The sum of b and c is equal to 54.
What is quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Given is the following quadratic equation -
x² - 6x + 66
x² - 6x + 9 - 9 + 66
x² - 3x - 3x + 9 - 9 + 66
x(x - 3) - 3(x - 3) - 9 + 66
(x - 3)² + 57
The given form of resultant is -
(x + b)² + c
On comparing, we get -
b = - 3
c = 57
Therefore -
b + c = -3 + 57 = 54
Therefore, the sum of b and c is equal to 54.
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Which is bigger 1/10 1/12
a road sign that is 12 feet high casts a shadow that is 25 feet long. what is the height of the taller sign?
Final answer:
To find the height of the taller sign, we can use similar triangles and the concept of proportions and the height of the taller sign comes out o be 12 feet.
Explanation:
To find the height of the taller sign, we can use similar triangles and the concept of proportions. The height of the shorter sign is given as 12 feet, and its corresponding shadow length is 25 feet. We can set up the proportion:
Height of taller sign / Length of its shadow = Height of shorter sign / Length of its shadow
Substituting the given values, we can solve for the height of the taller sign:
Height of taller sign = (Height of shorter sign / Length of its shadow) x Length of its shadow
Plugging in the values, we get:
Height of taller sign = (12 feet / 25 feet) x 25 feet
Height of taller sign = 12 feet
Therefore, the height of the taller sign is 12 feet.
Determine all the factors for the following expression(Note: you will need to use the Rational Root Theorem more than one time) : f(x)=x^5+3x^4-5x^3-15x^2+4x+12? Please help im so confused and this assignment is due tomorrow!?
Possible rational roots: ±1,±2,±3,±4,±6,±12±1,±2,±3,±4,±6,±12
Actual rational roots: 1,−1,2,−2,−3
see attachments for all steps.
Please Help Me. Use an identity to find the exact value of each expression: Note: You are not allowed to use decimals in your answer. sin(96∘)cos(264∘)+cos(96∘)sin(264∘)= and sin(258∘)cos(33∘)−cos(258∘)sin(33∘)=
Utilize trigonometric identities to find exact values without decimals:
To find the exact values of the given trigonometric expressions, we can use the trigonometric identity sine of the sum of angles: sin(A + B) = sinA x cosB + cosA x sinB.
1. For the first expression, sin(96°)cos(264°) + cos(96°)sin(264°), using the identity, it simplifies to sin(96° + 264°), which equals sin(360°), and sin(360°) equals 0.
2. For the second expression, sin(258°)cos(33°) - cos(258°)sin(33°), applying the identity yields sin(258° - 33°), which is sin(225°), and sin(225°) simplifies to -√2/2.
I need help ASAP plzzzzzzz
For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what percent of the observatio
A 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground
We apply the Pythagorean theorem and differentiate it to relate the rates of the ladder's top slipping and the foot of the ladder moving away from the wall. Substituting given values in the differentiated equation gives us the speed at which the foot of the ladder is moving away.
Explanation:In this problem, we are dealing with a right triangle formed by the wall, ground and the ladder acting as the hypotenuse. The rate at which the top of the ladder is descending and the height at which the rate needs to be calculated are given. This problem applies the concepts of related rates in calculus.
According to the Pythagorean theorem, for a right triangle, the sum of the square of the two shorter sides is equal to the square of the longest side (the hypotenuse). Here, we have x² + y² = 15² where x is the distance of foot of the ladder from the wall and y is the height from the ground.
Differentiating both sides with respect to time (t), we get 2x(dx/dt) + 2y(dy/dt) = 0. Solve this differentiation equation to find dx/dt, the speed of the foot of the ladder moving away from the wall while y is 13.
To solve this, plug y = 13, dy/dt (rate at which top of ladder is descending) = -4 ft/sec into the equation and solve for dx/dt.
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Please help me with this Math question
F(x, y, z) = x2yz − xyz3, p(2, −1, 1), u = 0, 4 5 , − 3 5 (a) find the gradient of f.
Final answer:
The gradient of the function [tex]F(x, y, z) = x^2yz - xyz^3[/tex] can be found by taking the partial derivatives with respect to each variable x, y, and z.
Explanation:
The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. To find the gradient of the function [tex]F(x, y, z) = x^2yz - xyz^3[/tex], we need to find the partial derivatives with respect to each variable.
The partial derivative with respect to x is: [tex]Fx = 2xyz - yz^3[/tex]
The partial derivative with respect to y is: [tex]Fy = x^2z - xz^3[/tex]
The partial derivative with respect to z is: [tex]Fz = x^2y - 3xyz^2[/tex]
32.64 is 76.8 of what
Find the total capacity of twenty five containers of cranberry juice if each bottle holds 5 quarts 1 pint 6 oz
A) 142 pints 6 oz
B) 140 pints 6 oz
C) 142 pints 9 oz
D) 142 pints 1 pint 6 oz
E) None
what is the reflection rule
Answer:
what is the reflection rule
Step-by-step explanation:
In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; This set is called axis in 2 dimensions or plane in 3 dimensions of reflection.
Add: (3x3 - 2x2 - 6x) + (3x2 - 5x + 3).
Simplify the expression
(-5)^3
Answers:
–125
125
–15
25
What is the product in simplest form?(In fractions) -5 1/2*8 1/3
A.-20/39
B.-10/39
C.-5/39
D.3/25
Seventy hundredth is the same as 0.07
a total of 210 people attended the opening night of a School Musical, students tickets cost $3 each while general admission tickets cost $7.50 each. If total sales were $1,296, how many general admission tickets were sold?
Answer: The number of general admission tickets that were sold is 148.
Step-by-step explanation: Given that a total of 210 people attended the opening night of a School Musical, where students tickets cost $3 each while general admission tickets cost $7.50 each.
The total sales were $1,296.
We are to find the number of general admission tickets that were sold.
Let x and y represents the number of student tickets and the general admission tickets respectively that were sold.
Then, according to the given information, we have
[tex]x+y=210\\\\\Rightarrow x=210-y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]3x+7.50y=1296\\\\\Rightarrow 3(210-y)+7.50y=1296~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\Rightarrow 630-3y+7.50y=1296\\\\\Rightarrow 4.50y=1296-630\\\\\Rightarrow 4.50y=666\\\\\Rightarrow y=\dfrac{666}{4.50}\\\\\Rightarrow y=148.[/tex]
Thus, the number of general admission tickets that were sold is 148.
san francisco has recycled facility that accepts unused paint.Volunteers blend and mix the paint and give it away in 5-gallon buckets.Write and solve an equation to find the number of buckets of paint given away from the 30,000 gallons that are donated.
The problem is a simple division process. We set up the equation where the number of buckets, B is calculated by the total quantity of paint in gallons, divided by how many gallons each bucket holds. Solving this equation, we discover that 30,000 gallons of paint can fill 6,000 buckets.
Explanation:We can solve this problem by using a simple division process. Each bucket holds 5 gallons. So, if we have 30,000 gallons, we need to find out how many 5-gallon buckets this amount equals to.
If we denote the number of buckets by B, we can write an equation as follows:
5B = 30000.
To find B, we solve the equation by dividing both sides by 5: B = 30000/5
So, using a calculator, we find that B = 6000 buckets.
Therefore, the facility would be able to give away 6000 buckets of paint.
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Which equation is the equation of the line, in point-slope form, that has a slope of -1.8 and passes through the point (-0.5, 1.9)?
y minus 1.9 equals 1.8 open parentheses x plus 0.5 close parentheses
y minus 1.9 equals negative 1.8 open parentheses x minus 0.5 close parentheses
y minus 1.9 equals negative 1.8 open parentheses x plus 0.5 close parentheses
y minus 0.5 equals negative 1.8 open parentheses x plus 19 close parentheses
Answer: y minus 1.9 equals negative 1.8 open parentheses x plus 0.5 close parentheses.
Step-by-step explanation:
The point slope form of a line that has slope m and passes through (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Given : Slope = -1.8 and Point (a,b) = (-0.5, 1.9)
Then, the point-slope form of a line that has a slope of -1.8 and passes through the point (-0.5, 1.9) will be :-
[tex](y-1.9)=-1.8(x-(-0.5))\\\\\Rightarrow\ (y-1.9)=-1.8(x+0.5)[/tex]
Hence, the correct option is y minus 1.9 equals negative 1.8 open parentheses x plus 0.5 close parentheses.
Find the mean, median, and mode for the data set. Round answers to the nearest tenth if necessary
The mean of the dataset is 9.3, the median is 10, and the mode is 13.
To find the mean, median, and mode of the data set 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13, follow these steps:
1. Mean
Add all the numbers together:⇒ 15 + 13 + 9 + 9 + 7 + 1 + 11 + 10 + 13 + 1 + 13 = 102
Divide by the number of values in the data set:⇒ 102 ÷ 11 = 9.3 (rounded to the nearest tenth)
The mean is 9.3.
Median
First, arrange the numbers in ascending order: 1, 1, 7, 9, 9, 10, 11, 13, 13, 13, 15
Find the middle number:The 6th number (since there are 11 numbers) is 10.
The median is 10.
Mode
Identify the number(s) that appear most frequently:In this data set, 13 appears three times.
The mode is 13.
Complete question:
Find the mean, median, and mode of the data set. Round to the nearest tenth. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13
Round 3.38461370132 to the nearest hundred-thousandth.
Answer:
3.38461
Step-by-step explanation:
The given number is 3.38461370132 and we have to round it to the nearest hundred-thousandth.
In order to round this number to nearest hundred-thousandth, we round the fifth number after the decimal point.
So, must see if the sixth digit is less than 5 or not. If it is five or greater than five then we add 1 to the previous digit otherwise it will not change.
The fifth digit is 1
And the sixth digit is 3 < 5
hence, we'll keep the 5th digit as it is.
So, when rounded to the nearest hundred-thousandth the number is 3.38461
What reasoning and explanations can be used when solving radical equations?
Answer:
The common reasoning that can be use while solving a radical equation are shown below.
Step-by-step explanation:
Radical equations are the equations which contains radical expressions like [tex]\sqrt{x}\text{ and }\sqrt{x+2}[/tex], etc.
If a radical expression is defined as [tex]\sqrt{x}[/tex], then the sign [tex]\sqrt{}[/tex] is the radical and x is radicand.
The common reasoning that can be use while solving a radical equation are:
1. Isolate or separate the radical expression.
2. To remove radical square both sides of the equation.
3. After that solve the equation to find the unknown variable
4. Check the answer for solution or extraneous solution.
For example:
[tex]\sqrt{x+1}+1=x[/tex]
subtract 1 from both sides.
[tex]\sqrt{x+1}=x-1[/tex]
Taking square on both sides.
[tex]x+1=(x-1)^2[/tex]
On simplification we get
[tex]x+1=x^2-2x+1[/tex]
[tex]0=x^2-2x+1-x-1[/tex]
[tex]0=x^2-3x[/tex]
[tex]0=x(x-3)[/tex]
Using zero product property,
[tex]x=0,x-3=0\Rightarrow x=3[/tex]
Check the equation for x=0,
[tex]LHS=\sqrt{0+1}+1=1+1=2\neq 0=RHS[/tex]
Since LHS is not equal to RHS, therefore 0 is an extraneous solution.
Check the equation for x=3,
[tex]LHS=\sqrt{3+1}+1=2+1=3=RHS[/tex]
Since LHS is equal to RHS, therefore 3 is an solution.
WILL GIVE BRAINEST
Does this graph show a function? explain how you know.
Answer:
B.No the graph fails the vertical line test.
Step-by-step explanation:
A function in math is a correspondence where to any given number there is a result and it has two variables that are dependent and independent, in this case, the vertical line test is a test done to determine if a graph is a function or not, in order to test if it is a function you just draw a vertical line, parallel to the Y-axis and if it touches more than one point in the X then it is not a function, in order for a graph to be a function there must only exist one value of Y for each X value.
Explain how to use two bar diagrams to find 45% of $60.
Answer:
is there another example i really need this..?
sorry if i took the points..
Solve: 3x-15 over 2=4x
A. 11
B. 6
C. -3
D. -15
Simplify the expression
1.4 - 5.5 - 1.73 + 1.8 - 1.09
Answers:
–5.12
–1.66
–8.72
5.12
I find it convenient to rearrange the numbers so that positive numbers are added, negative numbers are added, then the two sums are added. Of course, you can do it any way you like. Your calculator does not care about the order of the numbers you enter.
... = (1.4 +1.8) -(5.5 +1.73 +1.09)
... = 3.2 - 8.32
... = -5.12
A) -5.12
... = (1.4 +1.8) -(5.5 +1.73 +1.09)
... = 3.2 - 8.32
... = -5.12
- Prodixy ☕
Po is trying to solve the following equation by completing the square: 49x^2+56x-64 = 0.He successfully rewrites the above equation in the following form: (ax + b)^2 = c,where a, b, and c are integers and a > 0. What is the value of a + b + c?
Halp
To solve the equation 49x²+56x-64 = 0 by completing the square, we first convert it to the format (ax + b)² = c. It is found that a=1, b=4/7, and c=16/49. Hence, a+b+c = 381/147 or approximately 2.59183673469.
Explanation:The equation to solve is 49x²+56x-64 = 0. By completing the square, we can rewrite the equation in the form (ax + b)² = c. To get to this form, Po first divided the entire equation by 49, giving x²+8/7x-64/49= 0. Following this, he then took half of the coefficient of x (which is 4/7), squared it (which is 16/49), and added it to both sides of the equation. This transforms the left-hand side of the equation into a perfect square giving us (x+4/7)²=16/49. Hence, we find that a=1, b=4/7, and c=16/49. Therefore a+b+c = 381/147 or approximately 2.59183673469.
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Part a give the number of total electron groups, the number of bonding groups, and the number of lone pairs for the geometry depicted in (a). express your answers as integers separated by commas.
It can be deduced that there are 4 electron groups, 4 bonding groups, 0 lone pairs.
What is an eletron?An electron means a very small particle that has a negative charge of electricity and it travels around the nucleus of an atom.
In this case, there are 4 electron groups, 4 bonding groups, 0 lone pairs; there are 5 electron groups, 3 bonding groups, 2 lone pairs; there are 6 electron groups, 5 bonding groups, 1 lone pair.
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What is the GCF of 72 and 36?
list all values of x such that 2 ((sin (x))^2)+((sqrt (3))sin(x))=(2sin (x)+sqrt (3))