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marusya05 [52]
3 years ago
8

When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.

Mathematics
1 answer:
Juliette [100K]3 years ago
6 0
x-the\ number\\\\x^2-(5+3x)=0\\\\x^2-5-3x=0\\\\x^2-3x-5=0

Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution

x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \  0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \  0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \  0

Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}
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CD is perpendicular to AB and passes through point C5, 12).
Aleksandr-060686 [28]

Answer:

x intercept of CD = 17

Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD mCD = -\frac{1}{mAB}

Hence we start from determining slope of AB

slope is given as

m= \frac{y_2-y_1}{x_2-x_1}

m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1

Hence mAB=1

There fore mCD=-1

(∵  Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

m=\frac{y-y_1}{x-x_1}

-1=\frac{y-12}{x-5}

-x+5=y-12

y=-x+17

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

0=-x+17

x=17

Hence the x intercept is 17

8 0
3 years ago
The distance between Cincinnati,Ohio and Charlotte,North Carolina,is about 336 miles. The distance between Cincinnati and Chicag
navik [9.2K]

336+247=583miles

charlotte-chicago

charlotte-ohio=336

ohio- Chicago-247

so charlotte-chicago=583miles

6 0
3 years ago
1.25 is closer to 1.04 or not ?<br> plz heelp
Ray Of Light [21]

Answer:

Yes 1.25 is closer to 1.04

Step-by-step explanation:

Hope this helps!

3 0
2 years ago
Read 2 more answers
Math help 30 points
mash [69]

Again here we're using like terms

a) -2x² + 12x² = 10x² (they have the same term that's why I grouped them together)

-4x + 2x = -2x

13 - 25 = -12

So the final answer is 10x² - 2x -12

b) 7x² - (-7x²) = 7x² + 7x² or 14x²

4x - (-3x) = 4x + 3x or 7x

-26 - 15 = -41

The final answer to this one is 14x² + 7x - 41

7 0
3 years ago
20 points
SVEN [57.7K]

Answer:

60in

Step-by-step explanation:

Given data

Length= 24 in

Width = 18 in

Diagonally, we need to find using the Pythagoras theorem

D^2= L^2+W^2

D^2= 24^2+18^2

D^2= 576+324

D^2= 900

Square both sides

D= √900

D= 30 in

For both sides

=30*2= 60in

8 0
3 years ago
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