write a polynomial function for each set of zeros
[tex]x = \sqrt{2} [/tex]
[tex] - i[/tex]
The required polynomial function is f(x) = (x + i)² which is degree 2 with the zeros x = √2 and x = -i.
We have to determine a polynomial function for each set of zeros:
x = √2, -i
To write a polynomial function with the zeros x = √2 and x = -i, we can start by setting the function equal to zero and substituting in the zeros:
f(√2) = 0
f(-i) = 0
We can then solve for the coefficients by expressing the polynomial function in terms of (x - √2) and (x + i).
For example, we can write:
f(x) = (x - √2)(x + i)q(x)
for some polynomial q(x).
Substituting in the zeros, we get:
f(√2) = (√2 - √2)(√2 + i)q(√2) = 0
f(-i) = (-i - √2)(-i + i)q(-i) = 0
Solving for q(x), we find:
q(x) = (x + i)/(x - √2)
Substituting this back into the original equation, we get:
f(x) = (x - √2)(x + i)(x + i)/(x - √2)
f(x) = (x + i)²
This is a polynomial function of degree 2 with the zeros x = √2 and x = -i.
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The graph of g(x) is a transformation of the graph of f(x) = 3^x enter the equation for g(x) in the box
Answer:
g(x)=3^x+7
Step-by-step explanation:
f(0)=3^0
that is the y-intercept
now we can take the known y-intercept of g(x) which is 8 and then we can get our b in the y=mx+b equation.
How do I find all the squares from 1 to 20?
Answer:
2.4.6.8.10
Step-by-step explanation:
that's the answer
Answer:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Step-by-step explanation:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, multiply all numbers frmo 1 to 10
Which of the following equations has infinitely many real solutions?
A.
3(x-6)= 3x + 18
B.
3(x-6)= 3x - 18
C.
3x+1=x-1
3x + 1 = 3x - 1
D.
Answer:
B: 3(x-6) = 3x-18
Step-by-step explanation:
The left and right sides of this equation are actually equal! We can see this by dividing the 3 on the left through the parentheses. This gives us [tex]3x-18[/tex], which is equal to the right-hand side of the equation!
To solidify this, we add 18 to both sides, and subtract 3x from both sides, which gives us that 0=0, so there are infinitely many solutions for x(since no matter what x is, it will result in 0=0 which is always true).
I hope this helps!
Are the lines C and D parallel? (The figure may not be drawn to scale). Giving brainliest for whoever answers correctly
1. Yes
2.no
3. Can’t be determined
The lines C and D are parallel.
What is a line?
In pure mathematics, a line is an infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas
Main body:
As Line LM cuts the line at C the angle made by both line is 48°
and line NP cuts the line at D , the angle made by line is 132°
we know that to make a line parallel , the sum of angle on one side of the line should be 180°
∠C +∠D = 48° +132°
= 180°
Hence , the lines C and D are parallel.
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50 POINTS IF ANSWERED PLSS!!!!!
Mr. Hansen has three sticks that measure 5 inches, 10 inches, and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
Answer:
No
Step-by-step explanation:
5+10=15, which cannot be less than 17
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x2 = 17.
The solution of the given quadratic equation is x = 1.37, - 1.37.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions .
Given quadratic equation:
9x² = 17
⇒ x² = (17 / 9)
⇒ x = ± √(17 / 9)
⇒ x = ± (√17) / 3
⇒ x = 1.37, - 1.37
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passes through (0, -5) and has vertex (-1, 4)
The equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The vertex of the parabola is at (-1, 4). Then the equation is given as,
y = a(x + 1)² + 4
The equation passes through (0, -5), then we have
y = a(x + 1)² + 4
-5 = a(0 + 1)² + 4
-5 = a + 4
a = -9
Then the equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4
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What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.
What is the mean's 90% confidence interval?We can be 90% certain that the interval contains the population mean,, if the level of confidence is 90%. The associated z-scores are 1.645. We can be 95% certain that the interval contains the population mean, if the level of confidence is 95%.
What happens when two confidence intervals overlap?In other words, the difference in effect estimates between the two subgroups is deemed to be statistically unimportant if the confidence intervals overlap.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.
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The numbers x,y and z are given by x =[tex]\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} } , y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} } and z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex] . What is the value of x,y and z
The values of the expressions are x = √6, y = 2√3 and z = √2
How to evaluate the expressions?From the question, we have the following parameters that can be used in our computation:
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
We have
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
Take the square of both sides
So, we have
[tex]x^2 =12-3\sqrt{7} + 12 + 3\sqrt{7} - 2(\sqrt{12-3\sqrt{7} } * \sqrt{12 + 3\sqrt{7} })[/tex]
This gives
x² = 12 - 3√7 + 12 + 3√7 - 2√81
Evaluate the roots
So, we have
x² = 12 - 3√7 + 12 + 3√7 - 18
Evaluate the sum and the difference
x² = 6
Take the square roots of both sides
x = √6
Using the same steps above, we have
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
Square both sides
So, we have
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * \sqrt{7-4\sqrt{3 } } * \sqrt{7 + 4\sqrt{3} }[/tex]
This gives
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * 1[/tex]
Evaluate
y² = 12
Take the square root of both sides
y = 2√3
Lastly, we have
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
Square both sides
[tex]z^2 = 2 + \sqrt 3 + 2- \sqrt 3 - 2 * \sqrt{2 + \sqrt{3} } * \sqrt{2 - \sqrt{3} }[/tex]
This gives
z² = 4 - 2 *1
Evaluate
z = √2
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In triangle XYZ, m∠Y = 62.45° and m∠Z = 41.8°. Determine the measure of the exterior angle to ∠X.
104.25°
75.75°
37.85°
18.94°
The exterior angle to ∠X is 104.25°
What is the exterior angle theorem?The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.
from the above definition , if ∠Y = 62.45° and ∠Z = 41.8°
It means from exterior angle theorem that
exterior ∠X = ∠Y + ∠Z
exterior ∠X = 62.45° + 41.8°
exterior ∠X = 104.25°
In conclusion the exterior angle X is 104.25°
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Sheri’s house is 0.05 miles from Abdul’s house. The post office is 0.1 mile from Abdul’s house. The school is 38mile from the post office.
If Sheri stops at Abdul’s house, and the post office on her way to school, how far will Sheri walk in all?
Answer:
39.05 miles
Step-by-step explanation:
0.05+0.1+38
Consider the functions
Answer:
(fog)(x) = 4x^2 -12x +10
(gof)(x) = 2x^2 -1
Step-by-step explanation:
(fog)(x) = (2x-3)^2 + 1
= 4x^2 + 9 -12x +1
= 4x^2 -12x +10
(gof)(x) = 2(x^2+1)-3
= 2x^2 +2 -3
= 2x^2 -1
Jethro and $50 to hi cafeteria account that had $40 on it already each time he buy lunch $4. 50 i deducted from the account write an equation in lope intercept form relating the number of lunche purchaed X to the amount of money remaining on the cafeteria count why what i the maximum number of lunche Jethro can purchae math problem
He has a total of $90 in his cafeteria wallet, thus the most lunches he may purchase is 20.
What is division?A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
Amount added=$50
Amount already in wallet=$40
Total amount in wallet=50+40
=$90
Cost of each lunch=$4.5
Number of lunch he can buy,
=90/4.5
=20
The maximum number of lunch he can buy is 20 lunch as he has a total of $90 in his cafeteria wallet.
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Simplify each ratio. Make sure to convert the units when needed
6 hours: 4 days (Hint: There are 24 hours each day.)
Answer:
1 : 16
Step-by-step explanation:
6 hours : 4 days
6 hours : 96 hours
1 hour : 16 hours
1… 1f21: 7: 4: 3a + 1 then what is 4th proportional?
B.
(8)
C
9
4
3
D.
3/4
1
9
2-Range of the data 112, 121, 184, 189, 177,190 is:
A.78 B.77 c 70 D.74
The 4th proportional of the given ratio is 4/3. option C
The range of the data 112, 121, 184, 189, 177, 190 is 78. option A
How to find 4th proportional?It follows from the concept of proportions that the ratios can be represented as follows;
21 : 7 = 4 : 3a + 1
21/7 = 4 / (3a + 1)
cross product
21 × (3a + 1) = 4 × 7
63a + 21 = 28
subtract 21 from both sides
63a = 28 - 21
63a = 7
a = 7/63
a = 1/9
So,
3a + 1
= 3(1/9) + 1
= 3/9 + 1
= 1/3 + 1
= 1 ⅓
= 4/3
21 : 7 = 4 : 4/3
Range of the data:
112, 121, 184, 189, 177, 190
Recall, the range of a dataset is the difference between the maximum and minimum data values and hence, we have;
Range = Highest data value - Lowest data value
= 190 - 112
= 78
Therefore, the range of the given set of data is 78.
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a dilation is a transformation that maps every point on a line segment to a point on a parallel line segment. the image has a length that is determined by the preimage and a scale factor, which is a fixed _[blank]_ of the original segment's length.
Answer:
multiple
Step-by-step explanation:
I had the same question and guessed and that was the answer lol
a grocer can buy strawberries for 1.38 per pound
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
1 pound = $1.38
175 pounds = $241.50
The number of pounds for the strawberries order of $241.50 is
175 pounds.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Cost of strawberries per pound = $1.38
The cost of a strawberry order = $241.50
The number of pounds for the order of $241.50.
1 pound = $1.38
Multiply 241.50/1.38 on both sides.
241.50/1.38 x 1 pound = $241.50
175 pounds = $241.50
Thus,
The number of pounds for the strawberries order of $241.50 is
175 pounds.
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The complete question is:
A grocer can buy strawberries for $1.38 per pound.
Write an equation relating c, the cost, and p, the pounds of strawberries.
A strawberry order cost $241.50.
How many pounds did the grocer order?
The
approximate average distances from
the sun to Venus and Mercury are listed
below:
Venus: 1.08 x 108 kilometers
Mercury: 5.79 × 107 kilometers
How much closer to the sun is Mercury?
Express your answer using scientific
notation.
The subtraction of significant figures between the distance is 5.01 × 10⁷km
SubtractionIn this problem, we have to subtract the difference between the distance of Venus and Mercury. When subtracting significant digits, the amount of significant digits that will be in the final answer is determined by the number of significant digits present after the decimal place in the numbers we are subtracting.
The distance between Venus and Mercury can be calculated as
1.08 × 10⁸ - 5.79 × 10⁷ = 50,100,000km
To express the value in significant figures, we will have
50,100,000 = 5.01 × 10⁷km
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Help meeee how do I solve
18x2 + 9x - 20
Answer:
18x^2 + 9x - 20
18x^2 + 24x - 15x - 20
6x(3x+4) - 5(3x+4)
Therefore, (6x-5)(3x+4)
Find the length indicated
Answer: 20
Step-by-step explanation:
Using the side splitter theorem yields:
[tex]\frac{?}{5}=\frac{12}{3}\\\\\frac{?}{5}=4\\\\?=20[/tex]
Answer:
20
Step-by-step explanation:
the scale factor from the little triangle to the larger triangle is 5/4
[tex]\frac{5x}{4}[/tex] = x + 5 Multiple through by 4 to clear the fraction
5x = 4x + 20 Subtract 4x from both sides
x = 20
Given triangle ABC with m
The lengths of AN=2.5cm and MN=3.5cm
What is similar triangle?
Similar triangles are triangles that have a similar form, however their sizes might vary.
Main body:
IN ΔAMN ≈ΔABC
Since MN∣∣BC
∠AMN=∠ABC (Corresponding angles)
∠ANM=∠ACB (Corresponding angles)
∴ΔAMN∼ΔABC(By $$AA similarity criterion)
⇒AM/AB =AN/AC=MN/BC (CPCT)
since , M is the mid point of AB.
AM = 1/2 AB , OR
AM/AB = 1/2
AM/AB =AN/AC = 1/2
AN/AC = 1/2
AN/5= 1/2
AN = 2.5 cm
AM/AB =MN/BC = 1/2
[∵BC=7cm]
MN/7 = 1/2
MN= 7/2 =3.5
Hence , the lengths of AN=2.5cm and MN=3.5cm
the complete question is :
In triangle ABC, M is mid-point of AB and a straight line through M and parallel to BC cuts AC at N. Find the lenghts of AN and MN, if BC=7cm and AC=5cm.
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xn+1=(xn)^3-1/4 x1=-1 what is x2
The required value of the x₂ is given as -0.500000.
Given that,
xₙ₊₁ = [[xₙ]³ - 1]/4, x₁ = -1
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
xₙ₊₁ = [[xₙ]³ - 1]/4, x₁ = -1
put n = 2
x₂ = [[x₁]³ - 1]/4
= -1 - 1 /4
= -2/4
= -1/2 = 0.500000
Thus, the required value of the x₂ is given as -0.500000.
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Henry is building an in-ground pool at his house. He is doing most of the work himself to save money. To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for how many days does he rent the backhoe?
To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.
What is backhoe?
A backhoe, also known as a rear actor or back actor, is a type of digging apparatus, often known as a digger, that has a digging bucket attached to the end of a two-part articulated arm. Usually, it is attached to the rear of a tractor or front loader, the latter of which is known as a "backhoe loader."
$286.50/$95.50= 3
Henry is building an in-ground pool at his house. He is doing most of the work himself to save money. To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.
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Solve the system of linear equations by substitution -5x+6y=-11 6y=x+5
Answer:
Step-by-step explanation:
y = 1/6x + 5/6
-5x + 6(1/6x + 5/6) = -11
-5x + x + 5 = -11
-4x + 5 = -11
-4x = -16
x = 4
y = 2/3 + 5/6
y = 7/6 or 1 1/6
(4, 7/6)
Literal Equations
help asap !!
Answer:
Step-by-step explanation:
y = 6x + 42
6x + 42 = y
6x = y - 42
x = (y - 42)/6
if each side is increased by 50℅.then find the increase percentage in its surface area
Answer:
Formula used:The surface area of cube = 6 side2
Calculation:According to the question,
Let the side of the cube be x
Each side of the cube increased by 50%.
= x(100 + 50)/100 = 1.5x
The surface area of the cube
⇒6x²
The new surface area of the cube (side = 1.5x)
⇒ 6 × 2.25x²
Increase percentage in the surface area
⇒((6 x 2.25 x²-6x²)/6 x² }× 100
⇒ 125%
The percentage increase in the surface area is 125%.Mary has 30 hats. She has 5 green, 7 blue, 12 red, and 6 brown. If she selects two hats at random, what is the probability that both hats are different colors?
P(Picking one Green Hat and Something Else)=
P(Picking one Blue Hat and Something Else)=
P(Picking one Red Hat and Something Else)=
p(Picking one Brown hat and something Else)=
Add the probabilities together to answer the question
The probability that both hats are different colors is; 0.7425
How to find the probability of selection?We are given;
Total number of hats = 30 hats
Number of green hats = 5 hats
Number of blue hats = 7 hats
Number of red hats = 12 hats
Number of brown hats = 6 hats
Now, if Mary selects two hats at random, then the probability that they are different colors is;
P(they are different colors) = 1 - P(both are the same color)
P(both are the same color) = (⁵/₃₀ * ⁴/₂₉) + (⁷/₃₀ * ⁶/₂₉) + (¹²/₃₀ * ¹¹/₂₉) + ( ⁶/₃₀ * ⁵/₂₉)
= (20 + 42 + 132 + 30)/(30*29)
= 224/(30*29)
= 0.2575
Thus;
P(they are different colors) = 1 - 0.2575
P(they are different colors) = 0.7425
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Describe fully the single transformation which takes shape A to shape B.
A
51
4
3
2
+
-5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
B
33/54 Maks
1 2 3 4 5
-X
D
Answer:
x=d
Step-by-step explanation:
-Wilson Middle School wants to rent tables for their weeklong art festival. One rental company charges a $20 setup
fee and $12 per table for the week. Another rental company charges a $30 setup fee and $10 per table for the week.
How many tables can the school rent for the charge to be the same for both companies?
Answer:
5 tables
Step-by-step explanation:
Let x be the number of tables the school needs to rent, and c be the total cost of renting the tables.
We can use the following equation to represent the cost of renting from the first company:
c = 20 + 12x
And we can use the following equation to represent the cost of renting from the second company:
c = 30 + 10x
As c is the same constant in both equations, we can say the following:
20 + 12x = 30 + 10x
Now we can solve this equation by simplifying:
20 + 12x = 30 + 10x
20 + 2x = 30
2x = 10
x = 5
Therefore, the school will need to rent 5 tables for the cost to be the same from both renting companies.
Answer: 5 tables
Step-by-step explanation:
The first rental company will charge $32 for one table.
The second rental company will charge $40 for one table.
So if we make a table, and keep adding $12 to the first company and $10 to the second it will look like this.
First company Second company Table
$32 $40 1
$44 $50 2
$56 $60 3
$68 $70 4
$80 $80 5
Therefore, the school can rent 5 tables for the same price in both companies.