Blake has xx dimes and yy nickels. He has a minimum of 13 coins worth at most $1 combined. Solve this system of inequalities graphically and determine one possible solution.

Answer:

-10, -8

Step-by-step explanation:

a + b = -18

a * b = 80

Solve:

from the first eq.

a = 18 - b

replacing this value in the secon eq.

(18-b)*b = 80

18*b + b*-b = 80

-b² + 18b = 80

-b² + 18b - 80 = 0

b = {-18±√((18)² - (4*-1*-80))] /(2*-1)

b = {-18±√(324.320)} / -2

b = {-18±√4} / -2

b = {-18±2} / -2

b₁ = {-18-2} / -2 = -20/-2 = 10

b₂ = {-18+2} / -2 = -16/-2 = 8

The two number must be negatives, so the numbers are:

-10 and -8

Check:

-10 + (-8) = -10 - 8 = -18

-10*-8 = 80

Answer:

7/24

Step-by-step explanation:

Hope this helps

Answer:

1/6

Step-by-step explanation:

Decimal Form 0.16

Answer:

n ≥ 8

Step-by-step explanation:

Let R and E stand for the number of cows owned by Richard and Ellis, respectively.

We are told that:

R = n

E = 4n

Then:

R = n+13   [Bought 13 cows]

and

E = 4n-9  [Sold 9 cows]

Still:

E > R  [Ellis still has more cows]

Therefore:

4n-9 > n+13

3n  > 22

n > 7 1/3

Since no rancher wants 1/3 of a cow, we need to round either up or down to a whole number.  The least value of n is therefore 8 cows or higher.  Since 8 is a valid number, change the > inequality to ≥.

n ≥ 8

Part A: Yes, Triangle DEF and DBC are the same triangle, but DBC is smaller than DEF because it is just a cut off of DEF.

Part B: I am pretty sure it is angle C.

Part C: I am pretty sure it is angle D.

Answer:

Step-by-step explanation:

Part A.

m < B = m < E   (corresponding angles, (BC parallel to EF))

m < C = m < F   ( as above)

So triangles DBC and DEF are similar ( by 2 equal angles).

Part B.

Line segment BC   ( as they are both opposite  < D)

Part C.

< C as its in same relative position to < F.

Answer:

x - 6 ≤ 9

Step-by-step explanation:

using the keywords 'less than', 'a number', and 'atmost' we can identify the problem.

Answer:

Danny is incorrect.

Step-by-step explanation:

1 loaf of bread = 1.2

1 bottle of mil = 0.7

2 packets of cheese = 4.6

1.2+0.7+4.6 = 6.5

10-6.5 = 3.5

Danny is incorrect as he should be given £3.50 change instead of £3.30 change.

Answer:

7.07

Step-by-step explanation:

Angle M is 63 degrees because all 3 angles must add to 180.

Now use the law of sines:

sin(90)/x = sin(63)/6.3

Cross multiply: 6.3 sin (90) = x sin (63)

Divide by sides by sin (63): (6.3 sin (90))/sin (63) = x

Use a calculator: 7.07

Answer:

18

Step-by-step explanation:

The question is pretty much asking to find the LCM of the denominators, which is the LCD, Least Common Denominator

First list out the two numbers, then list its multiples,

6: 6, 12, 18, 24

9: 9, 18, 27

since both of them have 18, and its the least, that is the LCD/LCM

Answer:

[tex] - 8(6x + 3) = - 8 \times 6x + - 8 \times 3 \\ = - 48x - 24[/tex]

Answer: 2,511 km

Step-by-step explanation:

5828.6*4.75 = 2,510.85 rounded to 2,511

It is 103.68 degrees :)

Answer:

The y-intercept of Function A is greater the Function B's.

Step-by-step explanation:

Function B's y-intercept is -5.

Function A's y-intercept is 5.

Answer:

Step-by-step explanation:

Answer:

2.5 x 10^7

Step-by-step explanation:

Answer:

-4.3

Step-by-step explanation:

a+(-1.2)= -5.5

a-1.2=-5.5

add 1.2 to both sides

a-1.2+1.2= - 5.5+1.2

simplify

a= - 4.3

Answer:

a=-4.3

Why?:

You would have to keep the answer negative, this is because if it were to be positive it would make the negative decrease.

You could easily get a line paper and line up-

-4.3

+ -1.2

_______

-5.5

-5.5-(-1.2) would make the equation end up like -5.5+1.2, and -5.5+1.2=-4.3

Therefore,

a=-4.3

Answer:

1

Step-by-step explanation:

5(x+1) = 12

5(x+1) = 5x + 12

5(x+1) = 5x + 5

5(x=1) = 0

what one is an infinite solution

Answer:

[tex]2 + \frac{b}{5} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

ye

Step-by-step explanation:

Answer:

[tex]x=2\\x=-\frac{1}{2}[/tex]

Step-by-step explanation:

1) Move terms to the left side.

[tex]3x=2x^{2} -2\\3x-(2x^{2}-2)=0[/tex]

2) Distribute.

[tex]3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0[/tex]

3) Rearrange terms.

[tex]3x-2x^{2} +2=0\\-2x^{2} +3x+2=0[/tex]

4) Common factor.

[tex]-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0[/tex]

5) Divide both sides of the equation by the same term.

[tex]-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0[/tex]

6) Use the quadratic formula.

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

[tex]2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2[/tex]

[tex]x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}[/tex]

7) Simplify.

Evaluate the exponent

[tex]x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]

Add the numbers

[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{25} }{2*2}[/tex]

Evaluate the square root

[tex]x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{3+5}{2*2}[/tex]

[tex]x=\frac{3+5}{4}[/tex]

8) Seperate the equations.

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

[tex]x=\frac{3+5}{4}[/tex]

[tex]x=\frac{3-5}{4}[/tex]

9) Solve.

Rearrange and isolate the variable to find each solution.

[tex]x=2\\x=-\frac{1}{2}[/tex]

Answer:

B, 5.4

Step-by-step explanation:

BC = 36

FE = 7.2

AB = 27

x = Unknown value

They are proportional so...

[tex]\frac{36}{27} =\frac{7.2}{x}[/tex]

x = 5.4

Answer:

10x+18

Step-by-step explanation:

2x*5x=10x

-3*6=18

10x+18=

x=1.8

Answer:

193

Step-by-step explanation:

87 divided by .45

193.333333333

Answer:

Step-by-step explanation:

What

Answer:

See image

Step-by-step explanation:

An equation is really like a scale with two equal things on both sides. You could use the idea of a scale and lift off the same amount from both sides to keep it balanced. But I will show you the algebra version. When we subtract the same thing from both sides that's how we work back to our answer while keeping the scale balanced.

Let m = weight of a marble

p = weight of a penny = 1 gram

q = weight of a quarter= 3 grams

The problem says how many of each marble, penny, quarter, then set them equal to each other. See image

Answer:

B - 2469 and F - 183

Step-by-step explanation:

B and F are whole numbers because they don't have any decimal places.

Answer:

b

Step-by-step explanation:

because it's a b so you would automatically wanna put down B because It's a B

Answer: 120

Step-by-step explanation:

Answer:

8, 2, 14

Step-by-step explanation:

sum the parts of the ratio, 4 + 1 + 7 = 12 parts , then

24 ÷ 12 = 2 ← value of 1 part of the ratio, then

4 parts = 4 × 2 = 8

7 parts = 7 × 2 = 14

The 3 numbers are 8, 2, 14

First, we can get rid of d(x) simply by looking at it because we can tell it's linear (it's a straight line). If we look at the table, we can see a(x) is also linear because it has a steady rate of growth. b(x) and c(x) both represent exponential growth. The curved shape of b(x) shows us this is exponential growth, and the exponent in c(x) tells us it's also exponential.

Hope this helps!

Answer: b(x) and c(x)

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation:

6.5 is 13 divided by 2. You can check your work by adding 6.5 to 6.5 or multiplying 6.5 by 2