Inez says you can plot 4/0 on a number line, but Jeremiah says you cannot. Who is correct?

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marin

djyliett [7]

Answer:

A) (7.6, 8.8)

which are the coordinates of the treasure.

Missing Problem Statement:

Given Options:

A) (11.4, 14.2)

B) (7.6, 8.8)

C) (5.7, 7.5)

D) (10.2, 12.6)

I have added the picture showing the traced map onto a coordinate plane to find exact location of treasure.

The coordinates of Tree are (16,21)

Coordinates of rock are (3,2)

Step-by-step explanation:

Let,

Coordinates of treasure be (a,b)

$d_{1}$ = distance from tree to treasure

$d_{2}$ =distance from rock to treasure

$d_{1}=\sqrt{(16-x)^2 + (21-y)^2}$

$d_{2}=\sqrt{x\2 + (y-2)^2}$

Given ratio between rock and tree, $\frac{d_{2}}{ d_{1}}=\frac{5}{9}$ = 0.55_______(Equation.1)

which will be used to locate the treasure.

Now we just need to cross check by putting the coordinates given in the options one by one to find out value of $d_{1}$ , $d_{2}$ and checking if it satisfies the Equation 1.

Check (A) (11.4, 14.2)

$d_{2}$ = 14.8, $d_{1}$ = 8.2,

$\frac{d_{2}}{ d_{1}}$ = 1.8

Check (C) (5.7, 7.5)

$d_{2}$ = 6.13, $d_{1}$ = 16.98,

$\frac{d_{2}}{ d_{1}}$ = 0.36

Check (D) (10.2, 12.6)

$d_{2}$ = 12.8, $d_{1}$ = 10.2,

$\frac{d_{2}}{ d_{1}}$ = 1.25

Check (B) (7.6, 8.8)

$d_{2}$ = 8.2, $d_{1}$ = 14.8,

$\frac{d_{2}}{ d_{1}}$ = 0.55

Which satisfies Equation 1, such that ratio between rock and tree is 5:9 or $\frac{d_{2}}{ d_{1}}=\frac{5}{9}$ = 0.55

So, the coordinates of the treasure are (B) (7.6, 8.8)

7 0

2 years ago

Read 2 more answers

You buy a pair of jeans at a department store. Jeans 39.99 Discount -10.00 Subtotal 29.99 Sales tax 1.95 Total 31.94 a. What is

Mariana [72]

A)

if 39.99 is the 100%, what is 10 in percentage? well

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
39.99&100\\
10&x
\end{array}\implies \cfrac{39.99}{10}=\cfrac{100}{x}$

solve for "x".

b)

now, with the discount, the amount is 29.99, thus if 29.99 is the 100%, what is 1.95 from it in percentage?

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
29.99&100\\
1.95&x
\end{array}\implies \cfrac{29.99}{1.95}=\cfrac{100}{x}$

solve for "x".

c)

the original price is 39.99, the markup on that is 60%, how much is that?
well

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
39.99&100\\
x&60
\end{array}\implies \cfrac{39.99}{x}=\cfrac{100}{60}\implies 39.99\cdot 60=100x
\\\\\\
\cfrac{39.99\cdot 60}{100}=x\implies 23.994=x$

now, after the discount, the price is 29.99, how much is 23.994 in percentage of 29.99?

well $\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
29.99&100\\
23.994&x
\end{array}\implies \cfrac{29.99}{23.994}=\cfrac{100}{x}$

solve for "x".

8 0

2 years ago

It costs 20 cents to receive a photo and 30 cents to send a photo from a cellphone. C is the cost of one photo (either sent or r

ddd [48]

Answer:

(a) PC(C)= $\left \{ {{0.6 \ \ \ \ x=20} \atop 0.4 \ \ \ \ {x=30}} \right. \\\ 0 \ \ \ \ \ \ \ else$

(b) E[C] = 24 cents

Step-by-step explanation:

Given:

Cost to receive a photo = 20 cents

Cost to send a photo = 30 cents

Probability of receiving a photo = 0.6

Probability of sending a photo = 0.4

We need to find

(a) PC(c)

(b) E[C]

Solution:

(a)

PC(C)= $\left \{ {{0.6 \ \ \ \ c=20} \atop 0.4 \ \ \ \ {c=30}} \right. \\\ 0 \ \ \ \ \ \ \ else$

(b)

Expected value can be calculated by multiplying probability with cost.

E[C] = Probability × cost

E[C] = $0.6\times20 +0.4 \times 30 = 12 + 12 = 24\ cents$

3 0

1 year ago

Unit 3 parallel and perpendicular lines homework 4 parallel line proofs

Alex17521 [72]

Answer:

1) c ║ d by consecutive interior angles theorem

2) m∠3 + m∠6 = 180° by transitive property

3) ∠2 ≅ ∠5 by definition of congruency

4) t ║ v ${}$ Corresponding angle theorem

5) ∠14 and ∠11 are supplementary ${}$ Definition of supplementary angles

6) ∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem

Step-by-step explanation:

1) Statement ${}$ Reason

m∠4 + m∠7 = 180° ${}$ Given

m∠4 ≅ m∠6 ${}$ Vertically opposite angles

m∠4 = m∠6 ${}$ Definition of congruency

m∠6 + m∠7 = 180° ${}$ Transitive property

m∠6 and m∠7 are supplementary ${}$ Definition of supplementary angles

∴ c ║ d ${}$ Consecutive interior angles theorem

2) Statement ${}$ Reason

m∠3 = m∠8 ${}$ Given

m∠8 + m∠6 = 180° ${}$ Sum of angles on a straight line

∴ m∠3 + m∠6 = 180° ${}$ Transitive property

3) Statement ${}$ Reason

p ║ q ${}$ Given

∠1 ≅ ∠5 ${}$ Given

∠1 = ∠5 ${}$ Definition of congruency

∠2 ≅ ∠1 ${}$ Alternate interior angles theorem

∠2 = ∠1 ${}$ Definition of congruency

∠2 = ∠5 ${}$ Transitive property

∠2 ≅ ∠5 ${}$ Definition of congruency.

4) Statement ${}$ Reason

∠1 ≅ ∠5 ${}$ Given

∠3 ≅ ∠4 ${}$ Given

∠1 = ∠5 ${}$ Definition of congruency

∠3 = ∠4 ${}$ Definition of congruency

∠5 ≅ ∠4 ${}$ Vertically opposite angles

∠5 = ∠4 ${}$ Definition of congruency

∠5 = ∠3 ${}$ Transitive property

∠1 = ∠3 ${}$ Transitive property

∠1 ≅ ∠3 ${}$ Definition of congruency.

t ║ v ${}$ Corresponding angle theorem

5) Statement ${}$ Reason

∠5 ≅ ∠16 ${}$ Given

∠2 ≅ ∠4 ${}$ Given

∠5 = ∠16 ${}$ Definition of congruency

∠2 = ∠4 ${}$ Definition of congruency

EF ║ GH ${}$ Corresponding angle theorem

∠14 ≅ ∠16 ${}$ Corresponding angles

∠14 = ∠16 ${}$ Definition of congruency

∠5 = ∠14 ${}$ Transitive property

∠5 + ∠11 = 180° ${}$ Sum of angles on a straight line

∠14 + ∠11 = 180° ${}$ Transitive property

∠14 and ∠11 are supplementary ${}$ Definition of supplementary angles

6) Statement ${}$ Reason

l ║ m ${}$ Given

∠4 ≅ ∠7 ${}$ Given

∠4 = ∠7 ${}$ Definition of congruency

∠2 ≅ ∠7 ${}$ Alternate angles

∠2 = ∠7 ${}$ Definition of congruency

∠2 = ∠4 ${}$ Transitive property

∠2 ≅ ∠4 ${}$ Definition of congruency

∠2 and ∠4 are corresponding angles ${}$ Definition

DA ║ EB ${}$ Corresponding angle theorem

∠8 and ∠9 are consecutive interior angles ${}$ Definition

∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem.

6 0

2 years ago

walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts p

laila [671]

Answer:

5 trees should be planted to maximize the yield per acre,

The maximum yield would be 1250

Step-by-step explanation:

Given,

The original number of trees per acre = 20,

Average pounds of nuts by a tree = 60,

Let x be the times of increment in number of trees,

So, the new number of trees planted per acre = 20 + x

∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,

So, the new number of pounds of nut = (60 - 2x)

Thus, the total yield per acre,

$Y(x) = (20+x)(60-2x)$

Differentiating with respect to t ( time ),

$Y'(x) = (20+x)(-2) + 60 - 2x = -40 - 2x + 60 - 2x = 20 - 4x$

Again differentiating with respect to t,

$Y''(x) = -4$

For maxima or minima,

$Y'(x) = 0$

⇒ 20 - 4x = 0

⇒ 20 = 4x

⇒ x = 5,

For x = 5, Y''(x) = negative,

Hence, Y(x) is maximum for x = 5,

And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,

i.e. 5 trees should be planted to maximize the yield per acre,

and the maximum yield would be 1250 pounds

4 0

1 year ago