The sum of 9 and the quotient of x and 7

Samantha saves at least 10% of the money she earns each month. She earns $120 each month for a year. Which inequality describes

viktelen [127]

Step-by-step explanation:

10 % each month is $12.00 12 months in a year 12 x 12.00 = $144.00

8 0

2 years ago

How many true solutions does the equation sinx=cosx-1 have over the interval 0 is less than or equal to x which is less than or

FrozenT [24]

$sinx=cosx-1 \\ \\ 
sinx-cosx=-1$

Using the identity: $sinx-cosx=- \sqrt{2}cos( \frac{ \pi }{4}+x)$ , we get:

$- \sqrt{2}cos( \frac{ \pi }{4}+x)=-1 \\ \\ 
cos( \frac{ \pi }{4}+x)= \frac{1}{ \sqrt{2} } \\ \\ 
$

There are two solutions to this equation:

1)
$\frac{ \pi }{4}+x= \frac{ \pi }{4} \\ \\ 
x=0$

Since the period of cosine is 2π, so 0 + 2π = 2π will also be a solution to the given equation

2)
$\frac{ \pi }{4}+x= \frac{7 \pi }{4} \\ \\ 
x= \frac{3 \pi }{2}$

Therefore, there are 3 solutions to the given trigonometric equation.

7 0

3 years ago

Read 2 more answers

The wall is 624 feet long and

m_a_m_a [10]

For this question you would simply divide the number of bamboo poles by the number of feet which would be:
6,500/624= 10.41666666666667
Since it says to round to the nearest whole number,

Your answer would be about 10 bamboo poles per feet

3 0

2 years ago

Solve x - 3 1/8 = 5/12

Anna007 [38]

Answer:

$\large\boxed{x=\dfrac{85}{24}=3\dfrac{13}{24}}$

Step-by-step explanation:

Convert the mixed number to the fraction:

$3\dfrac{1}{8}=\dfrac{3\cdot8+1}{8}=\dfrac{25}{8}$

METHOD 1:

$x-3\dfrac{1}{8}=\dfrac{5}{12}\\\\x-\dfrac{25}{8}=\dfrac{5}{12}\\\\\text{the common denominator is 24}\\\\x-\dfrac{25}{8}=\dfrac{5}{12}\qquad\text{multiply both sides by 24}\\\\24x-(3)(25)=(2)(5)\\\\24x-75=10\qquad\text{add 75 to both sides}\\\\24x=85\qquad\text{divide both sides by 24}\\\\\boxed{x=\dfrac{85}{24}}$

METHOD 2:

$x-3\dfrac{1}{8}=\dfrac{5}{12}\qquad\text{add}\ 3\dfrac{1}{8}\ \text{to oboth sides}\\\\x=\dfrac{5}{12}+3\dfrac{1}{8}\\\\x=\dfrac{5\cdot2}{12\cdot2}+3\dfrac{1\cdot3}{8\cdot3}\\\\x=\dfrac{10}{24}+3\dfrac{3}{24}\\\\x=3\dfrac{10+3}{24}\\\\\boxed{x=3\dfrac{13}{24}}$

7 0

3 years ago

1. In the diagram below , lines a and b are paraller and cut by traversal, t of angle 3 is 120 degrees, find the measure of angl

Lelu [443]

the complete question in the attached figure

1. In the diagram below , lines a and b are parallel and cut by traversal, t of angle 3 is 120 degrees, find the measure of angle 7.

∡3=∡7------------- > corresponding angles
the answer is ∡7=120 degrees

2. in the diagram below , lines a and b are parallel and cut by traversal, t of angle 2 is 50 degrees, find the measure of angle 8.

∡2=∡8------------- > alternate exterior angles

the answer is ∡8=50 degrees

3. In the diagram below , lines a and b are parallel and cut by traversal, t of angle 6 is 50 degrees, find the measure of angle 4.

∡6=∡4------------- > alternate interior angles

the answer is ∡4=50 degrees

6 0

3 years ago