Sixty percent of what number is equal to 45 percent of 80?

Answer:

Your answer would be 326.72

Step-by-step explanation:

2(pie) x 4 x 9= (roughly) 326.72

Answer:

B $22

Step-by-step explanation:

Final answer:

To find Bethany's expanded garden dimensions, we factored the quadratic equation x² + 8x - 48 = 0 to find that the original dimension is 4 feet, resulting in the new dimensions of 4 feet by 12 feet.

Explanation:

The student is tasked with finding the possible dimensions of Bethany's expanded garden, which will have an area of 48 square feet. The side lengths of the new garden are related by the fact that one side will be 8 feet longer than the other. We can use the given quadratic equation x² + 8x - 48 = 0 to model this situation.

Step-by-Step Factoring

First, we identify the coefficients in the equation, which are A=1 (coefficient of x²), B=8 (coefficient of x), and C=-48 (constant term).

To factor the quadratic equation, we look for two numbers whose product is A*C (-48) and whose sum is B (8). These numbers are 12 and -4.

Rewrite the middle term (8x) using the numbers found: x² + 12x - 4x - 48 = 0.

Factor by grouping: (x² + 12x) - (4x + 48) = 0 becomes x(x + 12) - 4(x + 12) = 0.

Factor out the common factor: (x - 4)(x + 12) = 0.

Solve for x: x = 4 or x = -12. Since a garden's dimensions must be positive, we disregard the negative solution. This leaves us with x = 4 feet as the original dimension and x + 8 = 12 feet as the expanded dimension.

Thus, the dimensions of Bethany's new garden are 4 feet by 12 feet.

the unit vector e which is collinear to vector a = (6,8) , and has the same direction is  [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .

Step-by-step explanation:

Here we have ,  vector a = (6,8)  . We need to find  the unit vector e which is collinear to vector a = (6,8) , and has the same direction. Let's find out:

We know that for a vector [tex]a = (x,y)[/tex] the unit vector is given by :

⇒ [tex](\frac{x}{|a|} ,\frac{y}{|a|} )[/tex] , where |a| is modulus of vector a . So , Modulus of vector a is :

⇒ [tex]|a| = \sqrt{x^2+y^2}[/tex]

⇒ [tex]|a| = \sqrt{6^2+8^2}[/tex]

⇒ [tex]|a| = \sqrt{36+64}[/tex]

⇒ [tex]|a| = \sqrt{100}[/tex]

⇒ [tex]|a| =10[/tex]

Hence , unit vector is given by [tex](\frac{6}{10} ,\frac{8}{10})[/tex] or ,  [tex](\frac{3}{5} ,\frac{4}{5})[/tex] . Vector is already collinear as it's in same direction of original vector as :

⇒ [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex]

Therefore , the unit vector e which is collinear to vector a = (6,8) , and has the same direction is  [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .

Answer:

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

I think this is right

Answer:

4.968 cm

Step-by-step explanation:

Given area of prism = 31.3 cm

This problem can be solved by using formula to calculate area of trapezium which is given below

Formula to calculate area of prism =( sum of parallel sides * perpendicular distance between parallel side )/2

let the perpendicular distance between parallel side = X

sum of parallel sides = 7.3+5.3 = 12.6 cm

Therefore by using formula

31.3 = (7.3+5.3)*X/2

=> 31.3 * 2 = 12.6*X

=> X = 62.6/12.6 = 4.968

Hence perpendicular distance between parallel side  is 4.968 cm

According to the given question, the length of AC on the number line is 5 units

The length of AC on the number line can be determined by subtracting the coordinate of point A from the coordinate of point C. Let's say point A is located at coordinate 2 and point C is located at coordinate 7. To find the length of AC, we subtract the coordinate of A from the coordinate of C: 7 - 2 = 5

Therefore, the length of AC on the number line is 5 units. Another way to think about this is by considering the distance between the two points. In this case, the distance between point A and point C is the same as the length of AC. If you have any further questions, please, let me know.

To know more about  length here

https://brainly.com/question/2217700

#SPJ2

By substituting the input values into each of the provided function rule options, it becomes clear that only the function rule y = 4 + 5x correctly represents the data in the given table.

The question is asking which function rule represents the data in the given input and output table.

Let's test each option:

As a result, only the function rule y = 4 + 5x matches the pattern in the given table correctly.

https://brainly.com/question/30349819

#SPJ12

Answer:

-12

Step-by-step explanation:

-6 times 3 is -18 and 2/3 of -18 is -12

The probability of choosing a blue marble is 2/5 or 0.4.

It is given that the jar contains 3 red marbles, 10 blue marbles, 8 green marbles, and 4 yellow marbles.

It is required to find the probability of choosing a blue marble.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

We have:

Number of total marbles = 3+10+8+4 ⇒25

Number of blue marble = 10

From the definition of the probability:

[tex]\rm Probability = \frac{Favourable \ outcomes}{Total \ outcomes}[/tex]

[tex]\rm Probability = \frac{10}{25}[/tex]

[tex]\rm Probability = \frac{2}{5 } \Rightarrow 0.4[/tex]

Thus, the probability of choosing a blue marble is 2/5 or 0.4.

Learn more about the probability here:

brainly.com/question/11234923

The answer is 440 in²

Here is what I added up!

25 + 4(40) + 4(20) + 100 + 75

I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!

Answer:

Answer is 71 degree

Step-by-step explanation:

AS we can see it is an isosceles triangle so base angles are equal

x + x + 38 = 180 ( sum of angles of triangle )

2x = 180 - 38

2x = 142

x = 142 / 2

Therefore x = 71 degree

Hope it helps :)

Answer:

5x - 2y - 23 = 0

Step-by-step explanation:

Line is passing through the points [tex] (3,\:-4)= (x_1, \:y_1) \: \&\: (5,\: 1)= (x_2,\:y_2) [/tex]

Equation of line in two point form is given as:

[tex] \frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \: \frac{y -( - 4) }{ - 4 -1} = \frac{x -3 }{3 -5 } \\ \\ \therefore \:\frac{y + 4 }{ - 5} = \frac{x -3 }{ - 2 } \\ \\ \therefore \: \frac{y + 4 }{ 5} = \frac{x -3 }{ 2 } \\ \\ \therefore \: 2(y + 4) = 5(x - 3) \\ \therefore \: 2y + 8 = 5x - 15 \\ \therefore \: 5x - 15 - 2y - 8 = 0 \\ \red{ \boxed{ \bold{\therefore \: 5x - 2y - 23 = 0}}} \\ is \: the \: required \: equation \: of \: line \: in \: \\ standard \: form.[/tex]

Answer:

A) 9cm/day

Step-by-step explanation:

72/8=9

Answer:

he made 12 shots

Step-by-step explanation:

since he missed 5/8 shots and 20 divided by is 4, you multiply (8-5) which is 3 by 4 and you get 12

Answer:

He made 32 shots

Step-by-step explanation:

8/5=?/20

put them together and make them as equal as possible.

Answer:

y=3

Step-by-step explanation:

This is an isosceles triangle because the two angles at the bottom are equal.

This means the two sides are equal

5y-2 = 13

Add 2 to each side

5y-2+2 =13+2

5y = 15

Divide each side by 5

5y/5 = 15/5

y =3

Final answer:

To solve this problem, we set up a system of equations representing the amount of oil in each tank. Using the fact that all three tanks end up with the same amount of oil, we determine that Tank A must have started with 1000 litres of oil.

Explanation:

You need to find the value of n which represents the amount of oil initially in Tank A, given that 500 litres are pumped from Tank A to Tank C, and that Tanks A, B, and C eventually contain the same amount of oil.

After transferring 500 litres from Tank A to Tank C, Tank A will have n - 500 litres left. Since tank C was empty and now has 500 litres, Tank B must also transfer enough oil to Tank C such that both B and C have the same amount of oil. Tank B started with n + 150 litres and must end up with the same amount as tank C, which we will refer to as x.

Therefore, we need to solve the following system of equations:

Tank A: n - 500 = x

Tank B: n + 150 - x = x

Tank C: 500 = x

From Tank C's equation, we know that x = 500. Substituting this into the equations for Tanks A and B gives us:

Tank A: n - 500 = 500

Tank B: n + 150 - 500 = 500

From Tank A's equation, we see that  n = 1000  litres.

Answer:

He would walk 1 1/2 a mile. Hope that helps

Step-by-step explanation:

Answer:

y=-3x^2+12x+63

Step-by-step explanation:

y=-3(x-7)(x+3)

y=-3(x^2-4x-21)

y=-3x^2+12x+63

Answer:

73/10

Step-by-step explanation:

7*10+3/10=

70+3/10=

73/10

Your answer would be 73/10.

Think of it this way, each whole number counts as 10/10. So by using that, just do 10 * 7 / 10...

So you would get 70/10.

Then you would add on the left over 3/10 that you had at the beginning.

70/10 + 3/10 = 73/10

This would get your final answer of 73/10.

Answer:

144°

If you look up 144° it matches exactly how it looks on a pie chart

I hope this helped

Answer:

69.08 inches

Step-by-step explanation:

Circumference of the wheel

= 2 pi r

Given

Pi = 3.14

Radius r = diameter/2 = 22/2

= 11

Therefore

Circumference = 2 x 3.14 x 11

= 69.08 inches

Answer:     Multiply both sides of the given equation by ax−2. When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

so answer is -3

Step-by-step explanation: Hope I helped, Pls mark brainliest. And say thx. But its up to you.

Answer:

the answer is 18

Step-by-step explanation:

can u put me as brainliest

Answer:

18x^5y

Step-by-step explanation:

Divide 36 by 2 first : 18

since you are dividing, you subtract the exponents:

x^8 - x^3= x^5

y^4-y^3= y^1 but you usually just write y

Dividing exponents in this equation  [tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex] is [tex]18x^{5} y[/tex]

How can the expression be simplified?

A mathematical action called an exponent, sometimes referred to as a power, is the result of repeatedly multiplying a base number by itself. A little number or variable to the right and above the basic number serves as a symbol for it. For instance, in the notation 2^3, the base and exponent are 2 and 3, respectively, denoting three times the product of 2 and itself: 2^3 = 2 x 2 x 2 = 8.

Given that;

[tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex]

Divide 36 by 2 first : 18

[tex]\frac{18x^{8}y^{4} }{x^{3} y^{3} }[/tex]

=[tex]18x^{5} y[/tex]

Answer:

17.043956

Step-by-step explanation:

Answer:

Step-by-step explanation:

17.043956 in decimal form

This is already in decimal form

Answer:

3

Step-by-step explanation:

The math books can all be in the middle with the other two on the sides, or the math books can be on the left side with the other books at the right side. Also, the math books can be on the right side with the other books at the left side.

Answer: I haven't done this test but I am good at math and I bilieve the answer is Trapazoid From the looks of it.

Step-by-step explanation: look at the shape your looking at and the one below.

Answer:

f(x) = - 4x² - 56x - 202

Step-by-step explanation:

We can simplify this quadratic function given in vertex form into standard form by simplifying the exponents and adding like terms.

f(x) = -4(x+7)^2 - 6

f(x) = -4(x^2 + 14x + 49) - 6

f(x) = -4x² - 56x - 196 - 6

f(x) = -4x² - 56x - 202

Answer: b

Step-by-step explanation: just took the quiz on egde.