Answers
Answer:
In order from smallest to largest:
g(x)=(1,-2)
now, f(x) and h(x) would reach the same height, so from left to right on the graph, if plotting all vertices:
h(x)=(-2,2)
f(x)=(4,2)
Step-by-step explanation:
f(x)
f(x)=-2(x-4)^2+2
This is the vertex form of a quadratic equation: The formula used is f(x)=a(x-h)^2+k, where (h,k) is the vertex. In this case, 4 is h and 2 is k, so the vertex of this equation is (4,2).
g(x)
g(x)=5x^2-10x+7
To find the vertex of a quadratic equation in standard form, you first have to find the x-coordinate of the vertex using the formula, -b/2a. In this equation, a=5 and b=-10, so plug into the formula: -(-10)/2(5)=10/10=1, so the x-coordinate of the vertex is 1. Now to find the y-coordinate of the vertex by plugging in the x-coodinate for x in the equation: 5(1)^2-10(1)+7=5(1)-10+7=5-10+7=-5+7=-2, so your y-coordinate is -2. Therefore, your vertex for this equation is (1,-2).
h(x)
So, this quadratic function is in the form of a graph. The vertex of the graph is the maximum of minimum value of the graph, depending on whether the graph is positive or negative. In this graph, it is the maximum point, which is (-2,2).
Related Questions
How do I solve this equation 1x - 15 = 5x + 13
Answers
Answer:
x = -7
Step-by-step explanation:
This is a multi-step equation in algebra. We are expected to isolate the given variable and find the constant value that it is equal to. In order to do this, we can follow some steps:
1x - 15 = 5x + 13 Subtract 5x on both sides of the equation.
-4x - 15 = 13 Add 15 to both sides of the equation.
-4x = 28 Divide by -4 on both sides of the equation.
x = -7
You can input this value and make sure that the answer is correct.
1(-7) - 15 = 5(-7) + 13
-7 - 15 = -35 + 13
-22 = -22
-22 equals -22, so x = -7 is the solution to the equation.
Answer:
x= -7
Step-by-step explanation:
We are given the equation:
1x-15=5x+13
We want to solve for x. Therefore, we must isolate x on one side of the equation.
First, let’s move all the terms with variables to one side. Subtract 1x from both sides.
1x-1x-15=5x-1x+13
-15= (5x-1x)+13
-15=4x+13
Next, move all the constants, or terms without variables to one side. Subtract 13 from both sides.
-15-13=4x+13-13
-15-13=4x
-28=4x
Finally, divide both sides by 4. We should divide because x is being multiplied by 4 and the inverse of multiplication is division.
-28/4=4x/4
-28/4=x
-7=x
Let’s check our solution. Plug -7 in for x and solve.
1x - 15 = 5x + 13
1(-7) - 15 = 5(-7) + 13
-7-15=5(-7)+13
-22= 5(-7)+13
-22= -35+13
-22=-22
This checks out, so we know our solution is correct.
The solution to 1x - 15 = 5x + 13 is x= -7
ASAP!!! Please solve this problem!!!!
Answers
Answer:
[tex]\frac{4}{3}[/tex] x² - [tex]\frac{19}{9}[/tex] x + [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Given
(2x - [tex]\frac{5}{3}[/tex] )([tex]\frac{2}{3}[/tex] x - [tex]\frac{3}{2}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
2x([tex]\frac{2}{3}[/tex] x - [tex]\frac{3}{2}[/tex] ) - [tex]\frac{5}{3}[/tex] ([tex]\frac{2}{3}[/tex] x - [tex]\frac{3}{2}[/tex] ) ← distribute both parenthesis
= [tex]\frac{4}{3}[/tex] x² - 3x - [tex]\frac{10}{9}[/tex] x + [tex]\frac{5}{2}[/tex]
= [tex]\frac{4}{3}[/tex] x² - [tex]\frac{27}{9}[/tex] x - [tex]\frac{10}{9}[/tex] x + [tex]\frac{5}{2}[/tex]
= [tex]\frac{4}{3}[/tex] x² - [tex]\frac{37}{9}[/tex] x + [tex]\frac{5}{2}[/tex]
Simplify the expression. [(7−3)⋅2+6]⋅3 a 21 b 26 c 42 d 96
Answers
Answer:
42
Step-by-step explanation:
[(7-3)2+6]3... [(4)2+6]3...[8+6]3....14(3)=42
Answer:
It should be c 42.
Step-by-step explanation:
Because [(7-3)2+6]3
[(4)2+6]3
[8+6]3
[14]3
42
Sorry if it's long
Solve the equation. −3=h+8÷2 h=?
Answers
Answer:
h = -7
Step-by-step explanation:
8 ÷ 2 = 4Plug 4 in: -3 = h + 4Subtract 4 from each side, so it now looks like this: -7 = hI hope this helps!
Simplify (please show work if possible)
Answers
Answer: -6x^7
Step-by-step explanation:
2x^3 × (-3x^4)
=(2×-3) · (x^3 × x^4) ⇔ multiply the like terms
=-6 × [x^(3+4)] ⇔ the multiplication of exponents works as addition if same base
=-6x^7
Answer:
[tex]-6x^7[/tex]
Step-by-step explanation:
So when doing this equation, you multiply the numbers, which is 2 × -3, and add the exponents, which is 3 + 4, so then you get the answer, and that is [tex]-6x^7[/tex].
how do do the work for 12c+6c=36
Answers
Answer:
c = 2
Step-by-step explanation:
To solve this equation, you need to combine like terms and then divide by the coefficient of the variable on both sides of the equation.
To start, add 12c and 6c because they are like terms.
12c + 6c = 18c
Then, divide by 18 on both sides of the equation to solve for c.
18c = 36
---- ----
18 18
c = 2
Is 7/13 greater than 1/2?
Answers
yes
Step-by-step explanation:
7/13 isore than 1/2
Answer:
No 7/13 is not greater then 1/2
Step-by-step explanation:
7/13=1/2
7/13 is 0.05 and 1/2 is only 0.5
2. Select ALL of the sets to which the number belongs. 144 Natural Whole Integer Rational Irrational
Answers
Answer:
144 is:
Natural
Whole
Integer
Rational
[tex]\sqrt{144}[/tex] is:
Irrational
Step-by-step explanation:
Natural-All positive integers (144 applies) ([tex]\sqrt{144}[/tex] does not apply)
Whole-All positive integers and zero (144 applies) ([tex]\sqrt{144}[/tex] does not apply)
Integer- All positive and negative whole numbers and zero (144 applies) ([tex]\sqrt{144}[/tex] does not apply)
Rational-All integers, fractions, and non-repeating decimals (144 applies) ([tex]\sqrt{144}[/tex] does not apply)
Irrational-A real numbers that are NOT rational (144 does not apply) ([tex]\sqrt{144}[/tex] applies)
Now if you want to find which groups [tex]\sqrt{144}[/tex] belongs to, you must ask if this applies to any rules.
On a coordinate plane, a line with a 90-degree angle crosses the x-axis at (negative 4, 0), turns at (negative 1, 3), crosses the y-axis at (0, 2) and the x-axis at (2, 0).
What is the range of the function on the graph?
Answers
Answer:
B
Step-by-step explanation:
The range of the function is {0, 3}.
The range of a function on a graph is the set of all possible output values (y-values) that the function can take. To find the range of the given function, we need to determine the y-values corresponding to the points where the function is defined.
Let's analyze the points provided:
The line crosses the x-axis at (-4, 0). This means the function's y-value is 0 when x = -4.
The line turns at (-1, 3). This point is on the line, so the function's y-value is 3 when x = -1.
The line crosses the y-axis at (0, 2). This means the function's y-value is 2 when x = 0.
The line crosses the x-axis again at (2, 0). This means the function's y-value is 0 when x = 2.
Now, let's consider the intervals between these points:
a) When x < -4 (to the left of -4): The function's y-value is 0, as the line is horizontal at y = 0.
b) When -4 ≤ x < -1: The function's y-value starts at 0 and increases to 3, as the line rises from (−4, 0) to (−1, 3).
c) When -1 ≤ x ≤ 2: The function's y-value remains constant at 3, as the line is horizontal at y = 3 between (−1, 3) and (2, 3).
d) When x > 2 (to the right of 2): The function's y-value decreases from 3 to 0, as the line descends from (2, 3) to (2, 0) and further to the right.
So, the range of the function is {0, 3}.
In mathematical notation, the range is written as:
Range = {y | y = 0 or y = 3}
To know more about range:
https://brainly.com/question/29204101
#SPJ2
A set of data with 1200 numbers is normally distributed with a mean of 27 and a standard deviation of 4. How many numbers in the data would you expect to be between 23 and 31?
What numbers would be between 19 and 35 as well?
Help!
Answers
Step-by-step explanation:
The mean is 27 and the standard deviation is 4.
23 is 1 standard deviation below the mean, and 31 is 1 standard deviation above the mean. According to the empirical rule, 68% of the population is between -1 and +1 standard deviations.
68% of 1200 is 816.
19 is 2 standard deviations below the mean, and 35 is 2 standard deviations above the mean. According to the empirical rule, 95% of the population is between -2 and +2 standard deviations.
95% of 1200 is 1140.
4 movie tickets cpst $48. At this rate, what is the cost of 5 movie tickets?
Answers
Answer:
60 dollars
Step-by-step explanation:
We can write a ratio to solve
4 tickets 5 tickets
-------------- = ----------------
48 dollars x dollars
4x = 5*48
Divide each side by 4
x = 5*48/4
x = 60
Answer:
[See Below]
Step-by-step explanation:
4 tickets equals 48 so to get the price for each ticket divide:
* 48 / 4 = 12
So then just add now:
* 48 + 12 = 60.
So the cost of 5 tickets is 60$.
Owen knows he only has three pencils in his backpack, and they are all yellow. He reaches into his backpack without looking and takes out a pencil. What is the probability that the pencil was yellow? Answer options with 5 options A. 0-thirds B. 1-third C. 2-thirds D. 3-thirds E. 3 over 1
Answers
Answer:
B. 1-third
Step-by-step explanation:
The formula for probability = Number of favorable outcomes/ Total number of outcomes
From the question, we are told that:
Owen knows he only has three pencils in his backpack, and they are all yellow. Hence, total number of outcomes = 3
He reaches into his backpack without looking and takes out a pencil.
Hence, total number of favorable outcomes = 1
What is the probability that the pencil was yellow?
Probability ( That the pencil is yellow) =
Number of favorable outcomes/ Total number of outcomes
= 1/3
Therefore, the probability that the pencil was yellow is 1/3 or one - thirds
Approximate the square root of √31 .Round to two decimal places
Answers
Answer: 5.57
Step-by-step explanation:
The square root of 31 is 5.56776436 and if you round that 2 decimals places you get 5.57 bc anything higher than 5 gets rounded up to the next number.
First time I have been on here for a while. Here goes. -4(-d - 4) = -4d + 6(2d + 6) I kinda need help AsAp
Answers
Answer:
d= -13
Step-by-step explanation:
-4 ( -d - 4 ) = - 4d + 6 (2d + 6 )
4d - 16 = -4d + 12d + 36
4d - 16 = 8d + 36
- 4d - 4d
- 16 = 4d + 36
-36 -36
-52 = 4d
-52/4 4d/4
-13 = d
Water from a leaking faucet is dripping into a cylindrical cup. The height of water in inches, y, after x hours is graphed below. Dripping Water A graph with hours on the x-axis and height (inches) on the y-axis. A line goes through points (1, 2), (2, 4), and (3, 6). Which describes the pattern of the data in the graph? The water level increases by 1 inch each hour. The water level increases by 2 inches each hour. The water level increases by a factor of one-half each hour. The water level increases by a factor of 2 each hour.
Answers
Answer:
y = 2x
Step-by-step explanation:
Step-by-step explanation:
Let
y ----> the height in inches
x ----> the time in hours
we have the ordered pairs
(1, 2), (2, 4), and (3, 6).
step 1
Find the slope
take two points to calculate the slope
(2, 4), and (3, 6)
The formula to calculate the slope between two points is equal to
m = 2 in/h
step 2
Find the equation of the line in point-slope form
we have
m =2
point (2,4)
Convert to slope-intercept form
isolate the variable y
y = 2x
Which graph matches the following description?
The function is decreasing over the interval (−∞,3) and increasing over the interval (3,∞). The function has a minimum of −2. The function has a y-intercept of (0,7).
Answers
Answer:
The third image is the correct answer.
Step-by-step explanation:
Answer:
3rd graph
Step-by-step explanation:
The answer is the 3rd graph.
The third graph has all the given characteristics.
It decreases from negative infinity to 3.
It increases from 3 to infinity.
It has a minimum value of -2.
It has a y-intercept of (0, 7).
how do I figure out the circumference of a circle
Answers
Answer:
[tex]\huge \boxed{\mathrm{C=\pi d}}[/tex]
Step-by-step explanation:
To find the circumference of a circle, you can multiply the value of the diameter of the circle with the value of pi.
[tex]\sf Circumference = \pi \times diameter[/tex]
[tex]\mathrm{C=\pi d}[/tex]
C=2•π•r
hope it helps;)
I need help!! Somebody help me I need this fast!
Answers
Answer;
m<EAD=29°
m<CAB=119°
Step-by-step explanation:
Angles on a straight line sum up to 180°
This implies that,
61°+90°+EAD=180°
151°+EAD=180°
Subtracting 151° from both sides,we obtain,
EAD=180°-151°
EAD=29°
Angles on a straight line add up to 180°.
this implies that,
CAB+61°=180°
Subtracting 61° from both sides,we obtain
CAB=180°-61°
CAB=119°
Thus,m<EAD=29° and m<CAB=119°
Answer:
29° and 119°
Step-by-step explanation:
Since CF is a straight line, then
90° + ∠ EAD + 61° = 180°, that is
∠ EAD + 151° = 180° ( subtract 151° from both sides )
∠ EAD = 29°
and
∠ CAB + 61° = 180° ( subtract 61° from both sides )
∠ CAB = 119°
2) 1 - 3p+2p - 9
Your
answer
This is a required question
Answers
Answer:
-p - 8
Step-by-step explanation:
1 - 3p + 2p - 9 = -p - 8
If a giant armadillo gets 127 hours of sleep per week and a platypus gets 98 hours of sleep per week, in one year how many more hours of sleep does the giant armadillo get then the platypus
Answers
Answer: 1508 hours of sleep
Step-by-step explanation:
the arm gets 29 more hours of sleep than the plat per week
52 x 29 is 1508
Which statement describes function composition with respect to the commutative property? Given f(x) = x² – 4 and g(x) = x – 3, (f ∘ g)(2) = –3 and (g ∘ f)(2) = –3, so function composition is commutative. Given f(x) = 2x – 5 and g(x) = 0.5x – 2.5, (f ∘ g)(x) = x and (g ∘ f)(x) = x, so function composition is commutative. Given f(x) = x² and g(x)=StartRoot x EndRoot, (f ∘ g)(0) = 0 and (g ∘ f)(0) = 0, so function composition is not commutative. Given f(x) = 4x and g(x) = x², (f ∘ g)(x) = 4x² and (g ∘ f)(x) = 16x², so function composition is not commutative.
Answers
Ansdwer:
D
Step-by-step explanation:
Answer:
Given f(x) = 4x and g(x) = x², (f ∘ g)(x) = 4x² and (g ∘ f)(x) = 16x², so function composition is not commutative.
Step-by-step explanation:
Edge
Evaluate the expression. 9−32÷4
Answers
Answer:
5.75
Step-by-step explanation:
9-32÷4
23÷4
5.75
Answer:
1
Step-by-step explanation:
PEMDAS
9-32 / 4
9-8
1
I am pretty sure I know the answer but I need to be certain. Please answer and give explanation if possible.
Answers
Answer:
Vertical opposite angles are the same so the answer is D.
Adjust the equation so the line passes through the points. Y=x+1
Answers
Answer:
Slope=
2.000
2.000
=1.000
x−intercept=
−1
1
=−1.00000
y−intercept=
1
1
=1.00000
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(x+1)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve y-x-1 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-x-1 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.00000
y-intercept = 1/1 = 1.00000
Calculate the X-Intercept :
When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x=-1.00000
x-intercept = 1/-1 = -1.00000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - 1.000 = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2.000/2.000 = 1.000
Geometric figure: Straight Line
1. Slope = 2.000/2.000 = 1.000
2. x-intercept = 1/-1 = -1.00000
3. y-intercept = 1/1 = 1.00000
The equation of the line that passes through the given points will be y=1.5x-4.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the line passes through (0,4) and (2,7)
The slope of the line is,
m = (7-4)/(2-0)
m=3/2
m=1.5
The equation of the line passes through the points (0,4) and (2,7) and has a slope of 1.5 will be,
y-4=1.5(x-0)
y-4=1.5x
y=1.5x-4
Thus, the equation of the line that passes through the given points will be y=1.5x-4.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x,
determine the numerical length of KL.
Answers
Answer:
8
Step-by-step explanation:
[tex]2x + 4x = x + 10 \\ 6x - x = 10 \\ 5x = 10 \\ x = 10 \div 5 \\ x = 2 \\ kl = 4x \\ 4 \times 2 = 8 \\ kl = 8[/tex]
If the value of x will be 2. Then the length of KL will be 8 units.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x.
Then the value of x will be
JL = JK + KL
x + 10 = 2x + 4x
5x = 10
x = 2
Then the length of KL will be
KL = 4x
KL = 4 (2)
KL = 8 units
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
#SPJ2
To which subset of real number does -2/5 belong in
Answers
Answer:
Rational Numbers.
Step-by-step explanation:
Rational numbers ( these can be written as a/v where a and b are integers, b not 0)
PLEASE HELP MEEE
Can someone calculate the area of this shape
Answers
Step-by-step explanation:
The 1st rectangle
16 *7=112
next triangle
find details
13-7=6
16-8=8
6*8
48÷2
24+112
136
Analyze the logical statements to fill in the missing information.
1. If a line is horizontal, then it has a slope of 0.
Hypothesis:
Conclusion:
2. A vertical line has an undefined slope.
The statement in equivalent "if-then" form would be:
Hypothesis:
Conclusion:
Answers
Answer: 1. hypothesis: line is horizontal
Conclusion: has a slope of 0
2. If a line is vertical, then it has an undefined slope.
Hypothesis : line is vertical
Conclusion: has undefined slope.
Step-by-step explanation:
Jack bought a car for $29,000. He sold it for $10,000 3 years later. What is the percentage loss that Jack made?
Answers
Answer:
19000%
Step-by-step explanation:
i hope this correct
The following represents age distribution of students in an elementary class. Find the mode of the values: 7, 9, 10, 13,
11, 7, 9, 19, 12, 11, 9, 7, 9, 10, 11.