g(x) = 2x² - 3x + 1 =
-2 = 2[tex](x+2)^{2}[/tex]+ 3(x+2) - 1
-2 = 2( [tex]x^{2}[/tex] + 4x + 4) + 3(x+2) - 1
-2 = 2[tex]x^{2}[/tex] + 8x + 8 + 3x + 6 - 1
-2 = 2[tex]x^{2}[/tex] + 11x + 13
0 = 2[tex]x^{2}[/tex] + 11x + 15
0 = ( 2x + 5 )(kx + 3 )
2x + 5 = 0 ---> kx= -5/2
x+3=0 ----> x = -3
Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output.
one of them sums up a function the best?
Recognize that a function is a particular kind of relation where a rule states that every input must be paired with exactly one output. So, this is the best choice.
The function's type is f/x)= 2x 2 + 3x 1.
Explanation: Since the polynomial f(x)=2x33x+1 is continuous and contains continuous derivatives of all orders for all real x, it unquestionably meets the theorem's hypotheses.
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Help with this equation I need to turn it in
Answer:
y=12x+40
Step-by-step explanation:
The earnings are the initial payment per month plus the pay per hour times the number of hours.
55=(5x+5) value of x
Answer:
x = 10
Step-by-step explanation:
55 = 5x + 5 Subtract 5 from both sides of the equation
50 = 5x Divide both sides by 5
10 = x
Answer:10
Step-by-step explanation:- 5 on both sides then you get 50=5x 50/5=10
Question is in the image
Answer:
0
Step-by-step explanation:
7 is not in the sample space, meaning it is impossible. Therefore, the probability is 0.
HELP ASAP NEEDS TO BE DONE BY TONIGHT (HELP WITH THE OTHER QUESTIONS TO CLICK MY PROFILE)
Hello!
Let's convert the equation, 3x + 4y = 7, into slope-intercept form:
⇒ slope-intercept form is where the y-variable is isolated to one side
[tex]3x + 4y = 7\\\\4y=-3x + 7\\\\y=-\dfrac{3}{4}x +7[/tex]
The other line that is parallel to the equation: has the same slope
==> thus this other's line slope is -3/4
Let's set up the point-slope form for this other line:
[tex](y-y_0)=m(x-x_0)[/tex]
(x₀,y₀): (-3, -9) <-- any point on the linem: -3/4 <-- slope of line[tex](y+9)=-\dfrac{3}{4} (x+3)\\\\y + 9=-\dfrac{3}{4}x-\dfrac{9}{4} \\\\y=-\dfrac{3}{4}x-\dfrac{9}{4} -9\\\\y=-\dfrac{3}{4}x-\dfrac{9}{4} -\dfrac{36}{4} \\\\[/tex]
[tex]y = -\dfrac{3}{4}x -\dfrac{45}{4}[/tex] <== Answer
Hope that helps!
2. John has $160 to spend on video
games. He spent $30 on a controller
and the rest on video games. If each
game costs $13, how many games did
he buy? (Write an equation using "g"
to represent the number of games.
Solve for g.)
He buy 10 games that costs $13.
What is equation?Equation, also known as a statement of equivalence between two expressions with variable- and/or number-based components. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Given Data
John has $160 to spend on video games.
He spent $30 on a controller the rest on video games.
If each game costs $13
Equation
30 + 13g = 160
13g = 130
g = 10
He buy 10 games that costs $13.
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If an experiment with a random outcome is repeated a large number of times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called what?.
If an experiment with a random outcome is repeated a large number of times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called The Law of Large Numbers.
The Law of Large Numbers states that on the off chance that a test with an irregular result is repeated a huge number of times, the empirical probability of an event is likely to be near the true probability. The bigger the number of redundancies, the closer together these probabilities are likely to be.The law of large numbers does not ensure that a given test, particularly a little test, will reflect the genuine population characteristics or that a test that does not reflect the genuine population will be adjusted by a subsequent sample. The law of large numbers demonstrates a greater test will speak to a population mean, whereas the central tendency theorem states a greater test will speak to a population's distribution.
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A gate is made out of 7 panels of wood, each in which is 15.7 cm wide. between the panels there is a gap of 14.9 cm how wide is the gate in total and in cm?
Answer:
Total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm
Step-by-step explanation:
GIVEN-
A gate is made out of 7 panels of wood, each of which is 15.7 cm wide. between the panels, there is a gap of 14.9 cm
THIS IS AN EASY SUMMATION PROBLEM-
FOR ONE PANEL WIDTH =15.7
FOR 7 PANEL'S WIDTH =15.7*7=109.9;
NOW, between the 7 panels, 6 gaps create
one gap =14.9 cm
six gap =14.9 * 6 =89.4 cm
so, the total width of the gate in cm is equal to=> 109.9+89.4=199.3 cm
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3/x-1-4x-1/x+1 =x^2+5/x^2-1-5
After thoroughly calculating the equation, we conclude that x⁴ + 4x³ - 6x² - 2x + 25 is the simplified form of 3/x - 1 - 4x - 1/x + 1 = x² +(5/x)²- 1 - 5
What is a simplified form?When the top and bottom of a fraction are the same size and still whole numbers, the fraction is said to be in its simplest form or simplified form.
Using 2/4 as an example, 1/2 can be written.
Simplify a fraction by multiplying its top and bottom by the biggest number that will divide them both exactly (they must stay whole numbers). the outcome will be what we call the simplified form.
We have been asked to simply the equation
3/x - 1 - 4x - 1/x + 1 = x² +(5/x)²- 1 - 5
⇒ 3/x - 4x - 1/x + 6 = x² +(5/x)²
⇒ 2/x - 4x + 6 = x² +(5/x)²
⇒ 2/x - 4x²/x + 6x/x = x² +(5/x)²
⇒ (2 - 4x² + 6x)/x = x² +(5/x)²
Multiplying x to both side
⇒ 2 - 4x² + 6x = x² +(5/x)² × x
⇒ 2 - 4x² + 6x = x³ + 25/x
⇒ x³ + 4x² - 2 = 6x - 25/x
⇒ x³ + 4x² - 2 = 6x²/x - 25/x
⇒ x³ + 4x² - 2 = (6x²- 25)/x
Multiplying x to both side
⇒ (x³ + 4x² - 2) x = 6x²- 25
⇒ x⁴ + 4x³ - 2x = 6x²- 25
⇒ x⁴ + 4x³ - 6x² - 2x + 25
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Find the slope of the line that passes
through these two points.
Point 1
(-4,6)
X1 Yı
m =
Point 2
(-1,3)
X2 Y2
92-91
X2-X1
m = [?]
The slope of the line is -1.
A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by the symbols y and x, respectively to calculate the slope.The common form for two-variable linear equations is Ax + By = C , where the slope is -A/C.For instance, the linear equation 7x + 3y = 1 uses standard form. Finding an equation's two intercepts (x and y) is fairly straightforward with this procedure, the slope is -7/3 .The cartesian equation for a straight line is Y = mx + c, where m stands for the gradient or slope of the line and c for the point at which it intersects the y-axis.Now the given points are : (-4,6) and (-1,3)
We know that the slope of a line is given by :
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]
Now we can put the values of the points to get the slope as
[tex]m=\frac{3-6}{-1-(-4)}\\\\[/tex]
or , m = -1
Hence the slope of the line is -1
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Write the equation of the line that is parallel to line 3x - 2y = 8 and passes through the point (6, -3). Show ALL steps!
[tex] - 2y = 8 - 3x \\ \frac{ - 2y}{ - 2} = \frac{8}{ - 2} - \frac{3x}{ - 2} \\ y = \frac{3}{2} x - 4[/tex]
PARALLEL LINES HAVE EQUAL GRADIENTS.AS WE SEE IN THE EQUATION ABOVE THE GRADIENT IS
[tex] \frac{3}{2} [/tex]
IT MEANS THE GRADIENT OF THE NEW EQUATION IS ALSO
[tex] \frac{3}{2} [/tex]
NOW GIVEN THE POINTS WE CAN USE THE KNOWNS TO GET THE VALUE OF C IN THE NEW EQUATION.
[tex] - 3 = \frac{3}{2} (6) + c \\ - 3 = 9 + c \\ - 3 - 9 = c \\ c = - 12[/tex]
[tex]y = \frac{3}{2} x - 12[/tex]
( 4, 2 ) is a solution to the system of equations below: 2x + 4y = 16 ( 1 / 2 ) x − 2y = 4
The system of equations has two solutions, that is (4, 2).
Given,
There is a system of equations:
Equation 1: 2x + 4y = 16
Equation 2: (1/2)x - 2y = 4
The solution to the system of equations = (4, 2)
Lets check for the solution:
The equations are in the form of,
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Here,
a₁ = 2 , a₂ = 1/2
b₁ = 4 , b₂ = 2
c₁ = 16 , c₂ = 4
Now we know that,
a₁/a₂ = b₁/b₂ = c₁/c₂
So,
a₁/a₂ = 2 / (1/2) = 4/1 = 4
b₁/b₂ = 4/2 = 2
c₁/c₂ = 16/4 = 4
Therefore, the system of equations has two solutions, that is (4, 2).
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A is in the interior of NFL. If m/NFA = 5x+10, m/AFL = 30-2x, and m/NFL = 58°, find the value of x.
If A is in the interior of NFL. If m/NFA = 5x+10, m/AFL = 30-2x, and m/NFL = 58°, the value of x would be 6
How to determine the valueIt is important to note that the formula for determining the sum of interior angles of a shape is expressed as;
(n-2) 180
Where 'n' is the number of sides
From the information given, we have that the shape has 3 sides, so we have
(3 -2)180
180°
Give the angles as;
m/NFA = 5x+10m/AFL = 30-2x m/NFL = 58°Equate the angles to m/NFL, we have
5x+10 + 30-2x = 58
Now, collect like terms
5x - 2x = 58 - 40
Subtract like terms
3x = 18
Make 'x' the subject by dividing both sides by 3, we have
x = 18/3
x = 6
Thus, the value of 'x' is 3
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Determine which equation is false based on the solution set.
S:{3}
−28 = 2(4p − 4)
5(b + 3) = 30
7 = 3y − 2
one third times x plus 18 equals 19
Based on the solution set S:{3} the equation which is false is
-28 =2(4p -4).
As given in the question,
Given solution set S:{3}
Equation which is false based on the solution set
1. −28 = 2(4p − 4)
Divide by 2 from both the sides
⇒ -14 = 4p -4
⇒ p = -10/4 ≠ 3
2. 5(b + 3) = 30
Divide by 5 from both the sides
⇒b + 3 =6
⇒ b = 3
3. 7 = 3y − 2
⇒ 3y = 9
⇒ y = 3
4. One third times x plus 18 equals 19
(1/3)x + 18 = 19
⇒(1/3)x =1
⇒x =3
Therefore, based on the solution set S:{3} the equation which is false is
-28 =2(4p -4).
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D is the midpoint of EF. ED = 4x + 27, DF = 5x + 21. Find x, ED, DF, and EF
What do the following two equations represent?
Choose 1 answer:
A.The same line
B.Distinct parallel lines
C.Perpendicular lines
D.Intersecting, but not perpendicular lines
Answer:
D
Step-by-step explanation:
[tex]2x-12y=24 \\ \\ x-6y=12 \\ \\ 6y-x=-12 \\ \\ 6y=x-12 \\ \\ y=\frac{1}{6}x-2[/tex]
The slopes of the lines are neither the same nor are they negative reciprocals, so the answer is D.
x = 3 over 5 + y = 1 over 3 x z = 2 and 4 over 5
could you please re post the question clearly as right now I don't understand what this means, you can try just taking a picture of the question and attach it to your post
What is the special angle pair relationship between 1 and 3?
Answer:
These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
Angle 1 and angle 3 are on the same side of the two parallel lines with a transversal line on them.
The special angle pair relationship between 1 and 3 is called the corresponding angles.
What are corresponding angles?Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
We have,
Angle 1 and Angle 3.
The angles are on the same side of the two parallel lines with a transversal line on them.
The angles can be called the corresponding angles.
Thus,
The special angle pair relationship between 1 and 3 is called the corresponding angles.
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pls pls help whoever gets it right gets marked brainliest
Answer:
option b) 5 units
Answer:
5 units
Step-by-step explanation:
You use Pythagoras' theorem
3squared + 4 squared = 25
square root of 25 is 5
Given the function f described by f(x)=8x^2+4x-5 find the function values.
The two solutions of the quadratic function are 0.58 and -1.1.
What is the solution of a quadratic equation?The solution of a quadratic equation can be obtained using the substitution method or formula method.
The solution of the given quadratic function is determined as follows;
f(x) = 8x² + 4x - 5
0 = 8x² + 4x - 5
The formula method of a quadratic function is given as;
[tex]x = \frac{-b \ \ \pm \ \sqrt{b^2 - 4ac} }{2a}[/tex]
from the above equation, a = 8, b = 4, c = -5
[tex]x = \frac{-4 \ \ \pm \ \sqrt{4^2 - 4(8\times -5)} }{2a}\\\\x = \frac{-4 \ \ \pm \ \sqrt{16 + 160} }{2(8)}\\\\[/tex]
x = 0.58 or -1.1
Thus, the function has two solutions, a negative and positive solution.
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Evaluate the expression 6 + 8f for f = 4.
A 8
B 18
C 38
D 56
P1-8
The answer is C:38
explanation: you multiply 8x4=32, so then you add 6 to 32
Hope this helped!
40 POINTS MATCH THEM PLS
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
25, 34, 43, 52, ...
explain :)
Answer:
205
Step-by-step explanation:
we first enter the desired number equaling the equation, so 21. then we enter the first term and find the common difference, in this case it's going up by 9. then we take the desired term, subtract 1 and we end up with 205 as the 21st term.
21 = 25 + 9 (21 - 1)
The table represents an absolute value function f(x).
x f(x)
−5 1
−4 0
−3 1
−2 2
−1 3
0 4
1 5
2 6
3 7
What are the vertex and range of the function?
The vertex of the function is (4, 0) and the range of the function is [0, 7]
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the vertex of the function?The table of values represents the given parameter
As a general rule, the vertex of a function is the smallest or the largest value of the function
On the table of values, we have the smallest function value is 0
The corresponding x value is -4
When these values are paired, we have
(x, y) = (4, 0)
This means that the vertex of the function is (4, 0)
How to determine the range of the function?The table of values represents the given parameter
Using the definition of range stated above, we have
Smallest function value = 0
Largest function value = 7
This means that the range of the function is [0, 7]
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Exterior angle, theorem, and triangle sum theorem
Answer:
x = 4
The two interior angles are
14x + 6 = 14 x 4 + 6 = 62°
16x + 4 = 16 x 4 + 4 = 68°
Step-by-step explanation:
The exterior angle of a triangle is the sum of the interior angles:
Here the exterior angle is 130° and the interior angles are
16x + 4 and 14x + 6
So 16x + 4 + 14x + 6 = 130
Gathering like terms and simplifying:
16x + 14x + 4 + 6 = 130
30x + 10 = 130
30x = 120 (subtract 10 from both sides)
x = 4
The two interior angles are
14x + 6 = 14 x 4 + 6 = 62°
16x + 4 = 16 x 4 + 4 = 68°
a) Give an example of discrete data that might consist of some decimal numbers.
b) Give an example of continuous data that might not have any numbers with fractional parts
Step-by-step explanation:
discretion data is something that will never change
continous data is data that will continue to become either larger or smaller
discret = ticket sales, number of employees
continuous = age,height
Which function has a domain of (-1, ∞) and a range of (-∞, ∞)?
O A. f(x) = log₂x - 1
OB. f(x) = log₂ (x-1)
C. f(x) = log₂(x + 1
D f(x) = log₂ x+ 1
The two essential characteristics of functions are domain and range. Function has a domain of (-1, ∞) and a range of (-∞, ∞), f(x) = log₂x - 1.
What is domain and range?Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range.
A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavor will be provided. As a result, domain depicts the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a Coke machine won't give you a cheeseburger. As a result, range refers to potential outputs, or in this case, soda tastes in machine. Let's discover how to graph and determine domain and range of a given function.
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Select the expression that is equivalent to (3d¹)²
6d6
A
9d8
B
9d6
C
3d8
D
The equivalent expression of (3d^4)² is 9d^8. Option B
What are algebraic expressions?Algebraic expressions are defined as expressions made up of terms, constants, factors, coefficients and variables.
They also consist of some mathematical operations, such as;
AdditionSubtractionMultiplicationParenthesesBracketDivision, etcWhat are equivalent expressions?Equivalent expressions are defined as expressions that have the same solution but usually differ in the arrangement of the values.
Given the expression;
(3d^4)²
Now, let's expand the bracket, we have
(3)²(d)^4×2
Find the squares
9d^8
Thus, the expression is 9d^8
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The complete question:
Select the expression that is equivalent to (3d^4)²
What is the expression in factored form? x 2 + 13 x + 42
The expression in factored form for x² 13 x + 42 will be (x + 6)(x + 7).
What is an expression?It should be noted that an expression is simony used in Mathematics to show the relationship between the variables that are expressed.
In this case, the expression in factored form for x² 13 x + 42 will be:
x² + 13x + 42
x² + 6x + 7x + 42
x(x + 6) + 7(x + 6)
(x + 6)(x + 7)
The expression is (x + 6)(x + 7).
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The Smithsonian Jellyfish Tank that regularly sells for $24.99 was on sale for 15% off with a special code. How much would be saved by using the code?
The saved amount after selling the tank and by using the code is $21.24.
What is selling price?
The selling price is the amount in the form of extra charges which was decided by the shopkeepers for the different commodities. The cost spent by the shopkeeper for the purchase is the cost price. And for profit selling price should be more than the cost price.
According to the question, the given parameter is as written below:
The selling price of the Jellyfish tank is: $24.99
And the discount with special code is: 15 percent
The calculated money saved by using the special code is:
Discount Amount = (24.99 x 15)/100 = 3.7485
Saved money = $24.99 - $ 3.7485 = $ 21.2415 ≅ $ 21.24
Hence, the saved amount after selling the tank and by using the code is $21.24.
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Consider the quadratic function f(x) =x - 5x + 6.
What are the values of the coefficients and constant in the function?
The values of the coefficients and constant in the quadratic function are a = 1, b = -5, and c = 6, where a and b are coefficients and c is the constant.
What are quadratic functions?A polynomial function with one or more variables, where the greatest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the highest degree term in a quadratic function is of the second degree. The formula for a quadratic equation is ax² + bx + c = 0, where a and b are referred to as the coefficients of x² and x, respectively. The function's constant is the c term.Given quadratic function f(x) = x² - 5x + 6.
The values of the coefficients and constant in the function are
a = 1
b = -5
c = 6
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