An equation of the quadratic function in standard form is equal to -2x² - 7x - 6 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-6 = a(-3)² + b(-3) + c ⇒ -6 = 9a - 3b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
-2 = a(-1)² + b(-1) + c ⇒ -2 = a - b + c .......equation 3.
From eqn. 2, we have:
c = -4a + 2b .....equation 4.
Substituting eqn. 4 into eqn. 1 and 3, we have:
-2 = a - b - 4a + 2b ⇒ -2 = -3a + b
-6 = 9a - 3b - 4a + 2b ⇒ -6 = 5a - b
By using the elimination method, we have:
-8 = 2a
a = -4
For the value of b, we have:
-2 = -3a + b
b = -2 + 3a
b = -2 + 3(-4)
b = -2 - 12
b = -14
For the value of c, we have:
c = -4a + 2b
c = -4(-4) + 2(-14)
c = 16 - 28
c = -12.
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-4x² - 14x - 12 = 0
-2x² - 7x - 6 = 0
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estimate. i need help
Answer:
350'000
Step-by-step explanation:
The real # is 369,852, so 350,000 is closest to all the other options.
I need to find the c intercept and write the equation
The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.
As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.
We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:
[tex]C=m\cdot t+b[/tex]Where (t,C) is any point on the line, m is the slope and b is the C-intercept.
By replacing the know values we can solve for b:
[tex]\begin{gathered} 0=-4\cdot30+b \\ 0=-120+b \\ \text{Add 120 to both sides} \\ 0+120=-120+b+120 \\ 120=b \end{gathered}[/tex]Therefore,
4(5x - 2) = 2(9x + 3)
Answer: x = 7
Explanation - 4(5x-2)=2(9x+3)
20x-8=18x+6
20x-18x=6+8
2x=14
x=14÷2
x=7
Hello there!
Here we need to solve for x.
The first thing that we're going to do is this:
Expand both sides by using the distributive property.[tex]\implies\boldsymbol{4(5x-2)=2(9x+3)}[/tex]
[tex]\implies\boldsymbol{20x-8=18x+6}[/tex]
Next, add 8 to both sides.[tex]\implies\boldsymbol{20x=18x+14}[/tex]
Then, subtract 18 from both sides.[tex]\implies\boldsymbol{20x-18x=14}[/tex]
[tex]\implies\boldsymbol{2x=14}[/tex]
Lastly, divide both sides by 2.[tex]\implies\boldsymbol{x=7}[/tex]
Therefore x=7. I hope this helps you, feel free to comment if you have any queries :)
Identify the Vertex. Let g be a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of. (Show Work)
The g graph exhibits a four-fold vertical stretch.
The graph of f (x)=[tex]x^{2}[/tex] is translated up to two units, then reflected in the X-axis.
The rule for g.
Identify the vertex
The g graph exhibits a four-fold vertical stretch.
=> g = 4f(x) (x)
an X-axis reflection
=> g = - 4f(x) (x)
(X-axis reflection of (X, Y) is (x , - y)
a conversion two units higher
=> g = -4f(x) + 2
f(x) = x²
=> g = - 4x² + 2
Vertex is at ( 2, 0)
What is a vertical stretch?
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
How to vertically stretch a function?
When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:
Ensure that the values for x remain the same, so the base of the curve will not change.
This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.
Take note of the new critical points, such as the new maximum point of the graph.
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Help with this problem pls
nswer:
[tex](f\circ g)(x)\text{ = 4x}^2+26x+29[/tex]Explanation:
ere, we want to solve the given composuite function
What we have to do is to replace the x in f(x) with the entirety of g(x)
We have that as:
[tex]\begin{gathered} (f\circ\text{ g\rparen\lparen x\rparen = f\lparen g\lparen x\rparen\rparen} \\ =\text{ f\lparen2x+9\rparen} \end{gathered}[/tex]Now, we replace x in f(x) with 2x+9 as stated
We have that as:
[tex]\begin{gathered} f(2x+9)\text{ = \lparen2x+9\rparen}^2-5(2x+9)\text{ - 7} \\ f(2x+9)\text{ = 4x}^2+36x+81-10x-45-7 \\ f(2x+9)\text{ = 4x}^2+36x-10x+81-45-7 \\ f(2x+9)\text{ = 4x}^2+26x+29 \end{gathered}[/tex]K
Solve.
(8v+5)(3v-9) = 0
and Relative Change
The value of a car dropped from $23,800 to $22,300 over the last year. Determine the absolute
and relative change in this sitation.
Absolute Change: This car's value decreased by $
Round your answer to the nearest dollar.
Relative Change: This car's value decreased by
Round your answer to the nearest tenth of a percent.
last year.
% last year.
The absolute change or the car's value decreased by $1500.
The relative change: The value of the car decreased by 6.302 %.
The car's value dropped from $23,800 to $22,300 over the last year.
So, the initial price of the car is I = $23,800, and the final value of the car after a year is F = $22,300.
Therefore,
The Absolute change will be:
= I - F
= $23,800 - $22,300
= $1500
Hence, the car's value decreases by $1500.
Now, the relative change is the percentage by which the price decreased over the year.
So,
As the price decreased by $1500.
Let x be the relative change.
Then,
$ 23,800 × x/100 = $1500
238x = 1500
x = 6.302
Hence, the car's value decreased by 6.302% last year.
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please help me with this problem
answer:
[tex]\frac{-c-d}{d+2c}[/tex]the third one
please help me solve this
Answer:
a: undefined
b: -15
c: 20
d: 25
Step-by-step explanation:
a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined
b: look at x 0 on graph, there is open dot at -15 meaning the limit is there
c: look at x -7 on graph, there is open dot at 20 meaning the limit is there
d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)
What is the probability of theft occurring in a room if it is left unlocked if 0.75 of dorm rooms are left unlocked, 3% of dorm rooms are affected by theft, and 84.2% of thefts occur in unlocked rooms
The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%
How to find the probability?To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room
The probability of an unlocked room being robbed is therefore:
= 0.75 x 0.03 x 0.842
= 0.0225 x 0.842
= 0.018945
= 1.89%
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A real estate agent working in a large city believes that, for three-bedroom houses, the selling price of the house decreases by approximately $2,000 for every mile increase in the distance of the house from the city center. To investigate the belief, the agent obtained a random sample of 20 three-bedroom houses that sold in the last year. The selling price, in thousands of dollars, and the distance from the city center, in miles, for each of the 20 houses are shown in the scatterplot. The table shows computer output from a regression analysis of the data.
(a) Describe the relationship between distance from city center and selling price.
(b) Find the linear regression equation. Interpret the slope and y-intercept in context.
) One house that was 11 miles from city center had a residual of -2.962. What was the actual selling price of the home?
The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275
How to determine the relationship?The given parameter is in the attached figure
Also from the question, we have:
House price decreases by approximately every mile
The above implies that the relationship is an approximately linear relationship
How to find the linear regression equation.From the table, we have
Coefficient constant = 301.7
Coefficient distance = -2.158
This means that
y-intercept = 301.7
Slope = -2.158
So, the equation is
y = y-intercept + slope * x
This gives
y = 301.7 - 2.158x
The interpretation of the slope and y-intercept in context are:
Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7
The actual selling price of the homeHere, we have
Residual = -2.962
Miles = 11
This means that
Predicted price = 301.7 - 2.158 * 11
Evaluate
Predicted price = 277.96
So, we have
residual = actual - predicted
This gives
actual = residual + predicted
So, we have
actual = -2.962 + 277.96
Evaluate
actual = 275
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The demand equation for a certain product is given by p=120-0.015x, where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R=xp.
Determine prices p that would yield a revenue of 7110 dollars.
Lowest such price = (Blank) dollars.
Highest such price = (Blank) dollars.
Show your work!
No incorrect answers!
No nonsense answers!
No spam answers!
Thanks!
The prices p that would yield a revenue of 7110 dollars are;
Lowest price = $0.895
Highest price = $119.105
How to solve demand equation?
We are told that the total revenue obtained by producing and selling x units is given by; R = xp.
Now, we are told that the demand equation for a certain product is given by p = 120 - 0.015x.
where;
p is the unit price (in dollars) of the product.
x is the number of units produced.
At a revenue of $7110, we will have;
(120 - 0.015x)x = 7110
120x - 0.015x² = 7110
0.015x² - 120x + 7110 = 0
Using quadratic equation calculator, we have;
x = 59.695 and 7940.305
Thus;
Lowest price = 120 - 0.015(7940.305) = $0.895
Highest price = 120 - 0.015(59.695) = $119.105
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Let A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)} what type of function is this? Give reason
It is observed that f is a subset of A×B
What is subset ?A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.
Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}
A={1,2,3}
B={7,8,9,10}
A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}
f={(1,7),(2,9),(3,8)}
A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B
It is observed that f is a subset of A×B
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What is the reciprocal of 3 7/8
The reciprocal of 3 7/8 is 8/31.
To find the reciprocal of a number, we invert the fraction by swapping the numerator and denominator.
Let's calculate the reciprocal of 3 7/8.
First, we need to convert the mixed number into an improper fraction. To do this, we multiply the whole number (3) by the denominator (8) and add the numerator (7). This gives us:
3 7/8 = (3 x 8 + 7) / 8 = 31/8
Now, to find the reciprocal, we invert the fraction:
Reciprocal of 31/8 = 8/31
Therefore, the reciprocal of 3 7/8 is 8/31.
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Please help
The second angle of a triangle is 104 more than the first angle. The third angle is two times the first. Find
the three angles.
First angle:
Second angle:
Third angle:
What is the value of x? The value of x is type your answer... 8xº (3x + 35)° (4x + 25)°
A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.
The number of different samples possible when the shopper selects a sample of 4 apples from the bag is 126.
How to calculate the combinations?Combinations are a method of calculating the overall results of an event where the order of the results is irrelevant. From the information, the bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.
It should be noted that the question has to do with a combination. The number of different samples that are possible will be:
Number of apples = 9
Number to be selected = 4
= ⁹C₄
= 9! / (9 - 4)! 4!
= 9 × 8 × 7 × 6 / 4 × 3 × 2
= 126
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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. How many different samples are possible?
x/25.75=sin47.5 degrees
The value of x in the equation is 18. 98
What are trigonometric identities?Trigonometric identities are defined as mathematical equations relating to several trigonometric functions, holding true for all the values in the domain of the functions.
The several types of trigonometric identities includes;
sinecosinetangentcotangentsecantcosecantIt is important to note that the trigonometric ratios for major identities are;
sine = opposite/hypotenuse
tangent = opposite/adjacent
cosine = adjacent/hypotenuse
Given the equation;
x/25.75=sin47.5 degrees
Take the following steps to determine the value of 'x'
We have;
cross multiply
x = sin47.5 × 25. 75
Find the value of sin 47. 5 and substitute the value
x = 0. 7373 × 25. 75
multiply through
x = 18. 98
Hence, the value of x is 18. 98
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The complete question:
x/25.75=sin47.5 degrees
Find the value of x
Given a piece of metal with a mass of 124 grams and a volume of 21 cubic centimeters (cm^3) what is its density? Use the correct formula to obtain your answer. You may work on a separate piece of paper.
13.6 g/cm^3
88 g/cm^3
5.9 g/cm^3
0.21 g/cm^3
We need to know about density to solve this problem. The density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex], so option (c) is the correct answer.
Density is a substance's mass per unit volume. The symbol commonly used for density is ρ. Density can be calculated by dividing the mass by volume. In this question we know that mass of the metal piece is 124 grams and the volume is given to be 21 cubic centimeters. The density can be calculated by dividing the mass by volume of the metal piece.
density =mass/ volume= 124/21=5.90 g/[tex]cm^{3}[/tex]
Therefore the density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex] , so option (c) is the correct answer.
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On a blueprint, a guest bedroom has dimensions 3 cm
by 5 cm. If the blueprint is drawn using the scale of
½ cm = 2 ft, what is the actual AREA of the guest
bedroom?
A. 12 square ft
B. 20 square ft
C. 240 square ft
D. 15 square ft
The actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.
What is dimension?The minimal amount of coordinates required to specify any point within a mathematical space (or object) is known as the dimension in physics and mathematics. As a result, a line has one dimension (1D), since only one coordinate is required to specify a point on it, such as the point at 5 on a number line.
A surface, like the perimeter of a cylinder or sphere, has two dimensions (2D) because two coordinates are necessary to specify a point on it. For instance, both a latitude and a longitude are necessary to pinpoint a point on the surface of a sphere.
The dimensions are 3cm by 5 cm meaning length = 5cm and breadth = 3cm
Given that ½ cm = 2 ft, that is
1 cm = 4 ft
Using the conversion method
3 cm = 3 × 4
= 12 ft
5 cm = 5 × 4
= 20 ft
Actual area = 20 × 12 ft
= 240 square ft
Thus, the actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.
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When 3x² + 7x - 6 + 2x³ is written in
standard form, the leading coefficient is
(1) 7
(2) 2
(3) 3
(4) -6
Answer:
Your leading coefficient is 2
Jared lost a total of $56.00 on his investment over 7 months. He lost an equal amount of money each month. Jared used this equation to figure out how much money he lost each money. -56.00/7=-8.00 what does -56.00/7=-8.00 tell us?
Answer:
I'm not so very sure but I really need points
Answer asap what’s the correct answer answer now for brainlis5?
Answer: Smooth muscle contractions
What is the slope of a line perpendicular to the line whose equation is 3x-6y=144
Answer: 1/2
Step-by-step explanation:
If we have an equaton in a standard form, that is y = mx + b, our slope is m (the coefficient of x). So, let's transform 3x - 6y = 144 into the standard form.
3x - 6y = 144
-6y = - 3x + 144
y = -3/(-6)x - 144/6
y = (1/2)x - 24
As I mentioned above, the slope is the coefficient of x. Here our slope is 1/2.
five more than the quotient of nine and three
Answer:
n / 9 + 5 = 3
Step-by-step explanation:
why is 25 a compiste number
Answer: 25 is divisible by 5, so it is composite
Step-by-step explanation:
the formula for finding the area of a rectangle is A=LWSolve this formula for LL=______if the length of a rectangle is 18 feet qnd the width is 9 inches. what is the area of the rectangle in units of square feet? _______ ft^2
1) Dividing the given formula by W we get:
[tex]\begin{gathered} \frac{A}{W}=\frac{LW}{W}, \\ \frac{A}{W}=L. \end{gathered}[/tex]2) We know that:
[tex]1in=\frac{1}{12}ft.[/tex]Therefore:
[tex]9in=9*\frac{1}{12}ft=\frac{3}{4}ft.[/tex]Then:
[tex]W=\frac{3}{4}ft.[/tex]Substituting W=3/4ft and L=18ft in the given formula we get:
[tex]A=(18ft)(\frac{3}{4}ft)=13.5ft^2[/tex]Answer:
1)
[tex]L=\frac{A}{W}.[/tex]2)
[tex]13.5ft^2.[/tex]DEEPER The scales shown are used to compare the weights of apples, tangerines, grapefruits, and bananas. How many tangerines
will balance one apple?
Justify your answer using a linear system. Let the weights of apples, tangerines, grapefruits, and bananas be represented by a, t,
g, and b respectively.
Equation for first picture:
Equation for second picture:
Equation for third picture:
4 Tangerines will balance 1 apple.
Given that
Weight of Apple is represented by: a
Weight of tangerine is represented by: t
Weight of Grapefruit is represented by: g
Weight of Banana is represented by: b
Consider 1st picture:
1 apple and 1 tangerine balance 1 grapefruit.
⇒ a+t = g ...(1)
Consider 2nd picture:
1 banana and 1 tangerine balance 1 apple.
⇒ b+t = a ...(2)
Consider 3rd picture:
2 grapefruits balance 3 bananas.
⇒ 2g = 3b
g = 1.5b ...(3)
The system of equations are:
First balance: a+t = g
Second balance: b+t = a
Third balance: g = 1.5b
Putting the value of g from equation (3) to equation (1), we get
a+t = 1.5b ...(4)
Now, putting the value of b from equation (2) to equation (4), we get
a+t = 1.5(a-t)
1.5a - 1.5t = a+t
0.5a = 2t
a = 4t
Hence, one apple is balanced by 4 tangerines.
Refer to the full question given below in the image.
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Write the equation of a Circle with the given information.Center: (-4,7) Point on the Circle: (8,-4)
Given:
Center of circle: (-4, 7)
Endpoint on the circle: (8, -4)
Let's write the equation of the circle with the given information.
Apply the equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
Center of circle: (h, k) ==> (-4, 7)
Radius = r
Substitute the values of (h, k) in the equation:
[tex]\begin{gathered} (x-(-4))^2+(y-7)^2=r^2 \\ \\ (x+4)^2+(y-7)^2=r^2 \end{gathered}[/tex]To find the radius, let's find the distance between the points (-4, 7) and (8, -4).
Apply the distance formula:
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]Given:
(x1, y1) ==> (-4, 7)
(x2, y2) ==> (8, -4)
Thus, we have:
[tex]\begin{gathered} d=\sqrt[]{(-4-7)^2+(8-(-4))^2} \\ \\ d=\sqrt[]{(-4-7)^2+(8+4)^2} \\ \\ d=\sqrt[]{(11)^2+(12)^2} \\ \\ d=\sqrt[]{121+144} \\ \\ d=\sqrt[]{265} \\ \\ d=16.3 \end{gathered}[/tex]Therefore, the radius is 16.3
Therefore, we have the equation of the circle as:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]ANSWER:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]please show all work
Domain and Range of Functions
Given a function y = f(x), the domain of f is
The range of f is the
We are given the function:
[tex]f(x)=\frac{1}{2x}-3[/tex]It's required to find the domain and range of the inverse function.
We must recall that, if the inverse function exists, its domain is the range of f, and its range is the domain of f.
Since f(x) is a rational function, it may not exist for the values of x where the denominator is 0.
Concretely, for x=0, the denominator is 0 and the function does not exist, thus the domain of f consists of every real number except x=0.
This can be written as (-∞,0) U (0,∞). This is also the range of the inverse function.
Now let's find the inverse function. We must solve for x the equation:
[tex]y=\frac{1}{2x}-3[/tex]Adding 3:
[tex]y+3=\frac{1}{2x}[/tex]Multiplying by x and dividing by y+3:
[tex]x=\frac{1}{2(y+3)}[/tex]Swapping letters:
[tex]y=\frac{1}{2(x+3)}[/tex]This is the inverse function of f.
Thus the domain of the inverse is:
-3-3
And the range:
Answer: Choice d