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4 years ago

Let ABCD be a parallelogram such that AB = 10 , BC = 14, and Angle A = 45. Find the area of the parallelogram.

Mathematics

1 answer:

murzikaleks [220]4 years ago

4 0

Answer:

Area of a parallelogram is base times height. Note that CD = AB & AD = BC

to find the height, draw a line from angle B perpendicular to the base b. Lets call the point of intersection at the base E. This constitutes a right triangle with AB as the hypotenuse. Using the law of sine to calculate the height h:

h/sin(A) = AB/sin(90°) ( sin(90°) = 1)

h = AB * sin(45°)

h = 10 * sin(45°)

Area = 14 * 10 * sin(45°) = 140 * sin(45°) ≈ 98.99 QEDexplanation:

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Mattie Evans drove 350 miles in the same amount of time that it took a turbopropeller plane to travel 1350 miles. The speed of t

Murljashka [212]

let

d1 = 250 mi the distance that Mattie Evans drove

v1 = the speed of Mattie Evans

d2 = 1300 mi the distance the plane traveled

v2 = the speed of the plane

The speed of the plane was 190 mph faster than the speed of the car:

v2 = v1 + 190

since time = distance/speed and they both traveled the same time we have

d1/v1 = d2/v2

250/v1 = 1300/v2 cross multiply

250v2 = 1300v1 divid eboth sides by 50

5v2 = 26v1

by solving the system of equations:

v2 = v1 + 190

5v2 = 26v1

we find

v1 = 45.24 mph

v2 = 235.24 mph

6 0

3 years ago

Read 2 more answers

2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

$f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0$

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1 10 35 50 24

| 0 -1 -9 -26 -24

1 9 26 24 0

Hence quotient is $x^{3} +9x^{2} +26x+24$

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

$(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0$

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1 9 26 24

| 0 -2 -14 -24

1 7 12 0

Hence quotient is $x^{2} +7x+12$

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

$(-3)^{2}+7(-3)+12=-9-21+12=0$

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1 7 12

| 0 -3 -12

1 4 0

Hence quotient is x+4.

So, $f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)$

Please have a look at the graph attached.

4 0

3 years ago

Find the volume of the figure. Round your answer to the nearest tenth if necessary. Use 3.14 for T.

seraphim [82]

Answer:

$\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)$

Step-by-step explanation:

Given dimensions:

Radius of the cylinder = 7 metres
Height of the cylinder = 3 metres

Given value of π :

π = 3.14

To find:

The Volume of the cylinder

Solution:

Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.

$\pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}$

where,

π = 3.14
r² = (radius)²
h = height

Plug/substitute them onto the formulae,then simplify it using PEMDAS.

[We'll substitute the value of π later]

$\rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3$

$\rm \: Volume_{(Cylinder)} = \pi(49)(3)$

$\rm \: Volume_{(Cylinder)} = 147\pi \:$

Now substitute the value of π.

$\rm \: Volume_{(Cylinder)} = 147 \times 3.14$

$\rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3}$

$\boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \:$

Hence, we can conclude that:

The volume of the cylinder is approximately

461.6 m³.

$\rule{225pt}{2pt}$

3 0

3 years ago

Amanda made $221 for 13 hours of work. At the same rate, how many hours would she have to work to make $187

Anika [276]

Answer:

she will have to work 11 hours

Step-by-step explanation:

221 divided by 13=17

therefore she makes 17 dollars an hour

so 187 divide by 17 = 11

4 0

4 years ago

Read 2 more answers

What place value do micrometers go too?

BigorU [14]

Answer:

The place value of micrometers is the millionths.

Explanation:

Place value is how much a digit is worth according to the position it has in the number.

In a one digit number, the only digit is in the place of the ones. That means, that the digit is itself. For instance 8, values 8 × 1, because it is in the place of the ones.

In a two digit numbers, the number to the right is in the place of the ones, and the number to the left is in the place of the tens. Then, the number on the left values 10 times itself. For instance in the number 28, 8 values 8×1 and 2 values 2×10 = 20. That makes 20 + 8 = 28.

From rigth to left the place values are:

Ones
Tens
Hundreds
Thousands
Ten-thousands
Hundred-thousands
Millions

For the decimals, you count the place values from left to right. They are:

Tenths
Hundreths
Thousandths
Ten-thousanths
Hundred-thousanths
Millionths

Micrometers is a unit that is one-millionth of a meter:

1 mcirometer = 10⁻⁶ meter

1 micrometer = 0.000001 meter

Hence, the place value of micrometers is the millionths.

5 0

3 years ago