The decimal point is to be placed three places to the left.
What are decimal numbers?
When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.
If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.
Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.
The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.
The decimal point is to be placed three places to the left.
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Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses what is the coordinate location of the Hill
The coordinate location of the hill halfway between them is (1, -1).
How to find the distance between two points?Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses.
The coordinate location of the hill can be calculated as follows:
using mid point formula,
(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
using the end points (-2, 3) and (4, -5)
(x, y) = (-2 + 4 / 2, 3 - 5 / 2)
(x, y) = (2 / 2. -2 / 2)
(x, y) = (1, -1)
Therefore, the coordinate location of the hill is (1, -1).
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14. Harold borrowed $9,000 for 5 years at an APR of 3.6%.
a. What is Harold's monthly payment? Round to the nearest cent. (Round your answer to the nearest cent and use the rounded answer for further calculations)
b. What is the total amount that Harold paid in monthly payments for the loan?
c. What is the amount Harold will pay in finance charges?
a. Harold's monthly payment is given as follows: $164.13.
b. The total amount paid is given as follows: $9,847.8.
c. The finance charge is of: $847.8.
What is the monthly payment formula?The monthly payment formula is defined as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are listed as follows:
P is the initial amount.r is the interest rate.n is the number of payments.The values of these parameters for this problem are given as follows:
P = 9000, r = 0.036, n = 5 \times 12 = 60.
Then:
r/12 = 0.036/12 = 0.003.
Then the monthly payment is calculated as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]
A = $164.13.
Then the total amount paid is of:
Total = 60 x 164.13 = $9,847.8.
Meaning that the finance charge is given as follows:
9847.8 - 9000 = $847.8.
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Explain Harvey's error in the following scenario.
Harvey's sow has just delivered five piglets. The veterinarian has examined the mother and babies, the
piglets have nursed, and it is time for everyone to get some rest. Harvey has filled the pen with clean, dry
straw, and he puts all the pigs in the pen to spend their first night together.
Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.
How should we treat a newborn pig?When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.
Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.
Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.
According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.
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how much less is the value including 13% VAT in Rs.3200 than Rs.3820
The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."
Here, we have VAT.
A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.
Value on Rs. 3200 with 13% VAT
= 3200 + 30% of 3200
= 3200 + 960
= 4160 rupees
Now, the less value,
= 4160 - 3820
= 340 rupees.
Therefore, the less value is 340 rupees.
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the average iq test scores of an srs of 31 seventh-grade girls in a midwest school district is 105.84. suppose that the standard deviation of iq scores in this population is known to be 15. iq scores in a broad population are supposed to have mean of 100. is there evidence that the mean in this district di ers from 100? use signi cance level
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
X = 89 represent the mean of seventh-grade girls in Midwest school district
s = 15 represent the standard deviation for the sample
n = 31 sample size
μ = 100 represent the value that we want to test
'a' represent the significance level for the hypothesis test.
't' would represent the statistic (variable of interest)
[tex]p_{v}[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses,
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis: μ = 100
Alternative hypothesis: μ ≠ 100
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] ) (Equation-1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]
t = -4.08
Calculate the P-value
First we need to calculate the degrees of freedom given by:
[tex]df = n-1[/tex]
[tex]df = 31 -1[/tex]
[tex]df = 30[/tex]
Since is a two tailed test the p value would be:
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )
[tex]p_{v}[/tex] = 0.00031
Therefore,
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
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alyssa has $75 less than three times eric together they have $905 how much money do they each have
Alyssa has the money of worth $660
Eric has the money of worth $245
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the amount Alyssa has.
Let y be the amount Eric has.
alyssa has $75 less than three times eric
=> x= 3y - 75
Together they have $905
=> x + y =905
Substitute x
=> 3y - 75 +y = 905
4y = 905 +75 = 980
y = 980 /4 = 245
x= 3y - 75 = 3(245) - 75 = 660
Alyssa has $660
Eric has $245
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the perimeter of a square is 48 centimeters, what is the area in square centimeters
Answer:
144cm²
Step-by-step explanation:
If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.
48/4 = 12cm
Then, to find the area, you need to multiply 12 by 12.
12 cm x 12 cm = 144cm²
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a dark eyed man marries a dark eyed woman, but they have a blue eyed child. what is the probability that their second child will have blue eyes?
The probability that their second child will have blue eyes is 1/4.
Here dark eye is dominant trait and blue eyes is recessive trait.
So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.
Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).
So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.
Hence we get the required answer.
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Which parent function is represented by the graph?
O A. An exponential parent function
• B. The quadratic parent function
• C. The absolute value parent function
O D. The linear parent function
Parent function is represented by the graph is
B. The quadratic parent function
What is Parent function?
A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.
A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.
The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.
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It costs $270 for 3 people to go on a fishing trip. How many people can go for $1,080?
Answer:12
Step-by-step explanation:
270/3=90, this is the amount it costs for 1 person to go
1080/90=12
12 people can go for $1080
fillings how much do prices vary for filling a cavity? to find out, an insurance company randomly selects 10 dental practices in california and asks for the cash (non-insurance) price for this procedure at each practice. the interquartile range is $74.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.
2. The insurance company then computes the interquartile range of the prices for each practice.
3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
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5(x+6) - 2x = 3(x+10)
Answer:
All Real Numbers
Step-by-step explanation:
I assume you are solving for x.
The Interval Notation would be: (-∞,∞)
7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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A worker in a silver mine descends 26 feet use an integer to represent the change in the workers position
Answer: -26 feet
Step-by-step explanation:
at the city museum, child admission is $5.30 and adult admission is $9.80. on thursday, 143 tickets were sold for a total sales of $1149.40. how many adult tickets were sold that day?
The number of adult tickets which were sold that day as calculated from the given data is 29.
First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.
To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.
This is represented by the following equation,
$8.90A + $5.30C = $928
Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:
3 * C = A
Now we can answer our first problem by substituting 3 * C for A.
8.9 (3C) + 5.3C = 928
26.7C + 5.3C = 928
32C = 928
C = 29
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the owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. she randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. what are the null and alternative hypotheses for this hypothesis test?
The null and different hypotheses for hypothesis test are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
Null hypotheses
Null hypothesis is usually what researchers or scientists try and confute, and if the null hypothesis is accepted, we have a tendency should modification our opinion, i.e., we have a tendency should modification our original opinion or statement so as to match the null hypothesis. H0 denotes the null hypothesis.Given that:
sample size (η)= 196
sample proposition (p^) = 114/196
Let p denote the population proportion of people who use a loyalty card.
The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]
Hence, the null and alternative hypothesis are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
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8 (a) The formula for the area of a trapezium is A = = h(c + d)
(* Find an expression for c in terms of A, hand d.
The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
What is the area of the trapezium?
The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.
To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:
A = h(c + d)/2
2A = h(c + d)
2A/h = c + d
c + d = 2A/h
Then, we can subtract d from both sides of the equation to solve for c:
c = (2A/h) - d
Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
What is the area of the trapezium?
The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.
To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:
A = h(c + d)/2
2A = h(c + d)
2A/h = c + d
c + d = 2A/h
Then, we can subtract d from both sides of the equation to solve for c:
c = (2A/h) - d
Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
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Someone please help me with this!! I’ll give u a brainless or whatever it’s called!
Answer:
New price = 0.06 x Original price
New price $1,968
The video game club lost 8 members which was 28% of their group.
What was the original attendance of the video game club?
HELP!!!
The original attendance of the video game club was 28.57 members.
To determine the original attendance of the video game club, you can use the following formula:
Original attendance = (Number of members lost) / (Percent of group that left)
Plugging in the values from the problem, we get:
Original attendance = (8 members) / (28%)
To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:
Original attendance = (8 members) / (0.28)
Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:
Original attendance = 28.57 members
Therefore, the video gaming club had 28.57 members when it first started.
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Which of the following best describes the second law passed under the Morrill Act?
Eastern schools had to research which crops were suitable for farms in Midwestern America.
Answer:
Step-by-step explanation:
Find the amount with the same value as:
70 x 7-2
A
0
B
14
C
149
D
17
The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numerical expression is given below.
⇒ 70 / (7 - 2)
Simplify the expression, then we have
⇒ 70 / (7 - 2)
⇒ 70 / 5
⇒ 14
The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.
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The correct expression is given below.
70 / (7 - 2)
What is the approximate value of y − x? 4.9° 6.2° 11.1° 17.2°
Answer:
Step-by-step explanation:
11.1
The approximate value of y - x is 17.2°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given a right triangle LMN.
Using the tangent function,
tan (y) = 19.1 / 14.1
= 1.3546
y = tan⁻¹ (1.3546) = 53.56°
We know that,
x + y = 90°, since the other angle is 90°.
x = 90 - 53.56° = 36.44°
y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°
Hence the value of y - x is 17.2°.
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7
10
1
2/5
Cedric has
3
of the pie
of the pie
of the pie
of the nie
4
of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
C
PR
The fraction of the pie left that each friend will receive is; 3/8 of the pie
How to divide fractions?Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.
The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.
For example, 3/8 divided by 3/4 would be;
3/8 divided by 3/4 = 3/8 * 4/3
Now, we are told that cedric has 3/4 of a pie left.
Now, he wants to share equally among two of his friends, it means that;
Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8
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Complete question is;
Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
Question 1 (1 point)
How many solutions does the system of equations have?
Answer: 0
Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.
A line passes through the points (−4, 7) and (5, −8). What is the slope of the line?
Answer:
-5/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1) ==> (x1, y1), (x2, y2) are the coordinates and
m is the slope
(x1, y1), (x2, y2) ==> (x1=-4, y1=7), (x2=5, y2=-8)
m=(-8-7)/(5-(-4)) ==> plug in known values
m=(-15)/(5+4) ==> simplify
m=-15/9
m=-5/3
Solve for y in this diagram. Justify your answer.
The value of y in the isosceles triangle is AC = 6 cm
What Is an Isosceles Triangle?
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ABC
Now , the angle ∠ABC = 25°
The angle ∠ACB = 25°
So , the 2 angles of a triangle is 25° so , the third angle is 130°
So , the triangle is an isosceles triangle
And , the two sides of the triangle is AB = AC
The measure of side AB = 6 cm
The measure of side AC = measure of side AB
Therefore , the measure of side AC = 6cm
Therefore , the value of AC is 6 cm
Hence , the measure of side AC of triangle is 6 cm
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A car traveled at an average speed of 60 mph for two hours. how far did it travel? responses 30 miles 30 miles 60 miles 60 miles 120 miles 120 miles 150 miles
Answer: 120 miles
Step-by-step explanation:
If a car goes 60 miles per hour then in two hours (60×2) it will go 120
The teacher grades 16 of the 48 quizzes before school.
If the teacher grades 15 of the remaining quizzes after school, how many quizzes still need to be graded?
Responses
8 quizzes
8 quizzes
23 quizzes
23 quizzes
25 quizzes
25 quizzes
40 quizzes
The number of quizzes still need to be graded is 17quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.
For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.
Algebraic equations in mathematics frequently have one or more variables.
It is given that,
grades of the teacher out of 48 quizzes before school = 16
grades of the teacher of the remaining quizzes after school = 15
Let us assume 'X' as the number of quizzes still need to be graded.
then X= 48-16+15
=48-31
=17
Hence, The number of quizzes still need to be graded is 17quizzes.
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The number of quizzes still need to be graded is 17 quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.Algebraic equations in mathematics frequently have one or more variables.It is given that,grades of the teacher out of 48 quizzes before school = 16, grades of the teacher of the remaining quizzes after school = 15.Let us assume 'X' as the number of quizzes still need to be graded.then X= 48-=48-31
=17
Hence, The number of quizzes still need to be graded is 17 quizzes.
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Madelyn and Kaia are competing to see who can sell the most tickets for the Winter Dance. On Monday, Madelyn sold 22 and then sold 30 per day after that.
Kaia sold 53 on Monday and then sold 20 per day after that.
Write an equation to represent the number of tickets that Madelyn sold.
Write an equation to represent the number of tickets that Kaia sold.
Write a system of equations. What is the appropriate method for solving the system?
Solve the system of equations. Explain the meaning of your solution.
The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;
Tickets sold by Madelyn is; y = 22 + 30·x
Tickets sold by Kaia is; y = 53 + 20·x
A system of equation obtained from the details in the question can be presented as follows
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.
The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.
What is an equation?An equation consists of two expressions that are joined by the 'equals to' (=) sign.
The number of tickets for the Winter Dance Madelyn sold = 22
Number of tickets per day Madelyn sold after that = 30 per day
Number of tickets Kaia sold on Monday = 53
Number of tickets per day Kaia sold after that = 20 per day
Let x represent the number of days since Monday, and let y represent the number of tickets sold
Therefore;
The number of tickets Madelyn sold, y = 22 + 30·x
The number of tickets Kaia sold, y = 53 + 20·x
The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x
30·x - 20·x = 53 - 22 = 31
10·x = 31
x = 31 ÷ 10 = 3.1
The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days
Learn more on writing equations here: https://brainly.com/question/15790322
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Help please asap!!!!
Answer:
y = 1/3x + 8/3
Step-by-step explanation:
The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.
The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope of the line and (x1,y1) is a point on the line.
In our case, the equation of the perpendicular line is:
y - 2 = 1/3(x - 4)
We can simplify this equation to obtain:
y = 1/3x + 8/3
Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.
