Answer:
Step-by-step explanation:
When you have four terms and 3rd degree equation (the highest power is 3) you will want to try to "factor by grouping"
Group together two terms, watch out for the negative signs!
x^3 + 2x^2-5x-10=0
(x^3 + 2x^2) - (5x+10)=0
Find a common factor in each group and factor it out. You're hoping that what is left in the parenthesis is the same in both cases.
x^2(x+2)-5(x+2)=0
Now you can factor out that (x+2) because it is both terms.
x^2(x + 2) - 5(x + 2)=0
~~~~ ~~~~
Pull these out.
What will be left is the x^2 and the - 5 (dont lose that - in front of the 5)
(x + 2)(x^2 - 5) = 0
If all you have to do is factor, then you're done. It is factored. But if you have to "solve" also, then put x+2=0 and x^2-5=0 and solve.
x = -2 and x = +- sqrt5
What is an equation of the line that passes through the points (2, -1) and (3,-4)
Answer:
Step-by-step explanation:
Given:
x1 = 2
x2 = 3
y1 = -1
y2 = -4
Solution:
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( -4 - -1 ) / ( 3 - 2 )
m = -3 / 1
m = -3
Then,
y - y1 = m ( x - x1 )
y - (-1) = -3 ( x - 2 )
y + 1 = -3x + 6
y = -3x + 6 - 1
y = -3x + 5
Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?
Answer:
[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle h(x) = [2 + f(\sin x)]''[/tex]
Step 2: Differentiate
Derivative Rule [Chain Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'[/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'[/tex]Derivative Rule [Chain Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'[/tex]Trigonometric Differentiation: [tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]From here, if you would like, you can take the 3rd derivative of the last piece.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
the state of California keeps track of how many millions of students are learning English as a second language each year: English Learners are shown in millions in the table.
find an equation for the median fit line
esterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?
Answer:6 six graders were late. 10% would be 12, and half of that is 6. You need to divide that in half because 5 is half of 10.
Answer:
6 sixth graders at school where late
Step-by-step explanation:
5% = 0.05
0.05(120) = 6
R, P, Q act on the base AB, BC, CA triangles ABC in alphabetical order, respectively. Show that P sec A + Q sec B + R sec C = 0, if the fluid of this power system passes through the center of the triangle.
Answer:
(i) In △ABD and △ACD,
AB=AC ....(since △ABC is isosceles)
AD=AD ....(common side)
BD=DC ....(since △BDC is isosceles)
ΔABD≅ΔACD .....SSS test of congruence,
∴∠BAD=∠CAD i.e. ∠BAP=∠PAC .....[c.a.c.t]......(i)
(ii) In △ABP and △ACP,
AB=AC ...(since △ABC is isosceles)
AP=AP ...(common side)
∠BAP=∠PAC ....from (i)
△ABP≅△ACP .... SAS test of congruence
∴BP=PC ...[c.s.c.t].....(ii)
∠APB=∠APC ....c.a.c.t.
(iii) Since △ABD≅△ACD
∠BAD=∠CAD ....from (i)
So, AD bisects ∠A
i.e. AP bisects∠A.....(iii)
In △BDP and △CDP,
DP=DP ...common side
BP=PC ...from (ii)
BD=CD ...(since △BDC is isosceles)
△BDP≅△CDP ....SSS test of congruence
∴∠BDP=∠CDP ....c.a.c.t.
∴ DP bisects∠D
So, AP bisects ∠D ....(iv)
From (iii) and (iv),
AP bisects ∠A as well as ∠D.
(iv) We know that
∠APB+∠APC=180
∘
....(angles in linear pair)
Also, ∠APB=∠APC ...from (ii)
∴∠APB=∠APC=
2
180
∘
=90
∘
BP=PC and ∠APB=∠APC=90
∘
Hence, AP is perpendicular bisector of
Step-by-step explanation:
HOPE ITS HELP YOU
How many times does 13 go in to 33
inverse of
f(x)=6x+5
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark ( 1 ) as the fraction bar if necessary.
10
(-4,8).
(-6,-4)
Answer here
Answer:
slope = 6
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (-6, - 4) and (x₂, y₂ ) = (- 4, 8) ← 2 points on the line
m = [tex]\frac{8-(-4)}{-4-(-6)}[/tex] = [tex]\frac{8+4}{-4+6}[/tex] = [tex]\frac{12}{2}[/tex] = 6
The slope of the line given in the task content is; m = 6.
What is the slope of the line?The slope of the line is the rate of change of the dependent variable with respect to the independent variable.
On this note, the slope of the equation is;
Slope, m = (-4-8)/(-6-(-4))
m = -12/-2
m = 6.
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If ALMN = AXYZ, which congruences are true by CPCTC? Check all that
apply.
Answer:
A C E
Step-by-step explanation:
these triangles can be mapped onto eachother. its basically asking which parts of the triangle would line up with eachother.
The required congruences that are true by CPCTC are LN ≅ XZ, ∠M ≅ ∠Y, and ML ≅ XY. Options A, C, and E are correct.
What is CPCTC?CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a theorem in geometry that states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent.
More formally, if two triangles are congruent, then the three pairs of corresponding sides are congruent, and the three pairs of corresponding angles are congruent.
Here,
Since the triangle LMN ≅ triangle XYZ,
By CPCTC, we can say that,
∠L ≅ ∠X
∠N≅ ∠Z
∠M ≅ ∠Y
ML ≅ XY
MN ≅ YZ
LN ≅ XZ
Thus, the required congruences that are true by CPCTC are LN ≅ XZ, ∠M ≅ ∠Y, and ML ≅ XY. Options A, C, and E are correct.
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If the distance between A(0, 4) and B(3,a) is 5 units then find the value of a.
Answer:
Step-by-step explanation:
a = 0
So that AOB makes a right triangle with sides 3-4-5
Answer:
a = 8
Step-by-step explanation:
Calculate AB using the distance formula and equate to 5
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (0, 4 ) and (x₂, y₂ ) = B (3, a )
d = [tex]\sqrt{(3-0)^2+(a-4)^2}[/tex]
= [tex]\sqrt{3^2+(a-4)^2}[/tex]
= [tex]\sqrt{9+(a-4)^2}[/tex] , then
[tex]\sqrt{9+(a-4)^2}[/tex] = 5 ( square both sides )
9 + (a - 4)² = 5² = 25 ( subtract 9 from both sides )
(a - 4)² = 16 ( take square root of both sides )
a - 4 = 4 ( add 4 to both sides )
a = 8
HELP THIS IS URGENT!!!!!!!!!!!!!1Fill in the blank so that the equation has the solution x=3
3x+ =5
Answer:
y = 3x + 5
Step-by-step explanation:
Since this is a linear function, its graph is a straight line stretching from - infinity to infinity on both x and y axes, hence domain and range is all real numbers from - infinity to infinity.
Help Plssss it is due tommorrow!!!!!
Answer:
none of the other answera are correct
Marla was given the point (1,3), (2, 1), and (-2, -15). She was asked to find a quadratic function that fit these 3 given
points. Marla created a system of three equations with three variables to solve the problem and then used the
matrix functions on her graphing calculator to find the equation. Which equation can be written given these 3
points?
The linear equations [tex]c_{2}+c_{1}+c_{o} = 3[/tex], [tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] and [tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] can be written given the points [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex].
A quadratic function ([tex]p(x)[/tex]) is a second order polynomial of the form:
[tex]p(x) = \Sigma\limits_{i= 0}^{2} c_{i}\cdot x^{i} = c_{2}\cdot x^{2}+c_{1}\cdot x + c_{o}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable[tex]i[/tex] - Monomial index[tex]c_{i}[/tex] - i-th coefficientTo determine the value of all coefficients, we need three distinct points on plane and create a resulting system of linear equations.
If we know that [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex], then the system of linear equations is:
[tex]c_{2}+c_{1}+c_{o} = 3[/tex] (2)
[tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] (3)
[tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] (4)
The linear equations [tex]c_{2}+c_{1}+c_{o} = 3[/tex], [tex]4\cdot c_{2} + 2\cdot c_{1}+ c_{o} = 1[/tex] and [tex]4\cdot c_{2} - 2\cdot c_{1} + c_{o} = -15[/tex] can be written given the points [tex](x_{1}, y_{1}) = (1, 3)[/tex], [tex](x_{2}, y_{2}) = (2, 1)[/tex] and [tex](x_{3}, y_{3}) = (-2, -15)[/tex].
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They are similar or not similar and why?
Answer:
Yes its similar because if you look at all the numbers they are all the same but the shape is just turned around
please consider brainliest <3
Answer:
Step-by-step explanation:
Yes its similar because if you look at all the numbers they are all the same but the shape is just turned around
love ELVIS
what is n? solve for n+5=2n-6
Answer:
n = 11
Step-by-step explanation:
n+5=2n-6
you add 6 on both sides and you get
n+11=2n
you then subtract n on both sides and get
11=n
Step-by-step explanation:
n+5 = 2n - 6 -> Original equation
5 = n - 6 -> Take n away from both sides
11 = n -> Add 6 to both sides
n = 11 -> Final answer
*Remember, we are trying to get n by using inverse operations.
In isosceles triangle the length of a leg is 17 cm, and the base is 16 cm. Find the length of the altitude to the base.
Answer:
altitude = 15 cm
Step-by-step explanation:
you can use the Pythagorean Theorem where you have a right triangle with a base of 8 (half of 16), a hypotenue of 17, and the altitude is 'a'
a² + 8² = 17²
a² + 64 = 289
a² = 225
a = [tex]\sqrt{225}[/tex]
a = 15
WILL GIVE BRAINLEST
Robert is ordering jerseys for the baseball team
A local company charges $5,25 for each jersey and $45 to create the design
An online company charges $7.75 for each jersey and $20 to create the design
For which number of jerseys is the cost the same at both companies?
A)26 jerseys
B)1 jersey
С)5 jerseys
D)10 jerseys
Answer: D) 10 jerseys
Step-by-step explanation:
Let j represent the number of jerseys and C for total cost
Local company eqn: C = 5.25j + 45
Online company eqn: C = 7.75j + 20
Set both sides equal to solve:
5.25j + 45 = 7.75j + 20
5.25j - 7.75j = 20 -45
- 2.5j = -25
[tex]\frac{-2.5j}{-2.5}=\frac{-25}{-2.5}[/tex]
j = 10
Therefore, the cost is the same for both companies when 10 jerseys are sold
PLEASE HELP TEST DUE SOON⚠️
What is the equation for the line in slope intercept form
Answer:
The answer should be [tex]y=mx+b[/tex]
Step-by-step explanation:
[tex]y=mx+b[/tex] is the only thing I can think of when your talking about the equation of the line in intercept form, but I'm 85% sure this is correct.
Hope this helps!
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Have a great day/night/afternoon!
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Each box of candy canes has 12 candy canes. How much does each candy cane cost?
Based on the information given, the cost of each candy cane will be $3.00.
This is an incomplete information as you didn't provide the cost of the box. Let's assume that the cost of the box is $36.
From the information given, we are told that each box of candy canes has 12 candy canes. Therefore, the cost of each candy cane will be:
= $36 / 12
= $3.
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38. In a certain school, 45% of the students are boys. 80% of the boys have brown hair while 50% of those with brown hair
are girls. What is the probability that a randomly selected girl does NOT have brown hair?
A) .19
B) .36
C) 55
D) .35
E) none of the above are correct
The probability that a randomly selected girl does not have brown hair is 34.54%.
Given that in a certain school, 45% of the students are boys, and 80% of the boys have brown hair while 50% of those with brown hair are girls, to determine what is the probability that a randomly selected girl does NOT have brown hair, the following calculation must be performed:
45 x 0.80 = 36% of the school are brown hair boys 36% of the school are brown hair girls 55 - 36 = 55 = 100 19 = X 19 x 100/55 = X 1900/55 = X 34.54 = X
Therefore, the probability that a randomly selected girl does not have brown hair is 34.54%.
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Which of these actions would decrease heat transfer between two objects?
increasing the temperature of the warmer object
increasing the area of their contact
reducing the thermal energy of the cooler object
reducing the time of their contact
(Fr ran out of free answers)
Answer:
increasing the area of their contact
do the values in this table represent a proportional relationship? x 2/4 6 8 y 1 2 3 4 yes, and the constant of proportionality is 12. yes, and the constant of proportionality is 2. no. i don't know.
Answer: No
Step-by-step explanation:
Which inequality is graphed below
What's the Answer ~
[tex] \sf \tiny{14 + 14 \div 7}[/tex]
Step-by-step explanation:
remember the priorities of the different mathematical operations
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
so,
14 + 14/7 = 14 + 2 = 16
Hey there!
14 + 14 ÷ 7
14 ÷ 7 = 2
= 14 + 2
= 16
Therefore, your answer is: 16
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Please Help Question In Picture
Answer:
A
Step-by-step explanation:
Since Angle XYZ is equal to Angle YZX,
XY=XZ
The two triangles are congruent.So,
VW=YZ
XY=UV
XZ=UW
Thus;
XY=UV
XZ=UW
XZ=XY=UV=UW
So the permieter is 5.7 + 5.7 + 3.7 = 15.1 cm
If 2 of the triangle sides are 8 m and one side is 6 m what kind of triangle is it
Answer:
An isosceles triangle has two side lengths the same and one different.
Step-by-step explanation:
find the output (y) of the function y= - 4/15 x +24 if the input (x) is 120
[tex]\text{Given that,}\\\\y = -\dfrac 4{15} x + 24\\\\\text{When x = 120,}\\\\y = -\dfrac 4{15} (120) + 24\\\\\implies y = - \dfrac{480}{15} +24\\\\\implies y=-32+24 \\\\\implies y = -8[/tex]
Find the measure of the missing angles. 99° e f d
Answer:
e = 99 , d = 90 , f = 81
Step-by-step explanation:
Answer:
81º
Step-by-step explanation:
Notice that angle f and 99º form a straight line. A straight line is 180º, so angle f = 180º - 99º = 81º.
How can I solve for t?
Answer:
This is not possible with 2 equal symbols
Broccoli costs $1.50 per pound at a store. How much money does 32 onces of broccoli cost
Answer:
$3.00
Step-by-step explanation:
1 pound = 16 ounces
2 pounds = 32 ounces
1.5 x 2 = 3