Answers
The solution to the given quadratic expression is x = -1 and x = 5
Factoring quadratic equationGiven the quadratic equation below
f(x) = x^2 - 4x - 5
Factorize
f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5
Hence the solution to the given quadratic expression is x = -1 and x = 5
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Answer:
x = -1; x = 5
Step-by-step explanation:
Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0
Given function: f(x) = x² - 4x - 5
⇒ a = 1, b = -4, c = -5
We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).
Factors that give a product of a • c: 1 • -5 = -5
Factors that give a sum of b: 1 + (-5) = -4
Step 1: Substitute f(x) = 0.
⇒ 0 = x² - 4x - 5
Step 2: Rewrite the equation with the factors.
⇒ 0 = x² + x - 5x - 5
Step 3: Factor out x and -5.
⇒ 0 = (x² + x) + (-5x - 5)
⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]
⇒ 0 = (x - 5)(x + 1)
Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)
a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x
b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x
Therefore, the missing solution for this quadratic function is x = 5.
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Related Questions
PLEASE HELP ( look at ss to answer )
Answers
The direct proportion is shown by table (B)
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.
Here the second table shows the direct proportion relation.
This is because the ratio of x/y remain same.
4/2= 7/3.5= 10/5= 11/5.5= 15/7.5 = 2/1
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5
6
7 8
10
TIME REMAINING
27:07
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value
of the car after x years, which function represents the car's value?
f(x)=20.000(085)*
Answers
Answer:
Step-by-step explanation:
Is there answer choices?
If a(x) = 3x 1 and b (x) = startroot x minus 4 endroot, what is the domain of (b circle a) (x)?
Answers
The composite function (boa)(x) is equivalent to √3x-3
Composite functionGiven the following functions
a(x) = 3x +1
b(x) = √x - 4
To determine the composite function (boa)(x)
b(a(x) = b(3x +1)
Substitute 3x + 1 into b(x) to have:
(boa)(x)= √(3x + 1) - 4
(boa)(x) = √3x-3
Hence the composite function (boa)(x) is equivalent to √3x-3
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Someone please help with this!!
Answers
Answer:
A
Step-by-step explanation:
Comment (and answer)
Both start with the plus x axis as one of the arms. The other arm of 110o goes anti clockwise until it is 30 degrees into the second quadrant.
The answer can be found by using 110 - 360 = negative angle.
So 110 - 360 = - 250 which goes clockwise from the plus x axis. The answer must be A.
Make sure you understand the concept of clockwise and anti clockwise. If you don't know, ask your teacher, write it down, and try not to forget it. The distinction comes up a lot.
if cos^4+cos^2=1 prove that cot^4a-cot^2a=1
Answers
Step-by-step explanation:
We can solve this kind of trigonometric problem
easily by the followings method :
Given :
cos^4a + cos^2a = 1
or, cos4^a = 1 - cos^2a
Therefore; cos^4a = sin^2a
Again,
To prove: cot^4a - cot^2a = 1
L.H.S = Cot^4a - cot^2a
= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a
= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a
= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a
= 1 - cos^2a ÷ Sin^2a
= Sin^2a ÷ Sin^2a
= 1 = R.H.S proved.
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5-4-3-2
16
6/ +
77?1?
x
Which is the general form of the equation of the circle
shown?
Ox²+²+4x-2y-4 = 0
Ox+y+4x-2y + 2 = 0
Ox² + y² 4x +2y-4 = 0
Ox² + y² 4x + 2y + 2 = 0
Answers
Answer:
1st option
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 2, 1 ) and r = 3 , then
(x - (- 2) )² + (y - 1)² = 3² , that is
(x + 2)² + (y - 1)² = 9 ← expand factors using FOIL
x² + 4x + 4 + y² - 2y + 1 = 9
x² + 4x + y² - 2y + 5 = 9 ( subtract 9 from both sides )
x² + 4x + y² - 2y - 4 = 0 , that is
x² + y² + 4x - 2y - 4 = 0 ← in general form
Answer:
[tex]\textsf{1)} \quad x^2+y^2+4x-2y-4=0[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusFrom inspection of the graph:
center of the circle = (-2, 1)radius of the circle = 3Substitute the found values into the formula:
[tex]\implies (x-(-2)^2+(y-1)^2=3^2[/tex]
[tex]\implies (x+2)^2+(y-1)^2=9[/tex]
Expand and simplify:
[tex]\implies (x+2)^2+(y-1)^2=9[/tex]
[tex]\implies x^2+4x+4+y^2-2y+1=9[/tex]
[tex]\implies x^2+y^2+4x-2y+5=9[/tex]
[tex]\implies x^2+y^2+4x-2y-4=0[/tex]
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1.1 divided by 1.54 simplified
Answers
Answer:
1•4
Step-by-step explanation:
1•54÷1•1
1•54
1•1
divide by 10 both side with can move decimal
15•4
11
=my answer is 1•4.
Answer:
The correct answer for algebraic expression 1.54÷1.1 is = 1.4.
Step-by-step explanation:
this is question based on simple algebra -
Simple Algebraic equations - An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.
these equations are two algebraic expressions that are joined together using an equal to ( = ) sign. An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials
so in the question algebraic operation used to solve is simple division.
therefore here in question we have to divide 1.54 with 1.1,
using the concept written above,
let the value of division be 'x'
we can write 1.54/1.1 = x
by dividing and multiplying the equation by 100 to remove the decimals.
(1•54/ 1•1)×100/100 = x
154/110 = x
now by simple division,
1.4 = x answer
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Ryan fills a bath with
22.6 litres of hot water
and 18.7 litres of cold.
He spills 2.5 litres
getting in.
How much water is in
the bath now?
Answers
Answer:
38.8 litres
Step-by-step explanation:
22.6 + 18.7 = 41.3
41.3 - 2.5 = 38.8
38.8 litres
Answer:
38.8 liters.
Step-by-step explanation:
Word problems with addition and subtraction:
To find the quantity of water inside the bath tub, add the quantity of hot water and cold water. Then from this subtract the water that is spilled.
Quantity of water in the bathtub = 22.6 + 18.7 - 2.5
= 41.3 - 2.5
= 38.8 liters
I’m still not sure how the answer would be D (CBA), couldn’t it also be ACB?
Answers
Answer: No it could not be ACB.
Step-by-step explanation:
Angles are named based on the vertex of the angle so this could be referred to as ∠B. The other way to name an angle is by saying the three points, However, when you say the three points the vertex must be in the middle. Hence, the answer is ∠CBA as the middle point of the angle is in the middle of the name.
Find the gradient of the line shown.
Answers
Answer:it is o to 10/5 which is 1/
Step-by-step explanation:
Help asap
What is the end behavior of the following graph
Answers
Using limits, it is found that the end behavior of the graph is given as follows:
It rises to the left, and stays constant at y = -4 to the right.
What is the end behavior of a function f(x)?It is given by the limits of f(x) as x goes to infinity.
In this problem, the function is given by:
[tex]f(x) = 4\left(\frac{2}{5}\right)^{x + 3} - 4[/tex]
Hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 4\left(\frac{2}{5}\right)^{x + 3} - 4 = 4\left(\frac{5}{2}\right)^{\infty + 3} - 4 = \infty - 4 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow -\infty} 4\left(\frac{2}{5}\right)^{x + 3} - 4 = 4\left(\frac{2}{5}\right)^{\infty + 3} - 4 = 0 - 4 = -4[/tex]
Hence:
It rises to the left, and stays constant at y = -4 to the right.
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The area of a rectangular carpet is 252 square feet. The length is nine feet more than the width. Find the length and the width of the carpet.
Answers
Answer:
Length = 30 feet Width = 21 feetGiven - Length is nine feet more
Area is 252
To find - Value of length and width
Solution-
let the width of the carpet be X
therefore length = 9 + X
Area of carpet = Length * width
252 = (9+x) * X
252 = 9x + x²
Solving the equation by splitting middle term
x² + 9x - 252 = 0
x²- 21x + 12x - 252= 0
x ( x - 21) + 12( x - 21) = 0
(x -21)( x + 12) = 0
X = 21 or X = (-12)
Length = 9 + X
= 30 or (-3)
negative is not possible so
length = 30
width = 21
Given the function f(x) below, evaluate 3f(-2) + f(1).
if z ≤-3
3z²-2z if -3
-2√2-1
if x > 0
7x-2
f(x) = 3x² - 2x
pls help
Answers
Answer: 45
Step-by-step explanation: I used a graphing calculator and input all the equations and all the restraints, and I found that you can’t use the first equation since x has to be less than or equal to -3, and the question calls for x to be -2. So, in the second equation, there’s a point (-2, 16) and in the third equation there’s a point (1, -3). You know you have to use these two points since in the second equation, the restraint only lets you use numbers greater than -3 or less than 0, which cannot be one, and in the third equation, the restraint only lets you use numbers greater than 0, which can’t be -2. I hope that made some sense. So then, with substitution the equation would be 3(16)+(-3) which equals 45. 3(16)=48. 48-3+=45
what is the area of the triangle formed from (0,1), (0,4), and (4,1)?
Answers
Answer:
6 square units
Step-by-step explanation:
base = 4 units
height = 3 units
[tex]\sf \boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*base*height}[/tex]
[tex]\sf =\dfrac{1}{2}*4*3\\\\ = 2*3\\\\ = 6 \ square units[/tex]
[tex]\Large❏ \: \large\begin{gathered} {\underline{\boxed{ \rm {\blue{Area \: of \: triangle \: = \: \frac{1}{2} \: \times \: Base \: × \: Height }}}}}\end{gathered}[/tex]
[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: \frac{1}{2} \: \times \: Base \: × \: Height [/tex]
[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: \frac{1}{2} \: \times \: 4 \: × \: 3 [/tex]
[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: \frac{1}{ \cancel2} \: \times \: \cancel{4} \: ^{\green2} \: × \: 3 [/tex]
[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: 2 \: \times \: 3[/tex]
[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: 6[/tex]
Hence , the area of triangle is 6 units.
Which of the following sets of data will have the smallest Standard Deviation?
1, 6, 2, 100, 4, 0, 0, 0, 0, 1
3, 33, 103, 4, 122, 1, 0, 245, 7, 99
1, 2, 3, 4, 5, 6, 7, 8, 8, 9
79, 79, 79, 79, 79, 79, 79, 79, 79, 79
Answers
Answer:
Step-by-step explanation:
The last one: 79, 79, 79, 79, 79, 79, 79, 79, 79, 79 because there isn't any difference in the numbers.
S.D.: 0
For 1-3, consider an investment of $6000
that earns 4.5% interest. Use a graphing
calculator if needed.
1. Write an equation to describe the value
V(t) of the investment at time t if the
interest is compounded daily.
Answers
Answer:
See below
Step-by-step explanation:
Period = 1 day
Periodic interest = .045 / 365 (since there are 365 days in a year)
V(t) = 6000 * ( 1 + .045/365)^t where t is in days
V(t) = 6000 * (1+.045/365)^(t * 365) where t is in years
Carol measured a straw and wrote down how long it was in inches. pete multiplied carol's straw length by and cut a straw to be that many inches long. joe multiplied carol's straw length by and cut a straw to be that many inches long. which straw belongs to whom?
Answers
Answer:
pete
Step-by-step explanation:
i think its pete???
On a map of scale 1:20000 the area of a forest is 50cm^2.On another map the area of the forest is 8cm^2.Find the scale of the second map.
Answers
Answer:
The answer is 1: 50000... If you look down here↓:
Step-by-step explanation:
With a scale of 1:20000, a unit length on the map represents a length of 20000. So 1 cm^2 = 1 cm* 1 cm which represents 20000*20000 cm^2 will be = 4*10^8 cm^2.
50 cm^2 represents that 4*50*10^8 cm^2 = 200* 10^8 cm^2.
Now, on the other hand, the map has the same. 200* 10^8 is represented by 8 cm^2. So the scale is sqrt [ 200* 10^8 / 8 ] = sqrt [ 25* 10^8 ] = 5* 10^4 = 50000.
Therefore the scale on the second map is 1: 50000.
a list of 8 numbers has a mean of 6. work out the total of the numbers.
Answers
Answer:
48
Step-by-step explanation:
The mean of a number is the sum of all the numbers divided by how many numbers there are. We can set up this formula: [tex]mean = \frac{sum}{amountnumbers}[/tex].
When we plug our values into this equation, we get: [tex]6 = \frac{sum}{8}[/tex]. Solving this equation gets us sum = 6 * 8 = 48
40 points, please help lol
Answers
The simplified expression of [tex]x^{-2/3} . x^{6/7}[/tex] is [tex]x^{4/21}[/tex]
How to simplify an expression?The expression [tex]x^{-2/3} . x^{6/7}[/tex] can be simplified as follows:
using law of indices,
xⁿ . xᵇ = xⁿ⁺ᵇ
Therefore,
[tex]x^{-2/3} . x^{6/7}[/tex] = [tex]x^{-2/3 + 6/7}[/tex]
[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21}[/tex]
[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21} = x^{4/21}[/tex]
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if 13 sin θ=12 cos θ, find the value
Answers
From the given information, we have
[tex]13\sin(\theta) = 12\cos(\theta) \implies \dfrac{\sin(\theta)}{\cos(\theta)} = \dfrac{12}{13}[/tex]
In the expression of interest, divide through everything by [tex]\cos^2(\theta)[/tex] to get
[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\frac{\sin(\theta)}{\cos(\theta)}}{1 - \frac{\sin^2(\theta)}{\cos^2(\theta)}}[/tex]
Then plugging in the given info, we get
[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\times \frac{12}{13}}{1 - \left(\frac{12}{13}\right)^2} = \boxed{\dfrac{312}{25}}[/tex]
The x-coordinate of the point (50, 55) is ___________.
Answers
In an Ordered Pair, the first value is the x-coordinate or the abscissa and the second value is the y-coordinate or the ordinate. In the pair (50, 55), 50 is the abscissa and 55 is the ordinate.
The x-coordinate of the point (50, 55) is 50
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The distance of point (50, 55) perpendicular to y-axis
Thus, perpendicular distance = 50 units
The x-coordinate of the point (50, 55) is 50
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What is the completely factored form of this polynomial? 2x5 + 12x3 − 54x
Answers
Answer:
2x(x^2 - 3)(x^2 + 9)
Step-by-step explanation:
2x^5 + 12x^3 − 54x
2x(x^4 + 6x - 27)
Since -3 + 9 = 6 and -3 x 9 = -27:
2x(x^2 - 3)(x^2 + 9)
Answer:
[tex]2x(x^2-3)(x^2+9)[/tex]
Step-by-step explanation:
Given polynomial:
[tex]2x^5+12x^3-54x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies 2x(x^4+6x^2-27)[/tex]
To factor the trinomial [tex]x^4+6x^2-27[/tex]:
[tex]\textsf{Let }u=x^2 \implies u^2+6u-27[/tex]
Factor the quadratic by finding two numbers that multiply to -27 and sum to 6: 9 and -3
Rewrite the middle term as the sum of these two numbers:
[tex]\implies u^2+9u-3u-27[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+9)-3(u+9)[/tex]
Factor out the common term (u + 9):
[tex]\implies (u-3)(u+9)[/tex]
Substitute back [tex]u=x^2[/tex]:
[tex]\implies (x^2-3)(x^2+9)[/tex]
Therefore, the factored form of the given polynomial is:
[tex]\implies 2x(x^2-3)(x^2+9)[/tex]
it takes 3 machines 2 days to make a batch of products. How long does one machine take?
Answers
Answer:
it takes 6 days for 1 machine...
C
An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the
functions over the interval 0≤x≤1?
-1
-1
2
O The exponential grows at half the rate of the quadratic.
O The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic
Answers
The correct answer is option b which is the exponential grows at the same rate as the quadratic.
The complete question is given below with the graph attached:-
An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval
a. The exponential grows at half the rate of the quadratic.
b.The exponential grows at the same rate as the quadratic.
c.The exponential grows at twice the rate of the quadratic.
d.The exponential grows at four times the rate of the quadratic.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval
a ≤ x ≤ b
is given by
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval
0 ≤ x ≤ 1
is given by
[tex]\dfrac{f(1)-f(0)}{1-0}= \dfrac{2-1}{1}=1[/tex]
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval
0 ≤ x ≤ 1
is given by
[tex]\dfrac{g(1)-g(0)}{1-0}=\dfrac{1-0}{1}=1[/tex]
Therefore, the exponential grows at the same rate as the quadratic in the interval .
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In studies that use more than one data collector, how is the consistency of the data evaluated?.
Answers
In order to evaluate consistency in studies with more than one data collector, the Inter-rater reliability is used.
What is the Inter-rater reliability?This is a measure in research that is used to test the data presented by different data collectors, for consistency.
It essentially checks the extent to which the data collected from the different sources agree with each other.
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Dude this should be so easy but this is going in one ear and out the other how do I do this send help
Answers
Answer:
0.5 hours
Explanation:
Given:
speed: 17 miles/hourdistance: 8 milesFormula:
time taken = distance ÷ speedSolve:
time taken = 8 ÷ 17 = 0.4706 ≈ 0.5 hours (rounded to nearest tenth)A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?
Answers
Using the cosine ratio, the expression that can be used to determine the side length of the given rhombus is: x = 10/cos 30.
What is the Cosine Ratio?The cosine ratio that can be used to solve a right triangle is, cos ∅ = adj/hyp.
x represents the side of the rhombus as shown in the image attached.
Hypotenuse = x Adjacent = 10 in.∅ = 30cos 30 = 10/x
x(cos 30) = 10
x = 10/cos 30
Thus, the equation that would be used to determine the side length is: x = 10/cos 30
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Answer:
A
Step-by-step explanation:
10/cos 30°
Complete the table by converting from a fraction, a decimal, or a percent.
Answers
The value obtained by doing the operation are ,a=0.11,b=11,c=(111/250)d=44,e=(1/8),f=(83/500),h=0.375,i=37.5%,j=(111/125),k=0.888,i=(777/1000),m=77%,n=0.2,o=20%,p=(777/1000),q=66.6%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The procedure of changing the basis of a number is known as number conversion. A binary number is made up of only two numbers: 1 and 0. A decimal number is made up of ten digits ranging from 0 to 9.
The values obtained from the table the decimal and the percentage form are solved as;
[tex]\frac{1}{9} \\\\ 0.3111 \\\\\ 0.1111 \times 100 \\\\ 11.11 \%[/tex]
The other missing values are;
a=0.11
b=11
c=(111/250)
d=44
e=(1/8)
f=(83/500)
h=0.375
i=37.5%
j=(111/125)
k=0.888
i=(777/1000)
m=77%
n=0.2
o=20%
p=(777/1000)
q=66.6%
Hence all the missing values are given above.
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Need help (pic included)
Answers
Answer:
(-4,-2)
x=-4
y=-2
Step-by-step explanation:
-3x-4y=20
3(x-10y=16)=3x-30y=48
The reason I multiplied 3 to the second equation is for when we add the equations together the x will cancel out.
-3x-4y=20
+ 3x-30y=48
-34y=68
Divide -34 from both sides.
y=-2
To find x you need to plug in -2 for y into one of the equations.
x-10y=16
x-10(-2)=16
Remember a negative times a negative equals a positive.
x+20=16
Subtract 20 from both sides.
x=-4
Hope this helps!
If not, I am sorry.
