Answer:
Option C (d = 14n + 50).
Step-by-step explanation:
The observations for Year 1, 2, 3, and 4 are 64, 78, 92, and 106 respectively. It can be observed that the difference between second term and the first term is 78 - 64 = 14. This is also true for the third term and the second term. In fact, the difference between the terms is fixed. This means that the sequence is an arithmetic sequence, in which the difference between the terms is fixes for all the terms. The nth term in this case is defined as:
S = a + (n-1)*d; where S is the output at a given n, a is the first term, n is the position, and d is the common difference. In this question, S = ducks (d), a = 64, and d = 14. Therefore, plugging in the values in the above formula gives:
d = 64 + (n-1)*14.
d = 64 + 14n - 14.
d = 14n + 50.
Therefore, the model which best describes the amount of ducks that will be in the pond during the nth year is d = 14n + 50, i.e. Option C!!!
Answer: Third Option
[tex]a_n =14n+50[/tex]
Step-by-step explanation:
By subtracting consecutive terms from the number of ducks each year you will get a common difference of 144.
[tex]78-64 = 14\\92-78 = 14\\106-92 = 14[/tex]
This means that the data can be modeled by the equation of an arithmetic sequence
The arithmetic sequences have the following form:
[tex]a_n = a_1 + d(n-1)[/tex]
Where [tex]a_1[/tex] is the first term and d is the common difference between the consecutive terms.
So :
[tex]a_1 = 64[/tex]
[tex]d = 14[/tex]
Then the equation is:
[tex]a_n = 64 + 14(n-1)[/tex]
[tex]a_n = 64 + 14n-14[/tex]
[tex]a_n =14n+50[/tex]
how many terms are in the equation 4x+2x(3x-5)
Answer:
4
Step-by-step explanation:
a term is simply separated by either a + or a - which means the terms here is 4x,2x,3x and 5
Answer:
4
Step-by-step explanation:
There are 4 terms in the equation 4x+2x(3x-5).
4x,2x,3x and 5
The difference of x and a number is 6. What is the other number?
6
6 - (x-6)
0 6+*
Answer:
The number is x-6
Step-by-step explanation:
difference of x and a number is 6
Difference means subtract, is means equals
x-n = 6
Add n to each side
x-n+n = 6+n
x = n+6
Subtract 6 from each side
x-6 = n+6-6
x-6 =n
The number is x-6
Solve the following trigonometric equation for 0to2pi
(a) cos(4x) - 9 sin(2x) + 4 = 0
Answer:
x = pi/12, 5pi/12, 13pi/12, 17pi/12.
Step-by-step explanation:
Note that cos (4x) = 1 - 2sin^2 (2x)
Substituting we have:
1 - 2sin^2 (2x) - 9 sin(2x) + 4 = 0
2 sin^2 (2x) + 9 sin(2x) - 5 = 0
(2 sin 2x - 1 )(sin 2x + 5 ) = 0
sin 2x = 1/2 and sin 2x = -5.
sin 2x = 1/2, gives 2x = pi/6, 5pi/6, 13pi/6, 17pi/6.
There are no solutions to sin 2x = -5 because the range of sin x is -1 to +1.
So x = pi/12, 5pi/12, 13pi/12, 17pi/12.
To solve the trigonometric equation cos(4x) - 9 sin(2x) + 4 = 0, we can use trigonometric identities and algebraic manipulation. The steps to solve the equation are writing it as a quadratic equation, substituting with sin(x), solving the quadratic equation, and substituting back to solve for x.
Explanation:To solve the trigonometric equation cos(4x) - 9 sin(2x) + 4 = 0 for 0 to 2pi, we can use trigonometric identities and algebraic manipulation. Here are the steps to solve the equation:
Write the equation as a quadratic equation in terms of sin(x) and cos(x).Use the substitution u = sin(x) to rewrite the equation in terms of u.Solve the quadratic equation for u.Substitute back the value of u to solve for x.The solutions to the equation will be the values of x that make the equation true.
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y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necessary.
Answer:
3.7
Step-by-step explanation:
Inversely means we are taking the constant and dividing it.
So y varies inversely with x means "y=k/x".
k is a constant. We can find the constant if they give us a point on this curve.
The constant is a number that doesn't change no matter your input and output.
[tex]y=\frac{k}{x}[/tex]
So they actually give us k=8.88 and y=2.4 so let's input this:
[tex]2.4=\frac{8.88}{x}[/tex]
We need to solve this equation for x. You can do your favorite thing in cross-multiply. But how, Freckles? Well just slap a 1 underneath that 2.4. You can do that because 2.4/1 is still 2.4.
[tex]\frac{2.4}{1}=\frac{8.88}{x}[/tex]
Cross-multiply:
[tex]2.4x=8.88(1)[/tex]
[tex]2.4x=8.88[/tex]
Divide both sides by 2.4:
[tex]x=\frac{8.88}{2.4}[/tex]
[tex]x=3.7[/tex] when [tex]y=2.4[/tex].
grap f(x)=x^2+1/3(x-8)
Answer:
here is
Step-by-step explanation:
The map of a walking trail is drawn on a coordinate grid with three points of interest the trail starts at R(-2,4) and goes to S(3,4) and continues to T(3,-1) The total length of the walking trail is what units
Answer:
10 units
Step-by-step explanation:
Points R and S both have y-coordinate 4, so they are on the same horizontal line. The distance between them is the absolute value of the difference of the x-coordinates.
RS = |-2 - 3| = |-5| = 5
Points S and T both have x-coordinate 3, so they are on the same vertical line. The distance between them is the absolute value of the difference of the y-coordinates.
ST = |-1 - 4| = |-5| = 5
The total length of the trail is the sum of the two distances.
total length = 5 + 5 = 10
Answer:
Step-by-step explanation:
Using the formula for distance, D given 2 coordinates (see attached)
Given
R(-2,4) S(3,4) T(3,-1)
Distance RS = √ { [ (-2) -3]² + [4-4]² } = √25 =5 units
Distance ST = √ { [ (3 -3]² + [4-(-1)]² } = √25 = 5 units
Total distance = RS + ST = 5 + 5 = 10 units
If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25
Answer:
see explanation
Step-by-step explanation:
Using the identity
(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then
5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is
125 = a³ + b³ + c³ + 150 - 3abc, hence
a³ + b³ + c³ - 3abc = 125 - 150 = - 25
Using the cubic identity equation and the values given in the question, we can prove that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc equals -25.
Explanation:The equation required to prove is derived from the expansion of the cubic identity (a+b+c)³. The equation is a³+b³+c³-3abc = (a+b+c)[(a+b+c)²-3(ab+bc+ac)]. Let's use the values given in the question which are (a+b+c) = 5 and ab+bc+ac = 10.
Plug these values into the equation above. So, the proof becomes 5[5²-3*10].Work out the arithmetic for this equation. We find that 5[25-30] equals 5[-5], which results in -25.Therefore, we have proved that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc indeed equals -25.
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Which operations involving complex numbers have solutions represented by point A on the graph? PLEASE HELP
Answer:
Option 3 and 4
Step-by-step explanation:
We have to find the solutions represented by point A on graph
The point A is represented by (-6,7i)
Lets check all options one by one
1.
[tex]2(1-2i)-(4+3i)\\= (2-4i)-(4+3i)\\=2-4i-4-3i\\=2-4-4i-3i\\=-2-7i[/tex]
This option is not correct
2.
[tex]2(1+2i)+(-4-3i)\\=(2+4i)-4-3i\\=2+4i-4-3i\\=2-4+4i-3i\\=-2+i[/tex]
This option is also not correct
3.
[tex]2(-1+2i)-(4-3i)\\=(-2+4i)-4+3i\\=-2+4i-4+3i\\=-2-4+4i+3i\\=-6+7i[/tex]
This solution is same as point A so this option is correct
4.
[tex](-2+4i)+(-4+3i)\\=-2+4i-4+3i\\=-2-4+4i+3i\\=-6+7i[/tex]
Solution same as point A so this is correct option.
5.
[tex](-2-4i)+(4-3i)\\=-2-4i+4-3i\\=-2+4-4i-3i\\=2-7i[/tex]
Not correct
The correct options are option no 3 and 4 ..
In the complex plane, complex numbers are represented as points with the real part as the x-coordinate and the imaginary part as the y-coordinate. Therefore, various complex number operations like addition, subtraction, multiplication, or division could result in point A, depending on the specific numbers and operations involved.
Explanation:To understand which operations involving complex numbers would have solutions represented by point A on a graph, we need to firstly understand that in the complex plane, complex numbers are represented as points. The x-axis corresponds to the real part of the number and the y-axis corresponds to the imaginary part. For example, complex number a + bi would correspond to a point at coordinates (a, b) on the graph.
Various operations involving complex numbers could potentially yield the given point A, such as addition, subtraction, multiplication, or division of two complex numbers. However, without the specific coordinates of point A or other pertinent information (such as the specific complex numbers involved in the operation or the nature of the operation), we cannot definitively say which operation would result in point A output.
For instance, addition of two complex numbers can be visually depicted as adding the vectors for the two numbers together. Depending on what the two initial numbers are, their sum could land at point A.
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A parallelogram has base 20 cm and height 9 cm. What is its area?
To find the area, you multiply b×h. (Base × height) b=20 and h=9. Multiply it and you will get 180. The answer is 180 cm².
The area of the parallelogram is equal to 180 square meters.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called as the area of the parallelogram.
Given that a parallelogram has a base of 20 cm and a height of 9 cm. The area of the parallelogram is calculated by the formula,
Area of the parallelogram = Base x Height
Area of the parallelogram = 20 x 9
Area of the parallelogram = 180 square meters
Therefore, the area of the parallelogram is equal to 180 square meters.
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what is the percentage of 200,000 in
131,000,000 ?
Answer:
Step-by-step explanation:
Let assume that x% = 200,000
Lets assume that 100 % = 131,000,000 because it is the output value:
Therefore we have two equations:
x% = 200,000
100 % =131,000,000
Now observe that the L.H.S of both the equations have same unit. So we can write it as:
100%/x% = 131,000,000/200,000
Now just simply solve the values:
Multiply both sides by x
100/x *x = 131,000,000/200,000 *x
100=655x
Now divide both the sides by 655.
100/655 = 655x/655
100/655=x
0.15267175572519=x
Therefore the answer is 200,000 is 0.15267175572519% of 131,000,000 ....
just an addition to the reply above, which is correct, so to the risk of sounding redundant.
if we take 131,000,000 to be the 100%, what is 200,000 off of it in percentage? Bearing in mind that 1% of 131,000,000 is really 1,310,000, notice we simply chopped off two zeros, but that amount is larger than 200,000 and thus whatever 200,000 is, is less than 1%.
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 131000000&100\\ 200000&x \end{array}\implies \cfrac{131000000}{200000}=\cfrac{100}{x}\implies \cfrac{1310}{2}=\cfrac{100}{x} \\\\\\ 1310x=200\implies x=\cfrac{200}{1310}\implies x\approx 0.1526717557251908[/tex]
Which kind of symmetry do all of these figures have
The kind of symmetry the figures have are horizontal line symmetry and vertical line symmetry
Explaining the kind of symmetry the figures haveFrom the question, we have the following parameters that can be used in our computation:
The figures
The figures have horizontal line symmetry and vertical line symmetry
Horizontal line symmetry occurs when a shape can be divided into two identical halves by a horizontal line.
In other words, if you fold the shape in half along the horizontal line, the two halves will exactly overlap.
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Which of the following is an extraneous solution of (45-3x)^1/2=x-9?
A= -12
B= -3
C= 3
D= 12
Answer:
C. x =3
Step-by-step explanation:
Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.
Let's solve the equation first
[tex]\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6[/tex]
Hence, we can conclude that x=3 is an extraneous solution of the equation ..
Answer:
C
Step-by-step explanation:
HELP ASAP I WILL GIE 100 POINTS AND BRANLIEST HELP ASAP
Answer:
m=-1
Step-by-step explanation:
9m+13 =4
Subtract 13 from each side
9m+13-13 =4-13
9m = -9
Divide each side by 9
9m/9 = -9/9
m = -1
Answer:
m=-1
Step-by-step explanation:
Factor 7x3 - 28x2 + 3x - 12
Answer:Solution
(
−
4
)
(
7
2
+
3
)
Step-by-step explanation:
7
3
−
2
8
2
+
3
−
1
2
7x^{3}-28x^{2}+3x-12
7x3−28x2+3x−12
Grouping
1
Find one factor
Factor by grouping
Factor by grouping
Factor by grouping
(
−
4
)
(
7
2
+
3
)
{\color{#c92786}{({\color{#c92786}{x-4}})({\color{#c92786}{7x^{2}+3}})}}
(x−4)(7x2+3)
how do you say 75,000
seventy five thousand
Answer:
Step-by-step explanation:
I can't add much to this. The answer is 75 thousand.
What is the slope of a line perpendicular to y=-7/4x
Answer:
7/4
Step-by-step explanation:
Answer:
4/7
Step-by-step explanation:
To answer this, take the negative reciprocal of -7/4, obtaining 4/7.
Triangle ABC is similar to triangle A’B’C’. Which sequence of similar transformation could map triangle ABC onto triangle A’B’C’?
Answer: dilation and translation
Step-by-step explanation:
A dilation is a transformation that maps a similar image that is the exactly same shape as the original, but with a different size. A translation is a kind of rigid transformation used in geometry that moves a shape a particular distance.Here Δ ABC and ΔA'B'C' are similar triangles (By AAA similarity postulate), so one of the transformation used here is dilation and also the there is some distance between the triangles without any change in its orientation , so the other transformation used here is translation.
Factor completely x2 - 8x + 16.
(x + 4)(x + 4)
(X - 4)(x - 4)
(x + 4)(x - 4)
(x-2)(x - 8)
Answer:
(X - 4)(x - 4)
Step-by-step explanation:
x2 - 8x + 16
What two numbers multiply to 16 and add to -8
-4 * -4 = 16
-4 +-4 = -8
(x-4) (x-4)
(x-4)^2
Answer:
B
Step-by-step explanation:
(x - 4)(x - 4)
PLEASE HELP!!!!!
Camilla borrows a book from the library for d days. The library charges a late fee of 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it, the expression 0.10(d-21), represents the total late fee Camilla owes.
What does (d-21) represent in this context?
Choose 1 answer:
(Choice A)
The number of days Camilla borrows the book
(Choice B)
The late fee Camilla owes per day the book is late
(Choice C)
The late fee Camilla owes per day she borrowed the book
(Choice D)
The number of days the book is late
Answer: Choice D
Step-by-step explanation: Why? Because (d-21) is what how many days she was late. The problem is asking what (d-21) presents and Choice D says 'The number of days the book is late'. If the problem did have the 0.10 before (d-21) THEN it would've been Choice C.
In the expression 0.10(d-21), the term (d-21) represents the number of days the book is late, beyond the initial 21-day borrowing period.
Explanation:The expression (d-21) in the context of the late fee calculation represents the number of days the book is late. Since the library charges a late fee only if the book is returned more than 21 days after it was borrowed, subtracting 21 from the total days borrowed, which is represented by 'd,' gives us the number of days Camilla returned the book late. Multiplying this by the per-day late fee of $0.10 gives us the total late fee owed.
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-15
-3
3
15
Pls help idk this
Answer:
-3
Step-by-step explanation:
4^x = (1/8)^(x+5)
(2^2)^x = (2^-3)^(x+5)
2^2x = 2^(-3x - 15)
Since both sides have the same base of 2, then the exponents are equal
So
2x = - 3x - 15
5x = -15
x = -3
Answer:
-3
Step-by-step explanation:
see attached
What is the value of -3r+8 when r =4
Answer:
-4
Step-by-step explanation:
To find your answer, plug in 4 for r.
[tex]-3r+8\\-3(4)+8[/tex]
You can start by multiplying -3 by 4.
[tex]-3(4)+8\\-12+8[/tex]
Next, add -12 to 8 and you'll have your answer.
[tex]-12+8\\-4[/tex]
Answer:
-4.
Step-by-step explanation:
Substitute r = 4 into the given expression:
= -3(4) + 8
= -12 + 8
= -4.
Which equation can be used to find the measure of angle BAC?
Answer:
Step-by-step explanation:
let angle [tex]B[/tex] . be [tex]y[/tex] then,
using angle sum property,
x+y+90=180 (angle c is 90 because its given)
hence you have the equation
Answer:
Cos() = AC / AB
So in this case: Cos() = 5 / 13
Given the following functions f(x) and g(x), solve f[g(6)].
f(x) = 6x + 12
g(x) = x - 8
Answer:
f[g(6)] = 0
Step-by-step explanation:
f(x) = 6x + 12
g(x) = x - 8
f[g(6)]
First lets find g(6)
g(6) = 6-8 = -2
Then we substitute -2 in for g(6)
Putting -2 into f(x)
f[g(6)] = f(-2) = 6(-2)+12 = -12+12 =0
The Smith family has 80 movies in their collection. The types of movies are shown in the table below. Smith Family Movies Type of Movie Percentage Drama 10% Action 25% Animated/Children’s 50% Comedy 15% How many of the movies in the collection are action movies?
Answer:
20 movies
Step-by-step explanation:
no of movies= 80
action movies percentage=25%
no of action movies=25/100*80(25% of 80)
-3(-x)-6=-3x+10 solve
Answer:
[tex]\large\boxed{x=\dfrac{8}{3}}[/tex]
Step-by-step explanation:
[tex]-3(-x)-6=-3x+10\\\\3x-6=-3x+10\qquad\text{add 6 to both sideS}\\\\3x=-3x+16\qquad\text{add}\ 3x\ \text{to both sides}\\\\6x=16\qquad\text{divide both sides by 6}\\\\x=\dfrac{16}{6}\\\\x=\dfrac{8}{3}[/tex]
Which equations and/or functions represent the graphed line? Select four options. f(x) = 0.2x - 4
f(x) = 0.5x + 2
f(x) = 1/2x + 2
y – 3 = 1/2(x – 2)
y – 1 = 0.5(x + 2)
Answer:
f(x) = 0.2x - 4 (incorrect)
f(x) = 0.5x + 2 (correct)
f(x) = 1/2x + 2 (correct)
y – 3 = 1/2(x – 2) (correct)
y – 1 = 0.5(x + 2)
Step-by-step explanation:
Step 1 : Find two coordinates
(0, 2) (-4, 0)
Step 2 : Find the slope
Slope = m = Y2-Y1/X2-X1
m = 0-2/-4-0
m = -2/-4
m = 1/2 or 0.5
Step 3 : Find the y-intercept
Y-intercept is where the line intersects the y-axis
c = 2
Step 4 : Form the equation y=mx + c
Given Equations and their slope intercept forms:
1) f(x) = 0.2x - 4
This is incorrect because slope is 1/2 or 0.5 and y intercept is 2
2) f(x) = 1/2x + 2
y = 1/2x + 2
This is correct because slope is 1/2 or 0.5 and y intercept is 2
3) f(x) = 0.5x + 2
y= 0.5x + 2 (As m=0.5)
This is correct because slope is 1/2 or 0.5 and y intercept is 2
4) y – 3 = 1/2(x – 2)
Rearranging in slope intercept form:
y-3=1/2x - 1
y = 1/2x-1+3
y = 1/2x + 2
This is correct because slope is 1/2 or 0.5 and y intercept is 2
5) y – 1 = 0.5(x + 2)
y -1 = 0.5x+1
y = 0.5x +1+1
y = 0.5x + 2
This is correct because slope is 1/2 or 0.5 and y intercept is 2
!!
first off, let's notice something on this line, the graph touches the y-axis at 2, namely when x = 0, y = 2, so that's the y-intercept for this line.
now, let's notice something else, as the line moves from x = -4, to the right towards x = 0, the run is 4 units, the rise is 2 units, so its slope is rise/run or 2/4 or 1/2, that said, that gives us an equation of
[tex]\bf y=\cfrac{1}{2}x+2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\implies y=0.5x+2[/tex]
[tex]\bf y-3 = \cfrac{1}{2}(x-2)\implies y-3=\cfrac{1}{2}x-1\implies y=\cfrac{1}{2}x+2\qquad \textit{\Large\checkmark} \\\\\\ y-1=0.5(x+2)\implies y-1=0.5x+1\implies y=0.5x+2\qquad \textit{\Large\checkmark} \\\\\\ f(x) = 0.2x-4\qquad \bigotimes[/tex]
I need help with this
Answer:
The x-intercepts are x = 1 , x = 2 , x = 3
The y-intercept is -6
Step-by-step explanation:
* Lets explain how to solve the problem
- To find the x-intercept of a function substitute f(x) by 0
- To find the y-intercept of a function substitute x by 0
- To find the factors of quadratic function use the long division
* Lets solve the problem
∵ f(x) = x³ - 6x² + 11x - 6
∵ (x - 3) is one of its factors
- Use the long division to find the other factors
∵ x³ - 6x² + 11x - 6 ⇒ dividend
∵ x - 3 ⇒ divisor
# Divide the 1st term in the dividend by the 1st term of the divisor
∵ x³ ÷ x = x²
# Multiply x² by the divisor (x - 3)
∵ x²(x - 3) = x³ - 3x²
# subtract it from the dividend
∵ (x³ - 6x² + 11x - 6) - (x³ - 3x²) = (x³ - x³) + (-6x² + 3x²) +11x - 6
∴ The dividend is -3x² + 11x - 6
# Divide the 1st term in the dividend by the 1st term of the divisor
∵ -3x² ÷ x = -3x
# Multiply -3x by the divisor (x - 3)
∴ -3x(x - 3) = -3x² + 9x
# subtract it from the dividend
∵ (-3x² + 11x - 6) - (-3x² + 9x) = (-3x² - 3x²) + (11x - 9x) - 6
∴ The dividend is 2x - 6
# Divide the 1st term in the dividend by the 1st term of the divisor
∵ 2x ÷ x = 2
# Multiply 2 by the divisor (x - 3)
∴ 2(x - 3) = 2x - 6
# subtract it from the dividend
∴ (2x - 6) - (2x - 6) = (2x - 2x) + (-6 + 6) = 0
∴ (x³ - 6x² + 11x - 6) ÷ (x - 3) = x² - 3x + 2
∴ The factors of f(x) are (x - 3)( x² - 3x + 2)
- The factor (x² - 3x + 2) can factorize into two bracket
∵ The last term is positive and the middle term is negative than the
two brackets have the middle sign (-)
∵ x × x = x² ⇒ 1st terms in the two brackets
∵ 2 × 1 = 2 ⇒ 2nd terms in the two brackets
∵ 2 × x = 2x
∵ 1 × x = x
∵ 2x + x = 3x
∴ (x² - 3x + 2) = (x - 2)(x - 1)
∴ f(x) = (x - 3)(x - 2)(x - 1)
- To find the x-intercept put f(x) = 0
∴ (x - 3)(x - 2)(x - 1) = 0
- That means each bracket = 0
∵ x - 3 = 0 ⇒ add 3 for both sides
∴ x = 3
∵ x - 2 = 0 ⇒ add 2 for both sides
∴ x = 2
∵ x - 1 = 0 ⇒ add 1 for both sides
∴ x = 1
∴ The x-intercepts are x = 1 , x = 2 , x = 3
- To find the y-intercept put x = 0
∵ f(x) = x³ - 6x² + 11x - 6
∵ x = 0
∴ f(0) = 0 - 0 + 0 - 6 = -6
∴ The y-intercept is -6
using the discriminant, how many solutions and what type of solution(s) does 3p-9p^2=6 have?
a. 2; irrational
b. 2; rational
c. 1; rational
d. no real solutions
Answer:
d. no real solutions
Step-by-step explanation:
3p − 9p² = 6
0 = 9p² − 3p + 6
0 = 3p² − p + 2
The discriminant of ax² + bx + c is b² − 4ac.
If the discriminant is negative, there are no real roots.
If the discriminant is zero, there is 1 real root.
If the discriminant is positive, there are 2 real roots.
If the discriminant is a perfect square, the root(s) are rational.
If the discriminant isn't a perfect square, the root(s) are irrational.
Finding the discriminant:
a = 3, b = -1, c = 2
(-1)² − 4(3)(2) = -23
The discriminant is negative, so there are no real roots.
Final answer:
After rewriting the equation 3p-9p²=6 in standard quadratic form and calculating the discriminant, we find that the discriminant is negative, indicating the equation has d. no real solutions.
Explanation:
To determine the number and type of solutions the equation 3p-9p²=6 has using the discriminant, we first need to rewrite the equation in standard quadratic form, which is ax² + bx + c = 0. Moving all terms to one side gives us -9p² + 3p - 6 = 0, where a = -9, b = 3, and c = -6. The discriminant of a quadratic equation is defined as b² - 4ac.
A discriminant greater than zero indicates two real solutions, equal to zero indicates one real solution, and less than zero indicates no real solutions. Calculating the discriminant for our equation: (3)² - 4(-9)(-6)=9-216=-207, which is less than zero. Therefore, the equation -9p²+ 3p - 6 = 0 has d. no real solutions.
Solve for x. 7 – 4x = 31 A. x = 6 B. x = 9.5 C. x = –6 D. x = –9.5
7-4x= 31
Bring over 7 to the other side
Positive 7 changes into negative 7
7-7-4x= 31-7
-4x= 24
Divide by -4 for -4x and 24
-4x/-4= 24/-4
x= -6
Check answer by using substitution method
7-4x= 31
7-4(-6)= 31
7+24= 31
31= 31
Answer : C. x= -6
Answer:
C. x = -6
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 7 from both sides:
7 - 4x = 31
7 (-7) - 4x = 31 (-7)
-4x = 31 - 7
-4x = 24
Divide -4 from both sides to isolate the variable, x:
(-4x)/-4 = (24)/-4
x = 24/-4
x = -6
x = -6, or C. is your answer.
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the vertex of the parabola is (-3,6). which of the following could be it’s equation
Answer:
Step-by-step explanation:
The most general form of this, without seeing any of the options, would be:
[tex]y=(x+3)^2+6[/tex]
Again, there might have been a value outside the parenthesis that may or may not have been negative, but either way, this is the most basic translation of the parabola.