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
levacccp [35]
3 years ago
9

I need help from question 11- 16! Please help!

Mathematics
1 answer:
insens350 [35]3 years ago
3 0
<h2>11. Find discriminant.</h2>

Answer: D) 0, one real solution

A quadratic function is given of the form:

ax^2+bx+c=

We can find the roots of this equation using the quadratic formula:

x_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

Where \Delta=b^2-4ac is named the discriminant. This gives us information about the roots without computing them. So, arranging our equation we have:

4a^2-4a-6=-7 \\ \\ Adding \ 7 \ to \ both \ sides \ of \ the \ equation: \\ \\ 4a^2-4a-6+7=-7+7 \\ \\ 4a^2-4a+1=0 \\ \\ Then \ the \ discriminant: \\ \\ \Delta=(-4)^2-4(4)(1) \\ \\ \Delta=16-16 \\ \\ \boxed{Delta=0}

<em>Since the discriminant equals zero, then we just have one real solution.</em>

<h2>12. Find discriminant.</h2>

Answer: D) -220, no real solution

In this exercise, we have the following equation:

-r^2-2r+14=-8r^2+6

So we need to arrange this equation in the form:

ax^2+bx+c=

Thus:

-r^2-2r+14=-8r^2+6 \\ \\ Adding \ 8r^2 \ to \ both \ sides \ of \ the \ equation: \\ \\ -r^2-2r+14+8r^2=-8r^2+6+8r^2 \\ \\ Associative \ Property: \\ \\ (-r^2+8r^2)-2r+14=(-8r^2+8r^2)+6 \\ \\ 7r^2-2r+14=6 \\ \\ Subtracting \ 6 \ from \ both \ sides: \\ \\ 7r^2-2r+14-6=6-6 \\ \\ 7r^2-2r+8=0

So the discriminant is:

\Delta=(-2)^2-4(7)(8) \\ \\ \Delta=4-224 \\ \\ \boxed{\Delta=-220}

<em>Since the discriminant is less than one, then there is no any real solution</em>

<h2>13. Value that completes the squares</h2>

Answer: C) 144

What we need to find is the value of c such that:

x^2+24x+c=0

is a perfect square trinomial, that are given of the form:

a^2x^2\pm 2axb+b^2

and can be expressed in squared-binomial form as:

(ax\pm b)^2

So we can write our quadratic equation as follows:

x^2+2(12)x+c \\ \\ So: \\ \\ a=1 \\ \\ b=12 \\ \\ c=b^2 \therefore c=12^2 \therefore \boxed{c=144}

Finally, the value of c that completes the square is 144 because:

x^2+24x+144=(x+12)^2

<h2>14. Value that completes the square.</h2>

Answer: C) \frac{121}{4}

What we need to find is the value of c such that:

z^2+11z+c=0

So we can write our quadratic equation as follows:

z^2+2\frac{11}{2}z+c \\ \\ So: \\ \\ a=1 \\ \\ b=\frac{11}{2} \\ \\ c=b^2 \therefore c=\left(\frac{11}{2}\left)^2 \therefore \boxed{c=\frac{121}{4}}

Finally, the value of c that completes the square is \frac{121}{4} because:

z^2+11z+\frac{121}{4}=(x+\frac{11}{2})^2

<h2 /><h2>15. Rectangle.</h2>

In this problem, we need to find the length and width of a rectangle. We are given the area of the rectangle, which is 45 square inches. We know that the formula of the area of a rectangle is:

A=L\times W

From the statement we know that the length of the rectangle is is one inch less than twice the width, this can be written as:

L=2W-1

So we can introduce this into the equation of the area, hence:

A=L\times W \\ \\ \\ Where: \\ \\ W:Width \\ \\ L:Length

A=(2W-1)(W) \\ \\ But \ A=45: \\ \\ 45=(2W-1)(W) \\ \\ Distributive \ Property:\\ \\ 45=2W^2-W \\ \\ 2W^2-W-45=0 \\ \\ Quadratic \ Formula: \\ \\ x_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{1}=\frac{-(-1)+ \sqrt{(-1)^2-4(2)(-45)}}{2(2)} \\ \\ W_{1}=\frac{1+ \sqrt{1+360}}{4} \therefore W_{1}=5 \\ \\ W_{2}=\frac{-(-1)- \sqrt{(-1)^2-4(2)(-45)}}{2(2)} \\ \\ W_{2}=\frac{1- \sqrt{1+360}}{4} \therefore W_{2}=-\frac{9}{2}

The only valid option is W_{1} because is greater than zero. Recall that we can't have a negative value of the width. For the length we have:

L=2(5)-1 \\ \\ L=9

Finally:

The \ length \ is \ 9 \ inches \\ \\ The \ width \ is \ 5 \ inches

<h2>16. Satellite</h2>

The distance in miles between mars and a satellite is given by the equation:

d=-9t^2+776

where t is the number of hours it has fallen. So we need to find when the satellite will be 452 miles away from mars, that is, d=452:

d=-9t^2+776 \\ \\ 452=-9t^2+776 \\ \\ 9t^2=776-452 \\ \\ 9t^2=324 \\ \\ t^2=\frac{324}{9} \\ \\ t^2=36 \\ \\ t=\sqrt{36} \\ \\ \boxed{t=6h}

Finally, <em>the satellite will be 452 miles away from mars in 6 hours.</em>

You might be interested in
I need helpppppppppp!!!!!!!!!!
Genrish500 [490]

Answer:

m MN = 70°

Step-by-step explanation:

∠MLN is an angle formed by the chords ML and LN and is calculated as

∠MLN = 0.5( m arc MN ), that is

35° = 0.5 arc MN ( multiply both sides by 2 )

arc MN = 2 × 35° = 70°

4 0
3 years ago
WILL MARK BRAINLEST! HELP ASAP Pedro has a spinner with 4 sections numbered 1 through 4. Pedro spins the spinner 100 times and r
baherus [9]

The answer is A: A uniform probability model is a good model to represent probabilities related to the numbers generated in Pedro's experiment.

and B: It is likely that the spinner is fair.

3 0
3 years ago
Read 2 more answers
I really need help with this question <br> n+5≤16
ahrayia [7]

Answer:

the answer would be anything 11 and under (11,10,9,8,7,6,5,4,3,2,1,0)

Step-by-step explanation:

This is because if n+5 is less than or equal to 16 then 11+5=16 so that is equal to and less than would be using any number less than 11

hope this helps ;)

3 0
2 years ago
Read 2 more answers
The circle has a diameter of 16 inches. What is the area of the circle, rounded to the nearest square inch?
Ratling [72]

<u>Statement</u><u>:</u>

The circle has a diameter of 16 inches.

<u>To </u><u>find </u><u>out:</u>

The area of the circle.

<u>Solution</u><u>:</u>

  • Diameter of the circle = 16 inches.

  • Radius of the circle
  • = Diameter ÷ 2
  • = 16 inches ÷ 2
  • = 8 inches

  • π = 3.14

  • We know, area of a circle = πr² where r is the radius.

  • Therefore, the area of the circle
  • = 3.14 × (8)² square inches
  • = 3.14 × 64 square inches
  • = 200.96 square inches
  • = 201 square inches [rounded to the nearest square inch]

<u>Answer</u><u>:</u>

C) 201 square inches

Hope you could understand.

If you have any query, feel free to ask.

4 0
2 years ago
Read 2 more answers
for some reason brainly deleted this for not being "school related" even though it is so here's a repost, can anyone help me wit
tangare [24]

Answer:

1 tenth and 9 hundreds

Step-by-step explanation:

Ok so this is not a gud explanation but believe me that answer is correct

a tenth is 10% out of a hundred so thats 10/100 and since the 9 hundreds is already there 10/100+ 9/100= 19/100

Hope you have a gud day :)

6 0
2 years ago
Other questions:
  • 10) 28n4 + 16n? – 80n² = 0<br> Factoring quadratic
    10·2 answers
  • Write in pence the value of the 9 in £8.90
    15·1 answer
  • Marcos talks to his grandfather in Alabama for about 95 minutes per month. About how long does he talk each day? (Hint: Use 1 mo
    8·2 answers
  • Jane bought a packet of 12 cards for $15.00 <br>What would be the average price of a card?
    14·2 answers
  • Solve for x: 2x^2 + x - 4 = 0
    14·1 answer
  • The GCF of any two even numbers is always even. Determine whether the statement is true or false. If true, explain why. If false
    7·1 answer
  • Write an algebraic expression that represents A less than 27.
    9·1 answer
  • Of the vehicles on the road, 1/2 are cars and 1/8 are motorcycles. What fraction of the vehicles are not cars or motorcycles?
    15·1 answer
  • The Greenery landscaping company puts in an order for 2 pine trees and 5 hydrangea bushes for a neighborhood project. The order
    15·1 answer
  • Plz help me with this
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!