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3 years ago

11

Which of these ordered pairs is a solution to the linear inequality 2y-3x≤-10?

1 answer:

Alexandra [31]3 years ago

4 0

2y-3x≤-10
just insert your points into it:

a: 2*2-3*-4<=-10?
4+12<=-10? no

b: 2*3-3*1<=-10?
6-3<=-10? no

c: 2*-4-3*2<=-10?
-8-6<=-10?
yes c is a solution: -14<=-10

d: 2*4-3*4<=-10?
8-12<=-10? no

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HELP ASAP Solve for x. Show or explain your work.

irinina [24]

Answer:

$x=4.5$

Step-by-step explanation:

From AAA, both triangles in this figure are similar. Therefore, we can set up the following proportion:

$\frac{x}{9}=\frac{x+3}{15}$ or $\frac{x}{9}=\frac{3}{6}$ .

Cross-multiplying, we get:

$6x=9(3),\\6x=27,\\x=\frac{27}{6}=\fbox{$4.5$}$ .

7 0

3 years ago

F(x)=2x^2-x-6 g(x)=4-x (f+g)(x)

Semenov [28]

$\large \boxed{(f + g)(x) = f(x) + g(x)}$

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

$\large{ \begin{cases} f(x) = 2 {x}^{2} - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^{2} - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^{2} - x - 6 + 4 - x}$

Évaluate/Combine like terms.

$\large{f(x) + g(x) = 2 {x}^{2} - 2x - 2}$

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

$\large{(f + g)(x) = 2 {x}^{2} -2x -2}$

<u>Alternative</u>

$\large{(f + g)(x) = 2({x}^{2} -x - 1)}$

<u>Answer</u>

(f+g)(x) = 2x²-2x-2
(f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!

8 0

3 years ago

Find the side lengths of the triangle in this picture.

ozzi

Answer:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

Step-by-step explanation:

According to the statement, we have the following information about the lengths of the right triangle:

Hypotenuse

$3\cdot x + 14$

Long leg

$3\cdot x + 13$

Short leg

$x$

By the Pythagoric Theorem, we have the following expression:

$(3\cdot x + 14)^{2} = x^{2} + (3\cdot x + 13)^{2}$ (1)

$9\cdot x^{2}+84\cdot x + 196 = x^{2} + 9\cdot x^{2} + 78\cdot x + 169$

$9\cdot x^{2} + 84\cdot x + 196 = 10\cdot x^{2} + 78\cdot x +169$

$x^{2} -6\cdot x -27 = 0$

$(x-9)\cdot (x+3) = 0$

As length is a positive variable by nature, then the only possible solution is $x = 9$ . Lastly, the side lengths of the right triangle are:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

8 0

3 years ago

Kira has $40 to spend and used $20 to buy a new pair of jeans. Which integer best represents the situation of spending $20

kupik [55]

Answer:

20 because 40 is a positive and spent is negative

Step-by-step explanation:

5 0

3 years ago

The value of x is? What is the value of x in this problem?

snow_lady [41]

Answer:

$x=96$ °

Step-by-step explanation:

For the upper left angle, we know that they are supplementary, so we can find the first angle of the triangle by

$180-130=50$

For the bottom right angle, we know that they are supplementary, so we can find that angle by

$180-134=46$

As a triangle has 180 degrees, we can subtract the values of the other two angles to find the final upper right angle.

$180-50-46=84$

Lastly, The upper right angle and x are supplementary so we can find x by subtracting the angle from 180

$180-84=x\\x=96$

5 0

3 years ago

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