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
JulsSmile [24]
3 years ago
9

Plz help in solving these 2 questions with steps and explanation!!

Mathematics
2 answers:
Semmy [17]3 years ago
4 0

Answer:

Step-by-step explanation:

x^2 - 7x + 10 = 0 can be factored as follows:  (x - 5)(x - 2).  Note that -5x -2x combine to -7x, the middle term of this quadratic, and that (-5)(-2) = +10, the constant term.  Setting each of these factors = to 0 separately, we get:

x = 5 and x = 2.

x^2 - 2x = 20 should be rewritten in standard form for a quadratic equation before you attempt to solve it:  x^2 - 2x - 20 = 0.  This quadratic is not so easily factored as was the previous one.  Let's use the quadratic formula:

      -b ± √(b²-4ac)

x = --------------------

             2a

Here, a = 1, b = -2 and c = -20, so the discriminant b²-4ac = (-2)^2 - 4(1)(-20), or 4 + 80, or 84.  84 has only one perfect square factor:  4·21.  Because the discriminant is +, we know that this equation has two real, unequal roots.

They are:

       -(-2) ± √(4·21)         2 ± 2√21

x = ----------------------  =  ----------------- =   1 ± √21

             2(1)                            2

fomenos3 years ago
3 0

Answer:

\large\boxed{Q1:\ x=2\ or\ x=5}\\\boxed{Q2:\ x=1-\sqrt{21}\ or\ x=1+\sqrt{21}}

Step-by-step explanation:

\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\text{If}\ b^2-4ac0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================

\bold{Q1}\\\\x^2-7x+10=0\\\\a=1,\ b=-7,\ c=10\\\\b^2-4ac=(-7)^2-4(1)(10)=49-40=9>0\\\\\sqrt{b^2-4ac}=\sqrt9=3\\\\x_1=\dfrac{-(-7)-3}{2(1)}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\x_2=\dfrac{-(-7)+3}{2(1)}=\dfrac{7+3}{2}=\dfrac{10}{2}=5\\\\========================================

\bold{Q2}\\x^2-2x=20\qquad\text{subtract 20 from both sides}\\\\x^2-2x-20=0\\\\a=1,\ b=-2,\ c=-20\\\\b^2-4ac=(-2)^2-4(1)(-20)=4+80=84>0\\\\\sqrt{b^2-4ac}=\sqrt{84}=\sqrt{4\cdot21}=\sqrt4\cdot\sqrt{21}=2\sqrt{21}\\\\x_1=\dfrac{-(-2)-2\sqrt{21}}{2(1)}=\dfrac{2-2\sqrt{21}}{2}=1-\sqrt{21}\\\\x_2=\dfrac{-(-2)+2\sqrt{21}}{2(1)}=\dfrac{2+2\sqrt{21}}{2}=1+\sqrt{21}

You might be interested in
What is 16.24 divided by 0.14
hammer [34]
16.24  divided by 0.14 equals 116 i hope this helps if not sorry :)
4 0
3 years ago
Read 2 more answers
How do you get this to its Standard Form?<br>And is it linear?
Alchen [17]

let's bear in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient


so, let's do away with the denominators by multiplying both sides by the LCD of all fractions, in this case 6.


\bf \cfrac{x}{2}=\cfrac{y+3}{6}\implies\stackrel{\textit{multiplying by }\stackrel{LCD}{6}}{6\left( \cfrac{x}{2} \right)=6\left( \cfrac{y+3}{6} \right)}\implies 3x=y+3\implies \stackrel{\textit{standard form}}{3x-y=3}

4 0
3 years ago
Read 2 more answers
The monthly sales of Sunny Electronics' new sound system are given by q(t)=4000t−100t² units per month, t months after its intro
zysi [14]

Answer:

The rate of change with respect to monthly sales is 4000 - 200t.

Step-by-step explanation:

The sales per month (monthly sales) of the new sound system being sold by Sunny Electronics is given by q(t)  = 4000t - 100t^2 units per month, where t is number of months from the introduction of the sound system.

The price of each unit of the sound system charged by Sunny Electronics is given by p(t) = 2000 - t^2.

The rate of change with respect to monthly sales will be given by the equation

\frac{dq(t)}{dt}  = \frac{d(4000t - 100t^2)}{dt}  = 4000 - 200t.

5 0
3 years ago
Use distributive property to write an expression equivalent to 6(24)
Amiraneli [1.4K]
6(12+12)
6(20+4)
6(10+14)
4 0
3 years ago
What are the properties of parallelogram ​
KIM [24]

Answer:

The properties of the parallelogram are simply those things that are true about it. These properties concern its sides, angles, and diagonals.

Step-by-step explanation:

The parallelogram has the following properties:

Opposite sides are parallel by definition.

Opposite sides are congruent.

Opposite angles are congruent.

Consecutive angles are supplementary.

The diagonals bisect each other.

If you just look at a parallelogram, the things that look true (namely, the things on this list) are true and are thus properties, and the things that don’t look like they’re true aren’t properties.

If you draw a picture to help you

7 0
3 years ago
Other questions:
  • Which is an equivalent ratio to 7:5? 14:12 21:10 21:15
    8·2 answers
  • Free points and brainlist .help me with this
    8·2 answers
  • Shontell spends $7 a month plus $0.10 per minute. Determine whether the cost per month is proportional to the to the number of m
    10·2 answers
  • Line m passes through point (–2, –1) and is perpendicular to the graph of y = –23x + 6. Line n is parallel to line m and passes
    7·1 answer
  • List the sides of the triangle in order from largest to smallest
    9·1 answer
  • There were 12 people on jury there were 4 more men than women how many men were there
    14·1 answer
  • F(x) = x2 + 4x + 3 symmetry of -2
    13·1 answer
  • I NEED HELP ASAP!!! I'LL GIVE BRAINLIEST TO THE CORRECT ANSWER!!!
    14·1 answer
  • A farmer feeds a cow 9300 milligrams of an antibiotic. Every hour, 50% of the drug breaks down in the cow's body. How much will
    11·1 answer
  • Determine whether the graph defines a function of x.<br> Yes or No
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!