3(bc - ac - ab)/(a²-ab+bc-ac) is the simplified form of the given equation.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given an expression:
(a²-4ac+3bc)/(a²-ab+bc-ac) + (a+3b)/(b-a) + (a+2c)/(a-c)
Simplifying Using PEMDAS starts from the right:
(a²-4ac+3bc)/(a²-ab+bc-ac) + [tex]\frac{a^{2} + 3ab - ac - 3bc }{-a^{2} + ab -bc +ac }[/tex]
Taking negative common from the last term
(a²-4ac+3bc)/(a²-ab+bc-ac) - (a² + 3ab - ac -3bc)/(a²-ab+bc-ac)
Since the base is the same,
(-4ac + 3bc - 3ab +ac +3bc)/(a²-ab+bc-ac)
3(bc - ac - ab)/(a²-ab+bc-ac)
therefore, the simplified form of the given equation is 3(bc - ac - ab)/(a²-ab+bc-ac).
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The solution involves evaluating a complex algebraic expression step by step after substituting given values for variables.
Given the expression, (a2-4ac+3bc)/(a2-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c), substitute a = 1, b = 0.0211, and c = -0.0211 to simplify.
After substitution, perform the necessary calculations to evaluate the expression step by step.
solve the inequality -8x-10>7x+20
Answer:
-2 > x
Step-by-step explanation:
-8x-10>7x+20
Add 8x to each side
-8x+8x-10>7x+8x+20
-10 > 15x+20
Subtract 20 from each side
-10 -20 > 15x+20-20
-30 > 15x
Divide by 15
-30/15 > 15x/15
-2 > x
As the figure shows Elton runs 500 m to point b first then he turns 100 degrees and runs another 350 m to point c how far is the distance from point a to c
Answer:
658.24 m
Step-by-step explanation:
Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:
[tex]AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^{\circ},\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.[/tex]
Answer:
658.24 m
Step-by-step explanation:
The figure makes a triangle with vertices abc.
Where ab = 500 m
bc = 350 m
The angle abc = 100°
Using the cosine rule we can find the distance ac.
ac² = 500²+350² - 2×500×350×cos100°
= 372,500 - -60,776.86
= 433,276.86
ac = √433,276.86
= 658.24 m
Let x △ y be defined by x △ y=x−5y. What is the value of 3 △ (−4)
[tex]x\Delta y=x-5y\\\\3\Delta(-4)\qquad\text{put the values x = 3 and y = -4 to the expression x - 5y}:\\\\3\Delta(-4)=3-5(-4)=3+20=23[/tex]
What is the largest fraction 3/4 7/8 8/10 7/9?
Answer:
7/8 ths
Step-by-step explanation:
3 divided by 4 is .75
* 7 divided by 8 is .875
8 divided by 10 is .80
7 divided by 9 is .77
If you divide the fractions you can compare the values and the highest value is your largest fraction.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator. The fraction 7/9 has the largest fraction.
Given information-
The set of the fraction given in the problem is,
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
What is the order of fraction?The order of the fraction is arranging the fraction number from the smallest to the largest number.
The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator.
To compare the fraction, make the denominator with same.
[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]
To make the denominator same find out the least common factor of denominators which are 4,8,10 and 9 which is 360.
Multiply and divide with 360 in the given fractions to bring the 360 in denominator,
[tex]\dfrac{3\times360}{4\times360}, \dfrac{7\times360}{8\times360}, \dfrac{8\times360}{10\times360}, \dfrac{7\times360}{9\times360}[/tex]
[tex]\dfrac{270}{360}, \dfrac{315}{360}, \dfrac{288}{360}, \dfrac{315}{360}[/tex]
As the numerator 315 is the highest among all. Hence the fraction 7/9 has the largest fraction.
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A worker climbed up a ladder to get on the roof of a building to make some repairs, and was placed 9 feet away from the base of the building. Which is closest to the height of the building ?
Answer:
Step-by-step explanation:
you dont have enough information to solve the problem, you need to know the length of the ladder in order to find the closet length of the building.
Is this a true proportion ? 3/4,8/12
Question
Is this a true proportion ? 3/4,8/12
Answer:
FalseStep-by-step explanation:
3/4 = 8/12
semplify
3/4 = 2/3
or you can solve in this way
3/4 = 8/12
0.75 = 0.66≈
The lowest temperature ever recorded is -89c. The highest temperature is 56.7c. What is the difference between the highest and the lowest recorded temperature
Answer:
The difference is 145.7
Step-by-step explanation:
89+56.7= 145.7
Answer:
-32.3
Step-by-step explanation:
I got -32.3 because when I subtracted -89 from 56.7 I got -32.3. If you don't know how to subtract integers it's simple, you just subtract 89 from 56.7 then choose the sign that has the greater absolute value. In this case -89 has the greater absolute value, so you take the negative sign.
what is the sum of 121/4+5 5/6 reduced to lowest terms thanks
Answer:18 1/12
Step-by-step explanation:i first added the whole numbers 12 and 5 to get 17; i then addled 1/4 and 5/6; i did this by finding a common denominator of both fractions and converted them into 6/24 and 20/24; i added them to get 26/24 which simplifies to 1 and 2/24, which equals 1 1/12; i added 1 to 17 and got 18, then added 1/12 to get 18 1/12
The sum of 121/4 and 5 5/6 is found by converting the mixed number to an improper fraction, finding a common denominator, adding the fractions, and simplifying if possible. The final answer is 433/12, which is already in its lowest terms.
The question asks for the sum of the numbers 121/4 and 5 5/6 reduced to the lowest terms. To answer this, we must first convert the mixed number to an improper fraction and then add it to the other fraction. Here's how to do it step by step:
Convert 5 5/6 to an improper fraction: 35/6.
Add 121/4 to 35/6. To do this, find a common denominator, which would be 12 in this case.
Convert both fractions to have the common denominator: 121/4 becomes 363/12, and 35/6 becomes 70/12.
Add the two fractions: 363/12 + 70/12 equals 433/12.
Reduce the fraction if possible. In this case, 433/12 is already in its lowest terms.
Therefore, the sum of 121/4 and 5 5/6 reduced to lowest terms is 433/12.
2x+y=3 passes from origin. is this statement true or false
Answer:
the answer is false.
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
2x+y=3
⇒ This equation can be written in the form of y = mx + c where m is the slope, c is the y-intercept and x and y are x and y coordinates respectively of the point where the the line passes.
2x+y=3
y = -2x + 3.
If the line passes through the origin (0,0), then c = 0. This is not the case in our eqation.
Again if the question passes through the origin, by substituting the point (0,0) in the question it would satify it.
2x+y=3 ⇒ 2(0) + 0 = 3
0 + 0 ≠ 3
0 ≠ 3
The statement is false.
These dot plox show the lenghs (in feet) from a sample of crocodiles and allogators
Answer:
C and D
Step-by-step explanation:
The Middles were the same length and the side of the alligator are slightly longer.
The correct options are:
C. Center-- The crocodiles have a greater median length than the alligators.
D. Spreads-- The lengths of the alligators are more spread out.
Step-by-step explanation:Median of the data--
The median is the central tendency of the data and it always exist in the middle of the data.
By looking at the data.
We observe that the Median of the data :
Crocodile lie at : 17
and that of the alligator lie at : 9
Hence, the median for the crocodile is more than for the alligators.
Spread--
The spread in the data means how far the data points are from the center of the data i.e. mean or median.
By looking at the data crocodile we observe that all the data points are close to the median.
whereas in the data alligator one of the data point is far from the median.
Hence, the spread in case of alligator is more as compared to that of crocodiles.
The five fifth grade teachers ans six fourth grade teachers ordered 2 large pizzas all together. Each pizza costs $13.75. If they are going to spilt the cost evenly, how much will each person need to pay?
Answer:
80 Cents
Step-by-step explanation:
Answer: Each person will need to pay $1.25
Step-by-step explanation: $13.75 divided by the 11 people = $2.25
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Your grandfather has been collecting marbles all his life. He owns an old chest that measures 5 feet by 4 feet by 3 feet high. Each of the marbles I collected, measures 1 inch in diameter. I have finally filled the chest to the top. A pproximately how many marbles are in the chest?
Answer:
Number of marbles are 200000
Step-by-step explanation:
Rectangular box:
length = 5 feet
width =4 feet
height =3 feet
now, we can find volume of box
[tex]V=L\times W\times H[/tex]
[tex]V=5\times 4\times 3[/tex]
[tex]V=60ft^3[/tex]
Volume of marbles:
We know that shape of marbles will be in sphere
we are given
diameter =1 inch
radius =0.5 inch
[tex]r=\frac{0.5}{12} ft[/tex]
now, we can find volume
[tex]V=\frac{4}{3}\pi r^3[/tex]
we can plug value
[tex]V=\frac{4}{3}\pi (\frac{0.5}{12})^3[/tex]
[tex]V=0.00030[/tex]
now, we can find number of marbles
Number of marbles = ( volume of box)/( volume of marbles)
So, number of marbles are
[tex]=\frac{60}{0.00030}[/tex]
[tex]=200000[/tex]
A flower bed is in the shape of a triangle with a base of 15 feet and a hight of 9 feet what is the area of the flower bed
Answer:
area of a triangle is 1/2bh
1/2 X 15 x 9 = 67.5 square feet
Step-by-step explanation:
For this case we must find the area of a flower bed with a triangle shape.
The area of a triangle is given by:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b: It's the base
h: It's the height
Substituting the given values:
[tex]A = \frac {15 * 9} {2}\\A = 67.5\ ft ^ 2[/tex]
Answer:
[tex]A = 67.5\ ft ^ 2[/tex]
Is 15 breaths every 36 and 90 breaths every 3 minutes equivalent
Final answer:
The question compares two breathing rates: 15 breaths every 36 seconds and 90 breaths every 3 minutes. When converted to breaths per minute, the rates are 25 breaths/minute and 30 breaths/minute respectively, indicating that they are not equivalent.
Explanation:
The question asks whether 15 breaths every 36 seconds and 90 breaths every 3 minutes represent an equivalent rate of breathing. To solve this, we need to determine if the two rates are the same when converted to a common time unit.
First, let's convert 36 seconds to minutes: 36 seconds is 0.6 minutes (since 1 minute is 60 seconds). Next, we calculate the breathing rate per minute for the first scenario by dividing the number of breaths by the number of minutes: 15 breaths / 0.6 minutes = 25 breaths/minute.
Now let's look at the second rate of 90 breaths every 3 minutes. This can be simplified by dividing the number of breaths by the number of minutes: 90 breaths / 3 minutes = 30 breaths/minute. Clearly, 25 breaths/minute is not equivalent to 30 breaths/minute. Therefore, 15 breaths every 36 seconds and 90 breaths every 3 minutes are not equivalent rates of breathing.
. Sarah drove 77 miles on 3.6 gallons of gas. If her car holds 15 gallons of gas, which proportion would she use to find out how far she can drive her car on a full tank of gas? a. 3.6/15 = x/77 c. 3.6/77 = x/15 b. 77/x = 15/3.6 d. 77/3.6 = x/15
Final answer:
To find out how far Sarah can drive on a full tank of gas, the correct proportion is '77/3.6 = x/15'. This compares the known miles driven to gallons used, scaled up to a full tank of 15 gallons, representing the distance with 'x'. So the correct option is d.
Explanation:
The student is working on solving a proportion problem related to fuel consumption and driving distances. To find out how far Sarah can drive her car on a full tank of gas, we need to set up a proportion that compares miles driven to gallons used, and then scale it up to a full tank of gas.
Since Sarah drove 77 miles on 3.6 gallons of gas, we can compare this to a full tank of 15 gallons to find the total distance she can drive, represented by 'x'. The correct proportion is 77 miles to 3.6 gallons as 'x miles' is to 15 gallons.
The correct proportion is d. 77/3.6 = x/15, as it reflects the direct relationship between miles driven and gallons of fuel. When the gallons are increased from 3.6 to 15, we expect the miles that can be driven to increase proportionally.
can someone help me find x
Answer:
Step-by-step explanation:
2 equal 90° angles, we can use an equation
x + 15 = 90
x = 90 - 75
x = 15°
-------------------------
check
90 = 15 + 75
90 = 90
the answer is good
Solve, using the substitution method.
y = 2x + 6
3x – y = 6
There are an infinite number of solutions.
(12, 30)
(14, 12)
There is no solution.
The solution to the system of equations is (12, 30).
Option B is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the system of equations using the substitution method,
We solve one equation for one of the variables and substitute the expression into the other equation.
Let's solve the first equation for y:
y = 2x + 6
Now, substitute y = 2x + 6 into the second equation and solve for x:
3x - y = 6
3x - (2x + 6) = 6
3x - 2x - 6 = 6
x = 12
Now that we have found x, we can substitute it back into either of the original equations to find y.
Let's use the first equation:
y = 2x + 6
y = 2(12) + 6
y = 30
Therefore,
The solution to the system of equations is (12, 30).
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Alexandria wants to go hiking on Saturday. She will choose from several parks considering these conditions:
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away from home.
• She can average 65 miles per hour to and from the park.
Choose and solve the inequality that represents the possible distances from Alexandria’s home to a park that satisfies the conditions above.
Answer:
The correct answer for this problem is 200 miles.
I REALLY NEED THIS SOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOPER BADLY
Write this number to two significant figures in scientific notation. Use the "^" character to indicate the exponent. 8,421,032.9266
Answer:
8.4 * 10^6
Step-by-step explanation:
8.4 * 10^6
1 million = 1 * 10^6
8 million 4 hundred thousand is 8.4 * 10^4 because this number is 8.4 times bigger than a million.
A basket is filled with 7 white eggs and 14 brown eggs. Half of the brown eggs are cracked.
An egg is randomly selected from the basket. What is the probability that it is a cracked, brown egg?
Write your answer as a fraction.
What is the value of (-3+3i)+(-2+3i)?
Answer:
The value is of given expression is -5+6i.
Step-by-step explanation:
The given expression is
[tex](-3+3i)+(-2+3i)[/tex]
It can be written as
[tex]-3+3i-2+3i[/tex]
Now combine like terms.
[tex](-3-2)+(3i+3i)[/tex]
[tex](-3-2)+(3+3)i[/tex]
Simplify each parenthesis.
[tex](-5)+(6i)[/tex]
[tex]-5+6i[/tex]
Therefore the value is of given expression is -5+6i.
University Theater sold 465 tickets for a play. Tickets cost $23 per adult and $13 per senior citizen. If total receipts were $7145, how many senior citizen tickets were sold?
Answer:
355 senior citizen tickets were sold.
Step-by-step explanation:
Assuming a to the the ticket of adults and s to be the ticket of senior citizens, we can write two equations as:
[tex]a +s=465[/tex] --- (1)
[tex]23a+13s=7145[/tex] --- (2)
From equation 1, [tex]a=465-s[/tex].
Substitute [tex]a[/tex] in equation 2 to get:
[tex]23 (465-s) + 13s = 7145[/tex]
[tex]10695 - 23s +13s =7145[/tex]
[tex]-10s = -3550[/tex]
[tex]s = 355[/tex]
Therefore, there were 355 senior citizen tickets sold.
whats is the ratio of 3 dogs to 4 cats
Answer:
3 to 4
or
3:4
Step-by-step explanation:
Joy wants to buy strawberries and raspberries to bring to a party strawberries cost $1.60 per pound and raspberries cost $1 .75 per pound. if she only has $10 to spend on berries which equality represents the situation where she buys x pounds of strawberries and y pounds of raspberries ?
Answer: 1.60x + 1.75y is less than or equal to 10
Step-by-step explanation:
Since the strawberries cost $1.60 per pound, it would be x pounds times $1.60 for the total cost of strawberries. Since the raspberries cost $1.75 per pound, it would be y pounds times $1.75 for the total cost of the raspberries. The total cost of both, or 1.60x + 1.75y, must be equal to or less than 10 because she cannot spend over 10 dollars.
The situation can be represented by the equation 1.60x + 1.75y = 10, where x represents the pounds of strawberries and y represents the pounds of raspberries. To find out how many pounds of strawberries and raspberries Joy can buy, we can rearrange the equation and solve for x and y.
Explanation:The situation can be represented by the equation 1.60x + 1.75y = 10, where x represents the pounds of strawberries and y represents the pounds of raspberries. To find out how many pounds of strawberries Joy can buy, we can rearrange the equation to solve for x: x = (10 - 1.75y) / 1.60. Similarly, to find out how many pounds of raspberries Joy can buy, we can rearrange the equation to solve for y: y = (10 - 1.60x) / 1.75.
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If f(x) = x2 -1, what is the equation for f–1(x)?
Answer:
[tex]f^{-1}=+-\sqrt{x+1}[/tex]
Step-by-step explanation:
f(x) = x^2 -1
We need to find f^-1(x)
WE find inverse of f(x)
Replace f(x) with y
[tex]y= x^2 -1[/tex]
Replace x with y and y with x
[tex]x= y^2 -1[/tex]
Solve for y
add 1 on both sides , [tex]x+1= y^2[/tex]
To remove square , take square root on both sides
[tex]\sqrt{x+1} =\sqrt{y^2}[/tex]
[tex]\sqrt{x+1} =y[/tex]
[tex]y=+-\sqrt{x+1}[/tex]
Replace y with f^-1
[tex]f^{-1}=+-\sqrt{x+1}[/tex]
Answer:
Inverse function is
[tex]f^{-1}(x)=\pm \sqrt{x+1}[/tex]
Step-by-step explanation:
Given that [tex]f(x)=x^2-1[/tex]
Now using that equation of f(x), we need to find equation of the inverse function
[tex]f(x)=x^2-1[/tex]
[tex]f^{-1}(x)[/tex]
Step 1: Replace [tex]f^{-1}(x)[/tex] with y
[tex]y=x^2-1[/tex]
Step 2: Switchx and y
[tex]x=y^2-1[/tex]
Step 3: Solve for y
[tex]x=y^2-1[/tex]
[tex]x+1=y^2-1+1[/tex]
[tex]x+1=y^2[/tex]
[tex]y^2=x+1[/tex]
take square root of both sides
[tex]y=\pm \sqrt{x+1}[/tex]
Hence inverse function is
[tex]f^{-1}(x)=\pm \sqrt{x+1}[/tex]
A line with a slope of 4 passes through the point 2,1 what is the equation y=mx+b
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = 4 and the point (2, 1). Substitute:
[tex]y-1=4(x-2)[/tex] use distributive property
[tex]y-1=(4)(x)+(4)(-2)[/tex]
[tex]y-1=4x-8[/tex] add 1 to both sides
[tex]\boxed{y=4x-7}[/tex]
What is the definition of a parallelogram? What are the properties?
Answer:
A parallelogram is a quadrilateral whose opposite sides are parallel.
It's properties include:
- The opposite sides of a parallelogram are parallel.
- A diagonal of a parallelogram divides it into two congruent triangles.
- The opposite sides of a parallelogram are congruent.
- The opposite angles of a parallelogram are congruent.
- The consecutive angles of a parallelogram are supplementary.
- The diagonals of a parallelogram bisect each other.
a quadrilateral whose both pair of opposite side are equal and parallel to each other is called a parallelogram
PROPERTIES OF PARALLELOGRAM opposite sides are equal and parallel opposite angles are equal adjacent angle are supplementary diagonal of a parallelogram bisect each other[tex]AREA OF PARALLELOGRAM => BASE X HEIGHT = BXH [/tex]
any side of parallelogram can be chosen as the base of parallelogram the perpendicular dropped on that side from opposite vertex is known as height attitude
What are the solutions of 8x^2=6+22x? Check all of the boxes that apply.
Answer:
What points do I check?
Step-by-step explanation:
Answer:
x= -1/4
x= 3
Step-by-step explanation:
do diagonals of a rhombus bisect the vertex angles???
Answer:
Yes, one of a rhombus's properties is that the diagonals bisect vertex angles.
The diagonals of a rhombus bisect the vertex angles.
Explanation:Yes, the diagonals of a rhombus bisect the vertex angles.
To understand this, we can consider that in a rhombus, the diagonals are perpendicular to each other, and when a diagonal bisects an angle, it creates two congruent triangles.
Therefore, the diagonals of a rhombus do indeed bisect the vertex angles.
Write the equation of the line with a slope of 17 and passing through the point (0,0)
Answer: y = 17x
Step-by-step explanation:
Note that the equation that will be used is: y = mx + b,in which m = slope and b = y-intercept.
Solve for b:
0 = 17(0) + b
Simplify:
0 = 0 + b
b = 0
Equation: y = 17(x)
~
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineABOUT PROBLEM:
Since the slope is 17, it represents m in Poin Slope Form0 represents Y10 represents X1y - Y1 = m (x - X1)
y - 0 = 17 (x - 0) --- IN POINT SLOPE FORM
Hope this helps you!!! :)