25% of what number is 20?​

Answer:

One possible equation is [tex]f(x) = (x + 3)\, (x - 5)[/tex], which is equivalent to [tex]f(x) = x^{2} - 2\, x - 15[/tex].

Step-by-step explanation:

The factor theorem states that if [tex]x = x_{0}[/tex]  (where [tex]x_{0}[/tex] is a constant) is a root of a function, [tex](x - x_{0})[/tex] would be a factor of that function.

The question states that [tex](-3,\, 0)[/tex] and [tex](5,\, 0)[/tex] are [tex]x[/tex]-intercepts of this function. In other words, [tex]x = -3[/tex] and [tex]x = 5[/tex] would both set the value of this quadratic function to [tex]0[/tex]. Thus, [tex]x = -3\![/tex] and [tex]x = 5\![/tex] would be two roots of this function.

By the factor theorem, [tex](x - (-3))[/tex] and [tex](x - 5)[/tex] would be two factors of this function.

Because the function in this question is quadratic, [tex](x - (-3))[/tex] and [tex](x - 5)[/tex] would be the only two factors of this function. In other words, for some constant [tex]a[/tex] ([tex]a \ne 0[/tex]):

[tex]f(x) = a\, (x - (-3))\, (x - 5)[/tex].

Simplify to obtain:

[tex]f(x) = a\, (x + 3)\, (x - 5)[/tex].

Expand this expression to obtain:

[tex]f(x) = a\, (x^{2} - 2\, x - 15)[/tex].

(Quadratic functions are polynomials of degree two. If this function has any factor other than [tex](x - (-3))[/tex] and [tex](x - 5)[/tex], expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of [tex]a[/tex] corresponds to a distinct quadratic function with [tex]x[/tex]-intercepts [tex](-3,\, 0)[/tex] and [tex](5,\, 0)[/tex]. For example, with [tex]a = 1[/tex]:

[tex]f(x) = (x + 3)\, (x - 5)[/tex], or equivalently,

[tex]f(x) = x^{2} - 2\, x - 15[/tex].

Answer:

2

a

x

−

5

a

−

10

x

+

25

Step-by-step explanation:

Answer:

18, 36, 54, 72

Step-by-step explanation:

As that sequence is common in the table of 18.

A.T.Q

18 x 1 = 18

18 x 2 = 36

18 x 3 = 54

18 x 4 = 72

Correct me, if I am wrong :)

Have a great day!

Thanks!

Answer:

a = 14, b = 2

Step-by-step explanation:

the initial amount was 14

the growth factor is 2

[tex]\orange{\bigstar\underline{\underline {\pmb{\frak{ \purple{Required~Answer}}}}}}[/tex]

Given:.

Steps :

470 × 0.88

£413.6

Answer:

it's 9

Step-by-step explanation:

you add up the numbers

Answer:

the answer is 9, if adding

Answer:

Step 3.

Step-by-step explanation:

If you look at the equation you can see that that -9 is gone from the left from being added by 9 and -4 is the result of 9 being added to -13. Step 2 would not be the correct answer because they haven't added the numbers yet. Hope this helps!

Answer: step 3

Step-by-step explanation:

Answer:

x = 5 , y = 2

Step-by-step explanation:

3y + 4y + 2x = 24

(3y)² + (4y)² = (2x)²

2x + 7y = 24 .............. (1)

25y² = 4x² ................ (2)

x = [tex]\frac{5}{2}[/tex] y   ------>  (1)  

2 ( [tex]\frac{5}{2}[/tex] y ) + 7y = 24

12y = 24

y = 2 ----------> (1)

x = 5

Answer:

It is B. (0,1)

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

a

Answer:

y = 4

Step-by-step explanation:

When given a point and a slope, we use slope-intercept formula:

y - y1 = m (x - x1)

m = slope  point: (-4,4)

y - y1 = m (x - x1)

y - 4 = 0 (x - 1)

y - 4 = 0x + 0

 + 4          + 4

y = 4

The answer can't be written in slope-intercept form, as the 0"s cancel out.

Hope this helps!

Answer: 1:  x=3, x=1

2:  x= -5

3:  There are 2 real solutions.

4:  There are 2 real solutions.

5:  There are no real solutions.

6.  There is 1 real solution.

7.  

8.  x= -6, x = -2

9.  x = -1/6, x=1

10.  

Explanation:

1.  The quadratic formula is

Substituting our known information we have:

2.  Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3.  The discriminant is b²-4ac.  For this problem, that is 20²-4(-4)(25)=400--400=800.  Since this is greater than 0, there are 2 real solutions.

4.  The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169.  This is greater than 0, so there are 2 real solutions.

5.  The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223.  Since this is less than 0, there are no real solutions.

6.  If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7.  Rewriting the quadratic we have 3x²-4x-2=0.  Using the quadratic formula we have:

8.  Factoring this trinomial we want factors of 12 that sum to 8.  6*2 = 12 and 6+2=8, so those are our factors.  This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0.  Solving these equations we get x= -6 or x= -2.

9.  Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5.  (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group.  In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0.  Solving these equations we get x=1 or x=-1/6.

10.  Substituting our information into the quadratic formula we get:

Step-by-step explanation:

Answer:

The two marked in the image.

Step-by-step explanation:

In scientific notation you will want only the most significant non-zero digit before the comma.

The first underlined number has two digits before it, the correct representation should be [tex]1.25\times10^4[/tex]

The second underlined number has a 0 leading digit, while the most significant non-zero digit is a 4. The correct represantation should be [tex]4.5\times 10^2[/tex]

An extra case could be made for the second number of the list, since it has no decimal part, but the way I read it means "the instrument used to measure the data has 0 decimal places accuracy"

Answer:

Rs 1210

Step-by-step explanation:

cost price = (100/100+10/100)×selling price

Answer:

$4.00+0.035+$4.00=8.035=$8.35

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 2/3 = 8/3

3 3/8 = 27/8

8/3 * 27/8 = 216/24

= 9

1) x = 5

2) x = 2

3) n = 6

4) n = 7

5) y = 12

[tex]4x+3=23[/tex]

→[tex]4x = 23 - 3[/tex]

→[tex]4x = 20[/tex]

→[tex]x = \frac{20}{4} [/tex]

→[tex]x = 5[/tex]

Hence, value of x is 5

[tex]24x - 18=30[/tex]

=>[tex]24x = 30 + 18[/tex]

=>[tex]24x = 48[/tex]

=>[tex]x = \frac{48}{24} [/tex]

=>[tex]x = 2[/tex]

Hence, value of x is 2

[tex]160+10n=220[/tex]

[tex]→10n = 220 - 160[/tex]

[tex]→10n =60[/tex]

[tex]→n = \frac{60}{10} [/tex]

[tex]→n = 6[/tex]

Hence, value of n is 6

[tex]51=30+3n[/tex]

[tex]→51 - 30 = 3n[/tex]

[tex]→21 = 3n[/tex]

[tex]→\frac{21}{3} = n[/tex]

[tex]→n = 7[/tex]

Hence, the value of n is 7

[tex]6y + 85=157[/tex]

[tex]→6y = 157 - 85[/tex]

[tex]→6y = 72[/tex]

[tex]→y = \frac{72}{6} [/tex]

[tex]→y = 12[/tex]

Hence, value of y is 12

Using proportions, it is found that:

A proportion is a fraction of a total amount.

In the sample, the most voted options were checking out books or studying, hence:

The most popular choice likely be either checking out books or studying.

Out of the 60 students, 10 = 1/6 are doing research, hence out of 540:

[tex]\frac{1}{6} \times 540 = 90[/tex]

Based on the sample, about 90 students will vote for doing research.

21 out of 60 students voted for checking out books, hence:

21/60 = 0.35 = 35%.

Based on the sample, about 35% of students will for checking out books.

More can be learned about proportions at https://brainly.com/question/24372153

Answer: Look at the attachment

Checking out books or studying

90

35%

Step-by-step explanation:

Answer:

Explanation:

use the formula: n(n+1)/2

                            where n is the number of nth position

(a)

n(n+1)/2

22(22+1)/2

253

(b)

11(11+1)/2

66

(c)

n(n+1)/2

31(31+1)/2

496

(d)

n(n+1)/2

40(40+1)/2

820

Answer:

a) 253

b) 66

c) 496

d) 820

Step-by-step explanation:

Triangular numbers : pattern of numbers that form equilateral triangles. Each subsequent number in the sequence adds a new row of dots to the triangle.

nth triangular number formula: [tex]T_n=\dfrac{n(n+1)}{2}[/tex]

a) if n = 22

[tex]T_{22}=\dfrac{22(22+1)}{2}=253[/tex]

b) if n = 11

[tex]T_{11}=\dfrac{11(11+1)}{2}=66[/tex]

c) if n = 31

[tex]T_{31}=\dfrac{31(31+1)}{2}=496[/tex]

d) if n = 40

[tex]T_{40}=\dfrac{40(40+1)}{2}=820[/tex]

Answer:

I hope this works

Step-by-step explanation:

look at the picture

Answer:

Step-by-step [tex]5x-4x =x \\4x^{2} -x^{2}=3x^{2} \\-24+11=-13\\3x^{2} +x-13[/tex]

Answer:

x^5 + 151x -264

Step-by-step explanation:

See the attached page.

Answer: 7596

Step-by-step explanation:

3.8%x7=26.6%

6000x26.6%=1596

6000+1596=7596

Answer:

D. 2.5

I hope it's help.......

Answer:

15/8

Step-by-step explanation:

I believe you mean 5 and 3/8, if that so well here's your answer:

Domenator (bottem number) stays same, numerator (top number) is timesed by the whole number (non-fraction number/left number)

So that'll be 5 * 3 = 15 making 15/8

The value of q when q varies inversely with p is 2.

The formula that can be used to represent inverse variation is:

p = k/q

Where:

The first step is to determine the value of the constant of proportionality

k = p x q

k = 15 x 4 = 60

Given the value of the  constant of proportionality, the value of q can now be determined.

30 = 60/q

q = 60 / 30

q = 2

To learn more about inverse proportion, please check: https://brainly.com/question/25748643

Answer:

Symbol for definite integralThe ∫ symbol is called an integral sign; it's an elongated letter S, standing for sum. (The ∫ is actually the Σ from the Riemann sum, written in Roman letters instead of Greek letters.) The dx on the end must be included; you can think of∫ and dx as left and right parentheses.

0.7 as a fraction:

Answer:

d

Step-by-step explanation:

-4 < 2x +4

-8 < 2x

-8/2

-4 < x

other side

2x + 4 < 8

8-4

2x < 4

4/2

x < 2

Answer:

The answer (as i checked i recommended doing is D)

Answer:

x = 1; y = 5/4

Step-by-step explanation:

7/x - 5/y = 3

2/x + 25/(2y) = 12

The LCD of first equation is xy. Multiply both sides of the first equation by xy.

xy(7/x) - xy(5/y) = 3xy

7y - 5x = 3xy

The LCD of second equation is 2xy. Multiply both sides of the second equation by 2xy.

2xy(2/x) + 2xy(25/2y) = 24xy

4y + 25x = 24xy

7y - 5x = 3xy

4y + 25x = 24xy

Multiply the top equation by -8 and add to bottom equation.

    -56y + 40x = -24xy

(+)     4y + 25x = 24xy

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

    -52y + 65x = 0

65x = 52y

x = 52y/65

7y - 5x = 3xy

7y - 5(52y/65) = 3(52y/65)y

455y - 260y = 156y²

156y² - 195y = 0

4y² - 5y = 0

y(4y - 5) = 0

y = 0  or  4y = 5

y = 0  or y = 5/4

7/x - 5/y = 3

y cannot equal zero.

7/x - 5/y = 3

7/x - 5/(5/4) = 3

7/x - 4 = 3

7/x = 7

x = 1

Solution: x = 1; y = 5/4