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2 years ago

What are the solutions to the system of equations? y=x2−7x+12y=−x+7

Mathematics

1 answer:

kap26 [50]2 years ago

3 0

Answer:

x = 1, y = 6

x = 5, y = 2.

Step-by-step explanation:

y=x2−7x+12

y=−x+7

Substitute for y in the first equation:

- x + 7 = x^2 - 7x + 12

x^2 - 7x + x + 12 - 7 = 0

x^2 - 6x + 5 = 0

(x - 1)(x - 5) = 0

x = 1, 5.

When x = 1, y = -1 + 7 = 6.

when x = 5, y = -5+7 = 2.

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A month with 31 days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first da

Anvisha [2.4K]

Answer: b. 3

Therefore, we will have the same number of Mondays and Wednesdays if the first day is either Monday, Thursday or Friday. Making 3 possible days

Step-by-step explanation:

Given that there are 31 days in the month.

And there are equal number of Mondays and Wednesdays within a 7 day bracket.

30 - 4(7) = 3days

After four weeks we are left with three days.

So, if the first day is;

Monday - we will have 5 Mondays and Wednesdays each

Tuesday - we have more Wednesday

Wednesday - we will have more Wednesday

Thursday - we will have 4 Mondays and Wednesdays each

Friday - we will have 4 Mondays and Wednesdays each

Saturday - we will have more Monday

Sunday - we will have more Monday

Therefore, we will have the same number of Mondays and Wednesdays if the first day is either Monday, Thursday or Friday. Making 3 possible days

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3 years ago

In the triangle, the length of side a is 5 ft., and m∠A=60°. Find the exact lengths of sides b and c.

Ivanshal [37]

Answer:

Lengths of B and c are 5 ft

Step-by-step explanation:

Since ∆is an equilateral ∆

6 0

3 years ago

Read 2 more answers

15. A cylindrical glass 10 cm tall and 8 cm in diameter is filled to 1 cm

ANTONII [103]

Answer:

No. The new height of the water is less than the height of the glass(6.33 cm<10 cm)

Step-by-step explanation:

-For the water in the glass to overflow, the volume of the inserted solid must be greater than the volume of the empty space or the ensuing height of water >height of glass.

#Volume of the golf ball:

$V=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\pi \times 4^3\\\\\approx 268.08\ cm^3$

#The volume of the water in the glass:

$V=\pi r^2 h\\\\=\pi \times 4^2\times 10\\\\\approx 50.27\ cm^2$

We then equate the two volumes to the glass' volume to determine the new height of the water:

$V=\pi r^2h\\\\(206.08+50.27)=\pi r^2 h\\\\h=318.35/(\pi \times 4^2)\\\\=6.33\ cm$

Hence, the glass will not overflow since the new height of the water is less than the height of the glass(6.33 cm<10cm).

4 0

3 years ago

Doug's garden produces 5.8 times as many vegetables as Kelsey's garden. Together, the gardens produce 102 pounds of vegetables.

muminat

Answer:

Doug's garden: 87 lbs
Kelsey's garden: 15 lbs

Step-by-step explanation:

Let k represent the pounds of produce coming from Kelsey's garden. Then Doug's garden produces 5.8k pounds of produce, and the total weight of it is ...

k + 5.8k = 102

6.8k = 102 . . . . . . . . . . . simplify

k = 102/6.8 = 15 . . . . . . pounds of produce from Kelsey's garden

5.8k = 5.8·15 = 87 . . . . pounds of produce from Doug's garden

3 0

3 years ago

Will mark brainliest!<br> What is the value of u?

Anastaziya [24]

Answer:

u=32

Step-by-step explanation:

Hey There!

Those are a pair of complementary angles we can tell because it has a square at the angle.

When angles are complementary they add up to 90

So given one angle we subtract that by 90 to find the missing angle

90-58=32

therefore u = 32

4 0

2 years ago