The value of x in the equation [tex](x-5)^{2} +3(x-5)+9=0[/tex]is x=(7+3[tex]\sqrt{3}i[/tex])/2,
(7-3[tex]\sqrt{3}i[/tex])/2.
Given equation [tex](x-5)^{2} +3(x-5)+9=0[/tex] .
We have to find the solution of the equation.
Equation is solved to find the value of variables. The number of values of the variable depends on the highest power of variables.
let (x-5)=u-------------------1
equation becomes [tex]u^{2} +3u+9=0[/tex]
solution of a quadratic formula
x=-b±[tex]\sqrt{b^{2} -4ac}[/tex]/2a
on comparing with general form a=1,b=3, c=9
u=-3±[tex]\sqrt{3^{2} -4*1*9} /2[/tex]
=-3±[tex]\sqrt{9-36}/2[/tex]
=-3±[tex]3\sqrt{-27}/2[/tex]
=-3±[tex]3\sqrt{3} i/2[/tex]
[tex]u_{1} =-3[/tex]+3[tex]\sqrt{3}/2[/tex] , [tex]u_{2}[/tex]=-3-3[tex]\sqrt{3}/2[/tex]
put the values of [tex]u_{1}[/tex] in equation 1
x-5=[tex]u_{1}[/tex]
x-5=-3+[tex]3\sqrt{3} /2[/tex]
x=-3+3[tex]\sqrt{3}i/2+5[/tex]
x=7+3[tex]\sqrt{3} i/2[/tex]
put the values of [tex]u_{2}[/tex] in equation2
x-5=[tex]u_{2}[/tex]
x-5=-3-3[tex]\sqrt{3} /2[/tex]
x=7-3[tex]\sqrt{3}/2[/tex]
Hence the values of x are 7+3[tex]\sqrt{3}i/2[/tex], 7-3[tex]\sqrt{3}i/2[/tex].
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Help pls I don’t understand WILL GIVE BRAINLIEST FOR FIRST ANSWER
Step-by-step explanation:
sin if -7.2 = -0.79 approximately -0.8
Hope you understand and hope this helps.
Good luck ✅.
In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure Describe the angles you would need to know to verify that BC¯, DE¯, and FG¯ are all parallel to each other, and CD¯, EF¯, and GH¯ are also parallel.
What could be an appropriate measure for ∠CDE? Be prepared to explain your choice for that angle. Use that measure to find all other angles involved.
An appropriate measure for ∠CDE would be
∠CDE = ∠ADE - ∠ADC
How to check for the appropriate measure of CDE.we have the following angles as parallel BC¯, DE¯, and FG¯ also CD¯, EF¯, and GH¯.
The angles that we have to check in order to measure would be
∠ABC, ∠AEG, ∠ADC, ∠AHG, ∠ADE, ∠AFE, ∠AHG.
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Find the area of the region defined by the region defined by the inequality 2|x| + 3|y-1| ≤ 6.
The area of the region defined by the inequality 2|x| + 3|y-1| ≤ 6 is 12 square units
How to determine the area?The inequality is given as:
2|x| + 3|y-1| ≤ 6
Next, we plot the inequality
From the graph of the inequality (see attachment), we have the following highlights:
The shape is a rhombusThe diagonals are 6 and 4 unitsThe area of a rhombus is:
A = 0.5 * d1 * d1
This gives
A = 0.5 * 6 * 4
Evaluate
A = 12
Hence, the area of the region is 12 square units
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Find the are of the trapezoid
Answer:
355.83 yd²
Step-by-step explanation:
A = (B + b)h/2
A = (21.6 yd + 19.3 yd)(17.4 yd)/2
A = 355.83 yd²
Students of different ages are kept in a row,All of them have age difference of 3 years who are consecutive to each other. The age of first students row is 8 years. a) Restate the formula of to find the nth term of AP b) find the age of fourth student in rowc) find the sum of total ages if there are 20 students in a row
The formula to find the nth term of the AP is 8 + 3(n - 1).
How to calculate the values?a = first term = 8
d = common difference = 3
The nth term will be:
= a + (n - 1)d
= 8 + (n - 1)3
= 8 + 3(n - 1)
The age of the 4th student will be:
= a + (n - 1)d
= 8 + (4 - 1)3
= 8 + 9
= 17 years
The sum of total ages if there are 20 students in a row will be:
= n/2[2a + (n - 1)d]
= 20/2 [2×8 + (20 - 1)3]
= 10 [16 + (19 × 3)]
= 10(16 + 57)
= 10(73)
= 730
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Surface area=
Please help me asap thanks
Answer:
100π
Step-by-step explanation:
The formula for the surface area of a sphere is SA = 4πr^2, where r is the radius of the sphere and SA stands for surface area. We are given that the radius is 5, so if we plug this into the formula, we get that SA = 4π*(5)^2, or SA = 4 * 25 * π. If we solve it out, we get 100π. If the software wants you to let π be 3.14 and evaluate, you will get approximately 314. I hope this helps
The number of visitors to the homepage of an online magazine can be modeled by the equation y = 1100.74x − 1976.47, where x = 5 represents the year 2005 and y represents the total number of visitors.
The function y = 1100.74x - 1976.47 represent the total number of visitors x years after 2005.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the total number of visitors x years after 2005. Hence:
y = 1100.74x - 1976.47
The function y = 1100.74x - 1976.47 represent the total number of visitors x years after 2005.
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A third-grade teacher is introducing the concept of multiplication using manipulatives, pictures, and arrays. Last year several parents asked why their child wasn't learning to multiply the same way that they did. What should the teacher do in order to address potential questions this year
Answer:
The 3rd-grade teacher should say that the school systems and ways of teaching get updated each year.
Step-by-step explanation:
Children's parent's schools would have probably taught different techniques and ways of learning a topic. As years go by, more efficient ways of learning that topic are presented and selected.
If the parent would like the child to learn that way, they may teach them at home, but the school has decided on a system for at-school learning that seems to have worked the best.
Hopefully, that should answer the parent's questions!
What is the answer to this?
Answer: J
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{3x-9}{x+8}=\frac{45}{30}=\frac{3}{2}\\\\2(3x-9)=3(x+8)\\\\6x-18=3x+24\\\\3x-18=24\\\\3x=42\\\\x=14\\\\\implies YX=14+8=22[/tex]
solve for the missing variable 9 4 and x pls help need in 2 hours
Answer:
81/4
Step-by-step explanation:
By the Pythagorean theorem, the length of the altitude drawn from the hypotenuse is
[tex] \sqrt{65} [/tex]
This means that by the geometric mean theorem, that out of the two segments the hypotenuse is split into, the one with unknown length has length 65/4.
Thus, x = 65/4 + 4 = 81/4.
Esto es una división por favor ayuda
El resultado de esta división es 0.010
¿Cómo solucionar la operación matemática?Para solucionar la operación matemática debemos realizar los siguientes pasos:
Como el 81 es menos que el 7593, debemos poner un cero en el cociente y agregarle un cero al 81, entonces quedaría 810 dividido 7593.Como el 810 sigue siendo menor que el 7593, añadimos coma (,) y otro cero en el 810, entonces quedaría 8100 dividido 7593.Una vez tenemos el 8100 dividido 7593 realizamos la división, en este caso vemos cuántas veces cabe 7593 en 8100 y lo multiplicamos por ese número de veces (1).Una vez tenemos estos números a 8100 le restamos 7593 y obtenemos como resultado 507.Nuevamente, 507 es menos que 7593, entonces debemos agregar otro cero en el cociente para conocer las siguientes cifras decimales que falta.Ahora debemos averiguar cuántas veces cabe 7593 en 50700. Este número cabe 6 veces, entonces lo multiplicamos por 6 y luego restamos 50700 - 7593.Para conocer las siguientes cifras decimales debemos ir agregando un número cero en el resto para poder realizar las restas y seguir la división.Aprenda más sobre división en: https://brainly.com/question/24592547
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Given: ΔABC is isosceles; AB ≅ AC
Prove: ∠B ≅ ∠C
Triangle A B C is shown. Sides B A and A C are congruent.
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that .
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the .
However, this contradicts the given information that . Therefore, , which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.
AB = AC, they are equivalent. Since an isosceles triangle has the congruent angle property, mB = mC cannot be shown until AB=AC.
What is Isosceles triangles?Generally, Isosceles triangles are those that have two sides that are equal in length and two angles that are also equal in size.
Hence The sides and angles theorem for triangles., and the side AB is equal to the other side AC,
In conclusion, Assuming that the base angles, mB, and mC, are of equal measure, the triangle sides and angles theorem states that segment AC is larger than AB. The bigger angle of a triangle is always opposite to the longer side, according to the theorem.
AB is congruent to AC cannot be proven unless AB=AC then,
m<B = m<C because the isosceles triangle has the congruent angle property
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Answer:
AB = AC
Triangle parts relationship theorem
side AB is congruent to side AC
angle B is congruent to angle c
Step-by-step explanation:
Dana is buying Grandparents' Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends 4/5 of that on a coffee mug for her grandfather. How much money does Dana spend in all?
The total money Dana spent in all is $24.75
Ratio and proportionsRatio are written as fractions of two integers. For instance a/b.
Amount spent for grandmother = $13.75
Amount spent on grand father = 4/5 * 13.75
Amount spent on grand father = $11
Take the sum
Total money spent = $13.75 + $11
Total money spent = $24.75
Hence the total money Dana spent in all is $24.75
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You are saving money to buy a pair of pants that costs $53. You have saved $32. How much more money do you need to save?
Answer:
you need to save $21
A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, positive 1, positive 2. The second column is labeled f(x) with entries negative 13, negative 10, negative 7, negative 4, negative 1. What is the rate of change of the linear function represented by the table? StartFraction one Over three EndFraction StartFraction one Over two EndFraction 2 3
The rate of change of the linear function represented by the table is 3
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the y intercept.
From the table, using the point (0, -7) and (2, -1):
m = [-1 - (-7)] / (2 - 0) = 3
The rate of change of the linear function represented by the table is 3
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Find the distance between (-4,3,-6) and the origin ((X,Y,Z) Graph)
The distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
How to determine the distance?The point is given as:
(x, y, z) = (-4,3,-6)
The origin is
(x, y, z) = (0,0,0)
The distance between the point and the origin is calculated as:
[tex]d = \sqrt{x^2 + y^2 + z^2[/tex]
So, we have:
[tex]d = \sqrt{(-4)^2 + (3)^2 + (-6)^2[/tex]
Evaluate
[tex]d = \sqrt{61[/tex]
Hence, the distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
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In the following exercises, multiply the binomials. Use any method.
246. (q − 5)(q + 8)
Answer:
Hence the expression [tex]$$(q-5)(q+8)=q^2+3q-40$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (q-5)(q+8).We have to multiply the given expression.Multiply the (q-5) by 8 , multiply the (q-5) by q then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & q & - & 5 \\ \times & {} & q & + & 8 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & {} & 8q & - & 40 \\ {{q}^2} & - & 5q & {} & {} \\ \end{matrix}}{\begin{matrix}{{q}^2} & + & 3q & - & 40 \\ \end{matrix}}}$$[/tex]
Choose the correct classification of 5x 3x4 − 7x3 10 by number of terms and by degree. third degree polynomial fourth degree polynomial sixth degree polynomial first degree binomial
The correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
The degree of a polynomial is the highest power of the variable in the expression.
In the expression 5x + 3x⁴ - 7x³ + 10, there are 4 terms, and the term 3x⁴ involves the highest power = 4.
Therefore, the degree of the polynomial is 4.
Hence, we can say that the correct classification of the expression 5x + 3x⁴ - 7x³ + 10, is that it is the fourth-degree polynomial.
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The sum of four consecutive evan numbers is 660. Find these numbers.
Answer:The numbers are 162,164,166,168,
Step-by-step explanation:
The solution is in the attached
Answer: The numbers are 162,164,166,168,
Step-by-step explanation:
Each side of a hexagon is 10 inches longer than the previous side. what is the length of the shortest side of this hexagon if its perimeter is 401 inches?
The length of the shortest side of the hexagon is; 41.833 inches
How to find the perimeter of a Polygon?
Let the length of the shortest side of the hexagon be x. Now, a hexagon has six sides and if the next side is 10 inches longer than the previous side, then the length of the six sides are;
x, x + 10, x + 20, x + 30, x + 40, x + 50
Perimeter is given as 401 inches. Thus;
x + x + 10 + x + 20 + x + 30 + x + 40 + x + 50 = 401
6x + 150 = 401
6x = 401 - 150
6x = 251
x = 251/6
x = 41.833 inches
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Please help
The question is:
Which shows how to find the value when x = (-2) and y = 5?
I attached the equation & choices
Answer:
i believe the answer is 3^2(-2)^6/ 5^4
Step-by-step explanation:
The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mu = 18 sec and standard deviation sigma = 1.2 sec. what percentage of the runners have times less than 14.4 sec?
The percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.
What is standard deviation?The standard deviation of a data set is defined as how the data is dispersed in relation to the mean.
From the question,
The raw time given (X) = 14.4 sec
The mean value(m) = 18sec
The standard deviation(d) = 1.2 sec
Using the formula,
z = X - m/ d
z= 14.4- 18/1.2
z = -3.6/1.2
z= -3
Using a Z table to find the percentage equivalent of P(x<14.4) is 0.0013499 which is approximately = 0.15%.
Therefore, the percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.
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ik this is a lot but pls helpp. thank you so much if you would help! this is due tomorrow
1. Five groups at summer camp have a total of 27 boxes of popsicles to share. How many boxes will each group recieve?
2. If 16 is divided by 5 what fraction would represent the remainder?
3. Suppose four friends want to share five cookies equally. How many cookies would each friend recieve?
4. If there are 90 minutes in a race and 4 teams of runners share this time equally, how many minutes will each team run?
5. Ten soccer teams are sharing 3 boxes of bottled water. How much of a box will each team get?
6. Dan has $695 in the bank. He wants to take out 2/5 of money. How much money should he take out?
7. You have 7 packs of paper share betweem you and 3 of your friends. If you share the paper equally, how much paper does each student get?
8. Four friends are taking a road trip. They want to share the driving equally. If the trip takes 6 hours, how long should each friend drive?
9. If 9 people want to share a 50-pound box of apples equally by weight, how many pounds of apples should each person get?
Which are other possible names for ∠RPE ? Choose each correct answer. ∠2 ∠EPR ∠RPF ∠P ∠DPF ∠PRE
The other possible names of ∠RPE are ∠P and ∠EPR
How to determine the other possible names?The angle is given as:
∠RPE
The angle is named after the middle alphabet.
The middle alphabet in ∠RPE is P
This means that ∠P is a possible name for ∠RPE
Also, the positions of R and P can be interchanged.
So, we have:
∠EPR
Hence, the other possible names of ∠RPE are ∠P and ∠EPR
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Need help.
Please show your work if possible!!
Answer:
e
Step-by-step explanation:
let x be the number of one- bedroom and y the number of two - bedroom apartments , then create 2 equations and solve simultaneously.
x + y = 12 ( subtract y from both sides )
x = 12 - y → (1)
360x + 450y = 4950 → (2)
substitute x = 12 - y into (2)
360(12 - y) + 450y = 4950 ← distribute parenthesis and simplify left side
4320 - 360y + 450y = 4950
4320 + 90y = 4950 ( subtract 4320 from both sides )
90y = 630 ( divide both sides by 90 )
y = 7
there are 7 two- bedroom apartments
A survey was conducted to determine which type of lunch was most popular among the school's football team. How many more players prefer salad lunches than hot dog lunches?
Chart:
pizza- 15
hot dog-8
chicken-5
salad-10
burger-12
A. 3
B. 4
C. 2
D. 5
Answer:
ok this is pretty simple we just have to look at the chart
8 like hot dog
10 like salad
10-8=2
Hope This Helps!!!
Answer:B.2
Step-by-step explanation:
How many terms are in (3x^2-3)(3x^2+3)
The number of terms in the expression given is; 2.
How many term are in the expression given?It follows from the task content that the expression given is; (3x^2-3)(3x^2+3).
It therefore follows the converse of law regarding difference of two squares that the expression given can be rewritten as;
= 9x⁴ -9
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2x² - 1 > 6x
Which values are included in the solution set of this inequality?
x = 4
Step-by-step explanation:
2x² - 1 > 6x
2(4)²-1 > 6(4)
2(16)-1 > 24
32-1 > 24
31 > 24
Graph the function f(x)=(−x−4)(x+2).
The points of the graph of function be (0,-8) , (1,-15) ,(2,-24).
Given f(x)=(-x-4)(x+2)
We have to first multiply both the expressions to get f(x)
Expression refers to combination of numbers, symbols, variables, etc. It is usually not in equal to form. It expresses the relationship between variables. To find out the graph we need to first points of function.
f(x)=[tex]-x^{2} -2x-4x-8[/tex]
Now we have to add 2x and 4x
f(x)=[tex]-x^{2} -6x-8[/tex]
Put the value of x=0
f(0)=0-0-8
=-8
Put the value of x=1
f(1)=-1-6-8
=-15
Put the value of x=2
f(2)=-4-12-8
=-24
Now plot these points on the graph to get the graph of function f(x)=(-x-4)(x+2).
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y=x^2+8
Find the Domain, explain your answer
Step-by-step explanation:
look at the attachment above ☝️