All categories

4 years ago

Joanna has a total of 7 rolls of coins worth $23. She has rolls of dimes worth $5 each, and

Mathematics

1 answer:

yawa3891 [41]4 years ago

6 0

Answer:

3 rolls of dimes and 4 rolls of nickels

Step-by-step explanation:

Number of rolls of dimes = x

Number of rolls of nickels = y

Total number of rolls = 7

x + y = 7 -------------------(i)

Total amount = $ 23

5x + 2y = 23 ----------------(ii)

Multiply equation (i) by -2. So when we are adding, y will be eliminated and you will get the number of rolls of dimes.

(i)*(-2) -2x - 2y = -14

(ii) <u>5x + 2y = 23</u> {Now add}

3x = 9

x = 9/3

x = 3

Plug in the value of x in equation (i)

3 +y = 7

y = 7- 3

y = 4

You might be interested in

Delete this question please. I don't know how to delete this question.

Serhud [2]

I don’t think you can delete questions

8 0

3 years ago

State the type of angles and solve for the yven vatizble.

Alika [10]

Answer:

1st option

Step-by-step explanation:

The 2 angles are alternate exterior angles and are congruent , so

3x = 2x + 20 ( subtract 2x from both sides )

x = 20

4 0

3 years ago

To check the condition that the sample size is large enough before applying the Central Limit Theorem for Sample Proportions, r

DaniilM [7]

Answer:

d.10

Step-by-step explanation:

Sample size is large enough if both n*p and n*(1 – p) are greater than or equal to 10.

8 0

4 years ago

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

GREYUIT [131]

Yes, the triangle is right angled.

Step-by-step explanation:

Given lengths are;

11 yards, 60 yards and 61 yards

From pythagoras theorem;

The sum of square of shorter lengths is equal to square of larger side.

Here;

a = 11 , b = 60 , c = 61

$a^2+b^2=c^2\\(11)^2+(60)^2=(61)^2\\121+3600=3721\\3721=3721$

As it satisfies the condition of Pythagoras theorem, the triangle is right angled.

Yes, the triangle is right angled.

Keywords: pythagoras theorem, addition

Learn more about pythagoras theorem at:

#LearnwithBrainly

8 0

4 years ago

Im giving 100 Points to anyone who could solve this for me please.

myrzilka [38]

Answer:

AB = 27.2

BC = 33.5

AC = 50.4

∠A = 38°

∠ABC = 112°

Step-by-step explanation:

<u>Trigonometric ratios</u>

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

$\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}$

$\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}$

$\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)$

$\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}$

$\implies \sf BD=29\tan(30^{\circ})$

$\implies \sf BD=\dfrac{29\sqrt{3}}{3}$

$\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}$

$\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}$

$\implies \sf AB=27.2\:(nearest\:tenth)$

$\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}$

$\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}$

$\implies \sf AD=21.4\:(nearest\:tenth)$

$\implies \sf AC=AD+DC=21.4+29=50.4$

The interior angles of a triangle sum to 180°

⇒ ∠A + 52° + 90° = 180°

⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

8 0

2 years ago