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2 years ago

Which graph shows a system of equations with a solution at (2, -1)?

Mathematics

1 answer:

OleMash [197]2 years ago

7 0

Answer:

THE one with the u shape going up, and the the red line in the tilting to the left.

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Please help ! 20 pts please

Ksenya-84 [330]

The given ratios expresses the number of time a value is larger or smaller

than another value.

The correct responses are;

3. (B) 12 and 24

4. (D) 6, 9, 21

5. $\underline{(E) \ \displaystyle \frac{11}{2}}$

6. $\underline{(E) \ \displaystyle \frac{5}{14}}$

7. (B) $\overline{EF}$ = 6, $\overline{AC}$ = 9·√5

8. (C) The values are equal

9. (A) The value in column A is greater

Reasons:

3. Given that the perimeter of the rectangle = 72

The ratio of the lengths of the sides = 1:2

Let a and b represent the sides, we have;

2·a + 2·b = 72

$\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}$

Which gives;

2·a = b

2·a + 2·(2·a) = 72

6·a = 72

a = 72 ÷ 6 = 12

b = 2·a = 2 × 12 = 24

The lengths of the sides are; (B) 12 and 24

4. Extended ratio = 2:3:7

The perimeter = 36

The lengths of the sides are;

$\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}$

$\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}$

$\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}$

The lengths are; (D) 6, 9, 21

5. The given equation is presented as follows;

$\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}$

5 × (x + 2) = 3 × (x + 7)

5·x + 10 = 3·x + 21

5·x - 3·x = 21 - 10

2·x = 11

$\displaystyle x = \mathbf{ \frac{11}{2}}$

The correct option is; $\displaystyle \underline{(E) \ \frac{11}{2}}$

6. The width to length ratio is $\displaystyle \mathbf{\frac{2.5}{7.0}}$

The simplified ratio is therefore;

$\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}$

The correct option is (E) $\displaystyle \underline{(E) \ \frac{5}{14}}$

7. The given ratio of the lengths is 3:1

Therefore;

$\overline{BC}$ : $\overline{EF}$ = 3:1

Which gives;

$\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}$

$\overline{BC}$ = 18

Therefore;

$\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}$

18 × 1 = 3 × $\overline{EF}$

$\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6$

$\overline{EF}$ = 6

By Pythagorean theorem, we have;

$\overline{DF}$ ² = $\mathbf{\overline{DE}}$ ² + $\mathbf{\overline{EF}}$ ²

Which gives;

$\overline{DF}$ ² = 3² + 6² = 45

$\overline{DF}$ = √(45) = 3·√5

Using the given ratio, we have;

$\overline{AC}$ = 3 × $\mathbf{\overline{DF}}$

Which gives;

$\overline{AC}$ = 3 × 3·√5 = 9·√5

$\overline{AC}$ = 9·√5

The correct option is; (B) $\overline{EF}$ = 6, $\overline{AC}$ = 9·√5

8. EF = 1, AB = 2

CD = 2, CE = 4

Therefore;

$\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}$

$\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}$

Which gives;

$\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}$

(C) The values are equal

9. AC = 6, BE = 8

DF = 3, BD = 6

Column A

$\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}$

Column B

$\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}$

$\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}$

Therefore;

Column A is greater than column B

(A) The value in column A is greater

Learn more about ratios here:

brainly.com/question/2774839

7 0

3 years ago

The top deck of a boat is 9 feet above the surface of a lake, while the bottom of the boat is 24 feet below the surface of the l

Lady bird [3.3K]

The distance between the top deck and the bottom of the boat is is 33.5

4 0

3 years ago

Quadrilateral QRST has two pairs of congruentes sides, but it is not a parallelogram. What figure is it? What further condition

Whitepunk [10]

Answer:

The correct answer is: [C]:

________________________________________________

" {The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } ."

________________________________________________

Step-by-step explanation:

________________________________________________

Note that "all" squares are "parallelograms" ; and that "all" rectangles are

"parallelograms" ;

yet: "Not All parallelograms" are "squares" or "rectangles".

________________________________________________

The question asks:

________________________________________________

"Quadrilateral QRST has two pairs of congruent sides, but it is not a parallelogram.

What figure is it?

What further condition would have to satisfy to be a parallelogram? " .

________________________________________________

So; we can rule out:

________________________________________________

"Answer choices:

[A]: "The figure is a square..." ;

________________________________________________

[B]: "The figure is a rectangle..." ; AND :

________________________________________________

[D]: "The figure is a square..." .

________________________________________________

We are left with:

________________________________________________

Answer choice: [C]:

________________________________________________

" { The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } " .

________________________________________________________

7 0

3 years ago

Divide and simplify.

vredina [299]

Answer:

$\frac{ {x}^{2} + 10x + 16 }{ {x } {}^{2} + 6x + 8} \div \frac{1}{x + 2}$

$\frac{ {x}^{2} + 8 x+ 2x + 16}{ {x}^{2} + 4x + 2x + 8} \times (x + 2)$

$\frac{x(x + 8) + 2 (x + 8)}{x(x + 4) + 2(x + 4)} \times (x + 2)$

$\frac{( x + 8)(x + 2)}{(x + 2)(x + 4)} \times ( x + 2)$

$\frac{( x + 8)(x + 2)}{(x + 4)}$

3 0

3 years ago

Help me with this question

Rudik [331]

Answer:

its a thrapizium.so you can find the area like this....

7 0

4 years ago