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Allisa [31]
3 years ago
11

Andrew walks along a road which can be modeled by the equation y=3x, where (0,0) represents his starting point. When he reaches

the point (12,36), he turns right, so that he is traveling perpendicular to the original road, until he stops at a point which is due east of his starting point (in other words, on the x-axis).
What is the point where Andrew stops?
Mathematics
1 answer:
Temka [501]3 years ago
7 0

Answer:

(120,0)

Steps:

y-36=-1/3(x-12)

(0)-36=-1/3(x-12)

(-3)(-36)=x-12

108=x-12

120=x

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I NEED HELP WITH THIS! ANYONE???
Aneli [31]

Answer:

y-axis, x-axis, y-axis, x-axis

Step-by-step explanation:

Alright, so this problem looks a lot harder than it really is. When you flip a point across the x axis, y becomes negative, and when it is flipped across the y axis, x becomes negative. This means that if the x value changes signs it was flipped on the y axis, and vice versa.

3 0
3 years ago
Katie is buying souvenir.gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magne
NikAS [45]
The total number of gifts = x+y.
The inequality is:
x+y  \geq 24

Key chains cost $1, Magnets $0.50
Total Cost = x + 0.5y
Inequality is:
x+0.5y  \leq 20

Without graphing you can solve system by using substitution:
y = 24 - x  \\  \\ x + 0.5(24-x) = 20   \\  \\ 0.5x +12 = 20  \\  \\ x = 16 \\  \\ y = 24-16 = 8

This is one solution where the maximum x value is given.
So the most keychains that can be purchased is 16. However, because magnets are cheaper, more can be purchased as long as cost remains under 20.

If you solve both inequalities for "y", you get the upper and lower bounds for how many magnets can be purchased given a quantity of keychains.

24-x  \leq y  \leq 40 -2x \\  \\ x \leq 16

This is complete solution which gives all possible combinations.
(Graph is Attached)

6 0
3 years ago
Is -14 a natural number, whole number, integer, rational or irrational number?
Sveta_85 [38]

Answer:

Step-by-step explanation:

-14 is an integer

We can also tell as rational number

as -14 can be written in the form p/q, ie -14/1

7 0
3 years ago
James earned a total of $900 this week. this total was $20 less than four times the amount he earned last week. how much money d
Vladimir [108]
<span>4x – 20 = 900
4x = 900+20
4x = 920
x = 920/4
x = 230
he earned $230
                                   </span>
7 0
3 years ago
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged
Temka [501]

Answer:

a) 0.283  or 28.3%

b) 0.130 or 13%

c) 0.4 or 40%

d) 30.6 mm

Step-by-step explanation:

z-score of a single left atrial diameter value of healthy children can be calculated as:

z=\frac{X-M}{s} where

  • X is the left atrial diameter value we are looking for its z-score
  • M is the mean left atrial diameter of healthy children (26.7 mm)
  • s is the standard deviation (4.7 mm)

Then

a) proportion of healthy children who have left atrial diameters less than 24 mm

=P(z<z*) where z* is the z-score of 24 mm

z*=\frac{24-26.7}{4.7} ≈ −0.574

And P(z<−0.574)=0.283

b) proportion of healthy children who have left atrial diameters greater than 32 mm

= P(z>z*) = 1-P(z<z*) where z* is the z-score of 32 mm

z*=\frac{32-26.7}{4.7} ≈ 1.128

1-P(z<1.128)=0.8703=0.130

c) proportion of healthy children have left atrial diameters between 25 and 30 mm

=P(z(25)<z<z(30)) where z(25), z(30) are the z-scores of 25 and 30 mm

z(30)=\frac{30-26.7}{4.7} ≈ 0.702

z(25)=\frac{25-26.7}{4.7} ≈ −0.362

P(z<0.702)=0.7587

P(z<−0.362)=0.3587

Then P(z(25)<z<z(30)) =0.7587 - 0.3587 =0.4

d) to find the value for which only about 20% have a larger left atrial diameter, we assume

P(z>z*)=0.2 or 20% where z* is the z-score of the value we are looking for.

Then P(z<z*)=0.8 and z*=0.84. That is

0.84=\frac{X-26.7}{4.7}  solving this equation for X we get X=30.648

5 0
3 years ago
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