Eden is working on an experiment for her science fair project. She is planting a total of 10 herbs for an herb garden. She is going to plant basil and mint. The basil plants cost $.50 per plant and the mint plants cost $.25 per plant. Eden has a total of $3 to spend on plants because she also has to purchase potting soil and a long planter pot. Write a system of equations and solve either using elimination or substitution.

Answer: x=-6

Step-by-step explanation:

[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]

Answer:

Step-by-step explanation:

We have:

2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)

2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)

2^(2x-1) x 2^-3+3x = 2^6x+2

2^5x-4 = 2^6x+2

on comparing both sides we get :

5x-4 = 6x +2

x = -6

Teaching two step equations is a standard that needs to be taught in both 7th and 8th grade middle school PreAlgebra Math.

Two step equations are algebraic equations that can be solved in exactly two steps and gives the final answer of the variable in two steps. Generally two step equations are of the form ax + b = 0  where a and b are real numbers.

A two-step equation is an equation that requires two steps to solve. We must eliminate any constant that is on the same side as the variable first. To solve first use the inverse operations to isolate the variable by itself. We can do only one operation in single step.

Now

we solve two steps equation in grade 7th and 8th.It is very easy to understand.

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Answer:

y = -3x + 12.96

y = [tex]\frac{-4}{3}[/tex] x + 11.31

Step-by-step explanation:

6x + 2y = 25.92  Subtract 6x from both sides

2y = -6x + 25.92  Divide all the way through by 2

y = -3x + 12.96

4x + 3y = 33.93  Subtract 4x from both sides

3y = -4x + 33.93  Divide all the way through by 3

y = [tex]\frac{-4}{3}[/tex] x + 11.31

y = 3x+4 ← equation of linear function.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have,

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = y_2-y_1/x_2-x_1

with (x₁, y₁ ) = (- 3, - 5) and (x₂, y₂ ) = (1, 7) ← 2 ordered pairs from the table

m = 7+5/1+3

  =12/4

   = 3 ,

So, y = 3x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (1, 7 ), we get,

7= 3 + c

⇒ c = 7-3

      = 4

Hence, y = 3x+4 ← equation of linear function

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Answer:

cos(2x)

Step-by-step explanation:

To simplify the expression cos²x - sin²x, we can use the identity cos²x - sin²x = cos(2x).

This identity can be derived by using the double angle formula for cosine:

cos(2x) = cos(x + x) = cos(x)cos(x) - sin(x)sin(x) = cos²x - sin²x

Therefore, the expression cos²x - sin²x can be simplified to cos(2x).

The frequency table for the given data is shown above.

A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.

Given is the age of people waiting in line for a movie as -

12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8

Arrange the data in ascending order -

6, 6, 8, 10, 12, 15, 27, 31, 45, 49, 55, 65

INTERVALS                      FREQUENCY

0 - 10                                       4  

11 - 20                                      2  

21 - 30                                     1

31 - 40                                     1

41 - 50                                     2

51 - 60                                     1

61 - 70                                      1

Therefore, the frequency table for the given data is shown above.

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The amount luke made more than alexa is $3.91 .

What is simple interest ?

simple interest can be defined as the ratio of product of principal amount , rate and time and 100.

Luke investment,

This is compound interest so the future value formula will be used:

= Amount * ( 1 + rate) ^ no. of years

= 4,000 * ( 1 + 1.8%)³

= $4,219.91

Alexa investment:

Simple interest is calculated with the formula:

= Amount * ( 1 + rate * time)

= 4,000 * ( 1 + 1.8% * 3)

= $4,216

Amount Luke made more than Alexa:

= 4,219.91 - 4,216

= $3.91

Hence , The amount luke made more than alexa is $3.91 .

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Answer: 35

Step-by-step explanation:

So first you plug 5 into the equation which is:

10(5)-15

which is 50-15

50-15 is 35

Answer:

35

Step-by-step explanation:

plug 5 in for x and u will get 35

On solving the question, by linear equation One bagel is 100*1.55 = 155 cents in dollars.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept.

A toast costs =  x dollars.

A bagel costs  = y dollars.

A muffin costs = z dollars.

It costs $3.15 for two pieces of toast and a bagel.

As a result, 2x + y = 3.15. To get the price of a bagel, we express x as a function of y,

2x = 3.15 —Y

x = -o.5y+ 1.575

It costs $3.30 for a bagel and a muffin.

Since x and z are functions of y,

—0.5y + 1.575 + + 3(3.3 — y) 9.15

—0.5y + 1.575 +2y + 9.9—3y = 9.15

—1.5y + 11.475 = 9.15

1.5y = 2.325

2.325

Y = 1.55

One bagel is 100*1.55 = 155 cents in dollars.

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The cost of one ticket in Virginia is $8

A System of Linear Equations is when we have two or more linear equations working together.

Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.

To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,

Let V represents the cost in Virginia that of in Maryland be M

Therefore,

4v+5m = 77.......(i)

8v+3m = 91........(ii)

Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]

(8v+10m = 154)  - (8v+3m = 91)

7m = 63

m = 9

Put m = 9 in eq(i)

4v+5(9) = 77

4v = 77-45

4v = 32

v = 8

Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.

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Therefore , the solution of the given problem of equation comes out to bem² + p² =z².

The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.

Here,

Given : a triangle of m,p,z of length of right triangle :

By using Pythagoras theorem :

The relationship comes out to be :

=> m² + p² =z²

Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.

Therefore , the solution of the given problem of equation comes out to be m² + p² =z².

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Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.

Here,

given  :

An aircraft is being followed by two radar stations, which are 4.3 miles apart.

Station A is 9.6 miles away from the plane in a straight line.

Thus,

To find the angle of elevation  from station A to plane :

Using Trigonometric ratios:

=> Sin A  = 8.5 / 9.6

=> Sin A = 85/96

=> A =  [tex]Sin^{-1}[/tex](85/96 )

=> A = 62.302840124651483 °

=> A = 62.3°

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

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Answer:

44 minutes

Step-by-step explanation:

Kiran reads 5 pages in 20 minutes, if we divide we will know that he reads 1 page in 4 minutes.

Multiply 4 by 11 to find out how long it will take him to read 11 pages.

11 times 4 = 44

It will take Kiran 44 minutes to read 11 pages.

So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).

Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.

(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80

Solving for x, we can get the amount of OMT powder in grams:

x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600

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Answer:

  4.6 km

Step-by-step explanation:

You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.

The distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.

  c² = a² + b²

  5² = 2² + b²

  21 = b²

  b = √21 ≈ 4.583

Santos walked about 4.6 km east.

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C) there is a 5% probability of rejecting a false null hypothesis

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.

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When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.

A number is itself divisible by nine if the total of its digits is also divisible by nine.

Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine without remainder.

By utilizing the aforementioned attribute, we can

1 + 3 + 4 + 5 = 9, 18, or 27.

4 +2A = 9, OR 18, OR 27

calculating based on sum equal to 18

2A = 18 - 4

2A = 14

A = 7

therefore 3771 is the number

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Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

Let the quantity of sold laptops, x

y —- the quantity of sold smartphones

The fact that to solve this problem we use inequality help

The problem's underlying inequity is equal to

=> 80x + 60y ≥6800

Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.

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Answer:

2:16

Step-by-step explanation:

maybe i don't know im not smart but that is the ratio equalivent i guess i have to make this 20 words long soooo

Answer:

To find the number that makes the ratio equivalent to 1:8, we need to set up the ratio as a fraction and solve for the missing value.

The ratio 1:8 can be written as the fraction 1/8. In this case, the missing value is the numerator (1) and the known value is the denominator (8). To solve for the missing value, we can multiply both the numerator and denominator by the same value.

For example, if we multiply both the numerator and denominator by 2, we have:

1/8 = (12)/(82) = 2/16

If we multiply both the numerator and denominator by 4, we have:

1/8 = (14)/(84) = 4/32

If we multiply both the numerator and denominator by 5, we have:

1/8 = (15)/(85) = 5/40

In each of these cases, the ratio is still equivalent to 1:8, but the missing value (the numerator) is different. In general, we can multiply the numerator and denominator by any value to find the missing number that makes the ratio equivalent to 1:8.

For example, if we multiply both the numerator and denominator by 10, we have:

1/8 = (110)/(810) = 10/80

In this case, the missing value (the numerator) is 10, which makes the ratio equivalent to 1:8.

Step-by-step explanation:

The solid that can produce the given two-dimensional shape when sliced vertically is option 2.

When we examine anything vertically, we see it from top to bottom. When something is standing, it is referred to as the alignment.

When we examine objects horizontally, we do it from left to right. When anything is in the sleeping posture, it is known as the alignment.

The given shape is a rectangle. When the rectangular prism is sliced in a vertical manner the solid will represent the given shape that is a rectangle.

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Answer:

55

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

18*1=18

18*2=36

In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm then the radiu of the circumcircle is 39

A chord is the line segment joining two points of the circumference of a circle as shown in the image attached.

If the chord is passing through the center of the circle then it will become diameter which means the diameter is the longest possible chord inside a circle.

A chord is always within the circumference because it is inside the circle.

Whats the definition of a circumference?

a line that goes around or encloses a circle. : the outer boundary of a figure or area. 3. : the distance around something. the circumference of the earth at the equator.

since ABC is an equilateral triangle

therefore SD bisects BC

BD= BC/2

BD= 36

IN Triangle ABC

since angle BDS = 90 degree

Therefore

BS = 39

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Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6 8 = 20x x = 8/20, simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar

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 is -

1200=300+5x

900 = 5x

x=180

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Answer:

help u with  what

Step-by-step explanation:

The 8-year-old car could be worth approximately $3000.

The graphs that show the association between two variables in a data collection are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.

The X-axis is used to represent the independent variable or characteristic, while the Y-axis is used to plot the dependent variable. These diagrams or graphs are frequently used to describe these plots.

In the graph attached below, we can see that when the age of the car is 8 years, the resale value of the car is between points 40 and 20.

Thus, The 8-year-old car could be worth approximately $3000.

(Refer to the image attached for the complete question and graph)

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The example of a proportion, is An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

The term proportionality describes any relationship that is always in the same ratio.

Given are some statements,

a) A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 miles in a town.

Solution:- In this case, we see, a car is using 3 and 4 gallons of gas for driving in a highway and in a town for 72 miles respectively.

Since, the distance is same and quantity of gases is different therefore, this can not be represented as a proportion.

b) A store charged $20 for 2 shirts and charged $25 for 3 shirts.

Solution:- In this, let's first find the unit prices for each,

for $20 there are 2 shirts, therefore, for 1 shirt it will be $10, and for 3 shirts it costs $25, therefore, for 1 shirt it will cost $8.3

Since, unit price for both is not equal, therefore, this can not be represented as a proportion.

c) A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.

Solution:- As in 2nd option, will here also find unit rate, since, yellow light is flashing 7 times in 28 seconds, therefore, in 4 seconds it will be flashed for 1 time, similarly, red  light is flashing 5 times in 35 seconds, therefore, in 7 seconds it will be flashed for 1 time,

Since, both unit rates are not equal, therefore, this can not be represented as a proportion.

d) An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

Solution:- Again we will find unit rate, since, the alarm is beeping 7 times in 6 seconds, therefore, it will beep for 1 time in 6/7 seconds, similarly, it is beeping 14 times in 12 seconds, so for 1 time it will beep in 12/14 = 6/7 seconds.

Here, we see that, both the unit rates are equal, therefore, this is an example of a proportion.

Hence, the last option is the correct example.

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Answer:

   - A bag of rice is $16.9

   - A bag of flour is $5.20

Step-by-step explanation:

Let R and F stand for the price of a bag of Rice and Flour, respectively.

We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)

A) 4R + 2F = 78   [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.

B)  3R + 4F = 71.5  [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50

We have 2 equations and 2 unknowns.  We can use substitution to find the answers.  Take one of the equations and reorganize it to isolate one of the variables (R or F).  We'll take the equation for A and isolate F

---

A) 4R + 2F = 78

     2F = 78-4R      [subtract 4R from both sides]

       F = 39-2R      [divide both sides by 2]

We've isolated F, and we can use this definition of F in the second equation:

===

B)  3R + 4F = 71.5

3R + 4(39 - 2R) = 71.5  [Use the definition of F derived above.  In this manner, we have legally eliminated one of the two variables.  (Sneaky, effective, and fun)]

3R + 156 - 8R = 71.5   [Multiply, combine like terms, and simplify]

-5R = -84.5                  [Isolate R]

R = $16.9                      A bag of rice costs $16.9

Now use the price of rice (R=$16.9) in one of the equations.  Since the rearranged equation we used above is already conveniently written for F, we'll use it:

F = 39 - 2R

F = 39 - 2(16.9)

F = 39 - 33.8

F = $5.20                     A bag of flour costs $5.20

===

CHECK:

Do these two prices satisfy both equations we first formulated?

Restaurant A:  4R + 2F = 78?

                        4(16.9) + 2(5.20) = 78  YES

Restaurant B:  3R + 4F = 71.5?

                        3(16.9) + 4(5.20) = 71.5  YES

These are the correct answers.

The total number of cookies baker sold in all are 350 cookies.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.

Let the total number of cookies be x.

Now, 38% of x=133

38/100 ×x=133

x=13300/38

x=350

Therefore, the total number of cookies baker sold in all are 350 cookies.

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