how much time with it take for 450 to yield 81 as interest at 4.5 per annum of simple interesst
​

Answer:

  60°

Step-by-step explanation:

The definition of cosine tells you ...

  cos(β) = 3/6 = 1/2

  β = arccos(1/2) . . . . use the inverse cosine function to find the angle

  β = 60°

_____

The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...

  1 : √3 : 2

The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.

Answer:

x = 6

Step-by-step explanation:

Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.

Therefore, PQ = QR. Which is:

[tex] 3x + 14 = 7x - 10 [/tex]

Solve for x. Collect like terms

[tex] 3x -7x = - 14 - 10 [/tex]

[tex] -4x = -24 [/tex]

Divide both sides by -4x

[tex] x = 6 [/tex]

Answer:

0

Step-by-step explanation:

16x2= 32 and 32x1=32 so 32-32=0

Answer:

a + s = 394     total tickets sold is 394 s = a - 56       56 fewer student tickets than adult substitute a-56 in place of s in 1st equation and solve for a a + (a - 56) = 394 2a - 56 = 394 2a = 450 a = 225 adult tickets sold s = a-56 = 169 student tickets sold

Hoped I helped

Answer:

[tex]\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }[/tex]

Step-by-step explanation:

Given equation is

[tex]x^2 + y^2 + 6x-8y - 25 = 0[/tex]

Adding 25 to both sides

[tex]x^2 + y^2 +6x-8y = 25[/tex]

Completing squares

[tex]x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25[/tex]

Both of their "b" is -3 and 4 respectively

So, adding (-3)² => 9 and (4)² => 16 to both sides

[tex](x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}[/tex]

Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex], where center = (h,k) and radius = r.

We get:

Center = (-3,4)

Radius = [tex]5\sqrt{2}[/tex]

Answer:

[tex]y=-0.5x+4.5[/tex]

Step-by-step explanation:

The slope of [tex]y=2x-6[/tex] is:

The negative reciprocal of that slope is:

So the perpendicular line will have a slope of [tex]-1/2[/tex]:

And now put in the point [tex](1,5)[/tex]:

And that answer is OK, but let's also put it in [tex]y=mx+b[/tex] form:

Answer:

-1/8

Step-by-step explanation:

[tex](-2)^-3 \\=\frac{-1}{2}^{3}\\=\frac{-1}{8}[/tex]

Answer:

-1/8

Step-by-step explanation:

[tex]\left(-2\right)^{-3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\\left(-2\right)^{-3}=\frac{1}{\left(-2\right)^3}\\\\=\frac{1}{\left(-2\right)^3}\\\\\left(-2\right)^3=-8\\\\=\frac{1}{-8}\\\\=-\frac{1}{8} \\\\\left(\mathrm{Decimal:\quad }\:-0.125\right)[/tex]

Answer:

9% of $1500 is $15 so she gains an extra $15 for each of the 18 years

$1500 in the bank each year for 18 years is $27000 after 18 years

$15 each year as well so that’s an extra $270 in the bank

The total in the bank is the sum of what she has invested and the interest so the total in the bank is $27270

Step-by-step explanation:

Answer:

1/46 is already in the simplest form.

Answer:

1/46 is already in its simplest form.

__________

D = 4

__________

i blelieve this is it.

Answer:

Step-by-step explanation:

[tex]3\pi d = 12 \pi\\\\divide\:both\:sides\:of\:the\:equation\:by\: 3\:\pi\\\frac{3 \pi d}{3\pi} = \frac{12 \pi}{3\pi} \\\\d=4[/tex]

Answer:

multiplication

Step-by-step explanation:

it seems the best

Answer:

13°

Step-by-step explanation:

The smallest angle in a triangle is the angle opposite the shortest side.

In this case the angle opposite side 9

let the angle be x, then using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{40}[/tex] , thus

x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{40}[/tex] ) ≈ 13° ( to the nearest degree )

The 3×3 Matrix is  [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object

A 3 x 3 matrix is calculated for a matrix having 3 rows and 3 columns

Given,

B=

1.2 1.4 3.1

2.2 1.1 5.6

3.7 4.2 6.7

Then the 3×3 matrix is

[tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]

Hence, The 3×3 Matrix is [tex]B=\left[\begin{array}{ccc}1.2&1.4&3.1\\2.2&1.1&5.6\\3.7&4.2&6.7\end{array}\right][/tex]

Learn more about Matrix and 3×3 Matrix here

https://brainly.com/question/12759849

#SPJ2

Answer:

Step-by-step explanation:

c11 =

⇒ 56.1  

c12 =

⇒ 12.1

c13 =

⇒ 236

Answer:

3/5^3

3/5^3 = 27

125

= 0.216

Step-by-step explanation:

Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e. for five-hundredths enter 5/100. If you are using mixed numbers be sure to leave a single space between the whole number and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.

Because slash is both signs for fraction line and division, we recommended use colon (:) as operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

Colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.

An asterisk * or × is the symbol for multiplication.

Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.

The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2

Calculator follows well-known rules for order of operations. Most common mnemonics for remembering this order of operations are:

PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction

BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.

GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.

Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

Answer:

[tex]\frac{536}{15}[/tex] or [tex]35\frac{11}{15}[/tex] (they're the same)

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{\mathrm{9}}[/tex]

Step-by-step explanation:

[tex]\Rightarrow \displaystyle \frac{18 \div 2 * 3}{5-2}[/tex]

Dividing first.

[tex]\Rightarrow \displaystyle \frac{9 * 3}{5-2}[/tex]

Multiplying and subtracting.

[tex]\Rightarrow \displaystyle \frac{27}{3}[/tex]

Division.

[tex]\Rightarrow 9[/tex]

We have [tex]h(p)=p^2+2p[/tex] and [tex]h(p)=3[/tex] which means we can equate:

[tex]p^2+2p=3[/tex].

Subtract 3 from both sides:

[tex]p^2+2p-3=0[/tex].

Then solve for p:

[tex]p^2+2p-3=0[/tex].

[tex](p-1)(p+3)=0[/tex].

So the product of two factors (p-1) and (p+3) is 0 which means at least one of the factors must be 0:

[tex]p-1=0\implies p_1=1[/tex].

Or

[tex]p+3=0\implies p_2=-3[/tex].

Hope this helps.

Answer:

  H = M/(2A +2T)

Step-by-step explanation:

Factor out H and divide by its coefficient.

  M = 2HA +2HT

  M = H(2A +2T)

  M/(2A +2T) = H

  H = M/(2A +2T)

Answer:

The z-score corresponding to an observed value of x of 2 is 0.215.

Step-by-step explanation:

We are given that a variable x has the possible observations shown below;

Possible observations of X: -3, -1, 0, 1, 1, 2, 4, 4, 5.

Firstly, we will find the mean and the standard deviation of X, i.e;

Mean of X, ([tex]\mu[/tex]) = [tex]\frac{\sum X}{n}[/tex]

                       =  [tex]\frac{(-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5}{9}[/tex]  

                       =  [tex]\frac{13}{9}[/tex]  = 1.44

Standard deviation of X, ([tex]\sigma[/tex]) =  [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]

                            =  [tex]\sqrt{\frac{(-3-1.44)^{2}+(-1-1.44)^{2}+......+(4-1.44)^{2}+(5-1.44)^{2} }{9-1} }[/tex]

                            =  2.603

Now, the z-score corresponding to an observed value of x of 2 is given by;

                  z-score =  [tex]\frac{X-\mu}{\sigma}[/tex]

                               =  [tex]\frac{2-1.44}{2.603}[/tex]  = 0.215.        

Answer:

The length of the rectangle would be 4.

Step-by-step explanation:

We can start by naming the width x.

Therefore, the length would 3x-2.

The perimeter of the rectangle would then be:

2(3x-2+x)

We can set up the given equation

2(3x-2+x)=12

Solve for x.

Divide both sides by 2.

3x-2+x=6

Combine like terms.

4x-2=6

Add 2 to both sides.

4x=8

Divide both sides by 4.

x=2

The width would then be 2.

We can plug that into the expression for length.

3x-2

3(2)-2

6-2

4

The length of the rectangle would be 4.

Answer:

W = 14

Step-by-step explanation:

7w=98

Divide

w=98/7

Done

w=14

Hope this helps! :)

(pls mark brainliest)

Answer:

w = 14

Step-by-step explanation:

98 = 7w

98/7 = 7w/7

14 = w

Hope this helps.

Answer:

eds bageles are $.22 per bagel and best bagels are $.23 per bagel.

Step-by-step explanation:

By Thales' theorem:

[tex]\[\begin{array}{l}\frac{{18}}{{2x + 2}} = \frac{{24}}{{3x + 1}}\\18(3x + 1) = 24(2x + 2)\\54x + 18 = 48x + 48\\6x = 30\\x = 5\\A.\end{array}\][/tex]

Answer:

7/4 = 1.75

Step-by-step explanation:

step 1: pick two points on the line that have nice integer coordinates.

--> (3,4) and (-1,-3)

step 2: calculate the y difference and the x difference

--> y difference: 4 - -3 = 7

    x difference: 3 - -1 = 4

step 3: the slope is y difference / x difference

--> slope = 7/4

Answer:

59.96

Step-by-step explanation:

when 67% if 89.5 is expressed in numbers,

[tex]\frac{67}{100}*89.5\\ \frac{5996.5}{100}\\ =59.96[/tex]

Answer:

The measure of angle RST = 120°

Step-by-step explanation:

Answer:

The measure of angle RST = 120°

hope this helps

Answer:

5.75

Step-by-step explanation:

11.25 - 5.5 = 5.75.

So, Ana must take 5.5 more mL of Medicine A than Medicine B.

Hope this helps!

Answer:

y = 1/5x - 6.4

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be 1/5

Then, plug the slope and the point into the equation y = mx + b to find b

y = mx + b

-7 = 1/5(-3) + b

-7 = -0.6 + b

-6.4 = b

Then, plug this and the slope into the equation

y = 1/5x - 6.4 will be the equation

Answer:

200,000

Step-by-step explanation:

To solve this, you can divide the 2019 total projected employment (210,000) by 1 + the growth rate (.05) to find the 2009 total employment.

210,000 / (1 + .05) = 200,000

I hope this helps!

-TheBusinessMan