A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. The various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.
What is a binomial expression?A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. x² + 4x is an example of a binomial polynomial.
The variable terms that are possible in the expansion of (3a + 4b)⁸ are terms whose sum of powers is equal to 8.
a²b³ → 3 + 2 = 5 ⇒ Not possiblea⁷b → 7 + 1 = 8 ⇒ Possibleab⁸ → 1 + 8 = 9 ⇒ Not possibleb⁸ → 8 ⇒ Possiblea⁴b⁴ → 4 + 4 = 8 ⇒ Not possiblea⁶b² → 6 +2 = 8 ⇒ Possiblea³b⁴ → 3 + 4 = 7 ⇒ Not possiblea⁸ → 8 ⇒ PossibleHence, the various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.
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Choose the single logarithmic expression that is equivalent to the one shown. log6 25 − log6 5
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(25) - log_{6}(5) [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) {}^{2} - log_{6}(5) [/tex]
[ property : x² = 2 log x ]
[tex]\qquad \tt \rightarrow \: 2 \: log_{6}(5) {}^{} - log_{6}(5) [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A company makes Citi bikes. 95% (i.e., 0.95) pass final inspection. Suppose that 5 bikes are randomly selected. ( use binomial distribution formula ) do I need to use a factorial symbol V! When showing steps by step
a) What is the probability that exactly 4 of these 5 sports bikes pass final inspection?
b) What is the probability that less than 3 of these 5 sports bikes pass final inspection?
I got disconnected with my tutor
Using the binomial distribution, it is found that the probabilities are given as follows:
a) 0.2036 = 20.36%.
b) 0.0011 = 0.11%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.95, n = 5.
Item a:
The probability is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.95)^{4}.(0.05)^{1} = 0.2036[/tex]
Item b:
The probability is P(X < 3), hence:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} \approx 0[/tex]
[tex]P(X = 1) = C_{5,1}.(0.95)^{1}.(0.05)^{4} \approx 0[/tex]
[tex]P(X = 2) = C_{5,2}.(0.95)^{2}.(0.05)^{3} = 0.0011[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0.0011 = 0.0011.
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What should you substitute for y in the second equation (bottom equation) in order to solve the system by the substitution method?
Answer:
C. 3x - 9
Step-by-step explanation:
3x – y = 9 ___(1)
8x – 4y = 0 ___(2)
From (1) eq.
3x – y = 9
– y = 9 – 3x
y = - (-3x + 9)
y = 3x – 9
Hence, 3x - 9 should be substituted in the second equation to get the required answer.
Answer:
c
Step-by-step explanation:
solve for y in the first equation
y = 3x - 9
when you substitute, you will get a value of 9 for x and 18 for y
Given the first degree function f(x) = 2x +3, what is the value of f(10)?
a) 23
b) 25
c) 30
d) 50
Answer:
a
Step-by-step explanation:
substitute x = 10 into f(x) , that is
f(10) = 2(10) + 3 = 20 + 3 = 23
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
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[tex]\large \bold {ANSWER}[/tex]
[tex]\boxed{\underline{\huge{\tt{\orange{\: \: a)23 \: \: }}}}}[/tex][tex]\large \bold {SOLUTION}[/tex]
Given the first-degree function:
[tex]\Large\begin{array}{c}\rm f(x)=2x+3\end{array}[/tex]
We were asked to determine the value of f(10), so, to find its value, just replace the 10 where there is x in the function, see:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(x)=2x+3\\\\ \rm f(10)=2\cdot 10+3\end{array}\end{gathered}[/tex]
You see, we put that dot there, which indicates multiplication, because when a number is next to a letter it indicates that it is multiplying, thus:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(10)=2\cdot 10+3\\\\ \rm f(10)=20+3\\\\ \red{\boxed{\rm f(10)=23}}\checkmark\end{array}\end{gathered}[/tex]
Hence, the value of f(10) in this function is equal to 23.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
83 ⁰
to
59°
The value of x is 38 degree.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three sides .
The sum of all angles in a triangle is equal to 180 degree
The angles of the triangle given are
83 degree and 59 degree and x degree
83 + 59 + x = 180
x = 38 degree
Therefore the value of x is 38 degree.
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Given A(-2, 5) and B(13, -7), find the midpoint of AB.
Select one:
a. (-2, 11)
b. (5.5, -1)
c. (11, -2)
d. (-1, 5.5)
[tex]\left(\frac{-2+13}{2}, \frac{5-7}{2} \right)=\boxed{\left(5.5, -1)}[/tex]
There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this?
12
4
77-7/22
12
12
3
12
03-1/2/
4
The proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex]
Given that there are 3 feet in 1 yard, which is equivalent to 12 feet in 4 yards.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
We need to determine the proportion that can be used to represent this.
Now, 1 yard = 3 feet implies 4 yards = 12 feet.
The required proportion can be written as [tex]\frac{3}{1} =\frac{12}{4}[/tex].
Therefore, the proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex].
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Enter the correct answer in the box.
Function g has the same a value as function f, but its vertex is 2 units below and 3 units to the left.
f(x) = x² - 4x - 32
Write the vertex form of the equation modeling function g.
The equation in the vertex form of g(x) is:
[tex]g(x) = (x + 1)^2 - 38[/tex]
How to get the equation of function g?
We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).
So first, let's rewrite f(x) to its vertex form:
[tex]f(x) = x^2 - 4x - 32[/tex]
The vertex is at:
[tex]x = -(-4)/2*1 = 2[/tex]
The y-value of the vertex is:
[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]
Then the vertex form of f(x) is:
[tex]f(x) = (x - 2)^2 - 36[/tex]
If we move this vertex 2 units below, and 3 units to the left, then we have:
[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]
That is the equation for g(x) in vertex form.
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Factor the binomial expansion. 81x4 – 648x3 + 1,944x2 – 2,592x + 1,296
Answer:
[tex]648[/tex]([tex]x^{3} + 3x^{2} - 4x + 2[/tex])
Step-by-step explanation:
When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.
Answer:
(3x – 6)4
Step-by-step explanation:
Solve by applying the counting principle. James is choosing a Four-digit Passcode for his smartphone. How many different Passcodes are possible? There are Ten digits that James can choose from. Enter Solve by applying the counting principle . James is choosing a Four - digit Passcode for his smartphone . How many different Passcodes are possible ? There are Ten digits that James can choose from.
Answer:
10k.
Step-by-step explanation:
1) if for the 1st position can be used 0-9 digits (10 digits), for the 2d - 0-9 digits, for the 3d - 0-9 digits and for the 4th - 0-9 digits, then
2) the required number of pwd is: 10*10*10*10=10⁴=10000.
Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?
D: [–1, 5]; R: [–7, 5]
D: [–5, 7]; R: [–5, 1]
D: [–5, 1]; R: [–5, 7]
D: [–7, 5]; R: [–1, 5]
The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have an ellipse equation:
[tex]\rm x^{2}+4y^{2}-2x+16y-19=0[/tex]
We can write the above equation as:
[tex]\rm \dfrac{\left(x-1\right)^{2}}{36}+\dfrac{\left(y+2\right)^{2}}{9}=1[/tex]
The domain will be:
D: [–5, 7]
The range will be:
R: [–5, 1]
Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]
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need to know asap
Which of the following best describes the correlation between two variables if the correlation coefficient is -0.544?
weak positive
weak negative
strong negative
strong positive
Is 9.3 X 100^9 in scientific notation
Answer:
No.
Step-by-step explanation:
This problem in scientific notation would be 9.3 * 10^10.
Suppose we have already saved $55 towards the cost of a new television set.
We plan to save $6 more each week for the next several weeks.
i) Write an equation for the total amount T we will have after w weeks from now.
ii) Find the total amount that would be saved after 8 weeks.
Step-by-step explanation:
T = 55 + 6w
after 8 week $103
square root of the quantity x plus 7 end quantity minus 11 equals 2
An equation is formed when two equal expressions are equated together. The value of x in the equation [√(x+7)]-11=2 is 162.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for x in the equation [√(x+7)]-11=2 can be solved as,
[tex]\sqrt{x+7}-11=2\\[/tex]
Using the addition property of equality,
[tex]\sqrt{x+7} -11+11= 2+11\\\\\\\sqrt{x+7} = 13[/tex]
Squaring both the sides of the equation,
x + 7 = 169
Using the subtraction property of equality,
x + 7 - 7 = 169 - 7
x = 162
Hence, the value of x in the equation [√(x+7)]-11=2 is 162.
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Select the correct answer.
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
OA. The lines in a system cannot be parallel.
There are infinitely many solutions.
B.
OC. There is exactly one solution.
D. There is no solution.
Reset
Next
Answer:
Look below!
Step-by-step explanation:
From the picture, the answer is A.
From the points, calculate the slope using y2-y1/x2-x1
you will find that the slope is -1
parallel lines have the same slope
so y = -x+1 is the correct answer
now,
parallel lines never intersect
therefore, they have no solution.
I need help with this question
A trapezoid is a quadrilateral with one or more pairs of parallel sides.
O A. True
OB. False
Suppose that land in downtown Savannah is valued at $20 per square foot. What is
the value of a triangular lot with side lengths of 112, 148, and 190 feet?
Answer:
$165554
Step-by-step explanation: I use the Law of Cosines to find one of the angles of the triangle. Then use the formula for the area of the triangle: A = (1/2)absinC.
C= 92.856 degree
Area = (1/2)(112)(148)sin(92.856°) = 8277.7 ft^2
To find the price just need to take 8277.7 time 20 = 165554
So the answer is $165554
In a certain Algebra 2 class of 26 students, 16 of them play basketball and 9 of them
play baseball. There are 5 students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball or baseball?
Answer:
.7692307692 or 10/26
Step-by-step explanation:
You solve this problem by finding the total number of sports playing students and dividing it by the total, in this case 26. Since we know there are 5 students that play both sports, you subtract that 5 from the total number of basketball plyers and baseball players, so 16-5=11 and 9-5=4, then add those together, so 11+4=15. From there you add back in the students that play both which is 5, so 15+5=20. 20/26 is your answer.
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a trapezoid?
A. A cross section cut parallel with the bottom
B. A cut parallel to the vertical axis, but off the vertical axis
C. Cutting off one of the bottom corners
D. A cut parallel to the vertical axis, directly through the vertical axis
PLEASE HELP ME WITH MY MATH
The definition for the graphed function is the one shown in option d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Which piecewise function coincides with the graph?Here we have a piecewise function, where for the first part we have a linear equation with a negative slope (for x < 1, we know that the symbol "<" must be used because of the open dot at the end of the line).
Then, we have another linear equation with a negative (and steeper) slope. This time there is a closed dot, so the domain for this second part is x ≥ 1.
With that we can conclude that the correct option is:
d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Where you can see that the second part has a larger (in module) slope, and the domains are defined as we saw above.
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2x+3y=4 cual es la respuesta??
Answer:
y = 2/3x + 4/3
Step-by-step explanation:
Voy a suponer que necesitas resolver para y.
2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
With the information given, can you prove this quadrilateral is a parallelogram?
Could someone help me with this problem? I'm not sure if those lines are parallel, congruent, or both, because there are two arrows on each line instead of one.
Will give Brainliest for the best answer.
Answer:
it it a parallelogram
Step-by-step explanation:
it has 2 sets of 2 parallel lines
With the information given, we can not prove this quadrilateral is a parallelogram. Explanation is given.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
In order to prove, quadrilateral is a parallelogram:
We can prove either one of these following method;
1. Establish the congruence of the two pairs of opposing sides.
2. Show that the two opposing side pairs are parallel.
3. Show that one pair of opposed sides is parallel and congruent.
Here, we have AB = CD
And we have line AD and BC.
Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
AD and BC are at equal distance.
That means, AD II BC.
And to solve further, we do not have any statements.
Therefore, with given information, we can not prove this quadrilateral is a parallelogram.
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which is the most appropriate Venn diagram...
The most appropriate Venn diagram is known to be option b in the image shown.
What is a common multiple?A Common multiples are known to be the multiples that are said to be common to two or that have more numbers in them.
The Least Common Multiple ( LCM ) is known to be a term that connote the Lowest Common Multiple ( LCM ) and also that has the Least Common Divisor ( LCD).
From the image shown the lowest multiples are 5², 2⁶, 3 while the greatest common factor is 2⁶.
Option B is correct because the greatest common factor which is 2⁶ can only be found in the middle and this was gotten when you add:
2³ . 2³
Collect like terms
2 ³⁺³
2⁶
Therefore, the greatest common factor which is 2⁶
To get the Least Common Multiple, one need to add all the factors in the Venn diagram which are therefore:
5², 2³ . 2³, 3
=5², 2 ³⁺³, 3
=5², 2⁶, 3
Therefore, The most appropriate Venn diagram is known to be option b in the image shown.
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There are nine baseball players in the cafeteria The number of baseball players is one less than twice the number of golfers find the number of golfers
Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of baseball players.Variable y: Number of golf players.The number of baseball players is one less than twice the number of golfers, hence:
x = 2y - 1.
Since x = 9:
9 = 2y - 1
2y = 10
y = 5.
There are 5 golfers in the cafeteria.
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a single card is drawn from a standard 52-card deck calculate the probability and odds for the following event a jack or club is drawn
17/52
Step-by-step explanation: There are 13 clubs in a deck of fifty-two cards and there are four jacks in a fifty-two deck. So adding that up it's 17 out of 52 = 17/52. And you can not reduce it.
a² + b² + ab = 7
b² + c² + bc = 21
a² + c² + ac = 28 ab + bc + ac = ?
Answer:
ab+bc+ac = 7+21 + 28 =56
so the answer is 56
Observe that
[tex]a^2 + b^2 + ab = 7 \iff a^2 + b^2 - 2\cos(120^\circ) = \left(\sqrt 7\right)^2[/tex]
[tex]b^2 + c^2 + bc = 21 \iff b^2 + c^2 - 2\cos(120^\circ) = \left(\sqrt{21}\right)^2[/tex]
[tex]a^2 + c^2 + ac = 28 \iff a^2 + c^2 - 2\cos(120^\circ) = \left(\sqrt{28}\right)^2[/tex]
Drawing a comparison to the law of cosines, we see the first equation defines a triangle with sides [tex]a[/tex], [tex]b[/tex], and [tex]\sqrt 7[/tex]; the second equation defines one with sides [tex]b[/tex], [tex]c[/tex], and [tex]\sqrt{21}[/tex]; and the third equation defines another one with sides [tex]a[/tex], [tex]c[/tex], and [tex]\sqrt{28}[/tex]. We can then join these triangles at a point D to form a new triangle ABC with sides [tex]\sqrt7,\sqrt{21},\sqrt{28}[/tex]. (See attached sketch)
Now, the area of ABC is the sum of the areas of ABD, BCD, and ACD. The area of any of these triangles is equal to half the area of a parallelogram spanned by the sides involving the vertex D. The area of a parallelogram with adjacent sides [tex]x[/tex] and [tex]y[/tex] and with angle [tex]\theta[/tex] between them is [tex]ab\sin(\theta)[/tex].
For example, triangle ABD has area
[tex]\mathrm{area}_{\Delta ABD} = \dfrac12 \times ab \sin(120^\circ)[/tex]
Then the total area of triangle ABC is
[tex]\mathrm{area}_{\Delta ABC} = \dfrac12 \sin(120^\circ) (ab + ac + bc)[/tex]
We use Heron's formula to find the area of ABC. If [tex]s[/tex] is its semiperimeter, i.e.
[tex]s = \dfrac{\sqrt7 +\sqrt{21} + \sqrt{28}}2[/tex]
then, with a lot of algebraic simplification,
[tex]\mathrm{area}_{\Delta ABC} = \sqrt{s (s-\sqrt7) (s - \sqrt{21}) (s - \sqrt{28})} = \dfrac{7\sqrt3}2[/tex]
Finally, we find
[tex]\dfrac{7\sqrt3}2 = \dfrac12 \sin(120^\circ) (ab + ac + bc) \implies ab + ac + bc = \dfrac{\frac{7\sqrt3}2}{\frac12\times\frac{\sqrt3}2} = \boxed{14}[/tex]
Find the area of the shaded region
O100 m²
O 105 m²
O 75 m²
O 50 m²
5m
10 m.
5m
15 m
Brainliest to who answers :>
Answer:
L is not valid.
Step-by-step explanation:
For any triangle, the sum of the two legs must be greater than the hypotenuse. Otherwise the two legs would not be long enough to touch.
Answer:
L
Step-by-step explanation:
to add to the previous basically correct answer :
for a triangle the sum of any 2 sides must be greater than the third side (not just legs and Hypotenuse).
for all other options any combination of sum of 2 sides being bigger than the third side works.
but for L
2 + 5 = 7, which is smaller than the third side (8). so, this cannot be a triangle.