When can kids sing ABC?
Therefore , the kids can able to sings alphabets ABC by the age of 2 and by age of 4 children frequently know every letter of the alphabet .
What is alphabet?In alphabet, set of graphs, or characters, used to represent the phonemic structure of a language .The characters are often placed in a specific order, or sequence, in most alphabets (e.g., A, B, C, etc.).
Here,
By the age of two, children can sing or say out loud the "ABC" song and begin to recognise some letters.
By the age of three, children may recognise around half of the alphabet's letters and begin to associate letters with their sounds.
(S makes the sound /s/.)
Most kids are familiar with all 26 letters of the alphabet and their order by the time they are four years old.
Therefore , the kids can able to sings alphabets ABC by the age of 2 and by age of 4 children frequently know every letter of the alphabet .
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Children can begin to sing the alphabet by the time they are two years old.
Define the term alphabet.The phonemic structure of a language is represented by an alphabet, which is a system of graphs or symbols. In most alphabets, the characters are frequently arranged in a certain order, or sequence (e.g., A, B, C, etc.).
How many alphabets are there?There are 26 alphabets named from A to Z.
By the time they turn two, kids can sing or say the "ABC" song aloud and start to recognize some letters.
Around half of the alphabet's letters may be recognized by three-year-old, and they are starting to connect letters with sounds.
By the time they are four years old, the majority of children are familiar with all 26 letters of the alphabet and their placement.
As a result, children can begin to sing the alphabet by the time they are two years old, and by the time they are four, many of them are already familiar with all 26 letters.
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Please help and give a great answer get u brainlist
Answer:
7.62
Step-by-step explanation:
Simplify the following:
7 + 6/10 + 2/100
Express 6/10 in its lowest form by cancelling out gcd(6, 10) = 2 from the numerator and denominator. 6/10 = (2×3)/(2×5) = 3/5:
7 + 3/5 + 2/100
Express 2/100 in its lowest form by cancelling out gcd(2, 100) = 2 from the numerator and denominator. 2/100 = (2×1)/(2×50) = 1/50:
7 + 3/5 + 1/50
Put 7 + 3/5 + 1/50 over the common denominator 50. 7 + 3/5 + 1/50 = (50×7)/50 + (10×3)/50 + 1/50:
(50×7)/50 + (10×3)/50 + 1/50
50×7 = 350:
350/50 + (10×3)/50 + 1/50
10×3 = 30:
350/50 + 30/50 + 1/50
350/50 + 30/50 + 1/50 = (350 + 30 + 1)/50:
(350 + 30 + 1)/50
| 3 | 5 | 0
| | 3 | 0
+ | | | 1
| 3 | 8 | 1:
Answer: |
| 381/50
A woman put $580 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for the vear in dollars and cents? (Round to the nearest cent)
Answer:
580-80=500×6.5=3250 its ans iit
Part A Find the y-intercept and slope of the line.
Answer:
y-intercept = (0,6)
slope = -2
Step-by-step explanation:
⭐What is the slope of a line?
The slope of a line is how steep the line is⭐How can we find the slope of a line?
Use the formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]m = the slope[tex](x_1,y_1)[/tex] is one of the coordinates of the given line[tex](x_2, y_2)[/tex] is another coordinate of the given lineTo find the slope, pick two coordinates you see on the line, substitute them into the slope formula, and solve for the slope!
I am choosing the coordinates (0,6) and (3,0), but you can choose any 2 coordinates that you see on the line.
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{0-6}{3-0}\\m = \frac{-6}{3}\\m = -2[/tex]
∴ The slope of the line is -2.
⭐ What is the y-intercept of a line?
The y-intercept of a line is the point (0,y) at which the line intersects the y-axis⭐How do we find the y-intercept of a line?
Look at the graphFind the corresponding y-coordinate for when x=0When x=0, y=6
∴ The y-intercept of the line is (0,6)
What is postulate and theorem?
A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.
What is meant by postulate ?A claim that is accepted as true without evidence, also referred to as an axiom. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry. An unsupported assertion is referred to as a postulate. A postulate is also referred to as an axiom. For instance, you would believe Pam if she claimed that all of her siblings are at least five foot one tall if you knew that she is five feet tall and that all of her siblings are taller than her. A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.To learn more about postulate refer to:
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Use the order of operations to order the steps to evaluate the expression (60+15)/3-2(4)+2^3
Answer:
25
Step-by-step explanation:
(60+15)/3-2(4)+2^3
75/3 -2 x4 + 2^3
75/3 - 8 +2^3
75/3 - 8 +8
75/3
25
reasoning suppose le ol i and fe o gi. what else must you know in order to prove kfde and kghi are congruent by asa? by aas?
In order to prove that KFDE and KGHI are congruent by ASA, you need to know that KFDE and KGHI have two congruent angles (angle F and angle H) and a congruent side (side DE and side HI).
In order to prove that KFDE and KGHI are congruent by AAS, you need to know that KFDE and KGHI have three congruent angles (angle F, angle G, and angle H). This means that the angles in the triangle are equal, which implies that the sides in the triangle are also equal. Thus, for AAS, KFDE and KGHI must have two congruent sides (side DE and side HI).
Therefore, in order to prove that KFDE and KGHI are congruent by ASA or AAS, you must know that both triangles have two congruent angles and a congruent side (for ASA) or three congruent angles and two congruent sides (for AAS).
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the dat set for a random sample of 10 baseball players heights compared to their show sizes is summarized in the table. PLEASE!!!!!! HELP!!!!
Answer: a) The equation of the least-squares regression line is y = -1.66x + 78.83. b) Residual = 7.11 inches. c) The residual is the deviation of a data point from the fitted regression line. In this case, the residual is 7.11 inches, indicating that the player who wears a size 9 and is 71 inches tall is taller than what would be expected based on the trend in the data.
Step-by-step explanation:
What is the least square regression and residual?
Least squares regression is a statistical method that is used to find the line of best fit for a set of data points. It involves finding the line that minimizes the sum of the squares of the differences between the actual data points and the predicted values on the line. The residual is the difference between the actual data point and the predicted value on the line.
Part A: The equation for the least-squares regression line can be found by using the following formula: y = bx + a
To find the values for a and b, we need to calculate the following values:
x: the mean of the shoe sizes,
y: the mean of the heights.
S x y: the sum of the products of the differences between the shoe sizes and x and the differences between the heights and y.
S x x: the sum of the squares of the differences between the shoe sizes and x.
X = (7+10+12+8+9.5+10+11.5+12.5+13.5+10) / 10 = 10.5
Y = (64+69+72+67+69+70+75+73+71+68) / 10 = 69.4
To find S x y and S x x, we use:
S x y = ∑(x - x)(y - y)
S x x = ∑(x - x)^2
Inserting the values from the table, we get:
S x y =-47.5
S x x = 28.5
Using values, we can calculate the slope and y-intercept of the least-squares regression line:
b = S x y / S x x = -47.5 / 28.5 = -1.66
a = y - bx = 69.4 - (-1.66)(10.5) = 78.83
So the equation of the least-squares regression line is y = -1.66x + 78.83
Part B: We can use the equation for the least-squares regression line to determine the residual for a player who wears a size 9 and is 71 inches tall. We calculate the player's height using the size 9 into the equation:
y=-1.66x+78.83=63.89 inches.
The residual is then calculated by deducting the expected height from the actual height: 7.11 inches =71- 63.89 inches.
Part C: The residual is the variation between the dependent variable's actual value (height) and its anticipated value according to the least-squares regression line. The athlete in this instance, who wears a size 9 and is 71 inches tall, is taller than what might be anticipated based on the trend in the data, according to the residual of 7.11 inches.
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The equation of the least-squares regression line is y = -1.66x + 78.83. b) Residual = 7.11 inches.
What is the least square regression and residual?
Least squares regression is a statistical method that is used to find the line of best fit for a set of data points. It involves finding the line that minimizes the sum of the squares of the differences between the actual data points and the predicted values on the line. The residual is the difference between the actual data point and the predicted value on the line.
Part A: The equation for the least-squares regression line can be found by using the following formula: y = bx + a
To find the values for a and b, we need to calculate the following values:
x: the mean of the shoe sizes,
y: the mean of the heights.
S x y: the sum of the products of the differences between the shoe sizes and x and the differences between the heights and y.
S x x: the sum of the squares of the differences between the shoe sizes and x.
X = (7+10+12+8+9.5+10+11.5+12.5+13.5+10) / 10 = 10.5
Y = (64+69+72+67+69+70+75+73+71+68) / 10 = 69.4
To find S x y and S x x, we use:
S x y = ∑(x - x)(y - y)
S x x = ∑(x - x)^2
Inserting the values from the table, we get:
S x y =-47.5
S x x = 28.5
Using values, we can calculate the slope and y-intercept of the least-squares regression line:
b = S x y / S x x = -47.5 / 28.5 = -1.66
a = y - bx = 69.4 - (-1.66)(10.5) = 78.83
So the equation of the least-squares regression line is y = -1.66x + 78.83
Part B: We can use the equation for the least-squares regression line to determine the residual for a player who wears a size 9 and is 71 inches tall. We calculate the player's height using the size 9 into the equation:
y=-1.66x+78.83=63.89 inches.
The residual is then calculated by deducting the expected height from the actual height: 7.11 inches =71- 63.89 inches.
Part C: The residual is the variation between the dependent variable's actual value (height) and its anticipated value according to the least-squares regression line. The athlete in this instance, who wears a size 9 and is 71 inches tall, is taller than what might be anticipated based on the trend in the data, according to the residual of 7.11 inches.
c) The residual is the deviation of a data point from the fitted regression line. In this case, the residual is 7.11 inches, indicating that the player who wears a size 9 and is 71 inches tall is taller than what would be expected based on the trend in the data.
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Is rigid motion congruent?
Yes, rigid motion is congruent?
What is rigid motion congruency?A stiff motion occurs when an object is transported from one place to another while maintaining its original size and shape.
If and only if there is a stiff motion that establishes a correspondence of one figure as the likeness of the other, then two figures are said to be congruent. Interior angles are unchanged, as well as side lengths.
An object is rigidly moved from its initial place to the exact same location in a motion known as an identity motion. It appears as though the thing hasn't changed at all.
According to the Common Core, the "principle of superposition" states that two figures are congruent if there is a rigid motion projecting one onto the other.
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If sally has 29 apples but then bob takes 1 apple how many apples does sally have left?
Answer:
28 apples
Step-by-step explanation:
29 - 1 = 28 apples
Answer:
28apples
Step-by-step explanation:
simple:29-1
hope this helps
Least common multiple of 5y^2-45 and y+3
The common multiple of 5y²- 45 and y + 3 is (y + 3).
What is meant by common multiple?For any two or more expressions, if any one of their factors is common in all of them, then that factor is said to be the common multiple of those expressions.
Calculation:The given expressions are 5y²- 45 and y + 3
On factorizing them, we get
5y²- 45 = 5(y² - 9)
⇒ 5(y² - 3²)
From he binomial formula a² - b² = (a + b)(a - b), we can write
5y²- 45 = 5(y + 3)(y - 3)
Now, the second expression has no further simplification. The expression is itself a factor for it.
So, we can write their factors as
5y²- 45 = 5 × (y + 3) × (y - 3)
y - 3 = 1 × (y - 3)
From this, (y - 3) is the only factor that is a common factor for both the expression.
So, (y - 3) is the common multiple for the given expressions.
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What does discontinuity mean?
In mathematics, a discontinuity is a point or set of points at which a function or curve is not defined, or is not "well-behaved," meaning it exhibits some kind of sudden or unexpected change in behavior.
What does discontinuity mean?Discontinuities can occur in functions or curves of all types, including functions of one variable, functions of several variables, and geometric curves.
There are several types of discontinuities that can occur in a function. For example, a function may have a jump discontinuity, which occurs when the function has a finite limit from one side but a different finite limit from the other side at a given point.
In all, the presence of discontinuities in a function can make it more difficult to analyze or work with, as the behavior of the function may not be predictable at these points.
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How many terms are there in the expression x³ 4x² 7x − 2 *?
There are totally 4 terms in the given polynomial
We have a polynomial given by -x³+4x² +7x − 2
Algebraic expressions with coefficients and variables make up polynomials. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
Since there are 4 terms with either an addition or a subtraction performed between them, the total number of terms is given by 4.
Those 4 terms are -x³ ,4x²,7x,−2
Therefore, there are totally 4 terms in the given polynomial.
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What is called discontinuity?
A discontinuity in mathematics is when a function is not well defined
How to identify discontinuity?As earlier defined, discontinuity deals with a function that is not well defined.
Different functions have different discontinuity depending on the function
Good examples of discontinuity include
y=1/x this is a discontinuous function.
x=0 is also a discontinuous function as it is not well defined. because there is no value for y
The function TanA is a discontinuous function because it is not well defined.
Other discontinuities include
y=5п/3, 9п/4, 6п8, 4п/3
All these are discontinuous functions
In conclusion, a discontinuity in mathematics is when a function is not well defined
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Find the total surface area of the cone in the figure. (Use π = 3.14.)
A) 282.6 cm^2
B) 219.8 cm^2
C) 266.9 cm^2
D) 314.0 cm^2
The total surface area of the cone is calculated to be
A) 282.6 cm²How to find the total surface area of the coneInformation given in the problem
the total surface area of the cone in the figure. (Use π = 3.14.)
A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.
The formula of the total surface are of a cone is given by
T = πr(r + l) square units.
calculating for l
l = √(12² + 5²) = 13
= 3.14 * 5 (5 + 13)
= 3.14 * 5 *(18)
= 282.6 cm^2
282.6 cm^2 is the total surface area of the cone
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Sandra et the cruie control in her car to 69 mile per hour when he goe on road trip. Which equation can be ued to find how many hour, h, it will take her to drive m mile at her contant peed?
A. B. C. D
Sandra sets the speed to 69 miles per hour. The equation that express how many hours it will take her to drive m miles is: h = m/69.
Speed or velocity 69 miles per hour means: in 1 hour she will travel 69 miles
69 miles need 1 hour
1 miles need 1/69 hours
m miles need m x 1/69 hours.
If h is the amount of time need to take her to drive m miles, then:
h = m x 1/69 = m/69 hours
We can also solve the problem, using formula:
s = vt
Where:
s = distance
v = speed = 69 mph
t = time
In the given problem, the distance is m, hence s = m, and t = h
Hence,
t = s/v
h = m/69
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What is the slope if it is perpendicular?
The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].
What is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
What is perpendicular ?
The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.
Let y = 3x + 1 is perpendicular ,
differentiate respect of x
[tex]\frac{dy}{dx} = 3[/tex] , m = 3
Thus , [tex]-\frac{1}{m}[/tex]
then [tex]-\frac{1}{3}[/tex]
The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].
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multiply 17m 25cm by 24
Step-by-step explanation:
To multiply 17m 25cm by 24, you need to first convert the units of measurement to a common unit, such as meters or centimeters.
17m 25cm can be written as 17.25 m, since 1 meter is equal to 100 centimeters. Therefore, to multiply 17.25 m by 24, you can simply perform the calculation as follows:
17.25 m * 24 = 413 m
This means that the result of the multiplication is 413 meters.
Alternatively, you could express the result in centimeters by performing the calculation as follows:
(17 m * 100 cm/m) + (25 cm * 24) = 1700 cm + 600 cm = 2300 cm
This means that the result of the multiplication is 2300 centimeters.
Select all the expressions which are equivalent to –4/3p – 2/5.
–4/3p + 2/5
–2/5 – 4/3p
4/3p – 2/5
–4/3p + (−2/5)
2/5 + 4/3p
A collection of numbers, variables, and mathematical operations is referred to as an expression. The expression is -2/5- 4/3P and 2/5+4/3P
What is meant by expression ?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation .A collection of numbers, variables, and mathematical operations is referred to as an expression.
Given,
-4/3p - 2/5
= -20p - 6/15
= 2(10 p +3)/15
A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.
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Why is f called a linear function?
For a given function f, it is linear if the function has a constant slope and it doesnot contain the power of x greater than 1.
What is a function?An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
What does a linear function represent?A function which is also linear, represents a straight line in the graph. The graphs to the linear functions are straight lines which have constant slope throughout the graph.
A function f is referred to as linear if it meets both of the following criteria:
The slope of the function is constant. This indicates that the slope of the line is constant, independent of the value of x that you enter into the function.
There are no powers of x bigger than 1 in the function. This indicates that there are no terms in the function that have x2, x3, etc.
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Is longitude equidistant?
Latitude lines always have an equal distance between them, however longitude lines are separated from one another at the equator and come together at the poles. Longitude and latitude lines near the equator are equal in distance, with one degree covering 111 kilometers (69 miles).
Latitude lines are always equally spaced apart because they are always parallel to one another. Never do latitude lines converge or intersect. Distances north or south of the equator are measured by lines of latitude.
How do longitudes work?
Distance east or west of the prime meridian is measured by longitude. Meridians, which are also known as lines of longitude, are fictitious lines that divide the globe. They measure the distance either east or west, running from pole to pole from north to south. The units of longitude are degrees, minutes, and seconds.
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How is the literal equation y = a( bx + c) similar to the equation for converting °F to °C?
How would you solve this equation for the variable x ?
ans is 4 I don't really know how to explain it
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’, what will be the coordinate of D’?
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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the ratio 800g:1kg can be written in a form 1:n find out the value of n
If 800g:1kg is equal to 1:n then the value of n is 1/8.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
800g : 1kg = 1 : n
This can be written as,
800g/1kg = 1/n
Cross multiply.
n = 1kg/800g
[ 1 kg = 1000g ]
n = 1000g/8000g
n = 1/8
Thus,
The value of n is 1/8.
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plot the distance and time data for distance the train traveled on the grid below. plot the distance on the vertical axis and time on horizontal axis. label the axes and add a title to your plot.
Distance Traveled by Train
Time (h) Distance (km)
0 0
1 110
2 220
3 330
4 400
5 500
A graph of the distance and time data for distance traveled by this train is shown in the image attached below.
What is a scatter plot?In Mathematics, a scatter plot is sometimes referred to as scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting data points showing any association or correlation between the data set.
In this scenario, the time (in hours) would be plotted on the vertical axis (x-axis) of the scatter plot while the distance (in kilometers) would be plotted on the horizontal axis (y-axis) of the scatter plot by using an Excel worksheet.
From the scatter plot (see attachment) which models the relationship between the distance (in kilometers) and time (in hours), a linear equation for the line of best fit or trend line is y = 99.43x + 11.43.
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The mass of one methane (natural gas) molecule is 2.7x10^-23 grams. Find the mass of
60,000 methane molecures in grams.
The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g
what is mass of molecule ?
Watch your pronunciation. pronounced "muh-LEH-kyoo-ler mas" the total atomic mass of every atom in a molecule, calculated using a scale with hydrogen, carbon, nitrogen, and oxygen having atomic masses of 1, 12, 14, and 16, respectively.
solution:
The mass of one methane molecule should be "2.7 × 10⁻²³ gram" instead of "27 × 10⁻³ grams".
Mass of 60,000 molecules of methane
= (2.7 × 10⁻²³ g) × 60,000
= 1.62 × 10⁻¹⁸ g
Therefore,The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g
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What would the ratio be if you partition a line segment at point?
these are the fees for sending a package by media mail: $\bullet$ $\$2.41$ for the first pound $\bullet$ $\$0.41$ per additional pound for the next six pounds $\bullet$ $\$0.39$ per additional pound after that for example, a two-pound package costs $\$2.82$ to send by media mail. if a package full of books costs $\$7.99$ to send by media mail, how many pounds does the package weigh?
The weight of the package is 15 pound.
What is an linear equation?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
Given that the fees for sending a package by media mail
For first pound : $2.41
For the next six pounds: $0.41 per pound
For additional pound: $0.39 per pound
The cost of first 7 pounds is = $(2.41 + (0.41 × 6)) =$4.87
$4.87 < $7.99. Thus the weight of the package is more than 7 pounds
Assume that, the weight of the package is (7 + x) pound.
The fee for (7 + x) pounds package is $(4.87 + 0.39x)
According to the question:
4.87 + 0.39x = 7.99
Subtract 4.87 from both sides:
0.39x = 3.12
Divide both sides by 0.39
x = 8
The weight of the package is (8 + 7) = 15 pounds.
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What to numbers can equal 16?
1, 2, 4, 8, and 16 are the components that make up 16. Similarly, the negative components of 16 are -1, -2, -4, -8, and -16. factors of 16: 1, 2, 4, 8, and 16.
What two numbers make 16?The natural number 16 (or sixteen) comes after the number 15 and before the number 17. Since 42 = 4 4 is a square number, the number 16 is both a composite and a square. It has precisely five correct divisors, making it the lowest number. These are 1, 2, 4, and 8. The numbers 16 and 60 sound remarkably similar in English speech, which might lead to confusion.
There are three factor pairs of 16:
1 × 16 = 16.
2 × 8 = 16.
4 × 4 = 16.
1, 2, 4, 8, and 16 are the 16 factors. Likewise, the unfavorable factors of 16 are -1, -2, -4, -8, and -16. 1, 2, 4, 8, and 16 make up the number 16.
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what is the equation of a line perpendicular to y = 2x - 6 that passes through (5, 4)
(use y = m x + b)
(must solve for y to get slope)
The equation of the perpendicular line is y = -0.5x + 6.5
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 2x - 6
Also, from the question;
We have the following points
Point = (5, 4) i.e. (x, y) = (5, 4)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -1/2
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = -1/2
(x₁, y₁) = (5, 4)
So, we have
y = -1/2(x - 5) + 4
Evaluate
y = -0.5x + 6.5
Hence, the line has an equation of y = -0.5x + 6.5
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