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2 years ago

Hannah needs 78 inches of ribbon to make a picture frame.

Mathematics

1 answer:

Anton [14]2 years ago

7 0

Answer: There are 60 inches in 5 feet, so there are 60 ÷ 5 = 12 inches in 1 foot The unit rate is 12.

Because the number of inches, 78, is halfway between 72 and 84, the number of feet must be halfway between 6 and 7 feet There are 6 1/2 feet of ribbon in 78 inches

Hope this helps!!! Good luck!!! ;)

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7th grade math I need some help

brilliants [131]

Answer:

$33.60

Step-by-step explanation:

First we take 80% of $40.

1. $40 * 0.80 = $32

Next we take 105% of $32.

2. $32 * 1.05 = $33.60

4 0

3 years ago

Which statement is valid when a circumscribed circle of an acute triangle is

Anni [7]

<h3>There are two answers: Choice C, Choice D</h3>

Explanation:

For any acute triangle, the center of the circle is always inside the triangle.

For any right triangle, the center of the circle is the midpoint of the hypotenuse. The hypotenuse is the diameter of the circle.

For any obtuse triangle, the center of the circle is outside the triangle.

----------

Let's look at the answer choices more closely

A. False. This is only true if we have a right triangle as mentioned earlier.

B. False. This describes an inscribed circle.

C. True. As stated earlier.

D. True. This is based on how the circumscribed triangle is defined. It is set up to be the circle that goes through all three vertex points of a triangle. In other words, it is the smallest circle to completely enclose the given triangle.

4 0

2 years ago

PLEASE ANSWER ASAP!!!The grid you see below is in the shape of a rectangle. What is the area, in square units, of the shaded par

klasskru [66]

Answer:

I think it’s 12 sorry if I’m wrong!

8 0

3 years ago

dybincka [34]

Answer:

$57.2\ ft$

Step-by-step explanation:

we know that

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this problem

The tangent of angle of 5 degrees is equal to the quotient of "rise over run"

Let

y ----> the rise of the ramp

x ----> the run of the ramp

$tan(5^o)=\frac{y}{x}$

we have

$y=5\ ft$

substitute and solve for x

$tan(5^o)=\frac{5}{x}$

$x=\frac{5}{tan(5^o)}$

$x=57.2\ ft$

5 0

3 years ago

Beth is knitting mittens and gloves. Each pair must be processed on three machines. Each pair of mittens requires 2 minutes on M

anygoal [31]

Answer:

Two mittens and seven gloves

Step-by-step explanation:

I presume you are asking how many mittens and how many gloves Beth should knit to produce the most profit.

Let x = the number of mittens and

Let y = the number of gloves

1. Summarize the information in a table

$\begin{array}{cccc}&\textbf{Mittens}& \textbf{ Gloves} & \textbf{Minutes Available}\\\text{Machine A} & 2 & 4 & 32\\\text{Machine B} & 2 & 2 & 18\\\text{Machine C} & 4 & 1 & 24\\\text{Unit profit} & $8.00 & $10.00 & \\\end{array}$

2. List the constraints

(a) Beth can't make a negative number of mittens, so

x ≥ 0.

(b) Neither can she make a negative number of gloves, so

y ≥ 0.

2x + 4y ≤ 32.

(d) The total number of minutes on Machine B cannot exceed 18, so

2x + 2y ≤ 18.

(e) The total number of minutes on Machine C cannot exceed 24, so

4x + y ≤ 24.

3. Write an equation for the profit

P = 8.00x + 10.00y

4. Graph the constraints to identify the feasible region

See the figure below. The feasible region is the dark green area where all three regions overlap.

5. Determine the points of intersection between the constraints

(i) Constraints (c) and (d)

$\begin{array}{rcr}2x + 4y & = & 32\\2x + 2y & = & 18\\2y & = & 14\\y & = & \mathbf{7}\\2x + 14 & = & 18\\2x & = &4\\x & = & \mathbf{2}\\\end{array}\\$

The lines intersect at (2,7).

(ii) Constraints (c) and (e)

$\begin{array}{rcl}2x + 4y & = & 32\\4x + y & = & 24\\4x + 8y & = & 64\\7y & = & 40\\y & = & \mathbf{\dfrac{40}{7}}\\\\4x + \dfrac{40}{7} & = & 24\\\\4x & = &24 - \dfrac{40}{7}\\\\4x & = & \dfrac{128}{7}\\\\x & = & \mathbf{\dfrac{32}{7}}\\\\\end{array}\\$

The lines intersect at (27/7,32/7).

(iii) Constraints (d) and (e)

$\begin{array}{rcr}2x + 2y & = & 18\\4x + y & = & 24\\4x + 4y & = & 36\\3y & = & 12\\y & = & \mathbf{4}\\4x +4 & = & 24\\4x & = &20\\x & = & \mathbf{5}\\\end{array}\\$

The lines intersect at (5,4).

6. Determine the x- and y-intercepts of the feasible region

(i) x-intercept

$\begin{array}{rcr}4x + y & = & 24\\4x + 0 & = & 24\\x & = & \mathbf{6}\\\end{array}$

The x-intercept is at (6,0).

(ii) y-intercept

$\begin{array}{rcr}2x + 4y & = &32\\2(0) + 4y & = &32\\4y & = & 32\\y & = & \mathbf{8}\\\end{array}$

The y-intercept is at (0,8).

The five black dots are the vertices of the polygon that represents the feasible region.

7. Calculate the maximum profit

Calculate the profit at each of the vertices.

(i) At (0,0)

P = 8.00x + 10.00y = 8.00(0) + 10.00(0) = 0 + 0 = $0

(ii) At (2,7)

P = 8.00(2) + 10.00(7) = 16 + 70 = $86

(iii) At (5,4)

P = 8.00(5) + 10.00(4) = 40 + 40 = $80

(iv) At (6,0)

P = 8.00(6) + 10.00(0) = 48 + 0 = $48

The maximum profit occurs at (2,7)

Thus, Beth should knit two mittens and seven gloves.

7 0

3 years ago