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2 years ago

In the following shape, two semicircles

Mathematics

1 answer:

Andrei [34K]2 years ago

8 0

Answer:

The length around the figure in terms of r is 2r ( $\pi$ + 4).

Step-by-step explanation:

The perimeter of an object is the total length of the boundary of the object.

The figure consists two similar semicircle and a rectangle.

Adding the two semicircles, a complete circle is formed. The circumference of a circle = 2 $\pi$ r.

The rectangle has a length which is twice its height.

i.e l = 2h

But,

r = $\frac{h}{2}$ (the diameters of the semicircles equal the height of the rectangle)

⇒ h = 2r

Thus, one side length of rectangle = 2 × 2r (l = 2 × h)

= 4r

The length around the figure in terms of r is:

= 2 $\pi$ r + 4r + 4r

= 2 $\pi$ r + 8r

= 2r ( $\pi$ + 4)

The length around the figure in terms of r is 2r ( $\pi$ + 4).

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Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options. y

andriy [413]

Answer:

Step-by-step explanation:

We want a line parallel to 3x − 4y = 7. Any such line will have an equation of the same form but a different constant.

If the new line is to pass through the point (-4, -2), replace x with -4 and y with -2. We obtain:

3(-4) − 4(-2) = -12 + 8 = -4. Thus, the desired new equation is 3x − 4y = -4.

This could also be written as 3x − 4y + 4 = 0. We could also solve this for y, obtaining:

3x + 4 = 4y, or y = (3/4)x + 1.

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2 years ago

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All of Jenny's pets are dogs except one. All of her pets are cats except one. How many cats and dogs does Jenny have?

yarga [219]

She has 2 pets. 1 cat and 1 dog

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1 year ago

Derek bought a new car for $32,000. He made a down payment of $17,000 and financed the balance through the car dealer. He was un

Andreyy89

Answer:

$300

Step-by-step explanation:

Given that:

Derek bought a new car for $32,000;

The original amount of purchase = $32,000

Down payment = $17,000

Remaining amount = Original amount of purchase - Down payment

= $(32000 -17000)

= $ 15,000

Also;

rate of interest per month is 2%

and the Derek is unable to pay his first monthly payment

thus the interest amount is calculated on principal amount

so for the first month interest is calculated on total principal amount

The month interest payment is then calculated as :

= 15,000 × 2%

= 15,000 × 0.02

= $300

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2 years ago

A clothing store is analyzing merchandise prices to help make decisions on what to charge for clothing on clearance. The store o

Aleks [24]

The variable is Quantitative, has Interval level of measurement.

Variables which can be quantified & expressed numerically are Quantitative variables. Eg : as given , price

Variables which cant be qualified & expressed numerically are Qualitative variables. Eg : level of honesty, loyalty etc

Nominal & Ordinal are qualitative variables : signifying yes or no to a category (like men or women) , or ranks (x better than y) respectively. So price level is not such categorical & ordinal ratio.

Quantitative ratio variables are with reference to time , or are in forms of rate (like speed , growth per year). So, price level is not such ratio variable also.

Price is a quantitative variable, in which the ranking, its difference can be calculated. This is characteristic of a <u>Quantitative Interval Variable</u>.

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2 years ago

ΔABC underwent a sequence of rigid transformations to give ΔA′B′C′. Which transformations might have taken place?

Papessa [141]

Answer: The correct option is second, a rotation $90^{\circ}$ clockwise about the origin followed by a reflection across the x-axis.

Explanation:

From the given figure it is noticed that the vertices of ΔABC are A(-6,4), B(-4,6), C(-2,2) and vertices of ΔA'B'C' are A'(4,-6), B(6,-4), C(2,-2).

It means if the point is P(x,y) then after transformation it will be P'(y,x).

If a point P(x,y) reflection across the y-axis followed by a reflection across the x-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.

If a shape is rotated $90^{\circ}$ clockwise about the origin then the point P(x,y) will be P'(y,-x) and after that reflect across the x-axis, so the point after transformation will be P'(y,x), therefore it is the correct option.

If a shape is rotated $270^{\circ}$ clockwise about the origin then the point P(x,y) will be P'(-y,x) and after that reflect across the x-axis, so the point after transformation will be P'(-y,-x), therefore it is not the correct option.

If a point P(x,y) reflection across the x-axis followed by a reflection across the y-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.

Hence, the correct option is second, a rotation $90^{\circ}$ clockwise about the origin followed by a reflection across the x-axis.

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2 years ago

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