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My name is Ann [436]
3 years ago
6

A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 10 cm long and 4 cm wide. The di

ameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.
The area of the bookmark is cm2.

Plzz help me

Mathematics
1 answer:
Naddika [18.5K]3 years ago
3 0

Answer:

Area of the bookmark = 52.56 cm²

Step-by-step explanation:

The two semicircles attached at both end of the rectangle will give us a full circle.

Therefore,

Area of the bookmark = area of rectangle + Area of a circle

Area of the bookmark = L × W + πr²

Length (L) = 10 cm

Width (W) = 4 cm

radius (r) = ½(4) = 2 cm

π = 3.14

Plug in the values into the equation

Area of bookmark = 10 × 4 + 3.14 × 2²

= 40 + 12.56

= 52.56 cm²

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13 people are required to do so
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3 years ago
Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7,1). Write the equati
Nutka1998 [239]

the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.

it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.

check the picture below.

so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)


\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9


\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill

7 0
3 years ago
Answer choices:<br>A (3 , -4)<br>B (4 , -7/2)<br>C (-5 , 8)<br>D (5/2 , -17/4)​
zhuklara [117]

Answer: D (5/2, -17/4)

Step-by-step explanation:  Using elimination your goal is to get rid or 1 variable  so you can solve for the one that's left.  By adding the -2y and 2y you will get 0.  You will also add the 3x+x (4x) and -1+11 (10).  You have now gotten rid of the y and have 4x=10.  By dividing each side by 4 we now know x =2.5.  D is the only possible solution with x=2.5 (5/2) but to solve for y you plug 2.5 in to an equation as x so) x-2y=11

                                                                           2.5-2y=11

                                                                            -2y=8.5                                                                        Answer D (5/2,-17/4)                                      y=-17/4 (4.25)

4 0
2 years ago
At a clearance sale,Jill got 70% off a silver bracelet.If she paid the cashier $27 ,what was the original price of the bracelet​
mart [117]

Answer:

$38.57

Step-by-step explanation:

Make a proportion.

\frac{27}{x} = \frac{70}{100}

Cross multiply.

27 times 100 = 2700

2700 divided by 70 = 38.57142857

Round the result to the hundredths place.

38.57142857 ≈ 38.57

**Hope this helps!

4 0
3 years ago
Can someone please help me with this question? Please and thanks in advance
matrenka [14]
These two lines create vertical angles, which are congruent. That means angle z = 60 degrees. Since angle z and the angle represented by the expression 6x + 60 are supplementary (they are adjacent angles that add to equal 180 degrees), you can set up the following equation to find x:

6x + 60 + 60 = 180
6x + 120 = 180
6x = 60
x = 10

Answers:
x = 10
z = 60
3 0
3 years ago
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