Write down the next term in each of the following sequences
a)
12
17
22
27
b)
83
77
71
65

It's 8/25.

The reason its 8/25 is because u gotta add or subtract.

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

The simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

To simplify the expression (2⁵ x 5²² - 2 x 5²¹) / 25¹⁰.

we can use the properties of exponents and the fact that 25 = 5².

First, let's simplify the numerator:

(2⁵ x 5²² - 2 x 5²¹)

Using the distributive property, we can factor out 5²¹ from both terms:

= 5²¹ x (2⁵ x 5 -2)

= 5²¹ (32 x 5- 2)

= 5²¹ (160-2)

= 5²¹ x 158

Now, let's simplify the denominator: 25¹⁰

Since 25 = 5², we can rewrite it as (5²)¹⁰, which gives us:

=  (5²)¹⁰

= 5²⁰

Using the quotient rule of exponents \((a^m / a^n = a^{(m-n)})\), we can simplify further:

=  5²¹ x 158 / 5²⁰

= 5²¹⁻²⁰ x 158

= 5 x 158

= 790

Therefore, the simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

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Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)

Answer:

System 1 has an infinite number of solutions and System 11 has no solution.

Step-by-step explanation:

System 1:

x = y - 3

x - y = -3

2x - 2y = -6

Divide above by 2:

x - y = -3

So the 2 equations are identical

and they have an infinite number of solutions.

System 11:

5x + 2y = -7

15x + 6y = 21

Divide the above by 3:

5x + 2y = 7

Comparing this to the first equation the left sides are the same but right sides are different ( -7 and  7)/

There is no solution to this system.

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

(21,0)

Step-by-step explanation:

The function of the parabola is given in vertex form which is \(f(x) = a(x-h)^{2} +k\)

The vertex is equal to (h,k). Looking the function \(f(x)=8(x-21)^{2}\), we see that the h-value is equal to 21 and that the k-value is 0. So the vertex of the function is (21,0).

Answer:

11.7 degrees approximated to 12 degrees

Step-by-step explanation:

couldn't send the answer as 1 photo

let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

Step-by-step explanation:

Number 1

Number of spoons= no of boxes × individual no of spoons

= 100 × 8 = 800 spoons.

Number of cones = no of cones in a box × no of boxes

= 60 × 8 = 480

Number of cup = no of cups in a box × no of boxes

= 80 × 8 = 640.

Total = 800 + 480 + 640 = 1920

Number 2

If everyone needs a cup, spoon and cones, it means they all need 3 items.

no of people you can serve = 1920 ÷ 3

= 640 people.

Answer:

A = 378 in²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here b₁ = 6 + 15 + 6 = 27 , b₂ = 15 ( equal to middle section of b₁ ), h = 18, so

A = \(\frac{1}{2}\) × 18 × (27 + 15) = 9 × 42 = 378 in²

Answer:

DC = 16.5, CM = 16.5

Step-by-step explanation:

The centroid, C, would be the midpoint of DM if DM was a line between the midpoint of a side and it's opposite vertex. So DC and CM are half of DM. Hope this helps.

Answer:

1 cookie per minute??

Step-by-step explanation:

Answer:

one cookie per minute. Is that clear?

Answer: False

Step-by-step explanation:

25% of the data is between Q1 and the median.

The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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Answer:

10 dollars

Step-by-step explanation:

5 + 5

To make a regular polygon with 96 sides we can take a circle as a starting point and divide it into 96 equal sides.

To create a regular polygon with 96 sides, we must take into account that all its sides must be equal, so we can take a circumference as a starting point. In this case, the circumference has 360°, so we must divide this into 96 parts and the result would be the distance between the edges of the polygon.

In this case, we must make a circle with a protractor and mark every 3.75°, when we have completed this procedure in the entire circumference we will have a regular polygon with 96 sides.

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Answer:

D) -8

Step-by-step explanation:

If you add a positive and a negative, you end up subtracting. If your sum is lower than any of the numbers you are adding together, then there is a negative. In this case, your only negative number is -8, but if there were others, you could find this equation by doing negative six minus two (because the equation was originally addition, it would still be subtraction to check your work or find the answer in this case.)

Hopefully you find this useful :)

Answer:   -8

Step-by-step explanation:    lets take the unknown number as x,

so we have, 2 + x= -6

                 by using transposition method, x= -6-2( positive becomes  

                                                                       negative when transpositioning)

      so, x= -8                      

Answer:

10^2

Step-by-step explanation:

10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2

Answer:

100

Step-by-step explanation:

Hope it helps

Answer:

Step-by-step explanation:

mag jakol

Answer:

The length of the base would be 11.

Step-by-step explanation:

The formula of finding the area of a triangle is 1/2 base x height. Therefore, we know that since the area is 44 cm², the base and height would multiply to 88. 11 x 8 = 88 and 11 - 8 = 3. So, the base is 3cm longer which is 11.  

Answer:

The circle graph does not represent a function because it doesn't pass the vertical line test.

Step-by-step explanation:

Answer:

35/522 ≈ 0.067

Step-by-step explanation:

There are initially 29 names in the hat, 15 of which are girls' names.  So the probability is 15/29.

There are now 28 names in the hat, 14 of which are boys' names.  So the probability is 14/28.

There are now 27 names in the hat, and 14 girls' names.  So the probability is 14/27.

Finally, there are 26 names in the hat, and 13 boys' names.  So the probability is 13/26.

The total probability is:

P = (15/29) (14/28) (14/27) (13/26)

P = 35/522

P ≈ 0.067

Answer:

Step-by-step explanation:

There are initially 29 names in the hat, 15 of which are girls' names.  So the probability is 15/29.

There are now 28 names in the hat, 14 of which are boys' names.  So the probability is 14/28.

There are now 27 names in the hat, and 14 girls' names.  So the probability is 14/27.

Finally, there are 26 names in the hat, and 13 boys' names.  So the probability is 13/26.

The total probability is:

P = (15/29) (14/28) (14/27) (13/26)

P = 35/522

P ≈ 0.067

a:1/6×18/1=18/6 when simplified is 3

b:4/6×18/1=72/6 when simplified is 12

c.The relationship between the number of students with brown hair and the number of students with red hair is that they are equivalent to one another.

Answer:

The original price of petrol is R12.58 per litre and the new price is R13.28 per litre. To find the percentage increase in the price, we can use the following formula:

Percentage increase = ((new price - old price) / old price) x 100%

Substituting the values, we get:

Percentage increase = ((13.28 - 12.58) / 12.58) x 100%

Percentage increase = (0.70 / 12.58) x 100%

Percentage increase = 0.0557 x 100%

Percentage increase = 5.57%

Therefore, the percentage increase in the price of petrol is 5.57%.

Step-by-step explanation:

Answer:

O A. PQ = SU

Step-by-step explanation:

When two triangles are congruent then by CPCTC,

their corresponding parts ( angles and sides )  must be congruent.

In triangles PQR and STU,

Side PQ, QR and RP are corresponding to the sides ST, TU and US respectively,

Also, angles P, Q and R are corresponding to angles S, T and U respectively.

Here, Δ PQR ≅ Δ STU,

Thus, by the above property,

PQ ≅ ST, QR ≅ TU and RP ≅ US,

∠P ≅ ∠T, ∠Q ≅ ∠T and ∠R ≅ ∠U

Given the breadth of the bag is 12 cm and the length is 18 cm, and the assumed height is 6cm, t​he volume of the cooler bag is 1296 ml.

The volume of the cooler bag is determined using the formula;

Volume = length * breadth * height

Data given:

breadth = 12 cm

length = 18 cm

height = ?

The height is not given, therefore, an assumed height of 6 cm is used in the calculation.

Converting the measurements to millimeters:

Breadth = 12 cm * 10 mm/cm = 120 mm

Length = 18 cm * 10 mm/cm = 180 mm

Height = 6 cm * 10 mm/cm = 60 mm

Now, we calculate the volume of the cooler bag:

Volume = 180 mm * 120 mm * 60 mm

Volume = 1,296,000 mm³

To convert the volume from cubic millimeters to milliliters, we divide by 1,000

Volume = 1,296,000 mm³ / 1,000

Volume of cooler bag = 1296 ml

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