The quadratic formula is an algebraic formula that provides the solutions to a quadratic equation. A quadratic equation is an equation of the shape ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula gives the values of x that satisfy the equation and is expressed as:
x = (-b ± √ (b^2 - 4ac)) / (2a)
In other words, the quadratic formula provides a method for finding the two roots of a quadratic equation, even if the equation cannot be solved by factoring or other methods.
The formula works for all quadratic equations and is a widely used tool in mathematics and various scientific and engineering fields.
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Tonya i nine year younger than twice Marty’ age. Danielle i two year older than Tonya. The um of the age of the three ibling can be expreed a 3M 8 where M repreent Marty’ age. How old i Marty?
Marty is 21 years old. Translated the problem statement into mathematical expressions and then used algebraic manipulation to solve for the unknown variable, which in this case is Marty's age (M).
Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. It is used to study mathematical relationships and properties, and to solve problems using mathematical models. Algebraic equations involve one or more variables (often represented by letters such as x, y, or z) that represent unknown values.
Let M be Marty's age.
According to the problem statement, Tonya is 9 years younger than twice Marty's age, so 2M - 9 = T (where T is Tonya's age).
Danielle is 2 years older than Tonya, so T + 2 = D (where D is Danielle's age).
We know that the sum of the three siblings' ages can be expressed as 3M + 8.
So, we can set up the following equation:
M + (2M - 9) + (2M - 9 + 2) = 3M + 8
Solving for M, we get:
M = 21
Therefore, Marty is 21 years old.
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3 IS A
√
RATIONAL
NUMBER? PLEASE
EXPLAIN
CLEARLY WHY IT
EITHER IS OR
ISN'T.
Answer:
The square root of 3 is an irrational number
Step-by-step explanation:
A rational number is defined as a number that can be expressed as the division of two integers, i.e. p/q. where q is not zero.
√3 = 1.7320508075688772...and keeps getting longer. √3 is an irrational number because the decimal point does not end or repeat.
What is the gradient of y =- 3x 1?.
So, the gradient of y = -3x^1 is -3.
The gradient of a function y = f(x) with respect to x is the derivative of the function with respect to x, denoted by dy/dx or f'(x).
In the case of y = -3x^1, the gradient is -3.
It is a constant function, thus, the slope is always the same and equal to the coefficient of the x term, which in this case is -3.
The gradient of a function tells us the rate of change of the function with respect to x. In other words, it tells us how steep the function is at any given point. A positive gradient means that the function is increasing, while a negative gradient means that the function is decreasing.
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a) Fill in the gap to make the statement true: Even numbers are numbers that are divisible by b) 2 is the only even prime number. Write a sentence to explain why this is true.
a. Even numbers are numbers that are divisible by 2
b. prime number is the number that has two factors by 1 and itself, all even numbers are divisible by 2 hence any other even number aside 2 will be divisible by 1, 2 and itself and this does not define a prime number any more
What is prime number?A prime number is a positive integer greater than 1 that is only divisible by 1 and itself. In other words, a prime number has exactly two positive integer divisors: 1 and itself.
For example, the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and so on. The number 2 is the only even prime number, and all the other prime numbers are odd.
Prime numbers are important in mathematics because they play a crucial role in various fields such as number theory, cryptography, and coding theory. They are also used as basic building blocks for constructing larger composite numbers.
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Jayden i making frozen dog treat for hi puppy Spot. He mixe 1 quart of yogurt, 10 fluid ounce of peanut butter, and 6 fluid ounce of honey. Then, he freeze the mixture in ice cube tray. Each tray hold 16 fluid ounce of treat. How many tray of dog treat doe Jayden make?
Jayden makes 3 trays of dog treats for his puppy Spot
What is unit conversion?It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.
To solve this problem, we have to do the conversion of units with the given information:
Information about the problem:
Yogurt = 1 quartPeanut butter = 10 ouncesHoney = 6 ouncesTray capacity = 16 ounces/ trayNo. trays = ?1 quart is equal to 32 ouncesBy converting the unit from quart to ounce, we have:
1 quart * (32 ounce / 1 quart) = 32 ounce
Calculating the total of ingredients Jayden mixed we have:
Total ounces = Yogurt + peanut butter + honey
Total ounces = 32 ounces + 10 ounces + 6 ounces
Total ounces = 48 ounces
Calculating the number of tray that Jayden can make we have:
No. trays = Total ounces / tray capacity
No. trays = 48 ounces / 16 ounces/ tray
No. trays = 3 trays
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what is the solution to the system or equations graphed below?
y = -3/2 x + 2 y = 5x = 28
A. (-4,8)
B.(4,8)
C.(-8,4)
D.(0,2)
Answer:
It is A im preety sure
Step-by-step explanation:
very sorry if im wrong but im almost possitive its A
4. If a and b are the acute angles of a right triangle and sec a = 3/2, find the six trig function of b
sin b=
cos b=
tan b=
ctn b =
sec b =
csc b=
Sin b=4/5 cos b=3/5 tan b=4/3 ctn b=3/4 sec b=5/3 csc b=5/4
What is trigonometric functions?The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecanIn mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many othersTrigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, functions, identities, and formulas to solve problems based on it, especially for right-angled triangletrigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).To learn more about trigonometric functions refers to:
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State the postulate or theorem that can be used to prove the triangles congruent.If you cannot prove the triangles congruent, write not enough information.
To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.
What are the postulates?The postulates are:
SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.
ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.
SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.
AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.
HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.
From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.
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What is the slope intercept form of the following equation − 6x − 2y − 18?.
The slope intercept form of the following equation 6x - 2y = 18 is y = 3x - 9
We knwo that the slope intercept form of equation of line is y = mx + b, where m is the slope and b is the y-intercept.
Consider given equation,
6x - 2y = 18
6x - 2y - 6x = 18 - 6x .......(Subtract 6x from each side)
- 2y = 18 - 6x
- 2y × (-1) = (18 - 6x) × (-1) ......(Multiply each side by -1)
2y = -18 + 6x
2y/2 = (-18 + 6x)/2 ..........(Divide each side by 2)
y = -18/2 + 6x/2
y = -9 + 3x
y = 3x - 9
This equation is in the form y = mx + b
Here, slope m = 3 and the y-intercept b = -9
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The complete question is:
What is the slope intercept form of the following equation 6x - 2y = 18?
A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.
better same worse
Republican 38 104 44
Democrat 12 87 137
none 21 90 118
Express each of your answers as a percent rounded to the nearest tenth (for example, 12.3%).
What percent of survey respondents identified themselves as affiliated with neither party?
____%
What percent of survey respondents thought the economy was about the same?
____%
What percent of those affiliated with neither party thought the economy was about the same?
____%
Among survey respondents who thought the economy was about the same, what percent were affiliated with neither party?
____%
The percentages for this problem are given as follows:
Neither: 35.2%.Economy about the same: 43.2%.Economy about the same, neither: 39.3%.Neither, economy about the same: 32%.How to obtain the percentages?The percentages are obtained applying proportions, as a percentage is the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.
651 adults were surveyed, of which 21 + 90 + 118 = 229 were affiliated with neither party, hence the percentage is of:
229/651 x 100% = 35.2%.
104 + 87 + 90 = 281 said that the economy was about the same, hence the percentage is of:
281/651 = 43.2%.
90 people out of the 229 that were unaffiliated felt that the economy was the same, hence:
90/229 x 100% = 39.3%.
Of the 104 + 87 + 90 = 281 people that thought that the economy is about the same, 90 were affiliated with neither part, hence:
90/281 = 32%.
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A new roller coaster just opened at Friday Fun Park. When Lisa got in line, a sign said the wait from that point would be 45 minutes. The actual wait was only 35 minutes. What is the percent error for the park sign's estimate? If necessary, round your answer to the nearest tenth of a percent.
Answer:
28.6%
Step-by-step explanation:
10 minute difference, 10 is 28.6% of 35.
Zoe and Hannah hare tip in the ratio of 3:7, lat week Zoe recieved £24
How much did Hannah receive lat week?
Answer:
£56
Step-by-step explanation:
We know
The ratio Zoe and Hannah hare tip is
3:7
last week Zoe received £24
To find out how much did Hannah receive last week, we first take
24 / 3 = 8
Then we take
8 times 7 = £56
So, last wee Hannah receive £56
diagram shows a sphere and a cone
the cone has height h cm
the radius of the base of the cone is 3 times the radius of the sphere
given that volume is equal to the volume of the cone find an expression of the radius of the sphere in terms of h
give your expression in the simplest form
An expression of the radius of the sphere in terms of h is; h = ⁴/₃r
How to find the volume of the sphere?We are given;
Height of cone = h
Radius of cone = 3r
Radius of sphere = r
Volume of cone = Volume of sphere
Now, formula for Volume of cone = ¹/₃πr²h = ¹/₃π(3r)²h = 3πr²h
Volume of sphere = ⁴/₃πr³
Thus;
3πr²h = ⁴/₃πr³
Multiply both sides by 3/πr² to get;
9h = 12r
h = ⁴/₃r
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For each function, 1) find the inverse (if it exists), 2) find the domain and range for both f and f^-1
1) y=1/5^(1-x)+2
2)1-5^x/5^(x-1)
3)y=log1/5(x+1/2)-1
Answer:
1. y = 1/5^(1-x) + 2
The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.
So, x = 1/5^(1-y) + 2
To find the inverse, we need to solve for y:
y = 1 - log(5, x-2)
Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.
The domain of f is all x such that x > 2. And the range of f is all y such that y > 2. The domain of f^-1 is all x such that x > 2 and the range of f^-1 is all y such that y > 1.
----------------------------------------------------------
2. 1 - 5^x/5^(x-1)
The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.
So, x = 1 - 5^y/5^(y-1)
To find the inverse, we need to solve for y:
y = log(5, 1/(x+1)) + 1
Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.
The domain of f is all x such that x < 1. And the range of f is all y such that 0 < y < 1. The domain of f^-1 is all x such that x < 1 and the range of f^-1 is all y such that y > 1.
--------------------------------------------------------------
3. y = log1/5(x+1/2)-1
The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.
So, x = log1/5(y+1) - 1/2
To find the inverse, we need to solve for y:
y = 5^(x+1/2) - 1
Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.
The domain of f is all x such that x exists. And the range of f is all y such that y > -1. The domain of f^-1 is all x such that x exists and the range of f^-1 is all y such that y > 0.
-----------------------------------------------------------------
In summary,
1. f^-1(x) = 1 - log(5, x-2) Domain: x>2, Range: y>2.
2. f^-1(x) = log(5, 1/(x+1)) + 1 Domain: x<1, Range: 0<y<1.
3. f^-1(x) = 5^(x+1/2) - 1 Domain: x exists, Range: y>-1.
The table shows the depths of four plants. Order the numbers form least to greatest
Answer:
sea grass red algae green seaweed mangrove or -20 3/4, -15 1/2, -14 3/4, -1/4
Step-by-step explanation:
negatives switch around the rules of positive so the one with the number tat is bigger when not negative is the lowest when negative
When P x )= x³ 3x² 4x 32 is divided by x 2 The remainder is?.
When P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.
In the given question, when P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then we have to find the remainder.
The given equation is
P(x) = [tex]x^3-3x^2+4x+32[/tex]
We have to divide this equation by x+2.
To find the remainder we firstly equate x + 2 equal to zero to find the value of x.
x + 2 = 0
Subtract 2 on both side, we get
x = -2
Now we put x value in the given equation to find the remainder.
The equation
P(x) = [tex]x^3-3x^2+4x+32[/tex]
Put x = -2
P(x) = [tex](-2)^3-3(-2)^2+4(-2)+32[/tex]
Simplify
P(x) = -8 - 3×4 + (-8) + 32
P(x) = -8 - 12 - 8 + 32
P(x) = 4
Hence, when P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.
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The complete question is:
When P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2. The remainder is?
2.
Recall that Stella is the pacesetter the 4:10
pace group of a marathon and is required to
finish within 2 minutes of the pace time.
Stella must run between
minutes and
meet the requirement.
minutes in order to
Stella must run between 248 minutes and 252 minutes in order to meet the requirement.
What is the time-to-minute conversion?
As an hour consists of 60 minutes, we can convert hours into minutes by multiplying hour by 60. So, for example, if one wants to convert 3 hours into minutes, one can do it by multiplying 3 by sixty which will give 3 x 60 = 180 minutes.
To figure out the range of times within which Stella must finish the marathon in order to meet the requirement of finishing within 2 minutes of the 4:10 pace time,
we can use the following steps:
Convert the pace time of 4:10 to minutes.
Since there are 60 minutes in an hour, 4:10 is equal to 4 * 60 + 10 = 250 minutes.
Add 2 minutes to the pace time. Since Stella must finish within 2 minutes of the pace time, this gives us a finish time of 250 + 2 = 252 minutes.
Subtract 2 minutes from the pace time. Since Stella must finish within 2 minutes of the pace time, this gives us a finish time of 250 - 2 = 248 minutes.
The range of times within which Stella must finish the marathon in order to meet the requirement is 248 to 252 minutes.
Hence, Stella must run between 248 minutes and 252 minutes in order to meet the requirement.
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Please help yall!
What is the total sales for bicycles for store 1 and 2?
What is the total cost for bicycles for store 1 and 2?
What is the total profit for bicycles for store 1 and 2?
The total sales for bicycles for store 1 and 2 = 54 bicycles.
Thee total cost for bicycles for store 1 and 2= $7,530
The total profit for bicycles for store 1 and 2= $12,420
How to calculate the number of sales?The total sales for bicycles for store 1 and 2 can be calculated as thus;
Store 1 = 15+20 = 35
Store 2 = 10+9 = 19
Total sales for store 1 and 2 = 35+19 = 54
The total cost for bicycles for store 1 and 2=
Store 1 = 150×35= $5,250
Store 2 = 19× 120 = $2,280
The total cost for bicycles in both stores= $5,250+$2,280= $7,530.
The total profit for bicycles for store 1 and 2=
Store 1 = 230×35 = $8,050
Store 2 = 230×19 = $4,370
The total profit from both stores = $8,050+$4,370= $12,420.
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What is the solution to the equation 1 h 5 2 h 5?.
The solution to the equation 1 h 5 2 h 5 is 7.
In this case option A is correct
The solution can be obtained by following steps-
The given equation is the least common multiple of the denominators, which we multiply through to obtain, and then we eliminate common factors to obtain. Multiply 1 h5 1 h - 5 by h+5 h+5 h+5 h + 5 h + 5 to create a fraction with a common denominator. Multiply 2 h+5 by h+5 h+5 h- 5 h- 5 to get 2 h+5 written as a fraction with a common denominator.We group like terms to get, we expand the brackets to get, this simplifies to, we now divide through by three to get,
[tex]h+ 2h= 16-5+ 10\\3h= 21\\h=7[/tex]
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What is the solution to the equation 1 h 5 2 h 5?.
78903.8 liters= how many mL
A square floor is covered by a number of whole rectangular tiles of sides 54 cm by 30 cm such that a uniform margin of width 6 cm is left on a round the floor. calculate the least possible area of the floor giving me answer in square metres.
Answer: 7.9524 m^
Step-by-step explanation:
The square with the least area can only be formed when we take LCM of the dimensions of the rectangular tile I.e. 54 CM × 30 CM
LCM = 270
This means that a square of length 270 CM will be formed when we take least no. of tiles.
Also given in question, 6cm is left around the square that means 12cm is added on every side to make the floor with minimum area = 282 × 282 cm^2
minimum area = 79524 cm^
in m^2 = 79524/10000 = 7.9524 m^
4x+2y≥14 what is the y intercept?
The y-intercept of the line 4x + 2y ≥ 14 is y ≥ 7.
How to find y-intercept?The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a line is the value of y when x equals to zero.
In simpler term, the y-intercept of a function is the point(s) where the graph of the function crosses the y-axis.
Therefore, let's find the y-intercept of the inequality.
4x + 2y ≥ 14
let's substitute x as 0.
Therefore,
4x + 2y ≥ 14
4(0) + 2y ≥ 14
2y ≥ 14
divide both sides by 2
2y / 2 ≥ 14 / 2
Hence,
y ≥ 7
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3, -26, -1, -5, 4, 1, 3 Question 1 options: Either the Mean of the Median The Median Only The Mode Only
A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
How to explain the measure of deviation?MEAN =Sum of observations/Total number of observations.
MEDIAN= If n is odd, then the following formula is used: Value of (n+1/2th observation. If n is even, then the following formulae is used: {Value of (n/2) th observation + (n/2 +1)th observation/2}
MODE= Most number of times occurring value in the data
Note that your information wasn't properly written and a overview was given.
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How do you solve log base questions?.
The answer to the equation for the logarithm of 1 in base 7 is x=0, where x is the power to which 1 must be raised in order to obtain the value 7.
The definition of the logarithm function, which is the inverse of the exponential function and reads log b(x) = y, is by = x. To put it another way, it reflects the increment in base b that must be raised in order to obtain the value x.
When solving log 7(1), we are seeking the power to which 7 must be increased in order to obtain the value 1.
Since 1 is the result of raising any number to the power of 0, we may state that 70 = 1, which implies that log 7(1) = 0.
Finding the value of x that makes the equation log 7(x) = 1 true is necessary to solve log base 7 1.
Log b(x) = y signifies that b = y using the definition of a logarithm.
Therefore, we can put 1 = 7x and obtain x = log7(1) = 0 to solve log7(1).
So, x=0 is the answer to the logarithm in base 7 of 1.
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If cosine of x degrees equals three-fifths, what is the value of b?
triangle LMN in which angle M measures 90 degrees, angle L measures x degrees, LN measures 20 units, and LM measures 3b units
b = 4
b = 5
b = 6
b = 7
If cos x = 3/5 then the value of b = 4
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin(tetha) = opp/hyp
cos ( tetha) = adj/hyp
tan ( tetha) = opp/ adj
In the triangle adj = 3b and hyp = 20
cos x = 3b/20
cos x = 3/5
therefore 3/5 = 3b/20
multiply both sides by 20
3/5×20 = 3b/20 × 20
3b = 12
divide both sides by 3
b= 12/3 = 4
therefore the value of b is 4
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Answer:A: b = 4
Step-by-step explanation:
How tall will your hair be if its 3 inches and you make a mow Mohawk, and it gets another 1.5 inches how long your hair is.
We'll cut straight to it: On average, hair grows at a rate of about half an inch per month, or six inches per year. Each hair on your head grows from an individual follicle.
How tall will your hair be if its 3 inches and you make a mow Mohawk?We'll cut straight to it: On average, hair grows at a rate of about half an inch per month, or six inches per year. Each hair on your head grows from an individual follicle.
The average person's hair grows ½ an inch each month which sums up to 6 inches of growth per year.
For you I'd say maybe anywhere from 3 to 5 months it would be around the length you're looking for. It may take a year to get it to your shoulders.
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As societies exchange ideas, globalization is unable to keep up with the speed at which culture has spread. becomes more challenging at the speed that culture has spread. increases at the same speed at which culture has spread. is unaffected by the speed at which culture spreads.
Answer:
As societies exchange ideas, globalization is unable to keep up with the speed at which culture has spread.
Cameron want to download ome movie that cot $14. 50 and want an ebook that cot $22. 50. He ha $66 write and olve an equation that can be ued to find the number of movie he can download
Cameron can download 4 movies with his $66. He can solve an equation of 14.50x + 22.50y = 66 and x + y = 4
14.50x + 22.50y = 66
14.50x = 66 - 22.50y
14.50x = 43.50
x = 3 (43.50/14.50)
x + y = 4
3 + y = 4
y = 1
Cameron wants to download some movies and an ebook with his $66. To figure out how many movies he can download, he needs to solve an equation. The equation is 14.50x + 22.50y = 66, where x is the number of movies and y is the number of ebooks. By solving for x, he can figure out how many movies he can get, which is 3 (43.50/14.50). To find the number of ebooks, he can solve for y in the equation x + y = 4, which is 1. Therefore, Cameron can download 4 movies with his $66.
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QS is a midsegment of PRT
IF PT=x+67 and QS=x+27, what is the value of x?
The value of x is 13 if QS is a midsegment of PRT
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that QS is a midsegment of PRT
IF PT=x+67 and QS=x+27,
We need to find the value of x
From midsegment theorem we have
QS=1/2(PT)
x+27=1/2(x+67)
x+27=x/2+67/2
x-x/2=67/2-27
x/2=13/2
x=13
Hence, the value of x is 13 if QS is a midsegment of PRT
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What are the 4 lines of symmetry?.
The 4 lines of symmetry is square.
In math the imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
Here we need to find the 4 lines of symmetry.
As we all know that the line of symmetry is known as a balanced and proportionate similarity that is found in two halves of an object.
So, based on these definition, we have identified that A square has four lines of symmetry.
Because it can be folded in half over either diagonal or the horizontal segment which cuts the square in half or the vertical segment which cuts the square in half.
Therefore the square has four lines of symmetry.
To know more about line here.
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