Billy invested $18 of savings in two major business enterprises which paid interest at the rate of 3% and 6%, respectively. If his annual income for these two enterprises was equivalent to a return of 5% on the entire investment, find how much he invested at 3%.

in the II Quadrant, let's recall that the adjacent side or cosine is negative whilst the opposite side or sine is positive, thus

[tex]tan(\theta )=-\sqrt{\cfrac{19}{17}}\implies tan(\theta )=\cfrac{\stackrel{opposite}{\sqrt{19}}}{\underset{adjacent}{-\sqrt{17}}}\impliedby \qquad \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]c=\sqrt{(-\sqrt{17})^2~~ + ~~(\sqrt{19})^2}\implies c=\sqrt{17+19}\implies c=\sqrt{36}\implies c=6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{17}}}{\underset{hypotenuse}{6}}~\hfill[/tex]

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.

An equation is an expression used to show the relationship between two or more numbers and variables.

Ginger and Caleb each have $0.75

Ginger does not have any quarters. He might have 7 dimes and 7 pennies.

Caleb does not have any dimes. He can have 3 quarters and 2 pennies.

Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.

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Answer:

(2,-12)

Step-by-step explanation:

Correct equations:

  8x+y=4

 -2x-8=y

------------------

Rearrange the first equation:

8x+y=4

y=4-8x

Now use this value of y in the second equation:

-2x-8=y

-2x-8=4-8x

6x = 12

x = 2

When x = 2:

y=4-8x

y=4-8(2)

y = -12

(2,-12)

--

One can also graph the two equations and find the point they intersect.  See the attached graph.

Answer:

120 marbles

Step-by-step explanation:

we can find the answer by dividing the volume of the cylinder by the volume of the marble.

V of a cylinder is

pi×r^2×h = 1280pi

V of marble is

4/3 × pi × r^3

V is 32/3 pi

so final answer is 1280pi ÷ (32/3 × pi)

ANSWER IS 120 MARBLES

Answer:

4x/(x+1)(x2+x+6)

Step-by-step explanation:

Answer: A, C, F

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

20x(1+150%)

28x(1+1.5)

28x2.5

70

Answer:

Step-by-step explanation:

To make a guess as to the volume, it may be easier to guess in cups rather than centimeters or inches. One may visualize that a 12 ounce soda can is about 1.5 cups. This is equivalent to 354.88 cubic centimeters or 21.656 cubic inches.

Answer:

716

Step-by-step explanation:

Triangle = bh / 2

24 x 14 = 336, you should divide by 2 but there is 2 of them (front and back) so cancels out. 10 x 24 is 240 and cancels for same reason. 336 + 240 = 576. 14 x 10 = 140 and 576 + 140 = 716

Answer:

976 cm^2

Step-by-step explanation:

area of triangle is 1/2 times base times height

notice we have two triangles

so 14 * 24 * 0.5 is 168

168 times 2 is 336

now we have a rectangle on the bottom so its area is base times height

14 times 10 is 140

and now we have two rectangles on either side

25 times 10 is 250

250 times 2 is 500

500+140+336

976 cm^2

Answer:

(0,4) (0,7) (-2,4)

Step-by-step explanation:

The line x=1 is a vertical line that passes through the point (1,0). So we then place the new triangle at equal distance from the line.

I hope this helps!

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Answer:

i think you have to multiply

the answer is- 28.512

Step-by-step explanation:

i dont know if this is right im sorry but i think it is

Answer:

[tex]26[/tex] and [tex]28[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote the smaller one of the two even integers ([tex]x > 0[/tex] since both integers are positive.) The larger one of the two consecutive even integer would be [tex](x + 2)[/tex].

The square of the smaller integer would be [tex]x^{2}[/tex].

Five times the larger integer would be [tex]5\, (x + 2)[/tex].

Subtract five times the larger integer from the square of the smaller integer to get [tex](x^{2} - 5\, (x + 2))[/tex].

The value of this expression should be equal to [tex]536[/tex]. In other words:

[tex]x^{2} - 5\, (x + 2) = 536[/tex].

Rewrite and simplify this quadratic equation:

[tex]x^{2} + (-5)\, x + (- 546) = 0[/tex].

Apply the quadratic formula to find possible values of [tex]x[/tex]:

[tex]\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}[/tex].

[tex]\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}[/tex].

Since [tex]x > 0[/tex] (both numbers are supposed to be positive), [tex]x = 26[/tex] would be the only valid solution.

Therefore, the two integers would be [tex]x = 26[/tex] and [tex]x + 2 = 28[/tex].

Answer:

Your answer would be:
13.25

128 books in use + 84 books in the collection box =212 reference books on the shelf

212 books / 16 shelves =13.25 per shelf

Logically the answer 13.25 wouldn't make sense because you can't put a 25th of a book on a shelf, so that means you will need to put the "0.25 book" away. Technically your answer would be 13. Due to the question, however, it would be 13.25.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

9. (a) 1/4

   (b) remove 3 alphabet cards

   (c)  add 4 number cards

10.  1/8

Step-by-step explanation:

Question 9

Given:

⇒ total number of cards = 8 + 10 + 6 = 24 cards

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

(a) P(picture card) = 6/24 = 1/4

(b) P(alphabet card) = 10/24 = 5/12

If we remove 3 alphabet cards from the box

⇒ number of alphabet cards = 10 - 3 = 7

⇒ total number of cards = 24 - 3 = 21

Therefore, P(alphabet card) = 7/21 = 1/3

(c)  P(number card) = 8/24 = 1/3

If we add 4 number cards to the box:

⇒ number of number cards = 8 + 4 = 12

⇒ total number of cards = 24 + 4 = 28

Therefore, P(number card) = 12/28 = 3/7

--------------------------------------------------------------------

Question 10

Given:

⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²

As PR = SD = 4cm

Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²

P(point lies in ΔSDR) = 8/128 = 1/16

P(point lies in ΔPRQ) = 8/128 = 1/16

P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8

Answer:

The answer is D

Step-by-step explanation:

The parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.

It is given that the two functions one is the parent function [tex]\rm y = \sqrt[3]{-x}[/tex] and the transformed function [tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex].

It is required to find the transformation rules.

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have parent function:

[tex]\rm y = \sqrt[3]{-x}[/tex]

and transformed function:

[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]

If we multiply the parent function with a negative value it will f(x) over the x axis.

By the transformation rules of the function y = -f(x) reflects f(x) over x-axis.

After applying the transformation to the parent function:

[tex]\rm y = -\sqrt[3]{-x}[/tex]

By the transformation rules of the function if multiply the function with less than the unit value it will be compressed by the multiplied factor ie.

y = k f(x) and k<1, the function will be compressed by the k factor hence:

[tex]\rm y = -0.4\sqrt[3]{-x}[/tex]  (after applying the second transformation)

As we can see the transformed function is subtracted by -2

By rules of transformation, for y=f(x-A) it would be a horizontal translation of 'A' unit to the right.

After applying this transformation we get:

[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]  which is a transformed function derived after applying the transformation to the parent function.

Thus, the parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.

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Answer:

The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4

Step-by-step explanation:

Answer:

x - 7 [tex]\leq[/tex] -28

Step-by-step explanation:

I guarantee you that this is correct. It's pretty simple to understand.

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The fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

Slope of a line = change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Given the following points:

(4, 9) and (0, 5)

Slope of the line would be:

Slope = (5 - 9)/(0 - 4)

Slope = (-4)/(-4)

Slope = 1

Therefore, the fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

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Step-by-step explanation:

(2x - 3)×4

random number multiplied by 2, then minus 3 from that result, and multiply that result by 4.

Answer:

2n= 53

and you divide both sides by 2

2n/2 =53/2

2 divided by 2 is 1 and 53 divided 2 is 26.5

n= 26.5

Answer:

2 m/s or 7.2 km/h

Step-by-step explanation:

Time = 50 seconds

Distance = 100 meters

Velocity = distance/time = 100/50 = 2 m/s or 7.2 km/h

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[tex] \large \purple{ \rm{To \: find↦}}[/tex]

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[tex] \large \purple { \rm{Assumption↦}}[/tex]

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[tex] \large \purple { \rm{ To \: find \: speed \: we \: use↦}}[/tex]

[tex] {\boxed{ \rm{Speed= \frac{ Distance } {Time}}}}[/tex]

[tex]\rule{70mm}{2.2pt}[/tex]

[tex] \large \purple{ \rm{Substitute \: value \: according \: to \: formula. \: }}[/tex]

[tex] \large \rm{s = \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = \cancel \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = 2 m/s \: or \: 7.2km/h }[/tex]

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Answer:

1.c

2.a

3.d

4.e

5.f

6.b

Let's assume that all hours she worked were the first 35 hours of the week.

She would've made £22.80 x 35 = £798

So, she would've made 981.54 - 798 = 183.54 less than the actual amount

She is paid 15% more per hour after the first 35 hours -> She will get £26.22 per hour.

So, she work for 183.54 : 26.22 = 7(hours) after the first 35 hours

So in total, she worked for 35 + 7 = 42(hours).

Answer:

42 hours

We know she works at least 35 hours, so 35x22.80=798. This is her base pay without any extra hours.

981.54-798 =183.54. This is the amount she earnt for working extra hours. if we divide this by the rate she earns for extra hours (22.80x1.15=26.22), 184.54/26.22=7, we know she worked an additional 7 hours.

and 35 plus 7 = 42 :)

Answer:

1222 ft^2

Step-by-step explanation:

2(13x9) + 2(5x12) + 2(4.5x9) + 2(9x11) + 2(19x11) + (19x9)

Answer:

-14x + 6 (option D)

Step-by-step explanation:

To solve the given equation, you first need to distribute the negative 3.

So, you need to multiply

(4x)(-3)  ;  (-2)(-3)

(4x)(-3)= -12x

(-2)(-3)= 6

So, your new, distributed, equation would be:

-12x + 6 - 2x

If we combine like terms (-12x - 2x), our new equation will be:

-14x + 6

Answer:

20 meters

Step-by-step explanation:

Answer:

184

Step-by-step explanation:

80% of 230

0.8x230

8×23

=184

The value of 0.36 when converted to a fraction in the simplest form is 9/25.

Your information is incomplete. Therefore, an overview will be given. It should be noted that a fraction is in its simplest form when the numerator and denominator are prime.

From example, let's convert 0.36 to a fraction on its simplest form. This will be:

0.36 = 36/100 = 9/25

In conclusion, 0.36 is 9/25 in the simplest form.

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