The length of a rectangle is 6m more then the width. The area is 40m^2 . What is the length and the width?

ANSWER

[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]

or

[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]

EXPLANATION

The given equation is:

[tex]2 {x}^{2} - 5x + 1= 0[/tex]

Comparing this to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=2, b=-5, c=1

The quadratic formula is given by

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

We substitute the values to get,

[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)(2)} }{2(2)} [/tex]

[tex]x = \frac{ 5 \pm \sqrt{ 17} }{4} [/tex]

[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]

or

[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]

The answer is C: the average reading speed of the science fiction novel.

If x is her reading speed for the historical fiction novel, and her reading speed for the sci-fi novel is just two pages more than that of the historical fiction novel, then the equation to find out how fast she reads the science fiction novel would be x + 2, as you’re adding 2 to the reading speed of the historical fiction book (x)

Answer:

The answer to this question is correct but on PLATO the answer choice is actually A.

Step-by-step explanation:

PLATO

I think you forgot to put C and D but it is read out

The product of x and four divided by six

(x being some number)

i don't need it but brainliest it is appreciated

Answer:

- 2x - 3

Step-by-step explanation:

note that (f - g)(x) = f(x) - g(x)

f(x) - g(x) = x + 2 - (3x + 5) = x + 2 - 3x - 5 = - 2x - 3

Answer:

To sum consecutive numbers we use the formula:

n * (n+1) / 2

1 through 55 = (55 * 56) / 2 = 1,540

1 through 9 = (9 * 10) / 2 = 45

10 through 55 = 1,540 -45 = 1,495

********************************************************

EDITED

Gee, it seems I added ALL numbers from 10 through 55

ALL ODD numbers from 10 through 55 sum to

759

Step-by-step explanation:

Answer:

Step-by-step explanation:

6,18,8,4,18,20,10,10,21,6,17,18

Arrange the data in ascending order

4,6,6,8,10,10,17,18,18,18,20,21

Part A

Mean = 156/12 = 13 is correct

Median = 15 is incorrect because the data is not arranged. Median when there are even numbers will be: 10+17/2 = 13.5

Mode = 10 is incorrect, because mode is most repeating value and in the data set it is 18 so, Mode = 18

Part B

10,12 and 52 should be added in data set in ascending order

4,6,6,8,10,10,10,12,17,18,18,18,20,21,52

Mean = 230/15 = 15

Median = Middle term as odd numbers = 8th term = 12

Mode = 10 and 18

Part C

Both median and mean are used to measure central tendency.

The best measure of central tendency is considered median because the mean is affected by the presence of outliers while median is not affected by outliers.

Answer:

He is correct.

Step-by-step explanation:

I got 100% on my paper

ANSWER

C)

[tex] {x}^{2} + {y}^{2} = 10[/tex]

EXPLANATION

The center of the circle is (0,0).

The circle passes through (-1,-3).

The radius can be obtained using the distance formula:

[tex]r = \sqrt{(0 - 1)^{2} + {(0 - - 3)}^{2} } = \sqrt{10} [/tex]

The equation is given as:

[tex]( {x - h)}^{2} + ( {y - k)}^{2}= {r}^{2} [/tex]

Where (h,k) is the center and r is the radius.

This implies that;

[tex]( {x - 0)}^{2} + ( {y - 0)}^{2}= {( \sqrt{10)} }^{2} [/tex]

[tex] {x}^{2} + {y}^{2} = 10[/tex]

Answer:

-19000

Step-by-step explanation:

1000-20000=-19000

Answer:

C -19000

Step-by-step explanation:

          1,000

     - 20,000

----------------------=

        -19000

ANSWER

A) For all x > 0 the graph will be higher.

EXPLANATION

Jack's graph has equation

y=2x

This graph passes through the origin and has slope 2.

Nina's graph is y=5x.

This graph also passes through the origin and has slope 5.

Since 5 is greater than 2, for all x>0, Nina's graph will be higher.

Answer: A

Step-by-step explanation: Changing the 2 to a 5 makes an exponential growth function increase at a faster rate. Therefore, for all x > 0 the graph will be higher. At x = 0 the graphs will have the same value and for all x < 0, Nina's graph will be lower.

For this case we must find the inverse of the following function:

[tex]f (x) = x ^ 2 + 7[/tex]

For this we follow the steps below:

Replace f(x) with y:

[tex]y = x ^ 2 + 7[/tex]

We exchange the variables:

[tex]x = y ^ 2 + 7[/tex]

We solve the equation for "y", that is, we clear "y":

[tex]y^ 2 + 7 = x[/tex]

We subtract 7 on both sides of the equation:

[tex]y ^ 2 = x-7[/tex]

We apply square root on both sides of the equation to eliminate the exponent:

[tex]y = \pm\sqrt {x-7}[/tex]

We change y by[tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) =\pm\sqrt {x-7}[/tex]

Answer;

Option A

Answer:

(6,-5)

Step-by-step explanation:

As the point is 4 units to the left of X=2, the reflection must be 4 units to the right of X=2

Answer:

Option D.

[tex]A =96\pi\ cm^2[/tex]

Step-by-step explanation:

The area of the circular bases is:

[tex]A_c = 2\pi(a) ^ 2[/tex]

Where

[tex]a=4\ cm[/tex] is the radius of the circle

Then

[tex]A = 2\pi(4) ^ 2[/tex]

[tex]A = 32\pi\ cm^2[/tex]

The area of the rectangle is:

[tex]A_r=b * 2\pi r[/tex]

Where

[tex]b=8\ cm[/tex]

b is the width of the rectangle and [tex]2\pi r[/tex] is the length

Then the area of the rectangle is:

[tex]A_r=8 * 2\pi (4)[/tex]

[tex]A_r=64\pi\ cm^2[/tex]

Finally the total area is:

[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]

[tex]A =96\pi\ cm^2[/tex]

Answer:

The correct answer is option B.  96π

Step-by-step explanation:

Points to remember

Surface area of cylinder = 2πr(r + h)

Where r is the radius of cylinder and h is the height of cylinder.

From the figure we get r = 4 cm and h = 8 cm

To find the surface area of cylinder

Surface area = 2πr(r + h)

 = 2π * 4(4 + 8)

 = 96π

The correct answer is option B.  96π

Answer: option c

Step-by-step explanation:

You can use these identities:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]

Then, using the angle that measures 30 degrees, you know that:

[tex]\alpha=30\°\\opposite=8\\adjacent=b[/tex]

Substituting:

[tex]tan(30\°)=\frac{8}{b}[/tex]

Now you must solve for b:

[tex]b=\frac{8}{tan(30\°)}\\\\b=8\sqrt{3}[/tex]

Using the angle that measures 30 degrees, you know that:

[tex]\alpha=30\°\\opposite=8\\hypotenuse=c[/tex]

Substituting:

[tex]sin(30\°)=\frac{8}{c}[/tex]

Now you must solve for c:

[tex]c=\frac{8}{sin(30\°)}\\\\c=16[/tex]

ANSWER

The correct answer is C

EXPLANATION

The side adjacent to the 60° angle is 8 units.

The hypotenuse is c.

Using the cosine ratio, we have

[tex] \cos(60 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(60 \degree) = \frac{8}{c} [/tex]

[tex] \frac{1}{2}= \frac{8}{c} [/tex]

Cross multiply

[tex]c = 8 \times 2 = 16[/tex]

Also

[tex]\cos(30 \degree) = \frac{b}{c} [/tex]

[tex]\cos(30 \degree) = \frac{b}{16} [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{b}{16} [/tex]

Multiply both sides by 16

[tex]b = 16 \times \frac{ \sqrt{3} }{2} [/tex]

[tex]b = 8 \sqrt{3} [/tex]

The correct answer is C

y = 7x +3 slope is rise over run with would be 7/1 and y intercept is 3

The equation in the slope-intercept form is y=7x+3.

Given:

Find:

Solution:

We will use y = mx+b where m = slope and b = y-intercept.

y = mx+b

Now, putting (1,10) in the place of x and y and slope as 7, we get;

10 = 7*1 + b

b = 10-7

b=3

So, the y-intercept is 3.

Now, putting the y-intercept in the slope-intercept equation, we get;

y = 7x+3

Hence, the equation in slope-intercept form is y=7x+3.

To learn more about slope-intercept, refer to:

https://brainly.com/question/1884491

#SPJ2

Answer:

Both.

Step-by-step explanation:

This was so long ago but....

Answer:

both

Step-by-step explanation:

Answer:

[tex]\large\boxed{\left(\dfrac{2b}{3}\right)^4=\dfrac{16b^4}{81}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{2b}{3}\right)^4\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{2^4b^4}{3^4}=\dfrac{16b^4}{81}[/tex]

Answer:

16b^4/81

Step-by-step explanation:

I will say 1 block is 1 something okay cause I don’t have a key mini has an area of 2 (2x2=4/2=2) And the giant has an area of 32 (8x8=64/2=32) I don’t know if the small one became big or the big one became small so if the small to big is 16 big to small is 0.0625 or the numbers the other way around

Answer:

Area of left triangle = 2 * 2 / 2 = 2

Area of triangle on the right = 8 * 8 / 2 =32

32 / 2 = 16

Therefore the triangle on the right has 16 times the area than the triangle on the left.

Step-by-step explanation:

Answer:

298

Step-by-step explanation:

Given

(8 - (- 9))² + (-3 - (- 6))² ← evaluate the parenthesis before squaring

= (8 + 9)² + (- 3 + 6)²

= 17² + 3²

= 289 + 9

= 298

Answer: (8+9)^2 + (-3 + 6)^2

= 17^2 + 3^2

= 289 + 9

= 298. ANS.

Answer:

B

Step-by-step explanation:

Let x be the number of packages of paper towels.

Each package of paper towels costs $2.79.

Then x packages of paper towels cost $2.79x.

Hence, a function f(x) is

[tex]f(x)=2.79x[/tex]

Practically, you can buy 0 packages, 1 package, 2 packages and so on, only whole numbers of packages, so practical domain is all whole numbers.

Final answer:

The next time a museum tour and video both start at the same time after 10:00 a.m. is at 11:00 a.m., as that is when their intervals (every 20 minutes for tours and every 15 minutes for videos) have their Least Common Multiple.

Explanation:

The question is about finding the next time a museum tour and a video both start at the same time after 10:00 a.m. The tours start every 20 minutes and the videos start every 15 minutes. To find the next common start time, we need to calculate the Least Common Multiple (LCM) of 20 and 15 which is the smallest number that both 20 and 15 can divide into without leaving a remainder.

Multiples of 20 are 20, 40, 60, 80, 100, ...

Multiples of 15 are 15, 30, 45, 60, 75, ...

The first common multiple of the two intervals is 60 minutes. Therefore, since both the tour and the video start at the same time (10:00 a.m.), the next time they will both start together will be 60 minutes later, which is at 11:00 a.m.

Answer:

12a - 4x

Step-by-step explanation:

1. 7a + 2x + 5a - 6x

2. 12a + 2 x - 6 x

Answer:

r = 1.3 meters  

Step-by-step explanation:

A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle.

A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle.  

The python is 2.6 pi (2.6π) meters long.

What is the radius r of the circle that the python forms?

Now we have: C = π d, or (with d = 2 r):  C = 2 π r.

Changing that around: r = C / 2 π

So with our value of C = 2.6π meters, that gives us:

r = 2.6π/2π = 2.6/2, so r = 1.3 meters  

Answer:

The answer is 1.3

Step-by-step explanation:

Because it is half of the diameter which was 2.6

Answer:

Solution is (1,7).

Step-by-step explanation:

We need to find the solution of the system of following equations.

y= 5x + 2        eq(1)

3x = -y +10      eq(2)

We will solve the equations using Substitution method to find the values of x and y

we put value of y from eq (1) into eq (2), The eq(2) will be:

3x = - (5x + 2) + 10

3x = -5x -2 +10

3x+5x = -2+10

8x = 8

x= 1

Now, putting value of z in eq(1) to find value of y

y = 5x +2

y = 5(1) + 2

y = 5+2

y = 7

So, Solution is (1,7).

Answer:

A

Step-by-step explanation:

Substitute the values of n into the recursive formula and check result against values in table

A

[tex]a_{2}[/tex] = 3 + 5 = 8 ← correct

[tex]a_{3}[/tex] = 8 + 5 = 13 ← correct

[tex]a_{4}[/tex] = 13 + 5 = 18 ← correct

[tex]a_{5}[/tex] = 18 + 5 = 23 ← correct

Answer:

the answer is A

Step-by-step explanation:

Answer:

always.

Step-by-step explanation:

A ray has a starting point but no end point. Therefore if 2 opposite rays are connected at their endpoints, a line is formed. I cannot think of an exception to this because the definition of a ray is very rigid (the end point is always included).

Peter will be 75 years old in 47 years.

Answer:

In 47 years Peter will be 75 years old

Step-by-step explanation:

If Peter will be 54 years old in 26 years then subtract 26 from 54

54-26=28

This means that Peter is 28 right now, if you want to double check that work then add 26 to 28 implying that in 26 years Peter with be 54 years old

28+26=54

This shows that your calculations are correct! Now you have to figure out how many years from now will Peter be when he turns 75 years old, so you subtract his current age which is 28 from 75

75-28=47

Now to double check this add 47 to his current age which is 28

28+47= 75

This shows that your calculations are correct and it will take 47 years for Peter to be 75 years old!

Answer:

-109

Step-by-step explanation:

Arithmetic sequence formula:

an = a1  + d(n - 1) where d = -4 and a1 = 19

so

a(33) = 19 - 4(33-1)

a(33) = 19  - 4(32)

a(33) = 19 - 128

a(33) = -109

The missing term : -109

Answer:

-109

Step-by-step explanation:

As x changes from 1 to 2, 2 to 3, and 3 to 4, each change in x is 1. The  corresponding changes in y from 19 to 15, from 15 to 11, and from 11 to 7, are each a change of -4 in y. For each change of 1 in x, the corresponding change in y is -4. From 4 to 33 in x, the change is 33 - 4 = 29. The corresponding change in y is 29 * (-4) = -116.

7 + (-116) = -109

Answer:

Observe the attached image

Step-by-step explanation:

We have the graph of a line that passes through the points (0,5) and (2, 1).

The equation of the line that passes through these points is found in the following way:

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

Where

m = slope

[tex]m = \frac {y_2-y_1}{x_2-x_1}\\\\m = \frac{1-5}{2-0}\\\\m = -2\\\\b = y_2-mx_2\\\\b = 1 -(-2)(2)\\\\b = 5[/tex]

So

[tex]y = -2x + 5[/tex]

We must apply to this function the transformation[tex]f (x-4)[/tex].

We know that a transformation of the form

[tex]y = f (x + h)[/tex] shifts the graph of the function f(x) h units to the right if [tex]h <0[/tex], or shifts the function f(x) h units towards the left if [tex]h> 0[/tex].

In this case [tex]h = -4 <0[/tex] then the transformation [tex]f(x-4)[/tex] displaces the graph 4 units to the right.

Therefore if f(x) passes through the points (0,5) and (2,1) then [tex]f (x-4)[/tex] passes through the points (4, 5) (6, 1)

And its equation is:

[tex]y = -2(x-4) +5\\\\y = -2x +13[/tex]

Observe the attached image

Answer:

If x is greater than 1 it is growth, if it less than it is decay

Step-by-step explanation:

Answer:

[tex]\large\boxed{y=\dfrac{8}{37}}[/tex]

Step-by-step explanation:

[tex]Domain:\ 2+2y\neq0\to y\neq-1\\\\\dfrac{-30+15y}{2+2y}=-11\\\\\dfrac{-30+15y}{2+2y}=\dfrac{-11}{1}\qquad\text{cross multiply}\\\\(-30+15y)(1)=(-11)(2+2y)\qquad\text{use the distributive property}\\\\-30+15y=(-11)(2)+(-11)(2y)\\\\-30+15y=-22-22y\qquad\text{add 30 to both sides}\\\\15y=8-22y\qquad\text{add}\ 22y\ \text{to both sides}\\\\37y=8\qquad\text{divide both sides by 37}\\\\y=\dfrac{8}{37}[/tex]