Answers
Answer:
2. x = √3
3. y = 3√2
4. a = (2/3)√2
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.
___
2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x
___
3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve
12 = 2√2y
12/(2√2) = y = 6/√2 = 3√2
___
4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve
a = 2√2/3 = (2/3)√2
_____
Comment on "rationalizing the denominator"
"Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical:
1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/n
That is, ...
1/√2 = (√2)/2 . . . . for example.
Related Questions
nancy made a table runner that has an area of 80 square inches. the length and width are whole numbers. the length is 5 times greater than the width. what are the dimensions
Answers
Answer : The dimensions of table runner will be, 20 inch length and 4 inch width.
Step-by-step explanation :
Let the width of table runner be, x
and, the length of table runner will be, 5x
Given:
Area of table runner = [tex]80inch^2[/tex]
As we know that:
Area of rectangle = Length × Width
[tex]80inch^2=(5x)\times (x)[/tex]
[tex]80inch^2=5x^2[/tex]
[tex]x=4inch[/tex]
The width of table runner = x = 4 inch
The length of table runner = 5x = 5(4) inch = 20 inch
Therefore, the dimensions of table runner will be, 20 inch length and 4 inch width.
Which statement is true of an appropriate sample of a population?
A sample must be a group of people who are the target of the survey question.
A sample should have different characteristics than the population.
A sample must be very small.
A sample should include only boys or only girls.
Answers
A sample must be a group of people who are the target of the survey question
Answer:
The correct option is 1.
Step-by-step explanation:
The set of all observations is known as populate set.
A sample is a small subset of population set that is the representative of the entire population. The sample must have sufficient size and it should include all population.
A sample must be a group of people who are the target of the survey question. This statement is true.
Therefore the correct option is 1.
A sample should have different characteristics than the population. This statement is false.
A sample must be very small. This statement is false.
A sample should include only boys or only girls. This statement is false.
Therefore options 2, 3 and 4 are incorrect.
Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750 The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price. After purchasing the computer, how much does Hakim have left in his bank account?
Answers
Answer:
$111
Step-by-step explanation:
The bank balance is ...
$700 × (1 + 0.05) = $735
The cost of the computer is ...
$750 × (1 -0.20) × (1 +0.04) = $624
The remaining bank balance after paying for the computer is ...
$735 -624 = $111
_____
When you add a percentage, you effectively multiply by the sum of 1 and that percentage. The same is true if the amount "added" is negative (as for a discounted price).
(original amount) + (percentage)×(original amount)
Use the distributive property to factor out the original amount:
= (original amount)×(1 + percentage)
2. Quan plans to spend less than $80 for buying groceries. He plans to spend $68.25 on food and spend the rest on juice. Each juice carton costs $3. He is curious how many juice cartons he can purchase before he runs out of money.
(a) Use x to represent the number of juice cartons Quan can purchase and write an inequality that can be used to solve for x.
(b) Solve the inequality. Use the solution to determine the number of juice cartons Quan can purchase.
Check your answers if needed
Answers
He should have 27.5 left I'm 100% sure
What series of transformations from △ABC to △DEF shows that △ABC ≌ △DEF?
a). a reflection across the y-axis followed by a translation of 1 unit right and 2 units up
b). a clockwise rotation of 90º about the origin followed by a translation of 4 units right and 4 units up
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
d). a reflection across the line y=x followed by a positive rotation of 270º about the center
Answers
Answer:
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
Step-by-step explanation:
You want to know the transformations that map ΔABC onto ΔDEF.
TransformationsThe answer choices would ask us to consider some combination of the following transformations:
reflection across the y-axis: (x, y) ⇒ (-x, y)reflection across the x-axis: (x, y) ⇒ (x, -y)reflection across the line y=x: (x, y) ⇒ (y, x)clockwise rotation 90°: (x, y) ⇒ (y, -x)positive rotation 270°: (x, y) ⇒ (y, -x) . . . same as 90° CWtranslation by (h, k): (x, y) ⇒ (x+h, y+k) . . . h units right, k units upApplicationWe can apply these relations to the answer choices to see if they provide the desired mapping ...
A(-4, 1) ⇒ D(-3, -2)B(-6, 5) ⇒ E(-5, -6)C(-1, 2) ⇒ F(0, -3)a) Reflection across the y-axis, translation (1, 2)
A(-4, 1) ⇒ A'(4, 1) . . . reflection
A'(4, 1) ⇒ D(4+1, 1+2) = D(5, 3) . . . . not the correct point
b) Rotation CW 90°, translation (4, 4)
A(-4, 1) ⇒ A'(1, 4) . . . rotation 90° CW
A'(1, 4) ⇒ D(1+4, 4+4) = D(5, 8) . . . . not the correct point
c) Reflection across the x-axis, translation (1, -1)
A(-4, 1) ⇒ A'(-4, -1) . . . reflection
A'(-4, -1) ⇒ D(-4+1, -1+(-1)) = D(-3, -2) . . . . the correct location of D
d) Reflection across y=x, rotation CCW 270°
A(-4, 1) ⇒ A'(1, -4) . . . reflection
A'(1, -4) ⇒ D(-4, -1) . . . . not the correct point
The correct series of transformations is reflection across the x-axis followed by translation 1 right and 1 down.
Read the statement.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Check all that apply.
p → q represents the original conditional statement.
~p → ~q represents the inverse of the original conditional statement.
q → p represents the original conditional statement.
~q → ~p represents the converse of the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
Answers
Answer:
True, True , False , False , False
Step-by-step explanation:
Let us see the correction for the rest of the three False Statements
3) p→q represent the original conditional statement.
4) ~q → ~p represents the contrapositive of the original conditional statement
5) contrapositive of the original conditional statement will be ~q → ~p
There is one more implication called Converse of the original conditional statement . It is represented as q→p
How do i solve this?
Answers
Answer:
see below
Step-by-step explanation:
If the left-side tiles are numbered 1–7 from top to bottom, their order on the right is ...
7 — denominators factored
6 — common factors canceled
5 — make the left side have the same denominator as the right
3 — express the sum over the common denominator
2 — collect numerator terms
Find all pairs of natural numbers which can be the solution to the equation: x+y=11
Answers
Answer:
How many solution does ++=11
x
+
y
+
z
=
11
have where ,,
x
,
y
,
z
are non-negative integers. In light of the restrictions, its clear that ,,∈{0,1,2,..11}
x
,
y
,
z
∈
{
0
,
1
,
2
,
.
.11
}
. So, at face value I would assign a value for
x
and determine the different combinations that
y
and
z
can hold. For example,
For =0
x
=
0
, we have +=11
y
+
z
=
11
. With writing them out I found that there are 12
12
different assigned combinations for
y
and
z
that satisfy the equation. For =1
x
=
1
, I got 11
11
. Consequently, the pattern becomes clear whereby each one takes a value less by one. Hence, the number of solutions is 1+2+3+4+5+6+7..+12=78
1
+
2
+
3
+
4
+
5
+
6
+
7..
+
12
=
78
. I was wondering if there is an easier method perhaps with combinations equation (,)
C
(
a
,
b
)
..?
Step-by-step explanation:
(x,y)
1,10
2,9
3,8
4,7
5,6
6,5
7,4
8,3
9,2
10,1
Find the range of y=4sin2x+3
Answers
Answer:
[-1, 7]
Step-by-step explanation:
If you mean ...
y = 4sin(2x) +3
then you can substitute the range of the sine function into the equation and evaluate it to find the range of y.
The range of sin( ) is [-1, 1], so the range of y is ...
4[-1, 1] +3 = [4(-1)+3, 4(1)+3] = [-1, 7]
_____
Comment on the problem statement
The range of y = 4sin²(x)+3 will be different, and the range of 4sin(2x+3) will be different yet. It is usually a good idea to use parentheses around function arguments.
Answer:
-1,7
Step-by-step explanation:
got it right on odessyware
A plane flying at a certain altitude is observed from two points that are 3 miles apart. The angles of elevation made by two points are 55 and 72, as seen in the diagram. The altitude of the plane to the nearest tenth of a mile is ?
Answers
Answer:
The altitude of the plane is 8 miles
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC
tan(72°)=h/x
h=xtan(72°) -----> equation A
In the right triangle ABD
tan(55°)=h/(x+3)
h=(x+3)tan(55°) -----> equation B
equate equation A and equation B and solve for x
xtan(72°)=(x+3)tan(55°)
xtan(72°)-xtan(55°)=3tan(55°)
x[tan(72°)-tan(55°)]=3tan(55°)
x=3tan(55°)/[tan(72°)-tan(55°)]
Find the value of h
h=xtan(72°)
h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)]
h=8 miles
Answer:
8.0 is the right answer
Step-by-step explanation:
ur welcommmme ;)
Simply 6^-1(4^-2) plz help
Answers
Answer:
1/96
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
Then ...
[tex]6^{-1}\cdot 4^{-2}=\dfrac{1}{6}\cdot\dfrac{1}{4^{2}}=\dfrac{1}{6\cdot 16}=\dfrac{1}{96}[/tex]
given that a^b=x, evaluate the following: a^2b
Answers
Answer:
[tex]a^{2b}=x^{2}[/tex]
Step-by-step explanation:
we know that
[tex]a^{b}=x[/tex] ----> equation A
Find the value of [tex]a^{2b}[/tex]
Remember that
[tex]a^{2b}=(a^{b})^{2}[/tex]
[tex](a^{b})^{2}[/tex] ----> equation B
substitute equation A in the equation B
[tex](a^{b})^{2}=x^{2}[/tex]
therefore
[tex]a^{2b}=x^{2}[/tex]
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c?
Answers
Answer:
10$ an hour
Step-by-step explanation:
1/2c=6-1
c=2(6-1)
c=10
Answer:
Carey's hourly rate to babysit is $10.
Step-by-step explanation:
Given is -
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate.
Let Carey's hourly rate to babysit be represented by 'c'
So, Anderson's hourly rate will be = [tex]\frac{c}{2}+1[/tex]
Also given that Anderson earns $6 per hour.
So, equaling both, we get;
[tex]6=\frac{c}{2}+1[/tex]
[tex]6=\frac{c+2}{2}[/tex]
[tex]c+2=12[/tex]
[tex]c=10[/tex]
Hence, Carey's hourly rate to babysit is $10.
Find the equation of the perpendicular bisector of the given segment by following these steps. 1. Determine the slope of the given segment.
Answers
Answer:
The equation of the perpendicular bisector is 2x + 3y - 3 = 0
Step-by-step explanation:
* How to find the equation of a line from two points (x1 , y1)
and (x2 , y2) lie on it
- Find the slope of the line using the rule
The slope (m) = (y2 - y1)/(x2 - x1)
- Use the rule of the equation y - y1 = m (x - x1), where m is
the slope of the line and (x1 , y1) is a point on the line
* Remember if two line are perpendicular, then the product of
their slopes = -1, that means one of them is an additive inverse
and multiplicative inverse to the other
# Ex: if the slope of a line is a/b, then the slope of the
perpendicular to it is -b/a
* Now lets read the problem, we need the equation of the
perpendicular bisector to the line that passes through the
points (2 , 4) and (-2 , -2)
- Find the slope of the line in the graph by using the given points
# m = (-2 - 4)/(-2 - 2) = -6/-4 = 3/2
∴ The slope of the perpendicular line = -2/3 ⇒ multiplicative
inverse and additive inverse of it
* Bisector means intersect it in the mid-point of the given line
- The rule of the mid-point is [(x1 + x2)/2 , (y1 + y2)/2]
∴ The mid-point of the line is [(2 + -2)/2 , (4 + -2)/2] = (0 , 1)
* Now we have the slope and a point on the line, to find the
equation of the perpendicular bisector its slope is -2/3 and
a point (0 , 1)
∴ The equation: y - 1 = -2/3 (x - 0)
The equation : y - 1 = -2/3 x ⇒ Multiply both sides by 3
The equation : 3y - 3 = -2x ⇒ collect x , y in the same side
The equation : 2x + 3y - 3 = 0
* The equation of the perpendicular bisector is 2x + 3y - 3 = 0
Answer:3/2
Step-by-step explanation:
Given: circle k(O), DC ∥ AB , AC ∩ DB =0, m AD =124°Find: m∠C, m∠AOB.
Answers
Answer:
Part 1) The measure of angle C is [tex]62\°[/tex]
Part 2) The measure of angle AOB is [tex]56\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<C=\frac{1}{2}(arc\ AD)[/tex]
we have
[tex]arc\ AD=124\°[/tex]
substitute
[tex]m<C=\frac{1}{2}(124\°)=62\°[/tex]
step 2
Find the measure of angle AOB
we know that
In the isosceles triangle ODC
∠D=∠C=62°
Remember that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
∠D+∠C+∠DOC=180°
substitute the values
62°+62°+∠DOC=180°
∠DOC=180°-124°=56°
we have that
∠AOB=∠DOC -----> by vertical angles
so
∠AOB=56°
Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.
Answers
Answer:
The two consecutive positive integers are 7 and 8
Step-by-step explanation:
Let
x ----> the first positive integer
x+1 ----> the second consecutive positive integer
we know that
[tex]x^{2} -17=4(x+1)[/tex]
Solve for x
[tex]x^{2} -17=4x+4\\ \\x^{2}-4x-21=0[/tex]
Solve the quadratic equation by graphing
The solution is x=7
see the attached figure
Find the value of x+1
x+1=7+1=8
therefore
The two consecutive positive integers are 7 and 8
To find two consecutive positive integers, we can set up an equation and solve for the values of x and x + 1.
Let's assume the first positive integer is x. Since we need to find two consecutive positive integers, the second positive integer would be x + 1. According to the given condition, the square of the first decreased by 17 should be equal to 4 times the second. This can be written as:
x^2 - 17 = 4(x + 1)
Now, we can solve this equation to find the values of x and x + 1.
x^2 - 17 = 4x + 4
x^2 - 4x - 21 = 0
By factoring or using the quadratic formula, we can find the solutions for x. Once we have the values of x, we can calculate x + 1 to find the two consecutive positive integers.
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Maria is 7 years older than her brother Robert and in 2 years her age will be four times what Robert’s age was three years ago. Find their present ages.
Answers
Answer:
Robert is 7 years old and Maria is 14 years old.
Step-by-step explanation:
You can use 2 variables: m and r and write 2 equations:
m = r +7
m + 2 = 4( r -3)
So 3 * r = 21 or r= 7
Maria and Robert are currently with present ages as 14 and 7 years old, respectively.
What do you mean by an equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It demonstrates that the expressions on the left and right sides are connected in the same way.
An equation has components like as coefficients, variables, operators, constants, terms, expressions, and the equal to sign. The "=" sign and terms on both sides are required when generating an equation.
The information is ,
Let's say the equation looks like this: A
Right now, A is valued at
Let Maria's age be x.
Let Robert's age be y.
Maria now has a 7-year age gap with Robert.
Hence, the equation x = 7 plus y (1)
Also, in two years she will be four times Robert's age from the previous three years.
The equation is (x + 2) = 4 (y - 3). (2)
We obtain (7 + y + 2) = 4y - 12 y + 9 = 4y - 12 after simplifying.
We obtain 3y = 21 by subtracting y and adding 12 on both sides.
We obtain y = 7 years old by dividing both sides by 3.
Robert is therefore 7 years old.
And , x = 14 years old
And , the age of Maria is 14 years old
As a result, Maria and Robert are currently 14 and 7 years old, respectively.
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What is the length of ad
Answers
Answer:
15.7 cm
Step-by-step explanation:
The length (s) of an arc of a circle of radius r with a central angle of θ radians is ...
s = rθ
Here, the radius is given as 7.9 cm, and the arc of interest is the supplement of 66.4°, so is ...
θ = π·(1 - 66.4/180) ≈ 1.9827 . . . . radians
Then the arc length is ...
s = (7.9 cm)·(1.9827) ≈ 15.7 cm
A kudzu plant is 1 6/7 feet tall. Over time, the plant grows to 4 2/9 feet. About how much does the plant grow ? Use rounding to estimate
Answers
Answer:
The correct answer is 2 23/63
Step-by-step explanation:
To determine how much the plant grew, start by subtracting the starting whole number value from the ending whole number value.
4 - 1 = 3
Now do the same with the fractions. Use common denominators.
2/9 - 6/7
14/63 - 54/63
-40/63
Now add the two numbers together.
3 - 40/63 = 2 23/63
A machine can make 5 miles of ribbon in an hour. Graph the length of the ribbon the machine will make in eight hours. Another machine can make 8 miles of ribbon in an hour. Graph the length of the ribbon the machine will make in 8 hours. What is the difference in length for a 8 hour period between the two machines? Write an Equation in slope intercept for each machine.
Answers
The equations for the two machines are y = 5x and y = 8x, which represent their respective production rates. Over an 8 hour period, the first machine produces 40 miles of ribbon and the second produces 64 miles, resulting in a difference of 24 miles.
Explanation:The two machines described in the question produce ribbon at different rates, which can be represented with two linear equations in slope-intercept form (y = mx + b) where m is the rate of production (slope) and b is the initial amount of ribbon (y-intercept, in this case 0 as the machine starts with no ribbon).
The first machine can produce 5 miles of ribbon in an hour, so its rate is 5 miles/hour. This gives the equation y = 5x.
The second machine can produce 8 miles of ribbon in an hour, leading to the equation y = 8x.
In an 8 hour period, the first machine will produce y = 5*8 = 40 miles of ribbon, while the second machine will produce y = 8*8 = 64 miles of ribbon. The difference is 64 - 40 = 24 miles.
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The first machine will make 40 miles of ribbon in 8 hours, and the second machine will make 64 miles of ribbon. The difference in length for an 8-hour period between the two machines is 24 miles.
Explanation:To graph the length of ribbon each machine will make in 8 hours, we can start by determining the length each machine can make in one hour.
The first machine can make 5 miles of ribbon in an hour, so in 8 hours, it will make 8 times 5 = 40 miles of ribbon.
The second machine can make 8 miles of ribbon in an hour, so in 8 hours, it will make 8 times 8 = 64 miles of ribbon.
The slope-intercept form of an equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept. For the first machine, the equation would be y = 5x + 0, and for the second machine, the equation would be y = 8x + 0.
The difference in length between the two machines for an 8-hour period is 64 - 40 = 24 miles.
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Genise is making cookies. She needs 1 1/2 cups of flour for one batch, but she wants to make 2 1/2 batches. Write an equation that can be used to find how many cups of flour genise will need.
Answers
To calculate how many cups of flour Genise will need for 2 1/2 batches, multiply the amount of flour for one batch (1 1/2 cups) by the number of batches (2 1/2). This results in 3 3/4 cups of flour needed.
To find how many cups of flour Genise will need, we start by writing an equation that reflects the amount of flour needed for one batch times the number of batches she plans to make. Since she needs 1 1/2 cups of flour for one batch and she wants to make 2 1/2 batches, we set up the multiplication:
flour_needed = (cups of flour per batch) * (number of batches)
So the equation will be:
flour_needed = 1 1/2 * 2 1/2
Converting mixed numbers to improper fractions for easier multiplication, we have:
flour_needed = 3/2 * 5/2 = 15/4 cups
Then, we convert the improper fraction back to a mixed number, which is:
flour_needed = 3 3/4 cups of flour
I'd appreciate an answer to this.
Here are the 30 best lifetime baseball batting averages of all time, arranged in order from lowest to highest.
Answers
Answer:
C. 0.366
Step-by-step explanation:
In this stemplot, it is apparent that the number on the right is the least-significant digit (thousandths digit) of the batting average. The two most-significant digits are to the left of the vertical line.
Hence the value 0.36 | 6 represents an average that is 36 hundredths plus 6 thousandths: 0.366.
whats the difference between range and interquartile range?
Answers
Answer:
Step-by-step explanation:
The range is the difference between the highest and the lowest values in a set of data. The interquartile range, the IQR, is what's "inside" the box in a box plot, which consists of the difference between the central measures, which are the first and the third quartiles.
Range is the difference between the maximum and minimum values in a dataset, while the Interquartile Range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3), representing the spread of the middle 50% of the data.
Range is the simplest measure of variability in a dataset.It is calculated by subtracting the minimum value from the maximum value.
For example, if the highest score in a test is 95 and the lowest score is 55,
the range is 95 - 55 = 40.
Interquartile Range (IQR) is a more sophisticated measure of variability that focuses on the middle 50% of the data.To find the IQR, we first need to determine the first quartile (Q1) and the third quartile (Q3).
Q1 is the median of the lower half of the data, while Q3 is the median of the upper half.
The IQR is then calculated by subtracting Q1 from Q3.
For example, in a dataset:
If Q1 = 70 and Q3 = 90, then
IQR = 90 - 70 = 20.
The IQR is useful in identifying potential outliers and understanding the spread of the central data.
Write an exponential function for graph that passes through the following points (-3,80);(-1,20)
Answers
Final answer:
To find the exponential function that passes through (-3, 80) and (-1, 20), we use the general form y = abˣ. By solving a system of equations using these points, we find that the exponential function is y = 40*2ˣ.
Explanation:
To write an exponential function that passes through the points (-3, 80) and (-1, 20), we can use the general form of an exponential function, which is y = abˣ. Here, a and b are constants we need to find. Given two points, we can set up a system of equations to solve for a and b.
Using the first point (-3, 80):
80 = a*b⁻³
Using the second point (-1, 20):
20 = a*b⁻¹
Dividing the second equation by the first gives us:
b2 = 4 which simplifies to b = 2 or b = -2. However, in exponential functions, b is positive, so we choose b = 2.
Substituting b = 2 into the second equation gives a = 40. Thus, the exponential function is y = 40*2ˣ.
Can someone help with 2.6
Answers
Answer:
B
Step-by-step explanation:
Theta is found using the sin-1 function. Start off with the sin of theta.
sin(theta) = opposite over hypotenuse.
sin(theta) = 3/8 = 0.375
Theta = Sin-1 (0.375)
Theta = 22.02 degrees.
Answer: B
x-y-4z=-9
4x-3y-2z=-9
-x-3y-6z=-7
solve
Answers
Answer:
(x, y, z) = (-2, -1, 2)
Step-by-step explanation:
Your graphing calculator can usually solve systems of linear equations easily.
a) One of the roots of the equation 10x^2−33x+c=0 is 5.3. Find the other root and the coefficient c.
b)The difference between the roots of the quadratic equation x^2−12x+q=0 is 2. Find q.
c)The difference between the roots of the quadratic equation x^2+x+c=0 is 6. Find c.
Answers
Answer:
a) The other root is -2
The coefficient c = -106
b) q = 35
c) c = -8.75
Step-by-step explanation:
* Lets study the general form of the quadratic equation
* ax² + bx + c = 0
- Their roots are x1 and and x2
- The sum of them = -b/a ⇒ x1 + x2 = -b/a
- The product of them = c/a ⇒ (x1)(x2) = c/a
a) * Assume that the roots of the equation 10x² - 33x + c = 0
are m and n
∵ m + n = -b/a
∵ a = 10 and b = -33
∴ m + n = -(-33)/10 = 3.3
∵ m = 5.3
∴ 5.3 + n = 3.3 ⇒ n = 3.3 - 5.5 = -2
∴ n = -2
* The other root is -2
∵ m × n = c/a
∵ m = 5.3 , n = -2 , a = 10
∴ (5.3)(-2) = c/10
∴ -10.6 = c/10 ⇒ Multiply both sides by 10
∴ c = -106
* The coefficient c = -106
b) * Assume that the roots of the equation x² - 12x + q = 0
are m and n
∵ The difference between the roots is 2
∴ m - n = 2 ⇒ (1)
∵ From the equation m + n = -b/a
∵ a = 1 , b = -12
∴ m + n = -(-12)/1 = 12
∴ m + n = 12 ⇒ (2)
* Lets solve the two equation
- Add the two equation to eliminate n
∴ 2m = 14 ⇒ divide both sides by 2
∴ m = 7
* Substitute the value of m in (1) or (2)
∴ 7 - n = 2 ⇒ 7 - 2 = n ⇒ 5 = n
∴ n = 5
∵ mn = c/a
∵ c = q , a = 1
∴ mn = q/1 = q
∴ q = 7 × 5 = 35
* q = 35
c) * Assume that the roots of the equation x² + x + c = 0
are m and n
∵ The difference between the roots is 6
∴ m - n = 6 ⇒ (1)
∵ From the equation m + n = -b/a
∵ a = 1 , b = 1
∴ m + n = -(1)/1 = -1
∴ m + n = -1 ⇒ (2)
* Lets solve the two equation
- Add the two equation to eliminate n
∴ 2m = 5 ⇒ divide both sides by 2
∴ m = 2.5
* Substitute the value of m in (1) or (2)
∴ 2.5 + n = -1 ⇒ n = -1 - 2.5 = -3.5
∴ n = -3.5
∵ mn = c/a
∵ c = c , a = 1
∴ mn = c/1 = c
∴ c = 2.5 × (-3.5) = -8.75
* c = -8.75
Solve for x.
x2 - 2x - 24 = 0
A. -4, -6
B. -4, 6
C. 2, -6
D. 4, 6
Answers
Answer:
Your answer is
x = -4, 6 or (b)
Have a nice day and please mark me as brainliest!! (:|
~abelxoconda
The solution of the equation for the value of x will be (-4,6).
What is a quadratic equation?The polynomial equation with the degree of two will be termed as the quadratic equation or the highest power of the variable is 2 in the quadratic equation.
The given equation is:-
=x²-2x-24
Now we will split the equation
=x²-6x+4x-24
=x(x-6)+4(x-6)
=(x-6)(x-4)
Hence the value of x will be -4 and 6.
To know more about quadratic equation follow
https://brainly.com/question/1214333
#SPJ2
Please help someone..
Answers
Answer: [tex]\bold{\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\dfrac{DF}{AK}=\dfrac{4}{20}=\large\boxed{\dfrac{1}{5}}[/tex]
What is another way to describe an equilateral triangle?
A) acute
B) obtuse
C) right
D) scalene
Answers
I think it a but I sorry if it wrong