The final answer after subtraction is - 6x² + x - 18.
What is quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
What is subtraction?
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −.
Given,
(8x2 - 16x - 9) - (14x² - 17x + 9)
Subtract
= 8x² - 16x - 9 - 14x² + 17x + 9)
= 8x² - 16x - 9 - 14x² + 17x - 9
= - 6x² + x - 18
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A wheel on Ivan's bicycle is 1.1 m in diameter. Ivan races the bicycle for 165 m. How many times does the wheel turn as the bicycle travels this distance?Use the value 3.14 forn. Round your answer to the nearest tenth. Do not round any intermediate steps.
The radius(r) of the wheel is;
[tex]r=\frac{diameter}{2}=\frac{1.1}{2}=0.55m[/tex]The perimeter(P) of the wheel is given by the formula below:
[tex]P=2\pi r=2\times3.14\times0.55=3.454m[/tex]The distance travelled by Ivan is 165m.
So, the number(n) of times the wheel is:
[tex]n=\frac{165}{3.454}=\text{ 47.77}\approx\text{ 47.8}[/tex]Hence, the correct answer is 47.8
Sophie records the total number of cans of cat food she uses after different numbers of days. She wants to know if the number of cans of cat food she uses is proportional to the number of days. After 3 days – 6 cans After 4 days - 8 cans After 9 days – 18 cans 1. Complete the table # of Days (x) 3 4 (fill in the questions marks) # of Cans (y) 6 8 18 # of Days (x) # of Cans (y) = 2 3 2 2 8-2 4 니 2. Is the number of cans of cat food used proportional to the number of days? Explain. 3. How many cans of cat food will Sophie use after 12 days?
The number of cans is proportional to the number of days, because each day it uses 2 c
A group of 60 students arerandom randomly selected to take a one minute fitness test using a jump rope 30 students are in first grade and 30 students are in 7th grade the following following status information is calculated using the number of jumps completed him one minute they sell me samples what interest rate can be used
we get that the final price of a 16-ounce smoothie is:
[tex]3.69+1.06+0.94-0.75=4.94[/tex]$4.94
In the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand.
What is the probability that a player is dealt 4 hearts? =
The probability that a player dealt with four hearts = 0
What is probability?Probability is defined as the prediction of the occurrence of an event in a stated set.
This can be expressed in proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
From the question given, the 6 sets include the following;
9, 10, jack, queen, king and ace.
There are no hearts given in the set of the event that occurred, therefore, the probability that a player dealt with four hearts = 0.
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Write the quadratic equation that has roots √3 +1/2 and √3 −1/2 , if its coefficient with x^2 is equal to 9
The quadratic equation that has roots √3 + 1 / 2 and √3 - 1 / 2 and a leading coefficient of 9 is y = 9 · x² - 18√3 · x + 99 / 4.
How to find the quadratic equation associated with given real roots and leading coefficient
In this problem we must determine the quadratic equation such that its roots are √3 + 1 / 2 and √3 - 1 / 2 and whose leading coefficient is equal to 9. This can be found by substituting on factor form:
y = a · (x - r₁) · (x - r₂)
Where:
a - Leading coefficient.r₁, r₂ - RootsIf we know that r₁ = √3 + 1 / 2, r₂ = √3 - 1 / 2 and a = 9, then the quadratic equation is:
y = 9 · (x - √3 - 1 / 2) · (x - √3 + 1 / 2)
y = 9 · [x² - (√3 - 1 / 2) · x - (√3 + 1 / 2) · x + 3 - 1 / 4]
y = 9 · (x² - 2√3 · x + 11 / 4)
y = 9 · x² - 18√3 · x + 99 / 4
The quadratic equation is y = 9 · x² - 18√3 · x + 99 / 4.
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Para medir temperaturas podemos utilizar distintas escalas, las más utilizadas son las de grados centígrados y las de grados Fahrenheit, sabemos que 0 C es equivalente a 32F y 20C es equivalente a 68F, si conocemos que la relación entre ambas variables responde una función lineal
A) Encontrar la expresión de la función que permita transformar grados Fahrenheit a Centigrados
B) Encontrar la expresión inversa a la anterior
AYUDA PORFAVOR DOY LO QUE SEA POR ESTO
Using linear functions, it is found that:
a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.
b) The inverse expression is: y = 9x/5 + 32.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function are described as follows:
m is the slope of the function, representing the rate of change of the output y in relation of the input x of the function.b is the y-intercept of the function, representing the numeric value of the function when the input x is of 0.For the conversion of Fahrenheit to Celsius, we have two points, as follows:
(32,0), (68, 20).
When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:
m = 20/36 = 5/9
Hence:
y = 5/9x + b.
When x = 32, y = 0, hence the intercept b is calculated as follows:
0 = 5/9(32) + b
b = -5 x 32/9
b = -160/9
Hence the equation is:
y = 5/9x - 160/9.
To find the inverse expression, we exchange x and y and then isolate y, as follows:
x = 5/9y - 160/9.
5/9y = x + 160/9
5y = 9x + 160
y = 9x/5 + 32.
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Andre graphed the parent function f(x) and
1
a new line d(x). If d(x) will have a slope of 4
and a y-intercept of 9, write a function to
represent d(x) as a transformation of f(x).
Answer:Its d(x)=1/4f(x)+9, mate
Step-by-step explanation:I just guessed and got it correct lol, also its "1/4" as a fraction
Factor Sums and Differences of cubes 27x^3 - 64y^3
SOLUTION
The given question is
[tex]27x^3-64y^3[/tex]Simplify the expression
[tex]3^3x^3-4^3y^3=(3x)^3-(4y)^3[/tex]The difference of two cubes is given as
[tex]x^3-y^3=\mleft(x-y\mright)\mleft(x^2^{}+xy+y^2\mright)[/tex]Hence the given expression becomes
[tex](3x)^3-(4y)^3=(3x-4y)((3x)^2+3x(4y)+(4y)^2)[/tex]This gives
[tex](3x-4y)(9x^2+12xy+16y)[/tex]A circle has area of 361pi cm2 what is the circumference in centimeters of the circle
The area of the circle is given as:
[tex]A=\pi r^2[/tex]plugging the value given we have that:
[tex]\begin{gathered} 361\pi=\pi r^2 \\ r^2=361 \\ r=\sqrt[]{361} \\ r=19 \end{gathered}[/tex]Now, the circumference is given as:
[tex]C=\pi d[/tex]where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:
[tex]C=38\pi[/tex]Therefore the circumference is 38pi
Use point slope form to write the lines with the given slope and point in slope intercept form.m= -1(-5,-4)
The slope point form is
[tex]y-y1=m(x-x1)[/tex]m is the slope
x1, y1 are the coordinates of a point on the line
The slope of the line is -1
m = -1
point (-5, -4) lies on the line
x1 = -5 and y1 = -4
Let us substitute them in the form above
[tex]y-(-4)=-1(x-\lbrack-5\rbrack)[/tex]Remember (-)(-) = (+)
[tex]y+4=-1(x+5)[/tex]The equation of the line in the slope-point form is y + 4 = -1(x + 5)
find an equation parallel to y=-8 and passing through (-6, -7)
Given:
an equation is given as y = -8.
Find:
we have to find an equation parallel to the given equation and passing through (-6, -7).
Explanation:
Compare the given equation with y = mx + b,
we find that slope ,m = 0 ,
the equation of the line passing through (-6,-7) is
y - (-7) = m( x - (-6))
y + 7 = 0(x + 6)
y + 7 = 0
y = -7
Therefore, y = -7 is an equation which is parallel to y = -8 and passing through ( -6, -7).
The graph of both y = -8 and its parallel equation y = -7 which passes through (-6, -7) is given as below
Red line represents the equation y = -8
and blue line represents the equation y = -7 passes through the point (-6,-7).
Therefore, the equation of the line parallel to y = -8 and passing through (-6,-7) is y = -7.
The owner of a video store has determined that the profits P of the store are approximately given by
The profit of the store is represented by the quadratic formula:
[tex]P(x)=-x^2+90x+52[/tex]Where
P is the profit
x is the number of videos rented
The coefficients of the parabola are:
a= -1 (coefficient of the quadratic term)
b= 90 (coefficient of the x-term)
c=52 (constant)
The value of a is negative, which indicates that the parabola opens downwards and that its maximum value is represented by the vertex.
To determine the maximum profit, you have to determine the coordinates of the vertex.
First, calculate the x-coordinate of the vertex, to do so you have to use the following formula:
[tex]x_v=-\frac{b}{2a}[/tex]Replace it with the values of the coefficients a=-1 and b=90
[tex]\begin{gathered} x_v=-\frac{90}{2\cdot(-1)} \\ x_v=-\frac{90}{-2} \\ x_v=45 \end{gathered}[/tex]Second, replace x=45 in the equation to determine the y-coordinate of the vertex:
[tex]\begin{gathered} y_v=P(45) \\ y_v=-(45^2)+90\cdot45+52 \\ y_v=-2025+4050+52 \\ y_v=2077 \end{gathered}[/tex]The y-coordinate of the vertex represents the maximum profit.
So the maximum profit is $2077, the correct option is option A.
Sammy and Teemu were trying to describe parts of the expression 1/2bh + 4.
• Teemu said," is a coefficient."
Sammy said, "The entire expression is the sum of 4 terms."
Who is correct?
Choose 1 answer:
B
Only Teemu
Only Sammy
Neither student is correct.
Both students are correct.
option (c) is correct.
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given that,
An expression
1/2bh + 4
There are two terms in the first term b and h are variables and its coefficient is [tex]\frac{1}{2}[/tex] .
In the second term only 4 is a constant term.
It means this expression has two.
(a) Teemu said, "[tex]\frac{-1}{2}[/tex] is a coefficient"
In the first term [tex]\frac{1}{2}[/tex] is a coefficient of b and h.
(b) Sammy said, "The entire expression is the sum of 4 terms."
No this expression has only two terms.
Hence, Neither student is correct.
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Answer: Only teemu
Step-by-step explanation: Because 1/2 is the numerical factor in a product involving variables and although sammy said it is the sum of 4 terms, there is 2 in the expression.
4x + 6 <2x>-1 x<-1x<2x>2
The given equation is
[tex]4x+6<2[/tex]First, we subtract 6 on each side.
[tex]\begin{gathered} 4x+6-6<2-6 \\ 4x<-4 \end{gathered}[/tex]Then, we divide the inequality by 4.
[tex]\begin{gathered} \frac{4x}{4}<-\frac{4}{4} \\ x<-1 \end{gathered}[/tex]Therefore, the right answer is the second choice. x < -1I have no clue how to get the different
The distance between the two given points X(-3,3) and Z(4,4) in the given cartesian plane is XZ = √50 = 7.07 units.
As per the question statement, we are supposed to calculate the distance between the two given points X(-3,3) and Z(4,4) in the given cartesian plane. We know that the distance between any two points in the plane is given by:
d=√((x2 – x1)² + (y2 – y1)²), where "d" is the distance between the points (x1,y1) and (x2,y2). Using this formula to find the distance between the two given points X(-3,3) and Z(4,4).
XZ = √((4 +3)² + (4 – 3)²)
XZ = √((7)²+ (1)²)
XZ = √(50)
XZ = 7.07 units
Cartesian Plane: A Cartesian coordinate system in a plane is a system of coordinates that specifically identifies each point by a pair of numerical coordinates with one on X-axis and other on Y-axis. These numerical coordinates are the signed distances from two fixed perpendicular lines to the point, measured in the same unit of length.To learn more about Cartesian Plane click on the link given below:
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How much was the decrease dollar? How much was in his account the end of last year?
Explanation
We are given the following information:
• Amount at the beginning of an investment = $5500
,• Percent decrease = 24.6%
We want to determine the decreased amount in dollars and the amount in his account at the end of the year.
We can determine the decreased amount with the formula below:
[tex]Decreased\text{ }amount\text{ }=Percent\text{ }decrease\text{ }\times Amount[/tex]Therefore, the decreased amount can be calculated as:
[tex]\begin{gathered} Decreased\text{ }amount=24.6\%\times5500 \\ Decreased\text{ }amount=\frac{24.6}{100}\times5500=1353 \end{gathered}[/tex]Hence, the decreased amount is $1353.
At the end of last year, the amount left in his account can be calculated as follows:
[tex]undefined[/tex]Hence, the year-end amount is $4147.
help meeeeeee pleaseee !!!!
1) The Linear equation that models the average price of a new home is;
y = -800x + 294000.
2) The prediction of the average price of a new hom in the year 2014 is; $256000
How to solve the equation in slope intercept form?We are told that the average price in the year 2004 was $294000
We are told that y is the average price in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the y-intercept is $294000.
Since the line must pass through the points (0, 294000) and (7, 288400), it means that;
Slope = (288400 - 294000)/(7 - 0)
Slope = -5600/7
Slope = -800
Now, we know that the general formula for equation in slope intercept form is; y = mx + c
where; m is slope and c is y-intercept.
Thus;
1) Linear equation is; y = -800x + 294000.
2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years
Thus;
y = -800(10) + 294000
y = $256000
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Hailey read 48 pages of a book this week. Blake read half as many as Hailey. How many pages did they read combined?A)24B)60C)72D)96
Step 1
From the question, Hailey reads 48 pages of a book
Blake reads half as many as Hailey.
Hence Blake reads;
[tex]Blake=\frac{48}{2}=24Pages[/tex]The answer will be together they read;
[tex]48+24=72\text{ pages}[/tex]Answer; Option C
In baseball, Ken gets on base 60% of the time he bats. If Ken bats 5 times, how many times did he get on base?
Assuming Ken gets the same percentage as usuall in these 5 times, we can calculated how many times he did get on base by calculating 60% of 5.
To do this we transform 60% into decimal my dropping the percentage sign and dividing it by 100 and then we multiply the decimal by 5:
[tex]\frac{60}{100}\cdot5=0.6\cdot5=3[/tex]So, Ken got on base 3 times.
I am stuck on what to do after graphing points A, B and C
Remember that the coordinates are written in the form (x,y). Plot the points with the given coordinates: A(1,6), B(1,1) and C(5,1):
Draw a right triangle using the same measures for the legs in order to construct ΔDEF, as described below:
[tex]\begin{gathered} DE=5 \\ EF=4 \end{gathered}[/tex]Write the given equation of a line that passes through two given points (-2,-1) and (0,-5)
Answer:
y2-y1 x2-x1
Step-by-step explanation:
-5-(-1)
--------
0-(-2)
-4
---
2
-2
----
1
pls help me with this ill give brainlist
In the lab, Jane has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 12% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 176 milliliters of pure alcohol?
Using the concept of volume, 700 milliliters of Solution B was used.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
When dealing with unknowns, the first step is to represent the unknowns using variables, draw up equations based on the available data, and then solve those equations to account for the unknowns.
Volumes of solutions A and B are here which is unknown.
Put these factors in place for us
Let x = the amount of solution A that was mixed in milliliters.
Let y= the amount of solution B that was mixed in milliliters.
The amount of volume utilized for A is 400 ml less than the amount used
for B.
This can be expressed mathematically as y - x = 400.
Or,
- x + y = 400 [1]
The ratios of alcohol in A and B are provided to us.
A contains 12% alcohol, hence its real alcohol content is 12% of x ml.
= 0.12x (12% = 12/100 = 0.12)
Similar to A, B has an alcohol content of 0.20x.
If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.
and it is said that this amount is 176 ml.
Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].
We create an equation containing only the other term by using both equations and removing either the x or y terms.
We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.
Review the equations now:
- x + y = 400 [1]
0.12x + 0.20y = 176 [2]
x's coefficients should all be the same:
Increase [1] by 0.12
=> -0.12x + 0.12y =
= 0.12 x 400
=> 0.12x + 0.12y = 48 [3]
By adding [2] and [3], the x word is removed.
0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48
0x + 0.32 y = 224
=> 0,32y = 224
Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]
==> y = 700
Therefore, 700 cc of Solution B was utilized.
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ERROR ANALYSIS In Exercise 30, describe and correct the error in finding the inverse of the functionf(x)=1/7x^2, x>=0y=1/7x^2x=1/7y^27x=y^2+-√7x=y
Given the function
[tex]\begin{gathered} f(x)=\frac{1}{7}x^2 \\ x\ge0 \end{gathered}[/tex]To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.
We are already given the domain of f, all the real numbers equal or greater than zero.
The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.
Once we find the inverse function, we'll use this concept.
Step 1: Substitute f(x) for y:
[tex]y=\frac{1}{7}x^2[/tex]Step 2: Swap the variables:
[tex]x=\frac{1}{7}y^2[/tex]Step 3: Solve for y:
[tex]y=\pm\sqrt[]{7x}[/tex]But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:
[tex]f^{-1}(x)=\sqrt[]{7x}[/tex]HELPP Natasha is eating her backyard. The backyard is square in shape and has an area of 4,096 feet. What is a length of one side of Natasha's backyard?
We will determine how to evaluate the side length of a square given its area.
A square is a four sided 2D planar figure with all its sides at right angles and equal in magnitude as follows:
The side a square are all equal and will be denoted by a variable as follows:
[tex]\text{Side of a square = x}[/tex]We will now express the Area of the square in terms of its side length using the basic definition as follows:
[tex]\text{Area of square = Length}^2[/tex]We will now express the above in terms of the side length variable ( x ) as follows:
[tex]\text{Area of square = x}^2[/tex]We are given that Natasha's garden has the following area:
[tex]\text{Area of square = 4096 ft}^2[/tex]Now we will equate the result of area of a square with the side length ( x ) terms as follows:
[tex]4096=x^2[/tex]Evaluate(solve) the above the equation for the variable ( x ) by taking a square root on both sides of the equation as follows:
[tex]\begin{gathered} \sqrt{x^2}\text{ = }\sqrt{4096} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{=}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{\pm}\text{\textcolor{#FF7968}{ 64}} \end{gathered}[/tex]For practical sense, the variable ( x ) denotes the magnitude of the side length of the square which can not be negative. Hence, we have only solution for the side length ( x ) as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 64 feet}}[/tex]
Aliyah's school is selling tickets to the annual dance competition. On the first day of ticket sales
the school sold 8 senior citizen tickets and 15 child tickets for a total of $266. The school took in
$168 on the second day by selling 8 senior citizen tickets and 8 child tickets. What is the price
each of one senior citizen ticket and one child ticket?
Each senior citizen ticket costs $7.
One child's ticket costs $14.
Describe algebra.
Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.
S represents the senior citizen ticket cost.
C is the child's ticket cost.
Price is expressed as USD per ticket.
8S + 15C = 266
8S + 8C = 168
Subtract both equations now to get rid of S
8S + 15C = 266
8S + 8C = 168
———————————-
7C = 98
C = 98/7
C = $14
Changing the value of C in the first
8S + 15(14) = 266
8S + 210 = 266
8S = 266 - 210
8S = 56
S = 56 / 8
S = $7
Hence, $7 is the price for senior citizen
And, $14 is the price for child
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vector W has its initial point at (2,5) and its terminal point at (-4,-2)
For the given points, vector in component form equals -6i^ - 7j^ and its magnitude is 9.22
What is meant by vector?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity. Vector: The displacement is -4 feet, while the velocity is -40 miles per hour. Negative displacement and velocity indicate that the object is travelling counterclockwise.
Vector in component form -
(-4 -2)i^ + (-2-5)j^
= -6i^ - 7j^
Magnitude of the vector equals =
√(-6)² + (-7)² = √85 = 9.22
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Complete Question -
Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.
The points R, S, T and U all lie on the same line segment, in that order, such that the ratio of RS:ST:TURS:ST:TU is equal to 1:1:4.1:1:4. If RU=54,RU=54, find RS.RS.
The segment RS has a length of 9 units
How to determine the length of the segment RS?From the question, the partition of the line segment is given as
RS : ST : TU = 1 : 1 : 4
Where the endpoints of the line segments are R and U
This means that the length RS can be calculated using the following equation
Length RS = Ratio of RS/Sum of the ratios x The length of RU
Substitute the known values in the above equation
So, we have
Length RS = 1/(1 + 1 + 4) x 54
Evaluate the sum
Length RS = 1/6 x 54
Evaluate the products
Length RS = 9
Hence, the length of the segment RS is 9 units
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Gerard compares the offers at two different banks to decide where he should open a savings account. A. Draw a representation to show how much would be in the first savings account if Gerard's initial deposit were d dollars.
Explanations:
Given the following parameters
An initial deposit of Gerard is "d" dollars
For the savings with 5% interest, the interest on "d" dollars will be expressed as;
[tex]\begin{gathered} \text{Interest = 5\% of d} \\ \text{Interest = 0.05d} \end{gathered}[/tex]Get the total savings plus interest in the first account
[tex]\begin{gathered} \text{Balance}=\text{Initial deposit + Interest} \\ \text{Balance=d+0.05d} \\ \text{Balance=1.05d} \end{gathered}[/tex]Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars
For the other account:
Initial deposit = "d" dollars
Interest = $100
Since the interest will be added to the first deposit, hence;
[tex]\text{Balance=(d+100)dollars}[/tex]In Tabulated form:
Which expression is equivalent to the given expression?2x^2 – 14r + 24A. (2x – 12) (x - 2)B. 2(x – 3)(x – 4)C. 2(x - 5)(x - 2)D. 2(x – 8) (x + 3)
Step 1: We have the following expression:
[tex]2x^2\text{ }-\text{ 14x + 24}[/tex]Step 2: Fon finding the equivalent expression, we have to factoring the polynomial, this way:
[tex]2(x^2\text{ - 7x + 12)}[/tex]Step 3: Now we have to find two integer numbers that the result of adding them is - 7 and the result of multipliying them is 12
First number: -4
Second number: -3
Therefore, we have now:
2 (x - 4) (x - 3)
Step 4