Mathematics High School

Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Look at image for reference

Answers

Answer 1

Answer:

(3)11

Step-by-step explanation:

We are given that

[tex](x^2-12x+35)(x^2+10x+24)=504[/tex]

We have to find the sum of positive roots of the equation.

[tex]x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504[/tex]

[tex]x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504[/tex]

[tex]x^4-2x^3-61x^2+62x+840-504=0[/tex]

[tex]x^4-2x^3-61x^2+62x+336=0[/tex]

Factor of 336

2,3,4,6,8,7,

Let x=2

[tex]2^4-2^4-61(2^2)+62(2)+336\neq0[/tex]

x=2 is not the root of equation

x=-2

[tex](-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0[/tex]

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

[tex]3^4-2(3^3)-61(3^2)+62(3)+336=0[/tex]

Therefore, x=3 is the root of equation.

[tex](x+2)(x-3)(x^2-x-56)=0[/tex]

[tex](x+2)(x-3)(x^2-8x+7x-56)=0[/tex]

[tex](x+2)(x-3)(x(x-8)+7(x-8))=0[/tex]

[tex](x+2)(x-3)(x-8)(x+7)=0[/tex]

[tex]x-8=0\implies x=8[/tex]

[tex]x+7=0\implies x=-7[/tex]

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

Related Questions

I need to find angle BAC

Answers

Answer:

m<BAC = 60°

Step-by-step explanation:

Theorem:

In a triangle, the measure of an exterior angle equals the sum of the measures of its remote interior angles.

m<ACD = m<A + m<B

130° = m<A + 70°

m<A = 60°

m<BAC = 60°

What is the missing reason for the 3rd
step in the proof below?

Answers

Answer:

Multiplication property of the equality

The access code for a security system has five numbers. How many different codes are
there if repetition is allowed but the first and second numbers have to be less than four-
and - the third, fourth, and fifth numbers each have to be greater than 4?

Answers

Answer:

pretty sure it's just 9

Step-by-step explanation:

Let's assume the possible numbers are 1,2,3,4,5

There are only 3 numbers less than 4 (1,2,3) which means that there are 3*3 possbiblities out of the two spots

There's only 1 number greater than 4 (5) which means the third, fourth, and fifth are just 5

which means the answer is just 9

A sea turtle can swim 13 kilometers in 5 hours at this rate speed how far can it travel in 9 hours

Answers

Answer:

23.4 km

Step-by-step explanation:

We can use a ratio to solve

13 km x km

-------- = ---------------

5 hours 9 hours

Using cross products

13*9 = 5x

117 = 5x

Divide each side by 5

117/5 = 5x/5

23.4 =x

Answer:

It travel 23.4 km in 9 hours.

Step-by-step explanation:

Given :-

A sea turtle can swim 13 km in 5 hours at this rate speed .

To find :-

How far can it travel in 9 hours.

Solution :-

Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.

Let us assume that In 9 hours turtle swim x km.

Now, We solve by using ratio for x.

In 5 hours it swim = 13 km

And, In 9 hours it swim = x km

Calculate for x

5 hours = 13 km

9 hours = x km

Use cross multiplication method , we get

5 × x = 9 × 13

5x = 117

Divide both side by 5

5x / 5 = 117 / 5

x = 23.4

Hence, It can travel 23.4 km in 9 hours.

Which expressions are equivalent to the one below? Check all that apply.
7*3.7^x
A. 73-*
B. 493x
C. 343.7
D. (7.7)3
E. 73x
F. 73 + x

Answers

Answer: ur answer is correct ❤️

Step-by-step explanation:

You and your friend are playing a game by tosing two coins land on different sides your friend wins the table shows the possible outcome? Is this a fair game

Answers

Your question is marked strangely because we don’t know what he wants. The chances with two coin tosses are TT, TH,HT, and HH. This would mean if he is wanting. Tails, it is a 50/50 (1/2) chance of winning the toss. The game is fair because there was a chance you could have won.

The sum of the angles of all the sectors in a pie chart should add up to ???

a). 180⁰
b). 90⁰
c). 360⁰

Answer me please ...

Answers

Answer:

Step-by-step explanation:

Since the sectors all meet at the centre of the circle, then

The angles around a point sum to 360° → A

90°... See More

https//90°.com

Find the value please!!!

Answers

the answer is in the picture

5) Simplify the 1. (50x²+20xy)divide (-5x)

Answers

Answer:

-10x-4y

Step-by-step explanation:

Explanation is in the attachment

your answer will be 10x(1+2y)

hope it is helpful to you ☺️

Prove that the value of the expression: (3^5 - 3^4)(3^3 + 3^2) is divisible by 24. Answer format: The value of the expression is 24 • __

Answers

Step-by-step explanation:

(3^5 - 3^4) (3^3 + 3^2)

= (243 - 81) (27 + 9)

= (162) (36)

= 5832

24 = 8*3

since 832 is divisible by 8 and 5+8+3+2 = 18 is divisible by 3

5832 is therefore divisible by 24

check:

5832/24 = 243

a watch was bought for RS 4444. at what price should it be sould to gain rs444?

Answers

Answer:

Rs4000

Step-by-step explanation:

Given data

Step one

Selling price =RS 4444

Gain =rs444

Cost price =???

We want to find the cost price

Cost price =selling price - gain

Cost =4444-444

Cost=Rs4000

As an estimation we are told 5 miles is 8 km. Convert 17.8 km to miles.

Answers

Answer:

17.8km = 11.125 miles

Step-by-step explanation:

From 5 miles = 8km, we can form the ratio km:miles as 8 : 5.

We want to put the ratio in the form 1 : n, which gives us 1 : 0.625 (we divide both 8 and 5 by 8 to get this form).

Now, using the ratio km:miles as 1:0.625, we have to multiply both 1 and 0.625 by 17.8 to gain the ratio 17.8 : n, therefore giving us the ratio 17.8 : 11.125.

Hence, 17.8km = 11.125 miles

Answer:

11.125 miles

Step-by-step explanation:

Proportions:

5 miles ⇒ 8 km

A miles ⇒ 17.8 km

A = 17.8km*5miles/8miles

A = 11.125 miles

Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right

Answers

Since the shape won’t change. It won’t deform, nothing will happen to the interior angle.

So the interior angle would still be 135

Which of the ratios below is equivalent to 8:5? Select all that apply.

A) 12:9
B) 24:15
C) 40:25
D) 20:32
E) 16:10

Answers

Step-by-step explanation:

The answer is B 24:15,divide both by 3 and check out the answers

in a quadrilateral abcd the bisector of angle c and angle d meet at e. if angle a =70°and b=100°,find the measure of angle ced

Answers

Answer:

Step-by-step explanation:

Let CE and DE be the bisectors of ∠C and ∠D respectively. Then, ∠1 = 1/2∠C and ∠2 = 1/2∠D

In △DEC, we have

→ ∠1 + ∠2 + ∠CED = 180° [Sum of angles of a triangle]

→ ∠CED = 180° - (∠1 + ∠2). .....(i)

Again, the sum od the angles of a quadrilateral is 360°.

∴ ∠A + ∠B + ∠C + ∠D = 360°

→1/2(∠A + ∠B) + 1/2∠C + 1/2∠D = 180°

→1/2(∠A + ∠B) + ∠1+ ∠2 = 180°

→1/2(∠A + ∠B) = 180° - (∠1+ ∠2)....(ii)

From (i) and (ii), we get 1/2(∠A + ∠B) = ∠CED

Hence, ∠A + ∠B = 2∠CED

How many subsets can be formed from the set F?

Answers

Answer:

Step-by-step explanation:

I'm very confirm with my answer mark me as brainliest plsssss

SOMEONE HELP ME !!!

The side length of a smaller square is one-third the side length of a larger square.ee
the following statements describes the area of the smaller square?
F The area of the smaller square is I the area of the larger square.
27
G The area of the smaller square is 172 the area of the larger square.
H The area of the smaller square is the area of the larger square.
1 The area of the smaller square is
the area of the larger square,
3
1 / 2
SOMEONE HELP ME !!!

Answers

Answer:

Step-by-step explanation:

lets say the first big square has side s, so the area will be s²

then the side of the small square is s/3, and the area is (s/3)²= s²/3² =s²/9

the area of the smaller square is 1/9 smaller than the area of the big square

Mark and John share the cost of a birthday gift. The cost of the gift is $20.48. Mark pays for 2/3 of the gift and John pays for the remaining 1/3. How much did each boy pay?

Answers

Given:

Cost of gift = $20.48

Mark pays for [tex]\dfrac{2}{3}[/tex] of the gift and John pays for the remaining [tex]\dfrac{1}{3}[/tex].

To find:

The amount paid by each boy.

Solution:

We have,

Cost of gift = $20.48

Mark pays for [tex]\dfrac{2}{3}[/tex] of the gift. So, the amount paid by Mark is:

[tex]20.48\times \dfrac{2}{3}\approx 13.653[/tex]

John pays for the remaining [tex]\dfrac{1}{3}[/tex]. So, the amount paid by John is:

[tex]20.48\times \dfrac{1}{3}\approx 6.827[/tex]

Therefore, the amount paid by Mark and John are $13.653 and $6.827 respectively.

pplied for a job as a cashier at a hardware store. As part of her employment screening, she was asked to take an exam that had general mathematical aptitude questions in it. This type of selection test is referred to as a

Answers

Answer:

cognitive ability

Step-by-step explanation:

Find the measure of the indicated angle to the nearest degree.
1)

A) 19°
C) 36°
B) 43°
D) 47°

Answers

Answer:

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan? = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{17}[/tex] , then

? = [tex]tan^{-1}[/tex] ([tex]\frac{18}{17}[/tex] ) ≈ 47° ( to the nearest degree )

Integrate with respect to x

1/√(1-2x)

Answers

Answer:

-√(1 - 2x) + C

Step-by-step explanation:

1/√(1-2x)

We want to integrate it. Thus;

∫1/√(1 - 2x) dx

Let u = 1 - 2x

Thus;

du/dx = -2

Thus, dx = -½du

Thus,we now have;

-½∫1/√(u) du

By application of power rule, we will now have;

-½∫1/√(u) du = -√(u) + C

Plugging in the value of u, we will have;

-√(1 - 2x) + C

1. Ten students in Silverton J.H.S. took 9 days to weed the school compound. How long would 15 students take to weed the compound if they worked at the same rate?

Answers

Answer:

6 days

Step-by-step explanation:

No. of students | No. of days

10 | 9

15 | [tex]\frac{10}{15}[/tex] × 9 = 6

Since the number of students and the number of days is inversely proportionate (when one increases by a certain extent, the other decreases by the same extent), we can calculate the number of days by multiplying the number of days by the fraction of the number of students proportionate to the number of days and the number of students you want to find the number of days for.

It would take 6 days.

Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 EndFraction cups from the first orange, StartFraction 3 over 10 EndFraction cups from the second orange, StartFraction 9 over 20 EndFraction cups from the third orange, StartFraction 3 over 11 EndFraction cups from the fourth orange, and StartFraction 7 over 15 EndFraction cups from the fifth orange. Patel estimates that he needs 3 cups of orange juice for his family. About how much more orange juice does he need to reach his estimate?

Answers

Answer:A

Step-by-step explanation:this is not true

Answer:

It A

Step-by-step explanation:

I had the question hope this helps!!!!!

Solve the inequality.

–13.4 ≥ 6.7 + 4.3 + w

–24.4 ≥ w

24.4 ≥ w

23.4 ≥ w

–23.4 ≥ w

Answers

Answer:

-24.4 ≥ w

Step-by-step explanation:

-13.4 ≥ 6.7 + 4.3 + w

-13.4 - 6.7 - 4.3 ≥ w

-24.4 ≥ w

To get a B in math, I must average 80 on 5 test. My scores on the 1st 4 test were 83, 75, 83, amd 78. What is the lowest score that I can get on the last test to still get a B?

Answers

Answer81 is the lowest you can get on the last test and still get a B.

Step-by-step explanation:I used the mean average and guess and check.

Answer:

83+ 75+ 83+ 78=319

319 divided by 4=79.75 so a high c

83+ 75+ 83+ 78+80=399

399 divided by 5=79.8 not quite

83+ 75+ 83+ 78+85=404

404 divided by 5=80.8

83+ 75+ 83+ 78+81=400

400 divided by 5=80

so you have to get a 80 to still get a b

Find the value of "x" Wrong answer will be reported and explain please

Answers

Answer:

x = 20

Step-by-step explanation:

The consecutive angles in a parallelogram are supplementary, sum to 180°

5x + 4x = 180

9x = 180 ( divide both sides by 9 )

x = 20

Answer:

The value of x is 40⁰.

Step-by-step explanation:

5x + 4x = 360⁰

DUE TO THE SUM OF QUADRATIC ANGLE.

Devaughn is 7 years older than Sydney. The sum of their ages is 95. What is Sydney's age?

Answers

Answer:

Step-by-step explanation:

Let's say that Devaughn's age is D, and Sydney's age is S.

We know that D is 7 greater than S, so D = 7 + S.

We know that the sum of their ages, or D + S, is equal to 95, so D+S = 95

We have

D = 7 + S

D + S = 95

What we can do is plug D= 7 + S into the second equation to get

D + S = 95

= (7+ S) + S

= 7 + 2 * S

7+2 * S - 95

subtract 7 from both sides to isolate the coefficient and the variable

2 * S = 88

divide both sides by 2 to isolate the variable

S = 44

Sydney is therefore 44 years old

Write each as a percent. Use proportions.
7/25
2/3
3/8

Answers

28%
66%
37.5%
thats the answer

Tyna simplified the expression 3x^3/12x^-2 to x/4. What was tyna’s mistake?

Answers

Answer:

She added the exponents instead of subtracting them.

Step-by-step explanation:

Triangle ABC has an Area of 4 3/8 square feet. If the length of AC IS 1 2/3 feet, what is the length of BC?

Answers

Answer:

length of BC = 5 1/4 feet

Step-by-step explanation:

Area of a triangle = 1/2×base×height

Area = 4 3/8 square feet

Base = AC= 1 2/3 feet

Height = BC = ?

Area of a triangle = 1/2×base×height

4 3/8 = 1/2 × 1 2/3 × height

35/8 = 1/2 × 5/3 × height

35/8 = 5/6 × height

Height = 35/8 ÷ 5/6

= 35/8 × 6/5

= (35 × 6) / (8 × 5)

= 210 / 40

= 5 1/4 feet

Height = BC = 5 1/4 feet

length of BC = 5 1/4 feet

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Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is Look at image for reference

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Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Look at image for reference