Answer:
vertex = (4, - 25 )
Step-by-step explanation:
Given a quadratic function in standard form : f(x) = ax² + bx + c : a ≠ 0
The the x- coordinate of the vertex is
[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 8x - 9 ← is in standard form
with a = 1, b = - 8, thus
[tex]x_{V}[/tex] = - [tex]\frac{-8}{2}[/tex] = 4
Substitute x = 4 into f(x) for corresponding value of y
f(4) = 4² - 8(4) - 9 = 16 - 32 - 9 = - 25
vertex = (4, - 25 )
Answer:
vertex is (4,-25)
Step-by-step explanation:
[tex]f(x) = x^2 - 8x - 9[/tex]
To find out the vertex we use formula
[tex]x=\frac{-b}{2a}[/tex]
From the given f(x), the value of a=1, b=-8 and c=-9
Plug in the values in the formula
[tex]x=\frac{-(-8)}{2(1)}[/tex]
x=4
Now find the value of y
plug in 4 for x in f(x)
[tex]f(4) = 4^2 - 8(4)- 9=-25[/tex]
The value of y is -25
The vertex is (4,-25)
Sadie has a cousin Nanette in Germany. Both families recently bought new cars and the two girls are comparing how fuel efficient the two cars are. Sadie tells Nanette that her family’s car is getting 42 miles per gallon. Nanette has no idea how that compares to her family’s car because in Germany mileage is measured differently. She tells Sadie that her family’s car uses 6 liters per 100 km. Which car is more fuel efficient? Please explain everything
Sadie’s family’s car is slightly more fuel efficient than Nanette’s family’s car.
Answer:
Sadie's car is more fuel efficient.
Step-by-step explanation:
Consider the provided information.
For comparison both quantity should be same. So convert miles per gallon into kilometers per liter.
Sadie tells her family's car is getting 42 miles per gallon.
To convert miles per gallon into liters per km use the formula:
1 miles per gallon = 0.425144 kilometers per liter
Multiply both the sides by 42.
1×42 miles per gallon = 0.425144×42 kilometers per liter
42 miles per gallon = 17.856 kilometers per liter
That means Sadie's car millage is 17.856 kilometer per liter.
Nanette tells Sadie that her family’s car uses 6 liters per 100 km.
6 Liters = 100 km
Divide both sides by 6.
1 Liters = 16.66..
That means Nanette's car millage is approximately 16.67 kilometer per liter.
Hence, Sadie's car is more fuel efficient.
simplify by distributing and combining like terms
Answer: -9x + 24
Step-by-step explanation:
To do this, we need to multiply each term by -3
So -3(3x -8) turns into
-9x + 24
That’s the answer!
many trees have concentric rings that can be counted to determine the trees age. each ring represents one years growth. a maple tree with a diameter of 12 inches has 32 rings. if the tree continues to grow at about the same rate, how many rings will the tree have when its diameter is 20 inches?
Answer:
adout 53 Years old
Step-by-step explanation:
2. = 6=12=32. 32/2= 16
5.3=16=32= 16/3=5.333...
5.3x10=S3.3
so adout 53 Years old
Based on the tree's current growth rate of 2.67 rings per inch, if it continued to grow at the same rate, a maple tree with a diameter of 20 inches would have around 53 rings.
Explanation:The tree's growth can be understood as the relation between its diameter and the number of its concentric rings. In this case, we know that a maple tree with a diameter of 12 inches has 32 rings. This means that the tree grows approximately 2.67 rings per inch (32 rings / 12 inches = 2.67 rings per inch). So, assuming the tree continues to grow at the same rate, when the tree's diameter is 20 inches, it should have around 53 rings (20 inches * 2.67 rings per inch =~ 53 rings).
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On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?
That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)
Answer:
Well ,lets see∉ if you add theose numbers togetherФ it maybe it he answe ris 4=67 *64 ---4 67x54 5xe4t4 6xStep-by-step
Answer:
if i see them it my be 5x6x7=76 6(*)665_+65x673 then add those toether then sub em 56-78-463=738
Step-by-step explanation:
what does x equal and explain how
Answer:
x = 32Step-by-step explanation:
[tex]\dfrac{x}{8}+2=6\qquad\text{subtract 2 from both sides}\\\\\dfrac{x}{8}+2-2=6-2\\\\\dfrac{x}{8}=4\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup^1\cdot\dfrac{x}{8\!\!\!\!\diagup_1}=(8)(4)\\\\x=32[/tex]
I need help with this
#3 is 40 degrees Clockwise.
The age of a woman is 4 times the age of her daughter. 5 yrs hence,the age of the woman will be 3 times the age of her daughter. Find the present age of the daughter in yrs.
Answer:
10
Step-by-step explanation:
If W is the present age of the woman and D is the present age of the daughter, then:
W = 4D
W + 5 = 3(D + 5)
Substituting the first equation into the second:
4D + 5 = 3(D + 5)
4D + 5 = 3D + 15
D = 10
The daughter is 10 years old.
Find the value of x if R is the midpoint of QS QR=5x-7 and QS=96
Answer: The required value of x is 11.
Step-by-step explanation: Given that R is the midpoint of the line segment QS, where
QR=5x-7 and QS=96.
We are to find the value of x.
Since the point R is the midpoint of the segment QS, so we must have
[tex]QR=SR=\dfrac{1}{2}QR\\\\\\\Rightarrow QR=\dfrac{1}{2}QS\\\\\\\Rightarrow 5x-7==\dfrac{1}{2}\times96\\\\\Rightarrow 5x-7=48\\\\\Rightarrow 5x=48+7\\\\\Rightarrow 5x=55\\\\\Righatrrow x=\dfrac{55}{5}\\\\\Rightarrow x=11.[/tex]
Thus, the required value of x is 11.
If R is the midpoint of QS, then x = 11.
We have,
If R is the midpoint of QS, then QR is equal in length to RS.
Therefore:
QR = RS
Given that QR = 5x - 7 and QS = 96, we can set up an equation:
5x - 7 = QS/2
Now, plug in the value of QS:
5x - 7 = 96/2
5x - 7 = 48
Add 7 to both sides:
5x = 48 + 7
5x = 55
Now, divide both sides by 5 to isolate x:
x = 55 / 5
x = 11
So, the correct value of x is 11.
Thus,
If R is the midpoint of QS, then x = 11.
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Jaclyn used the slope formula to find the slope of the line in which step did Jaclyn make an error?
through the points given in the table.
In step 1, she switched the x and y values in point
2
In step 2, she used the wrong formula for slope
In step 3, she simplified the slope incorrectly
Jaclyn did not make an error
1. Point 1: (0,4); Point 2: (-3,0)
2. Slope V2 -6 - 4
3. Slope = 3
Answer:
Jaclyn did not make an error
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](0,4)\ B(-3,0)[/tex]
Substitute the values
[tex]m=\frac{0-4}{-3-0}[/tex]
[tex]m=\frac{-4}{-3}[/tex]
[tex]m=\frac{4}{3}[/tex]
therefore
Jaclyn did not make an error
Answer:
Jaclyn did not make error
Step-by-step explanation:
Step 1: He has taken two points from the given table.
(0, 4) and (-3, 0)
Step 2: Slope formula = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Step 3: Now plug in [tex]x_1 = 0, y_1 = 4, x_2 = -3 and y_2 = 0[/tex] in the above formula.
Slope = [tex]\frac{0 -4}{-3 - 0}[/tex]
Slope = [tex]\frac{-4}{-3} = \frac{4}{3}[/tex]
When we divide two negative numbers, the result will be in positive.
So, Jaclyn didn't make a single error.
Solve the inequality for x 24x > 18(4x – 6) – 30
Answer:
The required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]24x>18(4x-6)-30[/tex]
We need to solve the above inequity of x.
Open the parentheses.
[tex]24x>18\times 4x-18\times 6-30[/tex]
[tex]24x>72x-108-30[/tex]
[tex]24x>72x-138[/tex]
Subtract 72x from both sides.
[tex]24x-72x>72x-138-72x\\-48x>-138[/tex]
Multiply both sides by -1 and reverse the inequality.
[tex]\left(-48x\right)\left(-1\right)<\left(-138\right)\left(-1\right)[/tex]
[tex]48x<138[/tex]
Divide both side by 48.
[tex]x<\frac{23}{8}[/tex]
Hence, the required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
If the expression x-3 has a value of -5,then which of the following represents the value of 3x-9
Answer:
-15
Step-by-step explanation:
Italics by itself are comments, italics and underlines are helpful rules, bold highlights little facts.
x-3=-5 : since the expression 'x-3' is being assigned the value '-5'
We then isolate or leave the variable 'x' on one side, usually the left-hand side and move all constants (numbers without letters attached such as 3, 4, 5..etc.) and variables (letters such as x, y, a, b..etc.) that do not have 'x', to the right-hand side of the equality symbol (=). This also includes terms such as 5x, -2y, 50z..etc.
(Remember that the opposite of multiplication is division and vice versa and the opposite of addition is subtraction and vice versa).
To do that, we add 3 to both sides of the equation, because the opposite of subtraction is addition (in this case 3 is being subtracted by x, therefore in order to cancel 3 on the left, we do the opposite of the operation). By doing this, we effectively cancel 3 on the left and bring it to the right-hand side. After all, 3 cannot be in two places at once (well not in this equation).
x=-5+3 which is equal to -2.
Hence, x=-2
Now that we know what 'x' is we can work on the other expression: 3x-9
Substitute the value for 'x' (-2 is what we got) into the 'x' in the expression.
3(-2)-9=?
(Remember that a positive number multiplied by a negative number will ALWAYS be a negative number. In other words, (+) × (-) = (-). Yes, this also includes a negative number multiplied by a positive number).
Therefore, 3×(-2) will equal -6.
-6-9=-15
Hence, 3x-9=-15.
To make sure your answer is correct, do the equation backwards. Add 9 to -15 which would then give you -6.
Here's how that looks: 3x-9 (+9)= -15 (+9).
You would then be left with 3x=-6.
If you remembered the rule typed previously, I said in order to isolate 'x' we do the opposite of the operation. 3x means '3' multiplied by 'x', therefore the opposite of multiplication is division:
3x(÷3)=-6(÷3) ----> 3 divided by 3 equals 1. Anything multiplied by 1 will be equal to itself (x*1= x)
(An asterisk can also symbolise multiplication).
Therefore when 3x is divided by 3, the constants would cancel each other out, 1 would be left looking like this: 1x=... and 1x is the same as x by itself.
-6 divided by 3 is equal to -2 (a positive divided by a negative will always be negative and vice versa).
Hence, x=-2.
The value of the expression 3x - 9 will be - 15 if x - 3 is -5.
What is a numerical expression ?A numerical expression is in the form of numbers and their operations.
According to the given question the expression x-3 has a value of -5.
We have to determine the value of 3x - 9.
Let us solve for x in the equation
x - 3 = -5.
x = -5 + 3.
x = -2.
Putting this value of x in 3x - 9 would result in
3(-2) - 9
= -6 -9
= -15.
This can also be done in a different approach
x - 3 = - 5.
3x - 9 will be if we observe the equation has been multiplied by 3
3x - 9.
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Use A=12bh to find the height of a triangle that has an area of 180 in^2 and a base of 20 in.
Answer:
18 in
Step-by-step explanation:
A=1/2 bh
180 = (20* h)/2
180*2 = 20*h
(180*2)/20 = h
360/20 = h
18 in = h
what is 2 + 2 - 4 + 1500 x 2 - 300 - 2700 equal to?
What is the answer to this?
Answer:photo math
Step-by-step explanation:
Fourteen is 20% of
please help me in need
Answer:
14 / .20 = x
.20 x = 14
x = 14 / .20
x = 70
DOUBLE - CHECK
20 % of 70 = .20 * 70 = 14
Step-by-step explanation:
b. You used 13 gallons when you traveled 342 miles. How many miles did you
travel per gallon?
Answer:
26.307 miles per gallon
Step-by-step explanation:
Divide the miles traveled by the number of gallons used.
In this case, divide 342 by 13 to get the answer of 26.307 miles per gallon.
Using the numbers -4, 10, 8, 2, -3, -5, create two expressions that
equal 6.
The two expressions should be [tex]-4 \div 2 + 8 = 6\ and\ (10 \times -3) \div -5 = 6[/tex].
Given that,
The numbers are -4, 10, 8, 2, -3, -5.We need to develop two expressions that are equivalent to 6.Based on the above information, the calculation is as follows:
[tex]-4 \div 2 + 8 = 6\[/tex]
6 = 6
And,
[tex](10 \times -3) \div -5 = 6[/tex]
6 = 6
Therefore we can conclude that the two expressions should be [tex]-4 \div 2 + 8 = 6\ and\ (10 \times -3) \div -5 = 6[/tex].
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Two expressions using the given numbers that equal 6 are: Expression 1: 10 - 2 - (-3) + (-5) and Expression 2: 10 - 2 + 8 - (-4) - 5. The calculations are done using the order of operations (PEMDAS).
Explanation:The task is to create two mathematical expressions using the numbers -4, 10, 8, 2, -3, and -5, which result in 6. We can accomplish this by utilizing basic arithmetic operations such as addition, subtraction, multiplication, or division. The important thing is making sure all operations adhere to the Order of Operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Here are the two ways you could form expressions:
Expression 1: 10 - 2 - (-3) + (-5). The calculation goes as follow: 10 minus 2 equals 8, then we subtract -3 which is the same as adding 3, so 8 plus 3 equals 11, and finally we subtract 5 to get 6.Expression 2: 10 - 2 + 8 - (-4) - 5. Similarly, you calculate 10 minus 2 equals 8, plus 8 equals 16, add -4 (which is the same as subtracting 4) results in 12, and subtracting 5 gives us 6.Learn more about Mathematical Expressions here:https://brainly.com/question/30350742
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7. Find the product (3x + 2)(4x2 – 5x + 7).
Answer:
12x³ - 7x² + 11x + 14
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
3x(4x² - 5x + 7) + 2(4x² - 5x + 7) ← distribute both parenthesis
= 12x³ - 15x² + 21x + 8x² - 10x + 14 ← collect like terms
= 12x³ - 7x² + 11x + 14
Factor -4x + 24 - 4x^2
Answer:
- 4(x + 3)(x - 2)
Step-by-step explanation:
Given
- 4x + 24 - 4x² ← rewrite in standard form, that is
- 4x² - 4x + 24 ← factor out - 4 from each term
= - 4(x² + x - 6) ← factorise the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, hence
x² + x - 6 = (x + 3)(x - 2), and
4x² - 4x + 24 = - 4(x + 3)(x - 2)
Plz help me show the work plz
Answer:
all work is shown and pictured
What is the difference between a day and a line segment
Hello!
I do believe you meant to say:
"What is the difference between a ray and a line segment?"
The difference between a ray and a line segment is:
A ray has one endpoint and continues in one direction. a ray is infinite
A line segment has two endpoints. a line segment is finite
I hope this helps, and have a nice day!
Please answer this correctly
The answer would be Josh.
Use the graph to find the coordinates of each vertex in triangle ABC. is the coordinate of Point A. is the coordinate of Point B. is the coordinate of Point C.
Answer:
Point A-
(-2, 3)
Point B- (2, 4)
Point C- (0, -1)
Correct answers from edge 2022 :)
(-2, 3)
(2, 4)
(0, -1)
Calculating Profit Using this table, calculate the profit at each level of bicycle production. One bike: -$ Two bikes: $ Three bikes: $ Four bikes: $ Five bikes: $ Six bikes: $ Seven bikes: $
Answer:
One bike: -$
30
Two bikes: $
3
Three bikes: $
40
Four bikes: $
70
Five bikes: $
90
Six bikes: $
90
Seven bikes: $
80
Step-by-step explanation:
trust me:)
The profit gotten at each level of production of the bicycles are respectively; -$30, $3, $40, $70, $90, $90, $80
How to Calculate Profit from production
From the attached table, we see three columns showing respectively;
Column 1; Units of bicycles produced per day
Column 2; Total Cost of the Units of bicycles produced per day
Column 3; Total revenue from the sale of the units of bicycles produced per day.
Now, to find the profit we will just subtract the cost of producing the given number of units from the total revenue from the sale of that specific unit produced.
For the level of 1 bicycle produced; Profit = $50 - $80 = -$30
For the level of 2 bicycles produced; Profit = $100 - $97 = $3
For the level of 3 bicycles produced; Profit = $150 - $110 = $40
For the level of 4 bicycles produced; Profit = $200 - $130 = $70
For the level of 5 bicycles produced; Profit = $250 - $160 = $90
For the level of 6 bicycles produced; Profit = $300 - $210 = $90
For the level of 7 bicycles produced; Profit = $350 - $270 = $80
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The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V and five-sevenths represent?
the radius of the rubber ball when the volume equals five-sevenths cubic feet
the volume of the rubber ball when the radius equals five-sevenths feet
that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet
Answer: v[5/7] represents the volume of air inside a rubber ball with radius 5/7 units, such that
Step-by-step explanation:
Given: The volume of air inside a rubber ball with radius r can be found using the function.
Here volume is a dependent variable on radius (independent variable).
Therefore, the value of v[5/7] represents the volume of air inside a rubber ball with radius 5/7 units.
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Answer:
we know that
The volume of a sphere (rubber ball) is equal to
V = 4/3pi r^3
where r is the radius of the sphere (rubber ball)
The volume in function notation is equal to
V(r) = pi r^3
in this problem we have
V(5/7)
that means
The radius of the rubber ball is 5/7 ft and the volume of the rubber ball is V(5/7) ft^3
therefore, the answer is the option B
the volume of the rubber ball when the radius equals 5/7 feet
Two minor league baseball players got a total of 390 hits. Washington had 16 more hits than Sanchez. Find the number of hits for each player.
Washington had
hits. Sanchez had
hits.
Answer:
Sanchez had 179 hits, while Washington had 211 hits. Hope this helps!
Final answer:
To solve the problem, we set up two equations: W = S + 16 and W + S = 390. By substituting the first equation into the second, we found that Sanchez had 187 hits, and Washington had 203 hits.
Explanation:
The question involves determining the number of hits for each player given the total number of hits and the difference in hits between the two players. We can set up a system of equations to solve for the number of hits for each player. Let's denote the number of hits by Washington as W and the number of hits by Sanchez as S.
According to the problem, we have two relationships:
Washington had 16 more hits than Sanchez: W = S + 16
The total number of hits is 390: W + S = 390
We can substitute the first equation into the second to solve for S.
S + (S + 16) = 390
S + S = 390 - 16
2S = 374
S = 374 / 2
S = 187
Now we plug the value of S back into the first equation to solve for W:
W = 187 + 16
W = 203
Therefore, Washington had 203 hits and Sanchez had 187 hits.
What is the value of cos-1(-sqrt3/2)?
Answer:
The Correct Answer is C. 5pie/6
Step-by-step explanation:
Plato answer
The value of the inverse trigonometric function of the cosine function is [tex]\text{cos}^{-1}(-\frac{\sqrt{3} }{2} )=\frac{5\pi }{6}[/tex].
It is required to find the value of the inverse trigonometric function of the inverse cosine function:
[tex]\text{cos}^{-1}(-\frac{\sqrt{3} }{2} )[/tex]
It is known that:
[tex]\text{cos}^{-1}(-x)=\pi -\text{cos}^{-1}(x)[/tex]
Here, [tex]x=-\frac{\sqrt{3} }{2}[/tex].
Substitute the value of x to the result.
[tex]\text{cos}^{-1}(-\frac{\sqrt{3} }{2} )=\pi -\text{cos}^{-1}(\frac{\sqrt{3} }{2} )[/tex]
It is known that:
[tex]\text{cos}^(\frac{\pi }{6} )=\frac{\sqrt{3} }{2}[/tex]
So, [tex]\text{cos}^{-1}(\frac{\sqrt{3} }{2} )=\frac{\pi }{6}[/tex].
So, the value can be written as:
[tex]\text{cos}^{-1}(-\frac{\sqrt{3} }{2} )=\pi -\frac{\pi }{6}[/tex]
[tex]=\frac{6\pi -\pi }{6}[/tex]
[tex]=\frac{5\pi }{6}[/tex]
Hence, the value of the function is [tex]\frac{5\pi }{6}[/tex].
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BRAINLIEST PLUS 100 POINTS
Please show full working out and draw a neat diagram for question five and also note that this is trigonometry
Correct answers only please ;)
Thank you in advance :)
The exact answer is 4√2 + 4
The decimal answer is 9.6568 ( round the answer as needed.)
See the attached picture:
42 students arrived at the school dance after it started. in all 78 students attended. write and solve an equation to find how many students arrived at the dance before it started. plz help right when you see it!!!
Answer:
The answer is 36
Step-by-step explanation:
we know 42 students arrived after the dance started and 78 arrived in total. You have to subtract 42 from 78. how I remember this: part+part=whole whole-part=part
The sum of Chris and Mike’s scores on a math quiz is 39. Mike’s score is twice the sum of Chris’ score and 3. Find each student’s quiz score.
Answer: c=11, m=28
Step-by-step explanation:
c= Chris's score
m= Mike's score
c+m=39 we know from the equation that their scores
add up to 39, so this equation is a good starting
point.
c+2(c+3)=39 we also know that Mike's score is twice the sum of Chris's
score and 3 so we can substitute that in for his score.
now we can solve.
c+2c+6=39 distribute
3c+6=39 combine like terms
-6 -6
3c=33 addition property of equality
÷3 ÷3
c=11 multiplication property of equality
Now that we know Chris's score, we simply substitute that number in in our simple equation for earlier to find Mike's score.
11+m=39 substituted in 11 for c
-11 -11
m=28 addition property of equality
There you go! Don't worry, I had a lot of trouble with these types of problems too. That's why I'm so good at them now Hope this helps!