All categories

3 years ago

YO PLZ HELP!! MARKING BRAINIEST!!

Mathematics

1 answer:

Yuliya22 [10]3 years ago

8 0

Answer:

x = 26, 16

Step-by-step explanation:

( x-21) ^2 = 25

Take the square root of each side

sqrt(( x-21) ^2) = ±sqrt(25)

x-21 = ±5

Add 21 to each side

x-21+21 = 21±5

x = 21±5

x = 21+5 and x = 21-5

x = 26, 16

You might be interested in

What are the zeros of the quadratic function f(x) = 2x2 – 10x – 3?

Natasha2012 [34]

Answer:

$x=\frac{50+\sqrt{31}}{2},\frac{50-\sqrt{31}}{2}$ are zeroes of given quadratic equation.

Step-by-step explanation:

We have been a quadratic equation:

$2x^2-10x-3$

We need to find the zeroes of quadratic equation

We have a formula to find zeroes of a quadratic equation:

$x=\frac{b^2\pm\sqrt{D}}{2a}\text{where}D=\sqrt{b^2-4ac}$

General form of quadratic equation is $ax^2+bx+c$

On comparing general equation with b given equation we get

a=2,b=-10,c=-3

On substituting the values in formula we get

$D=\sqrt{(-10)^2-4(2)(-3)}$

$\Rightarrow D=\sqrt{100+24}=\sqrt{124}$

Now substituting D in $x=\frac{b^2\pm\sqrt{D}}{2a}$ we get

$x=\frac{(-10)^2\pm\sqrt{124}}{2\cdot 2}$

$x=\frac{100\pm\sqrt{124}}{4}$

$x=\frac{100\pm2\sqrt{31}}{4}$

$x=\frac{50\pm\sqrt{31}}{2}$

Therefore, $x=\frac{50+\sqrt{31}}{2},\frac{50-\sqrt{31}}{2}$

5 0

3 years ago

Read 2 more answers

The slope of two lines are 5/6 and 2/p. determine the value of p that will make the lines

Anni [7]

Parallel: the lines have = slopes. We thus need 5/6 to equal 2/p. then 5p must equal 12, and p = 12/5. (answer)

Check: Is 5/6 = 2 / (12/5)? YES

Perp.: The lines have slopes that are negative reciprocals of one another.

Then -6/5 = 2/p, or

-6 2
---- = ----
5 p Thus, -6p = 10, and p = -5/3 (answer)

7 0

3 years ago

Read 2 more answers

What's the solution of the equation 4[x+2(3x-7)]=22x-65

padilas [110]

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6 6

x = -3/2

8 0

3 years ago

Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s

Nataliya [291]

Answer:

$f(x)=\frac{1}{2}x^2-4x+5$

Step-by-step explanation:

A parabola is written in the form

$f(x)=a((x-h)^2+k)$ (1)

where:

$h$ is the x-coordinate of the vertex of the parabola

$ak$ is the y-coordinate of the vertex of the parabola

$a$ is a scale factor

For the parabola in the problem, we know that the vertex has coordinates (4,-3), so we have:

$h=4$ (2)

$ak=-3$

From this last equation, we get that $a=\frac{-3}{k}$ (3)

Substituting (2) and (3) into (1) we get the new expression:

$f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3$ (4)

We also know that the parabola contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

$-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6$

So we also get:

$a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}$

So the equation of the parabola is:

$f(x)=\frac{1}{2}((x-4)^2 -6)$ (5)

Now we want to rewrite it in the standard form, i.e. in the form

$f(x)=ax^2+bx+c$

To do that, we simply rewrite (5) expliciting the various terms, we find:

$f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5$

6 0

3 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

BabaBlast [244]

Step-by-step explanation:

the introduction of a fraction tells us that we are dealing with multiplications, and therefore a geometric sequence (where every new term is created by multiplying the previous term by a constant factor, the ratio r).

I think your teacher made a mistake, or you made one when typing the question in here.

there is no factor r that creates

15×r = 9

and

9×r = 5/27

it would mean that

15 × r² = 5/27

r² = 5/27 / 15 = 5/27 × 1/15 = 5/405 = 1/81

r = 1/9

but 15 × 1/9 = 5 × 1/3 = 5/3 is NOT 9

and 9 × 1/9 = 9/9 = 1 is NOT 5/27

so, this can't be right.

on the other hand

15 × r = 9

r = 9/15 = 3/5

and then

9 × 3/5 = 27/5

so, either the sequence should have been

15, 5/3, 5/27

or (and I suspect this to be true)

15, 9, 27/5

under that assumption we have

s1 = 15

r = 3/5

sn = sn-1 × r = s1 × r^(n-1) = 15 × (3/5)^(n-1)

s10 = 15 × (3/5)⁹ = 15 × 19683/1953125 =

= 3 × 19683/390625 = 59049/390625 =

= 0.15116544 ≈ 0.151

6 0

2 years ago