If kinaata goes for swimming lessons every 5 days while Wayo goes every 6 days. if both kinaata and Wayo had swimming lessons together at the pool today, after how many days will both meet again at the pool for lessons?​

Answer:

9: 50

10: 90

11: 60

12: 25 and 115

13: 130 and 40

Thats all i can do, im sorry but i hope this helps ^^

Answer: 36 m, 144 m

Step-by-Step Explanation:

a = 14 m

b = 12 m

c = 10 m

Perimeter = a + b + c

Therefore,

= a + b + c

= 14 + 12 + 10

= 26 + 10

=> 36

Perimeter = 36 m

Length of Fence required for Fencing 4 times = Perimeter * 4

Therefore,

= Perimeter * 4

= 36 * 4

= 144

Length of Fence required for Fencing 4 times = 144 m

Answer:

Step-by-step explanation:

(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.

(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.

(3) By definition, all angles of a regular polygon are congruent.

(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.

(5) This is true. (See statement (1)).

Answer:

Options B, C, E

Step-by-step explanation:

Step-by-step explanation:

7

4

1

----

12

reality

6.833

3.594

1.369

----------

11.796

The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.

From the information, we are told to convert 2 litres into ml. This will be:

= 1000 × 2

= 2000ml

The number of eggs that will be bought to make 500 muffins will be:

= 500 × 2

= 1000 eggs.

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Answer:

 Numbers are 5 , 7

Step-by-step explanation:

  Let the two consecutive odd numbers be (2x + 1) and (2x + 3)

         Their product = 35

(2x + 1)(2x + 3) = 35

Use FOIL method.

       2x*2x + 2x*3  + 1*2x + 1*3 = 35

              4x² + 6x  + 2x + 3       = 35

      Combine like terms

                            4x² + 8x  + 3    = 35

                         4x² + 8x + 3 - 35 = 0

                            4x² + 8x  - 32   = 0

 Solving:

                 4x² + 8x - 32 = 0

Divide the entire equation by 2

                [tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]

                  2x² + 4x - 16 = 0

Sum = 4

Product = -32

Factors = 8 , (-4)

When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.

Rewrite the middle term

2x² + 8x - 4x  - 16 = 0

 2x(x + 4) - 4(x + 4) = 0

   (x + 4) (2x - 4) = 0

2x - 4 = 0   {Ignore x +4 = 0  as it gives negative number}

2x = 4

   x = 4/2

   x= 2

2x + 1 = 2*2 + 1 = 5

2x + 3 = 2*2 +3 = 7

   The numbers are 5 , 7

By using the midpoint approach, the price elasticity of demand between each of the given prices are:

The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).

By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]

Price elasticity of demand = 1/-0.1818

Price elasticity of demand = 5.50.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]

Price elasticity of demand = 0.5/-0.2222

Price elasticity of demand = 2.25.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]

Price elasticity of demand = 0.33/-0.2857

Price elasticity of demand = 1.17.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]

Price elasticity of demand = 0.25/-0.4

Price elasticity of demand = 0.63.

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Hi Student!

This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression.  So let's plug in the values and solve.

Plug in the values

Factor out the exponent

Combine

Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.

The correct function shown in the graph is,

⇒ log₁₀ (ax) = 1

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:

⇒ log₁₀ (ax) = 1

or , ax = 10¹ = 10

Thus, x  = 10/a

So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .

⇒ log (3 × 3.33) = 0.99 ≈ 1

Thus, out of the given options only Option D seems to be the most probable answer.

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The value of x for each radical equation is 243 , 125,8,256 respectively.

The correct question is attached as an image with the answer.

When in an equation the variable is under a radical it is called a Radical Equation.

It is given in the question that

which radical matches to the solution

[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]

[tex]\rm x^4 = 81^5\\x = 243[/tex]

[tex]\rm x^4 = 625^3\\x = 125\\[/tex]

[tex]x^5 = 32^3\\x = 8\\[/tex]

[tex]\rm x ^3 = 64^4\\x = 256[/tex]

Therefore for each radical the value of x is determined.

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Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

#1

Volume

#2

Radius=10/2=5cm

Volume

#3

Volume

#4

#5

radius=8/2=4

Volume

Answer:

1)  314 cm³

2)  523.33 cm³

3)  87.92 in³

4)  11 cm

5)  502.4 cm³

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]

[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]

Given:

[tex]\implies 81=a^2[/tex]

[tex]\implies a=\sqrt{81}[/tex]

[tex]\implies a=9\: \sf cm[/tex]

Substitute the given values into the formula and solve for h:

[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]

The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)

The expression is given as:

x^3 + 4x^2 +5x + 20

Group the expression into two

(x^3 + 4x^2) + (5x + 20)

Factorize each group

x^2(x + 4) + 5(x + 4)

Factor out x + 4

(x^2 + 5)(x + 4)

Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)

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Answer:

$43

Step-by-step explanation:

$72.45 can be rounded down to $72.00

$28.98 can be rounded up to $29.00

$72-$29= $43

The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6

The solution sets on the number line are given as:

x = {-8, -4}

Calculate the average of the solutions

Mean = (-8 - 4)/2

Mean = -6

Calculate the difference of the solutions divided by 2

Difference  = (-4 + 8)/2

Difference = 2

The absolute value equation is the represented as:

|Difference - x | = Mean

Substitute known values

|2 - x| = -6

Hence, the absolute value equation is |2 - x| = -6

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Answer:

|b+6|=2

Step-by-step explanation:

Answer:

Mr. Garcia had 5 kilograms of blueberries at first

Step-by-step explanation:

to make this easiest, we can imagine that we're undoing mr. garcia's actions.

So, we can start by 'unpacking' mr garcia's bags

we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags

(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)

so,

1/4  x 9 = 9/4

(9 = 9/1 [if that is how you're used to multiplying a fraction])

Then, he also sold 2 3/4 kilograms

so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first

2 3/4 + 9/4 =  2 + 12/4

(12/4 = 3)

2 + 3 = 5

So, Mr. Garcia had 5 kilograms of blueberries at first

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

Pythagorean Theorem

[tex]c^2 = a^2 + b^2[/tex]

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]

Now let's factorize to get solutions for x.

[tex]0 = x(x-20)[/tex]

First solution:

[tex]x = 0[/tex]

Second solution:

[tex]x - 20 = 0\\x = 20[/tex]

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

The number is that was multiplied by 6 is 2.

The equation that can be derived from the question is :

7 + (6a) = 19

Where a is the unknown number that 6 was multiplied with

Given the above equation, in order to determine the value of a, take the following steps:

Combine similar terms: 6a = 19 - 7

Subtract similar terms: 6a = 12

Divide both sides by 6: a = 12 / 6

a = 2

Here is the complete question:

Seven increased by the product of six and the number is 19. What is the number?

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Answer: [tex]\sqrt{109} \text{ m }[/tex]

Step-by-step explanation:

If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.

The interval which the function is negative is (-∞, -6)

The equation of the function is given as:

[tex]g(x) = \sqrt[3]{x + 6}[/tex]

When the function is negative.

It means that g(x) is less than 0

i.e. g(x) < 0

So, we have:

[tex]\sqrt[3]{x + 6} < 0[/tex]

Take the cube of both sides

x + 6 < 0

Subtract 6 from both sides

x < -6

The above represents a value from negative infinity to -6

i.e.  (-∞, -6)

Hence, the interval which the function is negative is (-∞, -6)

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Answer:

No, right answer is = 1017.36

Answer:

1017.36

Step-by-step explanation:

All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:

[tex]\pi * 6^{2}*9 = 1017.88[/tex]

instead of

[tex]3.14*6^{2}*9 = 1017.36[/tex]

like you had written above. So the final is actually supposed to be 1017.36

Answer:

h(0.1) = 4.97

Step-by-step explanation:

See attached working :)

Remember that h(0.1) is the same as saying find what the equation is equal to when x = 0.1

Step-by-step explanation:

Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.

For example,

[tex] \frac{1}{x - 5} [/tex]

Set the expression in the denominator equal to 0, because you can't divide by 0.

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]

So the vertical asymptote is x=5.

Disclaimer if you see something like this

[tex] \frac{(x - 5)(x + 3)}{(x - 5)} [/tex]

x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.

Horizontal:

If we have a function like this

[tex] \frac{1}{x} [/tex]

We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.

Remember a constant can be represent by

[tex]a \times {x}^{0} [/tex]

For example,

[tex]1 = 1 \times {x}^{0} [/tex]

[tex]2 = 2 \times {x}^{0} [/tex]

And so on,

and

[tex]x = {x}^{1} [/tex]

So our equation is basically

[tex] \frac{1 \times {x}^{0} }{ {x}^{1} } [/tex]

Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.

So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.

Consider the function

[tex] \frac{3 {x}^{2} }{ {x}^{2} + 1} [/tex]

As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator

So in this case,

[tex]x = \frac{3}{1} [/tex]

Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.

Answer:

Dilation

Step-by-step explanation:

it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.

By using the pythagoras theorum you can find an unknown leg of right angled triangle.

Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-

(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2

H^2 = B^2 + P^2

Step-by-step explanation:

Answer:

? = 41.41°

Step-by-step explanation:

The known side length is adjacent to the angle we need to find hence we will use cosine

cosx = adjacent /hypotenuse

cos(?) = 6 / 8

simplify fraction, cos(?) = 3 / 4

? = arccos(3 / 4)

Answer:

£ 2121.8

Step-by-step explanation:

The formula to find the compound interest is :

[tex]A=P(1+\frac{R}{100} )^n[/tex]

Here,

A = Amount ⇒ ?

P ⇒ Principal ⇒ £2000

R ⇒ Interest rate ⇒ 3%

n ⇒ Time  ⇒ 2 years

Let us find now.

[tex]A=P(1+\frac{R}{100} )^n[/tex]

[tex]A=2000(1+\frac{3}{100} )^2[/tex]

[tex]A=2000(1+0.03 )^2[/tex]

[tex]A=2000(1.03 )^2[/tex]

[tex]A=2000*1.0609[/tex]

[tex]A=2121.8[/tex]

Therefore, there will be £ 2121.8 in the bank account after 2 years.

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³