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Related Questions
Ron is five years older than twice his cousin Pat’s age. The sum of their ages is less than 35. What is the greatest age that Pat could be? 7,8, or 10? Please more then one response so I know its right,
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Find an nth degree polynomial function with real coefficients satisfying the given conditions. calculator
Answers
To find an nth-degree polynomial function with real coefficients given certain conditions, we can write the polynomial as a product of its linear factors using the given roots.
Explanation:To find an nth-degree polynomial function with real coefficients, we need to use the given conditions. Let's say the conditions include the roots of the polynomial. If we have n distinct real roots, the polynomial will have n factors. So, if the roots are a, b, c, ..., we can write the polynomial as P(x) = (x - a)(x - b)(x - c)...
Example:To find a quadratic polynomial with roots 2 and -3, we can write the polynomial as P(x) = (x - 2)(x - (-3)) = (x - 2)(x + 3) = x² + x - 6.
Similarly, for higher-degree polynomials, we use the same approach. We write the polynomial as a product of its linear factors using the given roots.
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Let set A = {1, 3, 5, 7} and set B = {1, 2, 3, 4, 5, 6, 7, 8}
Which notation shows the relationship between set A and set B?
@ganeshie8,
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Which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?
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the magnitude of an earthquake s
M=log[I/S]
where
I----------> is the intensity of the earthquake
S---------> is the intensity of a standard earthquake
in this problem
I=100S
then
M=log[100S/S]
this equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake
M=log(100)-----------> M=2
The magnitude of this earthquake is 2 on the Richter scale
To represent an earthquake that is 100 times more intense than a standard earthquake, an increase of 2 on the Richter scale is required due to the logarithmic nature of the scale.
Explanation:The magnitude of an earthquake that is 100 times more intense than a standard earthquake would be represented by an increase of 2 on the Richter scale. This scale is logarithmic, meaning that each whole number increase on the Richter scale represents a tenfold increase in amplitude. To be 100 times more intense, we need a tenfold increase for each magnitude, so an increase from, for example, magnitude 3 to 5 would represent an earthquake that is 100 times more intense.
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Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
A) f(0) = 7
B) f(0) = −7
C) f(−7) = 0
D) f(7) = 0
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When (x + 7) is a factor, f(-7) = 0. Thus, option C is correct: f(-7) = 0.
When the polynomial f(x) has (x + 7) as a factor, it implies that when x is replaced by -7, f(x) becomes zero.
This follows from the factor theorem which states that if (x - c) is a factor of a polynomial f(x), then f(c) = 0.
Therefore, to satisfy this condition, f(-7) = 0.
Consequently, option C, stating that f(-7) = 0, must be true when (x + 7) is a factor of f(x).
Thus, the correct answer is C) f(-7) = 0.
what is the y- coordinate of the y- intercept of the line that passes through the points (-4,-4) and (4,8)
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[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}y-(-4)=\cfrac{3}{2}[x-(-4)] \\\\\\ y+4=\cfrac{3}{2}(x+4)\implies y+4=\cfrac{3}{2}x+6\implies y=\stackrel{slope}{\cfrac{3}{2}}x\stackrel{y-intercept}{+2}[/tex]
notice the slope-intercept form, that's the y-coordinate.
use substitution to solve 3x-2y=11 and x+2y=9
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.. 2y = 9 -x
Substitute that into the first equation.
.. 3x -(9 -x) = 11
.. 4x -9 = 11
.. 4x = 20
.. x = 5
Using our expression for 2y above,
.. 2y = 9 - 5
.. y = 4/2 = 2
The solution is (x, y) = (5, 2).
how do you simplify x^2-4x-21 divided by x+3
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Notice how
3 plus -7 = -4
3 times -7 = -21
which helps us factor the trinomial
After you've factored it, we can cancel out a pair of (x+3) terms leaving us with the final answer of x-7
Note: the cancellation happens because (x+3)/(x+3) = 1. Divide anything (except 0) over itself and you'll get 1. A simpler example of this is 5/5 = 1.
Use the quadratic formula to find both solutions to the quadratic equation given below 2x^2-3x+1=0
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(2x2 - 3x) + 1 = 0
(x - 1) • (2x - 1) = 0
x-1=0
x = 1
Answer:
[tex]x_1=1\\x_2=\frac{1}{2} =0.5[/tex]
Step-by-step explanation:
Given a equation of the form:
[tex]ax^2+bx+c=0[/tex]
The roots of this equation can be found using the quadratic formula which is given by:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
In this case we have this equation:
[tex]2x^2-3x+1=0[/tex]
So:
[tex]a=2\\b=-3\\c=1[/tex]
Using the the quadratic equation :
[tex]x= \frac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(1) } }{2(2)} = \frac{3\pm\sqrt{9-8 } }{4}=\frac{3\pm 1}{4}[/tex]
Therefore the two roots would be:
[tex]x_1=\frac{3+ 1}{4}=\frac{4}{4}= 1\\x_2=\frac{3- 1}{4}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]
1. Solve the equation. -4x = 0
X = -4
X = 4
X = 0
X = 1
2. decide whether the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17 ?
Yes or no
3. simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x2 + 8x
4. Name the property shown. 12x( y ) = 12(xy)
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2. is yes
3. is 6x
4. is associative property of multiplication
What exponential function is the best fit for the data in the table?
x f(x)
2 −3
3 0
4 12
f(x) = 4(4)x − 1 + 4
f(x) = 4(4)x − 1 − 4
f(x) = one fourth(4)x − 1 + 4
f(x) = one fourth(4)x − 1 − 4
Answers
[tex] \frac{1}{4} 4^{x-1}-4[/tex]
Explanation:
1) the pair x = 3 f(x) = 0, leads you to probe this:
f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0
=> A [4^2] = - C
A[16] = - C
if A = 1/4
16 / 4 = 4 => C = - 4
That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4
2) Now you verify the images for that function for all the x-values of the table:
x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check
x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check
x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.
Therefore, you have proved that the answer is the fourth option.
Math question!!! PLEASE HELP
solve for x in the triangle
a. 1.7
b. 2.6
c. 2.7
d .3.0
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Write a trinomial in one variable of degree 5 in standard form.
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A polynomial of one-variable is given by following expression :-
[tex] Ax^n + Bx^{n-1} +Cx^{n-2}+Dx^{n-3}+Ex^{n-4}+..... [/tex]
where A, B, C, D, E are the coefficients of terms in the polynomial and x is variable of the equation.
A is the leading coefficient and it can not be zero i.e. A≠0.
n is the degree of the polynomial.
It says to write a trinomial in one variable of degree 5.
Trinomial means only three terms with non-zero coefficients, and degree 5 means n = 5.
There could be many answers, but an example of "trinomial of degree 5" would be :-
[tex] Ax^5 + Bx^4 + Cx^3 [/tex]
[tex] 3x^5 + 5x^4 + 2x^3 [/tex]
A trinomial in one variable of degree 5 in standard form is [tex]\( ax^5 + bx^3 + cx \),[/tex] where [tex]\( a \), \( b \), and \( c \)[/tex] are non-zero coefficients and [tex]\( a \neq 1 \)[/tex].
A trinomial is a polynomial with three terms. The degree of a polynomial is the highest power of the variable that appears in the polynomial with a non-zero coefficient. Since we are asked to write a trinomial of degree 5, the highest power of the variable x must be 5.
The standard form of a polynomial lists its terms in descending order of their degrees. Therefore, the first term of our trinomial must be [tex]\( ax^5 \),[/tex] where a is a non-zero coefficient, and [tex]\( a \neq 1 \)[/tex] to ensure that the coefficient is explicit.
Since we want a trinomial, we need two more terms. The next term should have a lower degree, and since we're dealing with a degree 5 polynomial, the next possible lower odd degree is 3 (we choose an odd degree to maintain the trinomial structure with distinct powers). This gives us the second term [tex]\( bx^3 \),[/tex] where b is also a non-zero coefficient.
The third and final term of our trinomial must have a degree lower than 3. The next possible lower odd degree is 1, which gives us the term [tex]\( cx \),[/tex] where c is again a non-zero coefficient.
Putting it all together, we have the trinomial [tex]\( ax^5 + bx^3 + cx \)[/tex] as the standard form of a degree 5 polynomial with three terms.
Factor the expression. x2 – 10xy + 24y2
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1. You have the following expression given in the problem above:
x²-10xy+24y²
2. When you factor the expression x²-10xy+24y², you obtain the following:
(x-4y)(x-6y)
3. To verify the result you can apply the distributive property and the result must be x²-10xy+24y².
Therefore, the answer is: (x-4y)(x-6y)
Answer:
the answer is: (x-4y)(x-6y)
Step-by-step explanation:
A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount added to each
sidhttps://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS7/7.043.pnge?
Answers
A=LxW
A is the area of the rectangle
L is the length of the rectangle.
W is the widht of the rectangle
2. You have that:
-The rectangular Corn Hole area has a width of 5 feet and a length of 10 feet, so:
L1=10 feet
W1=5 feet
- When a uniform amount is added to each side (x), the area is increased to 84 feet². Then, you have a different length (L2) and a different width (W2):
3. The new length is:
L2=L1+x+x
L2=L1+2x
L2=10+2x
4. The new width is:
W2=W1+x+x
W2=W1+2x
W2=5+2x
5. The new area is:
A2=84 feet²
6. Then, you have:
A=LxW
84=(10+2x)(5+2x)
7. When you apply the distributive property, you obtain a quadratic equation:
4x²+30x-34=0
8. You can solve with by applyin the quadratic formula:
x=(-b±√(b^2-4ac))/2a
a=4
b=30
c=-34
9. Then, the answer is:
x=1 feet
Answer:
I can't believe this guy above me has a verified answer and it is wrong.... anyway the true answer to this is 2. I checked it myself when I put 1 as the answer and got this question wrong, and it showed me the correct answer is 2 so don't believe the verified answer.
Step-by-step explanation:
Review Question #7:
The answer to this question is 2ft, not 1ft.
This is because:
So the width of the second rectangle can be represented by 10+2x, and the length of the second rectangle can be represented by 5+2x. Lets make 2x equal y to make things easier though. Because the product of both 10+2x and 5+2x is 84 square feet, we must multiply the two equations together first.
(10+y)(5+y)=84
This then equals:
50+10y+5y+y^2=84
Then add the like terms:
y^2+15y+50=84
Then set the equation to zero by subtracting 84 from both sides:
y^2+15y-34=0
From that, you can use the box method, or any method to get:
(y+17)=0 and (y-2)=0
Which would then simplify to:
y=-17 and y=2
However, we substituted y for 2x, so plug 2x into y:
2x=-17 and 2x=2
Then simplify from here:
x=-17/2 and x=1
The answer cannot be negative, so that means the answer is x=1, however, even though this is true, the answer is that 2ft was added to EACH SIDE, because the question was asking for what amount was added to each side.
How do you solve binomials
Answers
To solve binomials, one can use the binomial theorem, which involves the use of binomial coefficients calculated via factorials. For large numbers, Stirling's formula can help manage calculations by using approximations of factorials through logarithms.
Understanding Binomials and the Binomial Theorem
To solve binomials and expand binomial expressions, we often use the binomial theorem. This theorem expresses the expansion of the power of a binomial as a sum of terms in the form of coefficients multiplied by powers of the two parts of the binomial. A binomial coefficient, represented by (n), counts the number of ways to choose r objects from n without regard to order and is computed using factorials.
When dealing with large binomial coefficients, calculators may return overflow errors. To handle this, one might use Stirling's formula, an approximation for logarithms of factorials. This approach makes it more feasible to work with large numbers.
Using the example of expanding (1 + x)³, we get 1 + 3x + 3x² + x³, where the coefficients 1, 3, 3, and 1 represent the binomial coefficients for each term. This pattern applies generally when using the binomial theorem for expansion.
PLEASE HELP ME ON THIS
Answers
The number of hours it will take is :
22h = 221-45
22h = 176
h = 176/22
h=8
so it takes them 8 more hours to finish learning the song.
Which net represents this solid figure?
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Answer:
Bottom Left.
Step-by-step explanation:
Did it got 100%! Thanks so much! Your welcome! Have a great week!
If the sin 60° = square root of three over two, then which statement is true? (6 points)
cos 30° = square root of three over two, because the cosine and sine are complements
cos 30° = 0, because the cosine and sine are complements
cos 120° = square root of three over two, because the cosine and sine are supplements
cos 120° = 0, because the cosine and sine are supplements
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Answer: The answer is (a) cos 30° = square root of three over two, because the cosine and sine are complements
Step-by-step explanation: Given that -
[tex]\sin 60^\circ=\dfrac{\sqrt 3}{2}.[/tex]
we are to select the correct statement from the given four options.
We know that sine and cosine functions are supplement of each other. So, we have
[tex]\sin 60^\circ=\cos(90^\circ-60^\circ)=\cos 30^\circ=\dfrac{\sqrt 3}{2}.[/tex]
Thus, the correct option is (a) cos 30° = square root of three over two, because the cosine and sine are complements.
Which of the following is a perfect square? 18 81 50 32
Answers
Answer:
The correct answer is 81
Step-by-step explanation:
Here are all the perfect squares.
1 2 1 × 1 1
2 2 2 × 2 4
3 2 3 × 3 9
4 2 4 × 4 16
5 2 5 × 5 25
6 2 6 × 6 36
7 2 7 × 7 49
8 2 8 × 8 64
9 2 9 × 9 81 81 Is a perfect square!
10 2 10 × 10 100
11 2 11 × 11 121
12 2 12 × 12 144
Can I have brainliest please?
In circle C, what is the value of X?
X=112 degrees
X=90 degrees
X=68 degrees
X=22 degrees
Answers
Answer:
x=22 degrees
Step-by-step explanation:
We are given a circle C
Centre is at C
A line passes through the centre makes angle x and 68 on either side
A triangle is formed with angles x, 68 and another angle at the circumference.
Since the line passing through the centre is diameter of the circle, we have
the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)
In the triangle sum of three angles
=90+x+68 =180
x =22 degrees
orginal price is 82$ the sales price is 65.60 what is the discount
Answers
82x=65.6
65.6/82=x
X=.8
So, you can say he got the item for 80%, but I suggest saying is was a 20% discount. You are taking 20 percent of 82 and subtracting it.
82•.2=16.4
82-16.4=65.6
So it was a 20% discount.
In the diagram, m<2 = 123 degrees. Find m<3.
Answers
<3 = 180 - 123
<3 = 57
answer is A. 57
In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe.
(b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.
Answers
RT×ST = TU²
b) Using the above relationship, fill in the given values and solve for TU.
(9 in)×(4 in) = TU²
TU = √(36 in²) = 6 in
Answer:
(a) The relation is RT × ST = TU²
(b) TU = 6
Step-by-step explanation:
(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).
Then RT × ST = TU²
(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²
Solving that equation, we have TU = √36 = 6
Thus TU = 6
What is the value of the 5 in 3 590 answer in words
Answers
If tan x=a/4 and cos x=4/b what is the value of sin x?
Answers
The value of sin x is sqrt(b^2 - 16)/16.
Explanation:
To find the value of sin x, we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.
Given that tan x = a/4 and cos x = 4/b, we can use the Pythagorean identity (1 + tan^2(x) = sec^2(x)) to find the value of sin x:
1 + (a/4)^2 = (4/b)^2
Simplifying the equation, we get: 1 + a^2/16 = 16/b^2Multiplying both sides by 16, we get: 16 + a^2 = 256/b^2Substituting the value of cos x, we get: 16 + a^2 = 256/(16/b^2)Further simplifying, we get: 16 + a^2 = 16b^2/16Cross multiplying, we get: 16 + a^2 = b^2Substituting the value of tan x, we get: 16 + (4a)^2 = b^2Simplifying the equation, we get: 16 + 16a^2 = b^2Subtracting 16 from both sides, we get: 16a^2 = b^2 - 16Taking the square root of both sides, we get: 4a = sqrt(b^2 - 16)Dividing both sides by 4, we get: a = sqrt(b^2 - 16)/4Substituting the value of a in the equation sin x = a/4, we get: sin x = sqrt(b^2 - 16)/16
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Please help me out!! :)
Answers
We need to find the area of the regular polygon as shown in the image.
Now in a regular hexagon the line joining the center and the vertex of a hexagon have the same length as the length of each side. (Refer the attached image)
[tex]10 \sqrt3cm=10 \times 1.732=17.32 cm[/tex]
A regular hexagon is made up of 6 equilateral triangles inside which means all the sides are of the same length.
Now, we know that the length of a side of an equilateral triangle is [tex]10 \sqrt 3[/tex] cm. So the area of one equilateral triangle is:
[tex]\frac{\sqrt 3}{4} \times (a)^2[/tex]
Where, 'a' is the side length of the equilateral triangle.
Therefore, area [tex]= \frac{\sqrt 3}{4} \times (10 \sqrt3)^2= \frac{\sqrt 3}{4} \times 100 \times 3=75 \sqrt3[/tex] square centimeters.
Now that we have the area of one equilateral triangle and there are 6 of them in a regular hexagon we can find the area of hexagon.
So, the area of given regular polygon is [tex]=6 \times 75 \sqrt 3=450 \sqrt 3 cm^2[/tex].
PLZ HELP ASAP WILL GIVE BRAINLIEST ANSWER!!!!!
What do you predict the current will be in the absence of sunlight?
Answers
Translate the following and then create real-world problems using these
expressions.
“6 less than a number”
“2 times the quotient of a number and two”
“4 times the difference of a number and 8”
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2. 2(x/2); Robert lost half his money in the stock market last week, and then doubled that amount this week.
3. 4(x - 8); 4 people spent $8 on a movie. How much money (x) did each person have before seeing the movie?
# 11 let f(x) =x^2 and g(x) =x-1. find (f o g)(-3)
#12 let f(x)= 5x+3 and g(x) =x^2-x+1
preform the function operating then find the domain.
g(x)-f(x)
Answers
g(x) = x-1
g(-3) = -3-1 .... plug in x = -3
g(-3) = -4
Plug this into f(x)
Now compute f(-4)
f(x) = x^2
f(-4) = (-4)^2
f(-4) = 16
Answer: 16
=======================================================
Problem 12
f(x) and g(x) are two polynomials. When subtracting any two polynomials, we end up with some other polynomial. This idea is known as set closure. Set closure is where you take two items from one set, apply an operation to them, and the result is another item from the same set. Another example of this is adding two whole numbers. Adding two whole numbers leads to another whole number.
So in short, h(x) = g(x)-f(x) is a polynomial
The domain of any polynomial is the set of all real numbers. We can plug in any x value we want to get some output value for y.
Let's find the result of g(x)-f(x)
g(x) - f(x) = [ g(x) ] - [ f(x) ]
g(x) - f(x) = [ x^2-x+1 ] - [ 5x+3 ]
g(x) - f(x) = x^2-x+1 - 5x-3
g(x) - f(x) = x^2-6x-2
Domain: Set of all real numbers