On solving the provided question, we cans ay that the value of x from the polynomial [tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex] is = 16 and 1
what are polynomials?A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.
here,
[tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex]
as x = 0 and y = 1
answer is = 16 and 1
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Prove that for any natural n: a the number 7^(n+4) −7^n is divisible by 30.
For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.
What is mathematical induction?An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.
Let, n = 0.
Therefore,
7⁴ - 7⁰.
= 2401 - 1.
= 2400.
= 30×80, Divisible by 30.
Similarly for n = 1 we have,
7⁵ - 7¹.
= 16807 - 7.
= 16800.
= 30×560.
Hence by induction, the cycle will continue.
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A bag contains 7 red cubes, 3 yellow cubes, 2 green cubes, and 4 blue cubes, one cube is selectef at random from the bag. What is the probability that the seleceted cube will not be blue.
The probability that the selected cube will not be blue is given as;
P(selected cube not blue) = 3/4
We are given that;
Number of red cubes = 7 cubes
Number of yellow cubes = 3 cubes
Number of green cubes = 2 cubes
Number of blue cubes = 4 cubes
Total number of cubes = 7 + 3 + 2 + 4
Total number of cubes = 16 cubes
Probability that the cube that is selected is blue;
P(selected cube is blue) = 4/16 = 1/4
Thus, probability that it will not be blue will be;
P(selected cube not blue) = 1 - (1/4)
P(selected cube not blue) = 3/4
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1. The backdrop of the altar in a church is triangular in shape. It has a base of 10.5 meters
and a height of 8.5meters. The priest instructed the layman to cover it from the center with
a white rectangular cloth measuring 4.5 meters long and 4 meters wide. How big was the uncovered backdrop?
A. 26.63 m² B. 18 m²
C. 44.63 m² D. 89.25 m²
------------------------------------
2. A circular portion of a cardboard having 7.6 centimeters radius was being cut out from the entire
squarepiece of a cardboard having a side of 34 centimeters. How big was the remaining piece of
a cardboard?
A.181.37 m² B.974.63 m²
C. 1156 m² D. 219.6 m²
Answer:
#1
Area of triangle backdrop:
A = 1/2bh = 1/2(10.5)(8.5) = 44.63 m²Area of the cloth:
A = 4.5*4 = 18 m²Uncovered area:
44.63 - 18 = 26.63 m²Choice A
#2
Area of the cut piece:
A = πr² = 3.14*7.6² = 181.37 cm²Area of the square piece:
A= a² = 34² = 1156 cm²Remaining piece is:
1156 - 181.37 = 974.63 cm²Choice B
Anna wants to buy 4 sweaters. The sweater come at a discount rate. If you buy one sweater regular price the other sweater is 40% off. How much percent is off of each sweater?
Answer:
20%------------------------
If you buy a sweater, the second one is at 40% discount.
Divide the discount between the two to get:
40%/2 = 20%You get a discount of 20% for each sweater.
Answer:
Discount percentage = 20%
Step-by-step explanation:
Discount of the sweaters,
→ first sweater = 0%
→ other sweater = 40%
The average discount percent is,
→ (first sweater + other sweater)/2
→ (0% + 40%) ÷ 2
→ (0 + 40)/2
→ 40/2
→ 20% off
Hence, the answer is 20% off.
Find the missing numbers 46 62 87 123 ---- 236
Answer:
The missing numbers are 74, 105, and 178.
If a= m2 + 2, what is the value of a when m=-3?
0-7
-4
11
00
Answer:
a=11
Step-by-step explanation:
a=m2 +2
a= (-3)2+2
a=9+2
a=11
Can y’all help me on question 20?!
Answer:
A. 84
Step-by-step explanation:
84 / 4 = 21
Answer:
Its a(84)
Step-by-step explanation:
2 cm
A glass bead has the shape of a rectangular prism with a smaller rectangular
prism removed. What is the volume of the glass that forms the bead?
]
2 cm
4 cm
7 cm
4 cm
(The figure is not to scale.)
The volume of the glass that forms the bead is cm3.
Answer:
80
Step-by-step explanation:
Explain what an exponential form is but leveled down for high schoolers
The required exponential function is given as y = aˣ where the value of a should be positive always.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
Since from the above definition exponential function is given as y = aˣ,
This shows the exponential increase and decrease, by means of exponential increase and decrease, a sudden in increase and sudden decrease of function as the value of a varies, see in the graph after the answer. And the value of an always remains positive.
Thus, the required exponential function is given as y = aˣ where the value of a should be positive always.
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The function f is defined by f(x) = 2x2 -7.
Find f(5x).
Answer:
10fx-7
Step-by-step explanation:
(:
-15 POINTS-
How many sides does a regular polygon have if one interior angle measures 144°
Answer: 10 sides
Step-by-step explanation:
You can always use the given formula to calculate but I (personally) find it much easier to calculate the number of sides using the exterior angle.
To calculate the exterior angle, it is 180 - the interior angle.
In this example, the exterior angle would be 180-144 = 36°
Because it is a regular polygon, we know that all the angles in the shape are the same.
In all polygons, the exterior angles always add up to 360 degrees.
So divide 360 by 36 (the size of each exterior angle), and you get 10.
360/36 = 10
4. What is the slope-intercept form of 9x + 3y = 15?
Oy=-3x+5
Oy=3x+5
Oy = 3x - 5
Oy=-3x - 5
The slope-intercept form of the equation 9x + 3y = 15 is y = -3x + 5.
What is slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The given equation is 9x + 3y = 15.
Rearranging it to get in slope-intercept form -
⇒ 9x + 3y = 15
⇒ 3y = -9x + 15
Dividing LHS and RHS by 3 -
⇒ y = -3x + 5
Here, the equation is the slope-intercept form y = mx + c.
So, the slope is m = -3 in the equation.
Therefore, the slope-intercept form is y = -3x + 5.
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2-3(3x+1)=2(7-6x) - SOLVE THE FOLLOWING EQUATION
Answer: X=5
Explaination: Did the problem.
Question #2
What is the value of the expression
35
?
23 – 1
A 5
B 7
C 12
Answer:
A. 5
Step-by-step explanation:
just use calculator tbh
what is the correct factorization of 100^12
Answer:
GCF of 12 and 100 by Prime Factorization
Prime factorization of 12 and 100 is (2 × 2 × 3) and (2 × 2 × 5 × 5) respectively. As visible, 12 and 100 have common prime factors. Hence, the GCF of 12 and 100 is 2 × 2 = 4.
GCF of 12 and 100 by Listing Common FactorsFactors of 12: 1, 2, 3, 4, 6, 12Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
There are 3 common factors of 12 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 100 is 4.
The square of a number minus six times a number equals negative five.
The equation is ?
The solutions to the equation is ?
Answer:
x² - 6x = -5
x = {1, 5}
Step-by-step explanation:
The square of a number minus six times a number equals negative five.
x² - 6x = -5
Add 5 to both sides
x² - 6x + 5 = 0
Factor
(x - 1)(x - 5) = 0
x = {1, 5}
Answer:
[tex]x^{2} - 6x = -5[/tex]
x = 1 or x = 5
Step-by-step explanation:
Let x = the no.
[tex]x^{2} - 6x = -5\\x^{2} - 6x + 5 = 0[/tex]
(x - 1)(x - 5) = 0
x = 1 or x = 5
A soccer team has 15 players and needs to choose a captain and an assistant captain. How many ways can those positions be selected?
Answer:
91 ways. So the answer to the problem's question is THIS : in 15*91 = 1365 ways.
Step-by-step explanation:
What is the area of the figure below? 7 cm 8 cm 3 cm 4 cm
Solve systems of equations by elimination -9x-2y=5 -9x-2y=11
Answer:
no solutions
Step-by-step explanation:
-9x-2y=5
- (-9x-2y=11)
-9x-(-9x) - 2y-(-2y) = 5 - 11 ==> subtract the top two equations
-9x + 9x - 2y + 2y = -6 ==> subtracting by a negative number is equivalent
to adding by a positive number
(-9x + 9x) - 2y + 2y = -6
0 - 2y + 2y = -6
0 - 0 = -6
0 [tex]\neq[/tex] -6 ==> Hence, there is no solutions.
PLEASE BE FAST
Find the constant of proportionality for the proportional relationship shown in the graph.
graph of a line going through 0 comma 0 and one half comma 5
p = 10
p = 5
p = 0.5
p = 0.1
The constant of proportionality is 10 for the proportional relationship shown in the graph.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
The proportional relationship is shown in the given graph.
As per the given graph, we take two points (1, 10) and (2, 20)
So, the constant of proportionality will be as:
⇒ (20 - 10)/(2-1)
⇒ 10/1
⇒ 10
Hence, the correct answer would be option (A).
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GIVING BRANLIEST ! NEED HELP! PLEASE
The probability that a birth will result in twins is 0.017. Assuming independence (perhaps not a valid assumption), what is the probability that out of 120 births in a hospital, there will be exactly 4 sets of twins?
The probability that there will be exactly 4 sets of twins is?
Answer:
0.0939 = 9.39% probability that there will be exactly 4 sets of twins.
Step-by-step explanation:
For each birth, there is only two possible outcomes. Either it results in twins, or it does not. The probability of a birth resulting in twins is independent of any other birth. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that a birth will result in twins is 0.017.
This means that [tex]p = 0.017[/tex]
120 births:
This means that [tex]n = 120[/tex]
The probability that there will be exactly 4 sets of twins is?
This is P(X = 4).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{120,4}.(0.017)^{4}.(0.983)^{116} = 0.0939[/tex]
0.0939 = 9.39% probability that there will be exactly 4 sets of twins.
what is equivalent to 2/8
Answer:
1/4,
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
Sarah completes 1/6 of a project in 1/4 of an hour. At this rate, how much of
the project does Sarah complete per hour? *
Find the measure of angle B. Round your answer to the nearest whole 10 points number. *
Answer:
38
Step-by-step explanation:
180 - 104 = 76
76 divided by 2 = 38
Here is the graph of a quadratic function f.
Select all equations that could define the function f.
Answer:
A B and D
Step-by-step explanation:
Given the parabola is opening downward, the function has to be negative. Therefore, A B and D are correct.
The following equations could define the given quadratic function.
1. -1(x-1)²+9
4. -x²+2x+8
6. (x+2)(x-4)
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
1. The function -1(x-1)²+9 represents a downward-facing parabola.
The vertex of the parabola is at point (1, 9), and it opens downward because the coefficient of the squared term (-1) is negative.
4. The function -x²+2x+8 represents a downward-facing parabola as well.
6. The parabola intersects the x-axis at x = -2 and x = 4.
Hence, the correct answer is options 1, 4, 6.
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pls help i’ll give brainliest
Answer:
94
Step-by-step explanation:
So
376= x + 3x
Where x is the hambugers and 3 x is cheeseburgers
so it is the same as
376= 4x
divide both sides by 4
x= 94
we can check by tripling x = 283 and adding the hamburgers we found to be 94 which gives us 376
-15 POINTS- Find the length of the indicated side of the similar figure X=[?]
help help help help pls
Answer:
67
Step-by-step explanation:
42+90=132
180-132=48
<A=48
if u use the 113 that you got than
113+48=161
180-161=19
<B= 19
48+19=67
17v = 62 (exponential equations with logarithms, solve)
Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.
Define log(Logarithm).The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
What is a function?A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).
Given the equation 17v = 62, we can take the logarithm base 17 of both sides:
log(17^v) = log(62)
v*log(17) = log(62)
Dividing both sides by log(17) gives us:
v = log(62) / log(17)
This is the solution for v, the unknown variable in the equation.
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It takes 7 hours for 12 men to paint a room.
How many men would be needed to paint the room in 3 hours?
Answer: 28 men would be needed to paint the room
q=number of men for 3 hours
q x 1/84 x 3 = 1
q x 1/28 = 28