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djverab [1.8K]
3 years ago
8

Factor by grouping. a^2+2ab-24b^2

Mathematics
1 answer:
coldgirl [10]3 years ago
3 0
You can rewrite that as:

a^2-4ab+6ab-24b^2  then factor 1st and 2nd pair of terms.

a(a-4b)+6b(a-4b) so you have

(a+6b)(a-4b)
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A figure is composed of a rectangle and a right triangle. What is the area of the figure?
strojnjashka [21]

QUESTION 1

The figure is a tra-pezoid.

The area of a trapezoid is given by the formula;

A=\frac{1}{2}(Sum\:of\:parallel\:sides)\times h

We substitute the values to obtain;

Area=\frac{1}{2}(13.2cm+8.4cm)\times 6cm

Area=\frac{1}{2}(21.6cm)\times 6cm

Area=64.8cm^2

QUESTION 2

The approximate length of the ribbon is equal to the circumference of the circular table cloth.

We can find this by using the formula for calculating the circumference of a circle.

C=2\pi r

where r=3.5ft is the radius of the circular table cloth.

We substitute this value and \pi=3.14 into the formula to get;

C=2(3.14)(3.5)ft

C=21.98ft

The approximate length of the ribbon is 22.0ft to the nearest tenth.

QUESTION 3

Type of quadrilateral:Rectangle

Explanation: A rectangle has 4 angles that are right angles.

The two pairs of opposite sides of a rectangle are also congruent.

QUESTION 4.

The circumference of a semi circle is calculated using the formula;

C=\pi r

where r=12.5cm is the radius of the semicircle.

C=3.14\times 12.5cm

C=39.25cm

QUESTION 5

The area of the entire figure is the area of the semicircle plus the area of the isosceles triangle.

Area=\frac{1}{2}\pi r^2+\frac{1}{2}bh

Area=\frac{1}{2}\times3.14\times12.5^2+\frac{1}{2}\times25\times 24

Area=345.3125+300

Area=645.3125cm^2

Area\approx645cm^2

QUESTION 6

The area of the parallelogram is given by the formula;

A=bh

From the diagram, b=y\:in.,h=3in..

Given, A=23.7 inches squared.

We substitute the values to obtain;

23.7=3y

y=\frac{23.7}{3}

y=7.9in.

QUESTION 7

The area of a rectangle is given by the formula;

Area=l\times b

The area of the bigger rectangle =9\times15=135in^2

The area of the smaller rectangle =8\times 13=104in^2

The area of the  shaded region =135-104=31in^2

5 0
3 years ago
Work out the length x.<br> 4.5 cm<br> 11 cm
Effectus [21]

Answer:

12.3

Step-by-step explanation:

A^2 + B^2 = C^2

11^2 + 4.5^2 = C^2

132 + 20.25 = C^2

152.25 = C^2

Square root of 152.25 = 12.3

5 0
3 years ago
The length of an equilateral triangle is increased by 5 cm. The perimeter of the new triangle is 72 cm. What is the side length
Igoryamba

Answer:

19cm

Step-by-step explanation:

An equilateral triangle is a triangle where the length of the 3 sides are the same.

the perimeter is the sum of the 3 sides

for example, if the length of the side of the an equilateral triangle is 5, the perimeter is 5 x 3 = 15

let x = unknown length of side

length after increase = x + 5

(x + 5) x 3 = 72

divide both sides of the equation by 3

x + 5 = 24

subtract 5 from both sides of the equation

x = 24 - 5 = 19cm

6 0
3 years ago
The weight distribution of parcels sent in a certain manner is normal with mean value 17 lb and standard deviation 3.3 lb. The p
Yakvenalex [24]

Answer: The value of c would be 26.514 lb.

Step-by-step explanation:

Since we have given that

Mean = 17 lb

Standard deviation = 3.3 lb

At 99%  level of significance, z = 2.58

So, it becomes,

Z=\dfrac{X-\mu}{\sigma}\\\\2.58=\dfrac{X-17}{3.3}\\\\2.58\times 3.3=X-17\\\\8.514+17=X\\\\X=25.514

So, the weight c would be

c=25.514+1\\\\c=26.514

Hence, the value of c would be 26.514 lb.

7 0
3 years ago
Jakob rolls an 8-sided die that is numbered from 1 through 8 a total of 400 times. About how many times should Jakob expect to r
sergij07 [2.7K]
P(5 on one throw) = 1/8 
expected number of 5's in 400 throws = 1/8 * 400 = 50
3 0
3 years ago
Read 2 more answers
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