To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.
1. Identify the two numbers you want to compare as the numerator and denominator
2. Divide the numerator by the denominator
3. The resulting answer is the ratio of the two numbers
To find a ratio in 8th grade math, divide the numerator by the denominator to get the ratio.
To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.
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what is the price per pound for chicken and the price per pound of the fish the food stand purchased?
One pound of chicken will cost ${x/y} and one pound of fish will cost ${B/A}.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the price per pound for chicken and the price per pound of the fish.
Assume that the {y} pound of chicken costs ${x}. Now, we can write that -{y} pound of chicken costs ${x}
{1} pound of chicken will cost ${x/y}
Assume that the {A} pound of fish costs ${B}. Now, we can write -{A} pound of fish costs ${B}
{1} pound of fish will cost ${B/A}
Therefore, {1} pound of chicken will cost ${x/y} and {1} pound of fish will cost ${B/A}.
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as one step in the statistical analysis of the effectiveness of the chw intervention, researchers examined differences in postnatal care use for mothers in 10 different regions. how could the researchers have increased the power of their analysis?
The researchers have increased the power of their analysis by increasing the sample size.
The number of subjects involved in a sample size is referred to as the sample size in market research.
Examine 15 randomly selected groups of subjects.
There are five main ways to increase the power of an experiment or study: increase the alpha level, decrease random error, conduct a one-tailed test, expand the sample size, or increase the effect size. Of these, only the first option, which increases the sample size, will increase power.
Thus, the researchers have increased the power of their analysis by increasing the sample size.
Complete question: As one step in the statistical analysis of the effectiveness of CHW intervention, researchers calculated the average percentage of postnatal care use found in 10 randomly selected groups of 50 mothers. How could the researchers have increased the power of their analysis?
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How many right triangles have integer leg lengths a and b and a hypotenuse of length b 1, where b < 100
The possible number of the right triangle is 6. Hence option A is the correct option.
What is the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Given that △ABC is a right triangle.
The legs of the △ABC are a and b which are integers. The hypotenuse is b+1. Since b is an integer thus b+1 is an integer.
Pythagorean theorem:
The sum of the square of the legs of a right triangle is the square of the hypotenuse.
According to Pythagorean theorem,
a² + b² = (b+1)²
Applying the algebraic formula (a+b)² = a² + b² + 2ab
a² + b² = b² + 2b +1
Cancel out b² from both sides:
a² = 2b + 1
2b is always a positive number since 2 is multiplied with b. Thus 2b+1 is an odd number.
Since a² = 2b + 1, thus a² is an odd number.
The square of an odd number is an odd number. Thus a is an odd number.
Again given that,
b<100
2b < 200
2b + 1< 201
Putting 2b + 1 = a²:
a² < 201
Now putting a=1 in a² < 201:
1² < 201 (true)
Now putting a=3 in a² < 201:
3² < 201 (true)
Now putting a=5 in a² < 201:
5² < 201 (true)
Now putting a=7 in a² < 201:
7² < 201 (true)
Now putting a=9 in a² < 201:
9² < 201 (true)
Now putting a=11 in a² < 201:
11² < 201 (true)
Now putting a=13 in a² < 201:
13² < 201 (true)
Now putting a=15 in a² < 201:
15² < 201 (false)
If a = 1, 2b+1 = 1 which implies b = 0. The length of a side of a triangle is never zero. Therefore a ≠ 1.
Thus the possible values of a are 3,5,7,9,11,13.
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Write all names that apply to each number
5.45
A straw is placed inside a rectangular box that is 10 inches by 3 inches by 5 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw
The length of the straw is equal to the length of the space diagonal of rectangular box, that is 11.6 inches.
The length of the straw is equal to the space diagonal of the rectangular box. Space diagonals are three-dimensional diagonals.
If the length of the sides of the box is a, b, and c, then the space diagonal can be computed by applying the Pythagorean Theorem.
D = √(a² + b² + c²)
Substitute the following dimensions:
a = 10 inches
b = 3 inches
c = 5 inches
Then,
D = √(10² + 3² + 5²)
D = √(100 + 9 + 25)
D = √134 = 11.6 inches
Hence, the length of the straw is 11.6 inches.
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what happens when a person has been dead for 2 minutes and comes back their experience of 2 minutues dead
When the person has been dead for 2 minutes and comes back their experience of 2 minutes dead then we call that the person is suffering from Lazarus Syndrome .
What is Lazarus Syndrome ?
The Lazarus syndrome is referred as to your blood circulation returning spontaneously after your heart stops beating and it fails to restart despite providing cardiopulmonary resuscitation (CPR).
In Simple words it can be called as returning to life after it appears that the person has died.
So, if the person comes back to life after experience of 2 minutes of dead , then we say that the person has Lazarus Syndrome and got a heart attack .
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what is 8y-5 is less than 3
Answer:
[tex]y < 1[/tex]
Step-by-step explanation:
[tex]8y - 5 < 3 \\ 8y < 8 \\ y < 1[/tex]
The price of an item has been reduced by 95%. The original price was $75.
Use the ALEKS calculator to find the price of the item now.
Suppose that a point (x, y) is chosen from the unit square S = [0,1]×[0,1] using the uniform probability law — the probability that (x, y) is in a subset A of S is equal to the area of A:
P ((x, y) ∈ A) = area(A) for all A ⊂ S.
(a)What is the probability that x + y <1/3 ?
(b)What is the probability that x + y <3/2 ?
(c)Find an algebraic expression F(u) for
F(u) = P (x + y ≤ u).
The probability that x + y <1/3 is 1/18, the probability that x + y < 3/2 is 0.875 and the algebraic expression for F(u) is: F(u) = 0, if u < 0; F(u) = 0.5u^2, if 0 <= u <= 1; F(u) = 1 - 0.5(2 - u)^2, if 1< u < 2; F(u) = 1, if u >= 2.
(a) The set of points (x,y) in the unit square S for which x+y < 1/3 is a triangle with vertices at (0,0), (1/3,0), and (0,1/3).
The area of this triangle is
0.5(1/3)^2 = 1/18
Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 1/9.
(b) The set of points (x,y) in the unit square S for which x+y < 3/2 is a polygon with vertices at (0, 0), (1, 0), (1, 0.5), (0.5, 1) and (0, 1) as S = [0,1]×[0,1] refer figure for clarity.
The area is
1*1 - 0.5*0.5²
= 1 - 0.125
= 0.875
Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 0.875
(c) To find an algebraic expression for F(u), we need to consider different cases for the value of u:
if u < 0, then the set of points (x,y) for which x+y <= u is empty, so F(u) = 0
if 0 <= u < 1, then the set of points (x,y) for which x+y <= u is a triangle with vertices at (0,0), (u,0), and (0,u). The area of this triangle is u^2, so
F(u) = 0.5u^2
if 1 <= u < 2, then the set of points (x,y) for which x+y <= u is a polygon with vertices at (0,0), (1,0) (1, u-1), (u-1, 1) and (0, 1). The area can be obtained by subtracting the area of triangle with vertices (1, u-1), (u-1, 1) and (1, 1), from area of square, that is 1 sq units.
F(u) = 1 - 0.5(2 - u)²
if u >= 1, then the set of points (x,y) for which x+y <= u is the entire unit square, so
F(u) = 1.
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at each handicap level, how does the percentage of women who think the greens are too fast compare to the percentage of men who feel the same?
According to the management at Oak Tree Golf Course received a few complaints about the condition of the greens. and with the Several players complained that the greens are emerged too fast. Rather than to react towards the comments of just a few, the Golf Association conducted in a survey of male and female golfers.
One of the biggest things in holding along with mid- and high-handicappers back is hitting more greens in regulation, mainly because of it’s the key (usually) to stress-free two-putt pars and to the occasional birdie. It’s also one of the best way to eliminate certain trouble. If mid- or high-handicappers are missing around the greens, that’s when problems can pile up into picture . But we all need certain goals. to Tina Tombs, a former LPGA pro and to a GOLF Top 100 Teacher, said a high-handicapper should set an certain goal at seven greens in regulation, while a lower handicap should be strive for 10 per round.
If they aren’t carrying any of the 200 yards, then they should play 6,000 or less then that and they don’t do that in terms of the Preisinger says. Because when you wanted to play too far back you can have four or five penalty shots off around the tee.
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Can someone solve this with units ?
In the graph the letter "J" has a height of 17 units.
What is a graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
According to the graph the distance from A to B is horizontal, so it need not be counted.
From B to C the distance is = 3 units
Again from C to O the distance is horizontal, so it need not be counted.
From O to D the distance is = 10 units
From D to E the distance is = 4 units
From E to F the distance is horizontal, so it need not be counted.
The distance from F to N need not be counted as it will be the repetition of the total height.
So, the total height is = 3 + 10 + 4 = 17 units
Therefore, the total height on the graph is 17 units.
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Three semicircles of radius 1 are constructed on diameter $\overline{AB}$ of a semicircle of radius 2. The centers of the small semicircles divide $\overline{AB}$ into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles
Therefore , the solution of the given problem of surface area comes out to be unused space is equal to 2π - (5π/6 + √3/2) m² .
Surface area definitionIts surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the face on each of the six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, & 2hw, the surface is exactly the same (SA). The region is represented by the surface area of the muti form.
Here,
Given:
AB = D = 4 m (R = 2 m)
The size of the AB semicircle is:
=> Area = πr²/2
=>A = 2π
The dimensions of the little semicircle are a=5/6 + 2/3/2 m2 and a=5/6 + 3/2 m2.
The remainder area is therefore equal to A- a.
= 2π - (5π/6 + √3/2) m²
The unused space is equal to 2π - (5π/6 + √3/2) m²
Therefore , the solution of the given problem of area comes out to be unused space is equal to 2π - (5π/6 + √3/2) m² .
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(1) tyler ate x fruit snacks, and han ate 3/4 less than that. write an expression for the number of fruit snacks han ate. (2) mai skated x miles, and clare skated 3/5 farther than that. write an expression for the distance clare skated
(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.
What is algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. It represents a value or a set of values, but it does not provide a specific numerical result until the variables are replaced with specific numbers.
(1) Let's say x is the number of fruit snacks Tyler ate.
Han ate 3/4 less than that, so the expression for the number of fruit snacks Han ate would be x - (3/4)x = x(1 - 3/4) = x/4.
(2) Let's say x is the number of miles Mai skated.
Clare skated 3/5 farther than that, so the expression for the distance Clare skated would be x + (3/5)x = x(1 + 3/5) = 8/5x.
(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.
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Which graph represents y=-2x
Answer:
The graph looks like the image below.
Step-by-step explanation:
-2x means that every time x increases by 1, y increases by -2.
When y increases by -2, y decreases by 2.
Hence, as the x-value increases by 1, the y-value decreases by 2.
Also, the graph goes through the point (0, 0) since when x=0, y=0:
y=-2x ==> 0 = -2(0)
Is it possible to construct a triangle when its sides are 5.4 cm 2.3 cm 3.1 cm?
No, it is not possible to construct the triangle with the given sides measurement of 5.4 cm, 2.3 cm, 3.1 cm .
As given in the question,
In the given triangle,
Measurement of the sides of the triangle are given by :
5.4 cm, 2.3 cm, 3.1 cm
To construct a triangle we need to follow the following property:
Sum of the measure of two sides of the triangle should be greater than the third side.
In the given measures:
( 2.3 + 3.1 ) cm = 5.4 cm which is equal to third side.
The property does not holds true.
Therefore, to construct a triangle with the given measure of the sides is not possible.
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Find the perimeter of the shape, round to the nearest tenth.
(Will give brainliest for the quickest answer :))
Answer: The perimeter of the shape is approximately 18.0 feet.
Step-by-step explanation:
The shape you described is a triangle, with one side of 8 feet and two sides of 5 feet. To find the perimeter of a triangle, we add up all the side lengths:
Perimeter = 8' + 5' + 5'
Perimeter = 8' + 10'
Perimeter = 18'
Rounding to the nearest tenth:
18 feet is the same as 18.0 feet rounded to the nearest tenth.
So, the perimeter of the shape is approximately 18.0 feet.
Who proved the fundamental theorem of algebra any polynomial has a complex root?
The fundamental theorem of algebra any polynomial was first proved by Carl Friedrich Gauss in 1799.
In 1799, Carl Friedrich Gauss was a German mathematician who proved that any polynomial equation with complex coefficients has at least one root in the complex plane. This is known today as the Fundamental Theorem of Algebra. Gauss started by examining a particular polynomial equation and then used his knowledge of the properties of polynomial functions to prove that any polynomial equation with complex coefficients must have at least one complex root. His proof used a combination of calculus and algebraic manipulations to establish that the coefficients of a polynomial equation must satisfy certain conditions in order for the equation to have a complex root. Once these conditions are satisfied, he showed that the equation must have at least one complex root.
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Car x travel 120 mile on 11 gallon of ga. Car y travel 100 mile on 9 gallon of ga which car get the better ga mileage
Car Y offers you more mileage than Car X per gallon.
The mileage of a vehicle is the number of miles that it can travel using one gallon or litre of fuel or gasoline.
To find the mileage per gallon, we find the distance that each car can travel using 1 gallon of gasoline.
For Car X,
Mileage = No. of miles/No. of gallons
= 120/11 = 10.909
For Car Y,
Mileage = No. of miles/No. of gallons
= 100/9 = 11. 11
Therefore, marginally, Car Y has the better mileage.
Thus, Car Y offers you more mileage than Car X per gallon.
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The variables A, B, and C represent polynomials where A = x + 1, B = x² + 2x − 1, and C = 2x. What is AB + C in
simplest form?
Ox³+3x-1
Ox³+4x-1
Ox³+3x² + 3x - 1
O x³ + 2x²-x+1
Answer:
C) [tex]x^{3} + 3x^{2} + 3x - 1[/tex]
Step-by-step explanation:
We have our equations. So, we will substitute them in our last equation, giving us:
[tex](x + 1) * (x^{2} + 2x - 1) + 2x[/tex]
Opening the parentheses gives us:
[tex]x^{3} + 2x^{2} - x + x^{2} + 2x - 1 + 2x[/tex]
Combining like terms:
[tex]x^{3} + 2x^{2} + x^{2} + 2x - x + 2x - 1[/tex]
Then, we combine:
[tex]x^{3} + 3x^{2} + 3x - 1[/tex]
So, your answer is C) [tex]x^{3} + 3x^{2} + 3x - 1[/tex].
Hope this helped!
Please give brainliest if possible!
The equation representing the polynomials are D = x³ + 3x² + 3x - 1
What is an 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.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as D
Now , the value of D is
Substituting the values in the equation , we get
A = x + 1
B = x² + 2x - 1
C = 2x
The value of AB + C = D
And , AB = ( x + 1 ) ( x² + 2x - 1 )
On simplifying the equation , we get
AB = x ( x² + 2x - 1 ) + ( x² + 2x - 1 )
AB = x³ + 2x² - x + x² + 2x - 1
AB = x³ + 3x² + x - 1
And , D = x³ + 3x² + x - 1 + 2x
D = x³ + 3x² + 3x - 1
Hence , the equation is D = x³ + 3x² + 3x - 1
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One of the roots of the equation 2x^2-bx-20=0 is -2.5. Find the other root.
Answer: If one of the roots of the equation 2x^2-bx-20=0 is -2.5, then by Vieta's Formulas, the other root is x = (20 + b)/4.
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
Given equation: 2x^2 - bx - 20 = 0
We are also given one of the solutions, which is -2.5.
We can start off by substituting -2.5 in place of x, in the given equation.
This is what it will look like:
2 * (2.5) ^2 - b (-2.5) - 20 = 0
After simplifying, the equation will now look like this:
12.5 + 2.5b - 20 = 0
Now, move all of the similar terms to one side of the equation:
2.5b = 20 - 12.5, which is basically 2.5b = 7.5
Divide 2.5 from both sides of the equation:b = 7.5/2.5, which is b = 3
Now that we know what the value of "b" is, let's go back to the given equation (2x ^2 - bx - 20 = 0), and substitute "3" in place of "b".
It will look like this:
2x^2 - 3x - 20 = 0
We can now apply the Quadratic formula. The formula looks like this:
(-b ± √b^2 -4ac)
2a
Substitute the values from the new equation into the formula:
3 ± √9 + 160
4
Simplify that:
3 ± 13
4
You should now have two solutions:
x1 = 3 + 13, which is x1 = 16/4 = 4
4
x2 = 3 - 13 , which is x2=-10/4, = -2.5
4
Now, the root that was given to us at the start of the problem was -2.5, so the other solution is 4, which we just solved for.
I hope this helps!!
How to convert 7cm 5mm in 'cm' using decimals
Can someone help me with this?
The formula for the area of a trapezoid is A = 1/2 h(b₁ + b₂), and where h is its height and b₁ and b₂ are the lengths of each base. Rewrite the area formula to solve for the height
are the lengths of each base.
Answer:
i think its A=12BH+12BiH
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the length l (in centimeters) of a scalloped hammerhead shark can be modeled by the function l = 266-219e -0.05t where t is the age (in years) of
the shark. how old is a shark that is 175 centimeters long? round your answer to the nearest tenth
With the help of equations we can say that the shark is 18 years old.
What are 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.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value
To determine the value A statement is not an equation if it has no "equal to" sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Hence, the shark is 18 years old.
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Question 1
Divide £1530 in the ratio 5 : 12
the bonneville salt flats, located in utah near the border with nevada, not far from interstate i80, cover an area of over 30000 acres. a race car driver on the flats first heads north for 4.69 km, then makes a sharp turn and heads southwest for 2.75 km, then makes another turn and heads east for 3.89 km. how far is she from where she started?
A race car driver is 3.79 km away from where she started.
Assume that a race car driver turns southwest, at an angle of 45 degrees.
Also she turns East making another 45 degree angle.
So, we get a right triangle.
Let ABC be right triangle with A = 90°, B = 45° and C = 45°
For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)
Consider the sine of angle B
sin(B) = Opposite side of angle B / Hypotenuse
sin(45) = x / 2.75
x = 1.94
sin(C) = Opposite side of angle C / Hypotenuse
sin(45) = y/2.75
y = 1.94
So, the distance to north before paths crossed would be,
N = 4.69 - y
N = 3.31
And the distance after she passed her northern path.
E = 3.89 - x
E = 1.85
Let m be the distance from Starting Point to End Point.
Using Pythagoras theorem,
m² = N² + E²
m² = (3.31)² + (1.85)²
m = 3.79 km
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How do you find the domain and range in inequalities of a function?
The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). The range of a function is the set of all possible output values (y-values) that the function can produce.
When working with inequalities, the domain and range can be found by analyzing the inequality and the context of the problem.
To find the domain of an inequality function, we need to identify any restrictions or limitations on the input values (x-values) that would make the inequality invalid.
For example, if the inequality contains a denominator that cannot be equal to zero, we need to exclude those values of x from the domain.
To find the range of an inequality function, we need to identify the set of all possible output values (y-values) that would make the inequality true.
For example, if the inequality is in the form y > x, we know that all values of y that are greater than x will satisfy the inequality.
In summary, finding the domain and range of inequalities of a function involves identifying any restrictions or limitations on input values and the set of possible output values that would make the inequality true.
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Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions
to the nearest hundredth.
x² + 12x+11-0
a. x = -11 or x = -1
b. x = 1 or x = 6
c.
d.
x = 10 or x = -3
x =0 or x = -6
The solution for the given quadratic equation is x = -11 or x = -1.
What is a quadratic equation?A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.
The standard form of a quadratic equation is ax² + bx + c = 0.
Where a, b and c are constants.
here, given that,
The given quadratic equation is,
x² + 12x + 11 = 0.
The graph of the equation is, plotted below.
From the graph,
The solutions are x = -1 and x = -11
The second approach to find the solution for the given quadratic equation is factorization method,
x² + 12x + 11 = 0
x² + 11x + x + 11 = 0
x(x + 11) + 1(x + 11) = 0
(x + 11) (x + 1) = 0
x = -11 or x = -1
So, the required solution is x = -11 or x = -1.
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When Sammy's school bus hastraveled 4.3 miles, Sammy hascompleted 40% of his trip homefrom school. How many miles doesSammy travel on the school bus fromschool to home?
Answer:
10.75 miles
Step-by-step explanation:
[tex]\frac{40}{100}[/tex]×x=4.3
40x=430
x=10.75
Round each fraction to help you estimate the solution for the following equation: 7/12 - 2/12 =
On solving the provided question, we can say that the fraction =5/12 = 0.4166666667 rounding off = 0
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here,
the fraction is
7/12 - 2/12
=5/12
= 0.4166666667
rounding off = 0
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One of the solutions to the equation 5x^2+bx+12=0 is -4/5. Find the other solution.
Answer:
b = 4+15
b =19
Step-by-step explanation:
5x^2 + bx + 12 = 0
the sum of its roots = –b/a
m + n = - b/a
-4/5 + n = -b/5
-4 + 5n = -b
5n= -b + 4 -------------1
product of its roots = c/a
m*n = c/a
-4/5 * n = 12/5
-4 n = 12
n = -3 is the other root -------------2
Plug-in equation 2 in 1
5(-3) = -b + 4
-15 = -b + 4
b = 4+15
b =19
One of the solutions to the equation 5x^2+bx+12=0 is -4/5.the other solution is 2.4 + (-4/5) = 2.
The other solution to the equation 5x^2+bx+12=0 can be found by using the fact that the solutions of a quadratic equation of the form ax^2+bx+c=0 are given by the formula: x = (-b ± √(b^2-4ac)) / 2a.
In this case, a=5, b=b and c=12. We know that the product of the roots is equal to c/a and sum of roots is equal to -b/a. so the product of the roots is 12/5 = 2.4and the sum of the roots is -b/5 .
since we know that one of the solutions is -4/5, we can find the other solution by using the above formulas: -4/5 = 2.4 - other solution so the other solution is 2.4 + (-4/5) = 2.
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