A board that is 2/3 of a yard long needs to be cut into four equal pieces. What will the length of each piece be? yd 2 yd yd yd

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x+3}[/tex]

Step-by-step explanation:

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

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

m - slope

b - y-intercept → (0, b)

From the graph we have the points (4, 4) and (0, 3) → b = 3.

We have the equation:

[tex]y=mx+3[/tex]

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Put the coordinates of the points:

[tex]m=\dfrac{3-4}{0-4}=\dfrac{-1}{-4}=\dfrac{1}{4}[/tex]

Finally we have:

[tex]y=\dfrac{1}{4}x+3[/tex]

Answer: 50 meters

Step-by-step explanation: I just finished the pretest

Answer:  The ball is 50 m off the ground after 2 seconds

Step-by-step explanation:

Given the function relating the height of an object off the ground to the time spent falling is a quadratic relationship.

Therefore if h=height and t=time then

[tex]h=a+bt+ct^{2}[/tex]       ----------(A)

where a,b and c are constants

Apply given conditions

At t=0s h=90 m

=> 90 m = a+0+0

=>a=90 m

Also the ball has been just dropped at t=0 s

=>[tex]\frac{\partial h}{\partial t}=0=>\frac{\partial (a+bt+ct^{2})}{\partial t}=0[/tex]

=>[tex]b+2ct=0[/tex]

For t=0s b = 0

Thus equation (A) is reduced to [tex]h=90+ct^{2}[/tex]

At  t= 3 s , h=0 m

[tex]\therefore 0= 90 +9c=>c=-10 \frac{m}{s^{2}}[/tex]

Finally we get [tex]h=90-10t^{2}[/tex]

Therefore at t= 2.0 s , [tex]h=(90-10\times 2^{2})m=50 m[/tex]

Thus the ball is 50 m off the ground after 2 seconds

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Answer:

the answer is y=-1

Answer: -1

Step-by-step explanation: The horizontal line represents the x axis and the verticle line represents the y axis. The line comes into contact with the verticle line at -1, making it your point of interception.

[tex]x+y=20\\\underline{x-y=40}\\2x=60\\x=30\\\\30+y=20\\y=-10[/tex]

-10 and 30

Answer:

The numbers are 30 and -10.

Step-by-step explanation:

The sum of two numbers is 20 (addition)

x + y = 20

The difference is 40 (subtraction)

x - y = 40

To solve an equation, you can only have one variable. Solve one of these for a variable (it doesn't matter which one).

x - y = 40   Add y to both sides

x = 40 + y

Now you have a new value for x (40 + y), so you can plug it into your other equation.

x + y = 20   Plug in (40 + y) for x

40 + y + y = 20   Combine like terms (y + y)

40 + 2y = 20   Subtract 40 from both sides

2y = -20   Divide both sides by 2

y = -10

Now, plug your y into either equation.

x + y = 20   Plug in -10 for y

x + (-10) = 20   Simplify

x - 10 = 20   Add 10 to both sides

x = 30

Check your work by plugging these numbers into both equations.

x + y = 20   Plug in

30 + (-10) = 20   Simplify

30 - 10 = 20   Simplify

20 = 20

and

x - y = 40   Plug in

30 - (-10) = 40   Simplify

30 + 10 = 40

40 = 40

Answer: The first choice

Step-by-step explanation: You alsways distribute inside the paranethesis, so 2(x+3)+5 > 2x+ (2*3)+5

Answer:

36

Step-by-step explanation:

Note that the missing side is X

30/20 = X/24

30/20(24) = X

36 = X

Answer:

V≈2.53×105^5

Step-by-step explanation:

Base edge:  54

Height:  260

Formula to find volume is: V=a^2h /3

Hope this helps!

For this case we have that by definition, the volume of a square base pyramid is given by:

[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]

Where:

L: It's the side of the square base

h: It's the height of the pyramid

According to the data we have:

[tex]L = 54\m\\h = 260\m[/tex]

Substituting in the formula:

[tex]V = \frac {1} {3} * (54) ^ 2 * 260\\V = \frac {1} {3} * 2916 * 260\\V = \frac {1} {3} * (758160)\\V = 252,720 \ m ^ 3[/tex]

Thus, the volume of the building is [tex]252,720 \ m ^ 3[/tex]

Answer:

[tex]252,720 \ m ^ 3[/tex]

Answer:

[tex]\frac{\pi }{2}[/tex]

Step-by-step explanation:

In order to find the reference angle of a given angle, we have to determine its quadrant.

Since the angle given is:

[tex]\frac{3\pi }{2}[/tex]

The angle lies in third quadrant.

If the angle lies in the third quadrant, [tex]\pi[/tex] is subtracted from the given angle:

So,

[tex]Reference\ Agnle= \frac{3\pi }{2}-\pi\\= \frac{3\pi -2\pi }{2}\\=\frac{\pi }{2}[/tex]

So the reference angle for [tex]\frac{3\pi }{2}[/tex] is [tex]\frac{\pi }{2}[/tex] ..

Answer:

The elapsed time is 7hrs and 1 minute.

The elapsed time from 5 in the afternoon to 1 minute after midnight is 7 hours and 1 minute, taking into consideration the division of a day into a.m. and p.m.

The key to solving this question is first understanding how we measure time in day and night, which are demarcated by a.m. and p.m.. Each cycle of 24 hours is divided into two parts: 12 hours from midnight to noon (a.m.) and another 12 hours from noon to midnight (p.m.).

Let's calculate the elapsed time from 5 in the afternoon to 1 minute past midnight. From 5 p.m to midnight, there are 7 hours. Adding the 1 minute past midnight, the total elapsed time is 7 hours and 1 minute.

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Answer:

D) y = x² + 6x + 7

x + y = 1

Step-by-step explanation:

Just simply substitute the solution into the equations to confirm their authenticities.

I am glad to help.

Answer:

The answer is D. y = x2 + 6x + 7

x + y = 1

Step-by-step explanation:

Answer:

B . [tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Step-by-step explanation:

Given function is:

[tex]f(x)=\frac{x}{1+x}[/tex]

Sall h is used to denote minor change in function. The value of the new function f(x+h) will be calculated by putting x+h in place of x in the function.

So putting x+h in place of x

[tex]f(x+h)= \frac{x+h}{1+(x+h)}\\=\frac{x+h}{1+x+h}[/tex]

So, option B is the correct answer ..

Answer:

The best possible answer is 3.

[tex]91 \div 31[/tex]

is the equivalent to 91/31. When divided, the answer comes out to 2.935483871 which, when rounded up, is 3.

The value of the given expression 91/31 will be; 3. The correct option is A.

Expression in maths can be defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression will be calculated by;

=   91  /  31

=   2.93

≅  3

Therefore the value of the given expression is 3. The correct option is A.

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Answer:

C) 5

Step-by-step explanation:

[tex]\frac{6x²+19x+10}{2x+5}[/tex]

= [tex]\frac{3x(2x+5)+2(2x+5)}{2x+5}[/tex]

= [tex]\frac{(2x+5)(3x+2)}{2x+5}[/tex]

= 3x+2

which means that if they want us to find what ax+b is, you can figure out that ax+b is similar to 3x+2 and plug in what they want us to solve for, a+b.

ax+b=3x+2 (hence 3=a and 2=b)

wants: a+b

answer: 3+2= 5

hope this helps! :)

y - y1 = m(x - x1) is the general point slope form

y - 3 = 5(x - 4) plug in the given values

y - 3 = 5x - 20

y = 5x - 20 + 3

y = 5x - 17

The answer in slope intercept form is y = 5x-17

If you want to convert to standard form, then

y = 5x - 17

y+17 = 5x

17 = 5x - y

5x - y = 17 which is the answer in standard form (Ax + By = C)

Answer:

Step-by-step explanation:

This can only be written one way.

Let the number = x

x^2 - 10

is how the statement translates.

x^2 = x*x

the 2 means that you need two xs.

The ^ means that you multiply the two xs.

Answer:

Hey there.. I will be more than happy to help you today..  :)

A Number squared decreased by ten

We will do this with steps:-

Step 1 - "A number ". So, Let's say any number be x

Step 2 -  "A number squared". Our number x is squared i.e. x²

Step 3 - "A number squared" ( i.e. x²  ) is decreased by ten

x² - 10  

This is your answer.

Hope this helps you :)

Step-by-step explanation:

Hope you got helped

Hello! My name is Zalgo and I am here to help you out today. The answer is -44. The real way to solve it is like this --> "2(3-5(2+1)2+5)".

I hope that this helps! :D

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Thank you! XP)

Answer:

  k = 5

Step-by-step explanation:

The sum of the zeros is the opposite of the coefficient of x, so is (k+6).

The product of zeros is the constant term, 2(2k+1), so half their product is (2k+1).

The problem statement asks us to find k so that these values are the same:

  k +6 = 2k +1

  5 = k . . . . . . . . subtract k+1

The value of k is 5.

_____

The zeros are 5.5±√8.25. Their sum is 11; their product is 22.

Answer:  [tex]\bold{(0,-\sqrt{26})\quad \&\quad (0,\sqrt{26})}[/tex]

Step-by-step explanation:

[tex].\qquad y^2-25x^2=25\\\\\implies \dfrac{y^2}{25}-\dfrac{25x^2}{25}=\dfrac{25}{25}\\\\\\\implies \dfrac{y^2}{25}-\dfrac{x^2}{1}=1\\\\\\Center: (0, 0)\\Length\ of\ foci:25+1=c^2\implies \sqrt{26}=c\\Foci: (0,0\pm \sqrt{26})[/tex]

Answer:

circumference is 21.99 and area is 47 and 2/35 unit squared sorry if its a little late

Answer:

B and F

Step-by-step explanation:

the are equivalent but the are just is different orders

Answer:

8d + 1/3 + 5/7

1/3 + 5/7 + 8d

Step-by-step explanation:

Answer:

100 + 40 + 40 + 40 + 40

Step-by-step explanation:

area of base = 10 x 10 = 100 square units

area of each triangular side = 0.5 x 10 x 8 = 40 square units.

Total area = 1 base + 4 sides

= 100 + 40 + 40 + 40 + 40

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}

Step-by-step explanation:

we have

[tex]f(x)=-x^{2}-2x+15[/tex]

This is a the equation of a vertical parabola open downward

The vertex is a maximum

The vertex is the point (-1,16)

see the attached figure

therefore

The domain of the function is all real numbers ----> interval (-∞,∞)

Te range of the function is

[tex]y\leq 16[/tex]

All real numbers less than or equal to 16 ----> interval  (-∞,16]

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}.

Step-by-step explanation:

B on edg

Points P and Q are not the same due to their different positions in the division of the directed segment. Point P is closer to A while Point Q is closer to B.

Point P and Q are not the same point. In the directed segment from A to B, Point P divides the segment in a way that the ratio of AP to PB is 1:3, meaning Point P is closer to A. On the contrary, Point Q divides the segment from B to A in a way that the ratio of QB to QA is 1:3, implying that Point Q is closer to B. Therefore, P and Q have different positions on the segment.

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No, Point P and Q are not the same. P is closer to A because it partitions the directed segment from A to B, whereas Q is closer to B as it partitions the segment from B to A, taking into account the directionality of the segments.

In mathematics, partitioning points on a directed segment refers to dividing the segment into distinct parts according to a given ratio. Point P partitions the directed segment from A to B into a 1:3 ratio, which means P is one part from A and three parts from B. On the other hand, Point Q partitions the directed segment from B to A into a 1:3 ratio, indicating that Q is one part from B and three parts from A.

Given this, P and Q are not the same point. P is closer to point A and Q is closer to point B since the directionality of the segment is taken into account. The direction from A to B is not the same as the direction from B to A, so the points P and Q that partition these segments in a 1:3 ratio will end up at different locations.

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Answer:

(D) 30pi inches

Step-by-step explanation:

First, we use the given volume, the given height, and the formula of the volume of a cylinder to find the radius of the base. Then we use the radius of the base to find the circumference of the base.

[tex] volume = \pi r^2 h [/tex]

[tex] volume = 6750 \pi~in.^3 [/tex]

We set the formula equal to the volume and replace h with 30 in.

[tex] \pi r^2 h = 6750 \pi~in.^3 [/tex]

[tex] \pi r^2 \times 30 ~in. = 6750 \pi~in.^3 [/tex]

Divide both sides by 30pi in.

[tex] r^2 = 225 ~in.^2 [/tex]

Take the square root of each side.

[tex] \sqrt{r^2} = \sqrt{225 ~in.^2} [/tex]

[tex] r = 15~in. [/tex]

The radius of the base is 15 in.

Now we use the radius of the base and the formula of the circumference of a circle to find the answer.

[tex] circumference = 2 \pi r [/tex]

[tex] circumference = 2 \pi \times 15~in. [/tex]

[tex] circumference = 30 \pi ~in. [/tex]

Answer:

x = 8,

Step-by-step explanation:

[tex]\displaystyle \frac{4}{x} = \frac{5}{10}[/tex].

[tex]x \ne 0[/tex] for it is a denominator. Multiply both sides with the product of the two denominators: [tex]10\;x[/tex]:

[tex]\displaystyle \frac{4}{x}\cdot (10\; x) = \frac{5}{10}\cdot (10\;x)[/tex].

[tex]40 = 5\; x[/tex].

Multiply both sides by one over the coefficient of x:

[tex]\displaystyle \frac{1}{5} \times 40 = \frac{1}{5}\times 5\; x[/tex].

[tex]x = 8[/tex].

Answer : Answer is 8

Step-by-step explanation:

Took the test

Answer:

Option C is correct.

Step-by-step explanation:

We need to solve the equation:

tan 45° - 10 cos 60°

Finding value of tan 45° and cos 60° and solving:

tan 45° = 1 and

cos 60° = 0.5

= 1 - 10(0.5)

= 1- 5

= -4

So, Option C is correct.

Answer:

Step-by-step explanation:

First pull out  the common factor of ab

ab(8a^3 + (1/125)b^3)

This is basically the sum of cubes. The linear factor is

(2a + 1/5 b)

The other factor is these two factors squared and their multiplicand subtracted.

(2a^2 - 2/5 ab + 1/25b^2)

Now put  all this together and you get

ab(2a + 1/5 b)((2a^2 - 2/5 ab + 1/25b^2)

Answer:

The triangle is reflected across the x-axis and then translated 1 unite to the right , 1 unit up

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 then the new point = (x , -y)

- If point (x , y) reflected across the y-axis

 then the new point = (-x , y)

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

- A triangle has three vertices

- The vertices are B (-3 , 0) , C(2 , -1) , D (-1 , 2)

- The images of the vertices are B" (-2 , 1) , C" (3 , 2) , D" (0 , -1)

 after two steps of transformations

- After comparing the points with their images we find

# The x-coordinates of the points are added by 1

∴ There is translation to the right

# The y-coordinates of the points not add or subtracted by the same

   number, that means there is a transformation before the translation

   for the y-coordinates

# The sign of y-coordinates of the points are changed , that means

   there is a reflection across the x-axis

∴ B' is (-3 , 0) , C' is (2 , 1) , D' is (-1 , -2)

- After comparing the 1st image with the 2nd images we find

# The x-coordinates of the points are added by 1 and the

   y-coordinates are add by 1

∴ B" is (-2 , 1) , C" is (3 , 2) , D" is (0 , -1)

- From all above

* The triangle is reflected across the x-axis and then translated 1 unite

  to the right , 1 unit up

Answer:

21 1/3

Step-by-step explanation:

Write this as an expression

3/4 x = 16

Now it is a one step equation

divide 3/4 from its self and 16

3/4 divided by 16 = 21 1/3

x= 21 1/3

Answer:

[tex]21\frac{1}{3}[/tex] or 21.3

Step-by-step explanation:

We are given that the product of [tex] \frac { 3 } { 4 } [/tex] and a number is [tex] 1 6 [/tex].

Assuming that number to be [tex] x [/tex], we can write it as:

[tex] \frac { 3 } { 4 } \times x = 1 6 [/tex]

Taking the denominator to the other side of equation and multiplying it to get:

[tex] 3 x = 1 6 \times 4 [/tex]

[tex] 3 x = 6 4 [/tex]

Isolating the variable to get:

[tex] x = \frac { 6 4 } { 3 } [/tex]

[tex] x = 21\frac{1}{3}[/tex] or [tex] x = 21.3[/tex]