1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pepsi [2]
3 years ago
11

The line $y = b-x$ with $0 < b < 4$ intersects the $y$-axis at $P$ and the line $x=4$ at $S$. If the ratio of the area of

triangle $QRS$ to the area of triangle $QOP$ is 9:25, what is the value of $b$? Express the answer as a decimal to the nearest tenth.

Mathematics
2 answers:
olga55 [171]3 years ago
6 0

Answer:

b=2.5

Step-by-step explanation:

The given line has equation: y=b-x

The x-intercept is (b,0)

The y-intercept is (0,b)

The area of triangle QOP =\frac{1}{2} |OQ|*|OP|=

=\frac{1}{2}b*b

=\frac{1}{2}b^2

The area of triangle QRS =\frac{1}{2} |RQ|*|RS|=

=\frac{1}{2}(4-b)*(b-4)

The area of triangle QRS and QOP are in the ratio 9:25

We must negate the area under the x-axis.

\implies \frac{- \frac{1}{2}(4-b)(b-4)}{\frac{1}{2}b^2} =\frac{9}{25}

\implies \frac{-(4-b)(b-4)}{b^2} =\frac{9}{25}

\implies {-(4-b)(b-4) =\frac{9}{25}b^2

\implies b^2-8b+16=\frac{9}{25}b^2

\implies 25b^2-200b+400=9b^2

\implies 25b^2-9b^2-200b+400=0

\implies 16b^2-200b+400=0

\implies 2b^2-25b+50=0

(2b-5)(b-10)=0

b=2.5\:or\:b=10

But 0<b<4

Therefore b=2.5

VERIFY

The area of triangle QOP

=\frac{1}{2}*2.5*2.5=3.125

The area of triangle QRS

=|\frac{1}{2}(4-2.5)*(2.5-4)|=|-1.125|=1.125

We must take absolute value because this area is below the x-axis.

\frac{1.125}{3.125} =\frac{9}{25}

Softa [21]3 years ago
3 0

Answer:

b=2.5

Step-by-step explanation:

The line y=b-x intersects the x-axis at the point where 0 = b-x, or x=b. So, we seek the x-coordinate of point Q.

Since the y-axis is parallel to the line x = 4, we see that angle QSR = angle QPO. Also QOP = QRS = 90 degrees. Thus triangle QOP is similiar to triangle QRS, so [QRS]/[QOP] =(QR/QO)^2, which means we have (QR/QO)^2/9/25, so QR/QO= 3/5. Since QR + QO= 4, we have 3/5(QO + QO) = 4, and QO =4 * 5/8= 5/2. Therefore, the x-coordinate of Q is 5/2 = 2.5

You might be interested in
A 6 oz paper cup is shaped like a cone with a diameter of 4 inches. How many ounces of water will a plastic cylindrical cup with
OleMash [197]

Answer:

The plastic cylindrical cup will hold <u>17.96 ounces</u> of water.

Step-by-step explanation:

Given:

A 6 oz paper cup is shaped like a cone with a diameter of 4 inches.

Now, to find ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup.

Volume of cone = 6 oz.

Diameter = 4 inches.

So, radius (r) = \frac{Diameter}{2} =\frac{4}{2} =2\ inches.

<u><em>Taking the value </em></u>\pi<u><em> = 3.14.</em></u>

Now, to get the height (h) we put formula:

Volume=\pi r^2\frac{h}{3}

Volume=3.14\times 2^2\times \frac{h}{3}

6=3.14\times 4\times \frac{h}{3}

<em>Multiplying both sides by 3 we get:</em>

18=12.56h

<em>Dividing both sides by 12.56 we get:</em>

1.43=h

h=1.43\ inches.

Now, to get the volume of cylindrical cup.

As, given it is the same height as the paper cup.

Height (h) = 1.43 inches.

Diameter = 4 inches.

Radius (r) = \frac{Diameter}{2} =\frac{4}{2} =2\ inches.

So, we put formula to get the ounces of water a plastic cylindrical cup will hold:

Volume =\pi r^2h

Volume=3.14\times 2^2\times 1.43

Volume=3.14\times 4\times 1.43

Volume=17.96\ oz.

Therefore, the plastic cylindrical cup will hold 17.96 ounces of water.

5 0
3 years ago
How many degrees are in a third of a full turn?
notka56 [123]

There are 120 degrees in a 1/3 turn.

6 0
3 years ago
Read 2 more answers
E is the midpoint of Df, DE=2x+4, and EF=3x-1. Find all segment lengths
sertanlavr [38]
If E is the midpoint, DE and EF are equivalent.
2x+4=3x-1
4=x-1
5=x

Plug the value of x in
2(5)+4
14

3(5)-1
14

14+14=28

Final answer: DE=14, EF=14, DF= 28
6 0
3 years ago
im confused with this please help i dont get any answers, it is about rounding, not sure why this question is confused
Shkiper50 [21]

Step-by-step explanation:

<u>13,789:</u>

Tens: 13,790

Hundreds: 13,800

Thousands: 14,000

Ten thousands: 10,000

<u>24,173:</u>

Tens: 24,170

Hundreds: 24,200

Thousands: 24,000

Ten thousands: 20,000

<u>861,630:</u>

Tens: 861,630

Hundreds: 861,600

Thousands: 862,000

Ten thousands: 860,000

7 0
2 years ago
74 divided by 2 but long division
Olin [163]

Answer:

69

Step-by-step explanation:

74/2

8 0
3 years ago
Other questions:
  • The cost function of a corn stand is C = 6n + 200, where n is the number of buckets of corn sold. The revenue function of this c
    13·2 answers
  • What would be the expression after distributing, -2(3m-4)?
    8·2 answers
  • Given the equation y = 7 sec(6x– 30)<br><br> The period is:<br><br> The horizontal shift is:
    12·1 answer
  • If x=9 and y=3 then |1-2x|+4y^2
    5·1 answer
  • I will give you 100 points and brainliest if you answer
    11·2 answers
  • X, y and mans shadow length?
    14·1 answer
  • Please help me with this question!!
    15·1 answer
  • Write a division number story with an answer of 1/4 my lil bro needs help on this so ya help before he explodes!!!!!!!!
    12·1 answer
  • Maria can weed the garden in 1.5 hours. If Janette helps her, they can finish the job in 30 minutes. How long does it take Janet
    14·1 answer
  • Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!