A student was asked to simplify the expression 2(x+3)+(4x−8)−7x .

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:

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.

Answer:

Step-by-step explanation:

2 2/3 = 8/3

3 3/8 = 27/8

8/3 * 27/8 = 216/24

= 9

Answer:

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

Step-by-step explanation:

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!

n=3

Step-by-step explanation:

24=3n-15

9=3n

3=n

Answer:

n = 13

Step-by-step explanation:

24 = 3(n - 5)

divide each side by 3

8 = n - 5

add 5 to each side

13 = n

check your work

24 = 3(13 - 5)

24 = 3(8)

24 = 24

Answer:

  2.5 cm

Step-by-step explanation:

Put the given values into the area formula, and solve for height.

  A = 1/2bh

  5 cm² = 1/2(4 cm)h . . . . . . . . . . . . . fill in the values

  (5 cm²)/(2 cm) = h = 2.5 cm . . . . . divide by the coefficient of h

The height is 2.5 cm.

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:

It is B. (0,1)

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

a

Answer:

2

a

x

−

5

a

−

10

x

+

25

Step-by-step explanation:

Answer:

D. 2.5

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

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.

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

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:

Ok, so to find the volume of a sphere, the volume is 4/3 (3.14 which is pie) times the radius cubed so r^3

so the radius of this sphere is 2 because 4-2=2

Step-by-step explanation:

so now we do 4/3 times 3.14 times 2^3 power=

now first we multiply 4/3 times 2 to the 3rd power bc we dont need to multiply pie (3.14) your answer would be 10.66667 so its 10.66667 pie (3.14) so round 10.66667 it would just be 10.7 because the 7 round up the 6 to a 7. Hope this helps!

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

Given:.

Steps :

470 × 0.88

£413.6

Answer: 7596

Step-by-step explanation:

3.8%x7=26.6%

6000x26.6%=1596

6000+1596=7596

0.7 as a fraction:

Answer:

See below

Step-by-step explanation:

Problem 4

[tex]H_0:\mu=145\\H_a:\mu>145[/tex]

The null hypothesis, [tex]H_0[/tex], comes from the fact that the nurse initially thinks that the average height of 7th graders is equal to 145 cm.

The alternative hypothesis, [tex]H_a[/tex], comes from the fact that the average height may be greater than 145 cm since the nurse measured the average height to be 147 cm from the random sample.

Problem 5

[tex]H_0:\mu\geq273\\H_a:\mu<273[/tex]

The null hypothesis, [tex]H_0[/tex], comes from the fact that the manufacturer initially thinks that the mean lifetime of a certain type of batteries is at least 273 hours.

The alternate hypothesis, [tex]H_a[/tex], comes from the fact that the sample taken may show that it's actually less given a sample mean of 270.5 hours.

Problem 6

The mass population data set would be most suitable because the average score of a test comes from all those who have taken the test while the sample is the class with 25 students. That sample represents the population of all those that have taken the test.

Problem 7

Because it would take a lot of time and money to check every single child in Africa, it would make the most sense to use the sample data set where your samples come from each village and those samples have the children from each village.

Problem 8

This is a population characteristic because the sample that Sarah took for the average number of children per family represents the entire population.

Problem 9

This is a sample characteristic because the size of the sample was clearly large, this was a study, and other claims made.

Answer:

a = 14, b = 2

Step-by-step explanation:

the initial amount was 14

the growth factor is 2

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:

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

Answer:

$1.004 so rounded it would be Answer D ($1.00)

Step-by-step explanation:

You multiply $25.10 by the decimal form of 4 percent, which gives you the tax.

25.10(.04)=1.004

1.004 is the tax, but with the way currency work, cents do not go to the thousandths place , so you round it to $1.00.

Incase you woudl also like to know, if you add that 1 dollar to the original price you get teh total price. which woudl be $26.10.

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:

1/10, 13%, 0.15, 16/100, 1/5

Step-by-step explanation:

Given the following question:

13%, 16/100, 1/5, 0.15, and 1/10

In order to find the answer to this question we can rewrite all the following fractions/percent into decimals and then compare.

[tex]\frac{16}{100} =16\div100=0.16[/tex]
[tex]\frac{1}{5} =1\div5=0.2[/tex]
[tex]\frac{1}{10} =1\div10=0.1[/tex]
[tex]13=0.13[/tex]

0.13, 0.16, 0.15, 0.2, and 0.1
0.1, 0.13, 0.15, 0.16, 0.2

1/10, 13%, 0.15, 16/100, 1/5

Hope this helps.

Answer:

6

Step-by-step explanation:

20% of 30 is 6. You can figure this out because 100 divided by 20 is 5, so you do 30 divided by 5, which is 6

Answer:

5.2y^3

Step-by-step explanation:

There are 3 y's which can be presented as y^3

5.2 times y^3 = 5.2y^3

( By the way, " ^ " is a square root sign )

Answer:

108

Step-by-step explanation:

450*0.24

Answer:

Step-by-step explanation:

V = Bh

V = 15(10)

V = 150 cm3