What is the sum of the first 50 natural numbers? How to solve it without adding 50 digits?

Answers

Answer 1

Answer: $1+2+3+4+5+\dots+50\n\n1;\ 2;\ 3;\ 4;\ 5;\dots;50\ are\ the\ terms\ of\ a\ arithmetic\ sequence\nwhere\ a_1=1\ and\ d=1\n\nSum:S_n=(a_1+a_n)/(2)\cdot n\n\nS_(50)=(1+50)/(2)\cdot50=51\cdot25=1275\leftarrow solution$

Answer 2

Answer: Look at the first one and the last one: 1 + 50 = 51
Look at the second one and the second-last one: 2 + 49 = 51
Look at the third one and the third-last one: 3 + 48 = 51

Every pair you construct in this way adds up to 51 .

There are ( 50/2 ) = 25 pairs.

They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275

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In triangle ABC, the measure of angle B is 90 degrees, BC=16, and AC=20. triangle DEF is similar to triangle ABC, where vertices D, E, and F corresponds to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. what is the value of sinF?(please show your work)
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Five less than a number is at least -28
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How many faces are there in a prism which has 24 edges

Answers

Final answer:

A prism with 24 edges will have 10 faces.

Explanation:

In a prism, each face is a flat surface. A prism has two parallel bases that are polygonal shapes, and the other faces are rectangular. The number of faces in a prism is determined by the shape of its bases. If the prism has a triangular base, it will have 3 rectangular faces on the sides, and the two triangular bases, making a total of 5 faces. If the prism has a rectangular or a square base, it will have 4 rectangular faces on the sides, and the two bases, making a total of 6 faces.

Since the prism in question has 24 edges, we can determine the shape of its bases by dividing the number of edges by the number of edges on each base. If the bases are polygons, we can find the number of edges by multiplying the number of vertices by the number of sides on each polygon. By trying different combinations, we find that a prism with 8-sided bases (octagon) will have 24 edges. Therefore, the prism has 2 octagonal bases and 8 rectangular faces, making a total of 10 faces.

Learn more about Faces in a Prism here:

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The grocery store sells kumquat for $4.50 a pound and Asian pears for $3.75 a pound write an equation in standard form for the weight of kumquat k and Asian pears p that a customer could buy with $16

Answers

Answer:

let k represents the kumquat weight(in pound) and p represents the Asian pears weight respectively.

As per the given conditions,

The grocery store sells kumquat for $ 4.50 a pound

⇒ for 1 pound $\rightarrow$ $4.50

then, in k pound = $4.50 k$

similarly,

The Asian pears for $3.75 a pound

⇒ for 1 pound $\rightarrow$ $3.75

then, in p pound = $3.75 k$

Standard form of the equation is in the form of Ax + By = C:

The weight of kumquat k and Asian pears p that customer could buy with $ 16,

then the standard form of equation is: 4.50k +3.75p = 16

1 pound kumquat = 4.50
1 pound pear = 3.75
4.50k + 3.75p = 16

Which is a linear equation?

Answers

Answer:

Step-by-step explanation:

eq of first degree is a linear equation.

y=x+1

Solve.
–30 = 6z
a. –5
b. –6
c. –24
d. –180

Answers

-30 = 6z

Plug in 6(-5) and you get -30

Answer is A

The correct answer is A. -5

The expression (x8 - 48) can be factored as (x2 - 42)2 (x2 + 42)2.
a. True
b. False

Answers

I think the answer is false, but I'm not sure. I wish I could help more ):

Solve 2cos^2x + cosx − 1 = 0 for x over the interval [0, 2 π ).a.π and π/3
b.π, π/3, and 5π/3
c.1 and 2π/3
d.1, 2π/3, and 4π/3
e.1, π/3, and 5π/3

Answers

Let cos x = a, then
2a^2 + a - 1 = 0,
solving the quadratic equation, we have:
a = 0.5 or -1.

i.e. cos x = 0.5 or cos x = -1
for cos x = 0.5,
x = pi/3, 2pi - pi/3 = pi/3, 5pi/3

for cos x = -1,
x = pi

therefore, x = pi, pi/3, 5pi/3
Answer: B

Answer:

Option B is correct for plato

Step-by-step explanation:

$\pi ,(\pi )/(3), and (5\pi )/(3)$

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