A pet store has 150
150
goldfish and betta fish altogether.
The ratio of goldfish to betta fish is 2:3
2:3
.

How many goldfish does the pet store have?


CLEAR CHECK
What fraction of the fish are goldfish?



How many goldfish does the pet store have? goldfish

Recall: SOHCAHTOA

Sin M = Opp/Hyp

Reference angle = M

Opp = 3√/21

Hyp = 15

Sin M = (3-√21)/15

Sin M = √21/5

Cos M = Adj/Hyp

Reference angle = M

Adj = 6

Hyp = 15

Cos M = 6/15

Cos M = 2/5

Tan M = Opp/Adj

Reference angle = M

Opp = 3√21

Adj = 6

Tan M = (3√21)/6

Tan M = √21/2

:Therefore: Sin M = √21/5

Cos M = 2/5

Tan M = √21/2

Answer:

[tex]\sf \sin M=\boxed{\dfrac{\sqrt{21}}{5}}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\sf \sin M=\dfrac{3\sqrt{21}}{15}\quad\cos M=\dfrac{6}{15}\quad\tan M=\dfrac{3\sqrt{21}}{6}[/tex]

[tex]\implies \sf \sin M=\dfrac{3\sqrt{21}}{15}=\dfrac{\sqrt{21}}{5}[/tex]

Answer:

15

Step-by-step explanation:

to get from 10 to 25 you time by 2½

so then times 6 by 2½ and the answer is 15

Answer:

The value of x = 3.5 or -4

Step-by-step explanation:

=> 2x² = 28 – x

=> 2x²+ x - 28 = 0

=> 2x² + 8x - 7x - 28 = 0

=> 2x ( x + 4 ) - 7 ( x + 4 ) = 0

=> (2x - 7 ) ( x + 4 )

=> x = 7/2 = 3.5 or x = -4

Answer:

x = –4 or x = 3.5

Step-by-step explanation:

[tex]2x^{2}=28-x\Longleftrightarrow 2x^{2}+x-28=0[/tex]

                    [tex]\Longleftrightarrow 2x^{2}-7x+8x-28=0[/tex]

                    [tex]\Longleftrightarrow x(2x-7)+4(2x-7)=0[/tex]

                    [tex]\Longleftrightarrow (2x-7)(x+4)=0 \ \ \ \ \text{factor out} \left( 2x-7\right)[/tex]

                    [tex]\Longleftrightarrow 2x-7=0 \ \ or\ x+4=0\ \ \ \ \text{(zero product rule)}[/tex]              

                    [tex]\Longleftrightarrow x=\frac{7}{2} \ \ or\ x=-4[/tex]

Answer:

3

Step-by-step explanation:

3 to get to 15, multiply by 3, same for other sides.

Answer:

C

Step-by-step explanation:

9 divided by 3 is 3, 15 divided by 5 is 3, and 12 divided by 4 is 3. it all adds up to three

Answer:

280 m³

Step-by-step explanation:

Volume of a Triangular Prism

Solving

Answer:

280

Step-by-step explanation:

So first lets establish the formula for a Triangular Prism :

1/2 * b * h * l

now lets use the mesurements given to substitute into the formula :

1/2 * 7 * 8 * 10

now lets solve it by first multiplying all the whole numbers together!

7 * 8 = 56

56 * 10 = 560

Finally lets multiply 560 by 1/2 or in other words, divide 560 by 2 :

560/2 = 280

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$\stackrel{12000~~ + ~~1200}{13200}\\ P=\textit{original amount deposited}\dotfill &\$12000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1.8 \end{cases}[/tex]

[tex]13200=12000\left(1+\frac{~\frac{r}{100}~}{1}\right)^{1\cdot 1.8}\implies \cfrac{13200}{12000}=\left( 1+\cfrac{r}{100} \right)^{1.8} \\\\\\ \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{1.8}\implies \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \\\\\\ \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\left[ \left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \right]^{\frac{5}{9}}\implies \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\cfrac{100+r}{100}[/tex]

[tex]\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=\cfrac{100+r}{100}\implies 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=100+r \\\\\\ 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}-100 = r\implies 5.44\approx r[/tex]

Step-by-step explanation:

-y is the same as writing -1y. if we forget about the y’s, -1 + 2 = 1. so -1y + 2y = 1y, or just y to be simpler :)

i hope this helps :)

[tex]-y+2y=2y-y=(2-1)y=y[/tex]

It is positive because the coefficient is positive.

Median:

The median in this set is the 5th term.

Therefore the median in this set is 23.

Answer:

lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex] ⇒ Answer D is correct

Step-by-step explanation:

First, let us find the area of the semi-circle.

Area = [tex]\frac{1}{2}[/tex] × π × r²

Given that,

diameter of the semi-circle is ⇒ l

∴ radius ⇒ l / 2

Let us find it now.

Area = [tex]\frac{1}{2}[/tex] × π × r²

Area =  [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]

Secondly, let us find the area of the rectangle.

Area = length × width

Given that,

length ⇒ l

width ⇒ w

Let us find it now.

Area = length × width

Area = l ×w

Area = lw

And now let us find the total area.

Total area =  Area of the rectangle + Area of the semi - circle

Tota area = lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]

Answer:

Step-by-step explanation:

The general standard form of an equation is written in expressed as shown;

(x-a)²+(y-b)² = r²

(a,b) is the centre of the circle and r is the radius

Given the equation of the circle x^2 + y^2 - 4x + 14y +28 =0, we need to find the centre of the circle and its radius.

comparing the equation given with x²+y²+2gx+2fy+c =0

(-g, -f) is the centre

radius = √g²+f²-c

On comparison,

2gx = - 4x

g = -4/2

g = -2

2fy =  14y

f = 14/2

f = 7

c = 28

r = √(-2)²+7²-28

r = √4+49-28

r = √25

r = 5

comparing centre (a,b) to (-g, -f)

a = -g = -(-2)

a = 2

b = -f = -7

b = -7

substituting the centre (a, b) and the radius r into the equation

(x-a)²+(y-b)² = r²

The required equation will be (x-2)²+(y+7)² = 5²

(x-2)²+(y+7)² = 25

Answer:

Step-by-step explanation:

y=-3x-1

The solution is Option A.

The value of x is given from proportion and x = 10 1/2 or x = 10.5

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the first rectangle be A

The dimensions of the rectangle A = 4 by 3

Let the second rectangle be B

The dimensions of the rectangle B = 14 by x

The two rectangles A and B are similar , so

Now , the proportion equation will be

3 / 4 = x / 14

Multiply by 14 on both sides of the equation , we get

x = ( 14 × 3 ) / 4

x = 42/4

x = 10.5

The value of x = 10 1/2

Therefore , the value of x is 10 1/2

Hence , the value of x of the rectangle is 10 1/2

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Applying the cosine ratio of trigonometry, the exact value of cos(-60°) which equals cos (π/3) is: C. 1/2.

In trigonometry, the vaue of the cosine ratio is the cosine of the reference angle which equals the ratio of the adjcent side over the hypotenuse.

To get the exact value of cos(-60°), convert 60 to radians.

π radian = 180

60° = (π/3) radians

Note: cos (-θ) = cos θ

Therefore, cos (-π/3) = cos (π/3)

cos (π/3) = 1/2

The exact value of cos(-60°) = 1/2 (option C).

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Answer:

1/3

Step-by-step explanation:

Answer:

1/6  

Step-by-step explanation:

2/3-1/2 =     find the denominator 3×2=6

4/6-3/6 =     rewrite with a denominator of 6

(4-3)/6 = 1/6     subtract numerators

Answer:

4) 97%

6) 13%

Step-by-step explanation:

4) We are given that 3% for 250 million are diesel.

100% - 3% = 97% NON DIESEL cars

97% of 250 million is 242.45 million.

______________________________

6) We know that 17% (buses) and 70% (cars) are part of that total.

We also know that the total needs to be 100%

So, we simply do this:

100 - (17+70) = 13 (%)

So, 13% of the survey participants had bikes

Answer:

20 x 12=240  

Step-by-step explanation:

The area of the lot with a shape of a parallelogram if its base measures 20 meters and the distance given is 160m².

Area of a parallelogram will be:

= Base × Height

= 20 × 8

= 160m²

The area of the triangular landscape that has a base of 24 meters and a height of 12 meters will be:

= 1/2 × base × height

= 1/2 × 24 × 12

= 144m²

The area of the trapezium will be:

= 1/2 × (a + b) × h

= 1/2 × (16 + 30) × 10

= 1/2 × 46 × 10

= 230m²

The area of the rectangular banner has a length of 5 meters and a width of 3 meters will be:

= Length × Width

= 5 × 3

= 15m²

The area of a soccer ground square in shape with a side of 8 meters will be:

= 8 × 8

= 64m²

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Answer:

b = 25 degrees

c = 81 degrees

d = 64 degrees

Answer:

x=26

Step-by-step explanation:

Since they are complementary

2x+38⁰=90⁰

2x=90⁰-38⁰

2x=52⁰

x=26⁰

I hope it helped you

Answer:

Step-by-step explanation:

This is self-explanatory, We just need to find the value of x by doing this:

Brainliest please. I didn't get one on this account.

Answer:

length times width equals area LxW=Area

Step-by-step explanation:

so,

4 times 4= 26 yards

1=4 square yards

then 26X4 = 104 square yards

Answer:

Step-by-step explanation:

Draw a box between the first quartile; third quartile

Answer:

\sqrt{45}

Step-by-step explanation:

A^2+B^2=C^2

36+?=81

81-36=45

[tex]\sqrt{45}[/tex]=

Answer:

Step-by-step explanation:

Pythagorean Theorem

Here, we are missing one of the altitudes, so we can arrange the equation to form :

Solving

Check the picture below.

so notice the top part of the picture

if we move the "4" and "17" sides  close to each other, till one is on top of the other, the side in red, can never be less than 17 - 4, or 13, it cannot be 13 either, because then both lines will be on on top and we wouldn't have a triangle just a flat-line, so whatever the red line is, it must be more than 13.

notice the bottom part of the picture

if we separate the "4" and "17" sides, and lay them flat, the most the red side can be is 4 + 17 or 21, it can never be greater than 21, it can't be 21 either because if we lay "4" and "17" flat, we lose the triangle and all we'd have is a flat-line.  So whatever the red side is, must be less than 21.

When tangent TA is parallel to KM, it can be proved that KS = MS since they're congruent.

It should be noted that when the tangent line TA is parallel to chord KM, it simply means that segment KS and MS are congruent.

Therefore, since they're congruent, SKM and SMK are equal. By the theorem of inscribed angle, we will have:

SKM = 1/2m(MS)

SKM = 1/2m(KS).

Since SKM = SMK

1/2m(MS) = 1/2m(KS).

MS = KS

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Answer:

22 ounces is more

Step-by-step explanation:

1 pound is equal to 16 ounces

Answer:

1 pound

Step-by-step explanation:

1pound=16oz 22oz= 1.375pound

Answer:

It will take 7 weeks for Sophie to catch up to Pete. Both of them will each have completed 48 missions.

Step-by-step explanation:

27 + 3x = 13 + 5x

27 + 3x - 3x = 13 + 5x - 3x

27 = 13 + 2x

27 - 13 = 13 + 2x - 13

14 = 2x

x = 7

27 + 3x

27 + 3(7)

27 + 21

48

13 + 5x

13 + 5(7)

13 + 35

48

Answer:

42qt

Step-by-step explanation:

First, multiply 2 x 3 x 7

2 x 3 = 6

6 x 7 = 42

Second, q x t

Qt

Third, put together

42qt

Answer:

[tex] \frac{7}{8} - \frac{1}{2} = \frac{7 - 4}{8} = \frac{3}{8} [/tex]

Step-by-step explanation:

I hope I helped you! :)

Answer:

B  at least 103 flights are on time. :)

Step-by-step explanation:

First we need to turn the percentage into a decimal :)

131 x 0.80 = 104.8

The answer should be B  at least 103 flights are on time.

Have an amazing day!!

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