Answers
Answer:
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Step-by-step explanation:
If we simplify that fraction, we get
[tex] \frac{ \alpha + \beta + \gamma }{ \alpha \beta \gamma } [/tex]
Keep that in mind.
If y, a ,b are zeroes of the cubic polynomial, then that means
[tex](x - \alpha )(x - \beta )(x - \gamma )[/tex]
make up the polynomial.
Notice that leading xoeffeicent will be 1, so the roots will multiply to
[tex] - d[/tex]
so
[tex] \alpha \beta \gamma = - d[/tex]
which gives us
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Proof:
Consider the function
[tex](x - 2)(x - 3)(x - 5)[/tex]
The roots are 2, 3, 5.
D is -30 so we get
Using the value,
[tex] \frac{2 + 3 + 5}{ 30} = \frac{1}{3} [/tex]
If we use the orginal equation, we get
[tex] \frac{1}{6} + \frac{1}{10} + \frac{1}{15} = \frac{10}{30} = \frac{1}{3} [/tex]
Answer:
Hey,mate
Notice that leading xoeffeicent will be 1, so the roots will multiply to
The roots are 2, 3, 5.
[tex]\sqrt{2} \sqrt{3} \sqrt{5}[/tex]
D is -30
Related Questions
The following scatter plot represents the relationship between a person's weight and the number of calories the person burns in one minute of jump roping. Using the line of best fit, about how many calories per minute could you expect a 100-pound person to burn while jump roping?
a. 6
b. 8
c. 7
d. 6.5
Please answer!
Answers
Answer:
b. 8
Step-by-step explanation:
the point asked has coordinates (100;8) (weight;calories)
let l be the line through A(4,-3) and B(t,-2) that is parallel to the line through P(-2,4) and Q(4,-1) find the value of t
Answers
Answer:
t = [tex]\frac{14}{5}[/tex]
Step-by-step explanation:
Parallel lines have equal slopes.
calculate the slope m of PQ and then equate the slope of AB to slope of PQ
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = P (- 2, 4 ) and (x₂, y₂ ) = Q (4, - 1 )
[tex]m_{PQ}[/tex] = [tex]\frac{-1-4}{4-(-2)}[/tex] = [tex]\frac{-5}{4+2}[/tex] = - [tex]\frac{5}{6}[/tex]
now calculate slope of AB
with (x₁, y₁ ) = A (4, - 3 ) and (x₂, y₂ ) = B (t, - 2 )
[tex]m_{AB}[/tex] = [tex]\frac{-2-(-3)}{t-4}[/tex] = [tex]\frac{-2+3}{t-4}[/tex] = [tex]\frac{1}{t-4}[/tex]
equating the slopes gives
[tex]\frac{1}{t-4}[/tex] = - [tex]\frac{5}{6}[/tex] ( cross- multiply )
5(t - 4) = - 6
5t - 20 = - 6 ( add 20 to both sides )
5t = 14 ( divide both sides by 5 )
t = [tex]\frac{14}{5}[/tex]
What is 2+4(4x49=4+39(563x7=
Answers
Answer:
Step-by-step explanation:
2+4(4x49)=4+39(563x7)
2+4x196=4+39x3941
2+784=4+153699
786=153703
This equation is
not possible because
786≠153703
Find the area of the trapezoid shown below. {?} square feet
Answers
Answer:
432
Step-by-step explanation:
Convert 191% to a decimal.
Answers
The answer is 1.91
Answer:
1.91
Step-by-step explanation:
191% means [tex]\sf \frac{191}{100}[/tex]
So to write 191% as a decimal, simply divide it by 100.
To divide a number by 100, move the decimal point to the left by 2 places.
[tex]\sf \implies 191 \div 100=1.91[/tex]
What is the range of this relation?
Answers
Answer:
{- 1, 0, 4 }
Step-by-step explanation:
the range is the y- coordinates of the plotted points
the coordinates of the points are
(- 4, - 1 ) , (1, 0 ) , (1, 4 ) with y- coordinates - 1, 0, 4
then range is { - 1, 0, 4 }
Which set of directions correctly describes how to plot the point (5, 7) on the coordinate plane?
1) Start at the origin. Move 5 units up, then move 7 units to the right.
2)Start at the origin. Move 5 units up, then move 7 units to the left.
3)Start at the origin. Move 5 units to the right, then move 7 units up.
4)Start at the origin. Move 5 units to the left, then move 7 units up.
Answers
Answer:3
Step-by-step explanation:
Which inequality is shown in the graph?
Answers
Answer:
Step-by-step explanation:
A square with side length s has an area of 324 square centimeters. This equation shows the area of the square ^{s^2}is 324
Answers
Answer:
the side s is 18
Step-by-step explanation:
s=?
Area of square(A)=324
Now,
A=s²
324=s²
√(324)=s
s=18
Tamara attends a cycling class that starts at 6:00. The class lasts 45 minutes. What time does class end?
Answers
Answer:
6:45
Step-by-step explanation: add 45 min to 6:00 and you have your answer
Answer:6:45
Step-by-step explanation: 6:00 + 45minutes would be 6:45
The following structure is composed of three right rectangular prisms: two that each measure 12 inches by 10 inches by 5 inches and one right rectangular prism that measures 10 inches by 8 inches by 36 inches. What is the total volume of the structure? Show your work and/or explain your reasoning..
Answers
The volume of the stucture made from three rectangular prism is 4080 ft³
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
The volume of the rectangular prism = length * width * height = 12 * 10 * 5 = 600 ft³
The volume of the other prism = length * width * height = 10 * 8 * 36 = 2880 ft³
Volume of the structure = 600 ft³ + 600 ft³ + 2880 ft³ = 4080 ft³
The volume of the stucture made from three rectangular prism is 4080 ft³
Find out more on volume at: https://brainly.com/question/12410983
Candice has already taken 5 pictures at home, and she expects to take 1 picture during every day of vacation. How many days will Candice have to spend on vacation before she will have taken 7 pictures?
Answers
Answer:
2 days.
Step-by-step explanation:
Candice has already taken 5 pictures total, so if she needs to have seven in total she will only have to go on vacation for two days.
a. Find the slope of the line that passes through these points.
The slope is
(Type an integer or a simplified fraction.)
b. Is the slope between (1,4) And (3,12) the same as the slope between (3,12) and (4,16)?
Explain.
O A. Yes. Both slopes are equal to
(Type an integer or a simplified fraction.)
O B. No. The slope between (1,4) and (3,12) is equal to (4,16)
. The slope between (3,12) and
th
Answers
slope formula : [tex]\bold{ \sf \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
a. coordinates : (3,12) and (4,16)
[tex]\sf \rightarrow \dfrac{16-12}{4-3}[/tex]
[tex]\sf \rightarrow \dfrac{4}{1}[/tex]
[tex]\sf \rightarrow 4[/tex]
b. coordinates : (1,4) and (3,12)
[tex]\sf \rightarrow \dfrac{12-4}{3-1}[/tex]
[tex]\sf \rightarrow \dfrac{8}{2}[/tex]
[tex]\sf \rightarrow 4[/tex]
⇒ A. Yes. Both slopes are equal to 4
The graph of $y = f(x)$ is symmetric across the line $x = 5$. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$
Answers
Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.
Which other point must lie on the graph?If a function has a line of symmetry at x = x₀, then we know that:
f(x₀ + x) = f(x₀ - x).
So we have symmetry around that line.
Then, if the line of symmetry is at x = 5 and we know that:
f(8) = f(5 + 3) = -7
We also must have:
f(2) = f(5 - 3) = -7
Then the point (2, - 7) must be on the graph.
If you want to learn more about symmetry you can read:
https://brainly.com/question/11408596
2 Which set of side lengths will form a triangle?
16 ft, 4 ft, 21 ft.
6 30 ft, 30 ft, 60 ft
12 ft, 12 ft, 20 ft
3ft, 5 ft, 10 ft
Answers
None of the above. To form a standard triangle, all 3 sides must be of equal length.
simplify 35x-35
over 14x-49
Answers
Answer: Distributive property a(b+c) = ab + ac
-5(7)x + 7(7) = -35x + 49 (D)
the following shape has 1 pair of parallel sides 2, 7, 3, 8
Answers
Answer:
I think it's 8
Step-by-step explanation:
because if you think of an octagon it has eight sides and the only parallel sides is pn the top of the octagon and the bottom of the octagon
PLS HELP ME FRENDS I NEED HELP HELP THIS IS MY LAST CHANCE What is the area of the real object that the scale drawing models?
Answers
Answer:
D. 16 square cm
Step-by-step explanation:
To solve this problem, we will have to look at the Scale factor.
1 : 8 = 1 cm (in the scale drawing) = 8cm (in the real object)
Since the area of the scale drawing is 2 cm, the equation will be 2 x 8 = 16.
Therefore, 16 will be the area of the real object.
-kiniwih426
Math need help asap ty po sa makaka sagot
Answers
please see analysis
Step-by-step explanation:[tex]\left\{\right.{ \triangle}\ RST\cong { \triangle}\ DE[/tex]F
[tex](SSS\ Congruence\ Postulate)[/tex]
[tex]2.\ { \triangle\ CAT\cong { \triangle\ BED\ \left\{\right.Given\left.\ \right\}[/tex]
[tex]\bar{AT}\cong\bar{ED}[/tex]
[tex]\overline{AT}=20[/tex]
[tex]so\ \overline{ED}=20[/tex]
[tex]DE=3x-7=20\rightarrow\ x=9[/tex]
I hope this helps you:)
solve 2-6(1-x)=6-4(-x-2) for x
Answers
Answer:
x = 9
Step-by-step explanation:
Simplifying
2 + -6(1 + -1x) = 6 + -4(-1x + -2)
2 + (1 * -6 + -1x * -6) = 6 + -4(-1x + -2)
2 + (-6 + 6x) = 6 + -4(-1x + -2)
Combine like terms: 2 + -6 = -4
-4 + 6x = 6 + -4(-1x + -2)
Reorder the terms:
-4 + 6x = 6 + -4(-2 + -1x)
-4 + 6x = 6 + (-2 * -4 + -1x * -4)
-4 + 6x = 6 + (8 + 4x)
Combine like terms: 6 + 8 = 14
-4 + 6x = 14 + 4x
Solving
-4 + 6x = 14 + 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
-4 + 6x + -4x = 14 + 4x + -4x
Combine like terms: 6x + -4x = 2x
-4 + 2x = 14 + 4x + -4x
Combine like terms: 4x + -4x = 0
-4 + 2x = 14 + 0
-4 + 2x = 14
Add '4' to each side of the equation.
-4 + 4 + 2x = 14 + 4
Combine like terms: -4 + 4 = 0
0 + 2x = 14 + 4
2x = 14 + 4
Combine like terms: 14 + 4 = 18
2x = 18
Divide each side by '2'.
x = 9
Simplifying
x = 9
B^2-7b-8 (b=-4) evaluate the expression
Answers
Answer:
4
Step-by-step explanation:
Is the function in this table linear or nonlinear and why?
Answers
A figure is made up of a triangle and a rectangle. The triangle has a height of 8 inches and a base of 9 inches. The rectangle has dimensions of 7 inches×9 inches. What is the area of the figure?
Answers
Step-by-step explanation:
area of triangles
1/2*9*8= 36
area of.rectangle
8*9= 72
36+72=108 square inches
What is the solution to the linear equation? –12 3b – 1 = –5 – b b = –2 b = –1.5 b = 1.5 b = 2
Answers
The solution of the linear system is given by using an arithmetic operation. Then the value of b is 2.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The linear equation is given below.
–12 + 3b – 1 = –5 – b
The value of b will be given as
Add b both sides, we have
–12 + b + 3b – 1 = –5 – b + b
–13 + 4b = –5
Add 13 on both sides, we have
13 – 13 + 4b = – 5 + 13
4b = 8
Divide both sides by 4, we have
b = 2
More about the linear system link is given below.
https://brainly.com/question/20379472
Answer:
The fourth option, 2
who can answer? ill give brainlist
Answers
Answer:
2.23
Step-by-step explanation:
we get this by making the fraction a decimal and finding out the value of each section
How do u find an area of a cuboid?
Answers
Answer:
To find the surface area of a cuboid, add the areas of all 6 faces.
Which number of degrees is the measure of the angle? explain how you know.
Answers
Can you please show me what angle?
n the past you paid $800 per month to rent your apartment. You now pay $900 per month for your rent. What is the percent increase in your rent?
Answers
Answer:
12.5%
Step-by-step explanation:
900 - 800 = 100
Gotta pay $100 more
100 / 800 = 0.125
PLEASE HELP I DONT UNDERSTAND IVE BEEN TRYING FOR 15 MINS AND STILL DONT GET IT
Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale. (picture of diagram included)
Answers
The values of the length of the missing sides of triangle is x = 7√2 and y = 7.
What are special triangles?Special right triangles are right triangles with three determined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°-90° triangle and the 30°- 60°-90° triangle are other names for the two unique right triangles. Before going further, let's review the fundamental characteristics of a right triangle.
One of the angles of a right triangle is 90 degrees, and the total of the other two angles is also 90 degrees. The triangle's hypotenuse, which is the longest side, is the side that faces the right angle.
From the given figure we observe that the two angles are 45 degree and 90 degree.
Using the angle sum property we have:
45 + 90 + third angle = 180
third angle = 45 degrees.
The triangle is thus a 45-45-90 triangle.
The sides of 45-45-90 triangle correspond to the lengths as x : x : x√2.
Here, the angle corresponding to 45 is 7.
Thus, y = 7 and x = 7√2.
Hence, the values of the length of the missing sides of triangle is x = 7√2 and y = 7.
Learn more about triangles here:
https://brainly.com/question/2269348
#SPJ1
A teacher puts five packages of craft paper into a cabinet each package has 80 sheets of paper what is the total number of sheets of craft paper that the teacher put into the cabinet and wears a.40 b.85 c.400 d.450
Answers
Answer:
C
Step-by-step explanation:
If we have 5 packages and each contains 80, we are basically doing 80+80+80+80+80 (5 TIMES) which is referred to as 80×5=400
Answer:
1 package contain 80 sheets of paper.
If there is 5 packages, there will be 'x' sheets of paper.
We replace the sheets of paper with 'x', because the value of x is unknown.
Now we set up the equation:
Sheets 80 x__________ _________ = _________, solve for x;
Packages 1 580/1 = x/5
*5 *5
400 = x