The length of a rectangle is shown below:

If the area of the rectangle to be drawn is 10 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle?

C(-1, 1), D(1,1)
C(-1, -2), D(1,-2)
C(-1, 5), D(1, 5)
C(-1, -7), D(1, -7)

The length of the diagonal path is approximately 70.71 yards.

To find the length of the diagonal path that divides the square park in half, we can use the Pythagorean theorem. A square park of 50 yards on each side means we are dealing with a right-angled triangle with both legs equal to 50 yards.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

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

Here, both a and b are 50 yards, so the equation becomes:

[tex]c^2[/tex] = 502 + 502 = 2500 + 2500 = 5000

Now we find the square root of 5000 to get the length of the diagonal:

c = √5000 ≈ 70.71 yards

Therefore, the length of the diagonal path is approximately 70.71 yards.

Answer:

Total distance = 53/4 miles = 13.25 miles

Step-by-step explanation:

Sage hiked from the start of the trail to Lookout Point.

Distance = 8 3/4 miles = 35/4 miles

She then hiked back to Giant Boulder

This means she traveled an additional

8 3/4 miles  - 4 1/4 miles = 35/4 mi - 17/4 mi = 18/4 mi = 9/2 mi

The total distance traveled by sage is the sum of both trajectories

Total distance = 35/4 miles + 9/2 miles =  53/4 miles

Total distance = 13.25 miles

Answer:

[tex]\large\boxed{1.\ y=-\dfrac{3}{5}x+\dfrac{12}{5}}\\\boxed{2.\ y=\dfrac{5}{4}x-\dfrac{3}{2}}[/tex]

Step-by-step explanation:

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]1.\\3x+5y=12\qquad\text{subtract 3x from both sides}\\\\5y=-3x+12\qquad\text{divide both sides by 5}\\\\\boxed{y=-\dfrac{3}{5}x+\dfrac{12}{5}}\\\\2.\\5x-4y=6\qquad\text{subtract 5x from both sides}\\\\-4y=-5x+6\qquad\text{divide both sides by (-4)}\\\\y=\dfrac{5}{4}x-\dfrac{6}{4}\\\\\boxed{y=\dfrac{5}{4}x-\dfrac{3}{2}}[/tex]

Answer:

Final answer is 1/3.

Step-by-step explanation:

Given that Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. Now we need to find about what fraction of the tomatoes did Mrs Jenkins use to make the salad.

Since she used 5/9 of the tomatoes to make pasta sauce.

Then remaining amount of tomatoes = 1- 5/9 = 9/9 -5/9 = 4/9

Then she used 3/4 of the remainder to make a salad. So fraction of the tomatoes did Mrs Jenkins use to make the salad = (4/9)(3/4)=12/36=1/3

Hence final answer is 1/3.

Divide the total subjects by total days:

150 / 28 = 5.357 per day. Round the answer as needed.

Answer: Approximately 5 subjects per days.

Step-by-step explanation:

To solve the exercise and calculate the number of subjects you need to do per day you must keep on mind the information given in the problem. You know that:

- The total number of subjects is 150.

- You had 28 days left.

Therefore, you need to divide 150 subjects by 28 days.

Then, you obtain the following result:

[tex]=\frac{150subjects}{28days}=5.35\frac{subjects}{day}[/tex]≈ 5 subjects per days.

4. Just look at the graph, and see which coordinates are on the line.

D, E, and F are on the line.

5. The y-coordinate is (0,4), and the slope is (4 + 8)/(0 - 4) = -3. Therefore, the equation of the line is y = -3x + 4. Plugging in the numbers we know gives us b = -3*8 + 4. b = -20.

6. Find the number of times P is on a line. There are two lines that do so.

Square on both sides..

x=16 !!!

[tex] \sqrt{x} = - 4 \\ { \sqrt{x} }^{2} = {( - 4)}^{2} \\ x = 16 [/tex]

(-) +(-) =+

Answer:

A, B, and C

Step-by-step explanation:

We can use guess-and-check.

A rectangle with the area 24 cm² has the sides that make the product of 24  (A = l * w)

1 * 24 is 24.

2 * 12 is 24.

3 * 8 is 24.

4 * 20 is 80.

12 * 12 is 144.

ANSWER

B. x=3,y=2

EXPLANATION

The given equations are

[tex]x - 3y = - 3...(1)[/tex]

and

[tex]x + 3y = 9...(2)[/tex]

We add the two equations to eliminate y.

This implies that that:

[tex] x + x - 3y + 3y = 9 + - 3[/tex]

Simplify:

[tex]2x = 6[/tex]

Divide both sides by 2.

[tex]x = 3[/tex]

We put x=3 into any of the equations to find y.

Let us substitute x=3 into equation (1) to get:

[tex]3 - 3y = - 3[/tex]

[tex] - 3y = - 3 - 3[/tex]

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

Divide both sides by -3 to get;

[tex]y = 2[/tex]

The solution is therefore x=,y=2.

Answer:  1b  2c  3e?  4d  5a

Step-by-step explanation:

There are 2 items that need to be checked.  

Midpoint:

[tex]Midpoint = \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\1)\ \bigg(\dfrac{-4+2}{2},\dfrac{-1+10}{2}\bigg)=\bigg(\dfrac{-2}{2},\dfrac{9}{2}\bigg)=(-1, 4.5)\implies \text{equation b}\\\\\\2)\ \bigg(\dfrac{1+7}{2},\dfrac{3-10}{2}\bigg)=\bigg(\dfrac{8}{2},\dfrac{-7}{2}\bigg)=(4, -3.5)\implies \text{equation c}\\\\\\3)\ \bigg(\dfrac{4-8}{2},\dfrac{-2+6}{2}\bigg)=\bigg(\dfrac{-4}{2},\dfrac{4}{2}\bigg)=(-2,2 )\implies \text{none of the equations}[/tex]

[tex]4)\ \bigg(\dfrac{6-4}{2},\dfrac{3-13}{2}\bigg)=\bigg(\dfrac{2}{2},\dfrac{-10}{2}\bigg)=(1, -5)\implies \text{equation d}\\\\\\5)\ \bigg(\dfrac{7-1}{2},\dfrac{5+8}{2}\bigg)=\bigg(\dfrac{6}{2},\dfrac{13}{2}\bigg)=(3, 6.5)\implies \text{equation a}[/tex]

Diameter:

distance between coordinates = 2√r² (from circle equation)

[tex]\text{formula for coordinates is: }d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\1)\ \text{Coordinates: } d=\sqrt{(-4-2)^2+(-1-10)^2}=\sqrt{36+121}=12.5\\b)\ \text{Circle: }2\sqrt{39.25}=12.5\\\\\\2)\ \text{Coordinates: } d=\sqrt{(1-7)^2+(3+10)^2}=\sqrt{36+169}=14.3\\c)\ \text{Circle: }2\sqrt{51.25}=14.3\\\\\\4)\ \text{Coordinates: } d=\sqrt{(6+4)^2+(3+13)^2}=\sqrt{100+256}=18.9\\d)\ \text{Circle: }2\sqrt{89}=18.9[/tex]

[tex]5)\ \text{Coordinates: } d=\sqrt{(7+1)^2+(5-8)^2}=\sqrt{64+9}=8.5\\a)\ \text{Circle: }2\sqrt{18.25}=8.5[/tex]

Check:

Graph to confirm your answers are correct (see attached)

Sam had 85$

James has 240+30=270 then 270/2 is 135

And because mom gave 50$ to sam subtract 50 135-50= 85 so sam had at first 85$

Final answer:

Sam had $170 at first given all the conditions.

Explanation:

Let's assume Sam had x dollars at first. Since James had $240 more than Sam at first, this means James had x + $240. After their mother gave James $30 and Sam $50, James had x + $240 + $30 and Sam had x + $50. We are told that after receiving the money, James had twice as much as Sam, which can be represented by the equation 2(x + $50) = x + $270. Solving for x, we get x + $100 = x + $270.

Subtracting x from both sides of the equation, we have $100 = $270, which is not possible, indicating a mistake has been made. We should redefine our equation as 2(x + $50) = (x + $240) + $30. Solving this correct equation, we get 2x + $100 = x + $270. Subtracting x and $100 from both sides, we find that x = $170. Therefore, Sam had $170 at first.

Hey there!

The interior angles of a triangle always have to add up to 180 degrees.

We are told that this is a right triangle, so one of the angles must be 90 degrees. This means that the measures of the other two angles must add up to 90.

90 + m<1 + m<2 = 180

If the smallest angle is 45 degrees less than the next largest angle, the only option for this would be for both of the remaining angles to be 45 degrees. The next largest angle would be the right angle, and 90 -  45 = 45.

We can't have any of the other angles be more than 90 degrees because then it wouldn't be a proper triangle.

So, the measures of the angles are going to be 90, 45, and 45.

Hope this helps!

The measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. The three angle of right are ( [tex]90^o, 45^o, 45^o[/tex] )

In a right angle triangle, the largest angle is equal to the 90 degrees, and the some of the other two angle is equal to the 90 degrees.

Given information-

The smallest angle in a right triangle is 45° less than the measure of the larger angle.

Suppose the smallest angle of the right triangle is x degrees.

Now as the smallest angle in a right triangle is 45° less than the measure of the larger angle and the value of largest angle is 90 degrees in the right angle triangle. Thus,

[tex]x=90-45\\x=45^o[/tex]

Hence, the measurement of the smallest angle is 45 degrees.

Let the other angle of the right angle triangle is y degrees.

As the some of the all the angles of a triangle is equal the 180 degrees. Thus,

[tex]x+y+90=180\\45+y=180-90\\y=90-45\\y=45[/tex]

Thus, the measurement of the other angle is 45 degrees.

Hence, the measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. The three angle of right are ( [tex]90^o, 45^o, 45^o[/tex] )

Learn more about the right angle triangle property here;

https://brainly.com/question/22790996

Answer:

ok so

Step-by-step explanation:

you basically hafta calulate funtion f w factor two

hope this helps!

Answer:

it is the 3rd choice

Step-by-step explanation:

3

➷ An irrational number cannot be written in the form of a fraction.

As you can see, the first two are already in fraction form, so it can't be those.

The square root of 4 is 2 which can be written as 2/1

This leaves the square root of 3, which is the answer.

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➶ Have A Great Day ^-^

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Answer:

Yes, because a quadrilateral have four sided figure. So True.

Answer + Explanation:

True, because all quadrilaterals are four-sided figures. Squares have four equal sides, so they are regular quadrilaterals.

The solution of given system of linear equations are x = 1 and y = -3.

Given system of linear equations are,

                                       [tex]4x+3y=-5 ..........(1)\\\\ -x+3y=-10..............(2)[/tex]

Subtract equation 2 from equation 1.

            [tex]4x+3y-(-x+3y)=-5+10\\ \\ 4x+3y+x-3y=5\\ \\ 5x=5\\ \\ x=5/5=1[/tex]

Substituting value of x in equation 1.

          [tex]4(1)+3y=-5\\ \\ 3y=-5-4=-9\\ \\ y=-9/3=-3[/tex]

Hence, The solution of given system of linear equations are x = 1 and y = -3.

Learn more:

https://brainly.com/question/7808225

Answer:

134

Step-by-step explanation:

670/5 = 134

The answer is 130=5*130

Answer:

6

Step-by-step explanation:

            red                blue               green           purple

red                           red/blue        red/green   red/purple

blue     red/blue                           blue/green  blue/purple

green   red/green   blue/green                       green/purple

purple  red/ purple  purple blue purple/green

i did not include red/red since the question asks for DIFFERENT PAIRS. same with the combinations that are repeated

plz give me a brainliesttttttt

To find the number of different pairs that can be made with four colors, we use the combinations formula C(4, 2), which calculates to 6. Thus, there are 6 different color pairs that can be made with red, blue, green, and purple.

To determine how many different pairs can be made with four colors: red, blue, green, purple, we use the concept of combinations from mathematics. A combination is a selection of items where the order does not matter. In this case, we are selecting two colors from the four available to form a pair.

To calculate the number of combinations without repetition, we can use the combination formula which is [tex]C(n, k) = \frac{n! }{ (k!(n - k)!)}[/tex], where n is the total number of items to choose from, k is the number of items to choose, and '!' represents the factorial of a number. For this scenario, n = 4 (four colors) and k = 2 (since we are forming pairs).

So, the number of combinations is C(4, 2) = [tex]\frac{4! }{2!(4 - 2)!} = \frac{4 \times 3 \times 2 \times 1 }{ 2 \times 1 \times 2 \times 1}[/tex] = 6. Therefore, there are 6 different color pairs that can be made with the colors red, blue, green, and purple.

Answer:

10:00 AM

Step-by-step explanation:

Frank drove at a speed of 50 mph, and traveled a distance of 150 miles.  This means he traveled for

150/50 = 3 hours.

7 AM + 3 hours = 10 AM

The solution is, at 10:00 AM Frank will arrive at the airport.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

here, we have,

given that,

Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph.

Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph.

Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport.

so, we get,

Frank drove at a speed of 50 mph,

and traveled a distance of 150 miles.  This means he traveled for

150/50 = 3 hours.

Thus, it takes Frank 3 hours to reach the airport.

so, we get,

since he departed at 7:00 AM, he will arrive at the airport at

7 AM + 3 hours = 10 AM

Hence, The solution is, at 10:00 AM Frank will arrive at the airport.

To learn more on speed click:

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Answer:

The number 4 is the first term of the sequence

Step-by-step explanation:

we know that

Counting backwards is when the numbers are count in reverse sequence

Is also know as 1 less

In this problem the sequence of counting backwards from 5 is equal to

4,3,2,1,0

therefore

The number 4 is the first term of the sequence

ANSWER

[tex]n = 8 \: or \: n = - 2[/tex]

EXPLANATION

The given function is

[tex]f(n) = {n}^{2} - 6n - 16[/tex]

To find roots of the equation, we set the equation to zero.

[tex]{n}^{2} - 8n + 2n- 16 = 0[/tex]

Split the middle term with -8n+2n

We now factor to get,

[tex]n(n - 8) + 2(n- 8) = 0[/tex]

[tex](n - 8)(n + 2) = 0[/tex]

Using the zero product property,

[tex]n - 8 = 0 \: or \: n + 2 = 0[/tex]

[tex]n = 8 \: or \: n = - 2[/tex]

Answer:

x = 12.8

Step-by-step explanation:

To find the value of x, set up a proportion between the two similar triangles. Then solve for x.

[tex]\frac{32}{32+x} = \frac{40}{56}[/tex]

Solve by cross multiplying and isolating x.

32(56) = 40(32+x)

1792 = 1280 + 40x

512 = 40x

12.8 = x

Check the picture below.

let's recall that a circle has 360°, so that means every two radii coming from the center of the hexagon, will split those 360° in 6 even pieces, 360/6 = 60, namely those two radii make up a 60° central angle, as you see in the picture.

running a perpendicular from the center, we end up with a 30-60-90 triangle, as you see there, and thus we can use the 30-60-90 rule to get the length of "a".

now, keeping in mind that the perimeter of the polygon is simply 4+4+4+4+4+4 = 24.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}dp~~ \begin{cases} d=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ d=2\sqrt{3}\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(2\sqrt{3})(24)\implies A=24\sqrt{3}[/tex]

➷ First calculate how many counters are 'not white'

12 - 7 = 5

We have 5 counters that are 'not white'

The probability of taking a white counter the first time is 7/12

For the next pick, there would be 1 less of the total counters as it is not being replaced

The probability of then taking a 'not white' counter is 5/11

The other way you could still get one white counter is:

The first counter (non white) probability would be 5/12

The second counter (white) probability would be 7/11

Multiply these values:

7/12 x 5/11 = 35/132

5/12 x 7/11 = 35/132

Add these two values together:

35/132 + 35/132 = 70/132

Your answer is 70/132

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➶ Have A Great Day ^-^

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Answer:

73.5

Step-by-step explanation:

To find the mean, sum the data and divide by the amount of data

mean = [tex]\frac{77+82+87+85+32+78}{6}[/tex]

          = [tex]\frac{441}{6}[/tex] = 73.5

The answer is 73.5. Just add all the numbers and divided by how many numbers there are. So you would add all the numbers and then divided by 6 since there are 6 numbers.

Answer:

Step-by-step explanation:

Answer:

It's A B and D, the brainliest is incorrect.

Step-by-step explanation:

Final answer:

If m is greater than n, then all the provided inequalities must be true, as they involve either adding the same amount to both sides or increasing the positive difference between m and n.

Explanation:

If m > n, then certain inequalities must hold true when we add, subtract, or compare these variables while keeping the inequality relationship consistent. Here are the inequalities that must be true based on the given condition:

m + 2.1 > n + 2.1: Adding the same number to both sides of an inequality does not change the relationship, thus this inequality must be true.

m - (-4) > n -(-4): Subtracting a negative is the same as adding a positive, so this inequality will also hold true.

m + 3 > n - 3: Adding a positive number to m and a negative to n will increase the difference between them, making this inequality true.

16.5 + m > 16.5 + n: Similar to the first point, adding the same number to both sides of an inequality maintains the inequality.

m > n + 1/2: Since m is greater than n, adding a positive fraction to n would still keep m greater than the modified n.

9 + m  > 6 + n: Adding different numbers to m and n still preserves the inequality, if the number added to m is not smaller than the number added to n.