(3)/(22)+(-(1)/(11) find the sum without use of a number line

Answer:

--1-- (of set 23456)

2   4

5 3

 6

--2-- (of set 23456)

2   3

5 4

 6

--3-- (of set 23456)

2   5

6 3

 4

--4-- (of set 23456)

2   3

6 5

 4

--5-- (of set 23456)

3   5

4 2

 6

--6-- (of set 23456)

3   2

4 5

 6

--7-- (of set 23456)

3   6

5 2

 4

--8-- (of set 23456)

3   2

5 6

 4

--9-- (of set 23456)

3   5

6 4

 2

--10-- (of set 23456)

3   4

6 5

 2

--11-- (of set 23456)

4   5

3 2

 6

--12-- (of set 23456)

4   2

3 5

 6

--13-- (of set 23456)

4   6

5 3

 2

--14-- (of set 23456)

4   3

5 6

 2

--15-- (of set 23456)

5   4

2 3

 6

--16-- (of set 23456)

5   3

2 4

 6

--17-- (of set 23456)

5   6

3 2

 4

--18-- (of set 23456)

5   2

3 6

 4

--19-- (of set 23456)

5   6

4 3

 2

--20-- (of set 23456)

5   3

4 6

 2

--21-- (of set 23456)

6   5

2 3

 4

--22-- (of set 23456)

6   3

2 5

 4

--23-- (of set 23456)

6   5

3 4

 2

--24-- (of set 23456)

6   4

3 5

 2

--1-- (of set 34567)

3   5

6 4

 7

--2-- (of set 34567)

3   4

6 5

 7

--3-- (of set 34567)

3   6

7 4

 5

--4-- (of set 34567)

3   4

7 6

 5

--5-- (of set 34567)

4   6

5 3

 7

--6-- (of set 34567)

4   3

5 6

 7

--7-- (of set 34567)

4   7

6 3

 5

--8-- (of set 34567)

4   3

6 7

 5

--9-- (of set 34567)

4   6

7 5

 3

--10-- (of set 34567)

4   5

7 6

 3

--11-- (of set 34567)

5   6

4 3

 7

--12-- (of set 34567)

5   3

4 6

 7

--13-- (of set 34567)

5   7

6 4

 3

--14-- (of set 34567)

5   4

6 7

 3

--15-- (of set 34567)

6   5

3 4

 7

--16-- (of set 34567)

6   4

3 5

 7

--17-- (of set 34567)

6   7

4 3

 5

--18-- (of set 34567)

6   3

4 7

 5

--19-- (of set 34567)

6   7

5 4

 3

--20-- (of set 34567)

6   4

5 7

 3

--21-- (of set 34567)

7   6

3 4

 5

--22-- (of set 34567)

7   4

3 6

 5

--23-- (of set 34567)

7   6

4 5

 3

--24-- (of set 34567)

7   5

4 6

 3

Step-by-step explanation:

This javascript code is extremely brute-force, but it does the job:

function checkIfInSet(i, set) {

   return i.toString().split('').sort().join('') === set;

}

function checkIfMagic(s) {

   return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))

}

function printMagic(s) {

   console.log(`${s[0]}   ${s[4]}`);

   console.log(` ${s[1]} ${s[3]}`);

   console.log(`  ${s[2]}\n`);

}

function checkSet(set) {

   let counter = 1;

   for(let i=1; i<99999; i++) {

       if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {

           console.log(`--${counter++}-- (of set ${set})`);

           printMagic(i.toString());

       }

   }

}

checkSet('23456');

checkSet('34567');

Answer:Conversion units

Step-by-step explanation: 1 ft^3= 0.028m^3 .: 1440ft^3=40.776m^3, so $1.75x40.776=$71.358~ $71.36.:

Answer:

$71.36

Step-by-step explanation:

1 foot = 0.3048 metros

1 cubic feet = (0.3048metros)³ = 0.02932 cubic meters   (aprox.)

1440 cubic feet = 1440*0.02932 = 40.7763 m

$1.75 por cubic meter:

1.75*40.7763 = $71.36

Answer:

? = 4.73

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp / hyp

sin 25 = 2 / ?

? sin 25 = 2

? = 2 / sin 25

? =4.732403166

To the nearest hundredth

? = 4.73

Answer:

11.8%

Step-by-step explanation:

Here in this question, we want to find the probability of no success in the binomial experiment for 6 trials.

Let p = probability of success = 30% = 30/100 = 0.3

q = probability of failure = 1-p = 1-0.3 = 0.7

Now to calculate the probability, we shall need to use the Bernoulli approximation of the binomial theorem.

That would be;

P(X = 0) = 6C0 p^0 q^6

6C0 is pronounced six combination zero

= 6 * 0.3^0 * 0.7^6 = 1 * 1 * 0.117649 = 0.117649

This is approximately 0.1176

If we convert this to percentage we have 11.76%

But we want our answer rounded to the nearest tenth of a percent and that is 11.8%

Answer:

d= 6

r= 6/2

r=3

V= π. r². h

V= π . 3². 14

V= π. 9 . 14

V= π 126 cm³

V= 126 π cm³ (π not in number)

hope it helps^°^

Answer:if you use the formula it is 126 pi cm cubed

The answer is c

Step-by-step explanation:

Answer:

21.4 m²

Step-by-step explanation:

To find the surface area of this whole triangular prism, we have to look at the bases (the triangles), find their surface area, then look at the sides (the rectangles) and find theirs.

Let's start with the triangles. The area of any triangle is [tex]\frac{bh}{2}[/tex]. The base of this triangle is 2m (because there are 2 one meters) and the height is 1.7m.

[tex]\frac{2\cdot1.7}{2} = \frac{3.4}{2} = 1.7[/tex]

So the area of one of these triangles is 1.7m. Multiplying this by two, because there are two triangles in this prism:

[tex]1.7\cdot2=3.4[/tex]

Now let's find the area of the sides.

The side lengths are 2 and 3, so

[tex]2\cdot3=6[/tex], and there are 3 sides (including the bottom/floor) so [tex]6\cdot3=18[/tex].

Now we add.

[tex]18+3.4=21.4[/tex] m².

Hope this helped!

Answer: 21.4 square meters^2

Step-by-step explanation:

For a given initial quantity A, a decrease of x% can be written as:

A - A*(x%/100%) = A*(1 - x%/100%)

With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:

P(t) = 300*(0.77)^t

Now let's see how we found that.

In this case, we know that:

The initial number of animals is 300.

They decrease at an anual rate of 23%.

This means that after the first year, the population will be:

P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)

After another year, the population decreases again, so we get:

P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2

Here we already can see the pattern, the population in the year t, we will get:

P(t) = 300*(0.77)^t

Then we can see that the correct option is C.

If you want to learn more, you can read:

https://brainly.com/question/16993154

Answer:

Area : 14+10+40=64 square unit

Step-by-step explanation:

the area of the top rectangle with sides  2 and 7

A=2*7=14 square unit

the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5

Area=5*2=10 square unit

the bottom rectangle : sides 10 and 4

Area=10*4=40

add the areas : 14+10+40=64 square unit

Answer:

11.21157846 =x

Step-by-step explanation:

We know log b (a) = c  can be written as b^c =a

log 3 (x) = 2.2

3^2.2 = x

11.21157846 =x

Answer:

[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]

Step-by-step explanation:

[tex]\large \sf log_3 (x)=2.2[/tex]

Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:

[tex]\large \sf log_b(y)=x[/tex]

[tex]\large{\sf y=b^x}[/tex]

Apply the relationship.

[tex]\large \sf log_3 (x)=2.2[/tex]

[tex]\large \sf x=3^{2.2}[/tex]

[tex]\large \sf x=11.21157845...[/tex]

[tex]\large \sf x \approx 11.21[/tex]

Answer:

The answer is (3×7) + (12×2) .

[tex](3 \times 7) + (12 \times 2)[/tex]

[tex] = 21 + 24[/tex]

[tex] = 45[/tex]

Answer:

x = 1

y = -1

Step-by-step explanation:

3x + 5y = -2

7x - 8y = 15

=> -8y = 15 - 7x

=> -y = 15/8 - 7/8x

=> y = -15/8 + 7/8x

3x + 5(-15/8 + 7/8x) = -2

=> 3x -75/8 + 35/8x = -2

=> 24/8x - 75/8 + 35/8x = -16/8

=> 59/8x - 75/8 = -16/8

=> 59/8x = 59/8

=> x = 59/8 x 8/59

=> x = 472/472

=> x = 1

x = 1

So, 3x + 5y = -2

=> 3 (1) + 5y = -2

=> 3 + 5y = -2

=> 5y = -5

=> y = -5/5

=> y = -1

So, x = 1

=>  y = -1

Answer:

(7, 5)

Step-by-step explanation:

(x+5)/2, ( y-3)/2)=(6,1)

(x+5)/2=6, x= 7

( y-3)/2=1, y=5

Answer:

The coordinates of A'C'S'T' are;

A'(-7, 2)

C'(-9, -1)

S'(-7, -4)

T'(-5, -1)

The correct option is;

B

Step-by-step explanation:

The coordinates of the given quadrilateral are;

A(-3, 1)

C(-5, -2)

S(-3, -5)

T(-1, -2)

The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward

Therefore, we have;

A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)

C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)

S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)

T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)

Therefore, the correct option is B

Answer:

When x = -4 and y = -6, p = 37.75

Step-by-step explanation:

Given that p = x² - y²/x² + x·y, we have;

p = (x² × x² -y² + x·y×x²)/x²

p = (x²⁺² - y² + x¹⁺² × y)/x²

p = (x⁴ - y² + x³·y)/x²

Therefore, p in the simplest form is given as follows;

[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]

To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;

[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]

Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.

Answer:

18

Step-by-step explanation:

3⋅6−2+2​

Use PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction

First we multiply, then add or subtract so,

18 - 2 + 2

Now we subtract,

16 + 2

Now we add,

18

Answer:

See explanation

Step-by-step explanation:

We have to prove the identity

[tex]tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }[/tex]

We will take right hand side of the identity

[tex]\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}[/tex]

[tex]=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}[/tex]

[tex]=tan(\frac{\Theta }{2})[/tex] [ Tan θ will be positive since θ lies in 1st quadrant ]

Answer:

4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Step-by-step explanation:

Simplify the following:

(2^(1/3))^7

Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.

Multiply exponents. (2^(1/3))^7 = 2^(7/3):

2^(7/3)

Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.

2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):

2^(6/3) 2^(1/3)

Hint: | Divide 6 by 3.

6/3 = (3×2)/3 = 2:

2^2 2^(1/3)

Hint: | Evaluate 2^2.

2^2 = 4:

Answer:  4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal

Hi there! :)

Answer:

[tex]\huge\boxed{m\leq 2}[/tex]

Equation:

8m - 6 ≤ 10

Add 6 to both sides:

8m ≤ 16

Divide both sides by 8:

8m/8 ≤ 16/8

m ≤ 2

Answer:

8m - 6≤ 10

m≤2

Step-by-step explanation:

8m - 6≤ 10

Add 6 to each side

8m - 6+6≤ 10+6

8m ≤ 16

Divide each side by 8

8m/8 ≤16/8

m≤2

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by

[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

So the distance between (-4,4) and (1,0) is

We have the final answer as

Hope this helps you

Answer: terminating

Step-by-step explanation:

Answer:

7.2 is a terminating decimal.

Step-by-step explanation:

Terminating decimals are decimals that have an end point. The decimal does not continue to go on and on with numbers but, it stops at one number which makes it terminating.

Repeating decimals are decimals that go on and on with the same number or same patterns of numbers.

So, since 7.2 has an endpoint, then it is a terminating decimal.

Answer:

m = -9

Step-by-step explanation:

2m-10=44+8m

Subtract 2m from each side

2m-2m-10=44+8m-2m

-10 = 44+6m

Subtract 44 from each side

-10-44 = 44-44+6m

-54 = 6m

Divide by 6

-54/6 = 6m/6

-9 = m

Answer:

solve by solving the salvation for equation don't be a slave get educated from what's gave

Answer:

80 feet

Step-by-step explanation:

1 inch represents 10 feet

Then 8 inches represent = 8 × 10

= 80 feet

Answer:

perimeter is  4 sqrt(29) + 4pi  cm

area is 40 + 8pi cm^2

Step-by-step explanation:

We have a semicircle and a triangle

First the semicircle with diameter 8

A = 1/2 pi r^2 for a semicircle

r = d/2 = 8/2 =4

A = 1/2 pi ( 4)^2

  =1/2 pi *16

  = 8pi

Now the triangle with base 8 and height 10

A = 1/2 bh

  =1/2 8*10

  = 40

Add the areas together

A = 40 + 8pi cm^2

Now the perimeter

We have 1/2 of the circumference

1/2 C =1/2 pi *d

         = 1/2 pi 8

        = 4pi

Now we need to find the length of the hypotenuse of the right triangles

using the pythagorean theorem

a^2+b^2 = c^2

The base is 4 ( 1/2 of the diameter) and the height is 10

4^2 + 10 ^2 = c^2

16 + 100 = c^2

116 = c^2

sqrt(116) = c

2 sqrt(29) = c

Each hypotenuse is the same so we have

hypotenuse + hypotenuse + 1/2 circumference

2 sqrt(29) + 2 sqrt(29) + 4 pi

4 sqrt(29) + 4pi  cm

Step-by-step explanation:

First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.

2pi4 so the perimeter for the half circle would be 8pi/2.

The area of that half circle would be piR^2 so 16pi/2.

Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2

16+100=C^2

116=C^2

C=sqrt(116)

making the perimeter of this triangle 2×sqrt(116)

The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.

We than just need to add up the perimeters and areas for both the half circle and triangle.

The area would be equal to 8pi+40

The perimeter would be equal to 4pi+4(sqrt(29))

Answer:

-6xy - 16x -24y -64

Step-by-step explanation:

(2x+8)(-3y-8) =

To find the answer,

First multiply, the first number on both sides,

2x * -3y = -6xy

Then the first number on the left side and the second number on the right side,

2x * -8 = -16x

Then the second number on the left side and the first number on the right side,

8 * -3y = -24y

Then the second number on the left side and the second number on the right side,

8 * -8 = -64

Now add all the answers,

-6xy -16x -24y -64

Answer:

-6xy-16x-24y-64

Step-by-step explanation:

(2x+8)(-3y-8)​

Foil

First 2x*-3y = -6xy

outer -8*2x = -16x

inner -3y *8 = -24y

last -8*8 = -64

Add them together

-6xy-16x-24y-64

Answer:

(A) [tex]y = x+3[/tex]

Step-by-step explanation:

Using the values of (-6, -3), (3,6), and (5,8) we can substitute the values into each equation and see if the equation meets the requirements for all 3.

Let's test A first.

[tex]-3 = -6+3[/tex]

Correct, let's try the second pair.

[tex]6 = 3+3[/tex]

Correct, let's try the third pair.

[tex]8 = 5+3[/tex]

So yes, this equation works.

For fun, let's try the other equations.

Let's test B.

[tex]-3 = -6-3[/tex]

This is not true as -6 -3 = -9. So this equation is immediately ruled out.

Let's test C.

[tex]-3 = 2\cdot-6[/tex]

Again this doesn't work, as -6 times 2 is -12. So this equation is also ruled out.

Let's try D.

[tex]-3 = \frac{1}{2}\cdot-6[/tex]

This works, as half of -6 is -3 - however the equation will only work if all 3 pairs work for it.

Let's try the second pair.

[tex]6 = \frac{1}{2}\cdot3[/tex]

This doesn't work, as half of 3 is 1.5. This equation is also ruled out.

Therefore, A is the only equation that works with these pairs.

Hope this helped!

Answer:

A

Step-by-step explanation:

Find the vertex form of the quadratic function below.

y = x^2 - 4x + 3

This quadratic equation is in the form y = a{x^2} + bx + cy=ax  

2

+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…

y = a(x - h)^2 + k

This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.

Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.

STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.

STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).

STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.

Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.

STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.

After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).

Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.

Example 2: Find the vertex form of the quadratic function below.

The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a  



​  

=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.

STEP 1: Factor out 22 only to the terms with variable xx.

STEP 2: Identify the coefficient of the xx-term or linear term.

STEP 3: Take that number, divide it by 22, and square.

STEP 4: Now, I will take the output {9 \over 4}  

4

9

​  

 and add it inside the parenthesis.

By adding {9 \over 4}  

4

9

​  

 inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(  

4

9

​  

)=  

2

9

​  

 to the entire equation.

Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.

STEP 5: Since I added {9 \over 2}  

2

9

​  

 to the equation, then I should subtract the entire equation by {9 \over 2}  

2

9

​  

 also to compensate for it.

STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.

It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(  

2

−3

​  

,  

2

−11

​  

).

Example 3: Find the vertex form of the quadratic function below.

Solution:

Factor out - \,3−3 among the xx-terms.

The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}  

4

1

​  

 inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(  

4

1

​  

)=  

4

−3

​  

 is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}  

4

3

​  

 outside the parenthesis.

Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(  

2

1

​  

,  

4

11

​  

).

Example 4: Find the vertex form of the quadratic function below.

y = 5x^2 + 15x - 5  

Solution:

Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}  

4

9

​  

.

Add {9 \over 4}  

4

9

​  

 inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(  

4

9

​  

)=  

4

45

​  

 is the number that we need to subtract to keep the equation unchanged.

Express the trinomial as a square of binomial, and combine the constants to get the final answer.

Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}  

2

−3

​  

,  

4

−65

​  

.

Answer:

(x - 1 )^2 - 3

Step-by-step explanation:

( x - 1 )^2 + ( -3)

x^2 - 2x + 1 - 3

x^2 - 2x - 2

Answer:

last option

Step-by-step explanation:

Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷  x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.

Answer:

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

Step-by-step explanation:

Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:

Speed = distance / time

The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.

For running:

Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:

5 = p / x

p = 5x

For biking:

Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:

12 = q / y

q = 12y

The total distance ran and biked by Suzette (d) = Distance biked + distance ran

d = p + q

80 = p + q

80 = 5x + 12y                 (1)

The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run

t = x + y

9 = x + y                         (2)

Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:

7y = 35

y = 35/7

y = 5 hours

Put y = 5 in equation 2:

9 = x + 5

x = 9 -5

x = 4 hours

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours