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3 years ago

Solve each equation 1. 3/4 f + 5 = -5 2.-1/5 b - 2/5 = -2 Please show work

1 answer:

4 0

Sole for f by simplifying both sides of the equation then isolating the variable so that means f=-40 over 3 for number one

for the second equation you do the same thing you did for number one and the answer will be
b=8

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The perimeter of △CDE is 55 cm. A rhombus DMFN is inscribed in this triangle so that vertices M, F, and N lie on the sides CD ,

tamaranim1 [39]

Answer:

CD=20 cm and DE=15 cm. CD=20 cm and DE=15 cm.

Step-by-step explanation:

A rhombus DMFN is inscribed in such a way that it is inscribed in triangle CDE with the vertices M, F, and N l on the sides CD , CE , and DE respectively.

Now, in rhombus, the parallel sides are always parallel, therefore

MF║DE, thus, $\frac{CM}{MD}=\frac{CF}{EF}$ by the basic proportionality condition.

It is given that CF=8 cm and EF=12 cm, therefore, $\frac{CM}{MD}=\frac{8}{12}$ .

That is CM=8 cm and MD=12 cm. Therefore, CD=CM+MD=8+12=20.

According to question, Perimeter of △CDE =55 cm

⇒CD+DE+CE=55

⇒20+DE+20=55

⇒DE=15 cm

Hence, CD=20 cm and DE=15 cm.

8 0

3 years ago

Read 2 more answers

9d-2d+4d=32 <br> Need help

Luden [163]

Answer:

=2.90d

Step-by-step explanation:

i think is that hope IT help

8 0

3 years ago

Elizabeth bought a plant and planted it in a pot near a window in her house. Let H represent the height of the plant, in inches,

adell [148]

Answer:

63.5 in

Step-by-step explanation:

y2-y1/x2-x1

28.5-21/2.5-1 = 5

y=mx+b

21=5(1)+b

21-5= 16

b=16

y=mx+b

y=5(9.5) + 16

=63.5

6 0

3 years ago

Read 2 more answers

Find the perimeter of shape ABCDE

EleoNora [17]

Answer:

Perimeter of a triangle = 2*(length + breadth)

SO = 2*18+41

= 77 is the perimeter

6 0

3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago