Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.. Which of the following rational functions is graphed below? In the graph, we can see that we have a vertical asymptote at x = -1.. …
Several people were asked to report the number of hours of sleep they average per night. The results are shown in thehistogram below. How many of those people average greater than 4.5 and less than 6.5 hours of sleep per night?
EXPLANATION
We can get the solution by calculating the frequency on the Histogram as shown as follows:
Hours Frequency
4.5-5.5 7
5.5-6.5 4
------------
Total Frequency ----------------------> 11
The number of people that average greater than 4.5 and less than 6.5 hours of sleep per night are 11 persons.
Jake and Mia sold muffins at the bake sale. Jake collected $38 for selling a number of chocolate and blueberry muffins, while Mia collected $20 for selling
the same type of muffins. The following system of equations represents the scenario where is the price of a chocolate muffin and y is the price of a
blueberry muffin. What does the coefficient 3 represent?
(No Calculator)
8x+3y=38
2x+6y=20
The coefficient 3 represents that the numbers of blueberry muffins sold by Jake is 3.
What is defined as the system of equations?In algebra, a system of equations is two or more equations that must be solved simultaneously (i.e., the solution must fulfill all equations in the system). The quantity of equations must match the total of unknowns for a system to produce a unique solution.For the given question;
Total amount = chocolate muffins's amount + blueberry muffins's amount
Jake's total sell = $38.
Mia's total sell = $20.
Let 'x' be the price of each chocolate muffins.
Let 'y' be the price of each blueberry muffins.
The system of linear equation is;
8x + 3y = 38
2x + 6y = 20
Thus, the coefficient 3 represents that the numbers of blueberry muffins sold by Jake is 3.
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Fill in the table given the visual pattern for the first 5 steps
The pattern consists of adding a new square on the right, and then adding a new square below previous squares.
Graph the parabola.y=x2 - 10x + 23Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click onthe graph-a-function button.12-110х5?42-1010-
Answer:
• Vertex: (5,-2)
,• Points to the left of the vertex: (3,2) and (4,-1)
,• Points to the right of the vertex: (7,2) and (6, -1)
Explanation:
Given the equation of the parabola:
[tex]y=x^2-10x+23[/tex]First, determine the vertex:
[tex]\begin{gathered} \text{Axis of symmetry: }x=-\frac{b}{2a} \\ x=-\frac{-10}{2\times1} \\ x=5 \\ \text{When x=5} \\ y=5^2-10(5)+23=-2 \\ \implies\text{Vertex}=(5,-2) \end{gathered}[/tex]A table of values for the function is given below with the vertex identified:
Thus, we have the graph below:
• Vertex: (5,-2)
• Points to the left of the vertex: (3,2) and (4,-1)
,• Points to the right of the vertex: (7,2) and (6, -1)
The topic of this problem is "Scale Factors". This is the information: Solid 1 has: * A surface area of 128 cm^2* A volume of 15360 cm^3 Solid 2 has: * An unknown surface area. * A volume of 6480 cm^3 I need to find the surface area of solid 2.
Let the unknown surface area be x
The ratio of the surface area to volume in solid 1 must be equal to the ratio of the surface area to volume in solid 2.
[tex]\begin{gathered} \frac{128}{15360}=\frac{x}{6480} \\ \Rightarrow x=\frac{128}{15360}\times6480=54\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area of solid 2 is 54 cm^2
A bike shop sells you a bicycle for $63 and
a helmet for $21. The total cost is 150% of
what the shop spent originally.
a. How much did the shop spend originally?
b. How much profit did the bike shop earn
by selling the bicycle and helmet to you?
(a) The initial cost that the shop spend is $56 and;
(b) The profit that the bike shop earned by selling the bicycle and helmet to you is $28.
The price of the bicycle is $63 in a shop.
The price of a helmet is $21.
The total price is 150% more than what the shop originally paid for these times:
The total cost, C = $63 + $21 = $84
The cost is 150% of the initial cost let's say K;
C = 150% of K
C = 150/100 × K
C = 1.5K
Hence, the initial cost will be:
K = C/1.5 = $84/1.5
K = $56
The difference between the two costs will be the profit:
P = C - K
P = $84 - $56 = $28
Hence, the amount the shop spend is $56 and the profit the bike shop earns by selling the bicycle and helmet is $28.
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Solve the equation 2x2 - x - 5 = 1 using the quadratic formula.
For a general quadratic polynomial of the form:
[tex]ax^2+bx+c=0[/tex]the solution is
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]this formula is called "the quadratic formula". There are 2 solutions indicated by the subindex 1 and 2 in x.
In our case, by comparing polynomials, we can see that
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-6 \end{gathered}[/tex]becuase our polynomial is
[tex]2x^2-x-6=0[/tex]in which we moved 1 to the left hand side as -1.
Then, by applying the quadratic formula, we have
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]Then ,the first solution is
[tex]x_1=\frac{-(-1)+\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]and the
Try to solve for x and y
Answer:
x = 7
y = 8
Step-by-step explanation:
Create two equations.
Equation 1
Both triangles are isosceles triangles since two of their sides are congruent. Therefore, the base angles of the top triangle are equal:
[tex]\implies y^2-8=x^2+x[/tex]
Equation 2
According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent. Therefore, the apexes of the triangles are equal. This means the sum of the base angles are equal:
[tex]\implies (y^2-8)+(x^2+x)=8x+8x[/tex]
[tex]\implies y^2-8+x^2+x=16x[/tex]
[tex]\implies y^2-8+x^2+x-x^2=-x^2+16x[/tex]
[tex]\implies y^2-8+x=-x^2+16x[/tex]
[tex]\implies y^2-8+x-x=-x^2+16x-x[/tex]
[tex]\implies y^2-8=-x^2+15x[/tex]
Substitute the first equation into the second equation and solve for x:
[tex]\implies x^2+x=-x^2+15x[/tex]
[tex]\implies x^2+x+x^2=-x^2+15x+x^2[/tex]
[tex]\implies 2x^2+x=15x[/tex]
[tex]\implies 2x^2+x-15x=15x-15x[/tex]
[tex]\implies 2x^2-14x=0[/tex]
[tex]\implies 2(x^2-7x)=0[/tex]
[tex]\implies x^2-7x=0[/tex]
[tex]\implies x(x-7)=0[/tex]
Therefore:
[tex]\implies x=0, \quad x=7[/tex]
If x was zero, some of the angles would be zero, which is impossible.
Therefore, the only valid solution is x = 7.
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y^2-8=(7)^2+7[/tex]
[tex]\implies y^2-8=49+7[/tex]
[tex]\implies y^2-8=56[/tex]
[tex]\implies y^2=64[/tex]
[tex]\implies y=8[/tex]
Solution
x = 7y = 8The table shows the number of bottles collected for recycling. Round the number of bottles collected by each grade to the nearest ten, nearest hundred, and nearest thousand. Choose from the rounded numbers in the box to fill in the table. 2,000 2,200 2,220 2,230 2,300 2,600 2,660 2,670 2,700 3,000 Grade Nearest Ten Nearest Hundred Number of Bottles Collected 2,227 2,664 Nearest Thousand 3 4
Explanation
Step 1
[tex]2227[/tex]a)nearest ten
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
so,In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tens place (2). The digit(s) at the right (7) becomes 0, thus we get 2230 as answer.
[tex]\begin{gathered} 2227\Rightarrow2230 \\ \text{because the 7 is greater or equak than 5} \end{gathered}[/tex]b)Nearest hundred
Remember that the hundreds place is three moves from the left of the decimal point (if it exists). To round to the nearest hundred (nearest 100), we use the tens place to determine whether the hundreds place rounds up or stays the same,so
in this case: 27
[tex]\begin{gathered} 2227\Rightarrow2200 \\ \cdot\text{because 27is smaller than 50} \end{gathered}[/tex]c)nearest thousand
Remember that the thousand place is four moves from the left of the decimal point (if it exists). To round to the nearest thousand (nearest 10000), we use the hundreds place to determine whether the thousands place rounds up or stays the same
so,in this case:227
[tex]\begin{gathered} 2227\Rightarrow2000 \\ \text{because 227 is smaller than 500} \end{gathered}[/tex]Step 2
now, for :
[tex]2664[/tex]a) nearest ten
[tex]\begin{gathered} 2664\Rightarrow2660 \\ \text{because 4 is smaller than 5} \end{gathered}[/tex]b)nearest hundred
[tex]\begin{gathered} 2664\Rightarrow2700 \\ \text{because 64 is greater than 50} \end{gathered}[/tex]c)nearest thousand
[tex]\begin{gathered} 2664\Rightarrow3000 \\ \text{because 664 is greater than 500} \end{gathered}[/tex]I hope this helps you
Find the product of (3 x 109) and (2 x 109). Write the final answer in scientific notation.
6 x 10^81
6 x 100^18
6 x 10^18
6 x 10^9
pls help
Answer:
C. 6 x 10^18
Step-by-step explanation:
This is the correct answer
I NEED HELP PLSSSSSS THIS IS NOT EASY FOR ME AND THIS IS DUE TMR!
The plus sign is a composite of rectangles . The shape is comprised of:
1. 4 congruent rectangles with sides 20 in and 12 in
2. A square at the center with sides 20 in by 20in
The total area of Demi's Tester ca be found using the formula:
[tex]Total\text{ area = 4 }\times\text{ l}\times\text{ b +}l^2[/tex]Substituting the given side lengths:
[tex]\begin{gathered} Total\text{ area = 4 }\times\text{ 20 }\times\text{ 12 + 20}\times\text{ 20} \\ =\text{ 1360 in}^2 \end{gathered}[/tex]Hence, the total area of Demi's poster is 1360 square in
Classify the expression by the number of terms.5y?-8+62%O not a polynomialO binomial
Given:
[tex]5y^2-8+6y^4[/tex]There are three terms in the given equation.
trinomial is the final answer.
I have a 93% in my ELAR grade, but today we took a CBA and I got a 72% on it. how much will that drop my grade in skyward. please help
we have the following:
[tex]\frac{93+72}{2}=\frac{165}{2}=82.5[/tex]therefore, the answer is 82.5%
el ancho de un rectángulo es el doble de su largo si el perímetro es de 78 pies cuál es el largo y el ancho?
The width of the rectangle is twice its length.
So lets assume the width to be------ 2x feet
Then the length will be ------ x feet
The perimeter is given as ---- 78 feet
The formula for perimeter of a rectangle is ; 2[ l+w ] where l is length and w is width
Use the assumed measurements in the equation for perimeter as;
2[ l+w ] =78
2{x +2x] =78
2x +4x =78
6x = 78
x=13 feet
Length = x = 13 feet
Width = 2x = 2*13 = 26 feet
R is perpendicular to U. S is parallel to T. m <1 = 39° . Find the remaining angles.
First, notice that angle 1 and angle 4 are vertical angles, therefore:
[tex]\measuredangle1=39\text{ = }\measuredangle4[/tex]then, we have that angle 1 and angle 2 are supplemetary angles, then:
[tex]\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \Rightarrow\measuredangle2=180-\measuredangle1=180-39=141 \\ \measuredangle2=141 \end{gathered}[/tex]Since angle 3 and angle 2 are vertical, we have the first measures of the diagram:
[tex]\begin{gathered} \measuredangle1=39 \\ \measuredangle2=141 \\ \measuredangle3=141 \\ \measuredangle4=39 \end{gathered}[/tex]Then, angle 1 and angle 5 are corresponding angles, then, we have the following:
[tex]\measuredangle1=39=\measuredangle5[/tex]Now, angle 5 and angle 6 are complementary angles, therefore:
[tex]\begin{gathered} \measuredangle5+\measuredangle6=90 \\ \Rightarrow\measuredangle6=90-\measuredangle5=90-39=51 \\ \measuredangle6=51 \end{gathered}[/tex]Angle 5 is vertical with angle 7, and angle 6 is vertical with angle 8. Also, we can see that angle 9 is a right angle, then, we have the next measures:
[tex]\begin{gathered} \measuredangle5=39 \\ \measuredangle6=51 \\ \measuredangle7=39 \\ \measuredangle8=51 \\ \measuredangle9=90 \end{gathered}[/tex]Finally, notice that angles 4, 9 and 10 are the angles of a right triangle, then, we would have the following:
[tex]\begin{gathered} \measuredangle4+\measuredangle9+\measuredangle10=180 \\ \Rightarrow\measuredangle10=180-\measuredangle9-\measuredangle4=180-90-39=51 \\ \measuredangle10=51 \end{gathered}[/tex]then, angle 10 and angle 11 are supplemetary, then:
[tex]\begin{gathered} \measuredangle10+\measuredangle11=180 \\ \Rightarrow\measuredangle11=180-\measuredangle10=180-51=129 \\ \measuredangle11=129 \end{gathered}[/tex]angle 10 is vertical with angle 13 and angle 11 is vertical with angle 12, then:
[tex]\begin{gathered} \measuredangle10=51 \\ \measuredangle11=129 \\ \measuredangle12=129 \\ \measuredangle13=51 \end{gathered}[/tex]Find the horizontal asymptote of the graph of the rational function. y = x^2 + 6 ———— 4^2 - 7 Identify the horizontal asymptote for the graph of the function.
Given:
[tex]y\text{ = }\frac{x^2\text{ + 6}}{4x^2\text{ -7}}[/tex]The rule for horizontal asymptote is shown below:
For the given rational function, the degree of the numerator is equal to the degree of the denominator.
Hence, the horizontal asymptote is:
[tex]\begin{gathered} y\text{ = }\frac{1}{4} \\ \\ 1\text{ is the leading coefficient of the numerator} \\ and\text{ 4 is the leading coefficient of the denominator} \end{gathered}[/tex]Answer:
[tex]y\text{ = }\frac{1}{4}\text{ \lparen Option A\rparen}[/tex]Write an equivalent exponential expression to the expression 2^6 x 8^6.A 10^6B 16^6C 16^12D 16^36
so the answer is B
Let z(t)= 2t^2 +7t -4, find z(-1) and z(2).
Let z(t) be the function:
[tex]z(t)=2t^2+7t-4[/tex]Then, to find z(-1), we evaluate directly into the function like this:
[tex]z(-1)=2(-1)^2+7(-1)-4=2(1)-7-4=2-11=-9[/tex]and we do the same thing for z(2):
[tex]z(2)=2(2)^2+7(2)-4=8+14-4=18[/tex]therefore, z(-1)=-9 and z(2)=18
One side of a triangle is 4 times longer than the shortest side and the third side is 3 centimeters less than twice the length of the shortest side. The perimeter of the triangle is 46.How long is the shortest side of the triangle?
Let's use the variable x to represent the shortest side of the triangle.
If one side is 4 times longer than the shortest side, it measures "4x".
If the third side is 3 cm less than twice the length of the shortest side, it measures "2x - 3".
So, if the perimeter is 46 cm, we have:
[tex]\begin{gathered} x+4x+2x-3=46 \\ 7x-3=46 \\ 7x=49 \\ x=\frac{49}{7}=7 \end{gathered}[/tex]So the shortest side measures 7 cm.
if f(x) and f1(x) are inverse functions of each other and f(x)=2x+5 what is f1(8)?-13/241/823
we have the following:
[tex]undefined[/tex]
4. Rangers in Montana wanted to estimate the number of elk in a certain area. They tagged 20
elk one Saturday and sent them back to mix with the other elk in the area. The rangers went back
once a month for the next three months and recorded the following.
Month 1 Month 2 Month 3
4
6
12
Tagged elk in sample
Total elk in sample
7
10
18
a. Estimate the size of the elk population for each month.
Month 1:
Month 2 =
Month 3
Based on the information in the provided table, the elk population for the first month is 11, the second month is 16, and the third month is 30.
In mathematics, what is a data table?Tables are a good way to organize data by using rows and columns. Tables are a versatile organizational tool that can be used to communicate information on their own or in conjunction with another type of data representation (like a graph).Using the information in the give table, we need to calculate the elk population size for each month.
For first month,
elk population = tagged elk + total elk
= 4 + 7
= 11
For second month,
elk population = tagged elk + total elk
= 6 + 10
= 16
For third month,
elk population = tagged elk + total elk
= 12 + 18
= 30
Therefore, the elk population for first month is 11, second month is 16 and third month is 30 which is calculated from the given table data.
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(8) Write the equation of the line that passes through the points (12, 4) and 1 (22,9).
Answer:
Step by step solution:
The
confused please help only (a) in exponential form please
On simplifying the given expressions we get-
a) [tex]5^{12}[/tex]
b) [tex]5^{18}[/tex]
Here, we are given two expressions in exponential form. Let us solve them one by one.
Firstly, we look at a property of exponentials as follows-
[tex]x^{a} x^{b} = x^{a+b}[/tex]
Theoretically, this means that when the bases are equal, the powers can be added in case of multiplication of exponentials.
Now, we have-
a) [tex]5^{2} 5^{10}[/tex]
here, the base is equal, that is, 5. So we just add the powers to get-
[tex]5^{2+10}[/tex]
= [tex]5^{12}[/tex]
b) [tex]5^{2} 5^{7} 5^{9}[/tex]
Here, we have 3 exponents, but the property will still remain the same. Bases are all equal to 5, thus the expression will become-
[tex]5^{2+7+9}[/tex]
= [tex]5^{18}[/tex]
Thus, on simplifying the given expressions we get [tex]5^{12}[/tex] and [tex]5^{18}[/tex] respectively.
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Directions: Answer the following questions using the figure below.
3. Name two right angles.
a. NOK, JOK
b. NOJ, NOL
C. NOJ, JOL
(C.) The two right angles in the diagram are NOJ and JOL.
What is right angle?
A right angle is formed when two straight lines intersect each other at 90˚ or are perpendicular to each other at the intersection.
A right angle is denoted by angle 90 degrees.
The symbol between NOJ indicates right angle because the measure of the angle is 90 degrees.
Since the sum of angles on a straight line is 180 degrees, and we know angle NOJ, angle JOL can be calculated as follows;
NOJ + JOL = 180
JOL = 180 - NOJ
JOL = 180 - 90
JOL = 90
Thus, the two right angles in the diagram are NOJ and JOL.
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What is 9^p/9^5= 9^3. What is p in tbe equation?
The value of "p" in the given equation 9^p/9^5= 9^3 is p = 8 using the concept of exponents and powers.
As per the question statement, we are given an equation which is as follows : 9^p/9^5= 9^3 and we are supposed to find the value of "p" in the given equation,
We will be using the concept of exponents and powers.
We know, a^m*a^n = a^(m+n)
and, a^m/a^n = a^(m-n)
Hence using the same formula, we get
9^p/9^5= 9^3
Left Hand side(LHS): 9^p/9^5 = 9^(p-5)
Right hand side(RHS): 9^3
As LHS = RHS
We get 9^(p-5) = 9^3
Now equating the powers, as the base is same, we get
p-5=3
p = 8
Hence, the value of "p" in the given equation 9^p/9^5= 9^3 is p = 8 using the concept of exponents and powers.
Equation: The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.Exponents and powers: In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.
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Simplify the following polynomial expression.
The simplified form of the polynomial expression is 5x⁴ - 37x³ - 6x² + 41x - 6
How to simplify polynomial?The polynomial can be simplified as follows:
Therefore,
(5x⁴ - 9x³ + 7x - 1) + (- 8x⁴ + 4x² - 3x + 2) - (-4x³ + 5x - 1) (2x - 7)
Therefore, we have multiply first
(-4x³ + 5x - 1) (2x - 7) = -4 (2x - 7)x³ + 5x(2x - 7) - 1(2x - 7)
Hence,
(-4x³ + 5x - 1) (2x - 7) = - 8x⁴ + 28x³ + 10x² - 37x + 7
Therefore,
5x⁴ - 9x³ + 7x - 1 - 8x⁴ + 4x² - 3x + 2 + 8x⁴ - 28x³ - 10x² + 37x - 7
Combine like terms
Therefore,
5x⁴ - 8x⁴ + 8x⁴ - 9x³ - 28x³ + 4x² - 10x² + 7x - 3x + 37x - 1 + 2 - 7
5x⁴ - 37x³ - 6x² + 41x - 6
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The tallest person who ever lived was approximately 8 feet 11 inches tall.
Write an inequality that represents the heights h (in inches) of every other person who has ever lived.
Answer: [tex]0 < h \le 107[/tex]
This is the same as writing [tex]h \le 107[/tex] where h is positive
======================================================
Work Shown:
1 foot = 12 inches
8*(1 foot) = 8*(12 inches)
8 feet = 96 inches
8 feet + 11 inches = 96 inches + 11 inches
8 feet + 11 inches = 107 inches
The tallest person is 107 inches tall.
If h is someone's height in inches only, then [tex]0 < h \le 107[/tex] is the inequality that describes all possible values of h.
We can simplify that into writing [tex]h \le 107[/tex] and write off to the side somewhere that h must be positive.
Answer: 0 < h < 107 inches
Step-by-step explanation:
First, we see this question asks us to represent in inches, so we will convert 8'11" into inches.
8 feet * 12 inches in a foot = 96 inches
96 inches + 11 inches = 107 inches
Next, we will write our inequality. If this person was the tallest, then everyone else will be less tall. We assume that nobody will be less than 0 inches tall, so that is the left side of our inequality.
0 < h < 107 inches
Since this question asks about every other person who has ever lived, we do not use ≤ (greater than or equal to) since the tallest person is the only height equivalent to 107 inches.
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Which expression is equivalent to 8x3 − 27 when factored completely?
The given expression is
[tex]8x^3-27[/tex]To find the equivalent expression, we use the formula for the difference of perfect cubes.
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]But, we have to express the numbers 8 and 27 as cubic powers.
[tex]\begin{gathered} 8=2\cdot2\cdot2=2^3 \\ 27=3\cdot3\cdot3=3^3 \end{gathered}[/tex]Then, we know that a and b are
[tex]\begin{gathered} a=2x \\ b=3 \end{gathered}[/tex]So, the difference would be
[tex](2x)^3-(3)^3[/tex]Once we have the difference expressed in cubes, we apply the formula using the a and b values we determined before.
[tex](2x)^3-(3)^3=(2x-3)((2x)^2+(2x)(3)+(3)^2)_{}=(2x-3)(4x^2_{}+6x+9)[/tex]Therefore, the factors are
[tex](2x-3)(4x^2+6x+9)_{}[/tex]Can someone please help me? Im confused.
Answer:
12
Step-by-step explanation:
9/12 to y/16 (the ratio of the short side relative to the long side)
0.75 = y/16 (a ratio can be expressed as a decimal)
16(0.75) = y (multiply 16 to both sides, isolate y)
y = 12 (b/c three-quarters of 16 is 12)
Answer:
y = 12
Step-by-step explanation:
Δ RSQ and Δ ROP are similar ( AA postulate ) then the ratio of corresponding sides are in proportion, that is
[tex]\frac{SQ}{OP}[/tex] = [tex]\frac{RS}{RO}[/tex] ( substitute values )
[tex]\frac{y}{16}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )
12y = 16 × 9 = 144 ( divide both sides by 12 )
y = 12
what is a inital value.Context: exponential functions.
Exponential functions have the form:
[tex]f(x)=a\cdot x^b.[/tex]The initial value of the function f(x) is given by the value of f(x) when x = 0:
[tex]\text{ initial value }=f(0)=a\cdot x^0=a\cdot1=a.[/tex]AnswerFor an exponential function:
[tex]f(x)=a\cdot x^b,[/tex]we have:
[tex]\text{ initial value }=f(0)=a[/tex]