For this case we have the following solutions:
[tex]x_ {1} = 1 + \sqrt {5}\\x_ {2} = 1- \sqrt {5}[/tex]
Then, the factorized equation is of the form:
[tex](x- (1+ \sqrt {5})) (x- (1- \sqrt {5})) = 0\\(x-a) (x-b) = 0[/tex]
We apply distributive property:
[tex]x ^ 2-bx-ax + ab = 0\\x ^ 2- (1- \sqrt {5}) x- (1+ \sqrt {5}) x + (1+ \sqrt {5}) (1- \sqrt {5}) = 0\\x ^ 2-x + \sqrt {5} x-x- \sqrt {5} x + (1 ^ 2- \sqrt {5} + \sqrt {5} - (\sqrt {5}) ^ 2) = 0\\x ^ 2-2x + (1-5) = 0\\x ^ 2-2x-4 = 0[/tex]
ANswer:
The equation is [tex]x ^ 2-2x-4[/tex]
How would you solve this?
Answer:
2 2/3 cups of flour
Step-by-step explanation:
2/3 • 4 = 2 2/3
That's because 2/3 already makes 2 dozen cookies and you need to make 8 dozen so you need to multiply by 4 to get your answer.
Solve for x: 2/3(x − 2) = 4x.
A. x = -2/5
B. x = -5/2
C. x = 2/5
D. x = −2
Answer:
a
Step-by-step explanation:
Answer:
[tex]\large\boxed{A.\ x=-\dfrac{2}{5}}[/tex]
Step-by-step explanation:
[tex]\dfrac{2}{3}(x-2)=4x\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}(x-2)=(3)(4x)\\\\2(x-2)=12x\qquad\text{divide both sides by 2}\\\\\dfrac{2\!\!\!\!\diagup^1(x-2)}{2\!\!\!\!\diagup_1}=\dfrac{12\!\!\!\!\!\diagup^6x}{2\!\!\!\!\diagup_1}\\\\x-2=6x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x-x-2=6x-x\\\\-2=5x\qquad\text{divide both sides by 5}\\\\\dfrac{-2}{5}=\dfrac{5\!\!\!\!\diagup^1x}{5\!\!\!\!\diagup_1}\\\\-\dfrac{2}{5}=x\to x=-\dfrac{2}{5}[/tex]
The coordinates of the verticals of JKL are J(-2,1), K(-1,3) and L(-3,4). Can someone please check my answer?
Please answer this correctly
Answer:
Kang
Step-by-step explanation:
Janelle ran longer than Kang
Janelle>Kang
Janelle ran shorter than Annette
Annette>Janelle>Kang
Janelle ran longer than John and John ran longer than Kang
Annette>Janelle>John>Kang
Assume that a bacteria population doubles every second. Which of the following tables of data, with X representing time in seconds and y representing the count of bacteria, could represent the bacteria population with respect for time?
(answers in the pic)
Answer: Table A
Step-by-step explanation:
Because it doubles every second. At 0s, its 3. Then at 1s, it doubles which means 3x2=6, which is in table. then at 2s, that doubles to 6x2=12....and so on
What type of number is -5.41? 1. Whole number 2. integer 3. Rational 4. Irrational
The number -5.41 can be classified as a Rational number because it can be expressed as a fraction where both the numerator (-541) and the denominator (100) are integers and it's not a whole number or an integer because it's negative and has a decimal part.
Explanation:The number -5.41 is a type of number classified as a Rational number. Rational numbers are numbers that can be written as a fraction, where both the numerator and the denominator are integers (whole numbers), and the denominator is not zero. They can also be positive, negative, or zero, and they can be represented as decimals that terminate (like 0.2 or -1.75) or repeat (like 0.333... or -0.666...).
The number -5.41 is not a positive whole number nor an integer because it is negative and has a decimal part, which disqualifies it from both categories. An irrational number, on the other hand, is a number that cannot be expressed as a simple fraction, which clearly does not apply to -5.41 as it can be easily expressed by the fraction -541/100.
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Mr. and Mrs. Khan paid interest on their mortgage this year. They also had deductible home related expenses. The interest and expenses total an amount greater than the standard deduction. Which action can they take to reduce their income tax liability?
A) They can use the interest expense as a credit to reduce the tax they owe.
B) They can itemize deductions and deduct the interest expense.
C) They can request a reimbursement of the interest expense from the IRS.
D) They can add the interest expense to the taxable income.
E) They can reduce their mortgage payment next year by the amount of Interest they paid.
Answer:
B) They can itemize deductions and deduct the interest expense.
Step-by-step explanation:
I just got this right on Plato!
HENCE OPTION B IS CORRECT
What is income tax ?
Income tax is a sort of tax levied by governments on income made by businesses and persons within their jurisdiction. To assess their tax responsibilities, taxpayers are required by law to file an income tax return each year.
How to solve?
Check which statement will help Mr and Mrs khan to reduce income tax liability-
A) They can use the interest expense as a credit to reduce the tax they owe.
- interest expenses are not tax deductible
B) They can itemize deductions and deduct the interest expense.
-itemize will deduction will reduce income tax liability.
C) They can request a reimbursement of the interest expense from the IRS.
-Reimbursement is not part of reduction it is part of cashback as it is type of discount.
D) They can add the interest expense to the taxable income.
- It wi not hep to reduce income tax liability
E) They can reduce their mortgage payment next year by the amount of Interest they paid
-reducing mortgage will infact increase tax liability. if mortgage is removed.
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Find the sum. Write the addition property you used. 28+29+42=
Step-by-step explanation:
28+29=57
57+42=99 so 99 should be your answer
Answer:
Step-by-step explanation:
First your gonna brake up each number and seperate them for example
28
29
42
then your going to add up the ones side, 8,9,2, to get 19.
Then your going to add the tens side, 2,2,4, to get 8.
take the one from 19 and put it in the tens place to get 9 in the tens and 9 in the ones.
put 9 and 9 together to get 99.
If every 9 Points Equals 1 Dollar How Many Points Do I Need To Make One Thousand Dollars?
First One To Answer Correctly Gets Brainliest!
It has to be correct.
pls hurry
Answer: 9,000$
Step-by-step explanation: if 9 = $1
You multiply 9 by $1,000 and get 9,000
What are the solutions of the following equation?
4|x -9| +9 = -3|x -9| +9 4∣x−9∣+9=−3∣x−9∣+9
Answer:
x = 9
Step-by-step explanation:
4∣x−9∣+9 = −3∣x−9∣+9
cancel equal terms on both sides of the equation
4∣x−9∣+9 = −3∣x−9∣+9the statement is true but only if both sides equal 0
4∣x − 9∣= −3∣x − 9∣4 x | x - 9| = 0−3∣x − 9∣= 0solve the equation for x
4x |x -9| = 0divide both sides of the equation by 4
|x-9| = 0when the absolute value of x - 9 equals 0, then x - 9 = 0
x - 9 = 0move the constant to the right side and change it´s sign
x - 9 = 0x = 9so the answer would be x = 9
Answer: it's x=9
Step-by-step explanation:
Fill in the table using this function rule.
y=28 - 3x
X Y
1
3
4
6
Answer:
So, you just end up plugging in your numbers.
y = 28 - 3(1)
y = 28-3
y = 25
Y = 28 - 3(3)
y = 28 - 9
y = 19
y = 28 - 3x
y = 28 - 3(4)
y = 28 - 12
y = 16
y = 28 - 3x
y = 28 - 3(6)
y = 28 - 18
y = 10
Step-by-step explanation:
The completed table is:
X Y
1 25
3 19
4 16
6 10
How to fill the tableTo fill in the table using the function rule y = 28 - 3x, we can substitute the given values of x into the equation to find the corresponding values of y.
X Y
1 28 - 3(1) = 28 - 3 = 25
3 28 - 3(3) = 28 - 9 = 19
4 28 - 3(4) = 28 - 12 = 16
6 28 - 3(6) = 28 - 18 = 10
So, the completed table is:
X Y
1 25
3 19
4 16
6 10
For each value of x, we substituted it into the function rule and performed the necessary calculations to determine the corresponding value of y.
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Evaluate 2x^2 – 1 when x=3
Answer:
17
Step-by-step explanation:
Given: 2x² – 1
when x=3
2(3)² – 1
= 2(9) -1
= 18 - 1
= 17
Answer:
17 .
Step by step explanation:
Substitute the value of x into the equation and square it.
the equation then becomes 2(3)^2- 1
but 3^2 =3×3 =9
So the equation is changed to 2(9)-1 after the simplification
given you 18-1
=17
what is 25 ties 3 divited by 19
Answer:3.9
Step-by-step explanation:
Answer: 25 x 3 divided by 19 is 3.94736842105
Match each polynomial expression to its additive inverse
Answer:
(1, 2, 3, 4) matches (A, C, B, D)
Step-by-step explanation:
The additive inverse of a term is formed by changing the sign. The additive inverse of the polynomial is formed by changing the sign of every term.
If we call the expressions on the left (top-to-bottom) 1, 2, 3, 4, and those on the right A, B, C, D, then the match-up in this presentation of the question is ...
1 - A
2 - C
3 - B
4 - D
_____
YMMV if the expressions are mixed differently
Answer:
Heres an ss of the answers
Step-by-step explanation:
Use complete sentences to describe what it means to prove a statement in Geometry.
Answer:
Step-by-step explanation:
To use the information and to show, using work, how to step by step solve a problem.
Answer:
He's correct.
Step-by-step explanation:
50 grams/Centimeters = kilograms/meters
Answer:
50g/cm is equal to 5 kg/m
Step-by-step explanation:
as we know that:
10g/cm = 1 kg/m
so,
50g/cm = 5kg/m
Your water is 5/6 full. After Tennis Practice, the bottle is 3/8 full. How much water did you drink?
Answer: 11/24
Step-by-step explanation:
5/6 - 3/8 = 11/24
A pond is being drained through an outlet pipe, then will be filled through an inlet pipe. If the inlet pipe can fill the pond in 9 hours and the outlet pipe can empty the pond in 15 hours, how long would it take to fill the pond if the outlet pipe was left open?
Answer:
22.5 hours
Step-by-step explanation:
I am using "1 pond" to mean the volume of water that fits in the pond.
The inlet pipe fills the pond in 9 hours.
The filling rate is (1 pond)/(9 hours) = 1/9 pond/hour
The outlet pipe empties the pond in 15 hours.
The emptying rate is (1 pond)/(15 hours) = 1/15 pond per hour
The difference in rates is the net rate at which the pond is filling up.
1/9 pond/hour - 1/15 pond/hour =
= 5/45 pond/hour - 3/45 pond /hour
= 2/45 pond/hour
The pond is filling at a rate of 2/45 pond/hour.
To find the time it takes to fill the pond, we divide 1 pond by the rate.
(1 pond)/(2/45 pond/hour) = 45/2 hour = 22.5 hours
Rewrite with common denominator then solve 7/9 subtract 2/3
to write them both with a common denominator, we simply multiply one by the other's denominator, so let's proceed,
[tex]\bf \cfrac{7}{9}\cdot \cfrac{3}{3}\implies \boxed{\cfrac{21}{27}}\qquad \qquad \qquad \cfrac{2}{3}\cdot \cfrac{9}{9}\implies \boxed{\cfrac{18}{27}}[/tex]
What is the reason for each step in the solution of the equation?
-5(x – 6) = 10x
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Step-by-step explanation:
-5(x – 6) = 10x
-5x+30=10x
-5x-10x = -30
-15x = -30
x= -30/-15 = 2
In which pair of numbers is the first number a multiple of the second number?
Group of answer choices
27, 9
25, 6
8, 72
52, 3
Answer:
27,9
Step-by-step explanation:
9x3=27
To do such problems we need to know the concept of multiple of a number.
A multiple is a number that is the result of multiplying a number by an integer (not a fraction).
Given options,
a.) 27, 9
We can write 27 as 9 x 3, therefore, we can see that 27 is a multiple of 9.
b.) 25, 6
We can write 25 as 5 x 5, we can see that 25 is not a multiple of 6.
c.) 8, 72
We can write 8 as 2 x 2 x 2, we can see that 8 is not a multiple of 72.
d.) 52, 3
We can write 52 as 2 x 2 x 13, we can see that 52 is not a multiple of 3.
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what is 80 + 80 equals 80 + 80 * 80 equals
Answer:
80+80=160
80+80+80=240
240 >160
so no it is not equal
thank you for your time!
Step-by-step explanation:
In Mathematics, the order of operations (BOMDAS or BIDMAS) dictates that multiplication operations should be performed before addition. Hence, in the mathematical expression '80 + 80 equals 80 + 80 * 80 equals', the multiplication operation (80*80) is performed first, resulting in '80 + 6400 = 6480'. Therefore, 80 + 80 equals 6480.
Explanation:In Mathematics, the operation order matters, this order is known by the acronym BOMDAS or BIDMAS, which stands for Brackets, Orders, Multiplication and Division, and Addition and Subtraction. it is used to clarify which procedures should be performed first in a given mathematical expression.
In your question, '80 + 80 equals 80 + 80 * 80 equals', we have both addition and multiplication operations. According to BIDMAS rules, we perform multiplication first before addition. Hence, the given expression is equivalent to 80 + 80 equals 80 + (80 * 80), where (80*80) should be calculated first.
Putting this into practice, we get: 80 + (80 * 80) = 80 + 6400 = 6480. Therefore, 80 + 80 equals 6480, based on the principles of BIDMAS or BOMDAS.
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help please and thank you!!!
Hello!
So, let's go over some information we know. We know that all the interior angles of a triangle add up to 180 degrees. We know that a line measures 180 degrees. We, therefore, know that angles which make up a line are supplementary, and must add up to 180 degrees.
So, first, we can find angle ABC. We can find this because angle ABC and ABT add up to 180 degrees, and we know the measure of ABT to be 125 degrees. Therefore:
ABC + 125 = 180
ABC = 55 degrees
Now, we can find angle ACB. We can find this as we have angle ABC and CAB, and angle ACB + ABC + CAB = 180 degrees (as they are the three interior angles of triangle ABC). ABC measures 55 degrees, and CAB 60 degrees. Therefore:
55 + 60 + ACB = 180
115 + ACB = 180
ACB = 65 degrees
Finally, we can find angle ACR based off of ACB, as ACB and ACR make up one line, and, therefore, add up to 180 degrees. ACB measures 65 degrees.
ACR + 65 = 180
ACR = 115 degrees
Therefore, your answer is choice 2, or 115 degrees.
Hope this helps!
Answer:
115°
Step-by-step explanation:
m∠ABC = 180° - 125° = 55° (angles in a straight line add up to 180°)
Given that m∠CAB = 60°,
Then m∠ACR = m∠CAB + m∠ABC (exterior angle is equal to the sum of opposite interior angles).
m∠ACR = 60° + 55° = 115°
If y(x) = 3(x+5) +-, what is
a + 2)?
Answer:
f(a + 2) = 3a + 21
Step-by-step explanation:
f(x) = 3(x+5)
x = a + 2
f(a + 2) = 3(a + 2 + 5)
f(a + 2) = 3(a + 7)
f(a + 2) = 3a + 21
What is the lower quartile of 27,5,11,13,10,8,14,18,7 a. 7 b. 7.5 c. 8 d. 8.5
Answer:
Lower Quartile = 7.
Step-by-step explanation:
Given : 27,5,11,13,10,8,14,18,7
To find : What is the lower quartile .
Solution : We have given 27, 5, 11, 13, 10, 8, 14 , 18 , 7.
Step 1 : Arrange in order
5 , 7 ,8 ,10 ,11, 13 , 14 ,18 , 27.
Step 2 : divide in to Quartile
Lower Q1 = 5 ,7 ,8
Middle Q2 = 10, 11 , 13.
Highest Q3 = 14 ,18 , 27.
Hence Lower Quartile = 7.
Therefore, Lower Quartile = 7.
Answer:
A=7!
Step-by-step explanation:
The center is open for 11 hours each day. Each party takes three hours what is the maximum number of parties the Center can host in a day
The maximum number of parties the Center can host in a day is 12.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.Mathematicians refer to equations with a degree of 1 as linear equations. The largest exponent of terms in these equations is 1, which equals. These can also be broken down into linear equations with one variable, two variables, three variables, etc. A linear equation with the variables X and Y has the conventional form aX + bY - c = 0, where a and b are the corresponding coefficients of X and Y and c is the constant.Given, the center is open for 11 hours each day and each party takes three hours. There are 4 rooms.
Therefore, 11 ÷ 3 = 3 (approx)
Each room can host 3 parties each day.
=3 × 4 = 12
The center can host up to 12 parties in a day.
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What is 40% of $20 show the work too please :)
Answer:
$8
Step-by-step explanation:
Convert 40% into decimal form: 0.4
Multiply it by 20.
=0.4 * 20
Simplify 0.4 * 20
= 8
It took Reza 2 hours to edit 6 math
problems. At that rate, how many math
problems could Reza edit in 45 hours?
Answer:
135
Step-by-step explanation:
My method 45 hours - 1 so i could divide by 2 because its 2 hours every 6 problems and 1 hour would be 3 math problems we can add that to the total
44 / 2 = 22, 22 * 6 = 132, 132 + 3 = 135
Alternate method
45 * 3 = 135
Donnie and Tania are math tutors. The amount Donnie charges for a session h hours long is represented by the function D(h) = 40h + 10. Tania charges a flat fee of $30 plus $15 an hour. Write a function, T(h), that represents the amount in dollars that Tania charges for h hours of tutoring. Graph both functions on the same coordinate grid, and label each line. Compare the slopes and y-intercepts of the graphs.
Answer:
Step-by-step explanation:
Answer:
[tex]T(h)=15h+30[/tex]
The graph is shown below.
Step-by-step explanation:
The amount Donnie charges for a session h hours long is represented by the function
[tex]D(h)=40h+10[/tex]
Tania charges a flat fee of $30 plus $15 an hour. The amount in dollars that Tania charges for h hours of tutoring is represented by the function
[tex]T(h)=15h+30[/tex]
Slope intercept form of a line is y=mx+b, where m is slope and b is y-intercept.
For Donnie:
Slope = 40 and y-intercept = 10
For Tania:
Slope = 15 and y-intercept = 30
It means slope of Donnie is greater than Tania and y-intercept of Tania is greater than Donnie.
Table of values for Donnie:
x y
0 10
1 50
2 90
Table of values for Tania:
x y
0 30
1 45
2 60
Plot these ordered pair on same coordinate plane and connect them to draw both functions.
The graph is shown below.
How do you find the product of -2(3.1)
Answer:
- 6.2
Step-by-step explanation:
The product of - 2 (3.1) is - 6.2.
Brackets mean to multiply so we have to multiply the - 2 by 3.1 which gives a result of - 6.2.