The quadratic equation will be; 3x² + 6x + 9
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.
The factors are; (x + 3) and (x + 1)
f(x) = a(x + 3)(x + 1)
As, a = 3.
Then we get;
f(x) = 3(x + 3)(x + 1)
= 3(x² + 2x + 3)
= 3x² + 6x + 9
The quadratic equation will be; 3x² + 6x + 9
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Which inequality is true?
A. 5π > 15
B. π+9<12
C. 6/2m > 1
D. 47-2<10
Answer: A
Step-by-step explanation:
[tex]\pi > 3 \implies 5\pi > 15[/tex]
Write this word sentence as an equation and then solve.
The nine less than the quotient of a number w and -3 is 54.
Value of w will be [tex]\frac{45}{Q}[/tex] + 3
What is division?Division is the process of dividing a bunch of items into equal portions. It is one of the four fundamental operations in mathematics and results in a just distribution of resources. The division of two numbers can be calculated using the following formula: Dividend Divisor = Quotient + Remainder. The number that is being divided in this case is known as the dividend. The number that divides the number (dividend) into equal parts is known as the divisor. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, "÷" or occasionally "/," is used in computer code.
Given Data
The nine less than the quotient of a number w and -3 is 54.
Let the quotient be Q
9 - Q( w - 3) = 54
Solving,
-Q(w - 3) = 54 -9
w-3 = [tex]\frac{45}{Q}[/tex]
w = [tex]\frac{45}{Q}[/tex] + 3
Value of w will be [tex]\frac{45}{Q}[/tex] + 3
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What mistake did Richard make? Explain what he needs to do to fix it.
Given:-
[tex]x^2-6x+8=0[/tex]To find the simplified form and the mistake.
So now we use the formula,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{6\pm\sqrt[]{6^2-4\times1\times8}}{2\times1} \\ x=\frac{6\pm\sqrt[]{36-32}}{2\times1} \\ x=\frac{6\pm\sqrt[]{4}}{2\times1} \\ x=\frac{6\pm2}{2} \end{gathered}[/tex]So now we get,
[tex]\begin{gathered} x=\frac{6\pm2}{2} \\ x=\frac{6+2}{2},x=\frac{6-2}{2} \\ x=\frac{8}{2},x=\frac{4}{2} \\ x=4.x=2 \end{gathered}[/tex]So the value of x is,
[tex]4,2[/tex]So the mistake is in step 5.
The graph shows the relationship between the number of cups of flour and the number of cookies made. Write an equation for the proportional relationship.
The equation for the proportional relationship is 16x-y=0 .
The equation of the line passing through the two points (a,b) and (c,d) is given by
(y-b) = m(x-a), where m is the slope .
In the question ,
Given in the graph that
x represents the number of cups of flour and y represents the number of cookies made .
From the graph we can see that
when 6 cups of flower is used , 96 cookies are made
So, the point on the line is (6,96),
when 12 cups of flower is used , 192 cookies are made
So, the point on the line is (12,192)
hence the line passes through the two points (6,96) and (12,192).
So the slope of the line is
m=(192-96)/(12-6)
m= 96/6
m=16
Substituting the values of a,b, c,d and m in the equation of line formula ,we get
y-96=16(x-6)
y-96 = 16x - 96
16x-y=96-96
16x-y=0
Therefore , The equation for the proportional relationship is 16x-y=0.
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if y = x^2 - 2 what is the value of y when x=3
Answer: y = 7
Step-by-step explanation: 3^2 is 9 and 9 - 2 is 7.
6s-3/4 simplified
very hard
The simplified form is 3/4( 2s-1).
The problem we dealing with here is related to factors of linear polynomial, where a linear polynomial is characterized as any polynomial expressed in the form of a condition of p(x) = ax + b, where a and b are real numbers and a ≠ 0. In a linear polynomial, the degree of the variable is rise to 1 i.e, the highest type of the variable is one, whereas a factor of polynomial P(x) is any polynomial that divides equitably into P(x). The factorization of a polynomial is its representation as a product of its variables.
The problem that is given to us is 6s-3/4 ,we just need to find common factor it to convert it into a simpler form.
We can see 3/4 is the common factor out here so it wil be
=3/4 (2s-1)
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Which interval describes where the graph of the function is negative?
The interval that describes where the graph of this function is negative is: C. 2 < x < ∞
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, a function is typically used for mapping an input variable to an output variable. In Mathematics, the value of y on the y-axis of a graph must be less than 0 (x < 0) for the graph of any function to be negative.
By critically observing the graph of this function, we can logically deduce that at point x = 2 is where the value of y becomes less than 0 (x < 0) and continues to infinity. Therefore, the graph of this function is negative is at an interval of 2 < x < ∞.
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The midpoint of line segment AB is M(3,-1). If the coordinates of A(8,4), what are the coordinates of B?
The coordinates of B are (-2 , 9)
Step-by-step explanation:
A (8, 4)
M (3 , -1)
To calculate a midpoint you have to add the corresponding coordinates of each point and divide them by 2
(Ax + Bx) / 2 = Mx
(8 + Bx) / 2 = 3
8 + Bx = 3 * 2
Bx = 6 - 8
Bx = -2
(Ay + By) / 2 = My
( -1 + By) / 2 = 4
-1 + By = 4 * 2
By = 8 + 1
By = 9
The coordinates of B are (-2 , 9)
A cylinder has a base diameter of 20 feet and a height of 8 feet what is the cubic volume
Write the linear equation that gives the rule for this table X 2,3,4,5 Y 1,2,3,4
Answer: [tex]Y=X-1[/tex]
Step-by-step explanation:
The standard linear equation for the table is expressed as y = mx + b with
m as the slope of the line and b as the y-intercept.
We will use coordinates (2,1) and (3,2) from the table to calculate the slope, m.
[tex]\begin{equation}\begin{aligned}m &=\frac{Y 2-Y 1}{X 2-X 1} \\m &=\frac{2-1}{3-2} \\m &=\frac{1}{1} \\m &=1\end{aligned}\end{equation}[/tex]
We can find the formula using the point-slope formula.
[tex](Y -Y 1)=\ m (X -X1)\\Y-1=1(X-2)\\Y-1=X-2\\Y=X-1[/tex]
What is the slope of the line that passes through the points (4,7) and
(7, 16)? Write your answer in simplest form.
The slope of the line passing through (4,7) and (7, 16) is 3
What is Slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run". It is denoted by "m".
Formula, m = rise / run = (y2 - y1) / (x2 - x1)
Given,
(x1, y1) = (4, 7)
(x2, y2) = (7, 16)
Now, put these values in slope (m) formula,
m = (y2 - y1) / (x2 - x1)
= (16 -7) / (7 - 4)
= 9/3
= 3
Therefore, the slope of the line passing through (4,7) and (7, 16) is 3.
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Using proportios (ratios) find the valure of x.
The value of x is 7.82
How to get values using proportions?Following these procedures will help us use proportions to solve challenges in the real world:
1. Set up two ratios comparing the identical quantities using the information from the problem.
2. Create a proportion by setting the ratios equal.
3. To find the proportional unknown, use cross multiplication.
[tex]AB/ AD = TS/ UT[/tex]
[tex]7/ 14.8= 3.7/ x[/tex]
On cross multiplying we get
7x= 54.76
x= 7.822
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Pls help step by step
Answer:
1/1power4
Step-by-step explanation:
=one on one,and there will be a power four on top of the one.
a 2000l tank containing 550l of water is being filled wiwter at the rate of 75l per min from full 1600l tank how long will it be before the two tanks have the same amount of water
By using the equation we can conclude that it will take 7 hours before the two tanks have the same amount of water.
What are equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the equation that will help to find the answer:
550+75x = 1600-75xSo, now solve for x as follows:
550+75x = 1600-75x150s = 1600-550150x = 1050x = 1050/150x = 7Therefore, by using the equation we can conclude that it will take 7 hours before the two tanks have the same amount of water.
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Put these numbers in order from greatest to least.
0.25
5 3/12
-5 18/40
Answer:
Step-by-step explanation:
5 3/12
0.25
-5 18/40
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Looking at this proof of the Pythagorean Theorem, which statement would be true?
Answer: a
Step-by-step explanation:
We know that [tex]a^2 +b^2 =c^2[/tex]. The left hand side is the same as the sum of the areas of the two green squares, and the right hand side is the same as the area of the one large green square.
A rectangular garden is 5 ft longer than it is wide. Its area is 300 ft. What are its dimensions?
The dimensions of the garden are l=20 ft and w=15 ft.
Given, the rectangular garden is 5 ft longer than it's width.
The area of the garden is 300 ft.
dimensions of the garden are = ?
let the width be represented by x.
therefore, length = 5+x
area of the rectangle = l×w
substitute the values.
x(5+x) = 300
5x + x² = 300
x² + 5x - 300 = 0
x²+20x-15x-300 = 0
x(x+20)-15(x+20)=0
(x+20)-(x-15)=0
x=-20 or x=15
hence the dimension cannot be negative.
hence x=15.
substitute x=15 in l=x+5
l=15+5
l=20
Therefore, length and width of the rectangle garden are 20 ft and 15 ft, respectively.
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Please help me please please
ok so at first if u have fractions like the first follow my instruction:
1st: u have 2/3---1/2, u will multiply 3 by 1 and 2 by 2 so u will get 6 and 4
but remember that 2/3 and 1/2 u cris cross it the left one comes first like 6 then 4 so it could balance and do the rest of the fractions like that.
2nd: if u have decimal u will check the number after the decimal but if the are the same u will compare the numbers before the decimal.
I hope it's usefull
Membership to a video game club is $50 a year and $3 per game rented. At the end of the year Harvey had spent $296. How many games had he rented?
Membership to a video game club is $50 a year and $3 per game rented. At the end of the year Harvey had spent $296. he played games had he rented 82 games.
What are mathematical operation?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
A set of numbers and operations make up a mathematical expression. The components of a mathematical expression that performs an operation are:
Operands: Operands are the numerical values that are employed in an operation. Different words are given to the operands depending on the type of operation.
Operator: An operator is the symbol used to represent a mathematical operation.
+ for the addition− for the subtraction× for the multiplication÷ for the division = for the equal to, indicates the equivalence, that is the left hand side value is equal to the right hand side value.Solving the above;
Membership costs him= $50
Per game rented= $3
Amount he spent = $296
Therefore, Number of games he rented=[tex]\frac{296-50}{3}[/tex]
= 82
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Which option shows the plan and which option shows the side elevation?
Option B picture shows the plan of the given 3D shape and Option I picture shows the side elevation of the given 3D shape.
Plan: When an object is viewed from the top, that section or part is called a plan view of that object.
Options C, G, F, and B- all are viewed from the top: however out of these four only Option B shows the real plan of this given 3D object while others change its dimension and shape.
(F is shown as an oval)(C is shown as small and inclined)(G is shown as smaller than the actual image)Elevation: When an object is viewed from one side of the object, that section or part is called an elevation view.
Options D, E, A, and I- all are in elevation view, however, only option I is satisfying and shows the real elevation of a given 3D object.
(A shows a bit of curve in the below edge )(D shows again a curve with a narrow structure)(E shows a perfect edge however it is also narrower than the actual image)Therefore, only option B and option I are showing the correct plan and elevation of a given image.
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The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3. What is the first term of this series
The first term of the series such that the sum of the first three terms of the geometric series is 171 is equal to 81.
What is the first term of a geometric series?
In this problem we find the sum of three consecutive elements of a geometric series. A geometric series is a set of elements generated by a discrete exponential expression of the form:
y = a · rⁿ ⁻ ¹
Where:
a - First term of the series.r - Common ration - Index fo the element.According to the statement, we find the following expression:
a · (2 / 3)² + a · (2 / 3)¹ + a · (2 / 3)⁰ = 171
(4 / 9) · a + (2 / 3) · a + a = 171
(19 / 9) · a = 171
a = 81
Then, the first term of the series is:
y = 81 · (2 / 3)¹ ⁻ ¹
y = 81
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A landscape designer drew a blueprint for a gardenhe was planning. the scale was 1 inch : 2.5 feet. the path through the garden is 5 inches long and 1.5 inches wide on the blueprint. the designer plans to cover 80% of the area of the path with crushed rocks. how many square feet of the actual path should be covered in crushed rocks
Given,
1 inch = 2.5 feet
∴ Area of garden = ( 5 x 2.5) x ( 1.5 x 2.5) feet
Since, 80% area will be used as path with crashed rock,
therefore, 12.5 x (1.5 x 2.5)/ 100 x 100 x 10 feet
= 37.5 sq. feet
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PLEASE HELP !!What is the slope of a line parallel to the line whose equation is 8x+10y=60.
Answer:
In slope intercept form -5y = -4 - 30
Step-by-step explanation:
Slope intercept form is y=mx + b
Rewrite your equation in this form
-10y = -8x - 60
Find GCF (Greatest Common Factor) in this case it is 2
Divide all by 2
-5y = -4x - 30
divide both sides by -5
y = 4/5x + 6
slope = 4/5
Answer:
8
Step-by-step explanation:
so we know the formula of a line is y=mx+b
1. arrange 8x+10y=60 into y=mx+b format
2. 10y=8x+6
3. we see that 8 = m
4. parallel line NEVER intersect so therefore they have the same slope (whereas perpendicular lines intersect so the slope for a perpendicular line would be -1/8)
where w is the width of the rectangle. Assume that w is a whole number. Use this function to answer Items 17-20. 17. Make a table of values and a graph of the function. 18. Attend to precision. Give a reasonable domain for the function in the context. Explain your answers 19. Identify the y-intercept of the function. What does the y- insert represent within this context? 20. What is the absolute maximum of the function? What is the absolute minimum?
Answer: I would use the max as 25
Step-by-step explanation: You use the variables of y, for the numbers os the maximum. so i would be high
cuanto es 1500x830 +321
The given expression 1500 x 830 + 321 can be solved as 12,45,321 using arithmetic operations.
What is multiplication and addition?Multiplication is the repeated addition of a number. If we multiply m by n, that means m is repeatedly added to itself for n times. The symbol for multiplication is ‘×’.
Addition is the process of combining two or more items (or numbers) to create a new sum.
Given the expression: 1500 x 830 + 321
Using BODMAS, first we do the multiplication.
So, 1500x 830 = 12,45,000
Now, continuing with the addition, we get
12,45,000 + 321 = 12,45,321
Therefore, the given expression can be solved as 12,45,321.
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"The given question is:
Calculate 1500 x 830 + 321"
i need help please , like really fast !
nvm i left
Step-by-step explanation:
Help me, I am struggling.
Answer:
term
Step-by-step explanation:
2/5m - 4/5 - 3/5m
PLEASE HELP!! ASAP
Answer:
-1
Step-by-step explanation:
All of them have the same denominator so we can take the denominator out
2-4-3 = -1 m
Is [tex]\sqrt{72}[/tex] irrational or rational , and why?
(please help im like a month late with this assignment)
Answer:Irrational
Step-by-step explanation:The answer does not end and is infinite.
Answer:
it is irrational number
Step-by-step explanation:
it just is irrational number
5. A man's taxable income is $35 200. He pays income tax at the rate of 25%. The amount of income tax payable is
If a man's taxable income is $35200 and he pays income tax rate of 25%, the amount of income tax payable is $8800
The man's taxable income = $35200
The income tax rate = 25%
The percentage is the hundredth part of any number.
The amount of income tax payable = The man's taxable income ×(The income tax rate/100)
Substitute the values in the equation
The amount of income tax payable = 35200×(25/100)
= 35200×0.25
= $8800
Hence, if a man's taxable income is $35200 and he pays income tax at the rate of 25%, the amount of income tax payable is $8800
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