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3 years ago

The sum of two numbers is 196. One number is 64 more than the other. Find the numbers.

Mathematics

2 answers:

anzhelika [568]3 years ago

6 0

Answer:

Step-by-step explanation:

Hi there!

Let one of the number be "x" then the next number is x+64.

According to the question,

The sum of two numbers is 196.

i.e x + (x+64) = 196

or, 2x +64 = 196

Subtract 64 from both sides,

2x +64-64 = 196 - 64

2x = 132

Divide both sides by 2,

$\frac{2x}{2}$ = $\frac{132}{2}$

x = 66

And x+64 = 66+64 = 130

Therefore, the one number was 66 and another was 130.

Hope it helps!

ValentinkaMS [17]3 years ago

4 0

Answer:

I just guessed random numbers until I got 66 and 130.

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State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli

nasty-shy [4]

Answer:

Part A

$f(n)=52-12(n-1)$

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$ Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right$

Part D:

$h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right$

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

$(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12$

Explicit Formula

To write an explicit formula is to write it as function.

$f(n)=52-12(n-1)$

Recursive Formula

To write it as recursive formula, is to write it as recurrence given to some restrictions:

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

$(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\$

Arithmetic Sequence, difference

$d=\frac{2}{4}$

Explicit Formula:

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)$

Recursive Formula

$g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.$

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

Explicit formula

$h(n)=1.1+0.4(n-1)\\$

Recursive Formula

$h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.$

6 0

3 years ago

WILL GIVE BRAINLIEST

EastWind [94]

Answer:

Let coordinates of vertex D be (x,y)

In parallelogram diagonals are bisect each other.

∴ Mid-point of AC= Mid-point of BD

⇒ (

3+(−6)

−4+2

)=(

−1+x

−3+y

)

⇒ (

−3

−2

)=(

−1+x

−3+y

)

⇒ (

−3

,−1)=(

−1+x

−3+y

)

Now,

⇒

−3

−1+x

⇒ −6=−2+2x

⇒ −4=2x

∴ x=−2

⇒ −1=

−3+y

⇒ −2=−3+y

⇒ 1=y

∴ y=1

∴ Coordinates of vertex D is (−2,1)

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Answer:

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