a³ + b³ + c³ + 3abc = ( a + b + c)(a² + b² + c² + ab + bc + ca)
if a + b + c = 0. then a³ + b³ + c³ = 3abc
here a + b + c = 15 + (-9) + (-6)
a + b + c = 15 - 15
a + b + c = 0
so a³ + b³ + c³ = 3abc
15³ + (-9)³ + (-6)³ = 3(15)(-9)(-6)
= 2430
so the answer is 2430
What are the solutions of the equation x2 + 5x + 6 = 0? A. −3, 2 B. 6, −1 C. 6, 1 D. −3, −2
Answer:
D. -3,-2
Step-by-step explanation:
Let [tex]x^{2} +5x+6=0=(x+2)(x+3)\\[/tex], then [tex]x+2=0[/tex] or [tex]x+3=0[/tex], thus [tex]x=-2[/tex] or [tex]x=-3[/tex]
if 6 = 68 degrees, find the measures of angles 4, 5 ,7
Answer:
4 = 68
5 = 112
7 = 112
Step-by-step explanation:
Hope it helps
I hope it's helpful .....
Expand and simplify (x - 2)(x - 1)
Answer:
x^2 -3x+2
Step-by-step explanation:
(x - 2)(x - 1)
FOIL
first: x*x = x^2
outer: -1*x = -x
inner: -2*x =-2x
Last: -2*-1 =2
Add together
x^2 -x-2x+2
Combine like terms
x^2 -3x+2
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{(x - 2)(x - 1)}[/tex]
[tex]\large\textsf{DISTRIBUTE}[/tex]
[tex]\large\textsf{x(x) + x(-1) - 2(x) -2(-1)}[/tex]
[tex]\large\textsf{x(x) = }\mathsf{\bf x^2}[/tex]
[tex]\large\textsf{x(-1) = -1(x) = \bf -1x}[/tex]
[tex]\large\textsf{-2(x) = \bf -2x}[/tex]
[tex]\large\textsf{-2(-1) = \bf 2}[/tex]
[tex]\mathsf{= \bf x^2 - 1x - 2x + 2}[/tex]
[tex]\large\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(-1x - 2x)}[/tex]
[tex]\mathsf{= \bf -3x}[/tex]
[tex]\large\textsf{SOLVE for the ANSWER:}[/tex]
[tex]\mathsf{x^2 - 3x + 2}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: }\mathsf{\bf x^2 - 3x + 2}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can you please write a paragraph using this Key Terms: amphibians larvae salamanders emerge habitat dormant migrate escort
Answer:
DESCRIPTION: Large for a modern amphibian, the male California tiger salamander can reach up to 8.5 inches in length, the female up to seven. Adults have protruding eyes and long tails, and their slick bodies are mostly black with brilliant yellow spots and stripes on their back, sides, and tail. Larvae are greenish gray in color.
HABITAT: California tiger salamanders can be found in annual grasslands and oak woodlands with hot, dry summers and cool, rainy winters. For most of the year, they reside in underground burrows created and abandoned by small mammals. They need ephemeral pools for breeding.
RANGE: Historically these salamanders ranged throughout California's Sacramento and San Joaquin River valleys, the surrounding foothills, and the lower elevations of the state's central coast. Now their distribution is limited to disjunct vernal pool complexes in the northern part of their historical range. The northernmost and southernmost populations, residing in Sonoma and Santa Barbara counties respectively, are genetically distinct and geographically isolated from others.
MIGRATION: Once fall and winter rains begin, adult tiger salamanders emerge from underground hibernation habitat in mammal burrows and migrate to breeding ponds. After breeding, adults disperse back to uplands habitat to retreat underground. Adults may migrate long distances between summering and breeding sites: salamanders have been found along roads more than 1.2 miles from any known breeding ponds. Juvenile salamanders dispersing from ponds have been trapped more than 1,200 feet from their natal ponds.
BREEDING: Following early-winter rains, California tiger salamanders nocturnally emerge from their burrows and lay their eggs in newly formed vernal pools. After the eggs are fertilized internally, a female can lay up to 1,300, which she deposits individually or in small batches. Adults move back to their terrestrial burrows after breeding.
LIFE CYCLE: Within two weeks of egg fertilization, salamander larvae hatch, remaining in their natal pools for two to three months. By late spring or summer, once they reach metamorphosis, juveniles roam up to two miles away to hibernate in terrestrial habitat. Salamanders are thought to have lifespans of 10 years or more.
FEEDING: For the first six weeks of life, juveniles eat small crustaceans, algae, and mosquito larvae. Adult salamanders prey on aquatic insects, invertebrates, and tadpoles of Pacific tree frogs, California red-legged frogs, western toads, and spadefoot toads.
THREATS: The California tiger salamander is threatened by habitat destruction due to urban and agricultural development, habitat fragmentation, pesticides, hybridization with nonnative tiger salamanders, introduced diseases, and predation by nonnative species.
POPULATION TREND: Surveys showed that by 1993, the California tiger salamander had been extirpated from at least half of its historic localities. By 2004, only six tiger salamander meta-populations within 48 breeding ponds remained in Santa Barbara County, and by 2005, only seven viable tiger salamander breeding sites remained in Sonoma County.
Step-by-step explanation:
In circle D, EDH LEDG.
1. Determine the length of JG using
circle D.
Show your work and write out your
justification.
E
57°
F
D
Be prepared to answer questions
about additional angles, arcs and
segments from circle D.
C
H
66°
G
2.
G H
In OK, m_HKG=x+10 and
m IKT=3 2 D
Answer:
hey mate
the question is not understandable
what is the height of this triangle?
Answer:
XY (height) is approximately 20.8 feet
Step-by-step explanation:
let h = XY
tan60° = h/12
h = 12·tan60°
h = 20.78 ft
h(x)=sqrt(x) and g (x)=4x^2+4, find h(g(sqrt(a))))
[tex]\begin{cases} h(x)=\sqrt{x}\\ g(x)=4x^2+4 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ g(\sqrt{a})=4(\sqrt{a})^2+4\implies g(\sqrt{a})=4\sqrt{a^2}+4\implies g(\sqrt{a})=\boxed{4a+4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(~~g(\sqrt{a})~~)\implies h\left( \boxed{4a+4} \right)=\sqrt{4a+4}\implies h(~~4a+4~~)=\sqrt{4(a+1)} \\\\\\ h(~~4a+4~~)=\sqrt{2^2(a+1)}\implies h(~~4a+4~~)=2\sqrt{a+1}[/tex]
What is an equation of the line that passes through the points (-5,6) and (7,6)?
Y-intersect of the liner function
Answer:
15
Step-by-step explanation:
The y- intercept is the value of y on the y-axis where the line crosses.
The line crosses the y- axis at 15 ← y- intercept
3x-4=4 What is the value of X
Answer:
3x-4=4
3x=8
x=8/3
hope this helps
have a good day :)
Step-by-step explanation:
Which of the following could be the measure of the angle below?
Answer:
There is nothing below.
Step-by-step explanation:
Lori is president of a book club. She has a message to get out to her book club members. On Monday, she called one member and asked that member to call to other members by noon the next day and repeat the message. How many calls were made by Friday afternoon?
Please help me!
Answer:
how many members are in the club??
What is this expression in simplest form? (x+2)/(4x^2+5x+1) * (4x+1)/(x^2-4)
Answer:
below
Step-by-step explanation:
that is the solution above
The simplest form of the given expression is [tex]\frac{1}{(x+1)(x-2)}[/tex].
What is Algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Here, given expression;
[tex]\frac{x+2}{4x^2+5x+1} X \frac{4x+1}{x^2-4}[/tex]
[tex]\frac{x+2}{4x^2+4x +x+1} X \frac{4x+1}{x^2-2^2}[/tex]
[tex]\frac{x+2}{4x(x+1)+1(x+1)} X \frac{4x+1}{(x+2)(x-2)}[/tex]
[tex]\frac{x+2}{(4x+1)(x+1)} X \frac{4x+1}{(x+2)(x-2)}[/tex]
[tex]\frac{1}{(x+1)(x-2)}[/tex]
Thus, the simplest form of the given expression is [tex]\frac{1}{(x+1)(x-2)}[/tex].
Learn more about Algebraic expression from:
https://brainly.com/question/953809
#SPJ2
Match each product of powers with its simplified expression
= 5-³ -³
= 5-⁶
= 1/5⁶
5⁷ × 5³= 5⁷+³
= 5¹⁰
5⁶×5 -⁴= 5⁶ - ⁴
= 5²
5-⁴×5⁴×5⁰= 5-⁴ + ⁴ × 1
= 5⁰
Answer:
answser in picturew
Step-by-step explanation:
7.8 is what percent of 78?
Answer:
10 %
Step-by-step explanation:
let the percent be x
according to the question
7.8 = x % 0f 78
7.8 = x /100 * 78
7.8*100 = 78x
780 = 78x
780/78 = x
10 = x
Answer:
10 percent
Step-by-step explanation:
7.8 is ? of the number 78.
So, we will multiply 7.8 by 100.
7.8 x 100 = 780
Now, we will divide 780 by 78.
780/78 = 10
So, our answer is 10.
Or, you can divide:
78 divided by 7.8 is 10
The pattern 96, 92, 88, 84, ________ follows the "subtract 4" rule. Study the pattern to find traits that are not obvious in the rule. Explain.
HELP ASAP
Answer:
80
Step-by-step explanation:
add from bottom to the top
z = 3. & y = 6
Evaluate the
expression: Y - Z
Answer:
6-3=3
3 is the answer because they gave you the value of Y and Z then they asked you to subtract
Can someone please help asap thank you
Answer:
1. -10 > x
2. No, because the more you raise the ticket price, the less people will attend.
3. C) -x - 6 > -3.5
4. you have to do yourself
Step-by-step explanation:
1. if you solve for 5 - 3x > 35 you get x < -30, which means that any answer will be less than -10
What is the length of AC?
A.72
B.96
C.136
D.132
Answer:
The answer is 136 .
Determinar el ángulo NPO, si el ángulo PON es igual a 132 grados y el segmento NP es bisectriz del ángulo P y N.
Aquí les dejo una pista, la respuesta correcta es: 24 grados.
The measure of ∠NPO is equivalent to 24°.
What are angles?In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral anglesGiven is that if the angle PON is equal to 132 degrees and the segment NP is bisector of the angle P and N.
Now -
OP = ON
So, this means that ∠OPN = ∠ONP = x° {say}
We can write -
∠OPN + ∠ONP + 132° = 180°
2x = 48°
x = 24°
Therefore, the measure of ∠NPO is equivalent to 24°.
To solve more questions on angles, visit the link below -
https://brainly.com/question/18166236
#SPJ2
{
Question in English is as follows -
Determine the angle NPO, if the angle PON is equal to 132 degrees and the segment NP is bisector of the angle P and N.
Here's a hint, the correct answer is: 24 degrees.
}
Just wanna double check my answer on this one. I got a profit of 60%
Answer:
Yes the answer is indeed 60%
the answer is 60% so you are correct
Zzzzzzzhelpzzzz zzzzzzzz
the answers are A and D hope this helped
ASAP I HAVE A MATH FINAL PLEASE
<2 and <6 -----> Neither
<1 and <4 ------> vertical
Hope it helps you...
Please help me solve my problem!!!
Amy is going on a 4 1 4 4 4 1 mile hike. She has already hiked 2 3 4 2 4 3 miles. How many more miles does she have left
Answer:
1 1/2 miles
Step-by-step explanation:
Amy is going on a 4 1 /4 miles hike. She has already hiked 2 3 /4 miles. How many more miles does she have left?
We solve the above question using the operation of Subtraction
The number of miles she has left is calculated by:
Total number of miles she must hike - Number of miles she has hiked
Total number of miles she must hike
= 4 1/4 miles
Number of miles she has hiked = 2 3/4 miles
Therefore:
The number of miles she has left to hike is = 4 1/4 miles - 2 3/4 miles
Lowest Common Denominator = 4
4 - 2 + ( 1/4 - 3/4)
2 + (1 - 3/4)
2 + -2/4
1 2/4
= 1 1/2 miles
PLEASE HELP FAST!!!!!!!!!
Answer:
First: [tex]y = \frac{4}{7} x + 2[/tex]
Second: [tex]y = -\frac{1}{7} x + 2[/tex]
Third: [tex]y = x + 2[/tex]
Fourth: [tex]y = \frac{1}{7} x + 2[/tex]
MATH QUESTION HELP ME PLS, KINDA URGENT!!
I need to resolve this with the elimination method
x +y +z = 13
x–z = −2
−2x +y = 3
how-?
Answer:
x= 2
y= 7
z= 4
Step-by-step explanation:
Equation 1: x+y+z=13
Equation 2: x-z= -2
Equation 3: -2x+y=3
Add equation 2 and 1
(x+y+z)+(x-z)= 13 -2
2x+y= 11
Add this to equation 3
(-2x+y)+(2x+y)= 11+3
2y= 14
y= 7
Plug in y= 7 to equation 3
-2x+(7)= 3
-2x+7=3
-2x= -4
x= 2
Plug x=2 into equation 2
2-z= -2
4 = z
2.
Find the value of x. If necessary, round to the nearest tenth.
A. 13.7 in.
B. 11.7 in.
C. 9.7 in.
D. 6.9 in.
Answer:
A
Step-by-step explanation:
13.7
Find the difference. Show your solutions as two steps: First rewrite the subtraction as addition; then carry out the addition to find the answer. 8 − 5 = 8 + 8+5 Incorrect: Your answer is incorrect. = 45 Incorrect: Your answer is incorrect.
Answer:
[tex]8 - 5 = 3[/tex]
Step-by-step explanation:
Given
[tex]8 - 5 =[/tex]
Required
Solve
Step 1: Write as addition
Simply change the positions of -5 and (+)8
[tex]8 - 5 = -5 + 8[/tex]
Step 2: Add
[tex]8 - 5 = 3[/tex]
Solve for x
[tex]8 {}^{2 + x} + 2 {}^{3x} = 32 {}^{ \frac{1}{2} } [/tex]
Answer:
8^2+x + 2^ 3x = 32^ 1/2
2^3(2+x) + 2^3x = 2^5^1/2
All two's will cancel out
3(2+x) + 3x = 5^1/2
6+3x + 3x = 5^1/2
6 +6x = 2.23
6x = 2.23 - 6
6x = -3.77
x = -3.77÷ 6
x = -0.63
