[tex] {x}^{2} + 4x - 7 = 0 \\ → {x}^{2} + 4x = 7[/tex]
Add the square of the half of the coefficient of the unknown(x) to both sides of the equation.
[tex] {x}^{2} + 4x + ( \frac{4}{2} {)}^{2} = 7 + ( \frac{4}{2} {)}^{2}[/tex]
[tex] {x}^{2} + 4x + (2 {)}^{2} = 7 + (2 {)}^{2} [/tex]
[tex] {x}^{2} + 4x + (2 {)}^{2} = 7 + 4[/tex]
Bring out x and 2 and square them as shown below:
[tex](x + 2 {)}^{2} = 11[/tex]
Now, square root both sides of the equation to find the value of x as shown below:
[tex] \sqrt{(x + 2 {)}^{2} } = \sqrt{11} [/tex]
Add a + or - sign since it is a quadratic equation
[tex]x + 2 = \binom{ + }{ - } \sqrt{11} [/tex]
[tex]x + 2 = \binom{ + }{ - } 3.3166[/tex]
[tex]x = - 2 + 3.166 [/tex] or
[tex]x = - 2 - 3.166[/tex]
Therefore:
[tex]x = 1.17[/tex] or
[tex]x = - 5.17[/tex]
to two decimal places.
Nineteen marbles are shared between some children.
Each child receives six marbles and there is one marble left over.
How many children share the marbles
find the value of x:
Answer:
The answer to the question is 35 degrees
What value of "x" makes the equation -4x+7=2x+13 true?
OA. -4
OB. -1
OC. 2
OD. O
Answer:
B. -1
Step-by-step explanation:
Let's solve your equation step-by-step.
−4x+7=2x+13
Step 1: Subtract 2x from both sides.
−4x+7−2x=2x+13−2x
−6x+7=13
Step 2: Subtract 7 from both sides.
−6x+7−7=13−7
−6x=6
Step 3: Divide both sides by -6.
−6x/−6 = 6/−6
x=−1
theo needs 1 1/2 cups of flour for one recipe and 2 3/4 cups of flour for a second recipe. Theo only has a 1/4 cup measuring cup. How many times will theo need to fill the 1/4 cup measuring cup to measure the flour he needs for the two recipes?
17 times theo will need to measure the flour for both the recipes.
WHAT IS BODMAS ?Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems. B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.
The order of operations (or operator precedence) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression. For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.
As a result, 1 + (2 3) = 7 rather than 1 + (2 3) = 9 is the value assigned to the expression 1 + 2 3. Exponents were first used in the 16th and 17th centuries, when addition and multiplication were given priority. Exponents could only be used as a superscript to the right of their base. Consequently, 3 + 52 = 28 and 3 52 = 75.
CALCULATIONfirst add the total amount of flour =
= [tex]1\frac{1}{2} + 2\frac{3}{4}[/tex]
= 1.5 + 2.75
= 4.25
no. of times = 4.25 * 4/1 = 17 times
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Solve 6-2x=3x
What would the answer be and step by step guide to completing it
Answer:
x=6/5
Step-by-step explanation:
6=2x+3x
5x=6
x=6/5
You start at (6,4) and move 4 units left and 2 units down what point will you end up on?
Answer:(2,2)
Step-by-step explanation:
because if you follow the steps you will end up there
plastic parts produced by an injection-molding operation are checked for conformance to specifications. each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. an inspector chooses 3 parts from among the 12 at random. two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications.
The probability that the inspector finds exactly one nonconforming part is 0.4091.
What is combination?Combination is a selection of items from a collection in which the order of selection is irrelevant. Probability is defined as the ratio of favorable outcomes to total outcomes.
Now, according to the question;
Let X represent the event in which the inspector discovers a nonconforming part.
An inspector selects three parts at random from among the twelve, and two cavities have been affected by a temperature malfunction, resulting in parts that do not meet specifications.
The total number of ways to select three parts from a total of twelve is ¹²C₃ = 220.
The number of possible ways for an inspector to identify just one defective part is:
²C₁×¹⁰C₂ = 2×45
²C₁×¹⁰C₂ = 90
The likelihood that the inspector will discover exactly one nonconforming part is provided by:
P (x=1) = (²C₁×¹⁰C₂)/¹²C₃
= 99/220
P (x=1) = 0.4091
The inspector has a 0.4091 chance of finding exactly one nonconforming part.
Now, the probability that inspector finds no nonconforming parts is given by:
P (x=0) = ¹⁰C₃×¹²C₃
= 120/220
P (x=0) = 0.5455
Therefore, the inspector has a 0.5455 chance of finding exactly none nonconforming part.
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The complete question is-
Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 3 parts from among the 12 at random. Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications. what is the probability that the inspector finds exactly one nonconforming part?
Joe has some pocket money. He spends three-quarters of it. He has fifty pence left. How much pocket money did he have
Answer:
He started with 1.25
Step-by-step explanation:
Joe started with 1.25 if he spends 3 quarters of that which is equal to .75 hell have .50 left
1.25-.75=.50
alysha is at a local library with her best friend. they've noticed a lot of cute boys in the library, and alysha bets that of the next twenty people to enter the library, exactly 12 will be cute boys. assuming there is a 50% chance that the next person to walk into the library is a cute boy, what is the probability that alysha will win the bet?
The probability that Alysha will win the bet is 0.12013
Let ‘x’ be the number of cute boys from next 20 persons that enter the library
And assume x be the integral values from 0 to 20
Given, the probability is 50% that the next person that enters the library is a cute boy,
total number of trials n=20 and probability of success p=50% = 0.5 = 1/2.
Hence, the p.m.f of X is given by
fX(x) = 20Cx(1/2)x(1−1/2)20−x
=20Cx(1/2)x(1/2)20−x
=20Cx(1/2)20
=20!(20−x)!x!⋅ 1220
=0,1,2,…,19,20
and the probability that X=x,
thus
P(X=x)=20!(20−x)!x!⋅1220
x=0,1,2,…,19,20
P(X=x)=20!(20−x)!x!⋅1220
x=0,1,2,…,19,20.
In particular, for X=x=12
P(X=12)=20!(20−12)!12!⋅1220
=20!8!12!⋅1220
≈0.12013
Hence, the probability that exactly 12 persons of the next 20 persons that walk into the library are cute boys is only approximately 0.12013.
Therefore, 0.1203 is less than 0.5, then it is more probable that Alysha will lose the bet than win it.
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: two six-sided dice are thrown. the numbers on the dice determine which player gets a point. player 1 gets a point if the product of the numbers on the dice is even. player 2 gets a point if the product is odd.
Both games A as well as B are unfair.
For the game to be fair, both players have to have equal possibilities of prevailing the sport.For sport A.player 1 gets a factor if the made from the numbers at the cube is even. player 2 receives a factor if the product is extraordinary.The fabricated from the numbers at the dice is even if:(i) both the numbers are even.(ii) one of the numbers is extraordinary and the other is even.The product of the numbers within the dice is ordinary simplest when each the numbers are unusual.hence, game A favours player 1.For game B.player 1 receives a point if the sum of the numbers on the cube is even. participant 2 receives a factor if the sum is bizarre.The sum of the numbers at the cube is even when:(i) each the numbers are even.(ii) both the numbers are bizarre.The sum of the numbers in the dice is odd only when one of the numbers is even and the alternative is unusual.subsequently, sport B favours player 1.accordingly, both games favour player 1 and are unfair.To learn more about probability, visit :
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Write a linear function f(x)=mx+b for the table
The standard form the linear function is f(x)= -3x-3.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+3. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
For the given example: m=5 and b=3.
You should replace in the minimum two given values for x and y in the standard form for a linear equation mx+b . Thus, you will write a system linear where from it, you can find the coefficients m and b. See below.
For x=0 and y=-3y=mx+b
-3=0*m+b
-3=b
For x=-2 and y=3y=mx+b
3= -2*m+b
Now, you find b=-3, then
3= -2*m-3
3+3= -2m
6=-2m
m= -3
Thus, you can write f(x)= -3x-3.
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Trisha and her three sisters to decide to purchase their mom a Christmas
gift. They decide that everyone will contribute an equal amount, up to
$60 per person. Write an inequality to find how much money the sisters
will spend on their mom for Christmas?
What is the answer to
|x+8|=|2x+1| ?
Answer:
[tex] \sf \large \: x=7 or x=−3[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
|x+8|=|2x+1|
Solve Absolute Value.
|x+8|=|2x+1|
We know eitherx+8=2x+1orx+8=−(2x+1)
x+8=2x+1(Possibility 1)
x+8−2x=2x+1−2x(Subtract 2x from both sides)
−x+8=1
−x+8−8=1−8(Subtract 8 from both sides)
−x=−7
−x/−1 = −7/−1
(Divide both sides by -1)
x=7
x+8=−(2x+1)(Possibility 2)
x+8=−2x−1(Simplify both sides of the equation)
x+8+2x=−2x−1+2x(Add 2x to both sides)
3x+8=−1
3x+8−8=−1−8(Subtract 8 from both sides)
3x=−9
3x/3 = −9/3
(Divide both sides by 3)
x=−3
Check answers. (Plug them in to make sure they work.)
x=7(Works in original equation)
x=−3(Works in original equation)
Answer:
7
Step-by-step explanation:
x+8=2x+1
Subtract x on both sides. Subtract 1 on both sides
x=7
HELP PLEASEEE
If g (x) = x² + 6 and ƒ (x) = 2x − 4, find g (ƒ (x))
Step-by-step explanation:
Plug in 2x-4 in the function g(x)
[tex]g(f(x)) = {(2x - 4)}^{2} + 6 \\ \\ g(f(x)) = (2x - 4)(2x - 4) + 6 \\ = 4 {x}^{2} - 8x - 8x + 16 + 6 \\ g(f(x)) = 4 {x}^{2} - 16x + 22[/tex]
HOPE THIS HELPS
b. Parallel lines are lines that will never intersect. Do parallel lines exist in spherical geometry? Explain your answer.
Yes parallel line exist in spherical geometry. The radius or diameter and the tangent can be a pair of parallel line in spherical geometry
How parallel can exist in spherical geometryThe tangent of the sphere refers to a line that make contact with only a point in the sphere. The tangent is perpendicular to the center and the radius can be drawn to be parallel to the tangent.
The radius refers to a line running from the center to an end of the circle. Two radius can be drawn say radius A and radius B. Radius A will be drawn perpendicular to the tangent and radius B drawn perpendicular to radius A.
The pair of lines tangent and radius B will be parallel to each other.
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Jenna can't wait to play in her new sandbox! Her mom fills the sandbox with seven 50-pound bags of sand. Then, Jenna uses her bucket to dump out sand 10 times. If she dumps out 8 ounces of sand each time, how many pounds of sand are left in the sandbox?
Answer:
345 pounds
Step-by-step explanation:
Each bucket dumps out 8 ounces of sand
8 ounces = 1/2 pound
So total sand dumped 10 times = 1/2 x 10 = 5 pounds
Originally sandbox had 7 x 50 = 350 pounds of sand
Sand left in box = 350 - 5 = 345 pounds
While shopping kyla found a dress that she would like to purchase but it cost $52.25 mor3 than she has
Kyla should babysit for 9.5 hours to buy the dress.
Double number line represents the comparison of numbers by representing them in equal ratio. The required double number line for the question is attached as figure.
The row I indicates the amount earned and row II indicates the number of hours Kyla should babysit. As is evident from the double number line, the average of last two amounts is the amount required by Kyla. Calculations are as follows -
Required amount = (49.5 + 55)/2
Required amount = 52.25
Now, the time between last two columns of row II will also be taken as average for calculation. So, time required to earn 52.25 after earning 49.5: (9 + 10)/2
Time = 0.5
Total time required to babysit = 9 + 0.5
Total time = 9.5 hours
Thus, Kyla should babysit for 9.5 hours to buy the dress.
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The complete question is -
While shopping, Kyla found a dress that she would really like, but it cost $52.25 more than she has. Kyla charges $5.50 an hour for babysitting. She wants to figure out how many hours she must babysit $52.25 to buy the dress. Use a double number line to support your answer.
Please help me with this geometry question. Answer should be entered like this (answer, answer) thank you
Answer:
Q is the point (3, 4).
Step-by-step explanation:
The formulae for the coordinates of a point (h, k) which divides a line joining the points (x1, y1) and (x2, y2) in the ratio m : n is:
h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)
Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and
m = 5 and n = 2.
So here, for point Q:
h = (5*5) + 2*-2)/(2+5)
= 21/7
= 3.
k = (5*8 + (-6*2) / 7
= 28/7
= 4.
g(x)=5/x,x≠0
h(x)=x²-2
find the compositions g*g and h*h
Answer:
hope you like my answer .
Step-by-step explanation:
g(g(x)) mean g of g of x
and same for h
a11
for -4, 8, -16, 32, …
Describe a real-world situation that can be modeled by the equation y = 1/20x be sure to describe which each variable represents
The equation can be modelled to a real scenario where every purchase can be use to calculate sales tax.
How to find a real world situation that models an equation?The equation to be modelled is as follows:
y = 1 / 20x
let
x = The total price of purchases
y = The amount of sales tax
This simply means a person pays 1 / 20 or 5% of every purchase he/she makes.
The total price of the purchase(including tax) is x while the actual amount of tax paid is y.
Let's say you buy a goods worth 400 dollars. Let's calculated the tax as follows:
x = $400
Therefore,
y = 1 / 20 × 400
y = 1 / 20 × 400
y = $20
Hence, the tax for a purchase of 400 dollars is 20 dollars.
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What is the answer rounded to the
hundredths
place?
9.3478 m
+2.73 m
12.0778 m
➜>>
→ [?] m
Answer:12.8
Step-by-step explanation: u just round it
Which table has a constant of proportionality between y and az of 0.6?
Choose 1 answer:
(G
z
Y
47
6
8
-8
4
9
14
H
10
13
y
2.4
5.4
8.4
y
3
2
9 6
15 10
Answer:
C
Step-by-step explanation:
if you divide the y by x, the answer it will give you will be 2/3 or .6
10. Sam earns a salary of $25,000 while Charlie earns a salary of $30,000. They each receive
a $2000 raise. Which of the following is true?
(a) Sam's raise is larger than Charlie's in both absolute and relative terms.
(b) The raises are the same in absolute terms, but Sam's is larger in relative terms.
(c) The raises are the same in relative terms, but Sam's is larger in absolute terms.
(d) The raises are the same in absolute terms, but Charlie's is larger in relative terms.
If the salary of Sam is $25000 and Charlie earns $30000 and each get a raise of $2000 then the statement "The raises are the same in absolute terms, but Charlie's is larger in relative terms" is true.
Salary of Sam = $25000
Raise in Sam's Salary = $2000
New Total Salary = $25000 + $2000 = $27000
Salary of Charlie = $30000
Raise in Charlie's Salary = $2000
New Total Salary = $30000 + $2000 = $32000
Hence the absolute value of their salaries are same but Charlie will get more in relative terms.
Hence, option d is correct.
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Sarah had a balance of $162 in her bank account at the start of the week. She withdrew $63.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday, she deposited $87.30.At the end of the week, Sarah had ___(less or more) money in her savings account than she had at the beginning of the week.
How much more or less? $_______
Answer:
Less; $25.90 less than at the beginning of the week
Step-by-step explanation:
162-(63.50+23.25+26.45)=162-113.20=48.80
48.80+87.30=136.10; 162>136.10
162-136.10=Δ$25.90
$25.90 less
in class, we proved that the number of ways of tiling a $1 \times n$ rectangle with $1 \times 1$ and $1 \times 2$ tiles is $f {n 1}.$ (a) use a tiling argument to give a combinatorial proof that \[f 1 f 2 f 3 \dots f n
Here is a straightforward recursion you may employ to calculate the value.
let's use rectangles with integer aspects to represent the quantity of tilings of a $2 instances n$ rectangle as $T(n)$. There are $22n-2$ techniques to accomplish this if no rectangles of height $2$ are hired, wherein case we lessen to two wonderful times of the $1 times n$ state of affairs. If no longer, we set a situation based at the top-proper rectangle's $2 height. With the preliminary conditions $T(0)=1$ and $T(1)=2$, this results in $$T(n)=22n-2+sum k=0n-1 T(okay)+sum 0leq k ell leq n-1T(ok)22(n-ell-1)$. The center term inside the recursion corresponds to the case where the rightmost rectangle of top $2$ is absolutely the rightmost rectangle inside the tiling.It should be noted that the formula $2n-1$ for the $1 times n$ case is incorrect if $n=0$.
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Show how 2/5 + 4/10 is the same as 4/5
Answer:
Explained through Step-by-step (Showed Work)
Step-by-step explanation:
Question: Show how 2/5 + 4/10 is the same as 4/5
Step-by-step:
2/5 and 4/10 are fractions. (So is 4/5)
To add fractions together, we need the denominators to be the same. This means that the bottom number of 2/5, which is 5 and the bottom number of 4/10 which is 10 have to be the same.
The easiest way to do this is to simplify 4/10. To simplify 4/10, we divide both the numerator (top number) and the denominator (bottom number) by the Greatest Common Factor.
In this case, 2 is the Greatest Common Factor because 4 divided by 2 is 2 and 10 divided by 2 is 5.
so, 4/10 can be simplified to 2/5.
Now, we can add 2/5 and 2/5 together by only adding the numerators. 2 + 2 = 4
so, 2/5 + 2/5 = 4/5
4/5 = 4/5
Therefore, 2/5 + 4/10 is the same as 4/5.
Hope this helps
What should I do when I finish High school and college
Answer: You should try to figure out the job you want and do that and maybe make a bucket list. Also, live your future out and your hapiness is what counts.
Step-by-step explanation:
please help im about to fail math solve for x: 5/2x+1/2x=7+7/2x
Answer:
yall smart
Step-by-step explanation:
solve the function please
for f(x) = x^2 - 2x + 1 , find f(x+h)-f(x) / h , h ≠ 0
For the given function f(x) = x^2 - 2x + 1, the difference quotient is {2x + h - 2]
How to find the difference quotient for the function f(x)?
Here we have the function f(x) = x^2 - 2x + 1
And we want to find the difference quotient, which is:
( f(x + h) - f(x))/h
Replacing the actual function there we get:
[ (x + h)^2 - 2*(x + h) + 1 - x^2 + 2x - 1]/h
Now we can simplify the numerator, we will get:
[ x^2 + 2xh + h^2 - 2x - 2h + 1 - x^2 + 2x -1]/h
[2xh + h^2 - 2h]/h
Taking the quotient we get:
{2x + h - 2]
That is the difference quotient for the function f(x).
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