Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find the area of lawn that remains.


Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?

He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.
He is incorrect. The path will have an area of 1/2(4)(40)=80 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 220 sq ft.

He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 140 sq ft.

He is incorrect. The path will have an area of (9)(40)=360 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 240 sq ft.

Answer:

B.44 mph and 46 mph

Step-by-step explanation:

This question is on relative speed

when cars move towards each other, you add their individual speeds to get their relative speed

Lets have two cars , A and B

Let  car A to have an average speed of x m/h towards the right hand side

Let car B to have an average speed of x+2 m/h towards the opposite direction

The distance between the cars is 270 miles

Time of meeting is 3 hours

The relative speed will be x+x+2=2x+2 miles per hour

Apply the formula for time=Distance/speed =D/S

[tex]t=\frac{D}{S} \\\\\\3=\frac{270}{2x+2} \\\\\\3(2x+2)=270\\\\\\6x+6=270\\\\\\6x=270-6\\\\\\6x=264\\\\\\x=\frac{264}{6} =44[/tex]

x=44 miles per hour

x+2=44+2=46 miles per hour

solution

44 mph and 46 mph

Final answer:

Two cars are traveling towards each other at speeds where one car is 2 mph faster than the other. They meet after 3 hours covering 270 miles. By setting an equation with the distance formula, we find that the slower car's speed is 44mph and the faster car's speed is 46mph. (Option B)

Explanation:

The question involves calculating the average speed of two cars traveling towards each other on the same road and meeting after a certain time. To solve this, we can set up an equation using the formula for speed, which is distance divided by time.

Let's denote the speed of the slower car as ‘s’ mph (miles per hour). Consequently, the faster car travels at ‘s+2’ mph. When they meet after 3 hours, both cars together will have covered a distance of 270 miles. Thus, the total distance covered by both cars can be written as:

Total distance = (speed of car A)×(time) + (speed of car B)×(time)

270 miles = s×3 hours + (s+2)×3 hours

This simplifies to:

270 = 3s + 3s+ 6

Combining like terms and simplifying, we get:

270 = 6s + 6

Subtract 6 from both sides to find:

264 = 6s

Dividing both sides by 6 yields:

s = 44 mph

Therefore, the slower car travels at 44 mph and the faster car at 44+2 = 46 mph.

The correct answer is B. 44 mph and 46 mph.

[1, 4, 3]

Solve for the first variable in one of the equations, then substitute the result into the other equation.

**For more information on how to solve a system of equations in three variables, paste and copy this link:

https://youtu.be/zcC7wsn3b2g

Subscribe to my channel [USERNAME: MATHEMATICS WIZARD].

I am joyous to assist you anytime.

***By the way, in the final line, that "+" next to the 6 should be replaced with an "=".

To find out which equation has no real solutions, we need to calculate the discriminant for each of these given equations.

For calculating the discriminant, we need to first compare these equations with the general formula which is ax²+bx+c.

So, let's get started.

1) x² + 4x + 16 = 0

a=1, b=4, c=16

D = b²-4ac

= (4)² - 4(1)(16)

= 16-64

= -48

√D = √-48

2) 4x² + 4x - 24 = 0

a=4, b=4, c=-24

D = b²-4ac

= (4)² - 4(4)(-24)

= 16 - 16(-24)

= 16 + 384

= 400

√D = √400 = +20 or -20

3) 5x² + 3x - 1 = 0

a=5, b=3, c=-1

D = b²-4ac

= (3)² - 4(5)(-1)

= 9 + 20

= 29

√D = √29

4) 2x² - 4x + 4 = 0

a=2, b=-4, c=4

D = b²-4ac

= (-4)² - 4(2)(4)

= 16 - 32

= -16

√D = √-16

Now from all these above calculations, we can see that discriminant was negative in first equation and in last equation.

If D<0 then roots does not exist, as the square root can not contain a negative value or the equation does not have any real solutions.

Roots in such case can be calculated but those roots are known as imaginary roots, which is a higher concept.

So Final answer is,

Equation 1 => x² + 4x + 16 = 0

and

Equation 4 => 2x² - 4x + 4 = 0

has no real solutions.

Answer:

Step-by-step explanation:

the answer is 4/5

Because there are 5 section and the blueberry takes up 4 of the sections it is 4/5

Answer:

4/5

Step-by-step explanation:

So he divided something into 5 sections.

He fills one section with graph jelly and 4 sections with blueberry jelly.

Since there are 5 sections and 4 are filled with blueberry, then 4/5 is the fraction of the table he filled will blueberry.

Answer:

[tex]\large\boxed{3m+(m+5)=4m+5}[/tex]

Step-by-step explanation:

[tex]3m+(m+5)=3m+m+5\qquad\text{combine like terms}\\\\=(3m+m)+5=4m+5[/tex]

Answer:

71.4

Step-by-step explanation:

For this, we will use Heron's Formula, or

[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex],

with p as the perimeter divided by 2, and a, b, and c are the side lengths.

Plugging our values in, (11.6+20+13)/2 = 22.3 = p, and

[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex] = [tex]\sqrt{5103.8679} =71.4[/tex] rounded to the nearest tenth

Answer:

5

Step-by-step explanation:

(-1) + 5 - (-6) - 5 =

    v          

4 - (-6) - 5 =

   v

10 - 5 =

   v

5

e = Euler's constant

e ≈ 2.718281828459045, rounded up e = 2.7183.

= 4.17356

the number after the line is lower than 5, round the number down (keep it the same). If the number is 5 and more than it round the number upwards. therefore in example 1 you need to round 4.17356 to 4 decimal places. This means you have 2 choices, either 4.17356 or 4.17357.

When we say round to 4 it means to fewer the digits to 4 to the right of the decimal point. The basic rule of remember is, if the number in the 5th place ( to round it any decimal place, consider this next digit) is > 5 then add 1 on the 4th digit and else remains the same.

Learn more about decimal place here https://brainly.com/question/17255119

#SPJ2

Answer:

[tex]\large\boxed{2^{4x}=2^{3x-9}}[/tex]

Step-by-step explanation:

[tex]8=2^3\to 8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{3(x-3)}\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=2^{(3)(x)+(3)(-3)}=2^{3x-9}[/tex]

If you want a solution of this equation:

[tex]2^{4x}=8^{x-3}\\\\2^{4x}=2^{3x-9}\iff4x=x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x=-3\qquad\text{divide both sides by 3}\\\\x=-1[/tex]

Answer:  the correct option is

(D)  [tex]2^{4x}=2^{3x-9}.[/tex]

Step-by-step explanation:  We are given to select the correct equation that is equivalent to the following equation :

[tex]2^{4x}=8^{x-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Equivalent equations means  two equations that can be obtained from one another using some properties of formula.

We will be using the following formula :

[tex](a^b)^c=a^{b\times c}.[/tex]

From equation (i), we have

[tex]2^{4x}=8^{x-3}\\\\\Rightarrow 2^{4x}=(2^3)^{x-3}\\\\\Rightarrow 2^{4x}=2^{3\times(x-3)}\\\\\Rightarrow 2^{4x}=2^{3x-9}.[/tex]

Thus, the required equivalent equation is [tex]2^{4x}=2^{3x-9}.[/tex]

Option (D) is CORRECT.

[tex]\( f(x) + g(x) \) equals \( 2x^2 - 5x - 8 \).[/tex] (option b)

To find [tex]\( f(x) + g(x) \)[/tex], we need to add the functions f(x) and g(x):

[tex]\[ f(x) + g(x) = (2x^2 + 3x - 4) + (-8x - 4) \][/tex]

[tex]\[ = 2x^2 + 3x - 4 - 8x - 4 \][/tex]

[tex]\[ = 2x^2 + (3x - 8x) + (-4 - 4) \][/tex]

[tex]\[ = 2x^2 - 5x - 8 \][/tex]

Therefore, the correct answer is:

[tex]\[ f(x) = 2x^2 - 5x - 8 \][/tex]

Complete question: If f(x)=2x²+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?

a-f(x)=2x²+5x+8

b-f(x)=2x²−5x−8

c-f(x)=2x²+11x−8

d-f(x)=2x²+5x

Answer:

[tex]\huge \boxed{z=176}\checkmark[/tex]

Step-by-step explanation:

Add by 135 from both sides of equation.

[tex]\displaystyle z-135+135=41+135[/tex]

Simplify, to find the answer.

[tex]\displaystyle41+135=176[/tex]

[tex]\huge \boxed{z=176}[/tex], which is our answer.

Hope this helps!

Answer: Z=176

Step-by-step explanation: All you need to do is isolate z. Add 135 to each side.

135+41=176=Z

Answer:

D one real solution

Step-by-step explanation:

x^2 - 8x + 16 = 0

This is in the form

ax^2 +bx + c = 0

so we can use the discriminant to determine the number of solutions

b^2 -4ac

(-8)^2 -4(1)(16)

64 - 64

0

Since the discriminant is zero, there is one real solution.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the slope m = -5, and the point (-1, -3). Substitute:

[tex]y-(-3)=-5(x-(-1))\\\\y+3=-5(x+1)[/tex]

Convert to the slope-intercept form (y = mx + b):

[tex]y+3=-5(x+1)[/tex]          use the distributive property

[tex]y+3=-5x-5[/tex]            subtract 3 from both sides

[tex]y=-5x-8[/tex]

Answer:

-1/4

Step-by-step explanation:

You can find the slope from a graph several ways.

Here are two ways of doing it.

Method 1. Slope formula

Find two points, then apply the slope formula, m = (y2 - y1)/(x2 - x1)

We read two easy  to read points of the graph: (0, -2) and (4, -3)

m = (y2 - y1)(/(x2 - x1) = [-3 - (-2)]/(4 - 0) = (-3 + 2)/4 = -1/4

Method 2. Rise/Run

Slope = m = rise/run

Pick two points. Start at one point and go to the other point by going vertically (rise) and horizontally). The vertical distance is the rise, and the horizontal distance is the run. Up is positive, and down is negative. Right is positive, and left is negative.

Pick points (0, -2) and (4, -3).

Start at (0, -2). To go to (4, -3), move 1 unit down. That is a rise of -1. Now go horizontally 4 inits to the right. That is a run of 4.

slope = rise/run = -1/4

Step-by-step explanation:

for x^a/x^b = x^(a-b)...eqn 1

thus for 5^6/5^2 = a^b,

if a = 5, following eqn 1...

then b = 6-2 = 4

Answer:

The vertex of the parabola is (105 , 7)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation of the parabola is y = a(x - h)² + k, where (h , k) are

  the coordinates of the vertex point of the parabola

- The points (0 , 27) , (52.5 , 12) , (105 , 7) ,  (157.6 , 12) , (210 , 27) are

 the points lie on the parabola

- We have three unknown a , h , k to find them we will substitute the x

 and y in the equation by the coordinates of some point on the

 parabola

- Lets start with point (0 , 27)

∵ x = 0 and y = 27

∴ 27 = a(0 - h)² + k

∴ 27 = ah² + k ⇒ (1)

- Lets use point (210 , 27)

∵ x = 210 and y = 27

∴ 27 = a(210 - h)² + k ⇒ (2)

- Equations (1) and (2) have the same L.H.S, so we can equate them

∴ ah² + k = a(210 - h)² + k ⇒ subtract k from both sides

∴ ah² = a(210 - h)² ⇒ divide both sides by a

∴ h² = (210 - h)² ⇒ take √ for both sides

∴ h = ± (210 - h)

∵ h = 210 - h ⇒ add h to both sides

∴ 2h = 210 ⇒ divide both sides by 2

∴ h = 105

∵ h = - (210 - h)

∴ h = -210 + h ⇒ no value of h from this equation so we will ignore it

∴ The value of h is 105

- Lets substitute this value of h in the equation

∴ y = a(x - 105)² + k

- Lets use the point (105 , 7)

∵ x = 105 and y = 7

∴ 7 = a(105 - 105)² + k

∴ 7 = a(0) + k

∴ k = 7

- The coordinates of the vertex point are (h , k)

∵ h = 105 and k = 7

∴ The vertex of the parabola is (105 , 7)

Answer:

105, 7 and then for the next one y= 0.0018(x – 105)2 + 7

Step-by-step explanation:

Answer:

Option C. 1:11

Step-by-step explanation:

Let

x-----> dollars  spent on office space

y ----> dollars spent  on other costs

we know that

x+y=$360,000 -----> equation A

x=$30,000 ----> equation B

substitute equation B in equation A and solve for y

30,000+y=360,000

y=360,000-30,000=$330,000

Find the ratio of dollars  spent on office space to dollars spent  on other costs

Divide the dollars  spent on office space by the dollars spent  on other costs

so

x/y

substitute

30,000/330,000=1/11

Answer:

0

Step-by-step explanation:

Anything multiplied by 0 gives you an answer of 0, therefore 2*2*2*2*0=0

Answer:

0

Step-by-step explanation:

In most cases, zero times anything is zero.

Here we have 2*2*2*2 = 2^4 = 16.  Thus,

2*2*2*2*0 = 16(0) = 0

Answer:

The distance from the pole is 11.8 ft

Step-by-step explanation:

Let

x------> the distance from the pole

we know that

The tangent of angle of 28 degrees is equal to divide the opposite side to angle of 28 degrees ( the height of the pole) by the adjacent side to angle of 28 degrees ( the horizontal distance from the pole)

so

tan(28°)=6.3/x

Solve for x

x=6.3/tan(28°)=11.8 ft

Final answer:

The distance from the pole is found by using the tangent function with the given angle of elevation (28 degrees) and the pole's height (6.3 feet), resulting in a distance of approximately 12.04 feet.

Explanation:

To calculate the distance from the pole given the angle of elevation and the height of the pole, you can use trigonometric functions. The angle of elevation is 28 degrees and the height of the pole is 6.3 feet. You can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.

Let d represent the distance from the pole. The tangent of the angle of elevation (28 degrees) equals the opposite side (6.3 feet) over the adjacent side (distance d).

tan(28°) = 6.3 / d

To find d, rearrange the equation: d = 6.3 / tan(28°). Using a calculator for tan(28°), you obtain d ≈ 12.04 feet.

Therefore, the distance from the pole is approximately 12.04 feet.

Answer:

$894

Step-by-step explanation:

$27,000+$2,200+$600= $29,800

$29,800*0.03=$894

Answer:

4:3

Step-by-step explanation:

You divide 8 and 6 by 2 to simplify it

Answer:

B. [tex]^\leftrightarrow_{AB}[/tex] and [tex]^\leftrightarrow_{CD}[/tex]  are perpendicular lines.

Step-by-step explanation:

We can quickly plot the points in the cartesian plane as shown in the attachment.

A visual representation will help us see that A,B,C, and D do not lie on the same line.

The slope of AB  is [tex]\frac{4-1}{-2--8} =\frac{3}{6}=\frac{1}{2}[/tex]

The slope of CD is [tex]\frac{5--1}{-6--3} =\frac{6}{-3}=-2[/tex]

The two slopes are negative reciprocals of each other.

It is true that line AB and line CD are perpendicular.

These two lines cannot be perpendicular and parallel at the same time.

It is also not possible that, the two lines are perpendicular but will not intersect

Therefore the correct choice is B

Answer:

B

Step-by-step explanation:

plato/edmentum

Answer:

220 miles

Step-by-step explanation:

Joe got $301 for an overnight trip.

As the employees get $125 for lodging. The lodging expense will be subtracted from the total amount to get the amount for the miles he drove.

So,

Expense by company for miles driver = 301 - 125 = $176

So, Joe received $176 for miles driven

Now,

amount for one mile = $0.80

Miles driven in $176 = 176/0.80 = 220 miles

Joe drove 220 miles ..

Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip, after considering the fixed lodging cost and the per mile reimbursement rate.

The student wishes to know how many miles Joe drove if his company reimbursed him $301 for an overnight trip wherein he receives $125 for lodging plus $0.80 per mile driven. To solve this problem, we start by subtracting the fixed lodging cost from the total reimbursement to find the total amount reimbursed for mileage. Let's denote the number of miles driven by Joe as m.

Total reimbursement for mileage = Total reimbursement - Lodging cost
$301 - $125 = $176

Now, since Joe gets reimbursed $0.80 per mile, we can calculate the number of miles driven as follows:

$176 / $0.80 per mile = 220 miles

Therefore, Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip.

Answer:

[tex]\large\boxed{a_n=5\left(\dfrac{1}{10}\right)^{n-1}}[/tex]

Step-by-step explanation:

Check:

[tex]n=1\\\\a_1=5\left(\dfrac{1}{10}\right)^{1-1}=5\left(\dfrac{1}{10}\right)^0=5(1)=5\qquad\bold{CORRECT}\ (1,\ 5)\\\\n=2\\\\a_2=5\left(\dfrac{1}{10}\right)^{2-1}=5\left(\dfrac{1}{10}\right)^1=5\left(\dfrac{1}{10}\right)=\dfrac{5}{10}=0.5\qquad\bold{CORRECT}\ (2,\ 0.5)\\\\n=3\\\\a_3=5\left(\dfrac{1}{10}\right)^{3-1}=5\left(\dfrac{1}{10}\right)^2=5\left(\dfrac{1}{100}\right)=\dfrac{5}{100}=0.05\qquad\bold{CORRECT}\ (3,\ 0.05)[/tex]

[tex]a_{n}[/tex] [tex]= 5 (\frac {1}{10} )^{n-1}[/tex]

Mathematical sequences are the set of numbers that makes a pattern or can be simple and complicated, finite and infinite. Explore sequences, terms in a sequence, and the different kinds of mathematical sequences, including the famous Fibonacci sequence.

Check:

n=1

[tex]a_{1} = 5 (\frac {1}{10} )^{1-1} = 5 (\frac {1}{10} )^{0} = 5 (1)=5[/tex]  True (1,5)

n=2

[tex]a_{2} = 5 (\frac {1}{10} )^{2-1} = 5 (\frac {1}{10} )^{1} = 5 \frac{1}{10} = 0.5[/tex] True (2, 0.5)

n=3

[tex]a_{3} = 5 (\frac {1}{10} )^{3-1} = 5 (\frac {1}{10} )^{2} = 5 \frac{1}{100} = 0.05\\[/tex] True (3, 0.05)

sequence chart is a series of the events and actions set in the order in which they take place. this is considered to be a fantastic way to represent the necessary steps taken to reach to the outcome.

Learn more about the sequence chart here https://brainly.com/question/444154?

#SPJ2

Answer:

20.2

The thousandth position doesn't affect the rounding of the numbers. Since the hundredth position contains a 5, you will round up, meaning the tenth position will change from a 1 to a 2.

Answer:

20.2

AMG Mark as brainlist!

Answer:

Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:

x                           y

2         2|x-4| + 3 = 2|2-4| + 3 = 7

3         2|x-4| + 3 = 2|3-4| + 3 = 5

4         2|x-4| + 3 = 2|4-4| + 3 = 3

5         2|x-4| + 3 = 2|5-4| + 3 = 5

6         2|x-4| + 3 = 2|6-4| + 3 = 7

The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.

Step-by-step explanation:

The absolute value parent function, written as function(x) = | x |, is defined as:

|x| = x          and           |-x| = x

In our case;

For x = 2        

y = 2|x-4| + 3

= 2|2-4| + 3

= 2|-2| + 3

= 2*2 + 3

= 4 + 3

= 7

Similarly, for all other values of x in the given domain, value of y can be calculated.

Answer:

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a<0\end{array}\right[/tex]

Put each value of x from the set {2, 3, 4, 5, 6}

to the equation y = 2|x - 4| + 3:

x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)

x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)

x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)

x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)

x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)

Mark the points in the coordinates system.

The domain is only five numbers, therefore the graph of this function is only five points.

Answer:

5 < √32 < 6.

Step-by-step explanation:

√25 = 5 and √36 = 6 so

5 < √32 <  6.

Answer:

1) 8x5

2) 8x10

3)8x20

Answer:

5040 ft^2

Step-by-step explanation:

The area of rectangle is: 7 ft by 5 ft

The scaling is done by multiplying the dimensions with the sale factor.

so,

The area of actual house will be:

(7*12) x (5*12)

= 84 * 60

= 5040 ft^2

So the area of actual building is 5040 ft^2 ..

This answer does not make sense because you can't buy half a movie ticket

Answer: If h(x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h(x))

Then the pair given is (6.5, $92.25)

Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)

So the domain of h(x) is only the natural numbers, then the possible solution of (6.5, $92.25) doesn't make sense because 6.5 is not a natural number.