Mary has $100. She spends $150. What is her balance?

Answer:

[tex]\displaystyle \cos(\theta) = \frac{\sqrt{7}}{4}[/tex].

[tex]\displaystyle \tan(\theta) = \frac{3\sqrt{7}}{7}[/tex].

Step-by-step explanation:

By the Pythagorean identity, for any given angle [tex]\theta[/tex], [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].

Given that [tex]\displaystyle \sin(\theta) = 3/4[/tex], solve this equation for [tex]\cos(\theta)[/tex].

[tex](\sin(\theta))^{2} + (\cos(\theta))^{2} = 1[/tex].

[tex]\displaystyle \left(\frac{3}{4}\right)^{2} + (\cos(\theta))^{2} = 1[/tex].

[tex]\begin{aligned} \cos(\theta) &= \sqrt{1 - \frac{9}{16}} \\ &= \sqrt{\frac{7}{16}} \\ &= \frac{\sqrt{7}}{4} \end{aligned}[/tex].

The tangent of an angle is equal to the ratio between the sine and cosine of that angle. In this question:

[tex]\begin{aligned} \tan(\theta) &= \frac{\sin(\theta)}{\cos(\theta)} \\ &= \frac{3/4}{\sqrt{7}/4} \\ &= \frac{3}{\sqrt{7}} \\ &= \frac{3\sqrt{7}}{7}\end{aligned}[/tex].

Answer:

x=20

Step-by-step explanation:

3^x=243^4

3^x=(3^5)^4

3^x =3^20

x=20

Answer:

it's A or C

Step-by-step explanation:

because if it was be it would round to .19 but c and a round to .18

Answer:

149+(13x+5)=180

154+13x=180

13x=26

x=2

Answer:

see explanation

Step-by-step explanation:

The 2 angles are adjacent on a straight line and sum to 180° , then

149 + 13x + 5 = 180 , that is

154 + 13x = 180 ( subtract 154 from both sides )

13x = 26 ( divide both sides by 13 )

x = 2

Then

unknown angle = 13x + 5 = 13(2) + 5 = 26 + 5 = 31°

Answer:

[tex]sum \: of \: exterir \: anges \: for \: a \: polygon = 360 \\ 5x - 5 + x + 4x - 5 + 4x + 20 = 360 \\ x \: terms \: togather \\ 5x + x + 4x + 4x - 5 - 5 + 20 = 360 \\ 14x + 10 = 360 \\ 14x = 360 - 10 \\ 14x = 350 \\ x = \frac{350}{14} = 25 \\ x = 25 \\ thank \: you[/tex]

Answer:

SUM OF EXTERIOR ANGLES=360

Step-by-step explanation:

5x-5+4x-5+4x+20+x=360

14x+10=360

14x=350

x=350/14

x=25

Answer:

Step-by-step explanation:

l*b = 9x+15

3*b=9x+15

b=9x+15/3

b=3x+5 ans

Step-by-step explanation:

-4|8-5n|=19

-4/-4|8-5n|=19/-4

|8-5n|=4.75

5n=4.75-8

5n=-3.25

5n/5=-3.25/5

n=-0.65

if it is wrong sory

Answer:

5

Step-by-step explanation:

you have to replace 2 were there's x in the function

f(2)=3(2)-1

=6-1

=5

I hope this helps

Hello :D

£1.45 + £2.85 = £4.30

£4.30 + £1.95 = £6.25

£6.25 to the nearest pound = £6.00

Answer: Selling fees = £6 (rounded to the nearest pound)

Step-by-step explanation:

Given information

Insertion fee = £1.45

Enhanced advert = £2.85

Selling fee = £1.95

Given expression deducted from the given information

Total = insertion + enhanced advert + selling

Substitute values into the expression

Total = (1.45) + (2.85) + (1.95)

Simplify by addition

Total = 4.3 + (1.95)

Total = 6.25

[tex]\boxed{Total=6}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: 12x + 9

Step-by-step explanation:

Given

(6 + 5x) + (7x + 3)

Put like terms together

=5x + 7x + 6 + 3

Combine like terms

=[tex]\boxed {12x+9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex] - (x^{2} - 3x + 2) - x(x - 4) \\ = ( - x^{2} + 3x - 2) + ( - x ^{2} + 4x) \\ = - 2 {x}^{2} + 7x - 2[/tex]

I hope I helped you^_^

Answer:

[tex] = - 2 {x}^{2} + 7x - 2[/tex]

Step-by-step explanation:

[tex] - ( {x}^{2} - 3x + 2) - x(x - 4)[/tex]

[tex] - {x}^{2} + 3x - 2 - x(x - 4)[/tex]

[tex] - {x}^{2} + 3x - 2 - {x}^{2} + 4x[/tex]

[tex] - {2x}^{2} + 3x - 2 + 4x[/tex]

[tex] \boxed{\green{ = - 2 {x}^{2} + 7x - 2}}[/tex]

[tex]stan \: \: Dreamcatcher \\ and \: \: stream \: \: BEcause \\answered \: \: by \: \: a \: \: fellow \: \: InSomnia[/tex]

Answer:

The answer is 3cm

Please give branliest!

Step-by-step explanation:

(S1×2)+(S2×2)=21cm

(S1+S2)×2=21cm

S1+S2=21÷2

7.5+S2=10.5

S2=10.5-7.5

S2=3

Breadth=3cm

Step-by-step explanation:

p=2(l+b)

21=2(7.5+b)

21=15+2b

21-15=2b

6=2b

6/2=b

b=3

475,805 rounded to the nearest ten thousand would be 476,000.

Answer:

-20 -d

Step-by-step explanation:

-(20+d)

Distribute he minus sign

-20 -d

Answer:

40

Step-by-step explanation:

Answer:

35/36  or about 0.972

Step-by-step explanation:

The probability of rolling the same number

first die 6/6

second die 1/6

third die 1/6

1(1/6)(1/6) = 1/36

so there is a 35/36 chance that you will not get it done on the first roll and need to attempt at least one more time.

Answer:

This formula can also be written as \(y - {y}_{1} = m\left(x - {x}_{1}\right)\). The standard form of the straight line equation is \(y = mx + c\) where \(m\) is the gradient and \(c\) is the \(y\)-intercept.

Answer:

it will be 736 speed faster than

Answer:

1/2 pound

Step-by-step explanation:

Answer:

2 cups is equal to 0.5 pounds.

Step-by-step explanation:

4 divided by 2 is 2 and 1 pound divided by 2 is 0.5.

Answer:

123.4

Step-by-step explanation:

Step-by-step explanation:

The circumcenter is the centre of the circumcircle. All the vertices of a triangle are equidistant from the circumcenter.In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle.

if my answer helps you than mark me as brainliest

[tex]3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10[/tex]

Complete the square on the left side:

[tex]3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196[/tex]

Then the equation becomes

[tex]\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}[/tex]

Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:

[tex]\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)[/tex]

Then in increasing order, the solutions are

c = log₃(14 - √186), c = log₃(14 + √186)

Answer:

A = W² + 6W

Step-by-step explanation:

The width is W.

The length is 6 units greater than the width, so the length is W + 6.

The area is the product of the length and width.

A = (W + 6)W

A = W² + 6W

Answer:

An additional assumption is that a is not negative.

Step-by-step explanation:

If a could be negative, then:

(-7)^2 < 3^2  would be false because

49 is not greater than 9

Answer:

5

Step-by-step explanation:

(4k + 2) ÷ 10

(4(12) + 2) ÷ 10

(48 + 2) ÷ 10

(50) ÷ 10

= 5

Hope this helps!! <3

The solution to the expression (4k + 2 ) ÷ 10 when k = 12 is 5

From the given expression, we are to solve for (4k + 2) ÷ 10

When

What we are going to do is that we will replace k with 12 wherever we see (k) in the expression given

∴

= (4k + 2 ) ÷ 10

= (4(12) + 2 ) ÷ 10

= (48 + 2) ÷ 10

= (50) ÷ 10

= 5

Learn more about mathematical expressions here:

https://brainly.com/question/20596193?referrer=searchResults

Answer:

place the decimal point in the product so that the number of decimal places in product is the sum of decilal places in the factors. keep all zeros in the product when you place the decimal point. you can drop the zeros on the right once the decimal point has been placed in the product.

Answer:

Does the side on which you choose to isolate the variable affect the solution?

Why might you choose one side over the other?

Answer:

c. It has a reflectional symmetry with 5 lines of symmetry

Step-by-step explanation:

Answer:

Step-by-step explanation:

(B). It has rotational symmetry with an angle of rotation of 120°.