Find the first five terms of the sequence described:
a sub 1 = 3
a sub n+1 = a sub n + 5

Answer:

Elimination would be a better method for solving the system.

[tex]\Rrightarrow \sf12x+10y=2[/tex]

[tex]\Rrightarrow \sf6x+5y=1.......(i)[/tex]

[tex] \sf\Rrightarrow-x+4y= -5 ............(ii)[/tex]

[tex]\large \sf \red{ \blue{[ (ii)×6]}}[/tex]

[tex]\sf\Rrightarrow-6x+24y= -30 ............(iii)[/tex]

[tex] \large \sf \red{(i) + \blue{ (iii)}}[/tex]

[tex]\Rrightarrow \small\sf6x+5y=1+(-6x+24y= -30)[/tex]

[tex]\Rrightarrow \sf29y = - 29 \\ [/tex]

[tex]\Rrightarrow \blue{\sf \: y = - 1}[/tex]

putting the value in equation (i)

[tex]\Rrightarrow \sf6x+5 \times - 1=1[/tex]

[tex]\Rrightarrow \sf6x - 5=1[/tex]

[tex]\Rrightarrow \sf6x = 6[/tex]

[tex]\Rrightarrow \red{\sf \: x = 1}[/tex]

[tex]\overline{\underline{\rule{209pt}{2pt}}}[/tex]

Answer:

z=15

Step-by-step explanation:

z-7+7=8+7 ( add 7 on btoh sides to cancel out)

z=15 ( left with 7)

The expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]

The function is given as:

[tex]f(x) = \sqrt{x[/tex]

When the function is stretched horizontally by a factor of 2, the rule is:

f'(x) = f(x/2)

So, we have:

[tex]f'(x) = \sqrt{\frac x2[/tex]

When the function is shifted left by 1 unit, the rule is:

f"(x) = f(x + 1)

So, we have:

[tex]f"'(x) = \sqrt{\frac {x - 1}2[/tex]

When the function is shifted up by 3 units, the rule is:

g(x) = f"(x) + 3

So, we have:

[tex]g(x) = \sqrt{\frac {x - 1}2} + 3[/tex]

Hence, the expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]

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The area of the sector rounded to 4 decimal place is 78.6396 cm²

area of sector = ∅/ 360 × πr²

Therefore,

Hence,

area of a sector = 46 / 360 × 3.14 × 14²

area of a sector = 46 / 360 × 3.14 × 196

area of a sector =   46 / 360 × 615.44

area of a sector =   28310.24 / 360

area of a sector = 78.6395555556

Hence,

area of a sector = 78.6396 cm²

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Answer: 42.308%

Step-by-step explanation:

Isolate x:

2x + 7y = -1

2x = -1 -7y

x = -1/2 - 7/2y

Substitute the equation of x:

4x - 3y = -19

4(-1/2 - 7/2y) - 3y = -19

-2 - 14 - 3y = -19

-3y = -19 + 14 + 2

-3y = -3

 y = 1

Substitute to find x:

2x + 7y = -1

2x + 7(1) = -1

2x = -1 - 7

2x = -8

x = -4

(-4, 1)

Multiply one or both equations through an integer in order that one time period has the same and contrary coefficients within the equations. Add the equations to provide a single equation with one variable. clear up for the variable. alternative the variable back into one of the equations and resolve for the other variable.

Conclusion: A system of equations is fixed of 1 or greater equations related to some of the variables. The solutions to systems of equations are the variable mappings such that every one component equations are satisfied—in other phrases, the locations at which all of these equations intersect.

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Answer:

First Question x = [tex]17\sqrt{2}[/tex] Second Question x = 36

Step-by-step explanation:

First Question:

Since The triangle is isosceles, [tex]17^2 +17^2=x^2[/tex] (Pythagoras)

[tex]x=17\sqrt{2}[/tex]

Second Question

This is half an equilateral triangle, so [tex](\frac{1}{2}x)^2+(18\sqrt{3})^2=x^2[/tex]

[tex]\frac{3}{4}x^2=972[/tex]

[tex]x^2=1296[/tex]

[tex]x=36[/tex] (cannot be negative)

Answer:

8

Step-by-step explanation:

because there is 8 in the question

Answer:

x^2=9

so we find the sqare root of both sides

x=square root of 9

x=-3 or 3

Hope This Helps!!!

First definition matches with expression, second matches with equation ,third matches with algorithm and fourth matches with equation.

Given  four definitions of equation, expression, algorithm but mixed.

We have to match the definitions with appropriate term.

We know that expression is a combination of numbers, symbols, fraction, coefficients, indeterminants mostly not found in equal to form. It exhibits a behaviour only.

Algorithm is a computer programming to do a specific task in a predetermined way.

Equation is a relationship between two variables expressed in equal to form. In this we have to put the value of variables and the equation gives us a value.

Hence  First definition matches with expression, second matches with equation ,third matches with algorithm and fourth matches with equation.

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Answer:

He will need to pay 5.4 Ghana cedis into his educational fund.

Step-by-step explanation:

We need to multiply 4 1/2 by 120 since it is a percentage. We convert 4 1/2 into a decimal which is 4.5. Now, we just need to multiply 120 by 4 1/2 to get an answer of 5.4.

The average rate of change is illustrated below.

The average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a).

In this case the interval is [0,2], then a=0, b=2

r=[f(2)-f(0)]/(2-0)

r=[f(2)-f(0)]/2

1) First function: h(x)

r=[h(2)-h(0)]/2

x=2→h(2)=(2)^2+2(2)-6

h(2)=4+4-6

h(2)=2

x=0→h(0)=(0)^2+2(0)-6

h(0)=0+0-6

h(0)=-6

r=[h(2)-h(0)]/2

r=[2-(-6)]/2

r=(2+6)/2

r=(8)/2

r=4

2) Second function: f(x)

A function, f, has an

x-intercept at (2,0)→x=2, f(2)=0

and a y-intercept at (0,-10)→x=0, f(0)=-10

r=[f(2)-f(0)]/2

r=[0-(-10)]/2

r=(0+10)/2

r=(10)/2

r=5

3) Third function: g(x)

r=[g(2)-g(0)]/2

From the graph:

g(2)=6

g(0)=2

r=(6-2)/2

r=(4)/2

r=2

4) Fourth function: j(x)

r=[j(2)-j(0)]/2

From the table:

x=2→j(2)=-8

x=0→j(0)=4

r=(-8-4)/2

r=(-12)/2

r=-6

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Answer:

[tex]\sf Total \ amount \ of \ walnuts \ and \ pecans \ needed = \dfrac{7}{12}[/tex]

Step-by-step explanation:

    [tex]\sf Amount \ of \ walnut \ needed = \dfrac{1}{4}[/tex]

    [tex]\sf Amount \ of \ pecans \ needed =\dfrac{2}{6} =\dfrac{1}{3}[/tex]

To find the total amount of walnut and pecans, we have to add the fractions.

LCM of 4 & 3 = 12

Equivalent fractions:

      [tex]\sf \dfrac{1}{4}=\dfrac{1*3}{4*3}=\dfrac{3}{12}\\\\\dfrac{1}{3}=\dfrac{1*4}{3*4}=\dfrac{4}{12}[/tex]

Now, add

   [tex]\sf \dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}[/tex]

                  [tex]\sf = \dfrac{7}{12}[/tex]

Step-by-step explanation:

The next term in the sequence is -1.

Given a sequence is defined recursively by the formula f(n+1)=f(n)+3.

An ordered list of integers that frequently follows a pattern or function is known as a sequence. Sequences can have a finite or indefinite length. Terms refer to the distinct components of a sequence. The individual numbers or parts that make up a sequence are known as its terms.

The first term of the sequence is -4.

That means f(1)=-4            .......(1)

When compare f(1) with f(n+1), we get

n=0

So, when n=0 then it is the first term of the sequence.

When n=1 then substituting this in the given formula, we get

f(1+1)=f(1)+3

f(2)=f(1)+3

Now, Substitute the value of f(1) from equation (1), we get

f(2)=-4+3

f(2)=-1

Hence, the next term in the sequence when the sequence is defined recursively by the formula f(n+1) = f(n)+3 and the first term of the sequence is –4 is -1.

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The length of one leg of the right triangle is 5√10

The leg of a right triangle can be found as follows;

Therefore, using trigonometric ratios,

sin 45 = opposite / hypotenuse

sin 45 = x / 10√5

1 / √2 = x / 10√5

cross multiply

10√5 = x√2

divide both sides by √2

x = 10√5 / √2

x = 10√5 / √2 × √2 / √2

x = 10√10 / 2 = 5√10

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Answer:

Step-by-step explanation:

A triangle with side lengths of 5 meters, 7 meters and 9 meters is

an obtuse triangle

The total amount will be $889123 after 16 years if the starting salary is $350000

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent [tex]y = a^x[/tex]

where a is a constant and a>1

We have:

Starting salary is $350000 and you receive a 6% increase at the end of every year.

We can find the total amount, from the exponential formula:

T = a(1 + r)ⁿ

T is the total amount

a is the starting amount

r is the rate

n is the total number of years

T = 350000(1 + 6%)¹⁶

T = 350000(1 + 0.06)¹⁶

T = 889123.08 ≈ $889123

Thus, the total amount will be $889123 after 16 years if the starting salary is $350000

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find the slope of a line passing through (-2,-7) and (-2,2)

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{6cm} To find the slope, \\ we use the formula below.\end{minipage}}[/tex]

[tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex]   | put in the values

[tex]\bf{\dfrac{2-(-7)}{-2-(-2)}}[/tex] | look what happens when I simplify!

[tex]\bf{\dfrac{2+7}{-2+2}}[/tex] | uh-oh

[tex]\bf{\dfrac{9}{0}}[/tex] ...

The operation above is an operation we can't do.

[tex]\bf{Slope=\;Not\;D e f ined}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

             [tex]\bf{=Slope=Not\;De fined}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Answer:

10.63 inches

(b)2+(h)2=(H)2

(8)2+(7)2=(H)2

64+49=(H)2

113=(H)2

H=10.63

The diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.

The diagonal of a rectangle having a length l and width w will be:

d = √(l² + w²).

In the question, we are asked to determine the diagonal length of the photo frame bought by Mike, having measurements of 8 inches in length and 7 inches in width.

We know the photo frame is in the shape of a rectangle, as it has a length and a width.

We also know that the diagonal of a rectangle having a length l and width w will be:

d = √(l² + w²).

So, by substituting l = 8 and w = 7, in the above relation, we can calculate the diagonal of the photo frame as:

d = √(8² + 7²),

or, d = √(64 + 49),

or, d = √113,

or, d = 10.63.

Therefore, the diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.

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Answer:

3(n-5)=2n+16

Step-by-step explanation:

3 lots of 'n' and 5 means 3 times both values so these values are put into a bracket with a common multiplier (ie. the 3)

3(5 - n)

16 more than 2 lots of 'n' means that n has to be doubled. n + n = 2n. add 16 to this and we have

2n + 16

if these values are both equal (hence why they are in an equation) then all that is needed is for them to be set equal alongside each other.

3(n-5) = 2n+16

:)

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The length of Jk can be either 10 or 26.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Since in a rectangle the opposite sides are equal, therefore, the sides NM and JK will be equal.

JK = MN

8x - 14 = x² + 1

0 = x² - 8x + 15

x = 5, 3

Hence, the length of Jk can be either 10 or 26.

The complete questions are:

Quadrilateral JKMN is a rectangle, if NM= 8x - 14 and JK= x squared + 1, find JK.

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The probability they choose a black and a brown puppy is 0.2857 (option B)

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability they choose a black and a brown puppy = (number of black puppies / total number of puppies) x ( (number of brown puppies / total number of puppies - 1)

3/7 x 4/6 = 0.2857

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The rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min. Computed using differentiation.

The sand is falling onto a conical pile, thus we get the pile in the shape of a cone, whose volume is given as:

V = (1/3)πr²h,

where V represents the volume of the cone, r represents its radius, and h represents its height.

In the question, we are given that the rate of piling is 16 ft.³/min, which implies that:

dV/dt = 16 ... (i)

We are also given that the diameter is three times the altitude (height), which can be shown as:

2r = 3h,

or, r  = (3/2)h.

Thus, the volume can now be shown as:

V = (1/3)π{(3/2)h}²h,

or, V = (3πh³)/4.

Differentiating this with respect to time, we get:

dV/dt = (3π/4)(3h²)dh/dt.

Now, we need to calculate the rate of change of height, when the height is  2 feet, thus we take h = 2

Using dV/dt = 16 from (i), we can write:

16 = (3π/4)(3(2)²)dh/dt.,

or, 16 = 9π(dh/dt),

or, dh/dt = 16/9π = 0.5659 ft./min.

Thus, the rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min.

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Answer:

ok sure will do the answer is

Step-by-step explanation:

Answer:

-5 and 6

Step-by-step explanation:

-5 * 6 = -30

-5 + 6 = 1

The expressions that gives the number of online math classes is as follows:

y = x - 15

The number of math classes offered online in the summer is 15 less than the number of math classes offered face-to face in the summer.

Let

the number  of math classes offered face-to face = x

the  number of math classes offered online  = y

Therefore, the expression that gives the number of online math classes is as follows:

y = x - 15

x = y + 15

Hence,

y = x - 15

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