a = amount invested at 4%
how much is 4% of "a"? (4/100) * "a", namely 0.04a.
b = amount invested at 5%
how much is 5% of "b"? (5/100) * "b", namely 0.05b.
we know the total amount invested is 5550, so whatever "a" and "b" might be, we know that a + b = 5550.
we also know that the yielded amount in interest is 259, so if we simply add their interest, that'd be 0.04a + 0.05b = 259.
[tex]a+b=5550\implies b=5550-a \\\\[-0.35em] ~\dotfill\\\\ 0.04a+0.05b=259\implies \stackrel{\textit{substituting from above}}{0.04a+0.05(5550-a)~~ = ~~259} \\\\\\ 0.04a+277.5-0.05a=259\implies 277.5-0.01a=259\implies -0.01a=-18.5 \\\\\\ a=\cfrac{-18.5}{-0.01}\implies \boxed{a=1850}\hspace{9em}\stackrel{ 5550~~ - ~~1850 }{\boxed{b=3700}}[/tex]
Consider the following statements:
Which of the statement(s) regarding the "limit" concept in
Mathematics is/are TRUE and which is/are FALSE?
I
A limit is a point or value that a pattern, function or sum of
a series, approaches as the number of terms in the series
increases.
II A limit is a value that a function approximates for a given
input value.
III A limit is a value we get closer and closer to, but never
quite achieve.
I: TRUE - A limit is a value that a function, pattern, or sum of a series approaches as the number of terms or input value increases.
What is a Limit in Mathematics based on the given context?II: TRUE - A limit can also be a value that a function approximates for a specific input value, especially when dealing with continuity or differentiability.
III: FALSE - Although a limit might seem like a value that is never quite achieved, it can be reached or even exceeded, depending on the function and its behavior.
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If f(x) is defined as follows, find (a) f(-3), (b) f(0), and (c) f(4).
x²
if x < 0
if x = 0
3x + 3 ifx>0
f(x) = 0
(a) f(-3)= (Simplify your answer.)
THE
For the given question the values,
f(-1) = 1f(0) = 0f(3) = 13Given value of the function when the condition for x is less than '0' is =
f(x) = x² for x < 0
The value of the function when the condition x is equals to '0' is =
f(x) = 0 for x = 0
The value of the function when the condition x is greater than '0' is =
f(x) = 3x + 4 for x > 0
From the above information,
To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1
To find f(0) we have to use x value as 0. So, f(0) = 0
To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.
From the above analysis, we find the values of f(-1), f(0), and f(3).
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help please Use inductive reasoning to predict the next number in this pattern: 3, 13, 22, 30, 37, 43…
A) 5
B) 48
C) 14
D) 50
Answer:
B) 48
Step-by-step explanation:
3, 13, 22, 30, 37, 43…
3 to 13 is +10
13 to 22 is +9
22 to 30 is +8
We are adding one less each time
3, 13 , 22, 30, 37, 43 …
+10 +9 +8 +7 +6 +5
Add 5 to 43
43+5 = 48
If the price of a round trip airline to Ireland is $1300 per person and Jan can spend at most $6000 what is the largest number of people for whom she can buy tickets
The largest number of people for whom she can buy tickets, is 4 people.
:: Available money = $6000
:: Cost per person = $1300
So,
No. of maximum tickets = 6000/1300 = 4.6
That is,
Only 4.6 persons can have the tickets, and since, number of persons can only be a positive integer, so we have to only take the integer part of the number and eliminate the decimal part.
Therefore, the largest number of people for whom she can buy tickets, is 4 people.
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Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
The equation accurately represents this statement is "Negative 3 less than 4.9 times a number, x, is the same as 12.8"
how to determine the equation that accurately represents the statementThe statement is "Negative 3 less than 4.9 times a number, x, is the same as 12.8." We can break it down into two parts:
"4.9 times a number, x": This means we need to multiply a number, x, by 4.9. So the first part of the equation is 4.9x.
"Negative 3 less than 4.9 times a number, x, is the same as 12.8":
This means we need to subtract 3 from the result of multiplying x by 4.9. So the second part of the equation is -3.
Putting it all together, we get:
4.9x - 3 = 12.8
This equation accurately represents the given statement.
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Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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Help with this question please l need it
Answer:
(x+4)(x-9)!!!!!!!!!!!!!!!!!!
A cylinder with a radius of 8 inches is cut from the prisim. What is the volume of the new object
The volume of the new object is approximately 439.3 cubic inches
What is the volume of the new object?To find the volume of the new object, we need to first know the volume of the prism before the cylinder is removed hence we do this:
The volume of a cylinder: = πr²h
where:
r = radius
h = height
Note that the volume of a rectangular prism is : = lwh
l = length
w = width
h = height
Assumption: In the above case, we will assume that the dimensions of the rectangular prism because the cylinder can be cut out from the center of one of the faces.
Hence the length and width of the prism will be taken to be twice the radius of the cylinder, that is 16 inches, and the height will be taken to be same as the radius of the cylinder, that ia 8 inches.
So V_prism = lwh
= 16 × 16 × 8
= 2048 cubic inches
V_cylinder = πr²h
= π × 8² × 8
= 512 π cubic inches
Hence To get the volume of the new object, we need to subtract the volume of the cylinder from the volume of the prism:
V_new = V_prism - V_cylinder
= 2048 - 512π
= 2048 - 1608.70
= 439.3 cubic inches
Hence, the volume of the new object is about 439.3 cubic inches
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Find m/_I. I need help on solving this problem please?
Answer:
∠ I = 60°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan I = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{HJ}{IJ}[/tex] = [tex]\frac{3\sqrt{30} }{3\sqrt{10} }[/tex] = [tex]\frac{\sqrt{30} }{\sqrt{10} }[/tex] = [tex]\sqrt{\frac{30}{10} }[/tex] = [tex]\sqrt{3}[/tex] , then
∠ I = [tex]tan^{-1}[/tex] ([tex]\sqrt{3}[/tex] ) = 60°
Answer:
60°
Step-by-step explanation:
You want the measure of angle I in right triangle HIJ, given that the side opposite is 3√30 and the side adjacent is 3√10.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
In this triangle, ...
tan(I) = (3√30)/(3√10) = √(30/10) = √3
Then the angle is ...
I = arctan(√3) = 60°
The measure of angle I is 60°.
__
Additional comment
The trig functions of 30° and 45° and their relationships to each other are based on the side relationships of the two "special" right triangles:
30°-60°-90° triangle has side ratios 1 : √3 : 2
45°-45°-90° triangle has side ratios 1 : 1 : √2
Of course, side lengths are in the same order as their opposite angles.
The mnemonic SOH CAH TOA can help you remember the necessary relationships:
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/Adjacentwhat are the answers? thank you.
Answer:
2, area=42.39 arc length=14.13
3, area=604.9 arc length=71.1
can someone solve -4 + 2 + -2 + -3x (with tiles!!!!!)
The simplified expression of given term is: -4 + 2 + -2 + -3x = -4 - 3x
What do you mean by Simplification ?Simplification refers to the process of reducing an expression to its simplest form by combining like terms, removing parentheses, and performing any necessary operations such as addition, subtraction, multiplication, and division. The goal of simplification is to make an expression easier to read and work with, and to reveal any patterns or relationships that may not have been obvious in the original expression. Simplification is an important part of solving equations, evaluating expressions, and performing mathematical operations in general.
We can simplify the expression by combining like terms.
Starting with -4, we add 2 to get:
-4 + 2 = -2
Next, we subtract 2 from -2:
-2 - 2 = -4
Finally, we subtract 3x from -4:
-4 - 3x
So the simplified expression is:
-4 + 2 + -2 + -3x = -4 - 3x
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A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 5 and the second roll is a total of at least 4.
The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4 is 0.764 or 76.4%.
What is the probability?The probability is the chance that an expected event occurs out of many possible events.
For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.
The event that the first roll is a total of at least 5 = A
In the event that the second roll is a total of at least 4 = B
The number of faces on each die, n = 6
The probability of event A = ³⁰/₆ = ⁵/₆
The probability of event B = ³³/₃₆ = ¹¹/₁₂
Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ × ¹¹/₁₂
= ⁵⁵/₇₂ = 0.764
Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.
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Please hurry due in an hour
Mrs Smith uses 5 lemons to make 2/3 gallon lemonade. How many gallons of lemonade can Mrs Smith make with 15 lemons?
Bob wants to break the school record of scoring 30 points in his basketball game. He scored 13 points in the first half. How many two point baskets must Bob make in the second half to break the school record?
Bob needs to make at least 9 two-point baskets in the second half to break the school record of scoring 30 points in his basketball game.
To break the school record of scoring 30 points, Bob needs to score more than 30 points in his basketball game. Since he scored 13 points in the first half, he needs to score at least 17 points in the second half to break the record.
Let's assume that Bob makes x two-point baskets in the second half. Since each two-point basket contributes 2 points to his score, his total score from two-point baskets would be 2x.
Therefore, to break the school record, we need to solve the following inequality:
2x + 13 > 30
Subtracting 13 from both sides, we get:
2x > 17
Dividing both sides by 2, we get:
x > 8.5
Since Bob cannot make a fractional number of baskets, he needs to make at least 9 two-point baskets in the second half to break the school record.
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The model for radioactive decay is y=y0e^-kt. a radioactive substance has a half-life of 170 years. if 40 grams are present today. in how many years will 15 grams be present? While solving this problem, round the value of k to seven decimal places. Round your answer to two decimal places.
It will take about 225.25 years of time for 15 grams to be present.
The half-life of a radioactive substance is the time it takes for half of the substance to decay.
For this substance with a half-life of 170 years, we can use the following formula to find the value of k:
[tex]0.5 = e^(^-^1^7^0^k^)[/tex]
Taking the natural logarithm of both sides, we get:
ln(0.5) = -170k
Solving for k, we get:
k = ln(0.5) / (-170)
= 0.004085
Now, we can use the model [tex]y = y_0e^(^-^k^t^)[/tex] to find the time t required for the substance to decay from 40 grams to 15 grams.
We have:
[tex]15 = 40e^(^-^0^.^0^0^4^0^8^5^t^)[/tex]
Dividing both sides by 40 and taking the natural logarithm of both sides, we get:
ln(15/40) = -0.004085t
Solving for t, we get:
t = ln(15/40) / (-0.004085)
= 225.25 years
Therefore, it will take about 225.25 years for 15 grams to be present.
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Kelly purchased a toaster for $115. She made a down payment of 10% and financed the rest for 9 months with payments of $16.78. Find (a) the down payment and (b) the total installment price of the toaster.
(A) The down payment of the toaster = $ 11.5
(B) The total installment price of the toaster = $151.02
(A) The down payment of the toaster made by Kelly is 10 % of $ 115
Down payment = 115 × 10/100
Down payment = 1150/100
Down payment = 11.5
The down payment of the toaster = $ 11.5
(B) Total installment price of the toaster for 9 months with payment of $ 16.78
Total installment price of toaster = 9 × 16.78
Total installment price of toaster = $ 151.02
The total installment price of the toaster = is $ 151.02
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What type of pay is modeled below?
(See chart)
A. Piece rate
B. Hourly pay with no bonus
c. Commission pay
D. Hourly pay with a bonus
The type of pay modeled in the given image is c. Commission pay.
What is commission pay?Commission pay is a form of variable pay where the employee is paid based on the percentage of sales that they make. In this case, the y-axis represents the pay earned and the x-axis represents the sales made.
The straight line represents the commission rate, which is constant at 15%. The more sales the employee makes, the more pay they will earn.
Therefore the correct option is C.
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Marcus looked up the path that he had taken on his run this morning on the map shown below.
To the nearest mile, the distance that Marcus ran is 6 miles.
How to calculate the distanceTo calculate the total distance that Marcus ran in the morning, we will sum up the distance for all the routes that he ran.
From the map, the distances that Marcus ran are as follows:
1 inches + 3 inches + 2 inches + 3 inches
= 8.3 inches
The scale then shows that 4 inches equal 3 miles. Now, we convert 8.3 inches to miles and this gives us:
8.3 inches × 3 miles/4 inches
= 6.225
To the nearest miles, this is 6 miles.
Complete Question:
Marcus looked up the path that he had taken on his run this morning on the map shown below.
To the nearest mile, what is the total distance that he ran?
6 miles
8 miles
11 miles
25 miles
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PLEASE HELP ME!!!!!
Write the expression of the graph the function represents.
The expression of the function which is represented by the given graph is given by,
xy = -8
The given figure is a rectangular hyperbola.
So the equation of the given graphed curve be, xy = c, where c is a constant.
We can clearly see that the curve passes through the point with coordinates (-2, 4). So it must satisfy the equation of the curve.
Substituting the point (-2, 4) in the equation of the curve xy = c we get,
(-2)*4 = c
c = -8
Hence the expression for the graph the function represents is given by,
xy = -8.
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what is x^2+y^2-16x+20y-5=0 in standard form
Answer:
(x - 8)^2 + (y + 10)^2 = 169
Step-by-step explanation:
you need to do completing the square
x^2 + y^2 -16x + 20y - 5 = 0
(x)^2 - 2(8)(x) + (y)^2 + 2(10)(y) - 5 = 0
(x)^2 + 2(-8)(x) + (-8)^2 - (-8)^2 + (y)^2 + 2(10)(y) + (10)^2 - (10)^2 - 5 = 0
[(x)^2 + 2(-8)(x) + (-8)^2] + [(y)^2 + 2(10)(y) + (10)^2] - (10)^2 - (-8)^2 - 5 = 0
### (a)^2 + 2(a)(b) + (b)^2 = (a + b)^2 ###
(x - 8)^2 + (y + 10)^2 -100 - 64 - 5 = 0
(x - 8)^2 + (y + 10)^2 -169 = 0
(x - 8)^2 + (y + 10)^2 = 169
difference of the place value of two sevens in 357476 is = to what
Step-by-step explanation:
Count numbers
There are six numbers that counted in
Thousands and tens
The number is 357476 which is three hundred and fifty seven thousands, four hundred and 76
To find the answer you cancel 35 and remains with 7 the other numbers 4 and 6 you turns them into zeros and remain with seven
Thousands and tens is the answer of placing a value of two sevens.
Fixed expenses are defined as those that do not very with changed in volume. Examples include:
A( direct staffing costs
B( lease costs and taxes
C( utilities and supplies utilized in production of service or product
D( utilities, rent, lease, depreciation
Answer:
B (lease costs and taxes) and D (utilities, rent, lease, depreciation) are examples of fixed expenses as they typically do not vary with changes in volume.
Direct staffing costs (A) and utilities and supplies utilized in the production of service or product (C) are generally considered variable expenses as they tend to vary based on the volume of production or sales. For example, if a business produces more goods or provides more services, it will typically need to hire more staff and use more supplies, leading to an increase in expenses.
Step-by-step explanation:
Exercise 17.5 Calculate the curved surface a cone whose height is 8 cm and base radius 5cm
The curved surface area of the cone is 148 cm².
Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,
The curved surface area gives the area of the face of an object.
The CSA of a cone = π × radius × slant height.
Slant height = √r²+h²
= √64+25
= 9.43 cm.
Now the csa = 3.14 × 5 × 9.43
= 148
Hence the curved surface area of the cone is 148 cm².
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Create a matrix for this linear system: 3x+2y+z = 26 X-4y = -11 2x+z = 13 The determinant of the coefficient matrix is _______. x = y = z =
Answer:
[tex]\mathrm{Matrix \: Form:}[/tex]
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]
[tex]\mathrm{Determinant\; of \;coefficient \;matrix = - 6}[/tex]
Step-by-step explanation:
The system of linear equations provided in the question:
[tex]\begin{aligned}3x+2y+z &= 26\\ x-4y&=-11\\ 2x+z&=13\\\\\end{aligned}[/tex]
can be represented in matrix form as
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]
The coefficient matrix is
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]
The determinant of this matrix can be obtained by the expansion formula:
[tex]\det \begin{pmatrix}a&b&c\\ \:d&e&f\\ \:g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ \:h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ \:g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ \:g&h\end{pmatrix}[/tex]
Therefore
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]
[tex]= 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}[/tex]
[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex]
[tex]\det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix} = \left(-4\right)\cdot \:1-0\cdot \:0 = -4[/tex]
[tex]\det \begin{pmatrix}1&0\\ 2&1\end{pmatrix} = 1\cdot \:1-0\cdot \:2 = 1[/tex]
[tex]\det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix} = 1\cdot \:0-\left(-4\right)\cdot \:2 =8[/tex]
Finally,
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\\\\\\ = 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}\\\\\\= 3\left(-4\right)-2\cdot \:1+1\cdot \:8\\\\= -12 - 2 + 8\\\\= -6[/tex]
Solve the following logarthlic equations : 3ln(2x) =12
Step-by-step explanation:
[tex]3 ln(2x) = 12[/tex]
[tex] ln(2x) = 4[/tex]
Let both sides be a power of a base e.
[tex]e {}^{ln(2x)} = e {}^{4} [/tex]
The e and ln would just cancel out so
[tex]2x = e {}^{4} [/tex]
[tex]x = \frac{ {e}^{4} }{2} [/tex]
A number cube with faces labeled from to will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number less than . If there is more than one element in the set, separate them with commas.
The sample space describing all possible outcomes is {1. 2. 3. 4. 5. 6}
Determining the sample space describing all possible outcomes.From the question, we have the following parameters that can be used in our computation:
A number cube with faces labeled from 1 to 6 will be rolled once.
This means that
Sample space = {1. 2. 3. 4. 5. 6}
Using the above as a guide, we have the following:
The outcomes for the event of rolling the number 1 ,3 , or 4. is
Outcome = {1, 3, 4} where we have
P(1) = 1/6
P(3) = 1/6
P(4) = 1/6
Altogether, we have
P(1, 3, or 4) = 1/6 + 1/6 + 1/6
P(1, 3, or 4) = 3/6
P(1, 3, or 4) = 1/2
Hence, the probability is 1/2
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Complete question
A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling the number 1 ,3 , or 4.
If there is more than one element in the set, separate them with commas.
Please help !
Part G
Fill in the table with the appropriate values of h(t) for the given values of t. Round each value to the nearest 10 meters.
Answer:0,2,4,6,8,10
Step-by-step explanation:
take it, spread it, find the bars.
3)
Which decimal number is equivalent to
73
100
?
which graph represents the linear equation y = 1/4 x + 1 on the coordinate plane
the line is passing through -2 for y and 4 for x
the line is passing through 2 for y and -4 for x
the line is passing through 1 for y and -5 for x
the line is passing through 1 for y and -4 for x
Answer:
the line is passing through 1 for y and -4 for x
Step-by-step explanation:
The function y = 1/4 + 1 contains all the information you need. The + 1 indicates the y intercept, so it is given. Since the slope of the line is 1/4, the graph would pass through (-4, 0) and (0, 1) as starting from a point would go up one unit and right 4 units.
