The zeroes of the equation f(x) is 3x² + 18x + 32 is x = -18 -7.75/ 6 and x = -18 + 7.75/ 6
What is polynomial?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
Given f(x) = 3x² + 18x + 32
3x^2 + 18x + 32 = 0
Here, a = 3
b = 18
c = 32
-b ±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
-18 ± [tex]\frac{\sqrt{18^2-4(3)(32)} }{2(3)}[/tex]
-18 ± [tex]\frac{\sqrt{324-84} }{6}[/tex]
-18 ± [tex]\frac{\sqrt{-60} }{6}[/tex]
-18 ± [tex]\frac{-7.75}{6}[/tex]
X = -18 (-7.75)/ 6 and x = -18 – (-7.75)/ 6
X = -18 -7.75/ 6 and x = -18 + 7.75/ 6
Therefore, the zeroes of the polynomial are X = -18 -7.75/ 6 and x = -18 + 7.75/ 6
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Which of the following is true? ( not multiple choice)
Answer: A
180-130= <D
50=<D
50+70= 120
180-120=<B
60=<B
m<BCD= 70
m<DBC= 60
70-60=10
Answer:
О A = 10°
Step-by-step explanation:
∡ DBC = 180 - 130 = 50°
∡ DBC + ∡ CBD + ∡ BCD = 180°
50° + 70° + ∡BCD = 180°
∡BCD = 180° - (50°+70°)
∡BCD = 180° - 120°
∡BCD = 60°
Then:
∡BCD - ∡DBC = 60° - 50° = 10°
x2+2x-12=0 vertex form
Taking into account the definition of vertex form, the quadratic function y=x² +2x-12 in vertex form is f(x) = 1(x - +1)² -13
Vertex form of a quadratic functionThe function f(x) = ax²+ bx + c with a, b, c real numbers and a ≠ 0, is a quadratic function expressed in its polynomial form.
The graph of a quadratic function is a curve called a parabola.
Every quadratic function can be expressed by f(x) = a(x - h)² + k
where
"a" is the main coefficient.the ordered pair (h;k) are the coordinates of the vertex of the parabola.The value of -b÷(2a) indicates the value of x or h and replacing this value into the function, you get the value of y or k of the vertex of the function.
Vertex form in this caseIn this case, the quadratic equation y=x² +2x-12, where:
a= 1b= 2c= -12The value of x or h of the vertex is calculated as -2÷(2×1)
Solving: -2÷2= -1
The value of y or k of the vertex of the function is calculated as y=(-1)²+2×(-1) -12
Solving y= -13
Finally, the quadratic function can be expressed in vertex form by f(x) = 1(x - +1)² -13
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On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours. What was the average change in temperature per hour?
Enter your answer as a decimal.
The average change in the temperature per hour is -1.5°F.
Average:
Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given,
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.
Here we need to find the average change in temperature per hour.
To find the average temperature we have to divide the given two temperature.
Temperature change in 9.6 hour = -14.4°F
So, the average change is calculated as,
=> temperature / hour
=> -14.4 / 9.6
=> -1.5°F
Therefore, the average change in temperature is -1.5°F per hour.
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The average change in the temperature per hour is -1.5°F.
Average:
Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given,
On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.
Here we need to find the average change in temperature per hour.
To find the average temperature we have to divide the given two temperature.
Temperature change in 9.6 hour = -14.4°F
So, the average change is calculated as,
=> temperature / hour
=> -14.4 / 9.6
=> -1.5°F
Therefore, the average change in temperature is -1.5°F per hour.
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who knows how to solve this! its geometry
Answer:
figure out how to get 180% from those 3 points
Step-by-step explanation:
solve y-59 equal to 80
Answer:
y=139
Step-by-step explanation:
add 59 to 80
What is the volume of the following cone?
The volume of the cone, to the nearest whole number, is: 50 cm³.
How to Find the Volume of a Cone?The volume of a cone is defined as the amount of space it contains. The volume can be calculated using the formula:
Volume of cone = 1/3 × π × r² × h, where h is the height of the cone, and r is the radius of the cone.
Given the parameters:
Height of the cone (h) = 3 cmRadius of the cone (r) = 4 cmPlug in the values:
Volume of the cone = 1/3 × π × 4² × 3
Volume of the cone = 1/3 × π × 16 × 3
Volume of the cone = 16π
Volume of the cone = 50 cm³
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Pls help!!!: select all the expressions that are equivalent to (1/2) to the power of negative 3. a). -(1/2) to the power of 3 b).2 to the power of 3 c).(1/1/2 to the power of 3) d).1/8 e).8
Answer:
option (e) 8
Step-by-step explanation:
using identity
==>1/(a^(-x))=a^x()
=(1/2)^(-3)
=(2)^3
=2*2*2=8
option (e)
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need help please as soon as possible please
The value of the trigonometric ratio sin C of the given right angle triangle is; A: a/b
How to use Trigonometric ratios?
We know that the three trigonometric ratios of a right angle triangle are given as;
sin θ = opposite/hypotenuse
cos θ = Adjacent/hypotenuse
tan θ = Opposite/Adjacent
Now, from the right angle triangle given to us, if we want to consider the angle C, then we will have the trigonometric ratios as;
sin C = a/b
cos C = c/b
tan C = a/c
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What are the domain and range of this relation? pt3 last one pls help
−14 = −21 +
C
11
Subract
Answer:
35
Step-by-step explanation:
Solve for b.
-14b + 1
4
<3 or b - 15 - 15b > 1
Write your answer as a compound inequality with integers, proper fr
fractions in simplest form.
or
Answer:
Step-by-step explanation:
guestion 24
determine the size of the angle
mark
The size of the angle marked t is 60 degrees.
We are given an isosceles triangle with one angle as 30 degrees.
We have to find the angle marked t.
Let us name the triangle.
Let the vertex formed by the intersection of two equal sides be A and,
The vertex with 30 degree angle be B and the third vertex be C.
We know that,
AB = AC
Hence,
∠ ABC = ∠ ACB = 30 degrees.
Hence, ∠ BAC = 180 - 30 - 30 = 120 degrees
We know that,
t + ∠ BAC = 180 degrees (supplementary angles)
Hence,
t + 120 = 180
t = 180 - 120
t = 60 degrees
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Type the correct number
Cars
4
12
16
Trucks
5
10
15
25
Answer:
cars= 32 , trucks= 55
Step-by-step explanation:
add all the cars up then the trucks
The zurn family ate at a restaurant that was having 15% discount on that day .Their meal costs 64.75,and they left a 20% tip .What is the total cost of the meal? (Note: the tip applies to the total cost of the meal before the discount was applied)
The total cost of the meal is 66.045
Given,
The cost of the meal = 64.75
The discount given on that day = 15%
The tip given by Zurn family = 20%
We have to find the total cost of the meal.
First we have to find the total cost including tip before discount is added.
That is,
120% of 64.75
= 64.75 × 120/100
= 6.475 × 12
= 77.7
Here, the total cost including tips before discount is 77.7
Now, we have to deduct the discount.
100 - 15 = 85
That is,
85% of 77.7 will be the total cost of the meal
= 77.7 × 85/100
= 6604.5 / 100
= 66.045
Therefore, the total cost of the meal is 66.045
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Help quickly please!
The equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) include C. 1 2/3x + 35 - 1 1/2x + 12
How to express the expression?It should be noted that an expression simply shows the relationship between the variables.
In this case, the value of the expression illustrated will be:
5(1/3x + 7) - 3(1/2x - 4)
= 5/3x + 35 - 3/2x + 12
= 5/3x - 3/2x + 35 + 12
= 10/6x - 9/6x + 47
= 1/6x + 47.
Therefore, the equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) will be 1 2/3x + 35 - 1 1/2x + 12. This was illustrated based on the information given as it has the final value of 1/6x + 47.
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Montel heated a 12-cup pot filled with soup. He served bowls of soup to his family.
How can Montel find out how much soup his family ate?
He can find out by using mathematical operation - subtraction.
What are Mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as a ternary operation, is the mixed product.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
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(c) A total of 1800 students attend St. John's College. The ratio
of teachers to students is 1:25.
(i) How many teachers are there at the college.
Three-quarters of the students own laptop computers.
(ii) How many students DO NOT own laptop computers?
Answer: the number of teachers are 14.4 and the amount of students that don’t own laptops of 5400
Step-by-step explanation:
Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
Answer:
x = -3 and y = 6
Step-by-step explanation:
by plugging the function (y = 3x + 15) into the y value in the function (3x + 3y = 9), you can then solve to find that x = -3
After solving for the x-value, plug -3 into the easiest equation to solve for the y-value (y = 3x + 15) to then find that y = 6
This is method of solving is called substitution
In WXY, m/W = (10x + 17)°, m/X = (2x - 9)°, and m/Y = (3x + 7)°. Find m/Y.
Answer:
m∠Y = 40°
Step-by-step explanation:
The sum of the three angles of a triangle must equal 180°
Thus
m∠W + m∠X + m∠y = 180°
→ (10x + 17) + (2x - 9) + (3x + 7) = 180
→ 10X + 17 + 2X + 9 + 3X + 7 = 180
Collecting like terms
→ 10X + 2X + 3X + 17 - 9 + 7 = 180°
→ 15x + 15 = 180
Subtract constant 15 from both ssides:
→ 15x + 15 - 15 = 180 - 15
→ 15x = 165
Divide both sides by 15
→ 15x/15 = 165/15
→ x = 11
m∠Y = 3x + 7
m∠Y = 3 x 11 + 7
m∠Y = 33 + 7
m∠Y = 40°
PLEASE help ill give brainliest
Answer:
A = 73°
Step-by-step explanation:
angle A + angle B = 180°
[tex](6x-35)+(3x+53) = 180[/tex]
[tex]6x+3x-35+53=180[/tex]
[tex]9x+18=180[/tex]
[tex]x=\frac{180-18}{9}[/tex]
[tex]x=18[/tex]
Angle A = 6(18) - 35 = 108 - 35 = 73°
Angle B = 3(18) + 53 = 54 + 53 = 107°
73 + 107 = 180
Hope this helps
answer the following questions for each set: (a) what are the limit points? (b) is the set open? closed? (c) does the set contain any isolated points?
a) limit point of a set A is 1
b) set A is neither open nor closed
c) all the element of set A are isolated point except -1 and 1
Let A={(−1)^n+2/n :n=1,2,3,.....} and B={x∈Q:0<x<1}
Answer the following questions for each set:
a) What are the limit points?
b) is the set open? closed?
c) does the set contain any isolated points?
a) the limit point of a set A are -1 and 1
-1 does not belong to set A
1 belong to set A
Therefore limit point of a set A is 1
b) A set is open if every point in is an interior point. A set is closed if it contains all of its boundary points
thus set A is neither open nor closed
c) a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S and there exists a neighborhood of x which does not contain any other points of S.
all the element of set A are isolated point except -1 and 1
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Two values of v satisfy the equation |2v- 13| +6 = 9. What is the sum of these values?
Answer: v = 8, 5; The sum of these values would be 13.
∣2v − 13∣ + 6 = 9
Combine like terms, utilizing the properties of equality. Do not forget to follow the order of operations!
∣2v − 13∣ + 6 = 9
Subtract 6 from both sides of the equation.
∣2v − 13∣ = 3
Consider the definition of absolute value (distance from the number zero); the absolute value of x and -x would both be x.
2v − 13 = 3
2v − 13 = −3
Add 13 to both sides of the equation.
2v = 16
2v = 10
Divide both sides of the equation by 2.
v = 8
v = 5
Add the sum of the values.
8 + 5 = 13
a container is in the shape of a square based prism with base measurement of 3m and the height is 5m. The top and bottom are made of steel and the sides are made of aluminum. If steel costs $2.95/m^ and aluminum costs $1.57/m^, how much would it cost to make the container?
The cost for making the container if steel costs $2.95/m and aluminum costs $1.57/m is $28. 27
How to determine the cost of the containerBased on the information given, we have that;
The base of the square prism is measured 3mThe height of the square prism is measured 5mWe also have the following deductions;
Steel was used for the top and bottom are both made of steelAluminum was used for the sides of the square prismThe properties of a square prism include;
Opposite sides are parallel Opposite sides are parallelOpposite sides are equalOpposite angles are equal The diagonals of the prism divide each otherThe cost for aluminum = 10($1.57)
Multiply the values by expanding the
The cost for aluminum = $10. 57
The cost for steel = 6($2.95)
Multiply through, we have;
The cost for steel = $17. 7
Total cost for the container = Cost of steel + cost of aluminum
Total cost for the container = $10. 57 + $17. 7
Total cost for the container = $28. 27
Thus, the value of the cost is $28. 27
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I’ll mark you brainliest for a correct answer!!! I have been reeling over this question forever
What is the range of the function shown on the graph?
Check the picture below.
1. Ganymede is one of Jupiter’s moons. It takes Ganymede 7 days, 3 hours, and 15 minutes to make one rotation around Jupiter. How many hours does it take Ganymede to complete a full rotation? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
The number of hours it would take Ganymede to complete a full rotation is 171.25 hours.
What is the number of hours?The first step is to convert days to hours. A day is equivalent to 24 hours. In order to convert days to hours, multiply 7 by 24.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
1 day = 24 hours
24 x 7 = 168 hours
The second step is to convert minutes to hours, In order to do this, divide 15 by 60. Division is the process that is used to determine the quotient of two or more numbers.
60 minutes = 1 hour
15 / 60 = 0.25 hours
Now, add all the converted hours together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Total hours = 168 hours + 3 hours + 0.25 hours = 171.25 hours
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Order 81%, 8/9, 0.79, and 9/11 from least the greatest.
Answer:
9/11, 8/9, 0.79, 81%
Step-by-step explanation:
i don't know how to explain but this is pretty much how you'd do it
Can u please answer this asap and thank you
Answer:
10 popcorn orders
Step-by-step explanation:
[tex]10 + 4.55 x = 8 + 4.75x \\ 4.55x - 4.75x = 8 - 10 \\ - 0.2x = 8 - 10 \\ - 0.2x = - 2 \\ x = \frac{ - 2}{ - 0.2} \\ x = 10[/tex]
Given: 1 || m, p || q Prove: 21 = 22
Answer:
Proved.
Step-by-step explanation:
l // m and p is transversal.
∠1 ≅ ∠3 ----------(I) {Corresponding angles}
p // q and l is transversal.
∠3 ≅ ∠2 -------(II) {Corresponding angles}
From (I) & (II),
∠1 ≅ ∠2
Hence proved.
To prove ∠1 = ∠2
What are parallel lines?
In a plane, parallel lines are those whose distances between them are constant. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given: l II m and p II q
According to the properties of parallel lines
∠1 and ∠ 3 are equal because l II m therefore ∠1 and ∠ 3 are corresponding angles.
Since p II q therefore ∠3 = ∠2 { angles present on the same sides of the parallel lines called corresponding angles are equal }.
Thus since ∠1= ∠3 and ∠3=∠2 therefore we can say that ∠1 = ∠2.
Hence proved.
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the table shows the number of questions answered incorrectly by each player on a game show.if each missed question is worth "-77" points,what is the change in olive sco due to the incorrect questions?
The change in Oliver's score due to the incorrect questions will be -63.
How to illustrate the information?It should be noted that the table shows the number of questions answered incorrectly by each player on a game show.
It should be noted that based on the information, every question missed is worth -7 points.
Therefore, the change in Oliver's score due to the incorrect questions will be:
= 9 ×-7
= -63
The change is -63.
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