All categories

2 years ago

Which system of inequalities is shown?

Mathematics

1 answer:

Oksanka [162]2 years ago

8 0

Answer:

y < x

y < 4

Step-by-step explanation:

Dotted line means < or >, and since the shaded region is below the lines y = 4 and y = x, the answer is A.

You might be interested in

Write an equation of the line

qwelly [4]

So the rise/run is -4/1 (since the line goes down 4 units when it hits a line directly, and wherever the line hits (in this case unit 1 on the x-axis)). This will be your m. Slope intercept form is y=mx+b, therefore your equation will be y==4/1x+b. to find b, you need to look at where the line hits the y-axis. It hits it at point 4. therefore your final answer will be y=-4/1x+4

8 0

3 years ago

A grocer sells milk chocolate at $2.60 per pound, dark chocolate at $4.40 per pound, and dark chocolate with almonds at $5.90 pe

Anon25 [30]

Answer: 15 pounds of milk chocolate, 10 pounds of dark chocolate and 25 pounds of dark chocolate with almonds is needed in the mixture.

Step-by-step explanation:

Let x represent the number of pounds of milk chocolate that would be in the mixture.

Let y represent the number of pounds of dark chocolate that would be in the mixture.

Let z represent the number of pounds of dark chocolate with almonds that would be in the mixture.

Since the mixture would be 50 pounds, it means that

x + y + z = 50- - - - - - - - - - - 1

He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.61 per pound. The total cost of the mixture would be 50 × 4.61 = $230.5. Milk chocolate would sell at $2.60 per pound, dark chocolate at $4.40 per pound, and dark chocolate with almonds at $5.90 per pound. It means that

2.6x + 4.4y + 5.9z = 230.5- - - - - - -2

The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. It means that

z = x + y

Substituting z = x + y into equation 1 and equation 2, it becomes

x + y + x + y = 50

2x + 2y = 50

Dividing both sides by 2, it becomes

x + y = 25

x = 25 - y- - - - - - - - - 3

2.6x + 4.4y + 5.9(x + y) = 230.5

2.6x + 4.4y + 5.9x + 5.9y = 230.5

2.6x + 5.9x + 4.4y + 5.9y = 230.5

8.5x + 10.3y = 230.5- - - - - - - - - 4

Substituting equation 3 into equation 4, it becomes

8.5(25 - y) + 10.3y = 230.5

212.5 - 8.5y + 10.3y = 230.5

- 8.5y + 10.3y = 230.5 - 212.5

1.8y = 18

y = 18/1.8

y = 10

x = 25 - y = 25 - 10

x = 15

Substituting x = 15 and y = 10 into z = x + y,

z = 15 + 10 = 25

8 0

3 years ago

What is the numerical expression 5/8 - 5/12 (3-1/4) + 2/3 A.9 B.2 C.1/2 D.1/9

Ronch [10]

The answer is B. 7/48
Hope this helps!

8 0

4 years ago

Given sinx=3/5 and x is in quadrant 2, what is the value of tan(x/2)

xxMikexx [17]

X is in the second quadrant means that x/2 is in the first quadrant.

Consider the right triangle drawn in the figure. Let tan(x/2)=a.

Then, let the length of the opposite side to x/2 be a, the adjacent side be 1 and the hypotenuse be square root of a squared +1, as shown in the figure.

sin(x/2)=|opp side|/ |hypotenuse| = $\frac{a}{ \sqrt{ a^{2}+1 } }$

cos (x/2) = |adj side|/ |hypotenuse| = $\frac{1}{ \sqrt{ a^{2}+1 } }$

from the famous identity: sin(2a)=2sin(a)cos(a), we have:

2sin(x/2)cos (x/2)=sin(x)

thus

$2* \frac{a}{ \sqrt{ a^{2}+1 } }*\frac{1}{ \sqrt{ a^{2}+1 } }= \frac{3}{5}$

$2* \frac{a}{ a^{2}+1 }= \frac{3}{5}$

$10a=3 a^{2} +3$

$3 a^{2}-10a +3=0$

(3a-1)(a-3)=0

thus a=1/3 or a=3

thus tan(x/2)=1/3 or tan(x/2)=3

Answer: {1/3, 3}