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3 years ago

9

Ron lives 6 miles due north of the ball field, and Stan lives 8 miles due west of the ball field. What is the straight line dist

ance between their homes? (It makes a right triangle.)
A.8 miles
B.10 miles
C.20 miles
D.50 miles

1 answer:

Marrrta [24]3 years ago

4 0

10 miles B because you do the pythagorean theorem so 8^2 + 6^2 = 100 then sqrt it so it will be 10

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Learning Task 3

ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. $Distance = 3682km$

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. $L < 38m$

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

$Perimeter = 160$

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

$Perimeter = x + x + 1 + x + 2 + x + 3$

This gives:

$160 = x + x + 1 + x + 2 + x + 3$

Collect Like Terms

$160 -1-2-3= x+x+x+x$

$154= 4x$

Divide both sides by 4

$38.5 = x$

$x =38.5$

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: $Inzo = 10 + Miz$

Five years ago: $Miz - 5= \frac{1}{3} * (Inzo-5)$ --- (Missing from the question)

Required: Determine their present ages

Substitute $10 + Miz$ for Inzo in the second equation

$Miz - 5 = \frac{1}{3} * (10 + Miz - 5)$

$Miz - 5 = \frac{1}{3} * (Miz + 5)$

Multiply both sides by 3

$3Miz - 15 = Miz + 5$

Collect Like Terms

$3Miz -Miz = 15 + 5$

$2Miz= 20$

Divide both sides by 2

$Miz = 10$

Substitute 10 for Miz in $Inzo = 10 + Miz$

$Inzo = 10 + 5$

$Inzo = 15$

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

$Speed = 100kph$

$Time = t$

Local Train:

$Speed = 45kph$

$Time = t + 45$

Required: Determine the distance between A and B

Distance is calculated as:

$Distance = Speed * Time$

For the express train:

$Distance = 100 * t$

For the local train

$Distance = 45 * (45 + t)$

Distance between both stations are equal; So,

$100 * t = 45 * (45 + t)$

$100 t = 2025 + 45t$

Collect Like Terms

$100 t -45t= 2025$

$55t= 2025$

Divide by 55

$t = 36.82$

Substitute 36.82 for t in $Distance = 100 * t$

$Distance = 100 * 36.82$

$Distance = 3682km$

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: $n + n + 2 > 24$

Sum less than 60: $n + n + 2 < 60$

So, we have:

$n + n + 2 > 24$

$2n + 2 > 24$

Collect Like Terms

$2n > 24-2$

$2n > 22$

$n > 11$

$n + n + 2 < 60$

$2n + 2< 60$

Collect Like Terms

$2n < 60-2$

$2n < 58$

Divide by 2

$n$

So, we have:

$n > 11$ and $n < 29$

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

$Perimeter < 152m$

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

$Perimeter =4 * L$

$Perimeter =4 L$

So, we have:

$4L < 152m$

Divide through by 4

$L < 38m$

Hence, length is less than 38m (e.g. 37m)

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3 years ago

Use the figure to find the measure of the numbered angles

ivanzaharov [21]

Answer:

angle 2, 4, 6 are 34 degrees

angle 7, 5, 1, 3 are 146 degrees

180-34= 146

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3 years ago

Use the properties of addition to simplify 2d + 2 - 7f+ 4d - f.

Rudik [331]

6d - 8f + 2

hope this helps

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3 years ago

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Please help me:<br><br>What's the domain?<br><br>What's the range?<br><br>Is it a function?

VladimirAG [237]

Answer:

$\displaystyle Yes \\ Range: Set-Builder\:Notation → [f(x)|-2 ≤ f(x) ≤ 4] \\ Interval\:Notation → [-2, 4] \\ \\ Domain: Set-Builder\:Notation → [x|0 ≤ x ≤ 7] \\ Interval\:Notation → [0, 7]$

Step-by-step explanation:

Just by looking at the graph vertically and horisontally, you can tell what the range and domain is, depending on whether the segments are <em>closed</em> or <em>opened</em>.

* This is a function because it passes the <em>vertical</em><em> </em><em>line test</em>.

** This is kind of like a sine wave.

I am joyous to assist you anytime.

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3 years ago

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300,000 is 10 times as much as _________

murzikaleks [220]

Answer:

30,000

Step-by-step explanation:

300,000 is 10 times as much as ________

so 10x=30,000

So we need to divide 10 on both sides to get our answer

300,000/10 divided 10x/10

10 / 300,000 is 30,000

30,000 x 10 is 300,00

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