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saw5 [17]
2 years ago
6

Find two consecutive positive integers such that the sum of their squares is 421

Mathematics
1 answer:
alexandr402 [8]2 years ago
6 0
14 and 15
14^2 = 196
15^2 = 225
225+196 = 421
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What is the measure of angle CBE?
GarryVolchara [31]

Answer:

72°

Step-by-step explanation:

180-3x=2x

5x=180

x=36

Angle CBE = 2(36) = 72

7 0
2 years ago
Find an equation in slope-intercept form for the line with slope -12 and y-intercept = 1/2
Kruka [31]
M = -12
point = (0, 1/2)

Find the slope-intercept equation
y - y₁ = m(x - x₁)
y - 1/2 = -12 (x - 0)
y - 1/2 = -12x
y = -12x + 1/2
4 0
2 years ago
Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
snow_tiger [21]

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

8 0
3 years ago
Andy and Christopher are measuring a liquid solution using graduated cylinders, Andy uses 3.5 liters of the liquid solution, and
Gre4nikov [31]

Answer:

Ratio = 0.74

Step-by-step explanation:

Represent

- Andy with A

- Christopher with C

A = 3.5L

C = 2580mL

Required

Determine the ratio of C to A

Ratio is represented as thus:

Ratio = C:A

Rewrite as fraction

Ratio = \frac{C}{A}

This gives

Ratio = \frac{2580mL}{3.5L}

Convert L to mL

Ratio = \frac{2580mL}{3.5*1000mL}

Ratio = \frac{2580mL}{3500mL}

Ratio = \frac{2580}{3500}

Ratio = 0.73714285714

Ratio = 0.74 --- Approximated

6 0
3 years ago
Question is attached, ill mark brainliest
Alborosie

Answer:

w=7

Step-by-step explanation:

3w+4w=49

7w=49

w=49/7

w=7

4 0
3 years ago
Read 2 more answers
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