The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.
Given that,
Use Euler's method with step size 0.5 to compute the approximate y-values y₁, y₂, y₃ and y₄ of the solution of the initial - value problem y' = y-2x. y(2)=1.
We have to find the values y₁
We know that,
What is Euler approximation?At Euler's approach, the curve of the solution can be roughly approximated at steps of h by the tangent in each interval (i.e., by a series of brief line segments). In general, using a short step size improves approximation accuracy.
By Euler approximation,
y₁ = y₀+hf(x₀,y₀)
=1+0.5(1-2(2))
=1-1.5
y₁=-0.5
Similarly,
y₂=-3.25, y₃=-7.825 and y₄=-15.3125
Therefore, The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.
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What is the possible value of a positive, even integer that's shaped like a 4?
Answer: It's not possible for a positive, even integer to have a specific shape, such as the shape of a 4. This is because integers are abstract mathematical concepts that represent whole numbers and do not have any physical properties, such as shape. Additionally, even integers are simply integers that are divisible by 2, and do not have any specific shape associated with them.
If you're asking about a specific number that has the shape of a 4, such as the number "4" written in a specific way, it's important to note that the value of a number does not depend on its physical appearance. For example, the number 4 written as "4" and the number 4 written as "IV" (the Roman numeral for 4) are both the same number, and have the same value.
Write the expression \[\frac{4+6a}{5}-\frac{1+3a}{4}\] as a single fraction.
The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
What is algebraic expression ?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
According to question
⇒ [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]
⇒ taking LCM of 4, 5 = 20
now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]
⇒ (16 +24a - 5 - 15a)/20
⇒ ((24a - 15a) - (16-5))/20
⇒ (9a - 11)/20
hence, the expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
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Can anyone help me ASAP?
Answer:
Equation 1 - x + 4y = 12
Equation 2 - 2x + 4x = 16
Cost of 1 Cheeseburger - $4
Cost of 1 Taco - $2
Step-by-step explanation:
Cheeseburger(x) and Taco(y)
x + 4y = 12 and 2x + 4y = 16
x = - 4y + 12
2(- 4y + 12) + 4y = 16
- 8y + 24 + 4y = 16
- 4y = - 8
y = 2
x + 4(2) = 12
x + 8 = 12
x = 4
Which of the following statements about histograms is true?
a. A histogram is a summary of interval data.
b. A histogram is made of a series of intervals, called classes.
c. The classes in a histogram cover the complete range of observations.
d. All of these choices are true.
The correct statement about histograms is given as follows:
d. All of these choices are true.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Each element is said in case that the histogram can represent element by element, but in the case of distribution with a wider range of possible output values, the histogram is divided into classes, and then the histogram shows the number of observations that were observed for each class, which cover the complete range of observations, meaning that the histogram is a summary of interval data.
The above paragraph, in case the histogram covers a wide range of data, means that all the statements in this problem are correct, and thus option d is correct.
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S.
5 Ester spends $40 to $50 at the
grocery store each week. She spends
about 20% of the amount on
vegetables and fruit. Which of the
following is a reasonable estimate of
the amount of money Ester will spend
on vegetables and fruit at the grocery
store the next 3 weeks?
The reasonable amount Ester will spend on vegetables is $27
How to determine the amount Ester spends?The amount is the value in $ which Ester will spend on vegetable and fruits in the grocery market. To determine the amount we have to determine the average of the current expenditure for the current period
The given parameters are
The range of values to spend
$40 to $50
Percentage of amount to spend = 20%
Number of weeks = 3
Average amount to be spend = (40+50)/2 = 90/2 = $45
(20/100)*45/1 = 9
In the next 3 weeks
In the nest 3 weeks Ester spends ($3*9)= $27
In conclusion, Ester spends $27 in the next three weeks
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Consider square ABCD. What is the angle of rotation about the center that maps AB to BC?
Recall that rotations are counterclockwise.
The angle of rotation is 90 degrees.
What is a square?
In a square, all the sides are equal in length and all the angles are right angles (90 degrees). The center of a square is the point that is equidistant from all four vertices, and it is also the point of intersection of the diagonals of the square.
The angle of rotation about the center that maps AB to BC is 90 degrees.
If we rotate the square about its center, the sides of the square will rotate to new positions. For example, if we rotate the square 90 degrees counterclockwise (as specified in the question), side AB will rotate to the position of side BC.
The angle of rotation that maps AB to BC is the angle through which the square was rotated.
Hence, the angle of rotation is 90 degrees.
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Slope =____
2
3
{1}/{3}
Answer:
slope of the line =
y2 - y1 / x2 - x1
take the appropriate point namely:
(-1,-3) as (x1,y1)
(1,3) as (x2,y2)
(you can change the position whether {-1,-3) as {x2,y2} or {1,3} as {x1,y1})
3 - (-3) / 1 - (-1)
3 + 3 / 1 + 1
6 / 2
= 3
Use the rational zeros theorem to list all possible rational zeros of the following.
h(x)= 7x^4+7x^3-2x^2-5x-5
All the possible rational zeros of h(x) are given as follows:
±1/7, ± 5/7 ± 1, ± 5.
What is the rational zero theorem?The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 7.Constant term of -5.The factors are given as follows:
Factors of 7: {1,7}.Factors of 5: {1,5}.Then the zeros are given as follows:
±1/7, ± 5/7 ± 1, ± 5.
As:
1/7 is the division of 1 by 7.5/7 is the division of 5 by 7.1 is the division of 1 by 1.5 is the division of 5 by 1.More can be learned about the rational zeros theorem at https://brainly.com/question/28782380
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A rock is thrown at 12 m/s at an angle of 60° above horizontal. (use g = 9.81 m/s2)
a. How high does the rock rise?
b. How long is it in the air if it falls to the same elevation at which it was thrown?
c. How far from the thrower does the rock land?
a) The maximum height of the rock is of: 5.50 metres.
b) The time that the rock was in the air is of: 2.12 seconds.
c) The distance which the rock landed is of: 12.72 meters.
How to model the height of the projectile?The height of the projectile is modeled using a quadratic function, as follows:
y = -4.905t² + v(0)sin(60)ºt + h(0).
The parameters are given as follows:
-4.905 is the acceleration of the gravity divided by 2.v(0) = 12 is the initial velocity.60º is the angle.h(0) = 0 is the initial height.Considering the values of these parameters, the function is given as follows:
y = -4.905t² + 10.39t.
The coefficients are given as follows:
a = -4.905, b = 10.39, c = 0.
The maximum height is obtained as the y-coordinate of the vertex, as follows:
Hmax = -(10.39² - 4(4.905)(0))/(4(-4.905)) = 5.50.
The rock hits the ground when:
y = 0.
Hence:
-4.905t² + 10.39t = 0
t(-4.905t + 10.39) = 0.
4.905t = 10.39
t = 10.39/4.905
t = 2.12 seconds.
The horizontal distance is given as follows:
x = v(0)cos(60º)t
Hence:
x = 12 x 0.5 x 2.12 = 12.72 meters.
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A reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours. If the tank originally contained 200 gallons of coolant, approximately how many gallons are in the tank after 8 hours?
The gallons after 8 hours will be 3400 gallons.
How to illustrate the expression?Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.
In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.
Therefore, the gallons after 8 hours will be:
= 200 + 400(8)
= 200 + 3200
= 3400 gallons.
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What is the product?
2•[-1]
[0]
Answer:
-2
Step-by-step explanation:
Solve the system if we x-3y=0 and 3x-6y=9 by combining the equations.
Step-by-step explanation:
Hope u get it x=3×3
x=9
It didn't include in the photo
Marisol needs to purchase AT LEAST 55 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Marisol purchase with $19.00 at the Party Palace?
The combination of streamers and balloons at the Party Palace will be 21 and 34, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Marisol necessities to buy Somewhere around 55 party enrichments. The Party Castle charges $0.50 per beautiful decoration and $0.25 per expansion, including the charge.
Let 'x' be the number of decorative streamers and 'y' be the number of balloons. Then the equations are given as,
0.50x + 0.25y = 19 ...1
x + y = 55 ...2
From equations 1 and 2, then we have
0.50x + 0.25(55 - x) = 19
0.25x = 5.25
x = 21
The value of y is given as,
21 + y = 55
y = 34
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A graphing calculator is recommended.
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.)
Weights of Student Lab Rats
Linda's rats Tuan's rats Javier's rats
46.3 49.8 53.3
42.3 42.7 43.1
44.1 41.8 40.2
48.7 48.9 47.7
40.8 46.5 51.5Enter an exact number as an integer, fraction, or decimal.
df(num) =
Enter an exact number as an integer, fraction, or decimal.
df(denom) =
State the distribution to use for the test.
A. F2, 12
B. F12, 2
C. F14, 2
D. F14, 12
E. F2, 14
What is the test statistic? (Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
A. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
B. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
C. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
D. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =
(ii) Decision:
reject the null hypothesisdo not reject the null hypothesis
(iii) Reason for decision:
Since α < p-value, we do not reject the null hypothesis.
Since α > p-value, we reject the null hypothesis.
Since α < p-value, we reject the null hypothesis.
Since α > p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
There is not sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
The graph representation of the given distribution is attached below.
The term graph in math refers the visual representation of the collection of data that has the x and y coordinate values.
Here we have given that Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams and we need to find the graphical representation of the distribution.
Here by using the values in the foregoing ANOVA table are quickly produced by the calculator, including the test statistic and the p-value of the test calculator shows :
=> F=0.66853555
=> p = 0.530548
And the FACTOR df =2 and SS=23.212
=> MS = 11.606
Here the ERROR df = 12
=> SS=208.324
=> MS = 17.36
Here by using the f distribution for the test of three different means.
Then the value of the test statistic (F-value) is 0.668 and the p -value for the test is 0.5301
When we plot the graph for the distribution then we get he graph like the following.
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Evaluate the expression for the given value of the variable 4c - 3. C= -2
Answer:
-11
Step-by-step explanation:
4c - 3 Substitute -2 for c
4(-2) - 3
-8 - 3
-11
Answer:
-11
Step-by-step explanation:
We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.
4c - 3 ⇒ 4(-2) - 3
Now, we can simplify this.
-8 - 3 = -11
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Graph the solution of the inequality on a number line.
2(x − 3) – 5x < x-2
Ο
Α.
OB.
OC
OD.
℗
-5 -4 -3 -2 -1 0 1 2
←
+1
-5 -4 -3 -2 -1 0 1
#2
0111
1
-5 -4 -3 -2 -1 0
2
3 4 5
3 4 5
3 4
+
5
4
110111
-5 -4 -3 -2 -1 0 1 2 3 4 5
Answer:
Choice D : x > - 1
Step-by-step explanation:
Left hand side (LHS) of the inequality can be siimplified
[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]
Inequality becomes
[tex]-3x-6 < x-2[/tex]
Move x to the left side and -6 to the right side:
[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]
Multiply both sides by -1(the inequality sign changes to >)
[tex]4x > -4\\\\[/tex]
Divide both sides by 4:
[tex]x > -1[/tex]
The number line corresponding to this is the fourth choice
Use the drawing tools to form the correct answer on the graph.
A buoy marks a channel for boat navigation and bobs up and down with the motion of the wave
the buoy above sea level, in feet, after t seconds.
The function f(t) = 2cos (∏/4 t) lowest at (4,-2), (12,-2),(20,-2). The points are pl0ted in the graph.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function is f(t) = 2cos (∏/4 t).
f(t) will be lowest when cos (∏/4 t) is lowest.
The value of cosine lies between -1 to 1.
When cos (∏/4 t) = -1, f(t) has lowest value.
Solve the equation cos (∏/4 t) = -1
cos (∏/4 t) = -1
∏/4 t =cos ⁻¹ (-1)
∏/4 t = (2n + 1)∏
t = (2n + 1)4 where n is a whole number.
The value of the function is lowest at t = 4, 12, 20.
The lowest points are (4,-2), (12,-2),(20,-2) etc.
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Answer: (4, -2) (12,-2)
Step-by-step explanation:
55]
Evaluate the expression a² + b ÷ 3 for each set of given values. Enter each number in the provided box.
a = 4, b=3 |
a=2,b=21
a = 3, b = 6
Evaluating the expression a² + b ÷ 3 for each set of given values we have
a = 4, b=3, and a² + b ÷ 3 = 17a=2, b=21, and a² + b ÷ 3 = 11a = 3, b = 6, and a² + b ÷ 3 = 11How to evaluate the expressionsThe expressions are evaluated using substitution as done below
for a = 4, b=3
substituting the the values of a and b
= a² + b ÷ 3
= 4² + 3 ÷ 3
= 16 + 1
= 17
For a=2, b=21
substituting the the values of a and b
= a² + b ÷ 3
= 2² + 21 ÷ 3
= 4 + 7
= 11
For a = 3, b = 6
substituting the the values of a and b
= a² + b ÷ 3
= 3² + 6 ÷ 3
= 9 + 2
= 11
substituting the values yielded the results as 17, 11 and 11
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noemi strings together x green beads at $0.75 each with 3 blue beads at $0.30 each. she makes a bracelet that averages $0.60 per bead. choose an equation to model the situation.
The equation to model on this situation is :
0.6 = (0.75x + 0.9)/(x + 3)
Noemi makes bracelets averaging $0.60 per bead, so we need to write an equation that models this average bead cost. This can be found by dividing the total bead cost by the number of beads used.
1. The total cost of a bead can be found by multiplying the price of each type of bead by the number used and adding these values together.
So:
Total Cost = 0.75x + 3*0.3
= 0.75x + 0.9
2. Total number of beads = x + 3
3. Thus, the average cost is:
(0.75x + 0.9)/(x + 3)
4. Using the value of the average cost per bead given to us ($0.60), we can now write up the full equation:
0.6 = (0.75x + 0.9)/(x + 3)
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The answers please I need answers
The scale factors of the given figures and their similarity statements are:
1. ΔHJG ~ ΔCAB; 1/3
2. ΔNPM ~ ΔABC; 2
3. KJML ~ CDAB; 2
Using proportions, the values of x are:
4. x = 10
5. x = 6
6. x = 30
How to Find the Scale Factor?The scale factor = the ratio of the corresponding sides of the similar figures = New figure/original figure.
1. The similarity statements of the given figures is, ΔHJG ~ ΔCAB
Scale factor = 4/12 = 1/3
2. ΔNPM ~ ΔABC
Scale factor = 14/7 = 2
3. KJML ~ CDAB
Scale factor = 12/6 = 2
4. 40/x = 20/5
Cross multiply:
20x = 200
Divide both sides by 20
x = 10
5. 18/x = 21/7
21x = 126
x = 6
6. 6/x = 3/15
3x = 90
Divide both sides by 3
x = 30
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Which expression shows how much greater the volume of the larger cube is than the volume of the smaller cube?
option D
Given;
larger cube edge length - 3x+2 units
smaller cube edge length - 2x-1 units
We know that volume of a cube = (Edge of the cube)3
volume of larger cube = (3x+2 )³
=27x³+8 +54x²+36x
volume of smaller cube=(2x-1)³
=8x³-1 -12x²+6x
Volume difference = volume of larger cube -volume of smaller cube
volume difference =( 27x³+8+54x²+36x)-(8x³- 1 - 12x²+6x)
= 19x³+9+66x²+30x
=19x³+66x²+30x+9
Hence volume of larger cube is greater by (19x³+66x²+30x+9)
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each year, 40% of a salmon population is extracted from a farming pond. at the beginning of the next year, the pond is stocked with an additional fixed amount of n caught wild salmon. let pn denote the amount of fish at the beginning of the n-th year assume that the initial salmon population on the pond is p0=5000
a. Write a recursion to describe Pn. b. Determine the value of N so the amount of fish remains constant at the beginning of each year.
(a) [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]
(b) [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]
Given,
Initial salmon population [tex]p_{0}=5000[/tex]
Extraction rate = 40% per year
(a) Formula for recursion,
For the first year,
[tex]p_{1} =p_{0} -0.4p_{0}+n[/tex]
For the second year,
[tex]p_{2} =p_{1} -0.4p_{0} +n[/tex]
For the n'th year,
[tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]
(b) The value of n,
From the above equation,
[tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]
[tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]
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Each year, 40% of the salmon population is extracted from a farming pond.
a. The recursion to describe Pn is Pn = 0.6 Pn-1 + N.
b. The value of N is 3000.
What is recursion?According to the recursion equation, the quantity of fish at the start of the nth year. Pn, is equal to 0.6 times the quantity at the start of the year before, Pn-1, plus the constant quantity of wild salmon that is restocked every year, N.
b. We can set the recursion equation equal to the initial population of 5000 fish in order to get the value of N that ensures the quantity of fish stays constant at the start of each year. Now we have the equation.
0.6Pn-1 + N = 5000. Solving for N gives us N = 3000.
Therefore, a. Pn = 0.6 Pn-1 + N. b. 3000.
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Translate the verbal expression into an algebraic inequality, solve and graph your answer:
The quotient of a number and -3 plus 5 is at least 12.
The complete answer for the verbal expression into an algebraic inequality is [tex]\frac{n}{-3} +5 \geq 12[/tex] .
What are inequality?
In arithmetic, the relationship between 2 values that are not equal is outlined by inequalities. difference means that not equal. Generally, if 2 values don't seem to be equal, we tend to use “not equal (≠)”.
Main body:
First, let's call "a number": n
"The quotient" means we are dividing.
Therefore, "the quotient of a number and -3" can be written as:
n÷ -3
now we need to add 5 to the expression ,
[tex]\frac{n}{-3} +5[/tex]
The quotient of a number and -3 plus 5 is at least 12.
so the expression found out till is equal to at least 12 which means sign used is " ≥"
Hence , the complete answer is [tex]\frac{n}{-3} +5 \geq 12[/tex] .
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Helppp pleaseee it’s due today pleasee
Answer:
4
6
y=4x+6
Step-by-step explanation:
check the attached file
Find the probability that if 10 different-sized washers are arranged in a row, they will be arranged in order of size. Use a graphing calculator and round the answer to six decimal places. The probability of the washers arranged by size is ______.
The probability of the washers arranged by size is 2.755731 ( six decimal places).
Probability
Probability is simply the possibility of something happening. When we are unsure about the outcome of an event, we can discuss the probabilities of various outcomes . Statistics is the study of probability-governed events.We can arrange them in 10! = 3628800 different ways.
There is only one way to arrange them in size order.
The washers arranged by size have a probability of
1/3628800 = 2.75573192
≈ 2.755731 (six decimal places)
Therefore, The probability of the washers arranged by size is 2.755731
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If a loading ramp is placed next to a truck, at a height of 8 feet, and the inclined portion of the ramp is 23 feet long, what angle (in degrees) does the ramp make with the ground?
Answer:
≈20.35°
Step-by-step explanation:
height = 8
hypotenuse =23
angle is x
sin(x) =8/23
[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°
x is about ≈20.35°
The ramp makes an angle of approximately 20.86 degrees with the ground.
Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,
we need to find the angle ramp make with the ground.
To find the angle that the ramp makes with the ground, we can use the sine function.
The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.
In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).
Let's calculate the angle:
sin(angle) = opposite/hypotenuse
sin(angle) = 8/23
To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:
angle = arcsin(8/23)
We can find the approximate value of the angle:
angle ≈ 20.86 degrees
Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.
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Find composition of A and B
A ={(1;2);(-3;0);(4;7)}
B ={(2;1);(0;3);(4;-3)}
A o B=
The composition of A and B represents by the set A o B = {(2,2),(4,0)}
What is a set of ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Given sets are
A = {(1,2), (-3,0), (4,7)}
B = {(2,1), (0,3), (4,-3)}
The inputs of B are 2, 0, and 4.
The outputs of B are 1, 3, and -3.
The inputs of A are 1, -3, and 4.
The outputs of A are 2, 0, and 7.
The composition can be written as A o B = A(B(x)
A(B(2)) = A(1) = 2
A(B(0)) = A(3) = not valid [Since 3 is not an input of A].
A(B(4)) = A(-3) = 0
The composition is {(2,2), (4,0)}.
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11. A triangle has a base length of 3.9 cm and a height of 9 cm. Which dimensions could
be the measurements of a similar triangle?
The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm
How to Identify a similar triangle?Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.
Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.
Thus, this means that a similar triangle will have same ratio of side lengths. Thus;
If new height is h and new base is b, then we have;
9/h = 3.9/b
Thus,
h/b = 9/3.9
If we multiply the right side top and bottom by 2, then we have;
h/b = 18/7.8
18 and 7.8 cm could be similar dimensions.
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Given the points (1, -4) and (4, 5), construct two equations in point slope form using each of the points. Construct and upload the graph of the line. Show your work and upload your graph for your teacher to review.
The equation of line passes through the points (1, -4) and (4, 5) will be;
⇒ y = 3x - 7
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, -4) and (4, 5).
Now,
Since, The equation of line passes through the points (1, -4) and (4, 5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-4)) / (4 - 1)
m = 9 / 3
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - (-4)= 3 (x - 1)
⇒ y + 4 = 3x - 3
⇒ y = 3x - 3 - 4
⇒ y = 3x - 7
Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;
⇒ y = 3x - 7
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Write another division problem that has a quotient of 3 and a remainder of 28.
Division problem with quotient of 3 and a remainder of 28 are-
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.Explain the term quotient of the division?The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient.In this example, the number being divided (15) is known as the dividend, as well as the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how 15 ÷ 3 = 5 is a correct equation even if you change the quotient and divisor. 15 ÷ 5 = 3.The given data is-
quotient=3remainder=28To estimate:
division problem?
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.To know more about the quotient of the division, here
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