Write in equation that represents the line

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.

Answer:

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

Step-by-step explanation:

Answer: 384

Step-by-step explanation: 12x8x4=384

Answer:

V =384 inches^3

Step-by-step explanation:

The volume of a box is given by

V = l*w*h

V = 12*8*4

V =384 inches^3

a) 18.68 minutes

b) 2.34%

c) 9.96 km/h

Step-by-step explanation:

a)

The velocity of Surya in the 1st segment (swimming part) is

[tex]v_1=4 km/h[/tex]

So, the distance covered by Surya in the swimming part is

[tex]d_1=4t_1[/tex]

where [tex]t_1[/tex] is the time taken to cover this part.

The velocity of Surya in the 2nd segment (biking part) is

[tex]v_2=40 km/h[/tex]

So the distance covered in the biking part is

[tex]d_2=40t_2[/tex]

where [tex]t_2[/tex] is the time taken to cover this part.

We know that the total distance covered in these 2 segments is

[tex]d=d_1+d_2=43.29[/tex]

So it can be rewritten as

[tex]4t1+40t_2=43.29[/tex] (1)

The total time taken to cover these two parts is

[tex]t=t_1+t_2=81.75 min =1.36 h[/tex]

So we have

[tex]t_2=1.36-t_1[/tex]

And substituting in (1) we can find t1:

[tex]4t_1 + 40(1.36-t_1)=43.29\\36t_1=11.21\\t_1=\frac{11.21}{36}=0.31 h = 18.68 min[/tex]

b)

The total distance covered in all 3 segments is

[tex]d=d_1+d_2+d_3=52.95 km[/tex]

where

where

d1 is the length of the swimming part

d2 is the length of the biking part

d3 is the length of the running part

We know that the distance covered in part 1 (swimming part) is

[tex]d_1=v_1 t_1 = (4)(0.31)=1.24 km[/tex]

Therefore we can find the percent that the swimming part correspond to the total race as:

[tex]\frac{d_1}{d}=\frac{1.24}{52.95}=0.0234 = 2.34\%[/tex]

c)

Here the total time taken by Surya for the race must be

[tex]t=140 min = 2.33 h[/tex]

And this is the sum of the times of the 3 segments:

[tex]t=t_1+t_2+t_3[/tex]

where

t1 is the time taken to complete the swimming part

t2 is the time taken to complete the biking part

t3 is the time taken to complete the running part

We know already that

[tex]t_1=0.31 h[/tex]

and

[tex]t_2=1.36-t_1=1.36-0.31=1.05 h[/tex]

So the time for the 3rd section must be

[tex]t_3=t-t_1-t_2=2.33-0.31-1.05=0.97h[/tex]

The distance to cover in the last part is

[tex]d_3=d-d_1-d_2=52.95-43.29=9.66 km[/tex]

So the average velocity of the last segment must be:

[tex]v_3=\frac{d_3}{t_3}=\frac{9.66}{0.97}=9.96 km/h[/tex]

Answer:

Average speed = 15

Step-by-step explanation:

To find the speed of the body, we can take the position equation and take the derivative in relation to time:

Speed = dY/dt = 2*3*t = 6t

Then, we need to find the speed at t=0 and the speed at t=5:

Speed(t=0) = 6*0 = 0

Speed(t=5) = 6*5 = 30

Now, we just need to make the average of both speeds:

Average = (0 + 30) / 2 = 15

Answer:

3x

Step-by-step explanation:

Using the triangle sum theorem the following are the missing values:

x = 25

m∠B = 65°

m∠C = 50°

According to the triangle sum theory, all the interior angles of a triangle will add up to 180 degrees.

Given:

m∠A = 65°

m∠B = (3x - 10)°

m∠C = (2x)°

Therefore:

65 + 3x - 10 + 2x = 180

Combine like terms

55 + 5x = 180

5x = 180 - 55

5x = 125

x = 125/5

x = 25

m∠B = (3x - 10)° = 3(25) - 10 = 65°

m∠C = (2x)° = 2(25) = 50°

Therefore, using the triangle sum theorem the following are the missing values:

x = 25

m∠B = 65°

m∠C = 50°

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The statement about the range of the logarithmic function F(x) = log_bx being positive real numbers is false; the range includes all real numbers.

The statement that the range of F(x) = logbx is the set of all positive real numbers is False. The range of a logarithmic function like F(x) = logbx, where b is the base and x is the argument, is actually all real numbers, not just the positive ones. This is because you can take the log of any positive number, but the result can be any real number, negative, positive, or zero (when x=1).

For example, if the base b is greater than 1, as x approaches zero from the positive side, logbx will approach negative infinity, illustrating how the range includes negative numbers.

Answer:

y -1 = -4(x +3)

Step-by-step explanation:

The point slope form of a line is given by

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y -1 = -4(x --3)

y -1 = -4(x +3)

Answer:

17.043956

Step-by-step explanation:

Answer:

Step-by-step explanation:

17.043956 in decimal form

This is already in decimal form

Answer:

mean id 45.6

we get it by adding then subtracting

Answer:

1.7x-2=8+2x

Step-by-step explanation:

collect like terms

7x-2x=8+2

5x=10

divide 5 both sides to get the value of x

5x/5=10/5

x=2

Answer:

1. x = 2

2. a = 2

4. a = 5.

Step-by-step explanation:

1. 7x - 2 = 8 + 2x

7x - 2x = 8 + 2

5x = 10

x = 2.

2.  4 ( 3a + 1 ) = 3a + 22

12a + 4 = 3a + 22

12a - 3a = 22 - 4

9a = 18

a = 2.

4. a - 3(2a) = -25

a - 6a = -25

-5a = -25

a = 5.

( I couldn't do number 3 because there is no variable in the equation).

Answer:

The answer should be 7.81

Step-by-step explanation:

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.

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:

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

I think this is right

Answer:

36.3

Step-by-step explanation:

145.2/4 = length of each side

145.2/4 = 36.3

Answer:

type b= 3/25

type ab= 1/25

b or ab= 4/25

Step-by-step explanation:

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:

-12

Step-by-step explanation:

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

Answer:

No

Step-by-step explanation:

8²+5²=89

√89

=9.43

=9.43+8+5

=22.43 cm

Answer:

No

Step-by-step explanation:

The side lengths of the triangle are 5-8-9

For the triangle to be a right triangle the square length of base and side length should be equal to square length of the hypotenuse

let's check if this triangle have criteria for a right triangle

5^2 + 8^2 = 25 + 64 and that is equal to 89

9^2 = 81

89 is not equal to 81 so this is not a right angled triangle.

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.

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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:

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

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.

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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:

6623.4375 feet²

Step-by-step explanation:

Distance is the radius

Area:

(135/360) × pi × r²

(135/360) × 3.14 × 75²

6623.4375 feet²

The area of the fairway watered by the sprinkler is 6,623.44 square feet

The shape of the golf course is a sector, Using the formula for calculating the area of a sector is expressed as:

[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]

Substitute the given parameters into the formula to have:

[tex]A=\frac{135}{360} \times 3.14 \times 75^2 \\A = \frac{2,384,437.5}{360}\\A= 6,623.4375ft^2[/tex]

Hence the area of the fairway watered by the sprinkler is 6,623.44 square feet

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Answer:

-3

Step-by-step explanation:

-15 divided by 5= -3

Answer:

The answers are options A, C, and D

Step-by-step explanation:

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

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 !!!