35-55-90 is a right-angle triangle because one of the angles is 90 degrees.
The explanation for a right triangle says that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or simply, a right triangle.
The right triangle formula can be presented in the following way: The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
In a right triangle we have: (Hypotenuse)² = (Base)² + (Altitude)²
Properties of Right Triangle:
The largest angle is always 90º.The longest side is called the hypotenuse which is always the side opposite to the right angle.The measurements of the sides obey the Pythagoras rule.It cannot have any obtuse angle.Read more about the right-angle triangle:
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Please help!!!! I'LL GIVE 5 STAR RATING AND A THANKS
Answer:
9.1
Step-by-step explanation:
For the first one, I just multiplied 4.55 and 0.5 by 2 somthey are proportional. Or divide distance by time!
Is the interval 0 1 Infinite?
Therefore, the interval (0, 1) must be countless and infinite. Since the interval (0, 1) is as large as R, R is also infinite.
Interval:
In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing (0, 1), and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).
Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.
Open Interval:
Open intervals do not include endpoints and are indicated by parentheses. For example, (0, 1) means greater than 0 and less than 1. This is (0, 1) = {x | 0 This interval can also be expressed as ]0, 1[ . Please refer to the following.
Closed Interval:
A closed interval is an interval that contains all boundary points and is indicated by square brackets. For example, [0, 1] means greater than or equal to 0 and less than or equal to 1.
Half- Open Interval:
A half-open interval contains only one of its endpoints and is represented by a combination of open and closed interval notation. Example: (0, 1) means greater than 0 and less than or equal to 1, [0, 1) means greater than or equal to 0 and less than 1.
Complete Question:
II. Identify the following terms described in each item. Quantitative & Quaeritated. It can be separated into different categories that are distinguished by some nonnumeric characteristics. 2. It consists of numbers representing counts or measurements. Quantitative Quantitative 3. The result from either a finite number of possible values or countable number of possible values as 0, or 1, or 2, and so on 4. The result from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions 5. It is characterized by data that consist of names, labels, or categories only. 6. It involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. 7. It involves meaningful amounts of differences between data. It has no true zero point or absolute zero. 8. It contains all the properties of the interval level but has true zero point or absolute zero. 9. It is a complete collection of all elements to be studied. 10. It is a branch of Mathematics that deals with the collection, organization presentation, analysis, and interpretation of data.
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Using the numbers 4. 3, -1. 07, and -2. 971,write an expression containing both addition and subtraction that simplifies to a negative number
Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.
Define expression.An expression is made up of a number, a variable, or a combination of both, along with certain operation symbols. Two expressions that make up an equation are separated by an equal sign. Example of a Word 8, 3, and the result is 11.
Here,
Given : the numbers 4. 3, -1. 07, and -2. 971
Using the above given numbers we can construct
an expression which contain both
addition and subtract
thus ,
In order to form we use + sign and - sign
We get,
-1.07+(-2.917)-4.3=-8.287
Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.
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which equation represents a line perpendicular to the given line x-4y=7
The equation of the line perpendicular to x - 4y = 7 can be written as:
y = 4*x + b
Where b could be any real number.
Which equation represents a line perpendicular to x - 4y = 7?Two lines are perpendicular if the product between the slopes of the lines is equal to -1.
Where a general line in the slope-intercept form is written as:
y =a*x +b
And the given line is:
x - 4y = 7
Writing this in the slope-intercept form we will get:
-4y = -x - 7
y = (-1/4)*x + 7/4
So the slope is -1/4, then the slope of our line must be such that:
a*(-1/4) = -1
a = -4*-1 = 4
a =4
So the line perpendicular to the given one is:
y = 4*x + b
Where b can be any real number.
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graphing piece wise functions
Answer:
thats by step overr.ic. yttt. .
How do you write an x-intercept as a point?
The X-intercept is the point where the line crosses the x-axis. This happens where the Y is equals to zero.
The point slope form of a line is an equation of the line that takes on the form y - y1 = m(x - x1). In this equation, m is the slope of the line, and (x1, y1) is a point on the line. The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. This always happens at the point where y is equal to 0. Therefore, we find the x-intercept of a line in point-slope form by plugging y = 0 into the equation and then solving for x. The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. It is said to be as the x-coordinate of a point where a line, curve, or surface intersects the x-axis.
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Work out the equation of the line shown below.
Give your answer in the form y = mx + c, where m and c are
integers or fractions in their simplest forms.
to get the equation of any straight line, we simply need two points off of it, let's use those from the picture below.
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{-100})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{140}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{140}-\stackrel{y1}{(-100)}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{(-10)}}} \implies \cfrac{140 +100}{30 +10} \implies \cfrac{ 240 }{ 40 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-100)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-10)}) \\\\\\ y +100 = 6 ( x +10)\implies y+100=6x+60\implies {\Large \begin{array}{llll} y=6x-40 \end{array}}[/tex]
Which linear graph represents a proportional relationship?
A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.
A graph of a straight line that passes through the points negative 1 comma 0 and negative 1 comma 1.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.
Answer: The answer is C
Step-by-step explanation: i took the test and got it right
Is 7x and 7x2 are like terms?
7x and 7x2 are NOT like terms.
Terms with identical variables (like x or y) and any exponents (like the 2 in x2). Similar phrases can be combined. Similar or like terms are those that only differ in numerical coefficient but have the same literal coefficients raised to the same powers. Related terms are those that have the same exponent applied to similar variables. Dissimilar or unlike terms are those that do not have the same literal coefficients raised to the same powers. Only the numerical coefficients can change in terms similar to those of algebra.
However, because to the various exponents, 7x and 7x2 are NOT similar expressions.
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What is the coefficient of x3y4 in 2x 3y2 5?
The coeficient of x^3+y^4 in the algebraic expression is the number 2
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
2x^3+ 2y^4
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.
2 is the coefficient of x^3+y^4
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Stella took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $1. 20 plus $1. 50 per mile. The total fare was $29. 70, not including the tip. How
many miles was the taxi ride?
09
Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.
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Find value of y
[tex] {y}^{2} - 58 = 25 \times 4 + 11[/tex]
Hello there!
Answer:
y = ± 13
Step-by-step explanation:
[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]
the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
[tex] \longmapsto \: 7x + 5x + 2x = 35820 \\ \\ x = \frac{35840}{14} = 2560[/tex] length equals to 7 into 2560 = 1792
Solve by factorising:
x^2+10x+21=0
Answer:
[tex]x = -7\\x = -3[/tex]
Step-by-step explanation:
The steps are in the image attached to this response.
I want the answer please
The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ lim θ → 0 ( sin θ / θ ) = 1
Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.
⇒ lim θ → 0 ( sin θ / θ ) = 1
Take LHS;
⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )
⇒ lim θ → 0 ( cos θ / 1 )
⇒ ( cos 0 )
⇒ 1
⇒ RHS
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Tamika is ordering a taxi from an online taxi service. The taxi charges $3. 50 just for the pickup and then an additional $0. 75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Cost for 5 miles:
Cost for m miles:
If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25 and cost for riding m miles is $[tex]3.50+0.75m[/tex] .
The pickup charge that taxi service charges is = $3.50 ;
the additional charge for per miles driven is = $0.75 ;
we have to find the cost for riding 5 miles ;
So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;
substituting the values , the total cost equation becomes ;
[tex]Total Cost = 3.50 + 0.75\times5[/tex]
= [tex]3.50+3.75[/tex]
= 7.25
So , the cost for 5 miles is = $7.25 ;
to find cost for driving "m" miles ,we substitute the number of miles = m;
[tex]Total Cost = 3.50+0.75\times m[/tex]
= [tex]3.50+0.75m[/tex]
Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .
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The moon orbits earth at 384400km. The distance from earth to the sun is 149600000km. The diamiter of the sun is 1391000km. What would the diamiter of earth have to be to appear the same size as the sun from the moon if the celestial objects are in the order shown here : Sun, earth, moon.
Answer:
The diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers
Step-by-step explanation:
To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to know the distance from the Moon to the Sun and the distance from the Moon to Earth.
Since the distance from the Moon to the Sun is much greater than the distance from the Moon to Earth, the angle subtended by the Sun at the Moon will be much smaller than the angle subtended by Earth at the Moon.
Therefore, the size of Earth as seen from the Moon will be much larger than the size of the Sun as seen from the Moon.
To find the ratio of the size of Earth to the size of the Sun as seen from the Moon, we can use the formula:
size ratio = (distance to Earth / distance to Sun) x (Sun's diameter / Earth's diameter)
Substituting in the given values, we get:
size ratio = (384400km / 149600000km) x (1391000km / Earth's diameter)
Simplifying, we get:
size ratio = 0.00257 x (1391000km / Earth's diameter)
To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to solve for Earth's diameter. Dividing both sides of the equation by 0.00257, we get:
Earth's diameter = (1391000km / 0.00257) = 54304839.858km
Therefore, the diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers.
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What are the 13 types of angles?
There are several types of angles, including: acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pair, vertically opposite angles, alternate interior angles, alternate exterior angles, and corresponding angles.
Acute angles: angles measuring less than 90 degrees.
Right angles: angles measuring exactly 90 degrees.
Obtuse angles: angles measuring greater than 90 degrees but less than 180 degrees.
Straight angles: angles measuring exactly 180 degrees.
Reflex angles: angles measuring greater than 180 degrees but less than 360 degrees.
Complementary angles: two angles that add up to 90 degrees.
Supplementary angles: two angles that add up to 180 degrees.
Adjacent angles: two angles that share a common vertex and a common side but no common interior points.
Linear pair: two angles that add up to 180 degrees and share a common side.
Vertically opposite angles: two angles formed by two intersecting lines that are opposite to each other.
Alternate interior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and inside the parallel lines.
Alternate exterior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and outside the parallel lines.
Corresponding angles: two angles formed by two intersecting lines that are in the same relative position.
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Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $356.46.
She buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72.
She plans to spend some or all of the money she has left to buy new biking outfits for $45.35 each.
Write and solve an inequality which can be used to determine
o
o, the number of outfits Gianna can purchase while staying within her budget.
Answer:
Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.
The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.
Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.
She wants to buy biking outfits that cost $45.35 each.
We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:
45.35o <= 372.81
This inequality can be solved by dividing both sides by 45.35:
o <= 8.24
Therefore, Gianna can purchase 8 biking outfits while staying within her budget.
Step-by-step explanation:
fraction bigger than 2 out of 5 and smaller than 2 out of 3. When i divided numerator by denominator , it will be 0.533.
The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3, 1/5 is a fraction.
We have,
Let the fraction be a/b.
2/5 < a/b < 2/3
Now,
a/b
= (2/3 + 2/5) / 2
= (10 + 6) / 30
= 16/30
= 8/15
= 0.533
Thus,
The fraction is 8/15.
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Its pre-algebra. I need it fast
Answer:
Obtuse and isosceles
Step-by-step explanation:
obtuse because an angle is more than 90* and isosceles because two sides are equal.
Hope this helps!
How do you write log2 in exponential form?
To change logarithmic form to exponential form, spot the logarithmic equation's base and move the base to another side to the equal sign. Moving the base will make the current number or variable into the exponent.
Do not move something but the base: the other numbers or value will not change sides, and the word "log" will be release.
Log Rules:
1. the first rule is logb(mn) = logb(m) + logb(n)
2. the second rule is logb(m/n) = logb(m) – logb(n)
3. the third rule is: log b (mn) = n · logb(m)
1. Multiplication can be turned outside the log into addition and vice versa can be turned.
2. Division can be spin outside the log into a subtraction, and vice versa.
3. An exponent can be proceeded as a multiplier outward on all within a log, and vice versa.
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explain what the slope and intercept mean in each situation the amount of money y in a cash box after x tickets are purchased for carnival games. The slope of the line is 1/4 and the y intercept is 8
Answer:
The (1/4) slope is the prive per ticket. The y intercept is the money in the cash box before any tickets were sold.
Step-by-step explanation:
Let y be the money and x the numbers of tickets sold, as requested. We are told that the equation for this situation is:
y = (1/4)x + 8
Let's assume the money is in units of dollars. The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents. The y-intercept is the value of y when x=0, which means zero tickets have been sold. That means that the cash box had $8 before any sales were made. [perhaps to use for making change].
2. A square playground has a side which measures 40 metres. What is its area?
The area of a square playground which has a side measures 40metres would be 100[tex]m^2[/tex].
How to calculate area?step1
Perimeter of square = 40m
We have given that perimeter of square is 40m. To find its area, we have to calculate its side first.
Perimeter of square = 4× side
Substituting values in formula
Area of square = 4 × side
=> 40 = 4 × side
=> side = 40÷4
=> side = 10m
Side of square is 10m.
step 2
Calculating area of square :
We found that side of square is 10m. To find it area, required formula is:
Area of square = (side)²
To find area, substitute values in formula :-
Substituting values in formula :-
Area of square = (side)²
=> Area of square = (10)²
=> Area of square = 10 × 10
=> Area of square = 100m
so if the perimeter of square is 40m then the area is 100m.
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What is the formula for a isosceles triangle?
The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.
The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.
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plsss help
For the given polynomial, determine which of the binomials listed are factors. Pick two.
f(x) = 2x3 + 9x2 + 13x + 6
A.x + 1
B.x – 1
C.x + 2
D.x – 2
E.x + 3
F.x – 3
The factors for the Polynomial are (x+1) and (x+2).
What is Factor Theorem?According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
Given:
f(x) = 2x³ + 9x² + 13x + 6
Now, first (x+1) =0
x= -1
put x= -1 in f(x) as
f(-1) = 2(-1) + 9(1) + 13(-1) + 6
= -2 + 9 - 13 + 6
= 0
So, (x+1) is factor of f(x).
Now, second (x-1)= 0
x= 1
put x= 1 in f(x) as
f(1) = 2(1) + 9(1) + 13(1) + 6
= 2 + 9 + 13 + 6
= 31
So, (x-1) is not a factor of f(x).
Now, second (x+2)= 0
x= -2
put x= -2 in f(x) as
f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6
= -16 + 36 - 26 + 6
= 0
So, (x+2) is factor of f(x).
Now, second (x-2)= 0
x= 2
put x= 2 in f(x) as
f(1) = 2(2)³ + 9(2)² + 13(2) + 6
= 16 + 36 + 26 + 6
= 84
So, (x-2) is not a factor of f(x).
Now, second (x+3)= 0
x= -3
put x= -3 in f(x) as
f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6
= -54 + 81 - 39 + 6
= -6
So, (x+3) is not a factor of f(x).
Now, second (x-3)= 0
x= 3
put x= 3 in f(x) as
f(1) = 2(3)³ + 9(3)² + 13(3) + 6
= 54 + 81 + 39 + 6
= 180
So, (x-3) is not a factor of f(x).
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What is the solution to the equation 1 h 5 2 h 5?
h = 7 is the solution to the equation 1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
The equation given that,
1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)
The least common multiple of the denominators is:
h² - 25 = (h - 5) (h + 5)
We multiply through with the LCM to obtain:
= [(h - 5) × (h + 5)] × [1 / (h - 5)] + [(h - 5) × (h + 5)] × [2 / (h - 5)]
= 16 / (h² - 25) × [(h - 5) × (h + 5)]
We cancel out common factors to obtain:
= 1 (h + 5) + 2 (h - 5)
= 16
We expand the brackets to obtain
= h + 5 +2h - 10
We group like terms to get:
h + 2h = 16 - 5 + 10
This simplifies to:
3h = 21
We now divide through by 3 to obtain:
h = 7
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A gallon of gas cost $3.50 at the beginning of the month. At the e of the month it cost $3.75. What was the percent change in the price of a gallon of gas?
ty:-;
Answer:
7.14%
Step-by-step explanation:
Any comparison with the increase or decrease in price has to be compared to the ORIGINAL price. (at the beginning of the month.)
The price increased from $3.50 to $3.75, an increase of $0.25
To find what percent it is use:[tex]\frac{change}{original}[/tex]×100%
[tex]\frac{0.25}{3.50}[/tex]×100%
Answer:
7.1428571% increase
7 1/7 % increase
Step-by-step explanation:
To find the percent increase ( we know this is an increase since the amount went up), take the new amount and subtract the original amount
3.75 - 3.50 = .25
Divide by the original amount
.25 / 3.50
.071428571
Multiply by 100 %
7.1428571%
7 1/7 %
Graph the line that passes through the points (-3, -1) and (1, -1) and
determine the equation of the line.
Answer:
y = -1
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)
The slope here is 0, and the y-intercept is located at (0,-1), so the equation is
y = -1
Answer:
y = -1
Step-by-step explanation:
a new health drink has 150% of the recommended daily allowance. there is a certain vitamin this vitamin is 40 mg. How many milligrams of the vitamin are in a drink?
The numbers of milligrams of the vitamin that are in a drink is 60 milligrams.
What is the vitamin about?The recommended daily allowance (RDA) for the vitamin is 40 mg. A new health drink has 150% of the RDA.
To find out how many milligrams of the vitamin are in a drink, you can use the following formula:
(RDA) x (percentage/100) = milligrams in a drink
So,
(40mg) x (150/100)
= 60mg
Therefore, there are 60 milligrams of the vitamin in a drink.
Note that the RDA of vitamins can vary depending on age, gender, and other factors, so always consult a doctor or nutritionist before starting to consume any new supplement.
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