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3 years ago

Find the solution to the system of equations

Mathematics

1 answer:

Vikki [24]3 years ago

4 0

Answer:

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Leo makes a cake by mixing flour, eggs and sugar in the ratio 5 : 3 : 2. If he uses 120 g of sugar, what weight of eggs will he

Verdich [7]

Answer:

180g of eggs

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Solve the equation: k^2+5k+13=0

mr_godi [17]

Step-by-step explanation:

k² + 5k + 13 = 0

Using the quadratic formula which is

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\$

From the question

a = 1 , b = 5 , c = 13

So we have

$k = \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)} \\ = \frac{ - 5 \pm \sqrt{25 - 52} }{2} \\ = \frac{ - 5 \pm \sqrt{ - 27} }{2} \: \: \: \: \: \: \\ = \frac{ - 5 \pm3 \sqrt{3} \: i}{2} \: \: \: \: \: \:$

Separate the solutions

$k_1 = \frac{ - 5 + 3 \sqrt{3} \: i }{2} \: \: \: \: or \\ k_2 = \frac{ - 5 - 3 \sqrt{3} \: i}{2}$

The equation has complex roots

Separate the real and imaginary parts

We have the final answer as

$k_1 = - \frac{5}{2} + \frac{3 \sqrt{3} }{2} \: i \: \: \: \: or \\ k_2 = - \frac{5}{2} - \frac{3 \sqrt{3} }{2} \: i$

Hope this helps you

8 0

3 years ago

Will the lengths 4, 9, 5 form a triangle

seropon [69]

Answer:

no.

Step-by-step explanation:

The sum of two side lengths have to be greater than the value of the remaining side length.

Hope this helps. Have a nice day you amazing bean child.

6 0

3 years ago

An acute triangle has side lengths 21 cm, x cm, and 2x cm. if 21 is one of the shorter sides of the triangle, what is the greate

madam [21]

Given that the sides of the acute triangle are as follows:
21 cm
x cm
2x cm

Stated that 21 cm is one of the shorter sides of the triangle2x is greater than x, so it follows that 2x MUST be the longest side

For acute triangles, the longest side must be less than the sum of the 2 shorter sides
Therefore, 2x < x + 21cm
2x – x < 21cm
x < 21cm

If x < 21cm, then 2x < 42cm
Therefore, the longest possible length for the longest side is 42cm

8 0

3 years ago

Read 2 more answers

Allison and Megan were at track practice. The track is 3/8 kilometers around.

Ad libitum [116K]

Allison ran 3/8 km (0.375 km) in 3 minutes.

Set up a proportion to find how long it takes for her to run 1 km

$\frac{0.375\textrm{km}}{3 \textrm{min}} = \frac{1\textrm{km}}{x \textrm{min}}$