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2 years ago

A length of string that is 22 feet long is being cut into pieces that are 1/3 foot long. how many pieces will there be

1 answer:

4 0

One foot is equivalent to 12 inches. If we get 1/3 of 12 inches, then it would be 4 inches. Given that the length of the string is 22 feet long, we first have to multiply 22 by 12 and we get 264 inches. Then divide this one by 4, so the number of pieces there will be is 66. Hope this answers your question.

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Which description does NOT guarantee that a trapezoid is isosceles?

babunello [35]

A trapezoid is isosceles if and only if

(1) The base angles are congruent

(2) The diagonals are congruent

(3) The opposite angles are supplementary

So the description does not guarantee that a trapezoid is isoceles for "Congruent bases".

3 0

2 years ago

For which equation does it make the most sense to solve by completing the square?

denis-greek [22]

Completing the square is a method used to solve a quadratic equation by changing the shape of the equation so that the left side is a perfect square trinomial.
The following equation makes more sense to solve it complete squares:
x² + 20x = 52
We have then:
x² + 20x + (10) ^ 2 = 52 + 100
(x + 10) ² = 152
Answer:
The most sense to solve by completing the square is for:
B) x² + 20x = 52

7 0

2 years ago

Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

5 0

2 years ago

HALP MEEEEEEEEEEEEEEE

nevsk [136]

Answer:

-1, 9, - 21, 69

Step-by-step explanation:

<u>Given recursive formula:</u>

a₁ = -1
aₙ = - 3aₙ₋₁ + 6 for n ≥ 2

<u>The first 4 terms are:</u>

a₁ = - 1, given
a₂ = - 3*(-1) + 6 = 3 + 6 = 9
a₃ = - 3*(9) + 6 = - 27 + 6 = - 21
a₄ = - 3*(-21) + 6 = 63 + 6 = 69

6 0

2 years ago

Suppose the band sells erasers for $2 per package and pencils for $5 per package. The band sells 220 packages in all and earns a

garik1379 [7]

Let e=erasers and p=pencils. So we know the total amount of erasers plus pencils sold is equal to 220. Therefore,

$e + p = 220$
We also know the cost of erasers and pencils totaled to $695 in earnings and so:

$2e + 5p = 695$
and so those are your two equations.

5 0

2 years ago