All categories

2 years ago

How is the product of 3 and -2 shown using integer tiles?

Mathematics

2 answers:

Anna71 [15]2 years ago

6 0

Answer:

It would be the first one

Step-by-step explanation:

because there are 3 positive and 2 negative

olga_2 [115]2 years ago

4 0

Answer:

The answer is A

You might be interested in

Samantha and Mia each left Julia’s house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 ki

Lena [83]

Mia walked 7km/h so after 1 hour, she is 7 km north of the house of Julia

Samantha walked 11km/h so after 1 hour, she is 11 km west of the house of Julia.

The points where Mia and Samantha are after 1 hour , and the house of Julia form a right triangle with sides 7 and 11 km. The distance between the girls, is the hypotenuse of his triangle.

by the pythagorean theorem:

$MS= \sqrt{ 7^{2} + 11^{2} }= \sqrt{49+121}= \sqrt{170}= 13 (km)$

Answer: 13 km

3 0

2 years ago

Read 2 more answers

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

2 years ago

After working satisfactorily for 6 months, Dave received a 7% raise. His original gross monthly salary was $1083.34. What is Dav

Dmitriy789 [7]

Answer:

Step-by-step explanation:

His original gross monthly salary was $1083.34. This means that the total amount that he earned that he earned in the first 6 months would be

6 × 1083.34 = $6500.4

After working satisfactorily for 6 months, Dave received a 7% raise. The amount by which it was raised would be

7/100 × 6500.4 = $455.00

His salary for the next 6 months would be

6500.4 + 455.00 = $6955.40

Dave's gross annual salary would be

6955.40 + 6500.4

= $13455.8

7 0

2 years ago

Read 2 more answers

Sweettooth frozen yogurt has 12 different toppings to choose from. if they add two new topping, how many ways more can ian choos

tester [92]

Assuming that the topping order is not important, you need to use the combination to solve this question. The number of toppings is 12 and then added 2, so the number will become: 12+2= 14 toppings

From 14 toppings, ian need to choose 3. The possible ways would be:
14C3= 14!/(14-3)!3!= 14*13*12/ 3*2= 364 possible ways

7 0

2 years ago

Read 2 more answers

Which percentage of weight was lost if a patient weighed 102 kg and is currently 96 kg?

galina1969 [7]

Answer:

Step-by-step explanation:

you have to make a box like this:

║ ---------- ║------------ ║ label one side percent and the other amount

║ x% ║ 96 kg ║

║ _ _ _║_____ _║ Now if the patient originally weighed 102 kg which

║100% ║ 120 kg ║ is 100% place the numbers in the bottom box.

║ _ _ _ ║ _ _ _ ║ and if the patient currently weighs 96 kg then let

Percent Amount percentage of the weight lost be x. Now cross multiply. You should get 100*96=120*x. Simplify that to get 9600=120x, now divide by 120 on both sides and you get 80 so x= 80. But the problem isn't done yet. Now you have to subtract 80% from 100% to find the weight lost, because 80% is the percentage of the current weight. after you have subtracted you get 20

20% of the original weight was lost.

4 0

2 years ago

How is the product of 3 and -2 shown using integer tiles? ​

How is the product of 3 and -2 shown using integer tiles?