which two values of x are roots of the polynomial below?
x^2 + 5x + 9
Answer:
The answer:
A. [tex]x= \frac{-5+ \sqrt{-11} }{2}[/tex]
F.[tex]x= \frac{-5- \sqrt{-11} }{2}[/tex]
Step-by-step explanation:
Step 1: Solve with quadratic formula
[tex]x_{1},2 = \frac{-b+- \sqrt{b^2}- 4ac }{2a}[/tex]For [tex]a=1, b=5, c=9\\x_{1},2 = \frac{-5 + \sqrt{5^2 -4 *1 *9} }{2*1}[/tex]Step 2: Simplify
[tex]\sqrt{5^2 - 4 *1 *9} : \sqrt{11} i[/tex]Multiply the numbers: [tex]4*1*9 = 36[/tex][tex]i\sqrt{ 36 -5^2}[/tex] = [tex]\sqrt{-5^2 + 36} = i\sqrt{11}[/tex][tex]5^2 = 25 = \sqrt{-25 + 36}[/tex]Add/subtract the numbers [tex]-25 +36 = 11 = \sqrt{11} = \sqrt{11}i[/tex]Step 3: Separate the solution
[tex]x_{1} = \frac{-5 + \sqrt{-11}i}{2} , x_{2} = \frac{-5 - \sqrt{-11}i}{2}[/tex]Answer:
[tex]\large {\textsf{A and F}}\ \implies \bold{x_1}=\dfrac{-5-\sqrt{-11}}{2},\ \bold{x_2}=\dfrac{-5+\sqrt{-11}}{2}[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0.
Given polynomial: x² + 5x + 9
⇒ a = 1, b = 5, c = 9
Step 1: Rewrite to Standard Form.
⇒ x² + 5x + 9 = 0
Step 2: Substitute the values of a, b, and c into the formula.
⇒ a = 1, b = 5, c = 9
[tex]x=\dfrac{-5\pm\sqrt{\bold{5^2}-4\bold{(1)(9)}}}{\bold{2(1)}}\\\\x=\dfrac{-5\pm\sqrt{25\bold{\ - \ 4(9)}}}{2}\\\\x=\dfrac{-5\pm\sqrt{\bold{25-36}}}{2}\\\\x=\dfrac{-5\pm\sqrt{-11}}{2}[/tex]
Step 3: Separate into two possible cases.
[tex]x_1=\dfrac{-5-\sqrt{-11}}{2}\\\\x_2=\dfrac{-5+\sqrt{-11}}{2}[/tex]
Other examples:
brainly.com/question/27988150
brainly.com/question/27740685
What can be concluded if ÐABC and ÐCBD are a linear pair? Select all statements that you think are correct.
If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.
What is Linear pair of angles?Linear pair of angles are angles formed when two lines intersect each other at a single point.
Now, the angles are also said to be linear if they are adjacent to each other after the intersection of the two lines and the sum of the linear pair of angles is always equal to 180°.
Looking at the definition above we can say that if ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.
Read more about Linear Pairs at; https://brainly.com/question/14061313
#SPJ1
Find the perimeter of the triangle.
23.
7 in.
(x + 4) in.
(4x + 1) in.
Answer:
17 in.
Step-by-step explanation:
There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.
Fraction
Puja Limbu did 8 out of 10 math problems and Raju lama did 11 out of 15 similar maths problems.Express the number of problems solved by each of them in fractions and identify who did better performance.
Using percentages, we have that Puja Limbu did 80% of the problems and Raju Lama did 73.3%, hence Puja Limbu had the better performance.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
The percentage for Puja Limbu is:
[tex]P = \frac{8}{10} \times 100\% = 80\%[/tex]
The percentage for Raju Lama is:
[tex]P = \frac{11}{15} \times 100\% = 73.3\%[/tex]
80% > 73.3%, hence Puja Limbu had the better performance.
More can be learned about percentages at https://brainly.com/question/10491646
#SPJ1
Find the nth term of the sequence 3, -1, -5, -9.
Answer:
-4n+7
Step-by-step explanation:
because you take away 4 each time and the nber that would come before 3 is 7.
please answer all of theses asap
Answer:
1. won 50 games and lost 32 games
2. 233 Democrats and 202 Republicans
3. 360 miles
4. 6 hours
5. 18 miles
Step-by-step explanation:
Question 1
let x = number of games lostlet y = number of games wonFrom the given information:
Equation 1: x + y = 82Equation 2: x = y - 18Substitute Equation 2 into Equation 1 and solve for y:
⇒ y - 18 + y = 82
⇒ 2y - 18 = 82
⇒ 2y = 100
⇒ y = 50
Substitute found value of y into Equation 2 and solve for x:
⇒ x = 50 - 18
⇒ x = 32
Therefore, the team won 50 games and lost 32 games.
Question 2
let d = number of Democratslet r = number of RepublicansFrom the given information:
Equation 1: d + r = 435Equation 2: d = r + 31Substitute Equation 2 into Equation 1 and solve for d:
⇒ r + 31 + r = 435
⇒ 2r + 31 = 435
⇒ 2r = 404
⇒ r = 202
⇒ d = 233
Substitute found value of d into Equation 2 and solve for r:
⇒ 233 = r + 31
⇒ r = 202
Therefore, there were 233 Democrats and 202 Republicans.
Question 3
Given:
v = 180 m/ht = 2 hDistance (d) = vt
⇒ d = 180 × 2
⇒ d = 360 miles
Question 4
Given:
v = 70 mi/hd = 420Time (t) = d ÷ v
⇒ t = 420 ÷ 70
⇒ t = 6 hours
Question 5
Let c = velocity of carLet b = velocity of busIf the velocity of the bus is 12 mph less than the car then:
⇒ c = b + 12
Given journey times:
Car: t = 30 mins = 0.5 hBus: t = 45 mins = 0.75 hDistance (d) = vt
Create two equations for distance:
Bus
⇒ d = b × 0.75 = 0.75b
⇒ d = 0.75b
Car
⇒ d = (b + 12) × 0.5
⇒ d = 0.5b + 6
Distance for both vehicles is the same. Equate the two equations for d and solve for b (velocity of bus):
⇒ d = d
⇒ 0.75b = 0.5b + 6
⇒ 0.25b = 6
⇒ b = 24 mph
Substitute the value of b into one of the distance formulas and solve for d:
⇒ d = 0.5(24) + 6
⇒ d = 18 miles
What is halfway between 4 /5 and − 2 /3 ?
Solve the following please:
Answer:
most likely b
Step-by-step explanation:
the more than symbol tells me that it is going to move past 10.
a^½ха^2/3/a^3/5
I need help
P
Answer:
15 sqrt a ^4
Step-by-step explanation:
Find the range of the given function y = 8x + 1, where x > 2.
The range of the function will be all values that are greater than 17 that is y > 17
Range of a functionThe range of a function is the dependent variable of the function for which it exists,
Given the linear function
y = 8x + 1
If the value of x is 2, hence;
y = 8(2) + 1
y = 17
Hence the range of the function will be all values that are greater than 17 that is y > 17
Learn more on range here: https://brainly.com/question/26098895
#SPJ1
The two conditional relative frequency tables below show the results of a survey asking students whether they are taking a foreign language or not.
A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.34, 0.66, 1.0. The third column is labeled not taking a foreign language with entries 0.64, 0.36, 1.0. The fourth column is labeled total with entries 0.4, 0.6, 1.0.
Table B: Frequency of Foreign-Language Studies by Row
A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.68, 0.88, 0.8. The third column is labeled not taking a foreign language with entries 0.32, 0.12, 0.2. The fourth column is labeled total with entries 1.0, 1.0, 1.0.
Which table could be used to answer the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?”
Table A, because the given condition is that the student is in high school.
Table A, because the given condition is that the student is taking a foreign language.
Table B, because the given condition is that the student is in high school.
Table B, because the given condition is that the student is taking a foreign language.
Option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.
What is a conditional relative frequency?It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.
We have two tables given in the question.
The conditional relative frequency tables show the results of a survey asking students whether they are taking a foreign language or not.
The condition is: "Assuming a student is taking a foreign language"
Table B can be used to answer the above statement.
Thus, option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.
Learn more about the conditional relative frequency here:
brainly.com/question/8358304
#SPJ1
Answer:
Option b: Table A, because the given condition is that the student is taking a foreign language.
Step-by-step explanation:
on ed
ABC has the points A(1,7) B(-2,2) and C(4,2) as it’s vertices
The measure of the longest side of ABC is _ units. ABC is_triangle. If ABD is formed with the point D(1,2) as it’s third vertex, then ABD is _triangle . The length of side AD is_units
Part 1
Using the distance formula,
[tex]AB=\sqrt{(-2-1)^{2}+(2-7)^{2}}=\sqrt{34}\\\\BC=\sqrt{(-2-4)^{2}+(2-2)^{2}}=6\\\\AC=\sqrt{(1-4)^{2}+(7-2)^{2}}=\sqrt{34}[/tex]
So, the measure of the longest side is 6 units.
Part 2
Triangle ABD will have vertices A(1,7), B(-2, 2), and D(1,2).
We already know that [tex]AB=\sqrt{34}[/tex]
Using the distance formula,
[tex]AD=\sqrt{(1-1)^{2}+(7-2)^{2}}=5\\\\BD=\sqrt{(-2-1)^{2}+(2-2)^{2}}=3[/tex]
So, ABD is a scalene triangle.
Part 3
From part 2, we know that the length of side AD is 5 units.
30 POINTS PLEASE HURRY
Jonathan and Kevin each rewrote and evaluated the expression (SEE PICTURE BELOW) They arrived at different answers.
Answer:
B. took test
Step-by-step explanation:
Answer:
B. Jonathan is correct. Kevin made an error at step 3.
Step-by-step explanation:
Please answer both questions math
Answer:
[tex]3[/tex] and perpendicular
Step-by-step explanation:
It's important to remember that equations of lines are always set up in the format of [tex]y=mx+c[/tex].
[tex]y[/tex] is the [tex]y[/tex] value, [tex]m[/tex] is the gradient/slope, [tex]x[/tex] is the [tex]x[/tex] value and [tex]c[/tex] is the y-intercept.
Therefore, we must always rearrange our line equations so that [tex]y[/tex] is the subject.
In the first question, we are given the equation [tex]2x+6y=12[/tex].
We rearrange to make [tex]y[/tex] the subject:
[tex]6y = 12-2x[/tex]
Then, we divide both sides by 6 to have the [tex]y[/tex] isolated:
[tex]\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x[/tex]
To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.
So here, the slope is [tex]-\frac{1}{3}[/tex].
So, the negative reciprocal of that would be [tex]3[/tex] because we inverse the sign (the negative becomes positive) and the fraction is flipped to create [tex]\frac{3}{1}=3[/tex].
So, the perpendicular slope is [tex]3[/tex].
In the second question, we have two equations. They both need to be rearranged to isolate the [tex]y[/tex].
[tex]4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3[/tex]
Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine [tex]4 = \frac{4}{1}[/tex], the fraction is flipped.
This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.
pleasee help with these functions
By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)
How to evaluate a composed function
Let be f and g functions, there is a composition of f with respect to g when the input of the former is substituted by the output of the latter. It is to notice that composition is a binary operation between functions.
If we know that f(x) = - (1/2) · x² + 5 · x, g(x) = x² + 2 and x = -2, then the composed function evaluated is:
f(g (x)) = - (1/2) · (x² + 2)² + 5 · (x² + 2)
f(g (- 2)) = - (1/2) · 6² + 5 · 6
f(g (- 2)) = 12
By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)
To learn more on composed functions: https://brainly.com/question/12158468
#SPJ1
3. A sequence of numbers is shown below. 1 5 9 13 17.
(a) Find an expression for the nth term of the sequence.
Answer:
Un= 1 + (n-1)4
Step-by-step explanation:
a=1
d=5-1=9-5=4
using the formula Un=a+(n-1)d
√2/√2+√3-√5 rationalise the denominater
Answer:
Multiply the denominator and numerator with root 2 to get a fair denominator and simplify if needed. Hope it helps
Answer:
1 + √3 - √5
Step-by-step explanation:
The given √2/√2 equals 1, and so we now have 1 + √3 - √5, whose denominator is the integer 1. There's nothing left to rationalize.
The circumference of a circle is 19 ft.
What is the area, in square feet? Express
your answer in terms of T.
Answer:
The area is approximately 28.73ft²
Step-by-step explanation:
Given: Circumference = 19 ft
The necessary formula area,
Area: A = πr²
Circumference: C = 2πr
Combine:
A = [tex]\frac{C^{2} }{4\pi }[/tex]
A = [tex]\frac{19^{2} }{4\pi } \\\\ \frac{361 }{4\pi }[/tex]
A = 28.72747
What is the standard form of this function?
f(x) = (x-4)² + 2
Standard form of quadratic equation: ax² + bx + c
Here given equation: f(x) = -(x - 4)² + 2
Simplify the equation:
⇒ f(x) = -(x - 4)² + 2
Use perfect square formula: (a + b)² = a² + 2ab + b²
⇒ f(x) = -(x² + 2(x)(-4) + (-4)²) + 2
⇒ f(x) = -(x² - 8x + 16) + 2
⇒ f(x) = -x² + 8x - 16 + 2
⇒ f(x) = -x² + 8x - 14
[tex]\hrulefill[/tex]
Here given equation: f(x) = (x - 4)² + 2
Simplify the equation:
⇒ f(x) = (x - 4)² + 2
⇒ f(x) = x² + 2(x)(-4) + (-4)² + 2
⇒ f(x) = x² - 8x + 16 + 2
⇒ f(x) = x² - 8x + 18
Answer:
f(x)=x²-8x+18
Step-by-step explanation:
f(x) = (x-4)² + 2
To find the answer for the first part (x-4)², you need to use the formula.
This is the formula: (a-b)²=a²-2ab+b²
Plug in x for a and -4 for b.
(x-4)²=x²-8x+16
Now, put x²-8x+16 for (x-4)².
f(x)=x²-8x+16+2
Add like terms.
f(x)=x²-8x+18
Our answer is already in standard form because it is from greatest to least.
Hope this helps!
If not, I am sorry.
HELP !
Which of the following best describes the slope of the line below?
• A. Negative
O B. Zero
• C. Positive
D. Undefined
The heights of adult men in the united states are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. use this information together with the 68-95-99.7 rule to make three statements about the height of adult men in the united states.
Answer:
Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.
x + y = 152,
8.5x + 12y = 1,656
How many hats were sold?
hats
Step-by-step explanation:
a) 74.857% of adult men are shorter than Michael
b) 84.134% of adult men are taller than Jack
c) 58.991% of adult men are of height between Jack and Michael
What is 68-95-99.7 rule?Within one standard deviation of the mean is 68% of the population. Within two standard deviations of the mean, 95% of the population is located. The median is within 3 standard deviations for 99.7% of the population.
Given:
µ = 70in, σ = 3in.
We know Z = (x-µ)/σ
a) Actor Michael B. Jordan is 6’0” (72”) tall.
Z = (72-70)/3 = 0.67
So, the probability of an adult man having a height of 0-72 inches, and no greater is 74.857%
b. Comedian Jack Black is 5’7’ (67”) tall.
Z = (67-70)/3 = -1
The corresponding value is .15866 which can be the probability of an adult man having a height of 0-67 inches, and no greater.
But the percentage of those taller than jack is = 1 – .15866 = 0.84134
c) P(X < 72) – P(x < 67)
= 0.74857 – 0.15866
= 0.58991
= 58.991%
Learn more about 68-95-99.7 rule here:
https://brainly.com/question/29255280
#SPJ1
The Question attached here is incomplete, the complete question is
a. Actor Michael B. Jordan is 6’0” (72”) tall. What percentage of adult men are shorter than Michael?
b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?
c. What percentage of adult men are of height between Jack and Michael?
A four line classified ad costs 25 for a week. Each additional line costs 2. What is the weekly cost for a 12 line ad
Answer: 41
Step-by-step explanation:
If each line costs 2, then for the four-line ad, the cost is the initial price plus 4(2), meaning the initial cost is 25-8=17.
Thus, the cost of a 12-line ad is 17+2(12)=41
Hii guys please answer this question
After how many places will the decimal expansion of 189/750 terminate ? Also write the decimal form
Answer:
3 decimal places; 189/750 = 0.252
Step-by-step explanation:
Answer:
3 decimal places.
189/750 = 0.252
Step-by-step explanation:
If you are allowed to use a calculator, you divide. 189/750 means 189 ÷ 750.
You will get 0.252, which is three decimal places. If you are not allowed to use a calculator, you must do long division. The 750 goes outside the dividing frame and the 189 goes inside. There is an unwritten decimal point after the 9 in 189. Since 750 does not go into 189, put 0. to begin and put zeros after the 189 to do the long division. See image. Hopefully you can just use a calculator.
The quotient of 7 more than three times a number m and the number 27 less than n
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.
(3m+7)/27 < n
Hence, the given statement can be modeled as (3m+7)/27 < n.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ1
2+2 I
dont know how but 4 was wrong guys am I not thinking right?
Answer:
Maybe the question could've been 2+2+1. I'd say read the question properly.
Step-by-step explanation:
In which case, 2+2+1= 5
Solve the inequality. –6 < 2 x – 4 < 4
Step-by-step explanation:
-6<2x-4<4
-2<2x<8
-1<x<4
x = (-1,4)
Graph the image of this figure after a dilation with a scale factor of centered at the origin.
Use the polygon tool to graph the dilated figure.
Polygon
+Move
10
9
8
7
6
5
3
2
y
Undo
Redo x Reset Graph the image of this figure after a dilation with a scale factor of 1/3 centered at the origin
A picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.
What exactly is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The complete question is;
"Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .
Use the polygon tool to graph the dilated figure."
The center of dilation and figure are first translated, making the origin the center of dilation.
We map every point because the point (2, 2), which is our center of dilatation, must be translated left 2 and down 2 to become the origin.
(x, y)→(x-2, y-2)
Each point will be multiplied by two when the scale factor is two, giving us the rule.
(x, y)→(2x-4, 2y-4)
In order to return the figure to its original location, we must translate it right 2 and up 2; this gives us the rule.
(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)
At the top of the original figure, the first point is (0, 6). When we use the transformation, we get
(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)
The pre-rightmost image's point is (2, 4). The results of using the transformation rule are;
(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)
The pre-leftmost image's point is at (-3, 3). The transformation rule being applied, w
(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)
Hence,an picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.
To learn more about dilation, refer to
https://brainly.com/question/13176891.
#SPJ1
how do i do this? i need to factor it conpletely with any method that goes with it
Answer:
(x-9)(x+8)
Step-by-step explanation:
Use the AC method
1. What is the binomial expansion of (x + 3)5?
Answer:
5x + 15
Step-by-step explanation:
To expand the binomial, you need to multiply each term inside the parentheses by 5.
(x + 3)5
= (x * 5) + (3 * 5)
= 5x + 15
Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 1 > 7/2
The graph is shown below:
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Rearrange unknown terms to the left side of the equation:
|x| > 7/2-1
Now,
|x| > (7-2)/ 2
Calculate the sum or difference:
|x| > 5/ 2
Convert the absolute inequality to standard inequality:
x> 5/2 or x< -5/2
Solve the inequality:
x> 5/2
Solve the inequality:
x< -5/2
Graph on number line is attached
Learn more about inequality here:
https://brainly.com/question/20383699
#SPJ1
