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Olin [163]
3 years ago
13

Rita earns $10 per hour. She puts 5% of her earnings in savings. Write inequality to find how many hours Rita must work to save

at least $25
Mathematics
1 answer:
Rina8888 [55]3 years ago
3 0

Answer:

Rita must work 50 days  to save at least $25.

Step-by-step explanation:

The amount Rita earns per hour  = $10

The saving percentage =  5%

So, the savings of Rita per hour =  5% of $10

⇒5% of $10  = \frac{5}{100}  \times 10  = 0.5

or Rita saves $0.5 per hour.

The amount she wants to save at minimum  = $25

So, let she works at the minimum of k Days.

⇒\textrm{The number of hours she has to work}  = \frac{\textrm{Amount she needs saving}}{\textrm{Amount saved in 1 hour}}

or, k = \frac{25}{0.5}  = 50

The number of hours she has to work  =  50 days

Hence,  Rita must work 50 days  to save at least $25.

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The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle
Mama L [17]

Answer:

The circumference of the circle is C=45.346 \:units.

Step-by-step explanation:

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

The area of a circle is given by A_{circle}=\pi r^2

The formula used to calculate the area of a sector of a circle is:

A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2

The circumference of a circle is the distance around the outside of the circle and its given by

C=2\pi r

We know the central angle \theta = 110º and the area of the sector 50 units squared.

First, we use the formula to calculate the area of a sector to find the radius.

50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}

The radius can't be negative. Therefore,

r=\sqrt{\frac{1800}{11\pi }}\approx 7.217 \:units

Next, we apply the formula for the circumference of a circle.

C=2\pi (7.217)=45.346 \:units

7 0
3 years ago
Help please its math I don't understand the question can you help me figure it out☺✌​
pishuonlain [190]
The angle sum of a triangle is 180 degrees
So add all the angles inside and equate it to 180: 5x+2x+3x= 180
10x=180
x= 18

Because you’re finding angle L, which is 3x, and we find what the numerical value of x is
Angle L = 3x18 = 54.
Hope this helps!
8 0
3 years ago
Read 2 more answers
Sort the words into a category based on whether they indicate a positive number or a negative number
ankoles [38]

Answer:

POSITIVE: gain, adding, above

NEGATIVE: loss, below, taking away

5 0
2 years ago
The slope of a line that is parallel to each line whose equation is given
Kobotan [32]
Parallel lines, slope is the same so
1) 3x+8y = 12
8y = -3x + 12
  y = -3/8(x) + 3/2, slope = -3/8

slope of a line that is parallel = -3/8

2)5x+4y = 5
  4y = -5x + 5
    y = -5/4(x) + 5/4; slope is -5/4

slope of a line that is parallel = -5/4
--------------------
perpendicular, slope is opposite and reciprocal

3)
3x+8y = 11
 8y = -3x + 11
   y = -3/8(x) + 11/8. slope = -3/8
slope of perpendicular line = 8/3

4)
x = -7, slope is undefined
so slope of perpendicular line is 0

5)
3x+2y = 12
2y = -3x + 12
 y = -3/2(x) + 6 ; slope = -3/2

5x - 6y = 8
6y = 4x - 8
  y = 2/3(x) - 4/3; slope is 2/3

slope is opposite and reciprocal, so the equals are perpendicular

6)
3x + y = 5
y = -3x + 5; slope = -3

6x + 2y = -15
2y = -6x - 15 
y = -3x - 7.5; slope = -3

both have slope = -3 so equations are parallel

3 0
3 years ago
ANSWER QUICK!! 75 PTS!!!
iogann1982 [59]

Answer:

2) x = -2 , y = 2

3) no solution exists

Step-by-step explanation:

Solve the following system:

{-2 x - 3 y = -2

y = 2 x + 6

Hint: | Perform a substitution.

Substitute y = 2 x + 6 into the first equation:

{-2 x - 3 (2 x + 6) = -2

y = 2 x + 6

Hint: | Expand the left hand side of the equation -2 x - 3 (2 x + 6) = -2.

-2 x - 3 (2 x + 6) = (-6 x - 18) - 2 x = -8 x - 18:

{-8 x - 18 = -2

y = 2 x + 6

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{-8 x - 18 = -2

y = 2 x + 6

Hint: | Isolate terms with x to the left hand side.

Add 18 to both sides:

{-8 x = 16

y = 2 x + 6

Hint: | Solve for x.

Divide both sides by -8:

{x = -2

y = 2 x + 6

Hint: | Perform a back substitution.

Substitute x = -2 into the second equation:

Answer: {x = -2 , y = 2

4 0
3 years ago
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