Look at the picture and answer the question

StartLayout Enlarged left-brace 1st row x² + y² = 25 2nd row 2x + y = 25 EndLayout 0, –5) and (–5, 5) (0, –5) and (5, –15) (0, –

Verdich [7]

Answer:

The line does not intersect the curve

Step-by-step explanation:

Assuming that we are looking for the points of intersection of

${x}^{2} + {y}^{2} = 25$

and

$2x + y = 25$

We make y the subject in the second equation to get:

$y = 25 - 2x$

When we substitute into the first equation:

${x}^{2} + {(25 -2 x)}^{2} = 25$

Let us expand to get:

${x}^{2} + 625 - 100x + 4 {x}^{2} = 25$

We obtain the standard form

$5 {x}^{2} - 100x + 600 = 0$

Divide through by 5

${x}^{2} - 20x + 120 = 0$

The discriminant is

${( - 20)}^{2} - 4 \times 1 \times 120 = - 80$

Hence the quadratic equation has no real roots.

This means the line and point has no point of intersection.

3 0

4 years ago

Read 2 more answers

Marissa substracted a negative number from a positive number. Her result was negative. Is that reasonable? Explain.

alexira [117]

Answer: It is not reasonable.

Step-by-step explanation: when subtracting a negative number from a positive number the answer is always going to be positive because two negatives make a plus. For example 3-(-5). The two negatives cancel each other out, so it’s 3+5=8

3 0

3 years ago

Question

ella [17]

Answer:

The money invested into bond is $8000

The money invested into stocks is $17,000

Step-by-step explanation:

* Lets explain how to solve the problem

- Vartan wants to invest $25,000

- He wants to put some of the money into a bond that pays 4% annual

interest and the rest into stocks that pay 9% annual interest

- He wants to earn 7.4% annual interest on the total amount

- We need to know how much money he should invest in each account

- Assume that he will put $x into the bond that pays 4% annual interest

- He will put the rest into stocks that pay 9%

- The rest = 25,000 - x

∴ The money earns = (4/100)(x) + (9/100)(25,000 - x)

∴ The money earns = 0.04 x + 2250 - 0.09 x

∴ The money earns = 2250 - 0.05 x ⇒ (1)

∵ He wants to earn 7.4% annual interest on the total amount

∵ Total amount is $25,000

∴ The money earns = (7.4/100)(25,000)

∴ The money earns = 1850 ⇒ (2)

- Equate (1) ans (2)

∴ 2250 - 0.05 x = 1850

- Add 0.05 x to both sides

∴ 2250 = 0.05 x + 1850

- Subtract 1850 from both sides

∴ 400 = 0.05 x

- Divide both sides by 0.05

∴ x = 8,000

∴ 25,000 - 8,000 = 17,000

∵ x represents the money invested into the bond

∵ 25,000 - x represents the money invested into the stocks

∴ The money invested into bond is $8000

∴ The money invested into stocks is $17,000

3 0

3 years ago

A printer can print 27 pages in 4.5 min. How much time does it need to print 324 pages?

lutik1710 [3]

Answer:

54 minutes

Step-by-step explanation:

We can write a proportion to solve this problem. Put the number of pages over the minutes

27 pages 324 pages

-------------- = ---------------

4.5 minutes x minutes

Using cross products

27 * x = 324 * 4.5

27x = 1458

Divide each side by 27

27x/27 = 1458/27

x =54

6 0

3 years ago

Anyone know the answers to these?

Anettt [7]

Answer:

3. No.

4. No, not necessarily.

5. Yes.

Step-by-step explanation:

3. No. With the two triangles, she knows that one angle of each is a right angle. She does not know anything about side lengths. She cannot prove the triangles are congruent.

4. We cannot prove the triangles are congruent. With the perpendicular segments, there is a pair of congruent, right angles. Then there are two pairs of sides that are congruent, but the order is SSA, and SSA does not prove triangles congruent.

5. Using the two sets of perpendicular lines, you have two congruent, right angles. Then you have the other pair of given congruent angles. Finally, segment RT is congruent to itself. This makes AAS. the triangles are congruent.

8 0

4 years ago