Two lines intersecting at a right angle

If you have apples 14 banana And 20 potatoes, Find The:

sattari [20]

Step-by-step explanation:

Firs prime factorisation then we will find their GCF and it is 2

7 0

3 years ago

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Write each sum using summation notation<br> 12 + 22 + 32 + 42 + ⋯ + 10000^2

Murljashka [212]

Answer:

50,00,70,000

Step-by-step explanation:

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

Here first we will find the number of terms

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 12, 22, 32, 42, ⋯ , 100002

a = 12, d = 10, n = ? and aₙ= 100002

∴ 100002 = 12 + (n - 1) × (10)

⇒ 99990 = 10(n - 1)

⇒ n = 10000

Now using the formula of Sum of Arithmetic Sequence,

Sₙ = n÷2[2a + (n - 1)d]

⇒ Sₙ = (10000÷2)[2 × 12 + 9999 × 10]

⇒ Sₙ = 5000 [ 24 + 99990]

⇒ Sₙ = 5000 × 100014 = 50,00,70,000

5 0

3 years ago

Which set(s) of points show x in DIRECT PROPORTION to y? A) {E, C, B} only B) {G, C, A} only C) {F, E, D} and {E, C, B} only D)

polet [3.4K]

Answer:{F, G, H} and {G, C, A} only

Step-by-step explanation:

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3 years ago

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What is the price if you mark up $50 by 10%

BARSIC [14]

Answer:

55

Step-by-step explanation:

Original price = 50 and percent markup is 10%

The increase is the original price times the percent markup

increase = 50 * 10%

increase = 50*.10

= 5

The new price is the original price plus the increase

new price = 50 + 5

= 55

8 0

3 years ago

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

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