Both solutions are valid, so the solutions to the quadratic function [tex]f(x) = 4x^2 - 9[/tex] are x = -3/2 and x = 3/2.
To solve the quadratic function [tex]f(x) = 4x^2 - 9[/tex] by factoring, we set the expression equal to zero and then try to factor it.
Step 1: Set f(x) equal to zero:
[tex]4x^2 - 9 = 0[/tex]
Step 2: Factor the quadratic expression:
The expression [tex]4x^2 - 9[/tex] is in the form of a difference of squares, which can be factored as follows:
[tex]a^2 - b^2 = (a + b)(a - b)[/tex]
In our case, a = 2x and b = 3:
[tex]4x^2 - 9 = (2x + 3)(2x - 3)[/tex]
Step 3: Set each factor equal to zero and solve for x:
First factor: 2x + 3 = 0
Subtract 3 from both sides:
2x = -3
Divide both sides by 2:
x = -3/2
Second factor: 2x - 3 = 0
Add 3 to both sides:
2x = 3
Divide both sides by 2:
x = 3/2
Step 4: Check the solutions:
Plug the values of x back into the original equation to verify:
For x = -3/2:
[tex]f(-3/2) = 4(-3/2)^2 - 9\\f(-3/2) = 4(9/4) - 9\\f(-3/2) = 9 - 9\\f(-3/2) = 0\\For x = 3/2:\\f(3/2) = 4(3/2)^2 - 9\\f(3/2) = 4(9/4) - 9\\f(3/2) = 9 - 9\\f(3/2) = 0[/tex]
Both solutions are valid, so the solutions to the quadratic function f(x) = [tex]4x^2 - 9[/tex] are x = -3/2 and x = 3/2.
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what is the nearest tenth to the square root of 46
PLEASE HELP
Answer:
6.8
Step-by-step explanation:
This is the answer because:
1) The square root of 46 is 6.78232998...
2) The nearest tenth of this is 6.8 because we have to round 7. Since 8 is greater than 5, we have to round 7 up.
Therefore, the answer is 6.8
Hope this helps! :D
What is the range of y = –3sin(x) – 4? all real numbers Negative 7 less-than-or-equal-to y less-than-or-equal-to 7 all real numbers Negative 7 less-than-or-equal-to y less-than-or-equal-to negative 1 all real numbers Negative 5 less-than-or-equal-to y less-than-or-equal-to 3 all real numbers Negative 1 less-than-or-equal-to y less-than-or-equal-to 1.
Range of a function is the extent to which any function may be varied. The range of the given function y= -3sin(x)-4 is [-7,-1].
What is a Range?The range of a function is the extent to which any function may be varied.
We know that the general range of the function of sin(x) is between [-1,1].
-1 ≤ sin(x) ≤ 1. . . . . . . . . .(A)
As our required function is y = -3sin(x) - 4
Now, in order to get this function, we will multiply each side in Equation (A) by -3, therefore,
-3 ≤ -3 sin(x) ≤ 3
Further, subtract from 4 from each side of the equation.
-7 ≥ -3sin(x)-4 ≥ -1
Hence, the range of the given function y= -3sin(x)-4 is [-7,-1].
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Answer: b
Step-by-step explanation:all real numbers (b)
What is the area of the triangle abc?
Answer:
Your answer is 35!
Step-by-step explanation:
I'm sure of it!
Given f(x) = 6(1 - x), what is the value of f(-8)?
Answer:
6(1-(-8)= 54
Step-by-step explanation:
Plug negative 8 in for x and solve the equation
Please help!! Prove AD is parallel to BC
Answer:
parallel lines are coplanar straight lines that do not intersect at any point. Lines AD and BC have no intersection.
Answer:
Correct me if I'm wrong!!!
if 10x = 40 million, then what is x
Answer:
× = 4,000,000
Step-by-step explanation:
40 Million = 40,000,000
40,000,000 ÷ 10
=
4,000,000
Checking:
4,000,000 × 10 = 40,000,000/ 40 Million
When dividing by zero, all you do is remove a zero or move the decimal place to the left.
solve the system of linear equations -x+5y=15 -1/5x+y=3
Answer:
[tex](0,3)[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}-\frac{1}{5}\left(15-5y\right)+y=3\end{bmatrix}[/tex]
[tex]\begin{bmatrix}-3+2y=3\end{bmatrix}[/tex]
[tex]+3[/tex] [tex]+3[/tex]
[tex]2y\f=6[/tex]
÷[tex]2[/tex] ÷[tex]2[/tex]
[tex]y=3[/tex]
[tex]\mathrm{for\:}x=15-5y[/tex] [tex]\mathrm{substitute\:}y=3[/tex]
[tex]x=15-5\cdot \:3[/tex]
[tex]5*3=15[/tex]
[tex]15-15=0[/tex]
[tex](x,y)[/tex]
[tex](0,3)[/tex]
What is the value of x . 3x+8+6x-4
Answer:
9x+4
Step-by-step explanation:
3x+6x is 9x
8-4 is 4
9x+4
if you are solving for x, you do 9/9 and 4/9
approximately .44 repeated
I can’t move on till I answer please help
Answer:
Step-by-step explanation:
Given the x-intercepts at -1 and 5, that means y=0 at x=-1 and x=5.
So (x+1) and (x-5) are root for the parabola.
y = (x+1)*(x-5)
That is the quadratic equation for Question B.
Back to A, the x-coordinate of vertex of this parabola is at x=2.
This is because the parabola is symmetrical at its vertex so the vertex must be at the mid-point between its x-intercepts, x=(-1+5)/2=2.
NEED ASAP!
Which number below comes first when the numbers are listed from least to greatest?
1/6
-4
square root of 2
-6/5
3.5
Answer:
-4
Step-by-step explanation:
1/6, the square root of 2, and 3.5 are all positive so it is between -6/5 and -4. -6/5 is equal to -1 and 1/5 which is closer to zero than -4. Hope this makes sense!
The first terms of a geometric sequence are as follows.
-810,-270,-90
Find the next two terms of this sequence.
Give exact values (not decimal approximations)
The fourth and fifth term of this sequence is -30 and -10 respectively.
Data;
first term (a) = -810common difference (r) = ?Common DifferenceThe common difference in a geometric progression is the ratio between two successive terms.
Let's find the common difference in this sequence
[tex]r = \frac{-270}{-810} \\r = \frac{1}{3}[/tex]
The nth term of a geometric sequence is given as
[tex]T_n = ar^n^-^1\\[/tex]
The next two terms of this sequence will be 4th and 5th term.
The fourth term of this sequence is
[tex]T_4 = ar^4^-^1\\T_4 = -810 * (\frac{1}{3})^3\\ T_4 = -810 * \frac{1}{27}\\ T_4 = -30[/tex]
The fifth term of this sequence is
[tex]T_5 = ar^5^-^1\\T_5 = -810 * (\frac{1}{3})^4\\T_5 = -810 * \frac{1}{81} \\T_5 = -10[/tex]
The fourth and fifth term of this sequence is -30 and -10 respectively.
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Anna and Betty share 24 sweets in the ratio 3:5. How many sweets do they get each?
Answer:
Anna 9 and Betty 15
Step-by-step explanation:
sum the parts of the ratio , 3 + 5 = 8 parts
divide number of sweets by 8 to find value of one part of the ratio
24 ÷ 8 = 3 ← value of 1 part of the ratio , then
3 parts = 3 × 3 = 9
5 parts = 5 × 3 = 15
Anna gets 9 sweets and Betty gets 15
Enter an expression equivalent to (3x2 + 2y2 – 3x) - (2x2 + y2 - 2x) using the fewest number of possible terms
Answer:
x2+y2-x
Step-by-step explanation:
subtract like terms.
The required equivalent expression is [tex]x^2+y^2-x[/tex].
Important information:
The given expression is [tex](3x^2+2y^2-3x)-(2x^2+y^2-2x)[/tex].Equivalent expression:The given expression can be written as:
[tex]3x^2+2y^2-3x-2x^2-y^2+2x[/tex]
Combining like terms, we get
[tex](3x^2-2x^2)+(2y^2-y^2)+(-3x+2x)[/tex]
On simplification, we get
[tex]x^2+y^2-x[/tex]
Therefore, the required equivalent expression is [tex]x^2+y^2-x[/tex].
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Pls respond fast I’m tired lol I can’t figure it out
Answer:
62°
Step-by-step explanation:
∠IKD=∠EIB=∠GJI =118° (Corresponding angles)
∠GJI+∠AJG=180° (Linear Pair)
∴∠AJG= 180°-118°
=62°
-15/8 + 1/4 = ??????
Answer:2 1/8 pls give me brainliest
Step-by-step explanation:first step is to change the 1/4 to 2/8. Then add and simplify.
what is negative 2 and 2/3 as a decimal
Hi friend! Hope you find this response helpful! :)
0.66666667
A mixture of purple paint contains 6 teaspoons of red paint and 15 teaspoons of blue paint. To make the same shade of purple paint using 35 teaspoons of blue paint, how much red paint would you need?
answer please answer
Answer:
slope is 3/2
Step-by-step explanation:
point A (20,10), point B (40,40)
slope= [tex]\frac{(y2-y1)}{(x2-x1)}=\frac{40-10}{40-20}=\frac{30}{20} =\frac{3}{2}[/tex]
Write the following ratios in its simplest form 56:112:28
Answer:
2 : 4 : 1
Step-by-step explanation:
First take common factors by factorization.
56 = 14 x 4 = 28 x 2
112 = 14 x 8 = 28 x 4
28 = 14 x 2 = 28 x 1
Remove the 28 common factor.
Therefore,
56 : 112 : 28
= 2 : 4 : 1
plzzzzzzzzzzzz help will get brainlist
When a construction worker is on a platform 10 feet above the ground, we can describe her elevation as +10 feet.
A construction worker digs down to 30 feet below the platform. What is her elevation?
-3.5y - 6.2y = - 87.3
Answer:
the answer is 9
Step-by-step explanation:
-3.5y - 6.2y = - 87.3
or, -9.7y = -87.3
or, y = -87.3/-9.7
or, y = 9.
Explain how to write an equation from a table in slope intercept form.
Answer:
the answer for this is y=mx+b
Answer:
The table gives you three points that are on the line:
(-5, -7), (0, -5), (3, -3)
use any two of them to find the slope.
The polygons are similar. Find the value of x.
2-
Р
X
X
20
21
14
5
Q 12 R
L
18
K
For the given similar polygons, the value of x equal to 30.
Similar PolygonsTwo polygons are classified as similar when their angles are congruent and their sides are proportional.
If the polygons of this exercise are similar. You can write:
[tex]\frac{LK}{QR}=\frac{JK}{PR}=\frac{JL}{PQ}[/tex]
Then,
[tex]\frac{LK}{QR}=\frac{JK}{PR}=\frac{JL}{PQ}\\ \\ \frac{18}{12}=\frac{x}{20}=\frac{21}{14}[/tex]
It is possible to note that the scale factor is [tex]\frac{3}{2}[/tex]. See it.
[tex]\frac{18:6}{12:6}=\frac{3}{2} \\ \\ \frac{21:7}{14:7}=\frac{3}{2}[/tex]
Therefore, you can find x from:
[tex]\frac{18}{12}=\frac{x}{20}\\ \\ 12x=18*20\\ \\ 12x=360\\ \\ x=\frac{360}{12} =30[/tex]
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Determine the value of the variable in the simplified expressions
What is the value of x in this simplified expression?
(-3)?
(-3)*
X
What is the value of y in this simplified expression?
1
K+m
-10
+
1
10
kym
y =
Answer:
x = 7
y = 5
Step-by-step explanation:
When the exponent is negative in the numerator, putting it into the denominator makes it positive.
When the exponent is negative in the denominator, putting it into the numerator makes it positive.
Write the decimal as a fraction or mixed number in simplest form.
5.22
Answer:
5 11/50
Step-by-step explanation:
i used an online calculator and thats what it said
Answer:
5 2/9
Step-by-step explanation:
What is the difference
-2 - 8 =
Answer:
-10
Step-by-step explanation:
-2 - 8 = -10I hope this helps!
Answer:
-10
Step-by-step explanation:
To find the answer to -2 - 8, we have to remember that when you subtract numbers, they go towards the negatives. So, since it is -2 - 8, you basically just add together the numbers but keep the negative sign, so the answer would be:
-2 - 8 = -10
Hope this helps :)
What is the slope of the line represented by the points in the table?
Answer:
I think the answer is -0.05
Step-by-step explanation:
How many kilograms of water must be added to 2. 5 g of methanol (CH30H) to make a 3. 0 m solution?
Answer:
Given: 150ml of 2.0M CH
3
OH is to be prepared.
Number of moles= M×Volume inL=2.0×0.150=0.3
Molar mass of CH
3
OH=32.04g/mol
∴ Weight of CH
3
OH to be added= 32.04×0.3=9.61g
Step-by-step explanation:
HURYYYYY BRAINLIEST
The ordered pairs in the table lie in the graph of the linear function whose equation is
y = 3x + 2.
Which ordered pair does not lie on the graph of this function?
A. (10, 32)
B. (8, 13)
C. (–5, –13)
D. (–8, –22)
y = 3x + 2 = 3 * x + 2
point (10 ; 32) on the line ?
so here we can read : x = 10 and y = 32
if x = 10
then y has to be = 3 * 10 + 2 = 30 + 2 = 32
so yes - on the line
same reasoning for the rest
The ordered pairs which does not lie on the graph of the function are (8,13).
What is function?Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have corresponding value of y.
The value which we put in the function is domain of the function and the value which we will get is known as codomain of the function.
How to find ordered pairs?We have been given a function y=3x+2 and we have to find the ordered pairs which does not lie on graph of function. The ordered pairs which lie on the graph must satisfy the function and the ordered pairs which does not lie on the graph must not satisfy the function.
First ordered pair is (10,32)
32=3*10+2
32=30+2
32=32
It lies on graph.
Second ordered pair is (8,13)
12=3*8+2
12=24+2
12≠26
So it does not lie on graph of function y=3x+2.
Hence the ordered pair which does not lie on the graph of function y=3x+2 is (8,13).
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What is the value of the expression 10z-3 when z=4?
Answer:
37
Step-by-step explanation:
10 x 4 - 3
40 - 3
37
Answer:
37
Step-by-step explanation:
10*4-3=40-3,which equals 37