How many real solutions does the equation have? √3x-1 =2x-5

The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].

If [tex]y = 2\cdot x + 3[/tex] is a line tangent to the parabola [tex]y = c\cdot x^{2}[/tex], then we must observe the following condition, that is, the slope of the line is equal to the first derivative of the parabola:

[tex]2\cdot c \cdot x = 2[/tex] (1)

Then, we have the following system of equations:

[tex]y = 2\cdot x + 3[/tex] (1)

[tex]y = c\cdot x^{2}[/tex] (2)

[tex]c\cdot x = 1[/tex] (3)

Whose solution is shown below:

By (3):

[tex]c =\frac{1}{x}[/tex]

(3) in (2):

[tex]y = x[/tex] (4)

(4) in (1):

[tex]y = -3[/tex]

[tex]x = -3[/tex]

[tex]c = -\frac{1}{3}[/tex]

The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].

We kindly invite to check this question on tangent lines: https://brainly.com/question/13424370

The area of a shape is the amount of space it can occupy.

The value of r is 13

From the question (see attachment), we have:

[tex]\mathbf{A =176}[/tex] --- area of the shaded region

[tex]\mathbf{w = 2}[/tex] --- the width of the shaded region

The area of the complete circle would be:

[tex]\mathbf{A_1 =\pi (r + w)^2}[/tex]

The area of the small circle is:

[tex]\mathbf{A_2 =\pi r^2}[/tex]

So, the area of the shaded region is:

[tex]\mathbf{A = A_1 - A_2}[/tex]

Substitute known values

[tex]\mathbf{176 =\pi (r + w)^2 - \pi r^2 }[/tex]

Substitute 2 for w

[tex]\mathbf{176 =\pi (r + 2)^2 - \pi r^2 }[/tex]

Expand

[tex]\mathbf{176 =\pi (r^2 + 4r + 4) - \pi r^2 }[/tex]

Open brackets

[tex]\mathbf{176 =\pi r^2 + 4\pi r + 4\pi - \pi r^2 }[/tex]

Cancel out line terms

[tex]\mathbf{176 =4\pi r + 4\pi }[/tex]

Divide through by 4

[tex]\mathbf{44 =\pi r + \pi }[/tex]

Factor out pi

[tex]\mathbf{44 =\pi(r+ 1) }[/tex]

Divide through by pi

[tex]\mathbf{r + 1= \frac{44}{ \pi} }[/tex]

Substitute 22/7 for pi

[tex]\mathbf{r + 1= \frac{44}{ 22/7} }[/tex]

Using a calculator, we have

[tex]\mathbf{r + 1= 14}[/tex]

Solve for r

[tex]\mathbf{r= 14 -1}[/tex]

[tex]\mathbf{r= 13}[/tex]

Hence, the value of r is 13

Read more about areas of circles at:

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Answer:

The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line).

C. Safe, reliable childcare for a single parent so they can go to work

[tex]2 - \sqrt{1} \\ = 2 - 1 \\ = 1[/tex]

Answer:

n = 1

Step-by-step explanation:

Represent the number by n.  Then "seven less than twice a number is -5 becomes 2n - 7 = -5

Next we must solve for n.  Adding 7 to both sides yields 2n = 2, so that

n = 1

Answer:

Maybe 16

Step-by-step explanation:

Answer:

8.50x plus 13y equals 160

Answer:

i don"t know ask your mom

Answer:

[tex](9n + 18) + (8n + 8) \\ = (9n + 8n) + (18 + 8) \\ = 17n + 26[/tex]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 2 ← is in slope- intercept form

Thus its graph is a straight line

crosses the y- axis at (0, 2 ) , that is c = 2

the 4 in 4x is the slope m of the line

Answer: (b+5)(b-5)

Step-by-step explanation:

both b^2 and 25 are square numbers, so square root both of them to give b and 5, then put into brackets with a + and -

Answer: thanks for this answer, I was working on this problem.

As x approaches negative infinity, g(x) approaches [ Negative] infinity.

As x approaches positive infinity, g(x) approaches [ Negative] infinity.

Answer:

X=22° ; Exterior Angle = 125°

Step-by-step explanation:

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

(2x) + (103 - x) = (6x - 7)

103 + 7 = 6x - 2x + x

110 = 5x -->(Divided by 5)--> x=22°

6(22) - 7 = 125°

Answer:

Step-by-step explanation:

So im gonna be using the substitution method because its easier

We divide the equations into two and solve for y

-6x+y=20

We add 6x to both sides

-6x+y+6x=20+6x

y=6x+20

Now we plug in 6x+20 for y into the other equation

2x+3y=10

2x+3(6x+20)=10 We can simplify now

20x+60=10

20x=-50

take 20 from both sides so its gonna be a fraction

-5/2

We plug in -5/2 for x

y=6(-5/2)+20

y=5

]so therefore x is -5/2 and y is 5

珠ɪᴢᴜᴍɪᴿᴬᴳᴱ

The equality of the expression after removing y by substituting y is 2x + 21 = 10 - 6x + 7 = 20.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

A formula known as an equation uses the same sign to denote the equality of two expressions.

In another word, the equation must be constrained with some constraints.

Given the expression,

2x + 3y = 10 -6x + y = 20

So,

2x + 3y = 20 and  10 - 6x + y = 20

To remove y we need to find y and substitute.

So by substituting,

10 - 6(20 - 3y)/2 + y = 20

y = 7

So,

2x + 21 = 10 - 6x + 7 = 20

Hence "The equality of the expression after removing y by substituting y is 2x + 21 = 10 - 6x + 7 = 20".

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The given question is in the Spanish language in English it is ;

{2x + 3y = 10 -6x + y = 20 if it is solved by the equalization method, what is the equality that results if the variable y is cleared from both equations?

Answer:

to create this figure, connect the three sets of opiate points of the hexagon. Construction angle bisectors for each new angle, creating six new intersections with the circle, for a total of 12 points. Connect the points to make a regular 12-sided polygon.

Step-by-step explanation:

Answer: Rs. 69

Step-by-step explanation:

Let the amount that the adults have to pay be Rs. “x” and the amount that the senior citizens have to pay be Rs. “y”.

Step 1:

According to the question, we get

Equation 1:

6x + 4y = 228  

Equation 2:

13x + 7y = 459  

Step 2:

Then, by multiplying equation 1 by 7 & equation 2 by 4, we get

7 * [6x + 4y = 228]

⇒ 42x + 28y = 1596 …. (iii)  

And,

4 * [13x + 7y = 459]

⇒ 52x + 28y = 1836 …. (iv)

Step 3:

Now, Subtracting eq. (iii) from eq. (iv), we get

52x + 28y = 1836

42x + 28y = 1596

(-)    (-)         (-)

---------------------------

10 x = 240

----------------------------

⇒ x = 240/10 = 24

Substituting the value of x in Eq. (1)

(6*24) + 4y = 228  

⇒ y = [228 - 144]/4 = 21

Step 4:

Thus,  

The total amount that 2 adults and a senior citizen have to pay to visit the exhibition is,

= 2x + y

= (2*24) + 21 ….. [substituting x= 24 & y = 21]

= Rs. 69

Step-by-step explanation:

Hope this helps

can i get braineist

Answer:

Step-by-step explanation:

Example: (1 2/3) (2 3/5)

Turn to improper fractions

1 2/3= 5/3   2 3/5= 13/5

5/3 x 13/5=?

5x13= 65

3x5= 15

Simplify/divide: 65/15 = 4 1/3

Another example. (2 5/6)(3)

Improper fraction:  2 5/6= 17/6

Turn Whole number to fraction: 3= 3/1

17/6 x 3/1

17x3= 51

6x1= 6

51/6

Simplify/divide: 8 1/2

Answer:

5/2.5 is 2. Airó makes 2 batches in an hour.

Step-by-step explanation:

i think..

9514 1404 393

Answer:

  3(4/3)^2543

Step-by-step explanation:

Using logarithms base 2, we have ...

  [tex](a_n)^{\log{a_n}}=(a_{n+1})^{\log{a_{n-1}}}\\\\(\log{a_n})(\log{a_n}) = (\log{a_{n-1}})(\log{a_{n+1}}) \\\\ \dfrac{\log{a_{n+1}}}{\log{a_{n}}}=\dfrac{\log{a_n}}{\log{a_{n-1}}}=\dots\dfrac{\log_2{16}}{\log_2{8}}=\dfrac{4}{3}[/tex]

That is, the ratio of each term to the previous is a constant equal to 4/3. This is the definition of a geometric sequence. This sequence has first term 3 and common ratio 4/3, so the general term is ...

  [tex]\log_2 a_n=3\left(\dfrac{4}{3}\right)^{n-1}[/tex]

and the 2544th term is ...

  [tex]\boxed{\log_2{a_{2544}}=3\left(\dfrac{4}{3}\right)^{2543}}[/tex]

Answer:

9/10

Step-by-step explanation:

I used a calculator ! :)

Answer:

What is the question

Step-by-step explanation:

Answer:3% went on Friday than on Saturday

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A converse to a statement is switching the IF part with the THEN part.

Since the statement says  IF point B bisects the line, THEN B is the midpoint.

The converse would then say

IF B is the midpoint, THEN point B bisects the line.

Answer:

Step-by-step explanation:

2x+20=12x

We can subtract 2x from both sides:

2x+20-2x=12x-2x

20=10x

20/10=x

x=2

Step-by-step explanation:

let the 3 consecutive odd number be

x + 1 , x + 3 , x + 5

as, there sum is 45. so, after inserting the values we got,

→ x + x + 1 + x + 3 = 45

→ 3x + 9 = 45

→ 3x = 45 - 9 = 36

→ x = 36/3 = 12

→ x = 12

therefore, 3 consecutive odd number are

→ x + 1 = 12 + 1 = 13

→ x + 3 = 12 + 3 = 15

→ x + 5 = 12 + 5 = 17

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

1:6

Step-by-step explanation:

A part-to-whole ratio of 1:6 means that there is 1 of something and the total is 6. It also means that there are 5 of something else. To convert a Part-to-Whole ratio such as 1:6, you replace the colon with a fraction bar to get this answer:

1:6 → 1/6

y = -5

or

y = -8

Answer above!