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almond37 [142]
2 years ago
9

Which proportion would be used to solve the following problem. The proportion of turtles to alligators at the reptile park is 5:

9. Since Beth counted 45 turtles, how many alligators are there?
Mathematics
2 answers:
spin [16.1K]2 years ago
6 0

Answer:

befor i go im trynna love you baby hopefully e

Step-by-step explanation:

jeyben [28]2 years ago
6 0

Answer/Step-by-step explanation:

There are 81 Alligators.

The original equation was 5:9. Since the 5 turtles have been scaled up(multiplied by) 9 times. The rate for alligator will be multiplied by 9.

45 ÷ 5 = 9

9 x 9 = 81

5:9 x 9 = 45:81

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andy constructed a triangle angle 1 and 2 are the same but angle 3 has a measurement of 100 degrees what is the measurement of a
attashe74 [19]
The triangle has one angle of 100 degrees, and the other two are equal. 
We know that the angles of a  triangle always add up to 180. To find the measurement of angle 1 and 2, let's solve for this equation. 
2x + 100 = 180, where x=angle 1 = angle 2. Subtract 100 from both sides
2x = 80                                                           Divide both sides by 2
x = 40
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3 years ago
Find the equation of the line with slope m=1 that contains the point (7,5).
katovenus [111]

Answer:

y = x - 2

Step-by-step explanation:

y = mx + b

5 = 1 (7) + b

5 = 7 + b

b = -2

So...

y = x - 2

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2 years ago
In ΔABC shown below, ∠BAC is congruent to ∠BCA: Triangle ABC, where angles A and C are congruent Given: Base ∠BAC and ∠ACB are c
Morgarella [4.7K]
1. Definition of bisector
2. ASA congruence theorem or ASA Postulate
6 0
2 years ago
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The half-life of a certain substance is 20 years. How much of a 100 gram sample will be left after 20 years?
cluponka [151]

\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50

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3 years ago
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Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola
mote1985 [20]

ANSWER

This is an ellipse. The equation is:

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

(a+b)^2=a^2+2ab+b^2

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

16x^2-32x=16(x^2-2x)

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

(x-1)^2=x^2-2x+1

To maintain the equation, we have to subtract 1,

16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

16(x-1)^2-16+9y^2+72y+16=0

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

9y^2+72y=9(y^2+8y)

Following the same reasoning as before, we have that the perfect binomial squared is,

(y+4)^2=y^2+8y+16

Remember to subtract the independent term to maintain the equation,

9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

16(x-1)^2-16+9(y+4)^2-144+16=0

Add like terms,

\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}

Add 144 to both sides,

\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}

As we can see, this is the equation of an ellipse. Its standard form is,

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\  \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1

Note that we can simplify a and b,

\frac{12}{4}=3\text{ and }\frac{12}{3}=4

Hence, the equation of the ellipse is,

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

3 0
1 year ago
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