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3 years ago

Which lists all the integer solutions of the equation |x| <3

Mathematics

1 answer:

wlad13 [49]3 years ago

7 0

Answer:

c -2 -1 0 1 and 2

Step-by-step explanation:

abs (x) < 3

Absolute value equations have 2 solutions, one positive and one negative ( remember to flip the inequality when taking the negative solution).

x<3 and x>-3

-3 <x<3

The integer solutions are -2,-1,0,1-2

We do not include 3 because there is no equals sign on the inequality.

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Questions 16-17 | Math 1 - 0 points Solve the graph Help needed !!

iris [78.8K]

Answer:

16) The area of the circle is 25.1 units²

17) JKLM is a parallelogram but not a rectangle

Step-by-step explanation:

16) Lets talk about the area of the circle

- To find the area of the circle you must find the length of the radius

- In the problem you have the center of the circle and a point on

the circle, so you can find the length of the radius by using the

distance rule

* Lets solve the problem

∵ The center of the circle is (1 , 3)

∵ The point on the circle is (3 , 5)

- Using the rule of the distance between two points

* Lets revise it

- The distance between the two points (x1 , y1) and (x2 , y2) is:

Distance = √[(x2 - x1)² + (y2 - y1)²]

∴ r = √[(3 - 1)² + (5 - 3)²] = √[4 + 4] = √8 = 2√2 units

∵ The area of the circle = πr²

∴ The area of the circle = π (2√2)² = 8π = 25.1 units²

* The area of the circle is 25.1 units²

17) To prove a quadrilateral is a parallelogram, prove that every

to sides are parallel or equal or the two diagonal bisect

each other

* The parallelogram can be rectangle if two adjacent sides are

perpendicular to each other (measure of angle between them is 90°)

or its diagonals are equal in length

- The parallel lines have equal slopes, then to prove the

quadrilateral is a parallelogram, we will find the slopes of

each opposite sides

* Lets find from the graph the vertices of the quadrilateral

∵ J = (0 ,2) , K (2 , 5) , L (5 , 0) , M (3 , -3)

- The opposite sides are JK , ML and JM , KL

- The slope of any line passing through point (x1 , y1) and (x2 , y2) is

m = (y2 - y1)/(x2 - x1)

∵ The slop of JK = (5 - 2)/(2 - 0) = 3/2 ⇒ (1)

∵ The slope of LM = (-3 - 0)/(3 - 5)= -3/-2 = 3/2 ⇒ (2)

- From (1) and (2)

∴ JK // LM

∵ The slope of KL = (0 - 5)/(5 - 2) = -5/3 ⇒ (3)

∵ The slope of JM = (-3 - 2)/(3 - 0)= -5/3 ⇒ (4)

- From (3) and (4)

∴ KL // JM

∵ Each two opposite sides are parallel in the quadrilateral JKLM

∴ It is a parallelogram

- The product of the slopes of the perpendicular line is -1

* lets check the slopes of two adjacent sides in the JKLM

∵ The slope of JK = 3/2 and the slope of KL = -5/3

∵ 3/2 × -5/3 = -5/2 ≠ -1

∴ JKLM is a parallelogram but not a rectangle

4 0

3 years ago

Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k

Alik [6]

The derivative of $f(x,y,z)$ at a point $p_0=(x_0,y_0,z_0)$ in the direction of a vector $\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k$ is

$\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}$

We have

$f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k$

and

$\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}$

Then the derivative at $p_0$ in the direction of $\vec a$ is

$3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}$

3 0

3 years ago

gavin deposited $1500 into his savings account that is compounded quarterly at an interest rate of 1.5%. How munch money will ga

creativ13 [48]

Answer:

The money will gavin have after 5 years is 1616.59$

Explanation:

We know that compound interest is given by

$A=P\left(1+\frac{r}{n}\right)^{n t}$

Where A = final amount

P = Principal amount = $1500 (given)

r = interest rate = 1.5% = 0.015

n = no. of times interest applied per time period = given quarterly = 4

t = time period = 5 years

So,

$A=1500\left(1+\frac{0.015}{4}\right)^{4 \times 5}$

$1500\left(1+\frac{0.015}{4}\right)^{20}$

= 1616.59$ which is the money will gavin have after 5 years

4 0

3 years ago

Identify the unlike terms in the expression: 3a + 11b + 30 + 4a + 3b

erastovalidia [21]

30 is the unlike term cause it doesn’t have a variable match like the others i don’t know if I did it wrong I’m sorry

3 0

3 years ago

Read 2 more answers

Tyler bought 3 7/16 pounds of oranges. Write this amount using a decimal.

Whitepunk [10]

3(7/16) in your calculator should do it

6 0

3 years ago