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Aloiza [94]
3 years ago
10

Let a, b, c, and d be non-zero real numbers. If the quadratic equation ax(cx + d) = -b(cx+d) is solved for x, which of the follo

wing is a possible ratio of the 2 solutions?
(1) -ab/cd(2) -ac/bd(3) -ad/bc(4) ab/cd(5) ad/bc
Mathematics
1 answer:
LiRa [457]3 years ago
4 0

Answer:

Option d

Step-by-step explanation:

given that a, b, c, and d be non-zero real numbers.

ax(cx + d) = -b(cx+d) \\acx^2+x(ad+bc)+bd =0

we can factorise this equation by grouping

(acx^2+xad)+)xbc+bd) =0\\ax(cx+d) +b(cx+d) =0\\(ax+b)(cx+d) =0

Equate each factor to 0 to get

x=\frac{-b}{a} , \frac{-d}{c}

Ratio of one solution to another would be

\frac{-b}{a} / \frac{-d}{c} \\=\frac{ad}{bc}

So ratio would be ad/bc

Out of the four options given, option d is equal to this

So option d is right

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F(n+1)=f(n)-8 if f(1)=100 what is f(6)
Svet_ta [14]

f(n+1)=f(n)-8\\\\ f(2)=100-8=92\\ f(3)=92-8=84\\ f(4)=84-8=76\\ f(5)=76-8=68\\ f(6)=68-8=60

8 0
3 years ago
bonnie runs 1 2/3 times as far as john each day if bonnie runs 5 miles on monday 3 1/2 miles on tuesday and 5 3/4 miles on wedne
nignag [31]

Answer:

3 miles on Monday

2¹/₁₀ miles on Tuesday

3⁹/₂₀ miles on Wednesday

Step-by-step explanation:

We are told that Bonnie runs 1⅔ (⁵/₃) times as far as John each day

This means that John runs ³/₅ times as far as Bonnie.

MONDAY:

Bonnie runs 5 miles on Monday, therefore, John runs:

³/₅ * 5 = 3 miles

TUESDAY:

Bonnie runs 3½ (⁷/₂) miles on Tuesday, therefore, John runs:

³/₅ * ⁷/₂ = ²¹/₁₀ = 2¹/₁₀ miles

WEDNESDAY:

Bonnie runs 5³/₄ (²³/₄) miles on Wednesday, therefore, John runs:

³/₅ * ²³/₄ = ⁶⁹/₂₀ = 3⁹/₂₀ miles

6 0
3 years ago
Find missing angle.
Vsevolod [243]
I don’t really know exactly to what degree you need to put in your solution. But I rounded to the nearest tenth degree.
A = 112 degrees
B= 28 degrees (180-112-40 bc all sides of a triangle must equal 180)
C= 40
a= 27.6 (this is the side opposite of angle A)
b= 14 (side opposite b)
c= 19.2 (side opposite c)

HOW TO SOLVE:
c= law of sines, so c/sin(40) = 14/sin(28), multiply both sides by sin(40) so c can be isolated and solved for. c = 14sin(40)/sin(28). Plug into calculator then get answer. c is approximately 19.2.
a = law of sines again, so a/sin(112) = 14/sin(28). Multiply both sides again by sin(112) then solve. a = 14sin(112)/sin(28). Calculator again. a is around 27.6
7 0
3 years ago
Alicia pays $180 to have cable and wi-fi installed in her home. Each month, she will pay $75 month for her cable
zhannawk [14.2K]

Answer:

In a year she will pay $900

The cost of the installation and a month would be $225

The cost of a year and installation would be $1,080

Step-by-step explanation:

         </3 PureBeauty

           

7 0
3 years ago
This question is from the similarity chapter. It would be really kind of you if you would answer this question.
katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

<u>1) Determine what is required for the answers</u>

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

<u>2) Prove similarity</u>

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

  1. Angles AYX and ACB are corresponding and they both measure 90 degrees
  2. Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

<u>3) Solve for part A</u>

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

\frac{XY}{BC}=\frac{AY}{AC}

Plug in known values

\frac{2}{300}=\frac{11}{AC}

Cross-multiply

2AC=11*300\\2AC=3300\\AC=1650

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

<u>4) Solve for part B</u>

To find the length of AB, we can use the Pythagorean theorem:

a^2+b^2=c^2 where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0
3 years ago
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