Nine years ago, Katie was twice as old as Elena was then. Elena realizes, "In four years, I'll be as old as Katie is now!" Elena writes these equations to help make sense of the situation: k - 9 = 2(e - 9)
e + 4 = k

If Elena is currently e years old and Katie is k years old, how old is Katie now?

Answer

2 =1

3=1.4

Step-by-step explanation:

hb=2A

b=2·5

10=1

hb=2A

b=2·14

20=1.4

Step-by-step explanation:

2 .) Using Pythagorean Theorem,

    [tex]a^{2} + b^{2} = c^{2}[/tex]

    [tex]5^{2}+ 10^{2} = c^{2}[/tex]

     [tex]25 + 100 = c^{2}[/tex]

      [tex]125 = c^{2}[/tex]

      [tex]\sqrt{125}= c[/tex]

       [tex]11 . 18 = c[/tex]

3.) Using Pythagorean Theorem,

     [tex]a^{2} + b^{2} = c^{2}[/tex]

     [tex]a^{2} + 14^{2} = 20^{2}[/tex]

     [tex]a^{2}= 20^{2}- 14^{2}[/tex]

      [tex]a^{2} = 400 - 196\\a^{2} = 204[/tex]

      [tex]a = \sqrt{204}[/tex]

       [tex]a = 14.28[/tex]

Answer: -3x^3-28x^2-x+14

Step-by-step explanation:

(3x-2)(-x^2-10x-7)

1: We would usually use the FOIL method, but since we don't have binomials we are going to start with the first number in our problem.

3x x -x^2=-3x^3

3x x -10x= -30x^2

3x x -7= -21x

-2 x -x^2=2x^2

-2 x -10x= 20x

-2 x -7=14

2. Add like terms

-3x^3-28x^2-x+14

Exact solution are - 1.2, -1, -0.1, 0.75 and approximate solution are -0.012, -0.01, -0.001, 0.0075.

The solution that has no uncertainly is known as exact solution. On the other hand, the solution that has some confusion is termed as approximate solution.

exact solution, y = - 1.2

                         m = - 1

                       n= - 0.1

                      w = 0.75

approximate solution in nearest hundredth,

                          y = - 0.012

                       m = -0.01

                      n = - 0.001

                   w = 0.0075

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Therefore , the solution of the given problem of unitary method comes out to be $54.

A single or distinct unit variable is referred to as being "unitary". Therefore, the goal of this technique is to define values in favor of a finite unit. For instance, the unitary method can be used to calculate how many kilometers a car will travel on one litre of gas if it goes 44 on two.

Here,

Given :

In place of every two sugar cookies, Natalie orders five chocolate chip cookies.

In total, she needs 42 cookies. Each sugar cookie costs $0.75, while each chocolate chip cookie costs $1.50.

thus ,

total cost is : 30 * 1.50 + 0.75*12

=> 54

Therefore , the solution of the given problem of unitary method comes out to be $54.

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The measure of 100 inches is given by the equations ,

100 inches = 2.77778 yards

100 inches = 8.33334 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 100 inches   be equation (1)

Now , the measure of 1 inch = 0.08333 feet

So , the measure of 100 inches = 100 x measure of 1 inch

Substituting the values in the equation , we get

The measure of 100 inches = 8.33334 feet

And , 1 inch = 0.0277778 yard

So , the measure of 100 inches = 2.77778 yards

Hence , the measure of 100 inches is 8.33334 feet

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Answer: $1.31

Step-by-step explanation:

if you use todays cast

The lowest price that would yield a profit of 35% is 1.18.

A product is sold at a profit if the price is higher than the cost price. When a product is sold for less than what it costs to produce, the seller suffers a loss.

Each bag contains 150g of sweets.

The total number of bags filled with a total of 3kg sweets can be calculated as follows:

3kg = 3000g

Number of bags = [tex]\frac{3000}{150}[/tex] = 20 bags

Profit is given by the following formula:

[tex]P= \frac{SP - CP }{CP} * 100[/tex]

The Cost price, CP = 17.60 and profit is 35%, substitute the value in the formula above:

[tex]35 = \frac{SP - 17.60}{17.60} *100\\ \\\frac{(35)(17.60)}{100} = SP - 17.60\\\\6.16 = SP -17.60\\\\6.16 + 17.60 = SP\\\\SP= 23.76[/tex]

Find the cost of each 30 bags as follows:

[tex]1 \text { bag} = \frac{23.76}{20}\\ \\1 \text { bag} = 1.18[/tex]

Hence the lowest price that would yield a profit of 35% is 1.18.

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Determining the cause of the problem, characterizing the problem, identifying, prioritizing, and choosing potential solutions, as well as putting the solution into action, all have values of 83 for f.

-74 f = -6,142 ⇒ f = -6,142 / -74 ⇒f = 83 .

One-step equations can be solved using any one of the following four methods: adding, subtracting, multiplying, or dividing. Both sides of an equation will stay equal if the same integer is added to both sides. A mathematical expression should be evaluated according to a rule known as the order of operations.

The PEMDAS acronym can help us recall the following in that order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right). A balance scale is like an equation. The scale (or equation) will become out of balance if we add or subtract from one side. Mathematical equations must ALWAYS be balanced such that both sides are equal when the equation is completed.

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The quotient between the two fractions will give:

(4/6)÷(3/12) = 8/3

Here we want to find the quotient between the fractions 4/6 and 3/12.

The quotient between any two fractions a/b and c/d can be solved as:

(a/b)÷(c/d) = (a*d)/(b*c)

Then our quotient can be solved in the following way as:

(4/6)÷(3/12) = (4*12)/(3*6)

(4*12)/(3*6) = (48/18)

Now we can simplify that fraction, if we divide both numerator and denominator by 2, we will get:

24/9

Now we can divide both by 3, then we will get the simplified fraction:

8/3.

That is the correct answer.

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Answer: The answer is 2 2/3

Step-by-step explanation:  I got it right on edge

Answer:

6.8125

Step-by-step explanation:

i goggled itttttt

Answer:

9,600/75,000, 16/125

Step-by-step explanation:

art+science=75000

9600

75000    =16/125

Answer:

Step-by-step explanation:

You want the price of a bagel and a can of OJ if 2 bagels and 1 can costs $8, and 3 bagels and 2 cans cost $13.

You can write an equation for the value of each purchase. The cost of a bagel can be represented by 'b', and 'j' can be used for the cost of an orange juice.

The coefficients of j are related by a factor of 2, so we can make the sum of coefficients of j be zero if we subtract the second equation from 2 times the first:

  2(2b +1j) -(3b +2j) = 2(8) -(13)

  b = 3 . . . . . . . . . . . . . . simplify

Now, we can use this value in the first equation to find j:

  2(3) +1j = 8

  1j = 2 . . . . . . . . . subtract 6

A bagel costs $3, and a can of orange juice costs $2.

The four steps in constructing a perpendicular bisector are follows.

Find the midpoint of the line segment: To find the midpoint of a line segment, take the average of the x coordinates and the average of the y coordinates. This can be written as a formula: M(x,y) = (x1 + x2/2, y1 + y2/2).

Find the slope of the line: To find the slope of the perpendicular bisector, take the negative reciprocal of the original line segment’s slope. This can be written as a formula: m = -1/m1, where m1 is the original line segment’s slope.

Find the equation of the line: To find the equation of the perpendicular bisector, plug in the slope and midpoint into the point-slope form of a line equation. This can be written as a formula: y – y1 = m(x – x1).

Construct the perpendicular bisector: To construct the perpendicular bisector, draw the line corresponding to the equation found in step 3. The line should be perpendicular to the original line segment, and should pass through the midpoint.

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The percent error for the given actual and estimated age of the fossils discovered by the researcher is equal to 11.11%.

As given in the question,

Actual estimated age of the fossil =3200 year old

Expected age discovered by the researcher of the fossil = 3600 year old

Formula for percent error is given by :

Percent error = | ( Actual age - Expected age ) / (Expected age) | × 100

Substitute the values we get,

Percent error = | ( 3200 - 3600 )/ 3600 | × 100

⇒ Percent error = 0.111111 × 100

⇒ Percent error = 11.11 %

Therefore, the percent error of the fossil discovered by the researcher is given by 11.11%.

The above question is incomplete , the complete question is :

A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating, a procedure used to determine the age of an object, the researcher discovers that the fossil is 3600 years old.

Find the percent error?

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As consumerism is wiping out American society, Sasse claims that young people have based their achievements and achievements on material goods.

He said parents influenced this by creating a population of young people who are empty in spirit and who will lead American society to grow without direction and positioning.

To support this claim, he provides details on how the country did not encouraged the children to have experiences, conquer and walk their paths, thereby resisting consumerism and presenting the rewards of hard work.

What is the central idea of the Vanishing American Adult?

Sasse tried to explore the causes of a generation that can't grow up in "The Vanishing American Adult" and offers a path for raising children to be active and engaged citizens.

He identifies core formative experiences that all young people should pursue: hard work to appreciate the benefits of labor, travel to understand deprivation and want, the power of reading, the importance of nurturing your body, and how parents can encourage them, and explains how they can be encouraged.

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The value of c would be 4.

What are similar triangles?

Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, the angles of similar triangles are congruent (congruent means the angles are equal in measure) and the corresponding sides are in proportion.

In the given figure, ΔGHF and ΔGDE,

∠G ≅ ∠G ---- Common angle

Side GH ≅ Side GH ---- Corresponding side

∠F ≅ ∠E -----Each 90°

so ΔGHF ~ ΔGDE-----ASA Test

sides of similar triangles are in proportion

GH/HF = GD/DE

5/c=10/8

c=5*8/10

c = 4

Hence, the value of c would be 4.

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If seven pound of fertilizer can cover 1400 square feet, 2 pounds of fertilizer can cover 400 square feet.

Therefore the answer is 400 square feet.

If seven pounds of fertilizer can cover 1400 square feet, we can set up the following proportion:

7 pounds / 1400 square feet = x pounds / y square feet

So y square feet = ( x pounds × 1400 square feet) / 7 pounds

To find out how many square feet can be covered by 2 pounds of fertilizer, we can solve for y by substituting in 2 for x:

y square feet = ( 2 pounds × 1400 square feet) / 7 pounds

y square feet = 2 × 1400 / 7

y square feet = 2800 / 7

y square feet = 400

So 2 pounds of fertilizer can cover 400 square feet.

--The question is incomplete, complete question is given below--

"Seven pound of fertilizer can cover 1400 square feet. How many square feet can be covered by 2 pound of fertilizer?"

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The aspect ratio is the proportional connection between the width of a video image compared to its height. It is usually expressed as width: height (separated by a colon), such as 16:9 or 4:3. The aspect ratio sets how wide a video is formatted and acts on how it will fit on your viewing screen.

When it comes to shooting video, the aspect ratio is tied to what resolution the camera records the image size in, with most DSLRs recording in a 16:9 aspect ratio.

The most popular aspect ratios for videos on the web are:

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As a result, the answer to the provided equation problem is 1.39500 profit and 2.400 loss.

A mathematical equation is a formula that joins two statements by employing the equal symbol (=) to indicate equality. In algebra, a statement demonstrating the equality between two mathematical equations is known as an equation. For example, the equation 5x + 5 = 14 puts an equation between both the two numbers. Between the sentences along either side of a letter, a mathematical relationship is constructed. Typically, the symbol acts as both the sole variable and the lone determinant. As an illustration, 8x - 4 = 2.

Here,

A C number of vehicles

Monthly expenses are subtracted from total monthly income to determine profit.

=> (25-6)C - (23500-6000) (23500-6000) (23500-6000)

=> P = 19C-17500

3000 autos need to be maintained,

Earnings are 19(3000)-17500.

Gain: $39500

If 900 automobiles are received in a given month, a profit or loss will result.

Earnings are 19(900)-17500.

Gain: -400.

Yes, a loss.

The solution to the given equation's issue is thus 1.39500 profit and 2.400 loss.

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The 4 steps to solve an equation:

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On solving the question, The polynomial is 2x + 3 the equivalent forms are (4x- 2x + 3), (x + x +2 +1)

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

The polynomial is 2x + 3

The equivalent forms are (4x- 2x + 3), (x + x +2 +1)

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Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1.

Answer:One

Step-by-step explanation:

Answer:

I can't comment, but we can't see what we are supposwd to bw doing

The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.

The Latin word "nomen," which also appears in words like "nominate" and "nomenclature," is the root of the English word "denominator," which means "name." And that's essentially what a fraction's denominator does: it "names" or denotes the kind of fraction that is specified by the numerator (the top part).

step1

{y + [(y - 3)/3]}/(5/9 + 2/3y)

multiply and divide with ‘9y'

9y/9y.{y + [(y - 3)/3]}/(5/9 + 2/3y)

9y.y + 9y.y - 3/3 / 9y(5/9) + 9y(2/3y)

9y.y + 3y(y - 3) / 9y(5/9) + 9y(2/3y)

9y.y + 3y(y - 3) / y.5 + 9y.2/3y

9y2 +3y2 -9y / 5y +6

12y2 - 9y / 5y + 6

The denominator will be 5y + 6

step2

The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.

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To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.

We can see that

[tex]4/(n + 5n^2) < = An < = (4 + 3n^2)/(n + 5n^2)[/tex]

As n tends to infinity, [tex]4/(n + 5n^2)[/tex]  tends to 0 and[tex](4 + 3n^2)/(n + 5n^2)[/tex]  tends to[tex]4/(5n^2)[/tex]  which also tends to 0.

So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0

We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.

Therefore, the sequence converges to 0.

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Answer: your answer is 2:6 or 1:3 simplified

The ratio to represent the relationship between hallies donation of jean and Mattie's donation of jeans is 2:6

2:6 simplified is 1:3

Step-by-step explanation: Hope this helps!! :)))

Answer: - 15x

Step-by-step explanation:

Solving the provided questions, we can say that the exponential growth for the provided data will be 11.

The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.

the growth rate will be

n(3) = [tex]85e^{0.l8(3)}[/tex]

n(3) = 145.86

[tex]85e^{0.l8(t)} = 600\\e^{0.l8(t)} = 7.059\\ln[e^{0.l8(t)}] = ln[7.059]\\0.18(t) = ln[7.059]\\\\t = 10.86 = 11[/tex]

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The type of function which f(x)=x^3 is the cubic function.

What is a cubic function?

A cubic function is a function in mathematics where the variables x can take on real values and the coefficients a, b, c, and d are complex numbers. In other words, it is a real function as well as a polynomial function of degree three.

F(x) = x³ denotes the "basic" cubic function. It is depicted in the graph below. The greatest power over the x variable(s) in a cubic function is 3. The graph can be made "wider" or "skinnier" by the coefficient "a," or it can be reflected (if the value is negative): The graph's y-intercept serves as the constant "d" in the equation.

A cubic function equation is of the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants (or real numbers) and a ≠ 0.

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