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3 years ago

An inequality for x is less than 12

Mathematics

1 answer:

mixer [17]3 years ago

3 0

Answer:

x < 12

Step-by-step explanation:

Note that the symbol for:

"less than" is <

"greater than" is >

"less than or equal to" is ≤

"greater than or equal to" is ≥

In this case, the question states that the variable "x" is less than 12. Set the equation: x < 12

x < 12 is your answer.

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RST has vertices R(0,0), S(10,5), and T(5,-5). R’S’T’ is the image of RST after a dilation with center (0,0) and scale factor 1/

AysviL [449]

The coordinates of the point S' is (2,1)

Explanation:

Given that the RST has vertices R(0,0), S(10,5) and T(5,-5)

The image R'S'T' is the image of RST after a dilation with center (0,0) and scale factor $\frac{1}{5}$

We need to determine the coordinates of the point S'

The coordinates of S' can be determined by multiplying both the x and y - coordinates of the point S with the scale factor $\frac{1}{5}$

Let us consider the x - coordinate of the point S and multiply it with the scale factor $\frac{1}{5}$

Thus, we have,

x - coordinate of the point S' is given by

$10 \times \frac{1}{5}=2$

Thus, the x - coordinate of the point S' is 2

Similarly, the y - coordinate of the point S' can be determined by multiplying the point S with the scale factor $\frac{1}{5}$

Thus, we have,

The y - coordinate of the point S' is given by

$5\times\frac{1}{5}=1$

Thus, the y - coordinate of the point S' is 1

Hence, the coordinates of the point S' is (2,1)

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3 years ago

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Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/22 , 2 1/4 ) and (−2

Nana76 [90]

Answer: $k=18\dfrac{8}{11}$ .

Step-by-step explanation:

If a line passing through two points, then

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

Endpoints of segment MN have coordinates (0, 0) and (5, 1).

Slope of MN $=\dfrac{1-0}{5-0}=\dfrac{1}{5}$

The endpoints of segment AB have coordinates $\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)$ and $\left(-2\dfrac{1}{4} , k\right)$ .

$A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)$

$B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)$ .

Slope of AB $=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}$

$=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}$

$=\dfrac{4k-9}{4}\times \dfrac{44}{-145}$

$=4k-9\times \dfrac{11}{-145}$

$=\dfrac{44k-99}{-145}$

Product of slopes of two perpendicular segments is -1.

Slope of MN × Slope of AB = -1

$\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1$

$\dfrac{44k-99}{-725}=-1$

$44k-99=725$

$44k=725+99$

$k=\dfrac{824}{44}$

$k=\dfrac{206}{11}$

$k=18\dfrac{8}{11}$

Therefore, the value of k is $k=18\dfrac{8}{11}$ .

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4 years ago

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Is a²b the same thing as ba² ? Please explain. Thanks so much!

Fiesta28 [93]

a²b is the same thing as ba²

b and a are two separate variables lets pretend a is 2 and b is 3

2² * 3 = 4 * 3 = 12

3 * 2² = 3 * 4 = 12

this is the commutative property of multiplication

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3 years ago

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Elenna [48]

Direct variations take the form y=kx. We need to solve for y in order to find k.

3x+5y=0 
5y=-3x 
y=(-3/5)*x 
k=-3/5.

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4 years ago

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An object has a mass of 7.2 kg and a density of 0.9 kg/m3. Find the volume of the object in mº.

musickatia [10]

Answer:

mass=180kg and the volume=6m³.

then the formula to find density is= mass/volume

using this formula,180kg/6m³=30kg/m³

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