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2 years ago

If DF = 9x - 39, find EF

Mathematics

1 answer:

andrezito [222]2 years ago

8 0

Answer:

EF = 58 units

Step-by-step explanation:

Given:

DF = 9x - 39

DE = 47

EF = 3x + 10

Find:

Computation:

DF = DE + EF

9x - 39 = 47 + 3x + 10

9x - 3x = 47 + 39 + 10

6x = 96

x = 16

EF = 3x + 10

EF = 3(16) + 10

EF = 58 units

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(01.02 LC)Simplify 9 − (−4).

levacccp [35]

Answer:

Step-by-step explanation:

When we subtract a negative, it is like adding

9 - -4

9 +4

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2 years ago

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Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below: 3x + 12 + 2 = 2 + 5x – 20 3x + 14 = 5x – 18 14 = 2x

konstantin123 [22]

First, she distributed $3*x=3x , 3*4=12, 5*x= 5x, 5* -4= -20$
Which gave her $3x+12+2=2+5x-20$
Then, she combined like terms $12+2=14 and 2+ -20 = -18$
Which gave her $3x+14=5x-18$
Then, she subtracted $3x$ from both sided
Which gave her $14=2x-18$
Then, she added $18$ to both sides
Which gave her $32=2x$
And finally sh edivided 32 by 2 and got $16=x$
hope this helps if you have any questions please pm me :)

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2 years ago

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Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters t

SashulF [63]

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

Angle of elevation = 60°

Angle of elevation 50 m back = 30°

As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be $h$ meters and $h= h_1+h_s$ .

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ. In ΔSPR.

⇒ $tan(60) = \frac{h_1}{x}$ ...equation (i) ⇒ $tan (30)=\frac{h_1}{x+50}$ ...equation (ii)

Dividing equation (i) and (ii)

⇒ $\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}$

⇒ $3 = \frac{x+50}{x}$

⇒ $3x=x+50$

⇒ $3x-x=50$

⇒ $2x=50$

⇒ $x=\frac{50}{2}$

⇒ $x=25$ meters

To find $h_1$ plugging $x=25$ in equation (i)

⇒ $h_1=x\times tan(60)$

⇒ $h_1=25\times 1.73$

⇒ $h_1=43.25$ meters

The height of the cliff from ground :

⇒ $h= h_1+h_s$

⇒ $h= 43.25+1.8$

⇒ $h=45.05$ meters

The cliff is 45 m tall to the nearest meter.

8 0

2 years ago

LESSON 1 SESSION 1

denpristay [2]

Answer:

Between which two tens does it fall? Between 25 and 26 tens

Between which two hundreds does it fall? Between 2 and 3 hundreds

Explanation:

The place-value chart is:

Hundreds Tens Ones

2 5 3

a) Between which two tens does it fall?

Using the place values you can write 253 = 25 × 10 + 3, i.e. 25 tens and 3 ones.

From that you can write:

250 < 253 < 260

250 = 25 × 10 = 25 tens

260 = 26 × 10 = 26 tens

Then, you conclude that 253 is between 25 and 26 tens.

b) Between which two hundreds does it fall?

Using the same reasoning:

253 = 2 × 100 + 5 × 10 + 3 = 253

200 < 253 < 300

200 = 2 hundreds

300 = 3 hundreds

Conclusion: 253 is between 2 hundreds and 3 hundreds.

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2 years ago

The average length of time that three lawn-service mowers operate on a given day is 930 minutes. None of the mowers operates for

Zielflug [23.3K]

Answer:

The answer is A. 990.

Step-by-step explanation:

Now, to find the greatest possible length of time any of the mowers operates.

The 3 lawn-service mowers operate at the average length of time = 930 minutes.

So, the total length of time the 3 lawn mowers take = $930\times 30=2790\ minutes.$

The least length a mowers operates = 900 minutes.

Now, to find the greatest possible length of time any of the mowers operates:

Let $x$ be the greatest possible length of time any of the mowers operates.

As, any one of the mowers operates greatest length.

So, rest of the two mowers be least at length.

According to question:

$x+900+900=2790$

$x+1800=2790$

Subtracting both sides by 1800 we get:

$x=2790-1800$

$x=990.$

Thus, the greatest possible length of time any of the mowers operates is 990 minutes.

Therefore, the answer is A. 990.

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2 years ago