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2 years ago

The rule g = b + 3 expresses the relationship between the

Mathematics

2 answers:

Pani-rosa [81]2 years ago

6 0

Answer:

g = 3 + b

b + 3 = g

3 + b = g

Step-by-step explanation:

jeka57 [31]2 years ago

3 0

Answer:

[see below]

Step-by-step explanation:

Rewriting the rule so 'b' would be the subject:

$g = b + 3\\\\g - 3 = b + 3-3\\\\g-3=b\\\\\boxed{b=g-3}$

Hope this helps.

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In △ABC, G is the centroid. If CG=12 find CD.

VladimirAG [237]

Answer:

CD = 24

Step-by-step explanation:

If G is the centroid, then CG = GD. (12 = 12)

Since CD is CG and GD combined, we would just add these two numbers to find the total length of CD.

CG + GD = CD

12 + 12 = 24

5 0

2 years ago

What is a solution of a linear inequality

horrorfan [7]

Solution of a linear inequality
The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system. Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality.

7 0

3 years ago

Determine the direction that is parábola opens: y=4x^2+8x+2

marissa [1.9K]

It should open up because the a which is 4 is positive

5 0

3 years ago

Jennifer hit a golf ball from the ground and it followed the projectile ℎ(t)= −15t^2+100t, where t is the time in seconds, and ℎ

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

In order to find the max height the ball reached, we have to complete the square on that quadratic. That will also, conveniently so, give us the number of seconds it will take the ball to reach that max height, that answer to part b. Let's begin to complete the square. Normally, you would move the constant over to the other side of the equals sign, but there is no constant here. The next step is to get the leading coefficient to be a 1, and ours right now is a -15. So we have to factor it out. Here's where we start the process of completing the square.

$-15(t^2-\frac{20}{3}t)=0$ Next step is to take half the linear term, square it, and add it to both sides. Our linear term is 20/3. Half of 20/3 is 20/6, and 20/6 squared is 400/36.

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0+???$ Because this is an equation, what we add to the left side also has to be added to the right. BUT we didn't just add in 400/36, because we have that -15 out front as a multiplier that refuses to be ignored. What we actually added in was -15(400/36):

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0-\frac{500}{3}$

The reason we do this is to create a perfect square binomial on the left which will serve as the number of seconds, h, in the vertex (h, k), where h is the number of seconds it takes the ball to reach its max height, k. Simplifying both sides then gives us:

$-15(t-\frac{20}{6})^2=-\frac{500}{3}$ Finally, we will move the right side over by the left and set the quadratic back equal to h(t):

$h(t)=-15(t^2-\frac{20}{3})^2+\frac{500}{3}$ and from that you can determine that the vertex is $(\frac{20}{3},\frac{500}{3})$ .

The answer to a. is vound in the second number of our vertex: k, the max height. The max of the golf ball was 500/3 feet or 166 2/3 feet.

Part b is found in the first number of the vertex: h, the number of seconds it took the golf ball to reach that max height. The time it took was 3 1/3 seconds.

Part c. is to state the domain (the time) and the range (the height) of the ball.

Domain is

D: {x | 0 ≤ x ≤ 3 1/3} and

Range is

R: {y | 0 ≤ y ≤ 166 2/3}

8 0

3 years ago

Jenny and Natalie are selling cheesecakes for a school fundraiser. Customers can buy chocolate cakes and vanilla cakes. Jenny so

IrinaVladis [17]

The cost of 1 chocolate cake is $ 6 and cost of 1 vanilla cake is $ 7

Solution:

Let "c" be the cost of 1 chocolate cake

Let "v" be the cost of 1 vanilla cake

Jenny sold 14 chocolate cakes and 5 vanilla cakes for 119 dollars

Therefore, we can frame a equation as:

14 x cost of 1 chocolate cake + 5 x cost of 1 vanilla cake = 119

$14 \times c + 5 \times v=119$

14c + 5v = 119 ------- eqn 1

Natalie sold 10 chocolate cakes and 10 vanilla cakes for 130 dollars

Therefore, we can frame a equation as:

10 x cost of 1 chocolate cake + 10 x cost of 1 vanilla cake = 130

$10 \times c + 10 \times v = 130$

10c + 10v = 130 -------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

28c + 10v = 238 ------ eqn 3

Subtract eqn 2 from eqn 3

28c + 10v = 238

10c + 10v = 130

( - ) --------------------------

18c = 108

c = 6

Substitute c = 6 in eqn 1

14(6) + 5v = 119

84 + 5v = 119

5v = 119 - 84

5v = 35

v = 7

Thus cost of 1 chocolate cake is $ 6 and cost of 1 vanilla cake is $ 7

8 0

2 years ago