The translated and reflected function is:
g(x) = f(-x) - 3 = 3x + 1.
How to find the equation of the transformed function?Here we want to transform a function f(x)= -3x + 4.
First, remember that a vertical translation is written as:
g(x) = f(x) + N
If N > 0, the translation is upwards.if N < 0, the translation is downwards.Then a translation of 3 units down is written as:
g(x) = f(x) - 3
Now we want to do a reflection across the y-axis, this just changes the sign of the variable, so we get:
g(x) = f(-x) - 3
Now we replace the actual function f(x) by -3x + 4, we will get:
g(x) = -3*(-x) - 3 + 4 = 3x + 1
g(x) = 3x + 1
We conclude that the transformed function is 3x + 1.
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Given two terms of each arithmetic sequence, find a₁ and d . a₁₀ = 17 and a₁₄=34
The two terms of each arithmetic sequence [tex]a_{10}[/tex] = 17 ,[tex]a_{14}[/tex] =34 are d = 17/4 and a = -21.25.
What is sequence?[tex]a_{10}[/tex] = 17
17 = a +9d.............1
[tex]a_{14}[/tex] =34
34 = a + 13d...........2
equating equation 1 and 2
17 = a +9d
34 = a + 13d
d = 17/4
d = 4.25 ..............3
from equation 3
a = -21.25
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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A not allowed
The students in a class were asked whether they preferred basketball,
netball or floorball. The ratio of students who preferred basketball to netball
to floorball was 10:9: 6. What percentage of students preferred netball?
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Answer>
Based on the given conditions, formulate: 9÷(6+10+9)
Calculate the sum or difference: 9/16+9
Calculate the sum or difference:9/25
Multiply a number to both the numerator and the denominator:9 x 4/25 x 4
Calculate the product or quotient: 36/100
Rewrite a fraction with denominator equals 100 to a percentage is 36%
therefore the percentage of the students preferred netball is 36%.
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.One percent is one hundredth of a whole. It can therefore be written as both a decimal and a fraction. To write a percentage as a decimal, simply divide it by 100. For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on.Percentages are used widely and in many different areas. For example, discounts in shops, bank interest rates, rates of inflation and many statistics in the media are expressed as percentages. Percentages are important for understanding the financial aspects of everyday life.to know more about percentage ;
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Find the sum.
2
3
+
1
5
Answer:
23+15 or 2/3+1/5
Step-by-step explanation:
23+15=48
2/3+1/5= 13/15
Add all numerators above the least common denominator then add the numbers
State the property that justifies each statement.
If x=5 and b=5 , then x=b .
Each assertion is backed up by property. This same transitive property of equality supports this.
What exactly is the transitive property?If x, y, and z are really the three quantities, as well as x is connected with y by some rule, and y is connected to z by the same rule, we can say x is connected to z using the same rule.
According to the given data:x=5
b=5
x=b.
That transitive property that equality justifies this.
because :
Transitive Property of Equality show If a = b and b = c, then a = c.
so in the given statement the x=5 and b=5 so x=b.
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| Identify the prime statements in the below compound statement
9 is odd and 9 is divisible by 3
A composite number is one that is greater than one and contains more than 2 factors.
For example, the number four can always be factorized in a variety of ways. As a result, the factors of 4 have been 1, 2, and 4. It contains more than two elements. As a result, 4 is a composite number.For the given statement;
9 is divisible by 3 can be written as;
9/3 = 3 ; as 3 is the prime number, the statement is regarded as prime statement.
For, 9 is odd.
As, 9 is not a prime but a composite number, the statement is considered as the compound statement.
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OFFERING 30 POINTS AND BRANLIEST IF YOU GET IT RIGHT!!
Sarah ordered 38 shirts that cost $7 each. She can sell each shirt for $16. She sold 31 shirts to customers. She had to return 7 shirts and pay a $2 charge for each returned shirt. Find Sarah's profit.
I didn't get this, please help me out.
Answer:
Profit = $216
Step-by-step explanation:
To solve this, let's first calculate the amount she spent buying 38 shirts at $7 each:
• total spent = 38 × 7
= $266
We are told that she then sold 31 shirts at $16 each. Using this information, let us now calculate the total amount she earnt selling these shirts:
• total earnt = 31 × 16
= $496
Next, she returned 7 shirts and paid a $2 charge for each returned shirt. Therefore, the amount she spent on returning was:
• total spent returning = 7 × 2
= $14
Therefore she earned a total of $496 and spent $266 and then $14. We can calculate her profit by subtracting the two expenditures from the earnings:
• Profit = $496 - $266 - $14
= $216
Hence her profit was $216.
Keith modeled the growth over several hundred years of a tree population by estimating the
number of the trees' pollen grains per square centimeter that were deposited each year within
layers of a lake's sediment. He estimated there were 310 pollen grains per square centimeter the
first year the grains were deposited, with a 1% annual increase in the number of grains per
square centimeter thereafter. Which of the following functions models P(t), the number of
pollen grains per square centimeter t years after the first year the grains were deposited?
A function which models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited is: D) P(t) = 310(1.01)^t.
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
Generally speaking, a mathematical model for any quantity (pollen grains) that increases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 + 0.01r)^t
Where:
P(t ) represents the number of pollen grains per square centimeter.t represents the time or number of years.I represents the initial quantity of pollen grains.Substituting the given parameters into the formula, we have;
P(t) = 300(1 + 0.01r)^t
P(t) = 310(1.01)^t
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Complete Question:
Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees’ pollen grains per square centimeter that were deposited each year within layers of a lake’s sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1% annual increase in the number of grains per square centimeter thereafter. Which of the following functions models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?
A) P(t) = 310^t
B) p(t) = 310^{1.01t}
C) P(t) = 310(0.99)^t
D) P(t) = 310(1.01)^t
What is the probability that a five card poker hand contains a flush that is five cards of the same suit?
The likelihood that a five-card poker hand will contain a flush (five cards of the same suit). = 0.001981
What is the significance of probability in everyday life?Probability is extremely important in everyday life. Weather forecasting, sports as well as gaming strategies, purchase or sale of insurance, online shopping and online games, blood group determination, and political strategy analysis
According to the given data:A standard deck of cards contain 52 cards. A five - card poker hand select 5 of the 52 cards.
C(52 , 5) = [tex]\frac{52 !}{5 !(52-5) !}[/tex]
= 52!/(5!47!)
= 2,598,960
Number of hand contenting a flush:
we need to select 1 of the 4 suits and then select 5 of the 13 cards from this suit.
C(4 , 1) = [tex]\frac{4 !}{1 !(4-1) !}[/tex]
= 4!/(1!3!)
= 4
C(13 , 5) = [tex]\frac{13 !}{5 !(13-5) !}[/tex]
= 13!/(5!8!)
= 1287
Using the product rule:
4*1287 = 5148
Probability:
5148 of the 2,598,960 hands will contain a flush.
The probability is calculated by dividing the number number favorable outcomes by the total number of possible possibilities.
P = 5148/ 2,598,960
= 33/16660
the likelihood that a five-card poker hand will contain a flush (five cards of the same suit). = 0.001981
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If 3% of a number equals 2, find 9% of that number.
Answer:
6
Step-by-step explanation:
2/.03 = 66.66...7 times .09 = 6
The number is 66.67. And the 9% of the number 66.67 will be 6.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let the number be 'x'. Then the equation is given as,
3% of x = 2
0.03 x = 2
x = 2 / 0.03
x = 66.67
Then the 9% of that number is calculated as,
⇒ 9% of 66.67
⇒ 0.09 x 66.67
⇒ 6
The number is 66.67. And the 9% of the number 66.67 will be 6.
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Which is an equivalent expression for (5^2 • 3^4)^3?
1518
5^6 • 3^12
5^2 • 3^12
5^5 • 3^7
The equivalent expression is 5^6 • 3^12.
What are laws of exponents and powers?Exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent.
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
a^m×a^n = a. ^(m+n)a^m/a^n = a. ^(m-n)(a^m)^n = a. ^(mn)a^n/b^n = (a/b)^ na^0 = 1.a^(-m) = 1/a^mGiven:
(5^2 • 3^4)^3
now, using
(a^m)^n = a^ (m*n)So,
(5^2 • 3^4)^3
= (5^2)^3 • (3^4)^3
=5^6 * 3^12
Hence, equivalent expression is 5^6 • 3^12
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TENNIS A double fault in tennis is when the serving player fails to land their serve "in" without stepping on or over the service line in two chances. Kelly's first serve percentage is 40%, while her second serve percentage is 70%.
a. Draw a probability tree that shows each outcome.
The probability tree for each outcome is drawn.
Probability for 1st successful serve is 0.4.Probability for 2nd successful serve is 0.42.Probability for no successful serve is 0.18.What is termed as probability?Probability is a mathematical concept concerned with determining the likelihood of occurrence of a given event, which is demonstrated as a range of 1 and 0. A certainty is an event with such a probability of one.
Now, as per the given question;
Kelly's first serve percentage is 40% = 0.4.
Kelly's second serve percentage is 70% which comprises of successful and faulty serve.
The probability that the second serve will be successful is;
= 0.6×0.7
= 0.42
Thus, probability that the second serve will be successful is 0.42.
Now, the probability the second serve will be unsuccessful is;
= 0.6×0.3
= 0.18
Thus, probability that the second serve will be unsuccessful is 0.18.
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1-8. For each equation below, find y if x = 2. y=7- |x| a. b. y=x²-1 C. y = √√x+14
The values of the function for x = 2.
for y = 7- |x| ; y = 5for y = x²-1 ; y = 3for y = √x+14; = 4What is defined as the linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero. A solution this, is a specific point on the graph where when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c.Part a: y = 7- |x|
The modulus function returns the magnitude and absolute value of a number, regardless of whether it is positive or negative. The modulus function is represented by y = |x| or f(x) = |x|, where f: R ---> R and x ∈ R.
Put x = 2 in the function;
y = 7- |2|
y = 7 - 2
y = 5
Part b: y = x²-1
put x = 2
y = 2²-1
y = 3
Part c: y = √x+14
Put x = 2
y = √2+14
y = √16
Squaring both side;
y = 4
Thus, the values for the function are obtained.
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The coordinates of the endpoints of QRQ (-11,-12) and (3,2). Point s is on QR and divides it such that qs:rs is 5:2
What are the corrdinates of s?
Answer:
S = (-1, -2)
Step-by-step explanation:
You want the coordinates of S on QR such that QS : SR = 5 : 2. The end points are Q(-11, -12) and R(3, 2).
Dividing pointThe coordinates of the dividing point S are the weighted sum of the end point coordinates of Q and R. The weights are the reverse of the division ratio.
S = (2Q +5R)/(2+5)
S = (2(-11, -12) +5(3, 2))/7 = (-22+15, -24 +10)/7 = (-7, -14)/7
S = (-1, -2)
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
a. Draw an acute triangle and find the circumcenter, centroid, and orthocenter.
Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.
What are acute triangles?
An acute angle triangle (also known as an acute-angled triangle) is a triangle with all of its interior angles being acute angles. Remember that an acute angle is one that is less than 90°.
A triangle with three acute angles is known as an acute triangle. An obtuse triangle has one obtuse angle and two acute angles. Because the angles of a triangle in Euclidean geometry must sum to 180°, no Euclidean triangle can have more than one obtuse angle.
Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.
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What is the conclusion of the given conditional
statement.
If it is a Thanksgiving, then we are not in
school.
Answer:
we are not in school
Step-by-step explanation:
Conditional: If it is a Thanksgiving, then we are not in school.
Hypothesis: If it is a Thanksgiving, then we are not in school.
Conclusion: If it is a Thanksgiving, then we are not in school.
Answer: we are not in school
If DM = 26 and point G lies on the perpendicular bisector of DM¯¯¯¯¯¯¯, what is the value of r? Segment D M with point G between the endpoints. Segment D G has length R plus 3, and segment G M has length 4R minus 28. A. 10 B. 13 C. 30 D. 52
Applying the segment addition postulate, the value of r is determined as: A. 10.
What is the Perpendicular Bisector?A perpendicular bisector is a line segment which divides another line segment into two equal parts, that is, the segments formed have equal lengths.
Since point G lies on the perpendicular bisector of segment DM, therefore:
DG = GM
Given the following:
DM = 25
GM = 4r - 28
DG = r + 3
Therefore:
DG + GM = DM [segment addition postulate]
Substitute
r + 3 + 4r - 28 = 25
Combine like terms
5r - 25 = 25
5r = 25 + 25
5r = 50
5r/5 = 50/5
r = 10
Thus, applying the segment addition postulate, the value of r is determined as: A. 10.
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Write an equation of each line in standard form with integer coefficients. y=4.2 x+7.9
The equation of the line y = 4.2x + 7.9 expressed in standard form is 42x - 10y = -79.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Given the equation of a line, multiply both sides by 10 to turn the decimals into integers.
y = 4.2x + 7.9
10y = 10(4.2x + 7.9)
10y = 42x + 79
Rewriting it in standard form ax + by = c,
10y = 42x + 79
42x - 10y = -79
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What is an equation for each vertical translation of y=2 x-1 ? 3/5 units up
f. y = 2x - (2/5)
g. y = 2x - (11/5)
h. y = 2x - 8/5
i. y = 2x + 1/5
The vertical translation equation of the given equation is y = 2x-(2/5). (First option)
You can do things with equations of the form y=f(x) that modify the graph in various ways.
Vertical movement means moving up and down the graph of a function. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. The form of the function remains the same, known as moving the chart along the Y axis.
Vertical translation translates each point on the graph by k units vertically and the graph/chart by k units vertically.
The vertical translation equation of y=2x-1 by 3/5 units up is y = 2x-(2/5) as y = f(x)+3/5
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(k^2-5k-2)(k^2+2) polynomial in standard form
Answer:
[tex]K^{4} -5k^{3} -10k-4[/tex]
Step-by-step explanation:
if 45 cookies will serve 15 students how many cookies are needed for 30 students
Answer: 30
Step-by-step explanation:
this is so easy
Answer:
1for 30 students i would need 90
i don’t know how to do this
Find the first six terms of each sequence. an =3 n+2
The first second third fourth and fifth term of the sequence
[tex]a_{n}[/tex] = 3n + 2 are 5, 8, 11, 14, 17 and 20 respectively.
According to the given question.
We have formula for finding the terms of the sequence, [tex]a_{n}[/tex] = 3n + 2 .
Therefore, the first term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{1}[/tex] = 3(1) + 2 = 5
The second term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{2}[/tex] = 3(2) + 2 = 8
The third term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{3}[/tex] = 3(3) + 2 = 11
The fourth term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by
[tex]a_{4}[/tex] = 3(4) + 2 = 12 + 2 = 14
The fifth term of the sequence [tex]a_{5}[/tex] = 3n + 2 is given by
[tex]a_{5}[/tex] = 3(5) + 2 = 15 + 2 = 17
The sixth term of the sequence [tex]a_{5}[/tex] = 3n + 2 is given by
[tex]a_{6}[/tex] = 3(6) + 2 = 18 + 2 = 20
Hence, the first second third fourth and fifth term of the sequence
[tex]a_{n}[/tex] = 3n + 2 are 5, 8, 11, 14, 17 and 20 respectively.
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Translate each sentence into an equation.
1. The sum of three times a and four is the same as five times a.
2. One fourth of m minus six is equal to two times the sum of m and 9.
3. The product of five and w is the same as w to the third power.
Translate each sentence into an equation. which are as follows the value of a is 2, the value of m is 13.71 and the value of w is the root of 5.
1. The sum of three times a and four is the same as five times a.
3a+4 = 5a
3a = 5a -4
4 = 5a-3a
4= 2a
2 =a
2. One-fourth of m minus six is equal to two times the sum of m and 9.
1/4m - 6 = 2 (m+9)
1/4m = 2m +18+6
1/4m = 2m + 24
2m -1/4 m = -24
7/4 m = -24
m = -24*4/7 = 13.71
The value of m is 13.71
3. The product of five and w is the same as w to the third power.
5*w = w.w.w
5 = w.w.w/w
5 = w.w
root of 5 = w
The value of w is the root of 5
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(-8) x (-2/3) =
hellpp !
Answer:
(- 8) × (- 2/3) = 16/3 = 5 1/3
Hope this helps :)
The perimeter of a square is 4 times as
great as the length of any of its sides.
Determine if the perimeter of a square is proportional to its side length. Explain.
Answer:
Perimeter of a square is proportional to side length
Step-by-step explanation:
We have the relation p = 4a, p = perimeter, a = side length
This is the equation for a proportionate relationship of the form y = k.x where y ∝ x , y directly proportional to x => y varies as x varies and always by the same constant
k is known as constant of proportionality
Here k = 4
Let's say the side of square is 1. Then perimeter = 4
If side is increased to 2, then perimeter = 4 x 2 = 8
If side is increased to 3, then perimeter is 4 x 3 = 12
So perimeter increases by a factor of 4 for every unit increase in side length
i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help
Answer:
Step-by-step explanation:
to find the bottom base you add the two numbers that make it
5+18=23
now put everything in the formula
[tex]\frac{1}{2}*12(12+23)\\[/tex]
parathesis first
12+23=35
[tex]\frac{1}{2} *12*35[/tex]
multiply in order
6*35
210
Step-by-step explanation:
i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help
1/2h (b1 + b2) is the formula for finding the area of the figure (trapezoid)
1/2 * 12 (18 + 5 + 12)=
6 * 35=
210 units²
Find the measure of ∠C F D . A. 66° B. 72° C. 108° D. 138°
The measure of CFD is 66°.
How to calculate the angle?It should be noted that vertically opposite angles are equal.
Therefore, AFE may be equal to BFD.
In this case, AFE is given as 108° while one of the other angles is given as 42°.
Therefore, the value of CFD will be:
= 102° - 42°
= 66°
The value of CFD is 66°.
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GEOMETRY HONORS
Answer Options:
Valid: Law of Syllogism
Valid: Law of Detachment
No Valid Conclusion
please answer asap, thank you all so much
Answer:
17. Invalid
Step-by-step explanation:
It is invalid because not only the angles matter but also the measurement of the sides, if one side is bigger than the other, it cannot be a square.
Which ordered pairs are solutions to the inequality y−3x<10?
(0,-4) , (0,-1) , (4,-1) are the ordered pairs are solutions to the inequality
y − 3x < 10 which is option (A) , (D) and (E) .
An inequality compares two values and indicates whether one is less than, greater than, or equal to another. a ≠ b indicates that a is not equal to b a < b indicates that a is less than b a > b indicates that a is greater than b (These two are known as strict inequalities) a ≤ b means that a is less than or equal to b a ≥ b means that a is greater than or equal to b.
We have to check whether the given options are the solutions to the inequality y− 3x < 10 . ...(1)
(A) If (0,-4) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -4 in equation (1) , we get
[tex]-4-3(0) < 10\\-4 < 10[/tex]
As the above condition is true so (0,-4) is the solution of given inequality
(B) If (-6,0) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -6 and y = 0 in equation (1) , we get
[tex]0-3(-6) < 10\\18 < 10[/tex]
As the above condition is not true so (-6,0) is not the solution of given inequality .
(C) If (-1,7) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -1 and y = 7 in equation (1) , we get
[tex]7-3(-1) < 10\\7+3 < 10\\10 < 10[/tex]
As the above condition is not true so (-1,7) is the not the solution of given inequality .
(D) If (0,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -1 in equation (1) , we get
[tex]-1-3(0) < 10\\-1 < 10[/tex]
As the above condition is true so (0,-1) is the solution of given inequality.
(E) If (4,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 4 and y = -1 in equation (1) , we get
[tex]-1-3(4) < 10\\-1-12 < 10\\-13 < 10[/tex]
As the above condition is true so (4,-1) is the solution of given inequality.
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Are these ratios equivalent?
7¢ per 3 pages
14¢ per 6 pages
Answer:
Hello!
Yes, these ratios are equivalent!
Step-by-step explanation:
Since, when we multiply both the numerator and denominator by the same number then we get an equivalent fraction.
We use multiplication or division. Whatever you do to one number of the ratio. You have to do the same thing to the other using multiplication or division. And you get an equivalent ratio.
Hope this helps!
