Answer:
(a + b)(a + b - 2c)
Step-by-step explanation:
Note that
(a + b)² = a² + b² + 2ab
Given
a² + b² + 2(ab - ac - bc) ← distribute parenthesis
= a² + b² + 2ab - 2ac - 2bc
= (a + b)² - 2ac - 2bc ← factor out - 2c from each term
= (a + b)² - 2c (a + b) ← factor out (a + b) from each term
= (a + b) [ a + b - 2c ]
= (a + b)(a + b - 2c) ← in factored form
The expression a² + b² + 2(ab - ac - bc) cannot be factorized using standard factorization techniques over real numbers, as a² + b² is not factorizable over the reals and there's no common factor for all terms.
To factorize the expression a² + b²+ 2(ab - ac - bc). To factorize this, we will look for a common factor and regroup the terms. Let's see if there's a way to rearrange the terms to resemble a known pattern or factor by grouping.
First, let's rewrite the expression by grouping terms with a common factor:
a² + 2ab - 2ac
b² - 2bc
However, we notice that the expression does not fit into a perfect square or any other easily factorizable form like (a + b)² or (a - b)² due to the nature of the terms a², b², and 2(ab - ac - bc). The expression is already in its simplest factored form as it stands because a²+ b² is not factorizable over the real numbers, and there's no common factor for all terms.
Therefore, the expression a² + b² + 2(ab - ac - bc) does not factorize further using real numbers and the usual factorization techniques.
Solve for x. 7 – 4x = 31 A. x = 6 B. x = 9.5 C. x = –6 D. x = –9.5
7-4x= 31
Bring over 7 to the other side
Positive 7 changes into negative 7
7-7-4x= 31-7
-4x= 24
Divide by -4 for -4x and 24
-4x/-4= 24/-4
x= -6
Check answer by using substitution method
7-4x= 31
7-4(-6)= 31
7+24= 31
31= 31
Answer : C. x= -6
Answer:
C. x = -6
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 7 from both sides:
7 - 4x = 31
7 (-7) - 4x = 31 (-7)
-4x = 31 - 7
-4x = 24
Divide -4 from both sides to isolate the variable, x:
(-4x)/-4 = (24)/-4
x = 24/-4
x = -6
x = -6, or C. is your answer.
~
grap f(x)=x^2+1/3(x-8)
Answer:
here is
Step-by-step explanation:
Which kind of symmetry do all of these figures have
The kind of symmetry the figures have are horizontal line symmetry and vertical line symmetry
Explaining the kind of symmetry the figures haveFrom the question, we have the following parameters that can be used in our computation:
The figures
The figures have horizontal line symmetry and vertical line symmetry
Horizontal line symmetry occurs when a shape can be divided into two identical halves by a horizontal line.
In other words, if you fold the shape in half along the horizontal line, the two halves will exactly overlap.
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I need help with this
Answer:
The x-intercepts are x = 1 , x = 2 , x = 3
The y-intercept is -6
Step-by-step explanation:
* Lets explain how to solve the problem
- To find the x-intercept of a function substitute f(x) by 0
- To find the y-intercept of a function substitute x by 0
- To find the factors of quadratic function use the long division
* Lets solve the problem
∵ f(x) = x³ - 6x² + 11x - 6
∵ (x - 3) is one of its factors
- Use the long division to find the other factors
∵ x³ - 6x² + 11x - 6 ⇒ dividend
∵ x - 3 ⇒ divisor
# Divide the 1st term in the dividend by the 1st term of the divisor
∵ x³ ÷ x = x²
# Multiply x² by the divisor (x - 3)
∵ x²(x - 3) = x³ - 3x²
# subtract it from the dividend
∵ (x³ - 6x² + 11x - 6) - (x³ - 3x²) = (x³ - x³) + (-6x² + 3x²) +11x - 6
∴ The dividend is -3x² + 11x - 6
# Divide the 1st term in the dividend by the 1st term of the divisor
∵ -3x² ÷ x = -3x
# Multiply -3x by the divisor (x - 3)
∴ -3x(x - 3) = -3x² + 9x
# subtract it from the dividend
∵ (-3x² + 11x - 6) - (-3x² + 9x) = (-3x² - 3x²) + (11x - 9x) - 6
∴ The dividend is 2x - 6
# Divide the 1st term in the dividend by the 1st term of the divisor
∵ 2x ÷ x = 2
# Multiply 2 by the divisor (x - 3)
∴ 2(x - 3) = 2x - 6
# subtract it from the dividend
∴ (2x - 6) - (2x - 6) = (2x - 2x) + (-6 + 6) = 0
∴ (x³ - 6x² + 11x - 6) ÷ (x - 3) = x² - 3x + 2
∴ The factors of f(x) are (x - 3)( x² - 3x + 2)
- The factor (x² - 3x + 2) can factorize into two bracket
∵ The last term is positive and the middle term is negative than the
two brackets have the middle sign (-)
∵ x × x = x² ⇒ 1st terms in the two brackets
∵ 2 × 1 = 2 ⇒ 2nd terms in the two brackets
∵ 2 × x = 2x
∵ 1 × x = x
∵ 2x + x = 3x
∴ (x² - 3x + 2) = (x - 2)(x - 1)
∴ f(x) = (x - 3)(x - 2)(x - 1)
- To find the x-intercept put f(x) = 0
∴ (x - 3)(x - 2)(x - 1) = 0
- That means each bracket = 0
∵ x - 3 = 0 ⇒ add 3 for both sides
∴ x = 3
∵ x - 2 = 0 ⇒ add 2 for both sides
∴ x = 2
∵ x - 1 = 0 ⇒ add 1 for both sides
∴ x = 1
∴ The x-intercepts are x = 1 , x = 2 , x = 3
- To find the y-intercept put x = 0
∵ f(x) = x³ - 6x² + 11x - 6
∵ x = 0
∴ f(0) = 0 - 0 + 0 - 6 = -6
∴ The y-intercept is -6
The map of a walking trail is drawn on a coordinate grid with three points of interest the trail starts at R(-2,4) and goes to S(3,4) and continues to T(3,-1) The total length of the walking trail is what units
Answer:
10 units
Step-by-step explanation:
Points R and S both have y-coordinate 4, so they are on the same horizontal line. The distance between them is the absolute value of the difference of the x-coordinates.
RS = |-2 - 3| = |-5| = 5
Points S and T both have x-coordinate 3, so they are on the same vertical line. The distance between them is the absolute value of the difference of the y-coordinates.
ST = |-1 - 4| = |-5| = 5
The total length of the trail is the sum of the two distances.
total length = 5 + 5 = 10
Answer:
Step-by-step explanation:
Using the formula for distance, D given 2 coordinates (see attached)
Given
R(-2,4) S(3,4) T(3,-1)
Distance RS = √ { [ (-2) -3]² + [4-4]² } = √25 =5 units
Distance ST = √ { [ (3 -3]² + [4-(-1)]² } = √25 = 5 units
Total distance = RS + ST = 5 + 5 = 10 units
A country's population in 1990 was 46 million.
In 2002 it was 49 million. Estimate
the population in 2006 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt
Answer:
50 million
Step-by-step explanation:
You don't need to go to the trouble to find the value of k in e^(kt). Rather, you can use the given ratio directly.
When t = years after 1990, the population of 49 million took 12 years to achieve. The estimate desired is for 16 years after the year 1990. The appropriate exponential formula for the population is ...
P = 46·(49/46)^(t/12)
Then for t=16, this is ...
P = 46·(49/46)^(16/12) ≈ 50.04 . . . . million
The population in 2006 is estimated at 50 million.
_____
The form of the exponential equation we used above is ...
f(x) = (baseline value)·(ratio to baseline)^(x/(interval corresponding to ratio))
¿Cuál de las siguientes funciones es una función constante? Seleccione una: a. Y=x+1 b. Y=x+2 c. X=y+3 d. Y=3
Answer:
Option D y=3
Step-by-step explanation:
The question in English is
Which of the following functions is a constant function?
we know that
A constant function is a function whose output value is the same for every input value
so
Verify each case
case A) y=x+1
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case B) y=x+2
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case C) x=y+3
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case D) y=3
This is a constant function
Is a function whose output value is the same for every input value
I HAVE NO IDEA HOW GO DO THIS!! PLEASE HELP!!
If measure of arc AXC = 260, what is m< ABC
Answer:
130°
Step-by-step explanation:
Since there are 360 degrees is a circle, measure of AXC = 260 means the measure of Arc AC is:
360 - 260 = 100
Now if we were to draw 2 lines, one from A to X and another from C to X, we would have an intercepted angle at X originating from AC.
The theorem is when the intercepted angle is at the opposite side of the circumference, the angle is HALF THAT OF THE ARC.
So, half of 100 is 50.
Angle X and Angle B add up to 180, hence Angle ABC is 180 - 50 = 130
Match each of the following types of angles to the correct definition.
Answer: There Ya go
Explanation:
evaluate 11 C4 and 1 P4
Answer:
Step-by-step explanation:
11C4 = 11! / (7!*4!) = 11 * 10 * 9 * 8 * 7!/ 7! * 4!
11C4 = 11*10 * 9 * 8 / 24
11C4 = 11*10 * 3
11C4 = 330
========
You can't do the second one. Permutations and Combinations always give an answer greater than 1 and integers.
-3(-x)-6=-3x+10 solve
Answer:
[tex]\large\boxed{x=\dfrac{8}{3}}[/tex]
Step-by-step explanation:
[tex]-3(-x)-6=-3x+10\\\\3x-6=-3x+10\qquad\text{add 6 to both sideS}\\\\3x=-3x+16\qquad\text{add}\ 3x\ \text{to both sides}\\\\6x=16\qquad\text{divide both sides by 6}\\\\x=\dfrac{16}{6}\\\\x=\dfrac{8}{3}[/tex]
HHHEEELLLPPP!!!! MY ENTIRE SUMMER DEPENDS ON THIS!!
IF YOU CAN’T LEGITIMATELY ANSWER, DON’T BOTHER EVEN TRYING.
Test to see how many boxes of Lucky Chocolate Oat Crunch need to be purchased to collect all eight dinosaurs. Use the spinner provided to simulate the purchase of the cereal boxes. Each time the spinner is spun, it represents the purchase of one cereal box. As you spin, you will need to keep track of your results. You will use the results to compute the experimental probability, which you will compare with the theoretical probability. Use the spinner below to determine how many boxes of cereal you might need to purchase to collect all eight dinosaurs. Continue until the spinner has landed on each dinosaur once. Be sure to stop spinning once the spinner has landed on each dinosaur one time. Each number on this spinner represents a different dinosaur. You need to complete the simulation three times. That is, after each dinosaur has been spun one time, record your results. Then, create a new chart for the next set of results. When you are finished, you will have three sets of data that will most likely not match.
(ALREADY COMPLETED THIS PART, THE CHARTS ARE BELOW)
Use all three sets of data to answer the following questions in complete sentences. For this exercise, the probabilities refer to the probability of getting any one dinosaur when making any one purchase. You do not need to determine the probability of the compound event of getting all eight of the dinosaurs. Make sure to have all three simulations done to help you answer these questions in the writer's box:
(NEED HELP WITH THIS. ANSWERED A FEW ALREADY, NEED HELP WITH THE ONES SHOWN)
1. How does the number of spins correlate to the number of boxes of cereal that you would need to purchase?
2. What was the experimental probability for EACH dinosaur from Trial 1? Trial 2? Trial 3?
3. How does the experimental probability of getting each dinosaur differ from the theoretical probability? Here, you are comparing the experimental vs. theoretical probability of getting each type of dinosaur in a single purchase. In other words, you are determining the probability for a single event, not a compound event.
4. If someone bought eight boxes of cereal and got all eight dinosaurs, would you be surprised? Why or why not?
5. How did the experimental probabilities change between the trials?
6. What are the advantages of using a simulation versus actually buying boxes of cereal?
have you finished this yet? im doing it rn and i need help on some of them. if you havent i can help you with a couple answers
Find the coordinates of the midpoint of the segment whose endpoints are H(2,1) and K(10,7)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{10+2}{2}~~,~~\cfrac{7+1}{2} \right)\implies \left( \cfrac{12}{2}~,~\cfrac{8}{2} \right)\implies (6,4)[/tex]
what is the percentage of 200,000 in
131,000,000 ?
Answer:
Step-by-step explanation:
Let assume that x% = 200,000
Lets assume that 100 % = 131,000,000 because it is the output value:
Therefore we have two equations:
x% = 200,000
100 % =131,000,000
Now observe that the L.H.S of both the equations have same unit. So we can write it as:
100%/x% = 131,000,000/200,000
Now just simply solve the values:
Multiply both sides by x
100/x *x = 131,000,000/200,000 *x
100=655x
Now divide both the sides by 655.
100/655 = 655x/655
100/655=x
0.15267175572519=x
Therefore the answer is 200,000 is 0.15267175572519% of 131,000,000 ....
just an addition to the reply above, which is correct, so to the risk of sounding redundant.
if we take 131,000,000 to be the 100%, what is 200,000 off of it in percentage? Bearing in mind that 1% of 131,000,000 is really 1,310,000, notice we simply chopped off two zeros, but that amount is larger than 200,000 and thus whatever 200,000 is, is less than 1%.
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 131000000&100\\ 200000&x \end{array}\implies \cfrac{131000000}{200000}=\cfrac{100}{x}\implies \cfrac{1310}{2}=\cfrac{100}{x} \\\\\\ 1310x=200\implies x=\cfrac{200}{1310}\implies x\approx 0.1526717557251908[/tex]
Which of the following describe an angle with a vertex at E?
Check all that apply.
O A. ZEFD
OB.HDEF
OC. ZFED
D. ZDFE
SUBMIT
Answer:
The answer would be option B and option C
∠DEF and ∠FED describe an angle with a vertex at E.
The correct answers are option (B) and option (C)
What is an angle?"It is the figure, in which two rays meet at a common point.""The common point is called the vertex.""It is denoted using the symbol ∠ "For given question,
We need to find the correct angle with a vertex at E.
We know that the vertex is the common point of the rays of an angle.
It is always written at the middle in an angle.
So, ∠DEF and ∠FED describe an angle with a vertex at E.
The correct answers are option (B) and option (C)
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how do you say 75,000
seventy five thousand
Answer:
Step-by-step explanation:
I can't add much to this. The answer is 75 thousand.
Which of the following is an extraneous solution of (45-3x)^1/2=x-9?
A= -12
B= -3
C= 3
D= 12
Answer:
C. x =3
Step-by-step explanation:
Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.
Let's solve the equation first
[tex]\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6[/tex]
Hence, we can conclude that x=3 is an extraneous solution of the equation ..
Answer:
C
Step-by-step explanation:
The difference of x and a number is 6. What is the other number?
6
6 - (x-6)
0 6+*
Answer:
The number is x-6
Step-by-step explanation:
difference of x and a number is 6
Difference means subtract, is means equals
x-n = 6
Add n to each side
x-n+n = 6+n
x = n+6
Subtract 6 from each side
x-6 = n+6-6
x-6 =n
The number is x-6
Given the following functions f(x) and g(x), solve f[g(6)].
f(x) = 6x + 12
g(x) = x - 8
Answer:
f[g(6)] = 0
Step-by-step explanation:
f(x) = 6x + 12
g(x) = x - 8
f[g(6)]
First lets find g(6)
g(6) = 6-8 = -2
Then we substitute -2 in for g(6)
Putting -2 into f(x)
f[g(6)] = f(-2) = 6(-2)+12 = -12+12 =0
y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necessary.
Answer:
3.7
Step-by-step explanation:
Inversely means we are taking the constant and dividing it.
So y varies inversely with x means "y=k/x".
k is a constant. We can find the constant if they give us a point on this curve.
The constant is a number that doesn't change no matter your input and output.
[tex]y=\frac{k}{x}[/tex]
So they actually give us k=8.88 and y=2.4 so let's input this:
[tex]2.4=\frac{8.88}{x}[/tex]
We need to solve this equation for x. You can do your favorite thing in cross-multiply. But how, Freckles? Well just slap a 1 underneath that 2.4. You can do that because 2.4/1 is still 2.4.
[tex]\frac{2.4}{1}=\frac{8.88}{x}[/tex]
Cross-multiply:
[tex]2.4x=8.88(1)[/tex]
[tex]2.4x=8.88[/tex]
Divide both sides by 2.4:
[tex]x=\frac{8.88}{2.4}[/tex]
[tex]x=3.7[/tex] when [tex]y=2.4[/tex].
how many terms are in the equation 4x+2x(3x-5)
Answer:
4
Step-by-step explanation:
a term is simply separated by either a + or a - which means the terms here is 4x,2x,3x and 5
Answer:
4
Step-by-step explanation:
There are 4 terms in the equation 4x+2x(3x-5).
4x,2x,3x and 5
choose the equation that represents a line that passes through points -3,2 and 2,1
5x+y=-13
5x-y=17
x-5y=-13
x+5y=7
Answer:
D. X+5y=7
passes through both coordinates
Answer:
all work is shown and pictured
In a circle, a 90° sector has area 167 ft2. What is the radius of the circle?
Answer:
[tex] \sqrt{\frac{668}{\pi} } [/tex] feet given the area is 167 ft squared
Step-by-step explanation:
Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle. The area of a circle is pi*r^2. We will only be using a 4th of that since are sector is only a 4th of the circle.
So the formula will be using for the area of our sector is A=1/4 *pi*r^2.
We are given the area is 167 so replace A with 167.
167=1/4 * pi *r^2
Multiply both sides by 4.
167*4 =pi * r^2
668=pi * r^2
Divide both sides by pi
668/pi =r^2
Square root both sides
[tex] \sqrt{\frac{668}{\pi} } =r [/tex]
if f(x)=4x^+1 and g(x)=x^-5, find (f-g)(x)
Answer:
(f-g)(x) = 4x - x^(-5)
Step-by-step explanation:
Please, enclose that negative exponent inside parentheses: g(x)=x^(-5). No need to type in the " + " in f(x)=4x^+1.
g(x) is to be subtracted from f(x). Write f(x):
f(x)=4x
followed by the negative of g(x): -g(x) = -x^(-5)
and now combine these two results:
f(x)=4x
-g(x)= -x^(-5)
---------------------
(f-g)(x) = 4x - x^(-5)
The expression for (f-g)(x) is (f-g)(x) = 4x² + 1 - 1/x⁵
What is a function?A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.
To find (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
We are given:
f(x) = 4x² + 1
g(x) = x⁻⁵ = 1/x⁵
Substituting these values into the expression for (f-g)(x), we get:
(f-g)(x) = f(x) - g(x) = (4x² + 1) - (1/x⁵)
Simplifying the expression, we can write:
(f-g)(x) = 4x^2 + 1 - 1/x⁵
Therefore, the expression for (f-g)(x) is:
(f-g)(x) = 4x² + 1 - 1/x⁵
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-15
-3
3
15
Pls help idk this
Answer:
-3
Step-by-step explanation:
4^x = (1/8)^(x+5)
(2^2)^x = (2^-3)^(x+5)
2^2x = 2^(-3x - 15)
Since both sides have the same base of 2, then the exponents are equal
So
2x = - 3x - 15
5x = -15
x = -3
Answer:
-3
Step-by-step explanation:
see attached
The Smith family has 80 movies in their collection. The types of movies are shown in the table below. Smith Family Movies Type of Movie Percentage Drama 10% Action 25% Animated/Children’s 50% Comedy 15% How many of the movies in the collection are action movies?
Answer:
20 movies
Step-by-step explanation:
no of movies= 80
action movies percentage=25%
no of action movies=25/100*80(25% of 80)
What is the value of -3r+8 when r =4
Answer:
-4
Step-by-step explanation:
To find your answer, plug in 4 for r.
[tex]-3r+8\\-3(4)+8[/tex]
You can start by multiplying -3 by 4.
[tex]-3(4)+8\\-12+8[/tex]
Next, add -12 to 8 and you'll have your answer.
[tex]-12+8\\-4[/tex]
Answer:
-4.
Step-by-step explanation:
Substitute r = 4 into the given expression:
= -3(4) + 8
= -12 + 8
= -4.
If the price of 1 dozens of apples is Rs 84, find the price of 4 apples.
Answer:
The price of 4 apples is Rs 28
Step-by-step explanation:
The price of 1 dozen apple is Rs 84
12 apples =Rs 84
1 apple = Rs 84÷12
1apple =Rs 7
Again
Price of 4 apples = Rs 7 × 4
= Rs 28 Ans,,
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot a point at the y-intercept of the following function on the provided graph.
3y = -5^x + 7
Answer:
The y-intercept is the point (0,2)
see the attached figure
Step-by-step explanation:
we have
[tex]3y=-5^{x}+7[/tex]
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
substitute in the equation and solve for y
[tex]3y=-5^{0}+7[/tex]
[tex]3y=-(1)+7[/tex]
[tex]3y=6[/tex]
[tex]y=2[/tex]
therefore
The y-intercept is the point (0,2)
using a graphing tool
see the attached figure
Answer: For Plato users plot a point on 2 at the y intercept.
Step-by-step explanation:
If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25
Answer:
see explanation
Step-by-step explanation:
Using the identity
(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then
5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is
125 = a³ + b³ + c³ + 150 - 3abc, hence
a³ + b³ + c³ - 3abc = 125 - 150 = - 25
Using the cubic identity equation and the values given in the question, we can prove that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc equals -25.
Explanation:The equation required to prove is derived from the expansion of the cubic identity (a+b+c)³. The equation is a³+b³+c³-3abc = (a+b+c)[(a+b+c)²-3(ab+bc+ac)]. Let's use the values given in the question which are (a+b+c) = 5 and ab+bc+ac = 10.
Plug these values into the equation above. So, the proof becomes 5[5²-3*10].Work out the arithmetic for this equation. We find that 5[25-30] equals 5[-5], which results in -25.Therefore, we have proved that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc indeed equals -25.
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