1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gekata [30.6K]
4 years ago
15

nicholas challenges rajiv with these instructions for finding his house after basketball practice. get on the subway at 14th Str

eet. The subway stops at 23rd, 28, 33rd, 42nd, 51st, 59th, 86th, and 96th streets. Get off at the first street you come to that is divisible by both 3 and 7. How can Rajiv solve this problem ? At which stop should he get off the subway ?
Mathematics
1 answer:
sergeinik [125]4 years ago
3 0
When a number is divisible, that means that why you divide that number by another, you will get a whole number. For example, 4 is divisible by 2 because 4 ÷ 2 = 2. The number 4 is not divisible by 3 because 4 ÷ 3 = 1\frac{1}{3} (which is not a whole number). 

We'll start with 3 - 
To find numbers that are divisible by 3, you can use the 3 Divisibility Rule. First, take the number you are given and add together all of the digits. Then, look at that sum and see if it can be evenly divided by 3. If it is, then that number is divisible by 3. For the numbers that you are given in the problem:
23 = 2 + 3 = 5 (not divisible by 3)
28 = 2 + 8 = 10 (not divisible by 3)
33 = 3 + 3 = 9 (9÷3 = 3, so 33 is divisible by 3)
42 = 4 + 2 = 6 (6÷3 = 2, so 42 is divisible by 3)
51 = 5 + 1 = 6 (6÷3 = 2, so 42 is divisible by 3)
59 = 5 + 9 = 14 (not divisible by 3)
86 = 8 + 6 = 14 (not divisible by 3)
96 = 9 + 6 = 15 (15÷3 = 5, so 96 is divisible by 3

Now let's look at numbers divisible by 7. There are rules for divisibility of 7, but they are more for 3-digit numbers. Since your numbers are small enough, we can use basic multiplication facts to check divisibility.
23 (7x3 = 21 and 7x4 =28, 23 is between these and is not divisible by 7)
28 (7x4 =28, so 28 is divisible by 7)
33 (7x4 = 28 and 7x5 = 35, 33 is between these and is not divisible by 7)
42 (7x6 = 42, so 42 is divisible by 7)
51 (7x7 = 49 and 7x8 = 56, 51 is between these and is not divisible by 7)
59 (7x8 = 56 and 7x9 = 63, 59 is between these and is not divisible by 7)
86 (7x12 = 84 and 7x13 = 91, 86 is between these and is not divisible by 7)
96 (7x13 = 91 and 7x14 = 98, 96 is between these and is not divisible by 7)

Now let's look at what we just figured out from the divisibility rules above.
Subway stops divisible by 3: 33, 42, 51, 96
Subway stops divisible by 7: 28, 42
The only number in common in those two lists is 42, so that is the stop that Rajiv should get off of the subway. 
You might be interested in
Please answer 2.) a and b!
KatRina [158]

1.a. correct

1.b. \sqrt{121} - \sqrt{9} = 11 - 3 = 8

1.c. correct

1.d. -\sqrt{36} - \sqrt{100} = -6 - 10 = -16

2.a. 7 - x + 3w - 9

Terms: 7, -x, 3w, -9

Variables: x, w

Coefficients: -1, 3

Constants: 7, -9

2.b. -g + 8k - 3 - 7

Terms: -g, 8k, -3, -7

Variables: g, k

Coefficients: -1, 8

Constants: -3, -7

3.a. correct

3.b. correct

3.c. -5+ 4x = -x

4.a. 4(2x + 3) = 8x + 12

4.b. -2(3x + 4) = -6x - 8

4.c. -5(2x - 3) = -10x + 15

7 0
3 years ago
1
antoniya [11.8K]

Answer:

4/5

Step-by-step explanation:

1, 2 , 3 and 4 are factors of 12

so 4 out of 5

4/5 is the probability of getting factor of 12

3 0
3 years ago
A radio antenna is kept perpendicular to the ground by three wires of equal length. The wires touch the ground at three points o
Elena-2011 [213]

Answer:

The coordinates of the base of the antenna is (-6. 1)

Step-by-step explanation:

Here  we are required to find the center of a circle given points on the circumference

The equation of  a circle is

(x - h)² + (y - k)² = r²

Where:

x and y are points on the circumference

h and k are coordinates of the center of the circle and

r = The radius of the circle

Since we have the values for the points on the circumference, we are left with three unknowns, which we can find with three equations as follows;

By plugging in the values for x and y at the respective points we get,

At (9, -19) → (9 - h)² + (-19 - k)² = r²...............(1)

At (-21, -19) → (-21 - h)² + (-19 - k)² = r².....,...(2)

At (14, 16 ) → (14 - h)² + (16 - k)² = r² ............(3)

Solving, we get  from (1)  (-19 - k)² = r² - (9 - h)²

Plugging in the value of (-19 - k)² in equation (2) we get

(-21 - h)² + r² - (9 - h)² = r²

So that (-21 - h)²  - (9 - h)² = r² -  r² = 0

and   (-21 - h)²  - (9 - h)² = 0 gives

60·h +360 = 0 or h = -6

Plugging in the value of h = -6 in equation (3) we get

(14 - (-6))² + (16 - k)² = r²

20² + (16 - k)² = r² .................(4)

similarly from equation (1) we get

(9 - (-6))² + (-19 - k)² = r²

15² + (-19 - k)² = r²  ................(5)

Subtracting equation (5) from (4) gives

20² - 15² +  (16 - k)² - (-19 - k)² = 0

Which gives

-70·k + 70 = 0

or k = 1

Therefore the coordinates of the base of the antenna = (-6. 1).

6 0
4 years ago
Part 1: Linear Systems and Line Segments
Nataly_w [17]

Answer:

y=8(x−8)(x+0.5)

Step-by-step explanation:

Part 1: Linear Systems and Line Segments

Create and attach a 1 page ‘cheat’ sheet for the Linear Systems Unit.

Solve each system by graphing:

y = x+2, y = 4-1

2x – y + 9 = 0, x + y – 3 = 0

Solve by substitution:

x – 2y = 4, 2x – 3y = 7

Solve by elimination:

3x + 8y = -3, x + 8y = -5

4x – 5y = -22, 5x +6y = -3

Find the length of the line segment joining each pair of points. (Express to nearest 10th of a unit)

(2,5) and (5,7)

(-1, -3) and (-2, -4)

Find the midpoint of each line segment.

M (-2, 2), P (4, 8)

A (3, 3), J (-9, 3)

The Midpoint of AB is M(-2, 1). IF A(-7, 3), what are the coordinates of B?

Page Break

Part 2: Trigonometry

Create and attach a 1 page ‘cheat’ sheet for the Trigonometry Unit.

Solve each right triangle:

Shape E

Shape F 62⁰ D

150 cm

ShapeText BoxA

Shape15⁰

ShapeB C

Page Break

Solve each triangle:

Shape L

58⁰

56⁰

M 19 cm N

ShapeJ

58⁰

18 mm 15 mm

K L

Khalid wants to be sure his boat is safely anchored. He knows that the angle of depression that the boat makes with the horizontal when anchored should be less than 12⁰. The boat is 100 m above the seabed and the anchor cable is 440 m long. Is Khalid safely anchored? Explain.

Part 3: Polynomials

Create and attach a 1 page ‘cheat’ sheet for the Polynomial Unit.

Simplify

(4x - 3) + (5x+4)

(2x2 – 3x + 4) – (x2 + 4x - 1)

(-6x3 yz2 )(-2xy2 z)

Factor, if possible

7x + 42

X2 + 7x + 12

3x2 = 12x = 9

X2 + 9

5x2 – 20x + 20

Page Break

Part 4: Quadratics

Create and attach a 1 page ‘cheat’ sheet for the Quadratics Unit.

Graph the data and write the relation in the form of

y=a(x−h)2

y=ax−h2

X

Y

-6

32

-5

18

-4

8

-3

2

-2

0

-1

2

Graph the data and write the relation in the form of

y=a(x−h)2

y=ax−h2

X

Y

-1

-8

0

-4.5

1

-2

2

-0.5

3

0

4

-0.5

Graph the relation by plotting the vertex and 2 other points.

y=(x+1)2−1

y=x+12−1

y=−2(x−6)2+2

y=−2x−62+2

For each, write the relation in standard form:

y=ax2+bx+c

y=ax2+bx+c

a=2, b=5, y intercept = 11

y=5x2+bx+c

y=5x2+bx+c

, vertex at (1, 4)

a=−3

a=−3

, passes through (2, 11) and (0, -5)

Factor:

x2−17x+66

x2−17x+66

x2−3x−18

x2−3x−18

x2+13x

x2+13x

x2−9

x2−9

Find the zeros.

y=(x+3)(x−3)

y=x+3x−3

y=−10x2

y=−10x2

y=8(x−8)(x+0.5)

y=8(x−8)(x+0.5)

4 0
3 years ago
Please help on B C D ONLY PLEASE
Rama09 [41]

The answer for B is: 40 - (7.50 x 4) = 10 Because 7.50 x 4 = 30 and 40 - 30 = 10 So they are left with $10 after paying for the tickets

The answer for C is: Miguel and his 3 friends started with $40 and had a fee of $7.50 for each ticket and there are 4 people. 4 x 7.50 = 30 and 40 - 30 = 10 so they are left with $10 to spend on snacks and other stuff!

Idk the answer for D sorry about that!

Hope this helps!

5 0
4 years ago
Other questions:
  • The sum of 12 1/4 + 5 5 /6.
    6·2 answers
  • tHe ages of Rahul and Haroon are in the ratio 7:5.Four years later the sum of their ages will be 56 years.Find their present age
    10·1 answer
  • The corner store sales peaches at a rate of three dollars per peach. If Vivian has $12 how many peach’s can Vivian buy?
    10·1 answer
  • Gretchen has 48 small shells. She uses 2 shells to make one pair of earrings. How many pairs of earrings can she make?
    12·2 answers
  • mervin works 40 hours a week at $8 per hour.he also works 6 hours overtime at time and a half rate . his deduction are $84.00 fo
    15·2 answers
  • 5 CDs cost $45.00. 3 CDs cost
    9·1 answer
  • Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as ai
    9·1 answer
  • There are four people in stevens family there shoe sizes are 6 8 10 and 10 what is the range shoe sizes in stevens family
    15·1 answer
  • This is question please hlep me
    13·1 answer
  • The line 10x + py = q is a tangent at the point (5, 4) in another circle with centre
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!