Answers
Answer:
1) The factorized form of the polynomial is [tex](x-5)\cdot (x+2) = 0[/tex].
2) The factorized form of the polynomial is [tex](x+6)\cdot (x-4) = 0[/tex].
3) [tex]r_{1} = -3[/tex], [tex]r_{2} = -2[/tex]. (Option D)
4) [tex]r_{1} = -7[/tex], [tex]r_{2} = 5[/tex]. (Option A)
Step-by-step explanation:
All exercise are case of factorization of second grade polynomials of the form [tex]x^{2} +(-r_{1} - r_{2})\cdot x + r_{1}\cdot r_{2}[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the two roots of the polynomial. Now we proceed to solve each polynomial:
1) [tex]x^{2}-3\cdot x-10 = 0[/tex]
In this case, the coefficients have the following characteristics:
[tex]-r_{1}-r_{2} = -3[/tex]
[tex]r_{1}\cdot r_{2} = -10[/tex]
The solution of this system of nonlinear equations is: [tex]r_{1} = 5[/tex], [tex]r_{2} = -2[/tex].
Then, the factorized form of the polynomial is:
[tex](x-5)\cdot (x+2) = 0[/tex]
2) [tex]x^{2}+2\cdot x -24 = 0[/tex]
In this case, the coefficients have the following characteristics:
[tex]-r_{1}-r_{2} = 2[/tex]
[tex]r_{1}\cdot r_{2} = -24[/tex]
The solution of this system of nonlinear equations is: [tex]r_{1} = -6[/tex], [tex]r_{2} = 4[/tex].
Then, the factorized form of the polynomial is:
[tex](x+6)\cdot (x-4) = 0[/tex]
3) [tex]x^{2} + 5\cdot x +6 = 0[/tex]
In this case, the coefficients have the following characteristics:
[tex]-r_{1}-r_{2} = 5[/tex]
[tex]r_{1}\cdot r_{2} = 6[/tex]
The solution of this system of nonlinear equations is: [tex]r_{1} = -3[/tex], [tex]r_{2} = -2[/tex].
Hence, the correct answer is D.
4) [tex]x^{2}+2\cdot x -35 = 0[/tex]
In this case, the coefficients have the following characteristics:
[tex]-r_{1}-r_{2} = 2[/tex]
[tex]r_{1}\cdot r_{2} = -35[/tex]
The solution of this system of nonlinear equations is: [tex]r_{1} = -7[/tex], [tex]r_{2} = 5[/tex].
Hence, the correct answer is A.
Related Questions
• How can the product of two whole numbers (e.g., 48
and 19) help us find the product of two decimals with
the same digits (e.g., 0.048 and 1.9)? Write your
explanation in the text box.
Answers
Let's say we already did the work and found the result of 48*19. That result is 912.
When it comes to multiplying 0.048 and 1.9, we're going to need to do two things to transform those numbers into 48 and 19.
Move the decimal point of 0.048 exactly three spaces to the right. This is the same as multiplying by 1000. So 1000*0.048 = 48
Move the decimal point of 1.9 exactly one space to the right. This is the same as multiplying by 10. So 10*1.9 = 19
Overall, we've multiplied by 1000*10 = 10,000. This means 48*19 = 912 is 10,000 times larger compared to the result of 0.048*1.9
To fix this, we need to divide by 10,000 to get 912/(10,000) = 0.0912
Dividing by 10,000 is the same as moving the decimal point to the left four spaces. Note how 10,000 = 10^4.
I recommend using your calculator to see that 0.048*1.9 = 0.0912 which matches with the previous result we got.
3y + 1 = 4y - 6 Please solve!
Answers
Answer:
y = 7
Step-by-step explanation:
3y + 1 = 4y - 6
-3y -3y
1 = y - 6
+6 +6
7 = y
Answer:
7 = y
3y + 1 = 4y - 6
-3y. -3y
------------------
1 = 1y - 6
+6 +6
------------------
7 = y
Please someone help me with this question
Answers
Answer:
Where's the question?
Which is the value of y in the solution of this system of linear equations? −10x+4y=46 6x=−18
A. y=−4
B. y=−3
C. y=4
D. y=19
Answers
it’s C i took a benchmark and the answer was c
plz anwser this plzzzzzzzzzzzzzzzzzz
Answers
Answer:1st one
Step-by-step explanation: the pointy side of the inequality sign will always lead u to draw the line to that side if u understand what i mean
Answer:
It's the first choice
Step-by-step explanation:
..................................
The force, F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them.
The force is 0.006 Newtons when the distance between the objects is 4 metres.
Work out d (rounded to 2 DP) when F=0.045 Newtons.
Answers
Answer:
d = 1.46 m
Step-by-step explanation:
We'll begin by obtaining the relationship between the force (F) and the distance (d). This can be obtained as follow:
From the question given above,
F is inversely proportional to square of d. This can be written as:
F ∝ 1/d²
F = K/d²
Cross multiply
K = Fd²
But:
Force (F) = 0.006 N
Distance (d) = 4 m
Constant (K) =?
K = Fd²
K = 0.006 × 4²
K = 0.006 × 16
K = 0.096 Nm²
Therefore, the relationship between the force (F) and the distance (d) is:
F = K/d²
F = 0.096 / d²
Finally, we shall determine the distance when the force is 0.045 N. This can be obtained as follow:
Force (F) = 0.045 N
Constant (K) = 0.096 Nm²
Distance (d) =?
F = K/d²
0.045 = 0.096 / d²
Cross multiply
0.045 × d² = 0.096
Divide both side by 0.045
d² = 0.096 / 0.045
Take the square root of both side.
d = √(0.096 / 0.045)
d = 1.46 m.
Find the zeros of the function.
Enter the solutions from least to greatest.
f(x) = 5x^2 - 20
lesser x =
greater x =
Answers
Answer:
lesser x = -2
greater x = 2
Step-by-step explanation:
The values of a function f(x) are the values of x for which f(x) = 0.
In this question:
[tex]f(x) = 5x^2 - 20[/tex]
So, finding the zeros:
[tex]5x^2 - 20 = 0[/tex]
[tex]5x^2 = 20[/tex]
[tex]x^2 = \frac{20}{5}[/tex]
[tex]x^2 = 4[/tex]
[tex]x = \pm \sqrt{4}[/tex]
[tex]x = \pm 2[/tex]
So
lesser x = -2
greater x = 2
Alfonso has 435 stamps in his collection. He wants to collect at least
815 stamps. Write and solve an inequality to determine how many
more stamps Alfonso must collect to reach his goal. Let d represent the
number of stamps Alfonso must collect to reach his goal.
435 + d-815; d-380
435 + > 815;d > 380
435 + d 2815;d > 815
435 +0 2 815; d 2380
Answers
Answer:
Inequality: [tex]435 + d \geq 815[/tex]
Solution: [tex]d \geq 380[/tex]
Step-by-step explanation:
He has 435 stamps in his collections.
He will collect d stamps, and he wants to collect at least 815 stamps, that is, the sum of 435 and d has to be at least 815.
So the inequality is given by:
[tex]435 + d \geq 815[/tex]
And the answer is given by:
[tex]d \geq 815 - 435[/tex]
[tex]d \geq 380[/tex]
Mrs. Harris divided up her leftover Halloween candy to her three children. If each child received 9 pieces of candy, how many pieces of candy did Mrs. Harris originally have?
I will give brainliest!
Answers
I.
What similarity condition would you use to prove that the triangles
are similar?
H
68
87
25
E
870
AA~
SAS
SSS-
Answers
Answer:
AA
Step-by-step explanation:
There are 20 pieces of fruit in a bowl and 5 of them are apples. What percentage of the pieces of fruit in the bowl are apples?
A. 5%
B.15%
C.25%
D.30%
Answers
Answer:
25%
Step-by-step explanation:
5/20 = 1/4 = 25%
PLEASE HELP WILL MARK BRAINLIEST!!!!!
Answers
The numbers inside the parenthesis is the value of x, uses the equation associated with the value of x and solve.
H(1) Since 1 fits 1≤x≤3 use x^3
x^3 1^3 = 1
h(1) = 1
h(4) 4 fits x >3, so use 5
h(4) = 5
A pitcher of Kool-Aid uses one packet of flavoring, 1 cup sugar, and 8 cups of water. 1 cup of sugar = 200 grams. If the pitcher of Kool-Aid was divided into 8 glasses, How many grams of sugar are there per glass?
A. 25
B. 50
C. 3 25/5
D. 3
E. 22
Answers
Answer:
A.
Step-by-step explanation:
200/8=25
Answer:
A. 25 grams
Step-by-step explanation:
I that answer by counting by 25s, 8 times
Hope this Helps! :)
i giveeeeee brainlilstt
Answers
Answer:
H. 16 ft
Step-by-step explanation:
15/ 24 = 5/8
10 / 5 =2
2x8 = 16
Answer:
the length of x is option H. x=16
i givee brainlilsttt
Answers
Answer:
( 2, 1 )
Step-by-step explanation:
x remains the same and y coordinate changes signs
Answer:
(2, -1)
Step-by-step explanation:
X=going to the right=Positive
Y=going down=Negative
X=(2)
Y=(-1)
Hope this helps
Q = (2,-1)
Help me please I’m struggling
Answers
If you plotted another point at 2 hours it would no longer be a function bc 2 would be an input they had more than one output.
what is 2(3+6) - 4......................
Answers
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
You have to use PEMDAS, so first you do the parentheses, (3+6)=9. Then you multiply 2 times 9=18. The last step is to subtract 4, so 18-4=14
(hope this helps!)
Can someone explain me on how to do these step by step
Answers
Answer: 46 miles per hour.
Step-by-step explanation: Just divide distance by time (in this case 690/15) and you get the velocity (46 mph).
Please answer this correctly without making mistakes
Answers
Answer:
3 ft 1 in
Step-by-step explanation:
As 12 in= 1 ft,
So, 3 in+ 10 in= 1 ft 1 in
Total= 2 ft + 1ft 1 in
= 3 ft 1 in
For what value of x is the rational expression below equal to zero?
X-4
X5
A. -6
B. -4
C. 6
D. 4
Answers
Help me please and thanks!
Answers
Answer:
1. B
2. A
Step-by-step explanation:
1. Because there are 9 zeros.
2.
4096 bytes = 1 page
(8 * 10^9) / 4096 = closet answer is A
Are these fractions equivalent to 4/9?
20/36
8/18
24/45
12/27
Answers
Answer:
No
Step-by-step explanation:
4/9 is not equvalent to 20/36
What is .24 as a whole number?
Answers
What is the equation of the line perpendicular to y = 1/2x + 3 passing through the point ( -3, 4)?
Answers
Answer:
y=-2x-2.
Step-by-step explanation:
m= -2 for perpendicular line
m= y2-y1/x2-x1
-2 = y-4/x+3
y=-2x-2
The random variable X has a uniform distribution with values between 16 and 24. What is the mean and standard deviation of X
Answers
Answer:
[tex]Mean = 20[/tex]
[tex]SD = 2.31[/tex]
Step-by-step explanation:
Given
[tex]a = 16[/tex]
[tex]b = 24[/tex]
Solving (a): The mean
The mean of a uniform distribution is:
[tex]Mean = \frac{1}{2}(a + b)[/tex]
This gives:
[tex]Mean = \frac{1}{2}(16 + 24)[/tex]
[tex]Mean = \frac{1}{2}(40)[/tex]
[tex]Mean = 20[/tex]
Solving (b): The standard deviation
The standard deviation is:
[tex]SD = \sqrt{\frac{(b - a)^2}{12}}[/tex]
This gives:
[tex]SD = \sqrt{\frac{(24 - 16)^2}{12}}[/tex]
[tex]SD = \sqrt{\frac{(8)^2}{12}}[/tex]
[tex]SD = \sqrt{\frac{64}{12}}[/tex]
[tex]SD = \sqrt{5.333}[/tex]
[tex]SD = 2.31[/tex]
I GIVEEE BRAINLILSTT
Answers
U(10,-10)
V(-5,5)
Answer:
vb b ccbbv bv
Step-by-step explanation:
vb vb vb vb vbvbncv
Pls help me this is due today I’ll brainlest for the right answer
Answers
Answer:
8.67 dollars per ft squared
Step-by-step explanation:
This is a fraction equal to
130 dollars ÷ 15 ft squared
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 15
130 dollars ÷ 15
15 ft squared ÷ 15
=
8.67 dollars
1 ft squared
=
8.67 dollars
ft squared
= 8.67 dollars per ft squared
Answer:
$8.67
Step-by-step explanation:
you have the the price for 15 square ft
and you are trying to get the price for 1 square ft
just divide the original price by 15
here's the equation format
130 = 15 x
solve for x
Can someone solve this pls
Answers
It isnt blurry, free brainlist
Answers
Answer:
10. y=3x-1
11. y=-4x+3
12. y=1/3x+4
Step-by-step explanation:
Hope this helps :)
Answer:
Answer:
you said you needed 22,23
22. y=7x-6
23. y=-x
Step-by-step explanation:
use math-way to put in the points
it explains for you
Step-by-step explanation:
A child stands at the foot of a tall slide and throws a ball toward the top of the slide. The foot of
the slide is located at the origin; the shape of the slide is modeled by the equation y = 2x; the
path of the ball through the air is modeled by y *? + 5x, where x is the horizontal distance
traveled by the ball and y is the height of the ball (both distances in feet). When the ball hits the
slide, how many feet off the ground will it be?
Your answer
Answers
Answer: 6, 6 feet
Step-by-step explanation:
