Answer:
Your answers are below ↓
Step-by-step explanation:
Given ↓
A) 2x-3y = 5 and 3x+4y = 6 ( The method this has to be solved in is the elimination method. )
Now using these,
(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12
therefore,
y = 3
putting the value of y in eqn. (1)
2x + 6 = 5
therefore,
x = -1/2
B) y=x^2 - 2x and y = 2x -3 ( The method this has to be solved in is the substitution method. )
Reduce the greatest common factor on both sides of the equation:
[tex]\left \{ {{4x-y=9} \atop {xy=-2}} \right.[/tex]
Rearrange like terms to the same side of the equation:
[tex]\left \{ {{-y=9-4x} \atop {xy=-2}} \right.[/tex]
Divide both sides of the equation by the coefficient of the variable:
[tex]\left \{ {{y=-9+4x} \atop {xy=-2}} \right.[/tex]
Substitute the unknown quantity into the elimination:
[tex]x(-9+4x)=-2[/tex]
Apply Multiplication Distribution Law:
[tex]-9x+4x^2=-2[/tex]
Reorder the equation:
[tex]4x^2-9x=-2[/tex]
Divide the equation by the coefficient of the quadratic term:
[tex]\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}=-\frac{1}{2}[/tex]
Add one term in order to complete the square:
[tex]x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Factor the expression using [tex]a^2$\pm$2ab+b^2=(a$\pm$b)^2[/tex]:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Simplify using exponent rule with the same exponent rule: [tex](ab)^n=a^n*b^n[/tex]
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}[/tex]
Calculate the power:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}[/tex]
Find common denominator and write the numerators above the denominator:
[tex](x-\frac{9}{8} )^2=\frac{-32+81}{64}[/tex]
Calculate the first two terms:
[tex](x-\frac{9}{8} )^2=\frac{49}{64}[/tex]
Rewrite as a system of equations:
[tex]x-\frac{9}{8} =\sqrt{\frac{49}{64} }[/tex] or [tex]x-\frac{9}{8} =-\sqrt{\frac{49}{64} }[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over the common denominator:
[tex]x=\frac{7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{16}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=2[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=-\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=-\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over common denominator:
[tex]x=\frac{-7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{2}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=\frac{1}{4}[/tex]
Find the union of solutions:
[tex]x=2[/tex] or [tex]x=\frac{1}{4}[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*2[/tex]
Calculate the first two terms:
[tex]y=-9+8[/tex]
Calculate the first two terms:
[tex]y=-1[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*\frac{1}{4 }[/tex]
Reduce the expression to the lowest term:
[tex]y=-9+1[/tex]
Calculate the first two terms:
[tex]y=-8[/tex]
Write the solution set of equations:
[tex]\left \{ {{x=2} \atop {y=-1}} \right.[/tex] or [tex]\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.[/tex] -------> Answer
C) y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )
Step 1: We start off by Isolating y in y = 2x - 3
y=2x-3 ----------> ( Simplify )
y+(-y)=2x-3+(-y) ---- > ( Add (-y)on both sides)
0=-3+2x-y
y/1 = 2x-3/1 --------> (Divide through by 1)
y = 2x - 3
We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x
(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ----> ↓
(Substituting 2x - 3 for y in y = x^2 -2x )
Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method
2x - 3 = x^2 - 2x
x = -b±b^2-4ac/2a Step 1: We use the quadratic formula with ↓
a = -1,b=4,c= - 3
x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic Formular
x = -4± 4/ - 2 x = 1 or x = 3 Step 3: Simplify the Expression & Separate Roots
x = 1 or x = 3 ------- ANSWER
Substitute 1 in for x in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (1) - 3 (Substituting)
y = -1 (Simplify)
Substitute 3 for in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (3) - 3 (Substituting)
y = 3 (Simplify)
Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are
x₁ = 1, y₁ = -1
x₂ = 3, y₂ = 3
Graph the solution to the following system of inequalities.
-5x+4y> -4
2x+3y2-6
Then give the coordinates of one point in the solution set.
Answer:
2/3 x 9=99+25x7(78)gxw/98
Step-by-step explanation:
PLEASE HELP ME IM SO CONFUSED ON THIS QUESTION??
Answer:
C.
Step-by-step explanation:
7 7/8 rounds up to 8
2 1/10 rounds down to 2
8-3(2)=2
8 - 6 = 2
he would have about 2 pounds left
so the three pounds left is not reasonable
Find five consecutive even integers such that four times the first number plus the fourth number is 35
The five consecutive even integers such that the four times the first number plus the fourth number is 35 are 6 , 8, 10, 12, and 14.
How to find the consecutive integers of the sequence?The even integers are consecutive. Therefore,
let the first even integer = x
Therefore, the sequence is as follows:
x, x + 2, x + 4, x + 6, x + 8.....
Therefore,
4x + x + 6 = 36
5x + 6 = 36
5x = 36 - 6
5x = 30
x = 30 / 5
x = 6
Therefore, the numbers are as follows;
66 + 2 = 86 + 4 = 106 + 6 = 126 + 8 = 14learn more on integers here:https://brainly.com/question/15381903
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I need help with (ii) both (a) and (b) thanks
Answer:
(i) 126 ways
(ii)
(a) 1/126
(b) 5/14
Step-by-step explanation:
(i) Possible selections
⁹C₄ = 9! / 5! 4!9 x 8 x 7 x 6 x 5! / 5! x 4 x 3 x 2 x 172 x 7 x 6 / 247 x 6 x 342 x 3126 ways(ii) (a) all girls
⁴C₄ 4! / 1! 4!1 wayP = 1/126(ii) (b) more boys than girls
3 boys, 1 girl⁵C₃ x ⁴C₁(5! / 2! 3!) x (4! / 3! 1!)(5 x 4 x 3!/ 2 x 3!) x (4 x 3! / 3!)10 x 440 ways2. 4 boys, no girls
⁵C₄5! / 1! 4!5 x 4! / 4!5 ways⇒ 40 + 5 = 45 ways
⇒ P = 45/126 = 15/42 = 5/14
Question 8 of 8
Lori wants to buy the same number of pencils and
pens for school this year. Pencils comes in packs of
16, and pens come in packs of 4. What is the least
number of packs of each she could buy?
4 packs of pencils and 4
packs of pens
1 pack of pencils and 4
packs of pens
ne is being recorded
1 pack of pencils and 1 pack
of pens
4 packs of pencils and 1
pack of pens
SUBMIT
Answer:
1 pack of pencils and 4 packs of pens
Step-by-step explanation:
Because, 1 pack of pencils has 16. And 1 pack of pens has 4. So...
1 pack of pencils = 16 and 4 packs of pens = 4 + 4 + 4 + 4 which equals 16 too.
Hope this helps! :)
Question 11(Multiple Choice Worth 5 points)
(03.06A LC)
Which statement is true for the equation 2x - 2x - 7 = -7?
O It has infinitely many solutions.
O It has two solutions.
O It has one solution.
It has no solution.
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
2x-2x-7=-7
We need to solve it first as follows:
[tex]2x-2x-7=-7[/tex]
[tex]2x-2x=-7+7[/tex]
[tex]0=0[/tex]
Since L.H.S. = R.H.S.
So, it satisfies the equation for all x.
So, there will be infinitely many solutions.
Hence, Option 'a' is correct.
EXTREMELY URGENT Which function, g or h, is the inverse function for function ƒ?
the function h because the graphs of ƒ and h are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the line y = x
the function h because the graphs of ƒ and h are symmetrical about the x-axis
the function g because the graphs of ƒ and g are symmetrical about the x-axis
Answer:
The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x
Step-by-step explanation:
A function and its inverse function become symmetrical across the line y = x.
(100) What’s the distance of all the sides combined, add the method.
Answer:
10cm2
Step-by-step explanation:
Answer:
As AE and BD intersect:
∠ACB and ∠ECD are vertically opposite angles and are therefore congruent.As AB is parallel to ED:
∠BAC and ∠DEC are alternate interior angle and are therefore congruent.∠ABC and ∠EDC are alternate interior angle and are therefore congruent.Therefore, we can use SSS Similarity Theorem to find the lengths of the sides:
[tex]\sf \dfrac{AC}{EC}=\dfrac{BC}{DC}=\dfrac{AB}{ED}[/tex]
[tex]\implies \sf \dfrac{400}{1000}=\dfrac{300}{ED}[/tex]
[tex]\implies \sf 400 \cdot ED=300 \cdot 1000[/tex]
[tex]\implies \sf ED=\dfrac{300000}{400}=750[/tex]
**The length of BC and CD cannot be determined without knowing an angle**
Therefore, the remainder of the calculations are based on the assumption that ∠BAC and ∠DEC are 90°
If ∠BAC = 90° then BC can be calculated using Pythagoras' Theorem
⇒ AB² + AC² = BC²
⇒ 300² + 400² = BC²
⇒ BC² = 250000
⇒ BC = 500
Using the side ratios stated previously:
[tex]\sf \dfrac{AC}{EC}=\dfrac{BC}{DC}=\dfrac{AB}{ED}[/tex]
[tex]\implies \sf \dfrac{400}{1000}=\dfrac{500}{DC}[/tex]
[tex]\implies \sf 400 \cdot DC=500 \cdot 1000[/tex]
[tex]\implies \sf DC=\dfrac{500000}{400}=1250[/tex]
Therefore, the distance of each side is:
AC = 400 mAB = 300 mBC = 500 mEC = 1000 mED = 750 mDC = 1250 mAssuming the sides are the solid lines marked with arrows only:
⇒ Total distance = AB + BC + DC + ED
= 300 + 500 + 1250 + 750
= 2800 m
Which polynomial represents twice the sum of -5x^2-x+6 and 7x^2+x-1?
1) 2x^2+5
2) 4x^2+10
3) 4x^2+5
4) 2x^2 + 10
The polynomial that represent twice the sum of [tex]-5x^{2}[/tex] - x +6 and 7[tex]x^{2}[/tex] + x -1 is : 4[tex]x^{2}[/tex]+10
What is a polynomial?
A polynomial is any algebraic expression that has the least value of the power of its variable as 2.
When the highest value of the polynomial is 2, it is a called a quadratic expression.
Analysis:
2( -5[tex]x^{2}[/tex] -x +6 + 7[tex]x^{2}[/tex] +x -1)
2( 2[tex]x^{2}[/tex] + 5) =
4[tex]x^{2}[/tex] + 10
In conclusion, the polynomial that represents the above expressions is 4[tex]x^{2}[/tex] + 10
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What is the mode of this data set?
{7, 10, 12, 9, 12, 4, 13, 14}
7
10
11
12
Answer:
12
Step-by-step explanation:
the mode is the number you see the most
Answer:
12
Step-by-step explanation:
Mode is the number that is most repeated it can be more than one number but in your question it's only 1 number that's 12 and it has been repeated 2 times as shown
once again you can earn free easy points just by answering this simple question :)
Answer:
D Rotainon.
Step-by-step explanation:
The shape is flipped.
What is the probability that a patient shows improvement
if it is known that the patient was given the drug?
Answer:
.3375
Explanation:
Total people who were given drug: 800
Total people who showed improvement: 270
Probability:
[tex]\boxed{ \sf \dfrac{favorable \ outcomes }{total \ possible \ outcomes}}[/tex]
insert values
[tex]\rightarrow \sf \dfrac{270}{800}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{27}{80}[/tex]
in decimals
[tex]\rightarrow \sf 0.3375[/tex]
Answer:
d) .3375Step-by-step explanation:
let E be the event : “the patient shows improvement”
D be the event : “the patient was given the drug”
here we are in a conditional probability situation:
Let E/D be the event “a patient shows improvement ,if it is known that the patient was given the drug”
[tex]p\left( E|D\right) =\frac{p\left( E\cap D\right) }{p\left( D\right) }[/tex]
[tex]=\frac{270}{800}[/tex]
[tex]=0.3375[/tex]
Is the answer b?????
Answer:
it should be A if not im sorry
Step-by-step explanation:
PLEASE HELP IF I DONT DO THIS
TOMORROW I DONT GRADUATE
Next we will draw in each deviation from the mean.
Now, think about the average size (length) of all of those deviations, and use this as an estimate for the size of the
Standard Deviation. Don't worry about whether the deviation is to the left or right of the mean. Just consider all of
the lengths. Draw the length of the standard deviation below.
The standard deviation is a measure of a collection of values' variance or dispersion. The standard deviation of the below graph can be drawn as shown below.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
The standard deviation of the below graph can be drawn as shown below.
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The amount of bacteria in a culture doubles every minute. The culture starts with
20 bacteria.
a. Write an equation modelling the number of bacteria, y, after x minutes.
Answer:
exponential function, x = time in minutes, y = number of bacteria
Step-by-step explanation:
y = 20 × (2)^x
pls someone help, my he is due by tonight
Answer:
I hope it helps................
What is the quotient of 9-x2/
3x
and
x2 +6x+9/
3x?
44 rem
Im sorry if its wrong
use the graph of f to solve for f(x)= -3 for x
Answer:
b
Step-by-step explanation:
Which is not a reason an athlete uses technology to assess performance?
A. To tailor to their training program.
B. To monitor development.
C. To send to college recruiters.
D. To analyze technique.
Answer:
C.) To send to college recruiters
Step-by-step explanation:
The correct answer is C.) because this answer choice has nothing to do with assessing an athlete's performance. All of the other options involve assessing performance in some manner. An athelete's performance is directly tied to their training program, development, and technique.
Simplify: 4 - 5.2 + 6 + 7.9 - 8
3.9x+0.8y is the answer to your question.
A square has an area of 121 square centimetres.
What is its perimeter?
Answer:
44 cm
Step-by-step explanation:
The area of a square is the square of the side length. This means the side length is the square root of the area.
s = √A = √(121 cm²) = 11 cm
The perimeter of a square is the sum of its side lengths. There are 4 equal-length sides, so the perimeter is 4 times the length of one side:
P = 4s = 4(11 cm)
P = 44 cm
The perimeter of the square is 44 cm.
Answer:
44 cm
Step-by-step explanation:
Finding Side Length
Area = (Side length)²Take the square root on each sideSide length = √121Side length = 11 cmPerimeter
A square has 4 sidesTherefore, the perimeter is 4 times the side length4 × 1144 cmA ladder 5m long rests against a house and makes an angle of 720 with the ground. How far does the ladder reach up the wall?
Need Help ASAP
y = 2x − 5
y = -6x + 3
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution.
Part B: Check your work. Verify your solution and show your work.
Part C: If the two equations are graphed, what does your solution mean?
Answer:
Part A
Solve by substitution.
Given equations:
y = 2x − 5y = -6x + 3⇒ 2x - 5 = -6x + 3
⇒ 2x - 5 + 5 = -6x + 3 + 5
⇒ 2x = -6x + 8
⇒ 2x + 6x = -6x + 8 + 6x
⇒ 8x = 8
⇒ 8x ÷ 8 = 8 ÷ 8
⇒ x = 1
To find y, substitute the found value of x into one of the equations:
⇒ y = 2(1) - 5
⇒ y = 2 - 5
⇒ y = -3
Therefore, the solution is (1, -3)
Part B
Substituting x = 1 into the equations:
y = 2x − 5
⇒ y = 2(1) − 5
⇒ y = 2 − 5
⇒ y = -3
y = -6x + 3
⇒ y = -6(1) + 3
⇒ y = -6 + 3
⇒ y = -3
When x = 1, both equations return a y-value of -3. Therefore, the solution is verified.
Part C
If the two equations are graphed, the solution will be the point of intersection.
if you need 4/5 of a cup for one pie how many do cups do you need for 9
Answer:
if you simplefy it, it would be 7 1/5
Step-by-step explanation:
see how many time 5 goes into 36= 7 times what is your remander = 1 and the denomorator is 5 so 7 and 1/5
Part 1:
Based on your knowledge of fair decision making and probability concepts, should the Power Pill be produced and distributed? Explain your reasoning.
Part 2:
What effect (if any) did telling two groups about expected outcomes have on results? Use statistics to provide proof for your reasoning and explain.
Part 3:
Are there any flaws in the testing process? Should any of the steps or protocol be changed/avoided during round two of testing? Explain your reasoning.
The knowledge of fair decision making and probability concepts illustrates that the Power Pill should be produced and distributed.
What is probability?It should be noted that probability simply means the likelihood of the occurence of a particular event.
In this case, the knowledge of fair decision making and probability concepts illustrates that the Power Pill should be produced and distributed.
It's important to adequately carry out a research on the pill and ensure that it's safe.
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How can you use the conversion rates of fluid ounces to cups, and cups to pints, to find the number of fluid ounces in a pint?
Answer:
multiply them
Step-by-step explanation:
Units work in algebraic equations the same way that variables do. They can be multiplied and divided as though they were variables.
For units conversion, we want to change the units without changing the value of the quantity. We do that by multiplying by a unit conversion factor that has a numerator equal to its denominator.
__
We know ...
1 cup = 8 fl oz
2 cups = 1 pint
These relations can be written as the conversion factors ...
(8 floz)/(1 cup) and (2 cups)/(1 pint)
Multiplying these together, the units of cups cancel, leaving fluid ounces per pint.
[tex]\dfrac{8\text{ fl oz}}{1\text{ cup}}\times\dfrac{2\text{ cup}}{1\text{ pint}}=\dfrac{8\cdot2\text{ fl oz$\cdot$cup}}{1\cdot1\text{ pint$\cdot$cup}}=\boxed{\dfrac{16\text{ fl oz}}{1\text{ pint}}}[/tex]
_____
Additional comment
The concept of "like terms" applies to expressions involving units as well as expressions involving variables. Terms can only be added or subtracted if they have the same units.
) Evaluate
42+(9 divided by 3 x 2) - 4
Answer:
44
Step-by-step explanation:
Parenthesis
Exponents
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
42 + (9 ÷ 3 x 2) - 4 <== divide first (left to right)
42 + ((9 ÷ 3) x 2) - 4
42 + (3 x 2) - 4 <== multiply
42 + 6 - 4 <== add
48 - 4 <== subtract
44
Final answer: 44
Hope this helps!
3.1 How will ensure that cooperative learning In Mathematics class take place
3.2 use polya's four steps to solve the following tutorial showing all the steps:
Explain each step using the given question.
3.2.1 The sum of three consecutive numbers is equal to 39. Determine the three numbers
3.2.2 A father is five times as old as his daughter. In five years' time he will be three times as old as his daughter. Find both the ages now.
Step-by-step explanation:
The father is presently 25 years old.
And his daughter is presently 5 years old.
Therefore, the father is 5 times older than his so. Currently.
In 5 years, the father will be 30 years old and the son will be 10 years old. So the father will be 3 times the daughters age.
please help will mark Brainliest!!
Answer:
-33.2
Step-by-step explanation:
The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207
The mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
What is the mean?The mean is the average of a set of data or numbers.
It is a typical value that averagely represents the dataset.
The mean can be computed by dividing the total by the number of data values.
Data and Calculations:Atlanta $163
Minneapolis $125
Boston 177
New Orleans 167
Chicago 166
New York 245
Cleveland 126
Orlando 146
Dallas 123
Phoenix 139
Denver 120
Pittsburgh 134
Detroit 144
San Francisco 167
Houston 173
Seattle 162
Los Angeles 160
St. Louis 145
Miami 192
Washington, D.C. 207
Total = $3,181
Mean = $159.05 ($3,181/20)
Question Completion:What is the mean hotel room rate?
Thus, the mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
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