Every day, Lindsey’s orange juice stand uses 1 ½ bags of oranges. How many days will 4 ½ bags of oranges last?

Someone please help me make a proof for the bottom question

Lerok [7]

Answer:

DB = CA (Proved)

Step-by-step explanation:

Statement 1.

∠D = ∠C, M is the midpoint of DC and ∠1 = ∠2

Reason 1.

Given

Statement 2.

Between Δ DBM and Δ CAM,

(i) DM = CM,

(ii) ∠D = ∠C and

(iii) ∠DMB = ∠CMA

Reason 2.

(i) given

(ii) given and

(iii) ∠ DMB = ∠1 + ∠AMB and ∠CMA = ∠2 + ∠AMB

Since ∠1 = ∠2, so, ∠DMB = ∠CMA.

Statement 3.

Δ DBM ≅ Δ CAM

Reason 3.

By angle-side-angle rule.

Statement 4.

DB = CA

Reason 4.

Corresponding sides of two congruent triangles. (Answer)

7 0

3 years ago

What percent of 420 is 70

Lapatulllka [165]

Answer:

16.67

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

How does 1/8 divided by 1/4 equal 1/2?

photoshop1234 [79]

When you divide a fraction by a fraction, you're really just multiplying by a reciprocal. A reciprocal is the fraction flipped around.
So, 1/8 ÷ 1/4 is the same thing as 1/8 x 4/1
Now, you just multiply. 1 times 4 is 4. 8 times 1 is 8.
1/8 x 4/1=4/8
4/8 simplified is 1/2
So that is how 1/8÷1/4=1/2

6 0

3 years ago

Point A is at (-1,-9) and Point M is at (0.5,-2.5).

leva [86]

Midpoint Formula: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$

So firstly, let's start with the x-coordinates. Since we know the midpoint's x-coordinate and point A's x-coordinate, we can solve for point B's x-coordinate as such:

$\frac{-1+x}{2}=0.5\\\\-1+x=1\\\\x=2$

Next, do the same thing except solve for the y-coordinate and using point A's y-coordinate and the midpoint's y-coordinate:

$\frac{-9+y}{2}=-2.5\\\\-9+y=-5\\\\y=4$

Putting it together, point B's coordinates are (2,4).

4 0

3 years ago