Answer:
The product of its roots is 6.
Step-by-step explanation:
Let [tex]m\cdot x^{2}-(6\cdot m +1)\cdot x+(m^{3}+m^{2}+4) = 0[/tex], all roots are calculated by Quadratic Formula:
[tex]r_{1} = \frac{6\cdot m +1 + \sqrt{(6\cdot m + 1)^{2}-4\cdot m\cdot (m^{3}+m^{2}+4)}}{2\cdot m}[/tex] (1)
[tex]r_{2} = \frac{6\cdot m +1 - \sqrt{(6\cdot m + 1)^{2}-4\cdot m\cdot (m^{3}+m^{2}+4)}}{2\cdot m}[/tex] (2)
According to statement, we know that:
[tex]r_{1}+r_{2} = 7[/tex] (3)
By applying (1) and (2) in (3), we have the following expression:
[tex]\frac{6\cdot m +1}{m} = 7[/tex]
[tex]6\cdot m + 1 = 7\cdot m[/tex]
[tex]m = 1[/tex]
If we know that [tex]m = 1[/tex], then the roots of the polynomial are, respectively:
[tex]x^{2}-7\cdot x +6 = 0[/tex]
[tex]r_{1} = 6[/tex]
[tex]r_{2} = 1[/tex]
And the product of the roots is:
[tex]r_{1}\cdot r_{2} = 6[/tex]
The product of its roots is 6.
An antique car sold at auction for $50,000. Its value
appreciates by 10% each year. What is the value of
the car after six years?
Answer:
80,000
Step-by-step explanation:
A circular swimming pool has a radius of 20 feet. A fence is going to be built so that there is a 4-foot space around the entire pool. What is the length of the fence? Sunitha solved the problem as shown. A circle with radius 20 feet. A larger circle is 4 feet larger than the smaller circle. Radius = 24 feet. Circumference = 24 pi. What was her error? She should have used 12 in the formula, not 24. She forgot to multiply the radius by 2 in the formula. She did not add the additional fence length to the pool’s radius. She should have used 4 ft in the formula.
Answer:
she forgot to multiply the radius by 2 in the formula (B)
Step-by-step explanation:
i got it right :)
Answer:
B.
Step-by-step explanation:
What is 589 divided by 31 with remainder?
Answer:
19 remainder 0
Step-by-step explanation:
When we divide 589 by 31 we get remainder 0.
Here we have to find the remainder when 589 is divided by 31
In order to this proceed with division,
Since we know that,
When the numerator is equal to or more than the denominator, the fraction is said to be inappropriate. It always has a value of one or higher. Since mixed fractions are simpler to understand, improper fractions are typically expressed in simplified mixed number form.
Now
31 ) 589 ( 19
- 31
_________
279
- 279
__________
0
Hence remainder after division is 0.
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PLS HELP (MARKING BRAINLIEST)
Answer:
there is a fraction calculator you can use
https://www.calculatorsoup.com/calculators/math/fractions.php
Step-by-step explanation:
Two geometrically similar jugs have volumes of 1000 cm3and 512 cm3.They have circular bases. The diameter of the base of the larger jug is 9 cm.
Complete Question
Two geometrically similar jugs have volumes of 1000 cm³and 512 cm³.They have circular bases. The diameter of the base of the larger jug is 9 cm.
Calculate the diameter of the smaller jug.
Answer:
7.2 cm
Step-by-step explanation:
To solve the above question,we have the proportion
Smaller volume/ Larger volume = (Smaller diameter/ Larger diameter)³
We are to find the smaller diameter
Hence our formula is give as
Cube root(Smaller volume/ Larger volume)= Smaller diameter/ Larger diameter
=cube root( 512/1000) = x/9
= 8/10 = x/9
Cross Multiply
10x = 8 × 9
10x = 72
x = 72/10
x = 7.2cm
Therefore, the diameter of the second jug is 7.2 cm
Mrs. Humble is filling bags with peanuts to give as gifts. Each bag will contain 1 and 3 over 4 pounds of peanuts. The peanuts cost $5.00 per pound. How much will the peanuts in one bag cost?Mrs. Humble is filling bags with peanuts to give as gifts. Each bag will contain 1\frac{3}{4} pounds of peanuts. The peanuts cost $5.00 per pound. How much will the peanuts in one bag cost?
Answer:
$8.75
Step-by-step explanation:
STEP TO TAKE TO DETERMINE THE ANSWER
Multiply 13/4 pounds by the cost of one pound of peanut. To do this, convert 13/4 to an improper fraction and then multiply it by $5
[tex]1\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
[tex]\frac{7}{4}[/tex] × 5 = [tex]\frac{35}{4}[/tex] = [tex]8\frac{3}{4}[/tex] = $8.75
What type of real numbers are these.
Please help me NO LINKS ASAP will give Brainilest
Answer:
width x height x length=volume so 5 x 14 x 10= 700cm cubed. Volume=700cm^3
Step-by-step explanation:
please help ASAP... here is a question WRITE 894 290 000 IN SCIENTIFIC NOTATION
Answer:
hey there, the answer is 8.9429 × 10^8
Answer:
8.9429 × 10^8
Step-by-step explanation:
ya the answer is 8.9429 × 10^8
The distance between the points P(–7, 2) and Q(5, –3) is
A. 12 units
B. 13 units
C. 11 units
D. 10 units
Answer:
B. 13 units
Step-by-step explanation:
Hope this helps
1. If X+Y=7 and xy = 10 , then x3+ y3
Answer:
final answer is 21
Step-by-step explanation:
since x+y=7 and xy=10
2+5=7 and 2(5)=10
so,
(5)3=15
(2)3=6
15+6= 21
A car was purchased for $24,000. Its value is predicted to decay exponentially, decreasing by 13% each year. Write an equation to determine the value of the car.
Answer:
y= P(0.87)^t
Step-by-step explanation:
Given data
Price P= $24,000
Rate of decay in price= 13%
The expression in terms of y, p and t is
y=P(1-r)^t
y= P(1-0.13)t
y= P(0.87)^t
Find an equation for the line below
John ran 5,000 meters on Monday. He
ran 6 kilometers on Tuesday. How many
total kilometers did John run?
Answer:
11 kilometers
Step-by-step explanation:
Since there are 1,000 m in 1 km, John ran 5 km on Monday. Combine that with the 6 km he ran on Tuesday, and you get 11 km in total.
Answer:
11 kilometers
Step-by-step explanation:
1000 meters=1 kilometer
5000÷1000=5
5+6=11
The equation of the line through (3, - 4) with slope 2/3
which of the following decimal has highest value is a 0.5 b 0.12 c 0.17 d 0.8
Answer:
d 80 cents or 0.8
Step-by-step explanation:
Change them all to money. Then look at it again.
0.5 = 50 cents
0.12 = 12 cents
0.17 = 17 cents
0.8 = 80 cents.
You get each of them by starting with a dollar. A dollar has 100 cents.
So 0.5 of a dollar is 1/2 a dollar.
1/2 a dollar is 0.5 * 100 = 50 cents
0.17 * 100 = 17 cents
0.12 * 100 = 12 cents
0.8 * 100 = 80 cents
The largest one is 8
Answer d) 0.8
Step-by-step explanation: Here is a tip, when you see a decimal like 0.5 compared to a bigger looking one like 0.12 add a 0 to the end. It will still have the same value and you won't be as confused.
0.80> 0.50> 0.17> 0.12
The next math test will contain 50 questions. Some will be worth three points while the rest will be worth six points. If the test is worth 195 points, how many questions are worth three-points and how many worth six-points?
Explanation is in the file
tinyurl.com/wpazsebu
The no of three-pointer questions is 35 and the no of six-pointer questions is 15.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The total no of questions = 50,
The total marks in the test = 195.
According to the question, the equation will be,
3x + 6y = 195 and x + y = 50
Here, x is the no of three mark question and y is the no of six marks question.
Solve the equation by elimination method, and we get,
x = 35 and y = 15
Therefore, the no of three-pointer questions is 35 and the no of six-pointer questions is 15.
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What is the multiplier?
A. 0.1
B. 0.01
C. 10
D. 100
Answer:
c
Step-by-step explanation:
0.6*10=6
6*10=60
Answer:
B or A
Step-by-step explanation:
What is the sale price of $160 airpods with an 18% discount?
Answer:
$131.20
Step-by-step explanation:
$160 is the full price, so it is 100% of the full price.
With a discount of 18%, you pay 100% - 18% = 82% of the full price.
82% of $160 =
= 0.82 * $160
= $131.20
Answer: $131.20
Please help with B...
Answer:
B
Step-by-step explanation:
The table tells us that when x=-1, y=5. This shows in graph B because it passes through the point (-1,5). The table also tells us that the curve passes through the origin, (0,0). Curve B is the only one that does.
I hope this helps!
help!
50 pts and brainiest
Answer:
303
Step-by-step explanation:
add all of them and you get 303, hope this helps :)
Answer:
Vertical. A vertical is an alignment in which the top is always above the bottom. It is a property of two or more points in which if a point is directly below the ...
Step-by-step explanation:
help i’ll give brainliest
Answer:
The 3rd one
Step-by-step explanation:
It's a translation. The rest are reflections.
Explain what it means for x and y to vary directly
Answer:
(Some textbooks describe direct variation by saying " y varies directly as x ", " y varies proportionally as x ", or " y is directly proportional to x . ") This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.
Help me plz 6th grade math
Answer: 66
Step-by-step explanation:
6+4^3-8÷2
4^3 = 64
6+64-8÷2
70-8÷2
70-4 = 66
Which side lengths form a right triangle?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
2
,
15
,
17
2,15,172, comma, 15, comma, 17
(Choice B)
B
1
,
8
,
65
1,8,
65
1, comma, 8, comma, square root of, 65, end square root
(Choice C)
C
2
,
80
,
9
2,
80
,92
Answer:
B
Step-by-step explanation:
could someone help me on this pleaseeee :)
Answer:
the slope is 1, y-intercept is (0,5) hope this helps!
Step-by-step explanation:
Given the definitions of f(x) and g(x) below, find the value of g(f(5)).
f(x) = 2x – 10
g(x) = x^2 + 6x – 8
I don’t need work I am just looking for the answer !
gf(x) = g(x^-1) = x^2 + 6x - 8
f(x) = 2x - 10
gf(x) = 6 ( 2x - 10) - 8
gf(x) = 12x- 60 - 8
gf(x) = 12x -68
gf(5) = gf(x) = 12x - 68
gf(5) = 12(5) - 68
gf(5) = 60 - 68
gf(5) = -8
Bernie can eat 20 oreos in 5 minutes. If Joe can eat oreos at 3/4
of Bernie’s pace, how many oreos can they eat together in half an hour?
a.200
b. 210
c. 220
d. 230
Answer:
b
Step-by-step explanation:
Pls help me with this
Answer ASAP pls pls ASAP
Answer:
it 5
Step-by-step explanation:
15-10= 5 so r=5
Answer:
The value of r will be 5.
Step-by-step explanation:
15=r+10
15-10=r
5=r