Final answer:
To calculate the sum of the squares of the roots of a quadratic equation, apply Vieta's formulas to find the sum and product of the roots and use them in the identity (α + β)² - 2αβ to avoid directly solving for the roots.
Explanation:
To find the sum of the squares of the roots of an equation, especially for a quadratic equation of the form ax²+bx+c=0, we use the relationship between the coefficients and the roots provided by Vieta's formulas.
The sum of the roots, denoted as α and β, is given by -b/a, and the product of the roots is c/a. To find the sum of the squares of the roots (α² + β²), you can use the identity (α + β)² = α² + 2αβ + β², or α² + β² = (α + β)² - 2αβ.
By substituting the sum and product of the roots from Vieta's formulas, you can calculate the sum of the squares without actually solving for the roots. This approach is especially useful in equilibrium problems or other situations where you might encounter square roots or higher powers and wish to simplify calculations.
Find the value of m angle 3-m<1
Answer:
The value of [tex]m\angle 3-m\angle 1[/tex] = [tex]50^{\circ}[/tex]
Step-by-step explanation:
Vertical Angle theorem: It is about the angles that are opposite to each other.
Also, vertical angle are congruent that means vertical angles are equal.
In the given figure; [tex]m\angle 3[/tex] and [tex]70^{\circ}[/tex] are vertical angle
then, by vertical angle theorem, [tex]m\angle3 =70^{\circ}[/tex].
Supplementary angle: the sum of the angles whose measure on the straight line is 180 degree.
From the figure, [tex]70^{\circ}[/tex] , [tex]\angle 1[/tex] and [tex]m\angle 2 =90^{\circ}[/tex] forms a straight line.
then, by the definition of Supplementary angle;
[tex]70^{\circ}+m\angle 1 +m\angle 2=180^{\circ}[/tex]
Substituting the value of [tex]m\angle 2 =90^{\circ}[/tex] in above equation:
[tex]70^{\circ}+m\angle 1 + 90^{\circ} =180^{\circ}[/tex] or
[tex]160^{\circ}+m\angle 1=180^{\circ}[/tex]
Simplify:
[tex]m\angle 1=180^{\circ}-160^{\circ} =20^{\circ}[/tex]
therefore, [tex]m\angle 1= 20^{\circ}[/tex] and [tex]m\angle 3=70^{\circ}[/tex],
the value of [tex]m\angle3-m\angle1= 70^{\circ}-20^{\circ} =50^{\circ}[/tex].
The graph of g(x) is the graph of f(x)=12x+6 compressed vertically by a factor of 13 .
Which equation describes the function g?
g(x)=12x+2
g(x)=4x+6
g(x)=4x+2
g(x)=36x+6
My number is a multiple of 2 & 7 my number is less than 100 but greater than 50 my number is the product of three prime numbers what number am i?
How many watches must he repair to have the lowest cost?
find x and y
x+y=5
x=y+7
1st equation: x +y =5
2nd equation: x = y +7
replace x in 1st with 2nd
y +7 +y =5
2y+7 =5
2y =-2
y = -1
now replace y in 2nd with -1
x = -1 +7
x = 6
answer:
x = 6
y = -1
Please help with these two questions thank you.
How many true conditional statements may be written using the following statements?
n is a rational number.
n is an integer.
n is a whole number.
a.
2 conditional statements
c.
4 conditional statements
b.
3 conditional statements
d.
5 conditional statements
ruby is visiting San Francisco. From her hotel she walks 1 block west ans 4 blocks south to a coffee shop. Then she walks 5 blocks east and 6 blocks south to a museum. Where is the museum in relation to her hotel
Answer:
The museum is 4 blocks east and 10 blocks south from her hotel.
Step-by-step explanation:
It is given that ruby is visiting San Francisco. From her hotel she walks:
(a) 1 block west and 4 blocks south to a coffee shop.
(b) Then she walks 5 blocks east and 6 blocks south to a museum.
First she moves 1 block west and 4 blocks south and reached at point B. After that she walks 5 blocks east and 6 blocks south and reached at point D.
From the below figure it is noticed that point D is 4 blocks east and 10 blocks south from the origin because
[tex]South=4+6=10[/tex]
[tex]East=5-1=4[/tex]
Therefore the museum is 4 blocks east and 10 blocks south from her hotel.
What is the equation for a circle centered at the origin
Answer: The equation of the circle is [tex]x^2+y^2=r^2.[/tex]
Step-by-step explanation: We are given to write the equation of a circle centered at the origin.
We know that the standard equation of a circle with center at the point (g, h) and radius 'r' units is given by
[tex](x-g)^2+(y-h)^2=r^2~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The co-ordinates of the origin are (0, 0).
So, if the center of the circle is at the origin, then we have
(g, h) = (0, 0).
Therefore, from equation (i), we have
[tex](x-0)^2+(y-0)^2=r^2\\\\\Rightarrow x^2+y^2=r^2.[/tex]
Thus, the required equation of the circle is [tex]x^2+y^2=r^2.[/tex]
There are 5,280 feet in 1 mile. If Riley ran 26,400 feet, how many miles did she run? [Type your answer as a number.]
Answer:
She ran 5 miles
Step-by-step explanation:
To solve this, we can easily use proportion.
The question state that there are 5,280 feet in a mile, We are ask to find the number of miles Rily run, if she ran 26,400 feet.
Using proportion;
Let x = the number of miles Rily can run
5,280 feet = 1 mile
26,400 feet = x
Cross-multiply
5280x = 26,400
To get the value of x, we will divide both-side of the equation by 5280
5280x/5280 = 26400/5280
(On the left-hand side of the equation, 5280 will cancel-out 5280 leaving us with x and on the right-hand side of the equation 26400 will divide 5280)
x = 26400 / 5280
x=5 mile
Therefore, If Rily ran 26400 feet, then she has ran 5 miles.
The volume of wax used in making a cylindrical candle is given by the formula v=nr2h what is the height of the candle in terms of the volume and radius?
Which can be a next step in the construction of an angle with a side on line l that is congruent to ∠ABC?
To construct an angle with a side on line l that is congruent to ∠ABC, follow these steps: Draw line l, measure ∠ABC, draw a ray from line l with the same angle, label the intersection point as B, and segment AB is congruent to side AC.
To construct an angle with a side on line l that is congruent to ∠ABC, you can follow these steps:
Draw line l.
Use a protractor to measure ∠ABC.
Draw a ray from line l, starting at point A and making the same angle as ∠ABC.
Label the point where the ray intersects line l as B.
Now, segment AB is congruent to side AC of ∠ABC.
How to calculate standard deviation given mean and sample size?
There is a step missing from the solution below. Which equation is the missing step?
P=17-√0.025x+7
25=17-√0.025x+7
8=-√0.025x+7
?
57=0.025x
2280= x
A. 64=0.025x+49
B. 8=0.025x+7
C. -8= √0.025x+7
D. 64=0.025x+7
Answer:
option: D is the correct answer.
( D. 64=0.025 x+7 )
Step-by-step explanation:
We are given step as:
[tex]P=17-\sqrt{0.025x+7}\\\\25=17-\sqrt{0.025x+7}\\\\8=-\sqrt{0.025x+7}------(1)[/tex]
?
57=0.025x
-----------(2)
2280= x.
We are asked to find the missing step.
Clearly after equation (1)
They have squared the equation both side to obtain:
[tex]64=0.025x+7[/tex]
and then they took the constant term to the left hand side to obtain equation (2).
[tex]64-7=0.025x\\\\57=0.025x[/tex]
Hence, the correct option is:
Option: D
D. 64=0.025 x+7
Answer: 64=0.025x+7
Step-by-step explanation:
a p e x
Which set represents the range of the function shown?
{(-1,5),(2,8),(5,3),(13,-4)}
A- {-1,2,5,13}
B-{-4,3,5,8}
C- {(5,-1),(8,2),(3,5),(-4,13)}
D-{-4,-1,2,3,5,5,8,13}
Answer:
B. {-4,3,5,8}
Step-by-step explanation:
We are given,
The set representing the function is {(-1,5),(2,8),(5,3),(13,-4)}.
It is required to find the range set of the function.
Now, as we know,
In the ordered pair [tex](x,y)[/tex], the y co-ordinate 'y' represents the range values of a function.
So, we see that,
The range values of the given function are 5, 8, 3 and -4.
Thus, the set representing the range of the function is {-4,3,5,8}.
The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls. Jalen’s Mobile Phone Cost Number of minutes, x 150 220 250 275 Cost, y $7.50 $11.00 $12.50 $13.75 If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation?
Answer:
[tex]y=0.05x[/tex]
Step-by-step explanation:
Given :
x Cost, y
150 $7.50
220 $11.00
250 $12.50
275 $13.75
To Find: If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation?
Solution:
To find equation we will use two point slope form.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(150,7.50)[/tex]
[tex](x_2,y_2)=(220,11.00)[/tex]
Substitute the values in the formula.
[tex]y-7.50=\frac{11-7.5}{220-150}(x-150)[/tex]
[tex]y-7.50=0.05(x-150)[/tex]
[tex]y-7.50=0.05x-7.50[/tex]
[tex]y=0.05x[/tex]
Hence the equation which represents the variation is [tex]y=0.05x[/tex]
180 is 10 % more than witch number ?
Simplify the product.
8x2(4x2 + 4y6)
a. 32x4 + 32x2y6
b. 12x4 + 12x2y6
c. 32x4 + 32xy8
d.12x4 + 12x2y6
Answer:
A
Step-by-step explanation:
What is the image of (5,-1) under same translation?
The image of point (5, -1) under the same translation that maps point P to P' is (1, -8). This translation vector is obtained by subtracting the coordinates of P from P'.
To find the image of point (5, -1) under the same translation T that maps point P to P', we can calculate the vector that represents the translation from P to P' and then apply the same translation to point (5, -1).
The translation vector is given by:
Translation vector = P' - P = (-6, -4) - (-2, 3) = (-4, -7)
Now, to find the image of point (5, -1) under the same translation, we simply add this translation vector to (5, -1):
Image of (5, -1) = (5, -1) + (-4, -7) = (5 - 4, -1 - 7) = (1, -8)
So, the image of point (5, -1) under the translation T is (1, -8). Therefore, the correct answer is B. (1, -8).
Learn more about image of point here:
https://brainly.com/question/32018278
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Leo is going to use a random number generator 400 times. Each time he uses it, he will get a 1 , 2 , 3 , 4 , or 5.What is the best prediction for the number of times that Leo will get an odd number?
Answer:
Close to 240 times but probably not exactly 240 times
Step-by-step explanation:
The sum of twice a number and four is fourteen. find the number.
2x +4 =14
2x =10
x =5
the number is 5
A total of 900 tickets were sold for a game for a total of $1,150. if adult tickets sold for $2.00 and children's tickets sold for $1.00, how many of each kind of ticket were sold?
If there are 365 days in a non-leap year, what number is christmas day?
What is the least common multiple of 50, 60, and 72?
The _____ ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.
The scale ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.
The ratio you're referring to is called the scale factor. The scale factor is the ratio of the length of one side of a polygon to the length of the corresponding side of a similar polygon. Let's denote this scale factor as ( k ).
To calculate the scale factor, you need to choose corresponding sides from the two similar polygons. Once you've chosen a pair of corresponding sides, divide the length of one side by the length of the corresponding side from the other polygon.
Let's say we have two similar polygons, Polygon A and Polygon B, and we want to find the scale factor between them. Let's denote the length of a side of Polygon A as [tex]\( L_A \)[/tex] and the length of the corresponding side of Polygon B as [tex]\( L_B \)[/tex]. Then, the scale factor, ( k ), is given by:
[tex]\[ k = \frac{L_A}{L_B} \][/tex]
This ratio will give you the scale factor between the two polygons.
the equation 5x+4y=20 represents a linear function in two variables. Identify the slope, x-intercept and y-intercept of this linear function
Assembly Line A produces 45 units in the same time that it takes Assembly Line B to produce 37 units. If Line B produces 555 units, how many units does Line A produce during the same time?
Assembly Line A will produce 24975 units during the same time that Line B produces 555 units.
Explanation:Let's assume that the time it takes for Assembly Line A to produce 45 units is equal to the time it takes for Assembly Line B to produce 37 units. This means that the time it takes for Line A to produce 1 unit is equal to the time it takes for Line B to produce 1 unit.
Now, we can set up a proportion to find how many units Line A will produce during the same time that Line B produces 555 units:
45 units / 1 unit = x units / 555 units
Cross-multiplying, we get:
45 * 555 = x units * 1
x units = 24975 units
Therefore, Line A will produce 24975 units during the same time that Line B produces 555 units.
solve for the variable r in this equation.
[tex] s=2 \pi rh[/tex]
Please and thanks! Also, it would help if you explained how you got your answer! (: ^-^
How do I solve for x within a triangle?
what is the value of the function f(x)=1/4x-3 when x=12
6
1
0
-6