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3 years ago

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The figure shown represents the pattern of a glass ceiling. Based on the markings shown, which triangles can be proven congruent

? answers: A) ΔQNI ≅ ΔNPK by SSS B) ΔJKL ≅ ΔNKP by SSA C) ΔJKL ≅ ΔNKP by AAS D) ΔPNK ≅ ΔIKN by SAS

1 answer:

umka2103 [35]3 years ago

5 0

Answer:

D) ΔPNK ≅ ΔIKN by SAS

Step-by-step explanation:

The Side Angle Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In this case, the congruent sides are IK with NP and NK with itself. And the included angle is ∠K in ΔIKN and ∠N in ΔPNK.

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What is negative 56 divided by -7

Vladimir79 [104]

The answer is just use a calc lol 8

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3 years ago

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Find the sum of the positive integers less than 200 which are not multiples of 4 and 7

taurus [48]

Answer:

$12942$ is the sum of positive integers between $1$ (inclusive) and $199$ (inclusive) that are not multiples of $4$ and not multiples $7$ .

Step-by-step explanation:

For an arithmetic series with:

$a_1$ as the first term,
$a_n$ as the last term, and
$d$ as the common difference,

there would be $\displaystyle \left(\frac{a_n - a_1}{d} + 1\right)$ terms, where as the sum would be $\displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n)$ .

Positive integers between $1$ (inclusive) and $199$ (inclusive) include:

$1,\, 2,\, \dots,\, 199$ .

The common difference of this arithmetic series is $1$ . There would be $(199 - 1) + 1 = 199$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}$ .

Similarly, positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $4$ include:

$4,\, 8,\, \dots,\, 196$ .

The common difference of this arithmetic series is $4$ . There would be $(196 - 4) / 4 + 1 = 49$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $7$ include:

$7,\, 14,\, \dots,\, 196$ .

The common difference of this arithmetic series is $7$ . There would be $(196 - 7) / 7 + 1 = 28$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $28$ (integers that are both multiples of $4$ and multiples of $7$ ) include:

$28,\, 56,\, \dots,\, 196$ .

The common difference of this arithmetic series is $28$ . There would be $(196 - 28) / 28 + 1 = 7$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}$ .

The requested sum will be equal to:

the sum of all integers from $1$ to $199$ ,
minus the sum of all integer multiples of $4$ between $1\!$ and $199\!$ , and the sum integer multiples of $7$ between $1$ and $199$ ,
plus the sum of all integer multiples of $28$ between $1$ and $199$ - these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

$19900 - 4900 - 2842 + 784 = 12942$ .

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4 years ago

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Answer:

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Step-by-step explanation:

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How to solve: a parade traveled 4 miles in 2 hours. how far did tge parade travel per minute?

jek_recluse [69]

There's a really easy way to convert any units to other units.

Right now, we have the fraction (4 miles) / (2 hours).

We want to find a fraction that's exactly equal to that one,
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Just take the original fraction, and multiply it by some other
fractions.

Each fraction you multiply it by must have the value of ' 1 ' so
you don't change the value of the original fraction. But it can
have different units, that cancel with other units to eventually
give you the units you want.

(4 miles / 2 hours) times (1 hour / 60 minutes)

The second fraction is equal to ' 1 ', because the top and the bottom
have the same value ... 1 hour is the same thing as 60 minutes.

Multiply the fractions: (4 miles x 1 hour) / (2 hour x 60 minutes)

Now you can cancel 'hour' from the top and the bottom, and you have

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   = (4 / 120) mile/minute = 0.0333... mile / minute .

Let's do it again, go a little farther, and get an answer that
might mean more and feel more like an answer.

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The 2nd and 3rd fractions both have the value of ' 1 ', because
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Multiply all three fractions:

   (4 miles x 5280 feet x 1 hour) / (2 hours x 1 mile x 60 minutes)

You can cancel both 'mile' and 'hour' out of the top and bottom,
and look what you have left:

   (4 x 5280 feet x 1) / (2 x 1 x 60 minutes)

= (4 x 5280) / (2 x 60) feet / minutes

= (21,120 / 120) feet/minute =    176 feet per minute

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3 years ago

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At the deli, 2 turkey subs and 5 veggie subs cost $29. 4 turkey subs and 3 veggie subs cost

MrMuchimi

Answer:

4/9 of sales are veggie 5/9 are turkey

4/(4+5)=4/9

5/(4+5)= 5/9

4/9 x 27 = 12

5/9 x 27 = 15

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15 turkey subs sold

12+15=27 total sold

Step-by-step explanation:

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3 years ago