All categories

3 years ago

Pls help 3.60 km 2.80 km 3.20 km 3.24 km

Mathematics

1 answer:

trapecia [35]3 years ago

8 0

Answer:

3.24 km

Step-by-step explanation:

Because the two triangles are similar, we can set the sides of as a proportion:

$\frac{TR}{QR} = \frac{ST}{PQ}$

Now, let's plug in the side lengths:

$\frac{1.25}{2.25} = \frac{1.80}{PQ}$

Lastly, Solve for PQ.

$\frac{1.25}{2.25} = \frac{1.80}{PQ}\\\\1.80*2.25 = 1.25*PQ\\\\4.05 = 1.25*PQ\\\\\frac{4.05}{1.25} = PQ\\\\3.24 = PQ$

You might be interested in

a triangle has sides 8cm and 5cm and an angle of 90 degree between them.calculate the smallest angle of the triangle

kakasveta [241]

Answer:

The smallest angle is 32 degrees

Step-by-step explanation:

The given parameters show that the triangle is a right angled triangle;

Let the two other angles be represented by x and y;

Since the angle between side 5 cm and side 8 cm is 90, we can represent any of this sides as the opposite and as the adjacent;

Scenario 1 (Calculating x)

Let opposite = 5 cm

Let adjacent = 8 cm

In trigonometry, The relationship between opposite and adjacent is Tangent;

$Tan\ x = \frac{Opposite}{Adjacent}$

$Tan\ x = \frac{5}{8}$

$Tan\ x = 0.625$

Take arctan of both sides

$x = tan^{-1}0.625$

$x = 32.0053832081$

$x = 32$ (Approximated)

Scenario 2 (Calculating y)

Let opposite = 8 cm

Let adjacent = 5 cm

In trigonometry, The relationship between opposite and adjacent is Tangent;

$Tan\ y = \frac{Opposite}{Adjacent}$

$Tan\ y = \frac{8}{5}$

$Tan\ y = 1.6$

Take arctan of both sides

$y = tan^{-1}1.6$

$y = 57.9946167919$

$y = 58$ (Approximated)

By comparing the angles, the smallest angle is 32 degrees

6 0

3 years ago

Six cups of popcorn are mixed with 7 cups of chips. How many cups of chips are needed for 36 cups of popcorn?

Alex777 [14]

Answer:

42 cups of chips

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the equation of the line that passes through the point (-3,5) and has a slope of -2

wariber [46]

Answer:

equation: y=-4x-7

Step-by-step explanation:

y=-4x+b

solve for b using given coordinates on the line (-3, 5)

5=-4(-3)+b

b=-7

6 0

4 years ago

Read 2 more answers

What is the volume of the prison below?

ioda

Answer:

3 1/2

Step-by-step explanation:

To find the volume of a rectangular prism, you multiply l*w*h.

We just have to multiply 1 3/4 by 2!

*This is because the 1 doesn't give you anything.*

That equals 3 1/2!

5 0

3 years ago

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