Stella has x in her checking account. She goes to the Dollar Store and spends $23.75. Now she has $9.30 left in the account. How much did Stella have in her account before she went to the store?

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x + cos²x = 1

Consider the left side

[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]

= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ← multiply numerator/ denominator of the whole fraction by cos²x

= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex]

= [tex]\frac{cos^2x-sin^2x}{1}[/tex]

= cos²x - sin²x

= cos²x - (1 - cos²x)

= cos²x - 1 + cos²x

= 2cos²x - 1

= right side , thus proven

[tex]\frac{1 - \tan^2(x)}{1 + \tan^2(x)}\\= \frac{\frac{\cos^2(x)}{\cos^2(x)} - \frac{\sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x)}{\cos^2(x)} + \frac{\sin^2(x)}{\cos^2(x)}}\\= \frac{\frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x) + \sin^2(x)}{\cos^2(x)}}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)} \cdot \frac{\cos^2(x)}{\cos^2(x) + \sin^2(x)}\\= \frac{(\cos^2(x) - \sin^2(x)) \cdot \cos^2(x)}{\cos^2(x) \cdot (\cos^2(x) + \sin^2(x))}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x) + \sin^2(x)}[/tex]

[tex]= \cos^2(x) - \sin^2(x)\\= \cos^2(x) - (1 - \cos^2(x))\\= \cos^2(x) - 1 + \cos^2(x)\\= 2\cos^2(x) - 1[/tex]

Answer:

-15625

Step-by-step explanation:

Hope this helped !! :)

Have a good day.

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

m = (4-0)/(0-(-8))

m = 4/8

y = mx + c

4 = (4/8)(0) + c

c = 4

Thus, the equation is y = (4/8)x + 4

Given :

You decide to run at least 7.5 miles per week during the week to train for the cross-country season in the fall.

During one week, you run 2 miles on Sunday and 2.5 miles on Wednesday.

To Find :

How many more miles, m, do you need to run before the week is over.

Solution :

Total number of miles we travelled till Wednesday :

t = miles run on Sunday + miles run on Wednesday

t = 2 + 2.5 miles = 4.5 miles.

Now, number of miles remaining :

R = Total target - t

R = 7.5 - 4.5 miles

R = 3 miles.

Therefore, we need to run 3 more miles before the week is over.

Hence, this is the required solution.

The total distance the bird flew in feet is 140 feet

Given the following parameters

The angle of elevation = 30 degrees

Height =  70 feet

total distance the bird flew in feet (D)

Using the SOH CAH TOA identity

sin 30 = 70/D
D = 70/sin30

D = 140eet

Hence  the total distance the bird flew in feet is 140 feet

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

Answer:

tenths

Step-by-step explanation:

the 2 is in the ones place and the 5 is in the hundreds meaning the 3 would be in the tenths

Answer:

x <4

Step-by-step explanation:

hope it helps

for any question comment me ❤❤

Answer:

0,6

Step-by-step explanation:

Answer: Y= -7/3x + 6

Answer:

Yes

Step-by-step explanation:

9 can go into 8397 evenly without any remainders.

Answer:

8397/9= 933

8397 is divisible by 9 if you divide 8397 by 9 and the quotient is an integer. The easiest way to determine if 8397 is divisible by 9 is to calculate the sum of the digits in 8397. If the sum of the digits is divisible by 9, then 8397 is divisible by 9.

8+3+9+7= 27

27 is divisible by 9

Step-by-step explanation:

Answer:

$560

Step-by-step explanation:

1/5th the original price just means 20%

20% of 700 is 140

700*.20= 140

Since it's 20% off that means subtraction

700-140=560

Hope this helps!

The total point is an illustration of arrangements

There are 6 different numbers that could the total points scored by Jordan

The different number (n) that can represent the total point is calculated as:

n = 2 points + 3 points + 1

Remove the units

n = 2 + 3 + 1

Evaluate the sum

n = 6

Hence, there are 6 different numbers that could the total points scored by Jordan?

Read more about arrangements at:

https://brainly.com/question/6032811

Answer:

[tex]5(n + 4)^{\frac{3}{2} }[/tex]  

I hope this helps!

Answer: One triangle

Step-by-step explanation:

-The triangle's dimensions are defined and fixed.

-Given the fixed dimensions, only one unique triangle can be constructed.

-Hence, only one triangle of the dimensions 7.2cm, 6.9cm and 12.8 cm can be formed.

Answer:

1

Step-by-step explanation:

The correct shape would be a scalene triangle, which can't be bent and twisted and still have the same side lengths.

Answer: A

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

Ava + her 3 friends = 4 people total.

The bill was $96

To split this evenly among 4 people we can divide the bill by 4.

96/4 = 24

Therefore each person would pay $24.

Hope this helps! :)

Answer:

[tex]in standard notation \: 9 { \times 10}^{ - 4} = 0.0009[/tex]

Answer:

9:22

Step-by-step explanation:

Find the LCM Least common multiple of all three numbers (minutes)

3,4,5  LCM is 60

Divide each one into the LCM

60/3 = 20

60/4 =  15

60/5 =  12

Totals =82

add that to the time 8:00

82 is an Hour and 22 minute so it would be 9:22

I looked at other problems and this is how they solved it.  I hope it helps

Answer: 18

Step-by-step explanation:

Answer:

x = 1 and x = 3

Step-by-step explanation:

Let's solve your system by substitution.

y=2x+1;y=3x

Step: Solvey=2x+1for y:

y=2x+1

Step: Substitute2x+1foryiny=3x:

y=3x

2x+1=3x

2x+1+−3x=3x+−3x(Add -3x to both sides)

−x+1=0

−x+1+−1=0+−1(Add -1 to both sides)

−x=−1

−x

−1

=

−1

−1

(Divide both sides by -1)

x=1

Step: Substitute1forxiny=2x+1:

y=2x+1

y=(2)(1)+1

y=3(Simplify both sides of the equation)

Answer:

x=1 and y=3

The right answer will be both I and II

I. In the effective rate formula, n is equal to one.

II.The nominal rate is 7.918%.

Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.

The formula for the compound interest is given as:

[tex]A=p(1+\dfrac{r}{n})^{nt}[/tex]

Here

A= amonut

P= principle

r=rate of interest

t=time period

n=for how much time compunded

Thus we can see in the question it is compounded annually so n = 1 and the rate is given as 7.918%

Thus the right answer will be both I and II

I. In the effective rate formula, n is equal to one.

II.The nominal rate is 7.918%.

To know more about compound interest follow

https://brainly.com/question/24924853

Answer:

i don't know I don't have ideas about it

Answer:

the mean

Step-by-step explanation:

mean is calculated average

Answer:

A: the mean

Step-by-step explanation:

Sorry for this very late response, but if anyone wasn't sure if answer A is correct, it is. I can confirm this because I just took the test, I hope I could help! (:

Answer:

13.8

Step-by-step explanation:

If Points X and Z are on a number line and point Y partition line XZ into two parts where XY: YZ = 1:4, this can be expressed as;

XY/YZ = 1/4

cross multiply;

YZ = 4XY

Also, if the coordinate of X is 1.3, and the coordinate of Y is 3.8, then the distance XY will be expressed as XY = 3.8 - 1.3

XY = 2.5

YZ = 4(2.5)

YZ = 10

Since Y is at 3.8 and YZ is 10, then coordinate Z will be YZ + Y

coordinate of Z = 10+3.8

coordinate of Z = 13.8

Answer: 32ft²

Step-by-step explanation:

The area of a trapezoid is given by the formula: A = [(b1+b2)/2] x h, where b1 and b2 are the two bases, and h is the height.

In our situation, b1 = 3, and b2 = 5. The height is given as 2.

Plugging these numbers into our formula:

A = (b1+b2)/2 x h

A = [(3+5)/2] x 2

A = (8/2) x 2

A = 4 x 2

A = 8ft²

8ft² is the area of one trapezoid. If Mr. Smith wants to fit 4 of these shapes into the room, the combined area will be 4 x 8 = 32ft².

Have a nice day :)

1750 litres.............50 cars

1960 litres.............n cars

so n x 1750 = 1960 x 50

n = 98000 : 1750

n = 56

56 cars tanks will be filled

Answer:

56

Step-by-step explanation:

1750 divided by 50 to find out how much litres each car gets. =35

so 35 litres per car so divide 1960 by 35. =56

56 cars can be filled

CHECK ANSWER.

the six extra cars so 35 multiplied by 6. =210

1750+210=1960!

Answer:

The truck will need to make 3 trips.

Step-by-step explanation:

First, we need to find the volume that the truck can carry. Using the dimensions of the truck and the volume formula, we have:

[tex]V=lwh\\V=8.5\times5\times3.5\\V=148.75\text{ ft}^3[/tex]

Since we need to move a total of 400 cubic feet, we will divide that amount by the truckload capacity (volume).

[tex]400 \div 148.75 \approx 2.689[/tex]

In context, he will need to take three truck loads: two loads will be full, and the third will not be full.

Answer:

The marathon runner runs 1 mile every 10 minutes.

Step-by-step explanation:

9/2 miles is equal to 4.5 miles. 3/4 hours is equal to 45 minutes.