Evaluate the expression shown below and write your answer as a fraction in simplest form.

11/2 + 5/4

Answer:

yes the solution is 8

Step-by-step explanation:

subtract 9 from both sides

1/2x+9-9=13-9

simplify

1/2x=4

multiply both sides by 2

2 x 1/2=4 x 2

simplify

x=8

Answer:

x = -84

y = -21

Step-by-step explanation:

4 - y = 17

4y = x

Use the first equation to solve for y

4 - y = 17

y = 4 -  17

y = -21

In the second equation, get y on its own.

4y = x

y = x/4

Substitute the new second equation into the new first equation

-21 = x/4

-21 * 4 = x

x = -84

Answer:

Part I)

[tex]a=-1\text{ and } c=2[/tex]

Giving the equation:

[tex]y=-x^3+x+2[/tex]

Part II)

(-1, 2)

Step-by-step explanation:

We have the equation:

[tex]y=ax^3+x+c[/tex]

Where a and c are constants.

We are given gradient/slope of the curve at the point (1, 2) is -2.

Part I)

We know that the gradient of the curve exactly at the point (1, 2) is -2.

So, we will differentiate our equation. We have:

[tex]\displaystyle y=ax^3+x+c[/tex]

Differentiate both sides with respect to x:

[tex]\displaystyle y^\prime=\frac{d}{dx}\big[ax^3+x+c\big][/tex]

Expand the right:

[tex]\displaystyle y^\prime=\frac{d}{dx}\big[ax^3]+\frac{d}{dx}\big[x\big]+\frac{d}{dx}\big[c\big][/tex]

Since a and c are simply constants, we can move them outside:

[tex]\displaystyle y^\prime=a\frac{d}{dx}\big[x^3]+\frac{d}{dx}\big[x\big]+c\frac{d}{dx}\big[1\big][/tex]

Differentiate. Note that the derivative of a constant is simply 0.

[tex]\displaystyle y^\prime=3ax^2+1[/tex]

We know that at the point (1, 2), the gradient/slope is -2.

Hence, when x is 1 and when y is 2, y’ is -2.

So (we don’t have a y so we can ignore it):

[tex]-2=3a(1)^2+1[/tex]

Solve for a. Simplify:

[tex]-2=3a+1[/tex]

Subtract 1 from both sides yield:

[tex]-3=3a[/tex]

So, it follows that:

[tex]a=-1[/tex]

Therefore, our derivative will be:

[tex]y=-3x^2+1[/tex]

Now, we can go back to our original equation:

[tex]y=ax^3+x+c[/tex]

Since we know that a is -1:

[tex]y=-x^3+x+c[/tex]

Recall that we know that a point on our curve is (1, 2).

So, when x is 1, y is 2. By substitution:

[tex]2=-(1)^3+1+c[/tex]

Solve for c. Simplify:

[tex]2=-1+1+c[/tex]

Then it follows that:

[tex]c=2[/tex]

Hence, our entire equation is:

[tex]y=-x^3+x+2[/tex]

Part II)

Our derivative is:

[tex]y^\prime=-3x^2+1[/tex]

If the gradient is -2, y’ is -2. Hence:

[tex]-2=-3x^2+1[/tex]

Solve for x. Subtracting 1 from both sides yields:

[tex]-3=-3x^2[/tex]

So:

[tex]x^2=1[/tex]

Then it follows that:

[tex]x=\pm1\\[/tex]

Since we already have the point (1, 2) where x is 1, our other point is where x is -1.

Using our equation:

[tex]y=-x^3+x+2[/tex]

We can see that our second point is:

[tex]y=-(-1)^3+(-1)+2[/tex]

Simplify:

[tex]y=1-1+2=2[/tex]

So, our second point where the gradient is -2 is at (-1, 2).

Answer: x₁=7, x₂=-1

Step-by-step explanation:

(x-3)^2= x^2-6x+9

2(x^2-6x+9)=28+4

x^2-6x+9=16

x^2-6x-7=0

you use the quadratic equation will give you 2 roots,

x₁=7, x₂=-1

Answer:

Phoebe surveyed teens and adults to find the average number of hours of sleep they get during the week. Her results are shown below. Which statement regarding her survey results is true?

Hours of Sleep for Teens

A box-and-whisker plot. The number line goes from 1 to 12. The whiskers range from 2.5 to 12, and the box ranges from 5 to 8.5. A line divides the box at 7.

adult have less variability in the sleep hours because well they work more then us and us teens we have school starting at 7:45 am and the adult have to wake up to go to work or having to stay up

hope this can help

The fifth term is 162 in the geometric sequence.

The geometric sequence defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio

A arithmetic sequence is defined as an arrangement of numbers which is particular order.

The formula to find the general term of an arithmetic sequence is,

aₙ = a₁ + (n-1)d

Given data :

First term of sequence geometric (a₁) = 2

The common ratio of geometric (r) = 3

To determine the fifth term of geometric sequence

Let the fifth term of sequence = a₅    

The nth term of a geometric sequence is expressed as :

Tₙ = a₁rⁿ⁻¹

Substitute the values of n = 5, a₁ =2 and r = 3 in the formula,

T₅  = (2)(3)⁵⁻¹  

T₅  = (2)(3)⁴

T₅  = (2)(81)

T₅  = 162

Hence, the fifth term is 162 in the geometric sequence

Learn more about geometric sequence here :

https://brainly.com/question/11266123

#SPJ5

Answer:

this is really good but very sad so if thats what you're going for then you did a really good job!! :(

Step-by-step explanation:

Answer:

i love it!!! very cool

Step-by-step explanation:

Answer:

Weak positive correlation

Step-by-step explanation:

Just trust me

Also it’s positive in a graph but it’s not changing that much so it’s weak

Rewrite the length of the movie as an improper fraction.

2 1/3 = 7/3

Now multiply the length of the movie by 3/4

7/3 x 3/4 = (7 x3) / (3 x 4) = 21/12 = 1 3/4 hours

Answer:

B

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

Differentiate using the product rule

Given f(x). g(x) then the derivative is

f(x). g'(x) + g(x). f'(x) ← product rule

Given

[tex]\frac{d}{dx}[/tex](x² secx )

with f(x) = x² and g(x) = secx , then

f'(x) = 2x and g'(x) = secxtanx, thus

[tex]\frac{d}{dx}[/tex](x² secx)

= x². secxtanx + secx. 2x ← factor out xsecx from each term

= xsecx(xtanx + 2) → third option

Answer:

104

Step-by-step explanation:

Answer:

appreciate it man

Step-by-step explanation:

best of luck

Answer:

[tex]39.5,44.5[/tex]

Step-by-step explanation:

[tex]Let\ the\ lower\ limit\ and\ the\ upper\ limit\ of\ the\ first\ interval\ be\ u_1,v_1.\\Let\ the\ lower\ limit\ and\ the\ upper\ limit\ of\ the\ second\ interval\ be\ u_2,v_2.\\Let\ the\ lower\ limit\ and\ the\ upper\ limit\ of\ the\ third\ interval\ be\ u_3,v_3.\\Hence,\\As\ the\ class\ marks\ are\ uniform\ with\ an\ a\ difference\ of\ 5, the\\ observation\ is\ continuous\ and\ the\ class\ size\ is\ 5\ too.\\Hence,\\v_1=u_2, v_2=u_3\\[/tex][tex]Now,\\Lets\ consider\ the\ first\ two\ classes.\\37=\frac{u_1+v_1}{2} \\42=\frac{u_2+v_2}{2}\\By\ adding\ the\ equations:\\79= \frac{u_1+v_1}{2}+\frac{u_2+v_2}{2}\\79=\frac{u_1+v_1+u_2+v_2}{2}\\79=\frac{(u_1+v_2)+(v_1+u_2)}{2}\\79=\frac{(u_1+v_2)}{2}+\frac{(v_1+u_2)}{2}\\Now,\\As\ the\ mid-point\ between\ two\ points\ can\ be\ calculated\ by\\ its\ average:\frac{u+v}{2} \\Hence,\\u_2\ lies\ in\ the\ mid-point\ of\ u_1\ and\ v_2.\\u_2=\frac{(u_1+v_2)}{2}\\[/tex]

[tex]Hence,\\By\ substituting\ u_2=\frac{(u_1+v_2)}{2},\\79=u_2+\frac{v_1+u_2}{2}\\As\ v_1=u_2[Proven],\\79=u_2+ \frac{u_2+u_2}{2}\\79=u_2+\frac{2u_2}{2}\\79=2u_2\\Hence,\\u_2=\frac{79}{2}\\u_2=39.5\\Now,\ as\ we\ already\ know\ that\ the\ class\ size=5,\\v_2-u_2=5\\Hence,\\v_2=5+u_2\\Here,\\v_2=5+39.5\\v_2=44.5\\Hence,\\The\ upper\ limit\ of\ the\ second\ interval=44.5\\The\ lower\ limit\ of\ the\ second\ interval=39.5\\[/tex]

Answer:

To calculate the perimeter of a circle we have this formula:

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

And, if we're going to calculate for a semicircle, we should divide it by 2

We should also take into account the diameter, as, if it's a semicircle, we also have to add the base of it, which will have the diameter length

Knowing this, we can see the formula to calculate this specific perimeter

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

Now, we can replace r by 22:

[tex]\frac{2\pi *22}{2} + 2*22 \approx 113.12[/tex]

So the perimeter is approximately 113.12 cm

Answer:

[tex]x<3[/tex]

Step-by-step explanation:

STEP 1: Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]5x<15[/tex]

STEP 2: Divide each term by [tex]5[/tex] and simplify.

[tex]x<3[/tex]

STEP 3: The result can be shown in multiple forms.

Inequality Form:

[tex]x<3[/tex]

Interval Notation:

[tex](-[/tex]∞[tex],3)[/tex]

Answer:

1. 2x + 1 ≤ 3

2. 1 + 3x ≥ -5

3. 5x - 7 ≥ 17

4. 5 - 3x ≥ 11

Step-by-step explanation:

Ok

5x - 7 ≥ 17

subtract 7 and u get 5x ≥ 10

divide that and you get ≥ 2

so 3 goes with that one

1 + 3x ≥ -5

subtract 1 and you get 3x ≥ -6

divide that and youll get x ≥ -2

so 2 goes with this one

2x + 1 ≤ 3

subtract 1 and u get 2x ≤ 2

divide them and you get x ≤ 1

so 1 goes with this one

5 - 3x ≥ 11

subtract 5 and u get -3x  ≥ 6

divide it and u get x ≥ -2

so 4 goes with this one

Hoped this helps :)

also btw Brainly steals half the points you give out so instead of 15 ur giving me 25.

Answer:

-2,-2

Step-by-step explanation:

-

Answer:

................(-2,-2)

Answer:

Here is the summary:

Step-by-step explanation:

Given the equation

The points which satisfy the equation y=13x+5

y = 13x+5

Checking the point (0, 5)

5 = 13(0)+5

5 = 0 + 5

5 = 5

TRUE

Checking the point (-2, -21)

-21 = 13(-2)+5

-21 = -26 + 5

-21 = -21

TRUE

The points which satisfy the equation y=-3x

y = -3x

Checking the point (0, 0)

0 = -3(0)

0 = 0

TRUE

Checking the point (-5, -15)

y = -3x

-15 = -3(-5)

-15 = -15

TRUE

Checking the point (-3, 9)

y = -3x

9 = -3(-3)

9 = 9

TRUE

The points which satisfy the equation y=x-10

y = x-10

Checking (8, -2)

-2 = 8 - 10

-2 = -2

TRUE

Therefore, from the above calculations we conclude the summary:

Here is the summary:

Answer:

4. the answer is 20      

5. x=12 y=30

6. MLV = TUV bySSS

7. ABC=HGF by SSS

to show work:

4. 15/12=25/x      (cross multiply)

  =15x=300         (divide both sides by 15)

  =  x=20    

5. the triangle is equilatieral so all the angles are the same. this means 60=2y.

if you isolate the variable and divide both sides by 2, you get y=30

6. 49/14 = 28/8 ?

if you solve both the division problems, they both equal 3.5, meaning the side lengths are the same so the rule would be SSS or side side side

and you do the same thing with the next triangle too

hope this helps!! also brainliest would be nice but you dont have to

Answer:

The related variation will be:

Step-by-step explanation:

We know that when 'y' varies inversely with 'x', we get the equation

y ∝ 1/x

y = k × 1/x

Here 'k' is the constant of proportionality

Given that the altitude H of a cylinder with a constant volume V is inversely proportional to the square of its radius R.

so the equation can be mapped as

H ∝ 1/R²

H = k/R²

In this case, the k is the constant volume. i.e. V = k

Thus, the equation becomes

H = V/R²

where H is the altitude, V is the constant volume and R is the radius.

Therefore, the related variation will be:

The variation equation showing the relationship between H, V and R is given by H = VR²

A direct proportional relationship is that in which as one variable increases the other variable increases and vice versa.

An indirect proportional relationship is that in which as one variable increases the other variable decreases and vice versa.

Let H represent the altitude and R represent the radius.

H ∝ R²

H = VR²; V (volume) is the constant of proportionality

The variation equation showing the relationship between H, V and R is given by H = VR²

Find out more at: https://brainly.com/question/13977805

Answer:

- 2

Step-by-step explanation:

It helps when u make a table using the points given

x         y

1          6

3         2

from 6 to 2 you need to subtract 4

from 1 to 3 you need to add 2

now its y/x

4/2 = 2

Since the line is going down that means your slope is negative so...

-2 will be your slope

Hope this helped!

Answer:

The slope is -2.

Step-by-step explanation:

There are two ways to solve this problem.

1st way is by looking at the graph:

*Identify what the rise over run is. In this case, it woult be 2 over 1 which if you divide 2÷1, it would be 2.

*Then, if the graph is going down, the slope is negative, and if the graph is going up, the slope is positive. If it's vertical, the slope is undefined, and if it's horizontal, the slope is zero. Since, it's going down, your slope would be negative.

2nd way is by subtracting y2 - y1 and x2 - x1:

(The order doesn't matter as long as you are subtracting correctly)

* First, 6 minus 2 is 4, and 1 minus 3 is  -2. After, divide 4 by -2, and you'll end up with -2.

* Or you can do it the other way round. First, 2 minus 6 is -4, and 3 minus 1 is 2. After, divide -4 by 2, and you'll end up with -2

Answer:

Step-by-step explanation:

Answer:

x plus 3y minus 63

Step-by-step explanation:

Answer:

slope is 2

Step-by-step explanation:

-11-(-1) =-10

4-9=-5

-10/-5

=2

Slope-2x

Answer:

117.8

Step-by-step explanation:

i used heron's formula

√s(s-a)(s-b)(s-c)

s= (20+16+33)/2 = 34.5

√34.5(34.5-20)(34.5-16)(34.5-33)

= 117.8

Answer:

x =  1/2 or 0.5

Step-by-step explanation:

Brainliest Please!!

- Hermionia

Answer:

The answer is -1/2

Step-by-step explanation:

5/x = 15/x+20

5/x-15/x=20

-10/x=20

-10=20x

x= -10/20

x= -1/2