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jolli1 [7]
2 years ago
8

jamie wants to run a total of 9 miles thid week. so far, she has run 4 5/8 miles. use the equation 4 5/8 + r = 9​. please help m

e!
Mathematics
1 answer:
____ [38]2 years ago
4 0

Answer:

r=4\frac{3}{8}

Step-by-step explanation:

Given the following question:

4\frac{5}{8} +r=9

<u>Rewrite the expression to find the value of r:
</u>
9-4\frac{5}{8}

<u>Subtract by finding the common denominator:</u>
9-4\frac{5}{8}
9=\frac{9}{1}
4\frac{5}{8} =8\times4=32+5=37=\frac{37}{8}
\frac{9}{1} -\frac{37}{8}
\frac{9}{1} \times8=\frac{72}{8}
\frac{37}{8} \times1=\frac{37}{8}
\frac{72}{8} -\frac{37}{8}
72-37=35
=\frac{35}{8}
\frac{35}{8} =35\div8=4\frac{3}{8}
r=4\frac{3}{8}
4\frac{5}{8} +4\frac{3}{8} =9

Hope this helps.

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3 years ago
Write an equation of the line with the given properties. Your answer should be written in standard form.
Vanyuwa [196]

Given:

The slope of the line is m=0.

The line passes through the point P(-9,-3).

To find:

The equation of the line in standard form.

Solution:

Standard form of a line is:

Ax+By=C

The slope intercept form of the line is

y-y_1=m(x-x_1)

Where, m is the slope and (x_1,y_1) is the point on the line.

It is given that the slope of the line is 3 and it passes through the point (-9,-3), so the equation of the line is

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3 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)

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