I don’t understand this question. Can you help me?
Answer:
0.5
Step-by-step explanation:
The two figures are similar
find the linear scale factor of the two figures
=L/l ......... 10/4
=2.5
use the linear scale factor to find the other side
2.5= 5/n
2.5n=5 divide both sides by 2.5
n=0.5
S(t) = 3.1 ln(t) + 22 billion dollars (2 ≤ t ≤ 12),
where t is the year since 2000.† What was the total spent in 2010 (t = 10)? (Round your answer to the nearest whole number.)
How fast was it increasing? (Round your answer to three decimal places.)
The total spent in 2006 is nearly 28 billion dollars.
What is Logarithm function ?A logarithmic function is a function of the form. which is read “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1. There are no restrictions on y.
here, we have,
The total spent on research and development by the federal government in the United States given by function,
S(t) = 3.1 ln(t) + 22
To find total spent in 2006.
We have to substitute t=6 in given function.
S(6) = 3.1 ln(6) + 22
= 5.5 + 22
=27.5
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In the figure below, I || h. Find the values of y and x.
81°
y (6x - 51)
y = 0
X =
The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.
What is transversal?There are several different kinds of lines that can exist in geometry, including parallel, perpendicular, intersecting, and so on. A transversal is a different line that we have in addition to that. A road crossing two or more other roads or a railway crossing several other lines are examples of this. These convey the fundamental concept of a transversal. If two or more other lines in the Euclidean plane are parallel, transversals are crucial in determining this. Learn the definition of a transversal line in this article, along with how it can be used to create angles with both parallel and non-parallel lines. Study additional geometrical ideas here.
Given, I || h
Using the same internal property of transversal
81 + x = 180° (angle sum property)
x = 180 - 81
x = 99°
For (3y + 33), vertical opposite angle rule can be applied so
x = (3y + 33)
3y + 33 = 99°
3y = 99 - 33
3y = 66
y = 66/3
y = 22°
Thus, The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.
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Correct question:
In the figure below, I || h. Find the values of y and x.
a clock loses 10 seconds in every two hours. in how many hours will it take to lose one hour
Answer:
The watch loses 5 seconds per hour. It is 5 minutes slow. 5 minutes is 300 seconds(5 x 60). 300 seconds therefore represents 300/5 hours=60 hours. From Tuesday 10.30 AM backwards 60 hours(2 1/2 days) brings you to 10.30 PM on Sunday evening as the date and time the watch was last set.
Step-by-step explanation:
For the right triangles below, find the values of the side lengths B and C .
Round your answers to the nearest tenth.
For the given right triangles the value of side b is [tex]4\sqrt{3}=6.9[/tex] meanwhile the value of side c is [tex]2.5\sqrt{2} =3.5[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem. The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The question asks the values of the side lengths b and c. The variables b and c represent one of the sides of the right triangles.
Finding the side b - You should apply the trigonometric ratio sin (Ф). Knowing that: sin (Ф)=[tex]\frac{opposite\ side}{hypotenuse}[/tex] and sin (60)=[tex]\frac{\sqrt{3}}{2}[/tex], you can write:sin (60)=b/8
[tex]\frac{\sqrt{3}}{2}=\frac{b}{8} \\ \\ 2b=8\sqrt{3} \\ \\ b=4\sqrt{3}=6.9[/tex]
Finding the side c - You should apply the trigonometric ratio sin (Ф). Knowing that: sin (Ф)=[tex]\frac{opposite\ side}{hypotenuse}[/tex] and sin (45)=[tex]\frac{\sqrt{2}}{2}[/tex], you can write:
[tex]\frac{\sqrt{2}}{2}=\frac{c}{5} \\ \\ 2c=5\sqrt{2} \\ \\ c=\frac{5}{2} \sqrt{2}\\ \\ c=2.5\sqrt{2}=3.5[/tex]
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In a group of 59 traders 26 sell gari 8 sell only rice 15 sell only maize 10 sell gari and rice 16 sell rice and maize and 42 sell maize.each trader sell at least one of the three items.find the number if traders who sell
A.gari or maize
B.gari and maize
C.only two food items
The number of vendors selling maize or gari Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. 16 sell wheat and maize, 10 sale gari and rice, 42 sell maize, and 6 sell gari.
How is math used in trading?To assess the trading strategies used by traders to complete a trade transaction, mathematical analysis is employed. Moreover, probability theory is used to evaluate the usefulness of money management strategies.
Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. Ten sell rice and gari, sixteen sell rice and maize, and forty-two sell maize.
Determine the quantity of dealers selling gari of corn using the formula below:
P(G ∪ R ∪ M) = P(G) + P(R) + P(M) - P(G ∩ R) - P(R ∩ M) - P(G ∩ M) + P(G ∩ R ∩ M)
59 = 26 + 8 + 15 - 10 - 16 - P(G ∩ M) + 42
59 - 42 = 49 - 26 - P(G ∩ M)
P(G ∩ M) = - 17 + 23
P(G ∩ M) = 6
Hence, there are 6 dealers selling gari or corn.
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A wine maker can make 14 bottles of wine with 80 pounds of grapes. If the wine maker picks 625 pounds of grapes, how many bottles of wine can be made? round to the nearest whole bottle.
Answer:First, we can calculate how many bottles of wine can be made per pound of grapes:
14 bottles / 80 pounds = 0.175 bottles / pound
Next, we can multiply this number by the number of pounds of grapes the wine maker has to find the total number of bottles of wine that can be made:
0.175 bottles / pound * 625 pounds = 110.31 bottles
Rounding to the nearest whole bottle, we find that the wine maker can make 110 bottles of wine with 625 pounds of grapes.
Step-by-step explanation:
Each equation below is a characteristic equation for a recurrence relation. Express the solution to each recurrence relation as a linear combination of terms. Note that you will not know the actual coefficients in the linear combination since you are not given the base cases, so you can use a1, a2, etc.
(a) (x − 1)(x + 2) = 0
(b) (x − 4)(x − 4) = 0
(c) (x − 4)(x − 4)(x + 5) = 0
(d) (x − 4)(x − 4)(x + 5)^4 = 0
The solutions to each recurrence relation can be expressed as a linear combination of terms:
The general solution to the recurrence relation can be written as a1 * 1^n + a2 * (-2)^n.The general solution to the recurrence relation can be written as a1 * 4^n.The general solution to the recurrence relation can be written as a1 * 4^n + a2 * 4^n + a3 * (-5)^n.The general solution to the recurrence relation can be written as a1 * 4^n + a2 * 4^n + a3 * (a root of (x + 5)^4)^n.For (a) The solution to (x - 1)(x + 2) = 0 is
x = 1 and x = -2.For (b) The solution to (x - 4)(x - 4) = 0 is
x = 4.For (c) The solution to (x - 4)(x - 4)(x + 5) = 0 is
x = 4, x = 4, and x = -5.For (d) The solution to (x - 4)(x - 4)(x + 5)^4 = 0 is
x = 4, x = 4, and the 4 roots of (x + 5)^4 = 0.These linear combinations of terms can be used to describe the general solution to each recurrence relation, but the actual coefficients in the linear combination are not given and depend on the base cases of the recurrence relation.
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Please help me out with this, thank you so much!
The ranges of each equation for the domain {-2,0,2} are given as follows:
y = -x -> {-2, 0, 2}.y = x² - 3 -> {1, -3}.y = 3 + x -> {1, 3, 5}.y = 0.5x + 1 -> {0, 1, 2}.How to obtain the ranges?The domain is the set of input values for each equation, hence the range will be the set of output values for the given domain.
For the equation y = -x, the range is obtained as follows:
x = -2 -> y = -(-2) = 2.x = 0, y = -0 = 0.x = 2, y = -2.Hence the range is:
{-2, 0, 2}.
The same procedure is applied to the other equations, the range is the set containing the numeric value of the function for each input value.
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Which number sentence is true?
A. 82 < |-82|
B. |-82| < |-83|
C. |-83| < |83|
D. |82| > |-83|
A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 15 ft, its width is 9 ft, and its surface area is 606 ft squared (In the figure, Assume that the given surface area includes that of the top lid of the box.)
the studentof class 5 had their sports day on 5th february.If they started parctising 35 days earlier on wich date did the parctice begin?
Answer:
January 2nd
Step-by-step explanation:
subtract 5 from February and 30 from January
Which of the answers is equal to sec(x)? *
O 1/cot(x)
O 1/sin(x)
O 1/cos(x)
O 1/csc(x)
The answer choice which is equivalent to sec (x) among the given answer choices is; 1 / cos(x).
Which answer choice is equal to sec (x)?It follows from the task content that the answer choice which is equivalent to sec (x) is to be determined among the given answer choices.
From trigonometric ratios concept, it follows that the inverses of the 3 basic trigonometric ratios are as follows;
1 / sin x = csc (x)
1 / cos x = sec (x)
1 / tan x = cot (x)
On this note, it follows that the answer choice which is equivalent to sec (x) is; 1 / cos x.
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See if you can find how many solutions these systems of two linear equations have.
Type 0, 1, or infinite in the answer box.
y=4x - 5
y=3x - 7
Answer:
1
Step-by-step explanation:
The two equations have one solution. This is because when the two equations are graphed, the lines intersect in only one point. Therefore, the system only has one solution.
What is the vertex of the function f(x)=-1/2|x+8|-5
Hello :3
Answer:
(-8,-5)
Hope this helps! :)
Please help with this question I will give brainleist
The number of phones and accessories sold are 8 and 24 respectively.
How to find the number of phone and accessories sold?Indigo works as a salesperson at an electronics store and sells phones and phone accessories. Indigo earns a $8 commission for every phone she sells and a $4 commission for every accessory she sells. On a given day, Indigo made a total of $160 in commission from all accessory and phone sales and she sold 3 times as many accessories as phones.
Therefore, the number of phones and accessories she sold can be calculated as follows:
Using equation,
let
x = number of phone sold
y = number of accessories sold.
Therefore,
8x + 4y = 160
y = 3x
Therefore,
8x + 4(3x) = 160
8x + 12x = 160
20x = 160
x = 160 / 20
x = 8
Hence,
y = 3(8) = 24
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Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]
The density function of [tex]U = Y1^2 +Y2^2[/tex] is given by the formula [tex]f_U(u) = (1/2π)∫_0^∞ f_Y1(y_1)f_Y2(√(u-y_1^2)) dy_1[/tex]. This can be calculated as follows:
Let u ≥ 0, then
[tex]f_U(u) = (1/2π)∫_0^∞ (1/√(2π))e^(-(y_1^2/2))(1/√(2π))e^(-(√(u-y_1^2)^2/2)) dy_1[/tex]
[tex]= (1/2π)∫_0^∞ (1/2π)e^(-u/2) dy_1= (1/2π)e^(-u/2) ∫_0^∞ (1/2π) dy_1= (1/2π)e^(-u/2)[/tex]
Therefore, the density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]
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ACTIVITY 2 Nomusa is a 65-year-old female educator who carned a gross income of R28 500 per month. A monthly deduction of 7,5% was made from her salary and paid into her pension fund. Use the 2019/2020 Income Tax table below to answer the questions that follow. TAX RATES FOR 2019/2020 TAX YEAR (1 March 2019 to 28 February 2020) TAX BRACKET TAXABLE INCOMET RATES OF TAX(R) 195 850 195 851 305 851 555 601 708 311 se 305 850 423 300 $$$ 600 708 310 1 500 000 1 500 001 and above TAX REBATES 2.1 Define the term gross salary. 2.2 Main member First dependant Each additional dependant U102/2023 Test 4 18% of taxable income 35 253 26% of taxable income above 195 850 63 853 +31% of taxable income above 305 850 100 263 + 36% of taxable income above 423 300 147 891 +39% of taxable income above 555 600 207 448 +41% of taxable income above 708 310 532 041 +45% of taxable income above 1 500 000 TAX THRESHOLD R79 000 R122 300 R14 220 R7 794 Primary Secondary (65 and older) Tertiary (75 and older) R2 601 R136 750 MEDICAL TAX CREDIT PER MONTH FOR MEDICAL FUND MEMBERS R310 R310 R209 What is the maximum taxable income for bracket 4 SOURCE: www.ars.g. 2.3 Determine Nomusa's monthly taxable income. 2.4 Identify the tax bracket Nomusa falls in based on his annual taxable income Marks 2.3 Calculate Nomusa's monthly tax in the 2019/2020 tax year. 2.6 Nomusa stated that if she were 10 years younger, she would have paid RS 502.34 monthly tax. Show with calculations whether Nomusa's statement is valid. 2.7 Nomusa is considering joining a medical fund. She plans to include his husband and two grandchildren. Determine the total monthly medical credits she would qualify for if she joined a medical 2.8 Nomusa's brother, who is 45 years old, earned a monthly taxable income of R45 980,17 during the 2019/2020 tax year. He is not a member of any medical scheme. Show, using calculations, that his monthly tax was R11 024,11 TOTAL (5) (3) 1307 Page c,z of 78
Nomusa's statement is not valid because her monthly tax is not equal to R502.34.
What do you mean by medical fund?A medical fund is a type of financial arrangement that individuals, families, or organizations set up to pay for medical expenses. The purpose of a medical fund is to help cover the cost of medical treatments, procedures, or medications that may not be covered by insurance. There are different types of medical funds, including personal savings accounts, health savings accounts (HSAs), flexible spending accounts (FSAs), and crowdfunding platforms that allow people to raise money for medical expenses. These funds can be used to pay for a variety of medical expenses, including doctor visits, surgeries, prescription drugs, and medical equipment. The goal of a medical fund is to provide individuals and families with a source of financial support for medical expenses, and to help reduce the financial burden associated with medical care.
Gross salary is the total amount of money earned by an individual before any deductions or taxes have been taken out.
2.3 Nomusa's monthly taxable income can be determined as follows: Gross salary = R28 500; 7.5% pension deduction = R28 500 x 7.5% = R2,137.5; Monthly taxable income = Gross salary - pension deduction = R28 500 - R2,137.5 = R26,362.5
2.4 Based on Nomusa's annual taxable income of R26,362.5 x 12 = R316,350, she falls in tax bracket 4, with a taxable income between R305,850 and R423,300.
2.5 Nomusa's monthly tax can be calculated as follows: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R316,350 - R195,850) = 26% x R120,500 = R31,230; Total tax = R35,253 + R31,230 = R66,483; Monthly tax = Total tax ÷ 12 = R66,483 ÷ 12 = R5,540.25.
2.6 To determine whether Nomusa's statement is valid, we would have to calculate her monthly tax if she were 10 years younger, and compare it to the stated amount of R502.34: If she were 10 years younger, she would not be eligible for the secondary tax threshold, so her monthly tax would be the same as calculated in 2.5: R5,540.25. This amount is not equal to R502.34, so Nomusa's statement is not valid.
2.7 If Nomusa joins a medical fund and includes her husband and two grandchildren, she would qualify for the following monthly medical credits: For herself: R310; For her husband: R310; For each grandchild: R209; Total monthly medical credit = R310 + R310 + 2 x R209 = R936.
2.8 To calculate Nomusa's brother's monthly tax, we can use the same process as in 2.5: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R45,980.17 - R195,850) = 26% x (R26,129.17) = R6,792.19; Total tax = R35,253 + R6,792.19 = R42,045.19; Monthly tax = Total tax ÷ 12 = R42,045.19 ÷ 12 = R3,503.77, which is approximately R11,024.11.
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You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
Frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
The independent variable is distance from the left end of the radio dial and its unit is centimeters.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
The given coordinate points are (53, 1.54), (60, 2.17), (70, 2.95), (80, 3.62), (100, 4.75)
Here,
1.a) The independent variable is distance from the left end of the radio dial and its unit is centimeters.
b) The dependent variable is frequency and its units is kilohertz.
2. a) A scatter plot of the data is given below in the attachment.
b) The distance from the left end of the radio as the frequency gets higher is increases.
c) The distance from the left end of the radio as the frequency gets smaller is decreases.
Therefore, the independent variable is distance from the left end of the radio dial and its unit is centimeters.
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An art teacher found that in a bin of markers,1/2 of the caps had been left off the markers. Of these markers,2/4 of them were dried up. Use the model to find what fraction of the markers had the lids left off and were dried up.
The surface area of a prism is 54 square inches. What is the surface area of a similar prism that is smaller by a scale of 1/3? Help!!!
Answer:
18 Square inches
Step-by-step explanation:
Surface Area of original prism: 54 square inches
Surface Area of similar prism:
1/3 x 54
=18 square inches
help
Find and simplify the expression if f(x) = x² - 8.
f(-3)=? (simplify)
What is the prime factorization of 246?
Step-by-step explanation:
Start by dividing it by a prime number and just go from there. The included pictures will show how :) Because the end result is all prime numbers it is prime factorization.
Which inequality shows the region represented by the
inequality in vertex form?
Oy2(x-50)² +625
O yz-(x +50)² +625
O y2(x +50)² +625
O yz-(x-50)² +625
The appropriate answer to that same previous information is y ≥ -(x-50)² + 25
Why does inequality matter?According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller share of their earnings than do poorer households, concentrated riches lower the amount of demand within the economy. The economy may suffer if low-income families have fewer possibilities.
Assume that the equation is y = a(x-h)² + k
y - a (x-50)² + 625
Put (61,504) in the equation
504 = a(61 - 50)² + 625
504 = a.121+625
121a = -121
a = -1
y = -(x-50)² + 625
Hence, y ≥ - (x-50)² + 625
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A case of vegetable costs $10.68. He can spend at most $50 for this project. what is the maximum amount of cases of vegetables he can buy
Answer:
4
Step-by-step explanation:
The maximum number of cases of vegetables that he can buy can be calculated by dividing the maximum budget of $50 by the cost of a single case of vegetables, which is $10.68:
$50 ÷ $10.68 = 4.67 cases
Since you can't buy fractional cases, the maximum number of cases he can buy would be 4. Round down to the nearest whole number, the maximum number of cases he can buy is 4.
A package contains II resistors, 2 of which are defective. If5 are selected, find the probability of getting the following results. Enter your answers as fractions or as decimals rounded to 3 decimal places. 0 defective resistors P (0 defective) = 3/11 I defective resistor P (l defective) = 252/462 2 defective resistors P(2 defective) =
If a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting
a) 0 defective resistors: 0.3164
b) 1 defective resistor: 0.4219
c) 3 defective resistor: 0.0469
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Probability
First step is to calculate the probability for a defective resistor and non-defective resistor:
Probability=3/12
Probability =0.25
Non-defective resistor:
Probability=(1-0.25)
Probability=0.75
Now let find the probabilities for defective resistors from 0 to 3
P(0)=1(0.75)^4 ×(0.25)^0
P(0)=0.3164
P(1)=4(0.75)^3× (0.25)^1
P(1)=0.4219
P(2)=6(0.75)^2× (0.25)^2
P(2)=0.2109
P(3)=4(0.75)^0×(0.25)^3
P(3)=0.0469
P(4)=1(0.75)^0 × (0.25)^4
P(4)=0.0039
Hence,
a. P(0)=0.3164
b. P(1)=0.4219
c. P(3)=0.0469
Therefore If a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting 0 defective resistors: 0.3164, 1 defective resistor: 0.4219, 3 defective resistor: 0.0469.
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demonstrating that there is a trade which will leave both players better
off. Suppose:
Amber can produce 24 apples or 48 pears in a day, and
Johnny can produce 8 apples and 32 pears in a day.
They also prefer to spend a half-day producing apples and a half- day
producing pears.
This trade will create a win-win situation for both players, leaving them both better off than they were before.
What is capacity?Capacity in math is the maximum amount that a container or figure can hold. It is typically measured in liters, gallons, or quarts and is determined by the size of the container or figure. Capacity is a measure of volume and is used in a variety of math problems, including those involving capacity conversion, calculating the amount of liquid that can be stored in a container, and determining the amount of material needed to fill a given area.
A trade that will leave both players better off is for Amber to produce all of the apples and Johnny to produce all of the pears. This way, Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. Amber has a higher capacity for producing apples while Johnny has a higher capacity for producing pears. Therefore, this trade makes the most sense.
The trade will leave both players better off because of the increased efficiency in production. Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. This means that they will both have more resources to spend on other things. They will also be able to divide their time more evenly between the two tasks, allowing them to be more productive and efficient.
In addition, the trade will also benefit both players in terms of their preferences. Amber will be able to spend a full day producing apples, which she prefers, and Johnny will be able to spend a full day producing pears, which he prefers. This trade will create a win-win situation for both players, leaving them both better off than they were before.
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convert to slope intercept form
: x- 2y=-6
Answer:
x-2y =6
x-2y =6
= 6-2y=x=4
Emma was given $16.09 for washing her neighbor's car. She now has $20.23. Let m equal the amount of money she had before washing the car. Choose the equation to solve the problem.
Answer: m = 20.23 - 16.09
Step-by-step explanation:
This math sheet is making me scratch my head. Can I have help with all of the questions? I just need the answers (check pdf or attached png). Number 3 and 4 are the tricky ones. (keeps getting taken down)
The system of equations are solved
a) y = 2x + 3
b) y = 3x
c) f = p + 3/2
d) y = 3x
e) The number of dogs Becca walks at the end of third month is y = 9 dogs
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
a)
The initial number of cards Stacy has = 3 cards
The number of cards she gets per week = 2 cards
So , the total number of cards after x weeks = 2x cards
And , the total number of cards = initial number of cards + number of cards after x weeks
Substituting the values in the equation , we get
y = 2x + 3
b)
The first point is P ( 3 , 9 )
The second point is Q ( -3 , -9 )
So , the equation of line is y = 3x
when x = 3 , y = 9
c)
f = p + 3/2 be equation (1)
when p = 1
f = 1 + 3/2
f = 5/2
when p = 2
f = 2 + 3/2
f = 7/2
when p = 3
f = 3 + 3/2
f = 9/2
d)
The equation of line is y = 3x and the graph is plotted with the points P ( 1 , 3 ) and Q ( 2 , 6 )
e)
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 1 )
Let the second point be Q ( 2 , 5 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 5 - 1 ) / 2
Slope m = 2
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 1 = 2 ( x - 0 )
y - 1 = 2x
Adding 1 on both sides of the equation , we get
y = 2x + 1
Now , when the number of years = 4
y = 2 ( 4 ) + 1
y = 9 dogs
Hence , the equation is solved
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