Answers
Answer:
1
Square on both the sides 2x - 3 = (x - 3)²2x - 3 = x² + 9 - 6x [(a+b)²=a²+b²+2ab]x² + 9 - 6x - 2x + 3 = 0x² - 8x + 12 = 0x² - 6x - 2x +12 = 0x(x - 6) - 2(x - 6)(x - 6)(x - 2)x = 6 or x = 22
Square on both the sides3x - 2 = (x - 2)²3x - 2=x² + 4 - 4xx² - 4x - 3x + 4 + 2x² - 7x + 6x² - 6x - 1x + 6x(x - 6) - 1(x - 6)(x - 6)(x - 1)x = 6 or x = 13
Square on both the sides2x + 6 = (x - 1)²2x + 6 = x² - 2x + 1x² - 2x - 2x + 1 - 6 = 0x² - 4x - 5= 0x² + 1x - 5x - 5 = 0x(x + 1) - 5(x + 1)(x + 1)(x - 5)x = - 1 or x = 5Related Questions
convert each of the following base-ten numberals in the indicated bases
456 in base 5
Answers
Answer:
3311
Step-by-step explanation:
The steps are as follows
1. Divide 456 by 5. This gives a quotient of 91 with a remainder of 1. This remainder becomes the least significant digit of the new base number. This would be the right most digit. So the number is _ _ _ 1
2. Take the quotient, 91, divide by 5 again. This gives a quotient of 18 with a remainder of 1. Put this remainder to the immediate left of the previous value. So we have the number as _ _ 1 1
3. Take the previous quotient, 18, divide by 5 again. 18/5 gives quotient of 3 with a remainder of 3. Put this to the immediate left of the previous number giving the number as _ 3 1 1
4. Repeat the division of the new quotient by 5. 3/5 gives a quotient of 0 with remainder of 3 so we stop
Number = 3 3 1 1
Best done by writing a program or using a calculator
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
If a regular hexagon with an area of 12 is divided into 6 identical triangles, what is the area of each triangle?
Answers
12 ÷ 6 = 2cm²
- BRAINLIEST answerer
can anyone help me ??? pleassee on both of em
Answers
Answer:
28. B
29. D
30. A
Step-by-step explanation:
28.
2 5/8 yd × 5/6 yd =
= 21/8 × 5/6 yd²
= 105/48 yd²
= 35/16 yd²
= 2 3/16 yd²
Answer: B
29.
2641 becomes 6241.
In 6241, the 6 is in the thousands place.
6 × 1000 = 6000
Answer: D
30.
90 + 7 × (7 - 1) =
Use the correct order of operations.
= 90 + 7 × 6
= 90 + 42
= 132
Answer: A
The average snail can move 1.81 X 10³ mi in 5 hours. What is its rate of speed in miles per hour?
Answers
Answer:
Step-by-step explanation:
How Far Can A Snail Travel In One Hour
If a snail can travel over half an inch per minute, that means in one hour a snail can travel up to 40 inches. If you want to think about how far this is in feet, it means that snails move up to 3.5 feet per hour.
Consider the fact that the average human being can walk about a mile, or 5280 feet, in one hour.
This means that snails can take up to 1,500 days, or over 4 years, to travel just one mile.
Find the volume of the parallelepiped with the given vertices:(1,2,1), (2,3,4), (3,4,5), (2,3,2), (3,3,3), (4,4,6), (4,4,4), (5,5,7)
Answers
Answer:
0
Step-by-step explanation:
three vectors are
\(u=(2,3,4)-(1,2,1)=(1,1,3)\)
\(v=(3,4,5)-(1,2,1)=(2,2,4)\)
\(w=(2,3,2)-(1,2,1)=(1,1,1)\)
volume is given by \(V=u \cdot(v \times w)\) \(v \times w=\left|\begin{array}{ccc}i & j & k \\ 2 & 2 & 4 \\ 1 & 1 & 1\end{array}\right|=(-2,2,0)\)
so volume is \(V=(1,1,3) \cdot(-2,2,0)=0\)
2
three vectors are \(u=(4,4,6)-(3,3,3)=(1,1,3)\)
\(v=(4,4,4)-(3,3,3)=(1,1,1)\)
\(w=(5,5,7)-(3,3,3)=(2,2,4)\)
volume is given by \(V=u \cdot(v \times w)\) \(v \times w=\left|\begin{array}{ccc}i & j & k \\ 1 & 1 & 1 \\ 2 & 2 & 4\end{array}\right|=(2,-2,0)\)
so volume is \(V=(1,1,3) \cdot(-2,2,0)=0\)
how can you use pythagora's theorem to solve problems involving right-angled triangles
Answers
Using Pythagorean theorem, the length of the ladder is 10ft
What is Pythagorean Theorem?In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:
x² = y² + z²
In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.
To calculate the length of the ladder, we can write the formula as;
x² = 8² + 6²
x² = 64 + 36
x² = 100
x = √100
x = 10
The length of the ladder is 10 feet
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-1000 2/3 is not real fraction. True or false
Answers
True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.
In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.
To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.
It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.
In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
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S. Determine which is the best buy. Show calculations and explain your answer Ed's Bagels 4 for $.89 Best Bagels Only $1.39 for 6
Answers
Answer:
eds bageles are $.22 per bagel and best bagels are $.23 per bagel.
Step-by-step explanation:
Explain your answer to the question in the picture with steps please, thank you.
Answers
Part (a)
Answer: Constant of proportionality = 5/8
Reason:
The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.
The direct proportion line must pass through the origin. In other words, the y intercept must be zero.
=====================================
Part (b)
Answer: Not Proportional
Reason:
The y intercept isn't zero.
Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.
An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 80% of people used the shredder were satisfied with it. Because of the high acceptance rate, the company decided to make the new shredder. Assume that 80% of all people who use it will be satisfied. On a certain day 7 customers bought the shredder.
Let x denote the number of customers in this sample of 7 who will be satisfied with this shredder. Using the binomial probabilities table, obtain the probability distribution of x and fill in the table
x 0 1 2 3 4 5 6 7
p(x)(for each number)
Answers
Answer:
Probability distribution of x
Step-by-step explanation:
Binomial Probability = N c x . (P)^x . (Q)^ n-x
N = Total trials, 7 customers here ; P = Prob of success, 0.80 satisfied here ; x = No. of success (1....7) ; Q = Prob of fail, 0.20 not satisfied here
P (x = 1) = 7c1 (0.80)^1 (0.20)^7 = 0.00035
P (x = 2) = 7c2 (0.80)^2 (0.20)^6 = 0.0043
P (x = 3) = 7c3 (0.80)^3 (0.20)^5 = 0.0286
P (x = 4) = 7c4 (0.80)^4 (0.20)^4 = 0.1146
P (x = 5) = 7c5 (0.80)^5 (0.20)^3 = 0.2752
P (x = 6) = 7c6 (0.80)^6 (0.20)^2 = 0.3670
P (x = 7) = 7c7 (0.80)^7 (0.20)^1 = 0.2097
-8-8-6-2 4 12 22
What is the nth term rule of the quadratic sequence
Answers
Answer:
\(n^2 -3n - 6\)
Step-by-step explanation:
Looking at the image attached, you must first work out the difference between each term. This is +0, +2, +4, +6, +8, +10 (shown in orange).
Because you now have a linear sequence, the difference is now the same each time. This is +2 (shown in blue).
Because the original sequence is a quadratic, you have to halve the second difference (the +2). This means that the value of \(n^2\) is 1, so 1\(n^2\) or just \(n^2\) .
If you write out the values of \(n^2\), you can work out how much more you need to add or take away. For example, take the first three terms in the sequence.
n = 1, 2, 3
x = -8, -8, -6
\(n^2\) = 1, 4, 9
Work out the difference between \(n^2\) and x:
1 - -8 = 9
4 - -8 = 12
9 - -6 = 15
This gives you yet another linear sequence, 9, 12, 15.
Working out the formula for this, the difference is 3 each time, so it is 3n. The first value of n is 1, so 3n is 1. The difference is 6, so the formula for this linear sequence is 3n + 6.
Because \(n^2\) is greater than x, you need to take 3n + 6 away from \(n^2\).
This gives \(n^2\) - (3n+6), so the final answer is:
\(n^2\) - 3n - 6.
Marla Opper currently earns $105,000 a year and is offered a job in another city for $122,000. The city she would move to has 11
percent higher living expenses than her current city.
(a) What minimum salary should Marla require before accepting the new position?
Minimum salary required
(b) Should Marla accept the new job?
•Yes
•No
Answers
Answer:
determine the area of the square ABCD with AB=5cm and BC=3cm
expressions.
1) What is the product of the two polynomials?
A) -3x2 - 22x - 24
B) 3x2 - 22x - 24
-3x2 - 14x - 24
D) -3x2 - 22x + 2
Answers
Answer:
A) -3x2 - 22x - 24
Step-by-step explanation:
A random number generator is used to model the patterns of animals in the wild. This type of study is called
a survey.
a random sample.
an experiment.
a simulation.
Answers
Answer:
The answer is simulation
Step-by-step explanation:
A random number generator is used to model the patterns of animals in the wild. This type of study is called a simulation.
Simulation is a way to model random events, such that simulated outcomes closely match real-world outcomes. The way of simulating something first needs that a model be advanced, the model shows the key characteristics and functions of the opted process. By observing simulated outcomes, researchers gain insight on the real world.
A random number generator is used to model the patterns of animals in the wild. This type of study is called a simulation.
Simulation is a technique used to study complex systems by modeling them using a computer.
In this case, a random number generator is used to model the patterns of animals in the wild.
By running simulations, researchers can study the behavior of animals in different environments and conditions, without actually observing them in the wild.
Simulations are useful tools for predicting and understanding the behavior of complex systems, such as ecosystems.
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Identify the algebraic rule that would translate a figure 3 units left and 2 units up.
Answers
The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). Option B.
To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.
When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.
Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.
Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.
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qustion to give kagimatoby a brainly
Answers
Answer:
wdym
Step-by-step explanation:
refer to the image pls!! Will give brainliest
Answers
Step-by-step explanation:
hmmm, it is all there, you only need to write it up.
so, please, let me know what you don't understand about such equations and variables.
(a)
2x + 5y = 45
8x + 3y = 44
(b)
to solve this we try to use either one equation to express one variable by the other. and solve for that remaining variable (and then drive the second one from that), or to combine both equations directly to eliminate one variable and solve.
I think the second option is best here.
so, we multiply the 1st equation by -4, and then we add both equations :
-8x - 20y = -180
8x + 3y = 44
-------------------------
0 - 17y = -136
-17y = -136
17y = 136
y = 8
2x + 5y = 45
2x + 5×8 = 45
2x + 40 = 45
2x = 5
x = 2.5
to rent a chair costs $2.50.
to rent a table costs $8.00.
solve: 2.40X=40 to find out how many cookies that cost $2.40 each can be bought with $40.
Answers
Answer:
2.40x= 40
Step-by-step explanation:
Jon's teacher wants to buy giant cookies for the entire class
cookies cost $2.40 each
Let x be the number of cookies bought
Each cookies cost is 2.40
x cookies cost is 2.40x
total amount is $40
So the equation is 40x=40
What is the congruence correspondence, if any, that will prove the given triangles congruent ?
Answers
Answer:
none.
Step-by-step explanation:
because FTP=ATJ,
P=A
J=F
The two triangles are not congruent. The correct answer is option A.
What is congruency?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In the image two triangles, ETP and ATJ are given. Angle F and angle J are equal due to the opposite angle property. Similarly, angle P and angle A are also equal by alternate angle property. But all the angles are not congruent.
Hence, the triangle FTP and ATJ are not congruent with each other.
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A wire 20 feet long is to be cut into two pieces. One piece will be shaped as a square and the other piece
will be shaped as an equilateral triangle. Express the total area A enclosed by the pieces of wire as a
function of the length x of a side of the equilateral triangle. What is the domain of A?
Answers
To answer this question we just need to calculate areas of the equilateral triangle and the area of the square:
Solution is:
At = (√3/4)×x² + ( 20 - 3×x )²/ 16 square units
for 0 ≤ x ≤ 6.66 and 18.87 ≤ A ≤ 25
In the equilateral triangle, all the interior angles are 60°.
The bisectrix of one of these angles divided one 60°angle into two 30° angles, and the opposite side in half, and two isosceles triangles are formed.
The area of the original equilateral triangle of side x will become the sum of the areas of the two isosceles triangles with common side ( and height) h = ( √3 /2)×x
cos 30° = √3 / 2 ⇒ h = (√3 / 2) ×x
Then as Aet = 2 × (1/2)×(x/2)× (√3 / 2) ×x
Aet = (√3/4)×x² square units
To obtain the area of the square we know that a square of side L will have an area of L², so we only need to find out what is the side of the square.
The length of the wire is 20 f.
we cut off to get the equilateral triangle 3×x then we got left
20 - 3×x so the perimeter of the square is
p = 20 - 3×x
In the case of square p = 4×L then L = p/4
L = ( 20 -3×x)/4
As= [ ( 20- 3×x)/4]² ⇒ As = ( 20 - 3×x )²/ 16 square units
Finally total area
At = (√3/4)×x² + ( 20 - 3×x )²/ 16 square units
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When 6 times a number is increased by 11 the result is 16 less than 9 times the number. Find the number.
Answers
Answer:
Brainly.in
Question
When 6 times a number is increased by 11 the result is 16 less than 9 times the number. Find the number.
Answer · 7 votes
Answer:6x+11=9x-163x=27X=9 Please mark it brainliest
Step-by-step explanation:
Please mark it brainliest
On the local swim Team, 6 members each swam 1,685 meters during the season. How many total kilometers did the 6 members swim during the season?
10.08 km
10 11 km
100 8 km
101 1 km
Answers
Answer:
let's go with 100 8 km
Step-by-step explanation:
because it's the highest number
The number of kilometers that the 6 members swim during the season will be 10.11 kilometers. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
On the local swim Team, 6 members each swam 1,685 meters during the season. Then the number of meters that they swam is given as,
⇒ 1,685 x 6
⇒ 10,110 meters
⇒ 10,110 / 1,000
⇒ 10.11 kilometers
The number of kilometers that the 6 members swim during the season will be 10.11 kilometers. Then the correct option is B.
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Which ordered pair maximizes the objective function p=3x+8y
(0,0)
(2,7)
(5,6)
(8,1)
Answers
Answer:
P(5,6) = 63
Step-by-step explanation:
Test each point to see which ordered pair maximizes the objective function:
(0,0): p = 3(0) + 8(0) = 0
(2,7): p = 3(2) + 8(7) = 6 + 56 = 62
(5,6): p = 3(5) + 8(6) = 15 + 48 = 63
(8,1): p = 3(8) + 8(1) = 24 + 8 = 32
Hence, (5,6) is the ordered pair that maximizes the objective function.
Wilbert needs a student loan to finish school. He needs $4200 and has two options.
Option A: 4 years at 4.5% interest with monthly payments of $95.77
Option B: 3 years at 4.7% interest with monthly payments of $125.31
Which loan should Wilbert choose and how much will Wilbert save with that loan?
First, calculate the total payback on each loan.
Answers
Answer:
A) 4596.96
B) 4511.16
Step-by-step explanation:
Wilbert should choose option B. The savings will be $85.8 for the loan.
What is the loan amount?The sum you borrow to purchase the home is known as the amount borrowed. Because most lenders don't always offer 100% financing, it usually differs from the purchase price.
It's also crucial to take the loan-to-value ratio into account. Lenders frequently discuss this value, which compared the loan amount with the purchase price.
Checking for 4 years at 4.5% interest with monthly payments of $95.77
4596.96-4200=396.96
Checking for 3 years at 4.7% interest with monthly payments of $125.31
396.96-311.16=85.8
Therefore, Wilbert should choose option B. The savings will be $85.8 for the loan.
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NEED HELP NOW DUE TODAY
Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)
Part B: Explain how you know the equation from Part A is correct. (1 point)
Part C: Solve the equation from Part A. Show every step of your work. (2 points)
Answers
Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5
Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).
Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.
What is equation?It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.
Part A:
The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.
Part B:
The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).
This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.
Part C:
Solving the equation from Part A:
x + 0.7 = 4.5
Subtract 0.7 from both sides:
x + 0.7 - 0.7 = 4.5 - 0.7
x = 3.8
Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.
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8^3-9×2÷3 I Need Help
Answers
Answer:
506
Step-by-step explanation:
Following PEMDAS you'd start with your exponent
8^3-9×2÷3
Then you'd move on to multiplication
512-9×2÷3
Then do the division
512-18÷3
Then finish the problem by subtracting these two
512-6
Answer:
506
Step-by-step explanation:
just follow PEMDAS
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
- For each expression, select all equivalent expressions from the list. (a) x+x+x 3+x 3x Ox+3 2x-X (b) 48y-40 8( 6-5) O 24y -20 D8y 8.6y-8:5
Answers
1) In this problem, we're looking for equivalent expressions. So we can write out the following:
\(a)x+x+x=3x\)Note that if we add them up, or multiply by three we'll get the same.
2) Now, for part B. We need to find the GCD between 48 and 40
Note that in this way of finding GCD we stop whenever we can divide both numbers simultaneously.
3) Therefore, we can write out the following equivalent expression by dividing 48 and 40 by 8 and placing inside the parenthesis the terms:
\(\begin{gathered} b)48y-40=8(6y-5)=8\cdot6y-8\cdot5 \\ \end{gathered}\)Note that there are two equivalent expressions
a Find the total surface area of a cuboid with dimensions 4cm × 3cm × 2cm.
B)If the length of the cube, 4cm, is doubled, what is the new surface area of the cuboid?
Answers
Answer:
24 millimeters B) Area of one side= 4*4
=16
Total number of faces= 6
Then total area= area of one side* number of sides
=16*6
=96 square cm
Step-by-step explanation:
What is the equation of a line that is parallel to 2x + 3y = 3 and passes through the point (3, -4)?
Enter your answer as a slope intercept equation (y=mx+b) in the box.
Answers
Answer:
y = - \(\frac{2}{3}\) x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
given
2x + 3y = 3 ( subtract 2x from both sides )
3y = - 2x + 3 ( divide through by 3 )
y = - \(\frac{2}{3}\) x + 1 ← in slope- intercept form
with slope m = - \(\frac{2}{3}\)
• Parallel lines have equal slopes , then
y = - \(\frac{2}{3}\) x + b ← is the partial equation
to find b substitute (3, - 4 ) into the partial equation
- 4 = - 2 + b ⇒ b = - 4 + 2 = - 2
y = - \(\frac{2}{3}\) x - 2 ← equation of parallel line