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3 years ago

How many solutions does the system have, and why?

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

3 0

Answer:
C. there are no solutions because the slopes are the same and the y-intercepts are different.

step-by-step explanation:
y = 2/3x - 6
3y - 2x = 9
y = 0
3(0) - 2x = 9
-2x = 9
/-2 /-2
x = -9/2 = -4.5
x = 0
3y - 2(0) = 9
3y = 9
/3 /3
y = 3
(-4.5, 3)
slope 2/3
y-intercept (0, 3)
there are no solutions because the slopes are the same and the y-intercepts are different

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Alan's dogs have a total of 24 legs (l). if each dog has 4 legs, which equation gives the number of dogs (

Slav-nsk [51]

4d = 24 would be the right equation. To double check you would divide both sides by 4 (the number of legs) to find the amount of dogs.

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4 years ago

Solve the formula for n. A=a+d(n-1) evaluate n when A=25, a=5, and d=13

ser-zykov [4K]

Answer:

Step-by-step explanation:

You;ll run into this formula a lot. Make sure you study it carefully.

A = 25

a = 5

d = 13

Find n

25 = 5 + 13*(n- 1)

20 = 13(n - 1)

This isn't going to work out. 20/13 does not give a whole number which it should.

8 0

3 years ago

How to simplify 1/2/1/8

kramer

Frist you simplify the mixed number: We have a 4/8. To simplify, we will use the common factor 4. Divide the numerator and denominator by 4 and you will get 1/2.

8 0

3 years ago

13. Write

Bingel [31]

First off, we factor out the expression:

$\displaystyle \large{y = 2 {x}^{2} - 12x + 16} \\ \displaystyle \large{y = 2 ( {x}^{2} - 6x + 8) }$

In the bracket, separate 8 out of the expression.

$\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}$

In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

$\displaystyle \large{ {(x - 3)}^{2} = {x}^{2} - 6x + 9}$

So we add +9 in x^2-6x.

$\displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}$

Convert the expression in the small bracket to perfect square.

$\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}$

Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.

$\displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}$

Then we distribute 2 in.

$\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\$

$\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }$

Remember that negative multiply positive = negative.

Hence the vertex form is y = 2(x-3)^2-2 or first choice.

4 0

3 years ago

a. For each of the Five Platonic Solids, count the number V of vertices, the number F of faces, and the number E of edges. Check

natita [175]

Answer:

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3. The octahedron has 6 vertices, 12 edges and 8 faces. Then V-E+F=6-12+8=2

4. The icosahedron has 12 vertices, 30 edges and 20 faces. Then V-E+F=12-30+20=2

5. The dodecahedron has 20 vertices, 30 edges and 12 faces. Then V-E+F=20-30+12=2.

8 0

3 years ago