rate of change for this linear equation, y = 5x - 1 is +5
the initial value of the linear equation, y = 5x + 2 is +2.
What is linear equation?A linear equation is an algebraic equation of the form y = mx+c, where m is the slope and c is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.
Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.
Given that,
y = 5x - 1 is a linear equation.
As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.
Therefore, for the given equation, rate of change is 5 and initial value is -1.
Given that,
y = 5x + 2
is a linear equation.
As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.
Therefore, for the given equation, rate of change is 5 and initial value is + 2.
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A specialty foods company sells "gourmet hams" by mail order. The hams vary in size from 4. 15 to 7. 45 pounds, with a mean weight of 6 pounds and standard deviation of 0. 65 pounds. The quartiles and median weights are 5. 6, 6. 2, and 6. 55 pounds.
a) Find the range and the IQR of the weights.
b) Do you think the distribution of the weights is symmetric or skewed? If skewed, which way? Why?
c) If these weights were expressed in ounces ( 1 pound = 16 ounces) what would the mean, standard deviation, quartiles, median, IQR, and range be?
d) When the company ships these hams, the box and packing materials add 30 ounces. What are the mean, standard deviation, quartiles, median , IQR, and range of weights of boxes shipped (in ounces)?
e) One customer made a special order of a 10-pound ham. Which of the summary statistics of part d might not change if that data value were added to the distribution?
The range and the IQR of the weights are 3.3 pounds and 0.95 pounds respectivly.
What is Mean , Median and Standard Deviation ?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.
The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
a) the range is the difference between the highest and lowest value:
range =7.5-4.15 =3.3 pounds
the IQR is the difference between the third and first quartile
IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds
b) Skewed because the mean and median are not the same value.
c) All values will be multiplied by 16
Mean: 96 ounce
Standard deviation: 10.4 ounce
Quartiles: 89.6 ounce and 104.8 ounce
Median:99.2 ounce
IQR: 15.2 ounce
Range: 52.8 ounce
d) The mean,quartiles and median increase by 30,the result remain unchanged:
Mean: 126 ounce
Standard deviation: 10.4 ounce
Quartiles: 119.6 ounce and 134.8 ounce
Median:129.2 ounce
IQR: 15.2 ounce
Range: 52.8 ounce
e) The median, quartiles and IQR might not changed,because they are unaffected by an outlier.
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Jason made a model stop sign for his model train
set. An actual stop sign measures 12 inches on
each side. Jason's model stop sign measures
1 inch on each side.
actual measures : model measures = 12 : 1 .
What is Ratio?In mathematics, a ratio shows how many times one number contains another. The comparison or simplified form of two quantities of the same kind is referred to as a ratio. This relation gives us how many times one quantity is equal to the other quantity. In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones.
The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’.
A ratio can be written as a fraction, say 2/5. We happen to see various comparisons or say ratios in our daily life.
Given,
Actual sign measures 12 inches on each side
Jason's model sign measures 1 inch on each side.
Ration between actual to model sign measurement=
Measurement of actual sign / Measurement of model sign
= 12/1
Ratio = 12:1
Hence, the ratio between actual to model sign measurement is 12:1.
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Gabriel wants to send a parcel to italy.
WeDeliver: The total cost of sending the parcel with WeDeliver is £64.00.
What is total cost?Total cost is the sum of all costs associated with a particular purchase, project, or investment. It includes the cost of materials, labor, and any other expenses incurred such as taxes, fees, and shipping. Total cost is an important factor in determining whether or not a project or purchase is feasible. When evaluating the total cost, one must consider any associated risks, such as the risk of a market downturn or currency fluctuations.
This is calculated by summing the three dimensions of the cuboid (10 cm + 20 cm + 40 cm) and then multiplying this sum by £0.80.
GoParcels: The total cost of sending the parcel with GoParcels is £48.00. This is calculated by multiplying the total area, in cm, of all 6 faces of the cuboid (10 cm x 20 cm x 2 + 10 cm x 40 cm x 2 + 20 cm x 40 cm x 2) by £0.02.
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In how many ways can Harold, Steve, John, Roslyn, Marian and Connie line up so that no two of Harold, Steve and John are next to each other ?
There are four general arrangents of boy/girl to consider:
BGBGBG, GBGBGB, BGGBGB, and BGBGGB.
For any one of these four basic arrangements, the boys can be
rearranged (permuted) among themselves in 3 × 2 × 1 = 6 different
ways. Similarly, the three girls can be rearranged among
themselves in 6 ways. Since the boys and girls can be rearranged
independently, the number of ways to create any one of the four
basic arrangements is 6 × 6 = 36.
So the total number of ways that 3 boys and 3 girls can line up so
that no two of the three boys are next to each other is
4 × 36 = 144 .
The total number of ways that 3 boys and 3 girls can line up so that no two of the three boys are next to each other is found to be as 144 .
It is given that there are four general arrangements of boys and girls,
Here, the boys can be arranged or rearranged (permuted) among themselves in a total of , 3 × 2 × 1 = 6 different ways.
Similarly, the three girls can be rearranged among
themselves in 6 ways.
We are given that both the groups can arrange themselves independently .
Therefore, the number of ways to create any one of the four basic arrangements is 6 × 6 = 36.
Therefore, the number of ways to arrange them is ,
4 × 36 = 144 .
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Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips. The maximum charge is $45. 00 per day plus $0. 40 per mile. Discounts apply when renting for longer periods of time or during off-peak seasons
A linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
What is linear inequality?
In mathematics, an inequality involving a linear function is referred to as a linear inequality. One of the inequality symbols is found in a linear inequality. In graph form, it displays the non-equal data.
Given:
Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips.
The maximum charge is $45. 00 per day plus $0. 40 per mile.
A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation, with the inequality sign replacing the equality sign.
According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.
So,
a linear inequality that models the total cost of the daily rental as a function of the total miles driven, m is:
c(m) ≤ 45 + 0.4m
Hence, a linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
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A cup of tea costs $3.25 at a local cafe. Alan and his wife, Patty, have a coupon for $1 off their order. Alan says the expression 3.25t - 1 represents the cost for t cups of tea. Patty says the expression 3t + (-1) represents the cost. Are their expressions equivalent? Explain.
Answer:
Step-by-step explanation:
The expressions are not equivalent. A cup of tea costs $3.25. $3.25t reprensents the total cost for the number of cups of tea (t) in one order. Subtracting the $1 coupon or adding the coupon as a negative results in the same discount. But Patty is using the wrong cost for a cup of tea, $3 instead of $3.25. Resulting in expressions that are NOT equivalent.
How do I write a system of equations
Find three additional points on the parabola that has vertex (1, -2) and passes through (0,– 5). Select all that apply. A. (2,-3) B. (-1,-14) C. (3,2) D. (2,-5) E. (3,-14) F. (-2,7)
Answer: The vertex form of a parabola is:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
In this case, we are given that the vertex is (1, -2), so the equation of the parabola will be:
y = a(x - 1)^2 - 2
We know that the parabola passes through (0, -5), and it is given by the equation.
-5 = a(0 - 1)^2 - 2
so,
a = 1/3
The final equation of the parabola is :
y = 1/3(x-1)^2 - 2
so, the points that are on the parabola are:
A. (2,-3)
B. (-1,-14) is not true,
y = 1/3 (-1 -1)^2 - 2 = -1/3 + 2 = 1/3 ≠ -14
C. (3,2)
D. (2,-5)
E. (3,-14) is not true
y = 1/3 (3-1)^2 - 2 = -4/3 ≠ -14
F. (-2,7) is not true
y = 1/3 (-2-1)^2 - 2 = -7/3 + 2 = -1/3 ≠ 7
Therefore A, C and D are the correct answers.
Step-by-step explanation:
Stella measures the diameters of a nickel, a dime, and a quarter. They are 21.2 mm, 17.8 mm, and 24.5 mm, respectively. Find the areas of each coin. Round to the nearest tenth.
The area of nickel is 353.0 mm²
The area of a dime is 248.8 mm²
The area of a quarter is 471.4 mm²
Given that,
The diameter of a nickel, a dime, and a quarter are 21.2 mm, 17.8 mm, and 24.5 mm, respectively.
Diameter = 2r (r=radius)
or, r = d/2
so, the Radius of a nickel, a dime, and a quarter are 10.6 mm, 8.9 mm, and 12.25 mm, respectively.
Thus, the area of a nickel, a dime, and a quarter => A= πr²
So, the area of the nickel = 3.14*10.6*10.6 = 353.0 mm²
The area of the dime = 3.14*8.9*8.9 = 248.8 mm²
The area of a quarter = 3.14*12.25*12.25 = 471.4 mm²
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What is the difference of the two polynomials 9x 2 8x 2x 2 3x?
The difference between the two polynomials (9x²+8x)-(2x²+3x) is 7x²+5x.
What is polynomial?A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here,
The difference between the two polynomials (9x²+8x)-(2x²+3x) is 7x²+5x.
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How did you compute sums ofdollar amounts that were not whole numbers? For example, how did you compute the sum of$5. 89 and$1. 45? Use this example to explain your strategy.
How did you compute products ofdollar amounts that were not whole numbers? For example, how did you compute the cost of4 pounds of beef at $5. 89 per pound? Use this example to explain your strategy
To compute the sum of dollar amounts that are not whole numbers and to compute products of dollar amounts that are not whole numbers you can use the standard arithmetic operation and place decimal point correctly.
To compute the sum of dollar amounts that are not whole numbers, such as $5.89 and $1.45, you can use the standard arithmetic operations of addition, just like you would with whole numbers.
$5.89 + $1.45 = $7.34
When adding or subtracting decimal numbers, you align the decimal points and perform the operation column by column, just like you would with whole numbers.
To compute products of dollar amounts that are not whole numbers, such as 4 pounds of beef at $5.89 per pound, you can use the standard arithmetic operation of multiplication.
4 × $5.89 = $23.56
When multiplying decimal numbers, you multiply as you would with whole numbers and place the decimal point in the product to the right of the last digit in the product that corresponds to the number of decimal places in the original factors.
In both examples, it is important to pay attention to the placement of the decimal point and to use proper arithmetic operations. In general, it is important to consider the decimal places when working with decimal numbers and ensure that the final result is rounded to the appropriate number of decimal places, if necessary.
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The radii of two concentric circles are in the ratio 3:5. If the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm, complete the following statements:
The length of the chord of the larger circle can be found by taking the square root [tex](5r)^2 - (2r)^2[/tex] which is equal to r√21, where r is the radius of the smaller circle.
The given problem states that there are two concentric circles with radii in the ratio of 3:5. This means that the radius of the smaller circle is 3r and the radius of the larger circle is 5r. The distance between the center of these two circles is 2r.
Also, it is given that the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm. Using this information, we can find the length of the chord of the larger circle by using the Pythagorean theorem.
The length of the chord of the larger circle is found by taking the square root of [tex](the radius of the larger circle)^2[/tex] - [tex](the distance between the two centers)^2[/tex] which is √21[tex]r^2[/tex]= r√21.
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Consider the parent function f(x) below and graph
The exponential function formula for the parent function is found to be
[tex]f(x) = 2^x[/tex]
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The general formula to find an exponential function is [tex]f(x) = ab^x[/tex]
From the given graph, we take two points on the graph : (1,2) and (2,4)
Substituting in the above equation, taking f(x) as y
[tex]ab^1 = 2\\\\ab^2 = 4[/tex]
Solving the above equations, we get
a= 1, b=2
So the parent function [tex]f(x) = 2^x[/tex].
Now using this function we can graph [tex]f(2x), -3f(x), 2f(2x)\\[/tex].
[tex]f(2x) = 2^{2x} = 4^x\\\\-3f(x) = -3 * 2^x\\2f(2x) = 2 * 4^x[/tex]
Therefore using the Desmos, the above exponential functions are graphed.
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Find the missing angle. 60° 75° 75° ?
Answer:
65?
Step-by-step explanation:
im not to sure but maybe 65
Dollhouse furnishing comes in different sizes depending on the size of the dollhouse. Write a ratio of the size of the dollhouse item to the size of the larger item.
dollhouse sofa: 1 1/2 in. Long
real sofa: 6 ft long
The ratio of the size of the dollhouse item to the doll house is 14 : 9.
What are ratios?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
The ratio is a mathematical expression that can be used to represent one item as a percentage of another.
First convert feet to inches
1 feet = 12 inches
12 x 6 = 72 inches
dollhouse item : doll house
112 : 72
14 : 9
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M(2,4) is the midpoint
between the points A(-2,9)
and B.
Find the coordinates of B.
The coordinates of B are (6,0).
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is given by the coordinates:
((x1 + x2) / 2, (y1 + y2) / 2)In this problem, we're given that the midpoint is (2, 4) and we need to find the coordinates of point B. Since we know the coordinates of the midpoint, we can set up the equation:
((x1 + x2) / 2, (y1 + y2) / 2) = (2, 4)We know that point A = (-2,9) is one endpoint, so we can substitute it into the equation
((-2 + x2) / 2, (9 + y2) / 2) = (2, 4)Solving for x2 and y2, we get x2 = 6 and y2 = 0 which is the coordinates of point B.
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. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western)
mean of the sampling distribution of the difference in sample proportions is 0.36.
Which approach is most likely to result in a random sample of your class's members?The best method for the random sampling will be to write the students' names on paper and pick them out of a hat, as each student will have an equal chance of being chosen.
22% of the population of eastern grey squirrels weigh more than 0.5 kg.
36% of the population of western grey squirrels weigh more than 0.5 kg.
Eastern grey squirrel sample size is 60.
There were 120 western grey squirrels in the sample.
Required:
The difference in sample proportions' mean of the sampling distribution (eastern minus western)
The difference of the mean yields the mean of the difference.
Mean = p1 - p2 is the sampling distribution's average for the difference in the sampling proportion from two populations.
Where;
p1 = 22% of the eastern grey squirrel, which equals 0.22.
p2 = 36% of the western grey squirrel, which equals 0.36.
Therefore;
p1 - p2 = 0.22 - 0.36 is the mean.
The right answer is (E) 0.22 - 0.36.
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#4 Real World Scenario
A bird starts flying away from a
tree and goes exactly 6 miles
south. It then turns and flics
exactly 3 miles east. What is
the shortest distance it needs to
fly to return to the original
tree? If necessary, round your
answer to the nearest tenth.
The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.
what is pythagoras theorem ?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool.
given
by pythagoras theorem :-
shortest distance = [tex]c^{2} = a^{2} + b^{2} \\[/tex]
[tex]c^{2} = 6^{2} + 3^{2} \\c^{2} = 36 + 9\\c^{2} = 45\\c = 3\sqrt{5}[/tex]
The smallest distance it has to go to get back to the starting tree is [tex]3\sqrt{5}[/tex]when traveling 6 miles to the south before turning 3 miles to the east.
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The price of an item has dropped to $42 today. Yesterday it was $60 . Find the percentage decrease.
Answer:
70% Decrease
Step-by-step explanation:
70% Decrease
The percentage decrease in price of an item is 30 %
Step by step solution:
The percentage decrease in price = [(original value - decreased value)/original value]*100
percentage decrease[tex]=\frac{(original value - decreased value}{original value} * 100[/tex]
percentage decrease=[tex]=\frac{60 - 42}{60} *100[/tex]
[tex]=\frac{18}{60} *100[/tex]
[tex]=0.3 *100[/tex]
30 %
Therefore, the percentage decrease in price of an item is 30 %
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How many terms are there in the expression 7x2 5x?
There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.
Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.
An algebraic expression with three terms is called a trinomial.
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SU is a midsegment of QRT
If QR=-5v+96 and SU = 19v-38 than what is the value of X
Considering the given triangle, the information given helped to apply similar triangle principle to determine v to be 3.9
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
TS and TR , SU and QR
The solution is worked out using sides WX and XV, WY and YU
TS / TR = SU / QR
TS / TR = 1/2 since it is a mid segment
1 / 2 = (19v - 38) / (-5v + 96)
-5v + 96 = 2 * (19v - 38)
-5v + 96 = 38v - 72
96 + 72 = 38v + 5v
168 = 43v
v = 3.9
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2-18. Frank wonders whether corresponding angles always have equal measure. For parts () through (d) below, use tracing paper to decide if corresponding angles have the same measure. Then determine if you have enough information to find the measures of x and y. If you do, find the angle measures and state the relationship .
The angles and their relationships are -
a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)
b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)
c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)
d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)
What is angle pair relationship?
In Geometry, there are five fundamental angle pair relationships:
Complementary Angles
Supplementary Angles
Adjacent Angles
Linear Pair
Vertical Angles
a) In the first diagram -
∠x = ∠a as they are both corresponding angles to each other.
So, ∠x = 135°.
Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.
So, ∠y = 135°.
b) In the second diagram -
∠y + ∠a =180° as they are both form a linear pair of angles.
So, ∠y = 180° - ∠a
∠y = 180° - 135°
∠y = 45°.
Now, ∠x cannot be deduced and no proper information is given in the image.
c) In the third diagram -
∠x = ∠a as they are both corresponding angles to each other.
So, ∠x = 135°.
Now, ∠y + ∠x =180° as they are both form a linear pair of angles.
So, ∠y = 180° - ∠x
∠y = 180° - 135°
∠y = 45°.
d) In the fourth diagram -
∠x + ∠a =180° as they are both form a linear pair of angles.
So, ∠x = 180° - ∠a
∠x = 180° - 135°
∠x = 45°.
Now, ∠x cannot be deduced and no proper information is given in the image.
Therefore, all the angles are and their relationships are found.
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What is the slope of this line? (5 points)
Show all work.
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{3 +4}{4 +2} \implies {\large \begin{array}{llll} \cfrac{7 }{ 6 } \end{array}}[/tex]
The area of the triangle is no more than 30 square inches. Right and solve inequality that represents a.
(HELP ASAP!)
The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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√≈≈≈≈≈Which of the following is a one-to-one function? y = [[2x]], y = x^2, f(x) = { 4x + 1;x < -2
The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
A function can either have one-to-one or many-to-one mapping.
One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.
The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.
They can be examined one by one as follows,
(a) y = [2x]
It is a greatest integer function.
At x = 1.1, y = [2 × 1.1] = [2.2] = 2
And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(b) y = x²
Find values of the function at two different x as,
x = -2, f(x) = (-2)² = 4
And, for x = 2, f(x) = 2² = 4.
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(c) f(x) = 4x + 1
It is a equation of a straight line.
Which implies it has different values for different values of x.
Thus, it is a one-to-one function.
Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.
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Jackson picked apples for his family. He picked a total of 6 pounds. He took 2
3
4
pounds to his aunt and 1
7
8
pounds to his mother. How many pounds of apples were left to give to his grandmother? Use the numbers and symbols to write an equation that represents the problem, then solve the equation. Symbols may be used more than once or not at all.
2
3
4
1
7
8
6 y + =
PLEASE HELPPPPPPPP
"17/8" pounds of apples were left to give to his grandmother.
Since we have given that
The quantity of apples he picked is given by 6.1/2⇒13/2 pounds.
The quantity of apples he picked for his aunt is given by 2.3/4⇒11/4 pounds.
The quantity of apples he picked for his mother is given by 1.5/8⇒13/8 pounds.
So, the total quantity left for his grandmother is given by
first we have to add the quality of apples he picked for his aunt and the number of apples he picked for his mother.
After subtracting from what he picked.
⇒13/2-(11/4+13/8)
⇒13/2-(22+13/8)
⇒13/2-(35/8)
⇒52-35/8
⇒17/8
Hence, 17/8 pounds are left for his grandmother.
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What is a 123 triangle?
This is a triangle whose three angles are in the ratio 1:2:3 and respectively measure 30° ( π/6), 60° ( π/3), and 90° ( π/2) and the sides are in the ratio 1:√3: 2.
These triangles are also known as special right triangles, such as 30-60-90 triangles, and 45°-45°-90° triangles. Among all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs, √2/4.
The 30°-60°-90° triangle is the right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. By dividing by 3, the angle α + δ must be 60°. The right angle is 90°, and the remaining angle is 30°.
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Find the general solution y''-y'-2y=-2t+4t^2
The general solution to the given differential equation is y = c₁e⁻t + c₂te⁻t + t².
The given differential equation can be written as y'' - y' - 2y = -2t + 4t², which is a second-order linear differential equation with constant coefficients. To solve this equation, the first step is to solve the associated homogeneous equation, which is y'' - y' - 2y = 0. This homogeneous equation can be solved by using the characteristic equation, r² - r - 2 = 0, which has two roots, r = 2 and r = -1.
The general solution of the homogeneous equation is then y = c₁e²t + c₂e⁻t. To find the particular solution of the non-homogeneous equation, the method of undetermined coefficients is used. Since the non-homogeneous term is 4t², the particular solution of the non-homogeneous equation is yp = t².
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5 multiply by c 24-47-48 divide 24
Answer:
70
Step-by-step explanation:
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All the backpacks at sports galore are on sale at 30% off the marked price. Tracy bought a backpack that was marked $60. What was the sale price?
Answer:
Step-by-step explanation:
we know the 30% off the marked price.
so the sale price is 60-60*30%=42
Answer:$42.00
Step-by-step explanation: