Answer:
It is always positive because the discriminant is negative and therefore has no roots. This can also be interperted as the equation will always be above the x-axis on the parabola and therefore always be positive.
Step-by-step explanation:
The value of the quadratic expression (x - 4)² + 4 will be always positive.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient. Then the equation of the parabola will be given as,
y = a(x - h)² + k
The quadratic expression is given below.
⇒ x² - 8x + 20
Convert the expression into a vertex form, then we have
⇒ x² - 8x + 16 + 4
⇒ (x² - 2 · x · 4 + 4²) + 4
⇒ (x - 4)² + 4
Thus, the value of the expression (x - 4)² + 4 will be always positive.
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help.me with Ap calc please
Answer:
[tex]\displaystyle f'(1) = 6[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = 5x - 1 + \ln x[/tex]
Step 2: Differentiate
[Function] Derivative Property [Addition/Subtraction]: [tex]\displaystyle f'(x) = \frac{d}{dx}[5x] - \frac{d}{dx}[1] + \frac{d}{dx}[\ln x][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle f'(x) = 5 \frac{d}{dx}[x] - \frac{d}{dx}[1] + \frac{d}{dx}[\ln x][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle f'(x) = 5 - 0 + \frac{d}{dx}[\ln x][/tex]Logarithmic Differentiation: [tex]\displaystyle f'(x) = 5 + \frac{1}{x}[/tex]Substitute in x: [tex]\displaystyle f'(1) = 5 + \frac{1}{1}[/tex]Simplify: [tex]\displaystyle f'(1) = 6[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Choose the linear equation written in slope-intercept
form that matches each graph.
Answer:A
Step-by-step explanation:
The line touches the y axis at -1. The line then goes up 1 over 2 but since it’s on the bottom part of the graph it has the be negative. Y=-1/2X-1
Answer:
Slope = rise/run
= -1/2 (negative because the slope is decreasing)
y - intercept = -1
Option A
y = -1/2x-1
write -9 7/10 as a decimal number
Answer:
9 7/10 is a decimal number is 9.7
Write the slope intercept form of the equation of the line
Answer:
y= x + 2
Step-by-step explanation:
HELP- 11 points!
Find three consecutive integers with a sum of -36. First, write an equation, then solve.
Select all the expressions that can be used to find the price of a $400 telescope after a 32% markup. A)400 • 0.32 B) 400 • 3.2 C)400 • 1.32 D)400 + 400(0.32) E)400 • 400(1.32)
Answer:
(D) 400 + 400(0.32)
Step-by-step explanation:
We need to find the price of a $400 telescope after a 32% markup.
32% markup means increase in the cost of telescope by 32%. It can be calculated as follows :
[tex]P=400+32\% \ of\ 400\\\\=400+\dfrac{32}{100}\times 400\\\\=400+0.32(400)[/tex]
Hence, the correct expression is option (d).
Answer:
(D) 400 + 400(0.32)
Step-by-step explanation:
We need to find the price of a $400 telescope after a 32% markup.
32% markup means increase in the cost of telescope by 32%. It can be calculated as follows :
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation x^2-19x+9=0 which number would have to be added to "complete the square"?
Answer:
90.25Step-by-step explanation:
Given the quadratic equation x^2-19x+9=0 re arranging we have;
x^2-19x+9 - 9=0 -9
x^2-19x = - 9
In order to complete the square we would add a number to both sides and the number will be the square of the half of coefficient of x in the expression as shown.
Coefficient of x = -19
half of coefficient of x = -19/2
square of the half of coefficient of x = (-19/2)²
square of the half of coefficient of x = 361/4
square of the half of coefficient of x = 90.25
Hence the number that would have to be added to "complete the square" is 90.25
If you have 2\10 of an apple, how many fifths do you have
Answer:
4/5
Step-by-step explanation:
1 - 2/10 = 8/10 = 4/5
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
You have [tex]\frac{2}{10}[/tex] ( divide numerator and denominator by 2 ), that is
[tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
Estimate the measure of
Answer:
148°
Step-by-step explanation:
it is very close to the 150 line and the option closest to 150 is 148
Barry must find the value of x in the equation below.
30x =48+22x
which of the following is the best step Barry could take to find the value of x in the equation?
Answer:
30x=48+22×
30x -22x=48
8x=48
x=6
When translating the point (3,5) 5 units up and 3 units to the left, we should get:
Answer:
(0, 10 )
Step-by-step explanation:
5 units up means add 5 to the y- coordinate
3 units left means subtract 3 from the x- coordinate
Translation rule is
(x, y ) → (x - 3, y + 5 ) , thus
(3, 5 ) → (3 - 3, 5 + 5 ) → (0, 10 )
What is the domain and range
What is the x-intercept
What is the y-intercept
Answer:
Domain: (-∞,∞)
Range: (-∞,∞)
**All real numbers, ℝ is an alternative to (-∞,∞)
x-intercept: -3
y-intercept: 5
You are planning your vacation and trying to figure out the total number of miles you will be traveling on a round trip from Portland, Oregon to Denver, Colorado, and back to Portland, Oregon. The scale for the map you are consulting shows that 1 inch = 4 miles. Measuring, you find that you will be traveling 31412 inches for the one-way trip. What is the total number of miles you will be traveling during the entire round trip?
Answer:
31,417 miles i think I hope it will helpThe total number of miles you will be traveling for the entire round trip is 125650 miles.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
The question states that 1 inch = 4 miles. Therefore, if you multiply 31412 inches by 4, you will get the total number of miles you will be traveling for the round trip.
31412 × 4 = 125650
Therefore, the total number of miles you will be traveling for the entire round trip is 125650 miles.
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Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 2:3:4.
How much more does Brian get over Paul?
Kara's car used 1/16 gallons
of gas to drive 1/8 of a mile. At
this rate, how many miles can
Kara's car drive using one
gallon of gas?
Zachary purchased a computer for $1200 on a payment plan three months after he purchased a computer his balance was $795. six months after he purchased a computer his balance was $390 what is the equation that models the balance y after X months
simplify the expression: 3x + 5 + 7x=
The answer would be 10x + 5
Hello!
The answer is 10x + 5!
Hopefully this helps! <3 ^^
Solve for x 12 + x = 27
Answer:
15
Step-by-step explanation:
subtract 12 on both sides and you get
x=27-12
x=15
Answer:
I think your answer is 15
Step-by-step explanation:
Hope this helped you
Are the roots of equation 4x^2-4x+1=0 is imaginary
Answer:
NO
Step-by-step explanation:
[tex]4x^{2} -4x+1=0\\(2x-1)(2x-1)=0\\x=1/2[/tex]
Translate the following sentence into a mathematical equation. The sum of 10 and five times a number is the same as the difference of the number and 6
Answer:
The sentence in mathematical form is: [tex]5x+10 = x-6[/tex]
Step-by-step explanation:
The given statement can be converted into a mathematical equation step by step.
First of all, we have to suppose a variable for the number as we don't know the exact number.
So,
Let x be the number then
five times a number => 5x
The sum of 10 and five times a number => 5x+10
the difference of the number and 6 => x-6
Putting in equation form we get
[tex]5x+10 = x-6[/tex]
Hence,
The sentence in mathematical form is: [tex]5x+10 = x-6[/tex]
Describe a principle that the philosophies of Locke, Montesquieu, and Rousseau have in common.
Look at the incomplete multiplication problem below.
632 times 29 = 5688. 5688 + question mark = blank
What value is missing?
Answer:
Locke, Rousseau and Montesquieu agreed that nations would be built on social institutions, or even what Montesquieu considered a legislation which would describe the laws of the country and put in concrete what privileges the citizens and the state have.
Answer:
d 18,328
Step-by-step explanation:
I did the math >:3
sorry if it's wrong
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. (3.-5) and (2-2)
А. -3, falls
В. 1/3, rises
C. 3, rises.
D. -1/3, falls
Answer:
Slope of line having points (3,-5) and (2,-2) is 3 and since the slope is positive do it rises. Option C is correct option.
Step-by-step explanation:
The formula calculate to find slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given points (3,-5) and (2,-2) so,
[tex]x_1=3, y_1=-5, x_2=2, y_2=-2[/tex]
Putting values in formula and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{2-3}\\Slope=\frac{-2+5}{1}\\Slope=3[/tex]
So, Slope of line having points (3,-5) and (2,-2) is 3 and since the slope is positive do it rises. Option C is correct option.
Which is the equation of a line that passes through the points (4, 6) and (-6, 1)?
Answer:
y=2x-8
Step-by-step explanation:
gradient = 1-6 / -6-4
= 2
y=2x+c
substitute one of the points
4=2*6+c
c=-8
y=2x-8
A survey found that 60% of shoppers at My-Way-Store like chocolate ice cream. If 240 boppers like chocolate ice cream, how many people were surveyed?
Answer:
400
Step-by-step explanation:
240/60=4, meaning 4 people per every percentage. Which when 4 is multiplied by 100, you get 400=100%
Answer:
400
Step-by-step explanation:
60/100 = 240/?
Bat and Ball ( when do proportional table make a x like shape between/through each number. The number going diagainal multiplies, number next to number is used to divide the product of the diagainal numbers.)
240 x 100 = 24,000
24,000 divided 60 = 400
400 were survreyed
Identify the domain of the rational function g(x)= 1/x-3
Answer:
Domain: (negative infinite, zero) U (0, infinite)
Range: ( negative infinite, -3) U (-3, infinite)
Step-by-step explanation:
I don't really know how to explain this because I can't use some symbols that are needed. But, yeah.
A partial construction of a median of a triangle JKL is shown below
complete the statements
Point _ is the midpoint of side JK. to finish the construction, draw a segment from vertex _ to point _
Then, segment _ is a median of triangle JKL
Answer:
1. E , 2. JK , 3. L , 4. E , 5. LE
Step-by-step explanation:
JUST TOOK THE TEST.
Answer:
Complete the statements.
Point
✔ E
is the midpoint of side
✔ JK
.
To finish the construction, draw a segment from vertex
✔ L
to point
✔ E
.
Then, segment
✔ LE
is a median of triangle JKL.
Step-by-step explanation:
1. Judy took $15 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $3. The price of each drink was half the price of a bag of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks.
Answer:
Let the number of popcorn be x and the number of drinks be y, then according to the question we have the following equation
.................> linear equation
To sketch the graph first we need to find two points on it.
EXAMPLE
put x=0, we get y=10
put y=0, we get x=6
Thus, we have points (0,10) and (6,0), now sketch a line through it .
Thus in the graph x - axis represents the number of popcorn and y axis represents the number of drinks.
The slope of the graph is
Step-by-step explanation:
(-8/9) divided by (-2/3)x(-4 1/2)
Answer:
-0.29629629629 or -0.3
Step-by-step explanation:
first do (-2/3)*(-4 1/2) which is 3
then divide (-8/9) by 3 and you get -0.29629629629 which can be rounded to -0.3
The Answer will be -8 using fraction operation.
What is a fraction?If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
First solve the 2nd part which is
[tex]\frac{-2}{3}*-4\frac{1}{2} \\=3[/tex]
Now -8/3 * 3 = -8
Hence the answer for the given question will be -8.
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x + 4 < 6
Drag your dot to a possible solution for the inequality.
Answer:
An open circle at 2, and an arrow facing left.
How many hours and minutes is this?