Answer:
all x intercepts [-4, 0] [4, 0]
Step-by-step explanation:
x-intercept, i.e. y=0
f(x) = x^3 - 4x^2 - 16x + 64 = 0
(x^3 + 4^3) - 4x^2 - 16x = 0 [FYI, x^3 + y^3 = (x + y)(x^2 - xy + y^2)]
(x + 4)(x^2 - 4x + 16) - 4x^2 - 16x = 0
(x + 4)(x^2 - 4x + 16) - 4x(x + 4) = 0
(x + 4)(x^2 - 4x + 16 - 4x) = 0
(x + 4)(x^2 - 8x + 16) = 0
(x + 4)(x - 4)^2 = 0
x = -4 or 4
all x intercepts [-4, 0] [4, 0]
Step-by-step explanation:
one thing immediately catches the eye : the factors of the terms in the function follow the powers of 4 :
4⁰, 4¹, 4², 4³
and they are going against the powers of x :
x³ has the factor 4⁰
x² has the factor 4¹
x has the factor 4²
x⁰ has the factor 4³
with that we see that one 0 solution (an x- intercept) is x = 4.
f(4) = 4³ - 4×4² - 4²×4 + 4³ = 4³ - 4³ - 4³ + 4³ = 0
so, the functional expression is
(x-4)(x² + ...)
the other 2 zero solutions are covered by the quadratic term.
to get the quadratic term we divide f(x) by (x-4).
x³ - 4x² - 16x + 64 ÷ x - 4 = x² - 16
- x³ - 4x²
-----------------------------
0 0 - 16x + 64
- - 16x + 64
----------------------‐--------
0 0
so,
f(x) = (x - 4)(x² - 16)
and as we know
(a² - b²) = (a + b)(a - b)
we get
f(x) = (x - 4)(x + 4)(x - 4) = (x - 4)²(x + 4)
so, x = 4 counts as 2 zero solutions, it is a point, where the curve makes a turn and only touches the x-axis, but does not fully intercept it (in the sense to continue on the other side of the x-axis).
and x = -4 is the third zero solution.
so, the x-intercepts are at x = -4, +4
100 pointss pls help!!!! characteristics of a quadratic function worksheet
Answer:
do u have the full sheet?????
How much of your lawn can you mow with
one gallon of gas, if you maintain the rate
of ⅕ gallon of gas per ⅛ of a lawn?
Answer:
5/8
Step-by-step explanation:
1/5 x 5
1
1/8 x 5
5/8
which fraction is equal to 5
A line passes through two sides of a rectangle.
12
34
56
78
The measure of Z1 is 50 degrees. What is the measure of 26?
O 50 degrees
80 degrees
130 degrees
O 150 degrees
Answer:
34
80 degrees
Step-by-step explanation:
I RELLAY HOPES THIS HELPS YOU PLEASE
Can a prism have the same volume and surface area EXPLAIN PLEASE URGENTLY ANSWER PLEASE
Answer:
Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm. A rectangular prism with side lengths of 1 cm, 1 cm, and 4 cm has the same volume but a surface area of 18 sq cm.
Giving 20 Brainly points pls solve
The volume of the cylinder is 254,571.43cm³.
The surface area of the cylinder is 22,628.57 cm².
What is the volume of the cylinder?A cylinder is a three-dimensional object. It is a prism with a circular base.
Volume of a cylinder =πr²h
π = 22/7r = radius = diameter / 2 = 60/2 = 30cm22/7 x (30²) x 90 = 254,571.43cm³
Surface area = 2πrh + 2πr²
(2 x 22/7 x 30 x 90) + (2 x 22/7 x 30²)
16, 971.43 + 5657.14 = 22,628.57 cm²
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1. The mark up price of a pair of shoes which costs $125. 00 is 8. 35%. A)What is the final price? If the tax is 6 1/2% How much will be paid for that pair of shoes?
Answer:
Step-by-step explanation:
Remark
The wholesale price of the shoes is 125 dollars
The retailer marks it uu to 35% more to the wholesale price.
So the price is now 125 + 35% * 125 dollars
That amount is 125 + 35/100 * 125 = 125 + 43.75 = 168.75
The government wants its cut of 6.5% of the selling price
So the final price is 168.75 + 168.75 * 6.5/100
The final price is 168.75 + 10.97 = 179.72
Answer: A customer pays 179.72 dollars.
Can a right triangle have the side lengths 4 mm, 13 mm, and 10 mm?
Justify your reasoning.
Answer:
No, because the given values do not produce a correct equation when plugged into the Pythagorean Theorem.
Step-by-step explanation:
To solve this question, we can use the Pythagorean Theorem. (Also called Pythagoras Theorem)
The Pythagorean Theorem is true for ALL right triangles, meaning that if the side lengths don't work for it, the given triangle can not be a right triangle.
The theorem simply states that the sum of the squares of the two legs must add up to the square of the hypotenuse.
Note that the hypotenuse of a triangle is the side opposite to the right angle.
The Pythagorean Theorem can be easily written as the following expression:
a^2+b^2=c^2
This is where a and b are the legs and c is the hypotenuse.
We can plug our given values in to see if it's correct.
If it is a right triangle, the longest side will always be the hypotenuse, so we can safely set c as 13.
4^2+10^2=13^2
Simplify to see if it's true
16+100=169
116≠169
Therefore, a right triangle can not have these given side lengths.
Hope that helps, please let me know if you have any further questions!
Are the circles tangent, concentric, or congruent?
Jada's property has a shape of a parallelogram with the
dimensions shown. If the perimeter of the property is 300
feet, what is the value of x?
x + 75
X +45
bru help please.... like r n
Answer: basically a rising straight line that goes through the origin
Step-by-step explanation:
a square pyramid measuring 7 in along each edge of the base with a height of 12 in
Answer:
196 in^3
Step-by-step explanation:
Volume of pyramid = 1/3 base * height
= 1/3 (7x7) (12) = 196 in^3
What is the slope and y-intercept of the given equation?
y = 2/3x + 5
Answer:
The slope is 2/3x and the y-intercept is 5.
alot of points and BRAINLIEST if possible. a. 1-1000 in roman numeral. b. fastest way of multiplication
Step-by-step explanation:
number 1 to 100 is in the table bove
use I =1 V=5 x=10 l=50 c=100 d=500 m =1000
for fast multiplication
6a[tex]6a^{2} + 2a (4a +3b) - 12ab[/tex]
Answer:
ASSUMING IT IS SIMPLIFICATION.....
[tex]2a(7a - 3b)[/tex]
Step-by-step explanation:
[tex] {6a}^{2} + 2a(4a + 3b) - 12ab[/tex]
Expand the bracket.
[tex] {6a}^{2} + {8a}^{2} + 6ab - 12ab[/tex]
[tex] {14a}^{2} - 6ab[/tex]
Take the common factors out.
[tex]2a(7a - 3b)[/tex]
The length of a rectangle is "a" inches and the width is 3 inches more than its length. find the perimeter and the area
Answer:
Step-by-step explanation:
Givens
Length = a
Width = a + 3
Formulas
P = 2L + 2w
Area = L * w
Solution
Perimeter
P = 2L + 2w
P = 2*a + 2(a + 3) Remove the Brackets
p = 2a + 2a + 6 Combine
P = 4a + 6
Area
Area = L * w
Area = a (a + 3)
Area = a^2 + 3a
Benny has 8.5 cups of milks. one batch of his recipe for
cookies calls for 1.25 cups of milks.
what is the maximum number of batches benny can bake?
[select]
will he have milk leftover? (select)
if yes, how many cups? [select]
the answer is; biodiversity resulting from few ancestors
adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.
STATE WHETHER THE WORKING SHOWN IN THE PICTURE BELOW IS TRUE OR FALSE.
Answer:
True
Step-by-step explanation:
i dont see a error-
casey sight the top of an 84 foot tall lighthouse at an angle of elevation of 58. if casey is 6 feet tall how far is he standing from the base of the lighthouse
Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
y < x -2
1
y <--2-5
22
Answer:
The answer is definitely C
Step-by-step explanation:
Following the system of inequalities will graph this solution best on the graph, it is the inequality represented in the graph.
ur wlcm :)
correct me if im wrong
brainliest please?
Is √50 greater or less then 7.8
Answer:
Less than.
square root 50 = 7.07
7.8 = 7.8
Answer:
Squareroot 50=7.07 Approx
So [tex]\sqrt50[/tex] is less than 7.8
Step-by-step explanation:
Pls give Brainliest.
Must complete all parts below
a) Draw the graph of the function f(x)=2^x+3
b) Translate the graph down 4 units and draw the new graph.
c) What is the equation of the new graph?
Answer: **Both functions must be present on your graph. Must have at least two specific points per function!
a. The graph is attached with the answer.
b. Translated graph is also attached with the answer.
c. The equation of the new graph will be (2x²+3)-4
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the quadratic equation we will get a curved parabola.
a. The graph of the function f(x)=(2x²+3) is attached with the answer. b. The translated graph of the function is also attached with the answer.
If the function is reduced by the constant value 4 then the equation of the function will become:-
F(x)= (2x²+3)-4
Hence the equation of the new graph will be (2x²+3)-4
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Alfonso wants to buy a $500 Series EE savings bond. How
much will he pay for the bond??? Helpppppppp pleaseeeee
Answer:
500
Step-by-step explanation:
I had the same question this week trust
4.5x67=
6/5x78=?
20-100=+3,000
can anyone help me with this slope-length activity? whoever answers will get 5 stars and brainliest, i know its a bit of work so I'd really appreciate it, I've been rlly struggling with this unit. this is 10th grade geometry
Answer:
Step-by-step explanation:
27.
The mass of a block of ice decreases from 80kg to 64kg.
Calculate the percentage decrease.
A percentage is a way to describe a part of a whole. The percentage decrease will be 20%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The percentage change is calculated as,
Percentage Change= (Initial Value - Final value)/Initial Value × 100%
Given initially the mass is 80kg, while the final mass is 64 kg, therefore, the percentage change can be calculated as,
Percentage change = (80-64)/80 × 100% = 20%
Hence, the percentage decrease will be 20%.
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Which expression represents the area of the base of the pyramid? x squared startroot 3 endroot units2 3 x squared startroot 3 endroot units2 4 x squared startroot 3 endroot units2 6 x squared startroot 3 endroot units2
The area of pyramid base with a dimension of x + 2 and x - 1 is given as x² + x - 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the base of the pyramid has a dimension of x + 2 and x - 1, hence:
Area of pyramid base = (x + 2)(x - 1) = x² + x - 2
The area of pyramid base with a dimension of x + 2 and x - 1 is given as x² + x - 2
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Answer:
D)6 x squared StartRoot 3 EndRoot units2
Step-by-step explanation: on edge
Please help this assignment is due in 20 mins!
Jayvalyn is buying milk. She needs 4 liters. A half-liter of milk costs $2.86. A 200-milliliter container of milk costs $1.19. What should Jayvalyn buy so she gets 4 liters at the lowest price?
Answer:
the half liter
Step-by-step explanation:
200 mL :
4,000 mL in 4 liters.
4,000/200=20
20x1.19=23.8
half liter :
4x2=8
8x2.86=22.88
Find the solution set of the inequality: 8x+2 > 34
x > or < or >= or =
Inequality are expressions that are not separated by an equal sign. The solution to the given system of equation is x > 4
Inequality functionInequality are expressions that are not separated by an equal sign.
Given the inequality
8x+2 > 34
Subtract 2 from both sides
8x + 2 - 2 > 34 - 2
8x > 32
Divide both sides by 8
8x/8 = 32/8
x > 4
Hence the solution to the given system of equation is x > 4
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12 ft
10 ft
Enter the volume of the cylinder, in cubic feet. Round your answer to the nearest hundredth.
Answer:
942.48
Step-by-step explanation:
hope this helps