extend the curve on both sides relative to the vertical asymptote.

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The solution to w in the equation 9(w - 4) - 7w = 5(3w - 2) is w = -2.

Now, According to the question:

The given Equation:

9(w-4)-7w=5(3w-2)

To solve for w we first need to simplify our equation, removing any brackets and adding together similar terms. This gives us:

9(w-4)-7w=5(3w-2)

9w - 36 -7w = 15w - 10

2w - 36 = 15w - 10

Next, we subtract 2w from both sides to have all the variables on one side of our equation, then we add 10 to both sides to move the numerical values to one side.

2w - 36 = 15w - 10

2w -2w - 36 = 15w - 2w - 10

-36 = 13w - 10

-36 + 10 = 13w - 10 + 10

-26 = 13w

Finally, we divide both sides by 13 to find the value of w.

w = -2

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The complete question is this :

What is the solution to the equation of 9(w - 4) - 7w = 5(3w - 2).

The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.

Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:

c² = a² + b² - 2abcosC

Therefore, you can rearrange the equation to solve for angle C:

C = arccos((a² + b² - c²) / (2ab))

For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.

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The number that should be added in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex]  , so that it is completely divisible by  [tex]x^{2} -3x+2[/tex] is  -14  .

What are Polynomials ?

A polynomial is defined as a type of algebraic expression where the exponents of all the variables is a whole number.

The exponents of the variables in any polynomial is a non-negative integer. A polynomial consists of constants and variables.

the polynomial expression is ⇒ [tex]x^{2} -3x+2[/tex], which can be written in factor form  as  : [tex](x-1)(x-2)[/tex] ,

that means the polynomial is divisible by both x = 1 and x = 2 ;

So , on substituting [tex]x=1[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,

we get , [tex]1^{3}-6\times1^{2} +11\times 1+8[/tex] = 14 ;

on substituting [tex]x=2[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,

we get , [tex]2^{3}-6\times2^{2} +11\times 2+8[/tex] = 14 ;

So , the remainder is 14  .

Therefore , -14 should be added in the given polynomial .

The given question is incomplete , the complete question is

What should be added in the polynomial x³ -6x² +11x +8 so that it is completely divisible by x² -3x +2 ?

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Answer:

The fraction 480/840 can be reduced to its lowest terms by dividing the numerator and denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd). This results in a reduced fraction of 4/7.

Step-by-step explanation:

Answer:

aida:$7500

Bernardo:$6000

Christiano :$4500

b.i $10500

b.ii 13/60

b.iii $13000

c. 24%

Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.

If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.

If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.

If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.

Therefore, the smallest number of students for the teacher's claim to be true is three students.

It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.

Step-by-step explanation:

The area of the scale drawing is 108 square inches.

I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108

Answer:

The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Answer: 7:20

Step-by-step explanation:

It seems like there are no options to choose from, but if that is one of the options, here's how:

You can simplify ratios by finding if there is a common multiple.

For 35 and 100, there is a common multiple of 5, so you can divide both sides by 5 to simplify the equation.

That leaves us with 7:20. Since one is a prime number, we can't simplify this further.

Answer:

The ratio equivalent to 35:100 is 7:20

Step-by-step explanation:

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,

Given ratio,

= 35 / 100

= 5× 7 / 20 × 5

= 7 / 20

The angle with the measure 360° is known as a complete angle. A complete angle is one full rotation measuring 360°.

When the final point coincides with the initial point, after one whole rotation, then the angle so created is known as the complete angle. A complete angle is also known as a full angle or a round angle.

The measure of a complete angle is equal to 2π radians = 360 degrees which is the central angle of a circle. Also, if we combine four right angles or two straight angles it makes a complete angle. A complete angle is identical to a zero angle but the difference is only the amount of rotation.

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The answer is 90 times to expect picking an apple or banana.

If the fruit is chosen 300 times, then it would be a 1:3 ratio of apple or banana to the other fruits. This means that 100 times out of the 300 times, you would expect to pick an apple or banana.

Predicting the outcome using the experiment results because 300 times is a sizable number.

8+4 is either an apple or a banana in 40 times.

Therefore, the solution would be x in 300 times.

[tex]x = \frac{300}{40}[/tex] x12

x = 90

Therefore, the probability of picking an apple or banana is 90 times.

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3u^2-84 = 0 then u=5.29 is the nearest hundredth

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

This category includes all natural integers, decimals, and fractions.

In the number system, real numbers are only the fusion of rational and irrational numbers.

These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.

Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Examples of actual numbers include 23, -12, 6.99, 5/2, and so forth.

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For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.

The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.

Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.

Since the radius of B is 3, AX = 4.

Assume AE = p.

Then EX and EY are radii of circle E and have length 4 + p.

AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.

Using the Law of Cosines on Δ CAE, we obtain

(6+p)² =p² + 64 - 2(8)(p) cos 60

The 2 and the cos 60 terms cancel out:

p² + 12p + 36 = p² + 64 - 8p

12p+ 36 = 64 - 8p

p = 28/20

= 7/5

The radius of circle E is 4 + (7/5)

= 27/5,

So, the answer is 27 + 5 = 32

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Therefore the product of two conjugates is a difference of two squares.

When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.

An integer known as a binomial number is produced by evaluating a homogeneous polynomial with two terms, also known as a binomial.

This statement is true.

The conjugates of a complex number are two complex numbers that differ only in their signs. They are of the form a + bi and a - bi.

When two conjugates are multiplied, the product is (a + bi)(a - bi) = a^2 + (bi)^2 = a^2 - b^2 + (2abi) = (a^2 - b^2) + (2ab)i.

which is in the form (a^2 - b^2) + (2ab)i = (a^2 - b^2) + (2ab)i = (a+b)(a-b)

So the product of two conjugates is a difference of two squares.

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The population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours.

Given that,

P_t = P_0 * 2^(t/d) , which refers to the formula for the calculation of the number of bacterial cell in a population.

In the given formula, P_t is the population after t hours, P_0 is the initial population, t is the time in hours and d is the doubling time in hours,

Therefore,

P_0 = 7100

d = 2

t = 15

so,

P_15 = 7100 * 2^(15/2) = 7100 * 181.019= 1285234.9 which is nearly equal to 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours, the population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

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    Given ,

To Find : Maximum number of small cube shaped boxes that can fit in the cuboid

Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]

Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]

                                      = [tex]14400cm^{3}[/tex]

Now to find the volume of a cube,

[tex]V = a^{3}[/tex]

[tex]V = 10X10X10[/tex]

[tex]V = 1000cm^{3}[/tex]

Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]

                                                                    = [tex]14boxes[/tex]

Hence , the number of cube shaped boxes that can fit in a cuboid are 14

The system of equations -3x + y = 4 and -9x + 5y = -1 has the solution (-3.5 , -6.5).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations. This is what is called as the solution.

Given two equations in x and y,

-3x + y = 4     (equation 1)

-9x + 5y = -1     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -3x + y = 4     ⇒     y = 3x + 4

-9x + 5y = -1     (equation 2)

-9x + 5(3x + 4) = -1

-9x + 15x + 20 = -1

6x = -21

x = -3.5

Substitute the value of x in equation of y and solve for y.

y = 3x + 4

y = 3(-3.5) + 4

y = -6.5

Hence, the solution to the following system of equations is (-3.5 , -6.5).

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Answer:

(-3.5 , -6.5)

Step-by-step explanation:

On solving the provided question, we can say that the equation will be 1.8x=7200 => x=4000

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation will be

1.8x=7200

x=7200/1.8

x=4000

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The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.

A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.

A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where

aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.

'x' is the variable.

p(x) means "polynomial in terms of variable x"

'n' is a non-negative integer, it is the degree of p(x).

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Answer:

NEED:

WANT:

Step-by-step explanation:

Right on Plato! <3

Have a wonderful day!

The needs listed are tuition and fees and staple foods, while the wants are a vacation, a Lamborghini, and a lavish wedding.

The listed needs and wants reflect different aspects of a person's life and priorities. "Tuition and Fees" and "Staple Foods" are necessities that are essential for a person's survival and well-being.

On the other hand, "Vacation," "Lamborghini," and "Lavish Wedding" are desires that are often seen as luxury items or experiences. While having wants is normal and human, it is important to understand that not all wants can be fulfilled, and it is equally important to prioritize needs over wants. Having a balanced approach to spending, budgeting, and financial planning can help ensure that both needs and wants can be met in a sustainable manner.

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Answer:

Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.

A three-degree equation is referred to as a cubic equation. The polynomials are referred to as cubic polynomials if they have a degree of three.

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. The polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

given

A three-degree equation is referred to as a cubic equation.

All cubic equations have roots that are either three real roots or one real root and two imaginary roots.

The polynomials are referred to as cubic polynomials if they have a degree of three.

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