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tatiyna
2 years ago
6

Please I need help ASAPpls explain your answer ​

Mathematics
1 answer:
USPshnik [31]2 years ago
7 0

Answer:

47.62 cm

Step-by-step explanation:

ABCD is a rhombus. Each side measures 15 cm.

m<A = 60°.

Here are some properties of a rhombus:

Opposite angles of a rhombus are congruent.

m<C = m<A = 60°

m<ADC = m<ABC

The sum of the measures of the interior angles of a quadrilateral is 360°.

The diagonals are perpendicular bisectors of each other.

m<A + m<C + m<ADC + m<ABC = 360°

60° + 60° + 2m<ADC = 360°

2m<ADC = 240°

m<ADC = 120°

Each diagonal of a rhombus bisects a pair of congruent, opposite angles.

m<ADB + m<CDB = m<ADC

m<ADB = m<CDB

m<ADB + m<ADB = 120°

m<ADB = 60°

Triangle ABD had two angles, <A and <ADB, that measure 60°. Therefore, the third angle, <ABD also measures 60°. That makes triangle ABD an equilateral triangle.

Draw segment AT.

T is the midpoint of BD. The segment AT is the perpendicular bisector of segment BD. Triangle ATD is a 30-60-90 triangle.

Using the ratio of the lengths of the sides of a 30-60-90 triangle, we can calculate the length of AT which is the radius of circle A.

TD : AT : AD

1    : √3 :   2

AD = 15 cm

TD = AD/2

AT = √3 × TD

AT = (AD√3)/2

AT = 7.5√3 = 12.99

AQ = 12.99

perimeter = QD + PB + m(arc)PTQ + BC + CD

perimeter = (15 - 12.99) + (15 - 12.99) + 60°/360° × 2π(12.99) + 15 + 15

perimeter = 47.62

Answer: perimeter = 47.62 cm

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The bases of the trapezoid are 6 and 10. The height is 4. Find the area.
kari74 [83]
<h2>Answer:</h2>

b. \ \boxed{32 \sq. \ units}

<h2>Step-by-step explanation:</h2>

A trapezoid is a quadrilateral where at least one pair of opposite sides are parallel. In a trapezoid, the both parallel sides are known as the bases of the trapezoid. So we have two bases, namely, b_{1}\,and\,b_{2}. Also, the height H of the trapezoid is the length between these two bases that's perpendicular to both sides. So the area of a trapezoid in terms of of b_{1},b_{2}\:and\:H is:

A=\frac{(b_{1}\text{+}b_{2})h}{2}

Since:

b_{1}=6, \ b_{2}=10, \ and \ H=4

The area is:

A=\frac{(6\text{+}10)4}{2}=\boxed{32 \sq. \ units}

6 0
3 years ago
Michael saves $423 dollars a month for college.
alexandr1967 [171]

Answer:

(a). $20,000

(b). The estimate will be lower than the actual amount.

Step-by-step explanation:

We have been given that Michael saves $423 dollars a month for college.

(a). We know that 1 year equals 12 months.

4 years = 4*12 months = 48 months.

\text{Actual amount saved}=\$423\times 48

Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:

423\approx 400\\\\48\approx 50

\text{Actual amount saved}=\$400\times 50

\text{Actual amount saved}=\$20,000

Therefore, Michael will save approximately $20,000 in 4 years.

(b).

The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.

Therefore, the estimate will be lower than the actual amount.

5 0
3 years ago
Jamir is training for a race and is running laps around a field. If the distance around the field is 250 yards, how many complet
aleksley [76]

Answer:

27 laps

Step-by-step explanation:

1 mile = 1,670 yards

1,670 x 4 = 6,680

6,680 / 250 = 26.72 rounded to the nearest hundreth = 27

6 0
3 years ago
9/8 divided by 3/8<br><br> 3/5 divided by 2/3
suter [353]
9/8 divided by 3/8 is 3 (because of the same denominator look at the first number)

3/5 divided by 2/3 is 0.9 hope this helps
8 0
2 years ago
The number of caps a new online store sells increases by a factor of 4 each month. The function f(x)=4^x represents the number o
sladkih [1.3K]

For this case we have the following variables:

x: number of months

f (x): number of caps sold

The function that models the problem is given by:

f (x) = 4 ^ x

By the time the store sells 64 caps we have:

4 ^ x = 64

From here, we clear the number of months:

log4 (4 ^ x) = log4 (64)\\x = log4 (64)\\x = 3

Answer:

the store sells 64 caps in 3 monts

A. month 3

8 0
3 years ago
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