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3 years ago

There are 1,657 souvenir paperweights that need to be packed in boxes. Each box will hold 17

Mathematics

1 answer:

blondinia [14]3 years ago

4 0

Answer:

Therefore we can say that 98 boxes will be needed to hold all the paperweights.

Step-by-step explanation:

i) there are 1657 souvenir paperweights that need to be packed in boxes.

ii) each box will hold 17 paperweights

iii) therefore the number of boxes that will be needed are

= $\dfrac{total\hspace{0.15cm} number\hspace{0.15cm} souvenir\hspace{0.15cm} paperweights}{number\hspace{0.15cm} of\hspace{0.15cm} paperweights\hspace{0.15cm} per\hspace{0.15cm} box}$ = $\dfrac{1657}{17}$ = 97.471

iv) Therefore we can say that 98 boxes will be needed to hold all the paperweights.

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Three vertices of parallelogram ABCD are A(2,-6),B(-1,2),C(5,3).find the coordinates of vertex D

salantis [7]

Check the first picture below.

for a parallelogram, it has to have two pairs of parallel sides, so BC || AD and AB || CD.

if two lines are parallel, they have the same slope, namely the same rise and run.

notice, the line BC has a run of 6 and a rise of 1, arrows in red, therefore, AD must also have a run of 6 and a rise of 1, so if we move from A 6 units over and 1 up, we'd end up at point D.

now, for part atop

Check the 2nd picture, in a parallelogram, opposite sides are parallel and opposite angles are equal, so if WLP is 144°, then PNW is also 144°.

in a parallelogram, diagonals bisect each other, so each cut the other in halves, so if PM is 9 then MW is also 9 and thus PW is just 9+9=18.

now, about QRST.

notice what we said about a parallelogram above, thus

$\bf 8x+13=11x-23\implies 8x+36=11x\implies 36=3x \\\\\\ \cfrac{36}{3}=x\implies \boxed{12=x} \\\\[-0.35em] ~\dotfill\\\\ 2y+12=4y-4\implies 2y+16=4y\implies 16=2y \\\\\\ \cfrac{16}{2}=y\implies \boxed{8=y}$

so then TQ ==> 2(8) + 12 ==> 16 + 12 ==> 28.

∡Q ==> 8(12) + 13 ==> 96 + 13 ==> 109°.

and since in a parallelogram, adjacent interior angles add up to 180°, then ∡Q + ∡T = 180°.

∡T ==> 180 - 109 ==> 71°.

3 0

3 years ago

Please answer ASAP it’s really important please

bazaltina [42]

Answer:

Letter A.

Step-by-step explanation:

0 is not divisible, so the last the last two alternatives are impossible.

The second one doesn't work, so I'd stick to letter A.

6 0

2 years ago

The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p=−0.

n200080 [17]

By solving a quadratic equation, it can be verified that

The owl population will disappear after 329.12 years

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

Here, a quadratic equation needs to be solved

The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p= $-0. 4t^2+128t+1,200$

For population to disappear, p =0

$-0. 4t^2+128t+1,200 = 0\\0.4t^2 -128t - 1200 = 0\\4t^2 - 1280t - 12000 = 0\\4(t^2 - 320 t - 3000) = 0\\t^2 - 320t -3000 = 0\\t = \frac{-(-320)\pm \sqrt{(-320)^2 - 4 \times 1 \times (-3000)}}{2 \times 1}\\t = \frac{320 \pm 338.23}{2}\\t = \frac{320 + 338.23}{2} \ or \ t = \frac{320 - 338.23}{2}\\t = 329.115 \ or \ t = -9.115$

But t = -9.115 is not possible as time cannot be negative

So, the owl population will disappear after 329.12 years

To learn more about quadratic equation, refer to the link-

brainly.com/question/1214333

#SPJ4

7 0

10 months ago

RIGHT ANSWERS ONLY I REALLY NEED TO PASS IF YOUR FAST AND CORRECT ILL GIVE YOU BRAINEST!!!

malfutka [58]

Answer:

1st option

Step-by-step explanation:

The domain and range are all real numbers , that is

domain { x | x ∈ R }

range { y | y ∈ R }

6 0

3 years ago

Parabolas y=−2x^2 and y=2x^2 +k intersect at points A and B that are in the third and the fourth quadrants respectively. Find k

OverLord2011 [107]

Answer:

-25

Step-by-step explanation:

(1) y = -2x²

(2) y = 2x² + k Subtract (1) from (2)

0 = 4x² + k Subtract 4x² from each side

k = -4x²

The parabolas are symmetrical about the y-axis.

Segment AB = 5, so x = +2.5 and x = +2.5.

k = -4(±2.5)² = -4 × 6.25 = -25

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2 years ago