9. The height of a triangle is 3 inches less than twice the length of its base. If the total area
of the triangle is 7 square inches, then find the lengths of the base and height.

Answer:

[tex]\lim_{x \to 5}f(x)=-5\\\lim_{x \to 1^-} f(x)=3\\\lim_{x \to 1^+} f(x)=3\\\lim_{x \to 1} f(x)=4\\[/tex]

Step-by-step explanation:

[tex]\lim_{x \to 5}f(x)[/tex]

This means "the limit of f(x) as x approaches 5"

In this case, f(x) is a basic linear function while x > 1, so a limit is not necessary but it can still be used as it is here. For this one, you can just calculate f(5), and that is:

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

[tex]f(5)=5-2(5)=5-10=-5[/tex]

[tex]\lim_{x \to 5}f(x)=-5[/tex]

===================

[tex]\lim_{x \to 1^-} f(x)[/tex]

This one is a little different. It means "the limit of f(x) as x approaches 1 from the negative (left) direction"

The negative direction of course means x will be less than 1, so we'll use this function:

[tex]f(x)=4-x[/tex]

It's easier if you graph it, but you can also do it like this:

[tex]f(0)=4+0=4\\f(0.5)=4-0.5=3.5\\f(0.75)=4-0.75=3.25\\f(0.9)=4-0.9=3.1\\f(0.99)=4-0.99=3.01[/tex]

There's a clear pattern there. You can see that f(1) should be 3, but this function only applies while x is less than 1 so it can never reach 3. It will get infinitely close, and that can be shown with the limit:

[tex]\lim_{x \to 1^-} f(x)=3[/tex]

===================

[tex]\lim_{x \to 1^+} f(x)[/tex]

This one works the same way, but from the positive (right) direction.

[tex]f(2)=5-4=1\\f(1.5)=5-3=2\\f(1.25)=5-2.5=2.5\\f(1.1)=5-2.2=2.8\\f(1.01)=5-2.02=2.98\\f(1.001)=5-2.002=2.998[/tex]

It will also get infinitely close to 3 when x = 1, but won't ever reach it because this function only applies when x is greater than 1.

[tex]\lim_{x \to 1^+} f(x)=3[/tex]

===================

[tex]\lim_{x \to 1} f(x)[/tex]

Here, the function for x=1 is just:

[tex]f(x)=4[/tex]

It's given already, so the limit is just:

[tex]\lim_{x \to 1} f(x)=4[/tex]

Answer:

16

Step-by-step explanation:

Since the perimeter of the rectangle is 80, we can set up the perimeter formula:

80=2L+2W=2(3x+3)+2(2x+2)=6x+6+4x+4=10x+10

10x=70

x=7

AB=2x+2=2(7)+2=14+2=16

Answer:

AB= 16

Step-by-step explanation:

2x+2+3x+3=40

Add like terms: 2x+3x= 5x and 2+3=5

New equation: 5x+5=40

Solve: 40-5= 35

Now we know that x is equal to 7.

2(7)+2= 16

Side DC equals 16.

Side AB has the same length as side DC since it's a rectangle.

Side AB equals 16.

Let's check: 16+16=32 (side DC and side AB)

24 must be the length of the other sides.

So, when you add all the sides together...

16+16+24+24= 80

You get 80, the perimeter!

I hope this helped!

Answer:

similar by angle angle similarity property.

Step-by-step explanation:

they have the right angles, and then the two vertical angles.

:))

Answer:

6 weeks

Step-by-step explanation:

8 quizzes = 4 weeks

So 2 quizzes/week

It will take her 12/2 weeks (6) to finish 12 quizzes

-Chetan K

Step-by-step explanation:

we have the data set given below here and using it, we want to find the sample mean X. Bar, the sample standard deviation S. And constructed 99% confidence interval for the population we knew, assuming the population is normally distributed. So since we have this data we can find expire and s using the appropriate definitions expire, is that some of the data divided by n 2.353 and s. Is the square root of the sum of deviations of the mean square divided by n minus one. In this case 1.3 Now with X. Bar and sample standard deviation S, we can use a student's t distribution to construct this confidence interval. So we can identify the appropriate T score. So for the degree of freedom and minus one equals 14 and critical values um providing probability 140.99 for the confidence interval,  to identify T C equals 2.977 Now, with this T. C, we can identify the margin of error E, which is given by this formula plugging in our T C. S and N. We obtain E equals 0.572 And now plugging into our confidence interval formula, which is that new falls between a sample mean minus C, and sampling plus E gives us our confidence interval. That new is between 1.781 and 2.9 to 5 with 99% confidence.

Answer:

odd

Step-by-step explanation:

cuz it can't be neither or even

Answer:

y + 6 = -1/4(x - 2)

Step-by-step explanation:

Point slope form:  [tex]y - y_{1} = m(x - x_{1} )[/tex]

[tex]y - y_{1} = m(x - x_{1} )[/tex]    Substitute slope = -1/4 and point (2, -6)

[tex]y - (-6) =\frac{-1}4} (x - 2)\\[/tex]

y + 6 = -1/4(x - 2)

Answer:

3x8= 24sf

5x7= 35sf

9x10= 90sf

13x2= 26sf

8x8= 64sf

Step-by-step explanation:

Answer:

i think this correct

Step-by-step explanation:

3.24=(1+9.4/100) x

then x= 2.961 $

Answer:

Step-by-step explanation:

here you go m = (y2-y1)/(x2-x1)

  = (11-(-9))/(3-(-1))

  = 20/4

  = 5

9514 1404 393

Answer:

  The correct answer is marked. (8·3)

Step-by-step explanation:

The order of operations requires that you start with by evaluating expressions in parentheses. Within parentheses, the order of operations applies, so you need to do multiplication before addition.

In this expression, the multiplication operation inside the parentheses is performed first. That is, you first compute 8·3.

_____

Additional comment

After that, you do the subtraction, to get ...

  11 ÷ (-12) +2⁴

Then the exponential term is evaluated, and you have ...

  11 ÷ (-12) +16

The division will result in a fraction, making it ...

  (-11/12) +16

And, finally, the addition gives you ...

  15 1/12

Answer:

pls ask the question in english pls i don't understand it

Answer:

(1, -3) (2, -1) (3, 1)

Step-by-step explanation:

if seconds=x and degrees celsius=y, the points are (1, -3) (2, -1) (3, 1). to graph, plot the points on a graph. (ordered pairs are written as x,y)

Answer:

Step-by-step explanation:

We need to find the coordinates of the vertex of the parabola.

[tex]f(x)=ax^2+bx+c\\\\v(p,\ q)-\text{vertex}\\\\p=\dfrac{-b}{2a};\ q=f(p)[/tex]

We have

[tex]h(t)=24+4t-5t^2=-5t^2+4t+24\\\\a=-5,\ b=4;\ c=24\\\\p=\dfrac{-4}{2(-5)}=\dfrac{-2}{-5}=\dfrac{2}{5}=0.4\\\\q=h(0.4)=-5(0.4)^2+4(0.4)+24=-5(0.16)+1.6+24\\\\=-0.8+25.6=24.8[/tex]

Answer:

x = 8, x = 10

Step-by-step explanation:

[tex]\sqrt{4x - 31}[/tex] = x - 7 ( square both sides )

4x - 31 = (x - 7)² ← expand using FOIL

4x - 31 = x² - 14x + 49 ( sub 4x - 31 from both sides )

0 = x² - 18x + 80 ← in standard form

0 = (x - 8)(x - 10) ← in factored form

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x - 10 = 0 ⇒ x = 10

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 8

left side = [tex]\sqrt{4(8)-31 }[/tex] = [tex]\sqrt{32-31}[/tex] = [tex]\sqrt{1}[/tex] = 1

right side = 8 - 7 = 1

Then x = 8 is a solution

x = 10

left side = [tex]\sqrt{4(10)-31}[/tex] = [tex]\sqrt{40-31}[/tex] = [tex]\sqrt{9}[/tex] = 3

right side = 10 - 7 = 3

Then x = 10 is a solution

HCF (2x, x) = x.

Factors of 2x = 2 × x × 1

Factors of x = x × 1

Common factors = x, 1

HCF = x × 1 = x

See the attachment too.

________

Hope it helps ⚜

Answer:

i dont know

Step-by-step explanation:

i dont know

Answer:

x=34

Step-by-step explanation:

2x-5=3(1/2x+4)

2x-5=3/2x+12

1/2x-5=12

1/2x=17

x=34

Answer:

x=34

Step-by-step explanation:

Answer:

Just keep adding 5 for each month.

Step-by-step explanation:

10 + 5 = 15

15 is first month

20 second

25 third

30 fourth

35 fifth

40 six

etc.

Equation :

10 + (5m)

m = number of months that have passed by.

Answer:

D

Step-by-step explanation:

or

This is the conditional distribution of style of dress for freshmen.

Answer:

5

Step-by-step explanation:

trust

Answer:

(4+6)/(2•1)

(4+6=10)/(2×1=2)

10÷2

5

Answer:

$9444 Is the difference

Step-by-step explanation:

$19,320 - $9876 = 9444$

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

1500

Step-by-step explanation:

112500/75=answer

answer=1500

Answer: 1 towel cost 1,500

Step-by-step explanation: When you divide $112,500 by 75 you get 1,500.

Answer:

17

Step-by-step explanation:

∠C is common in both triangles

equate them

∠C = 180- (x + 100) = 180 - ( 4x + 49)

x + 100 = 4x + 49

100 - 49 = 3x

51 = 3x

x = 51/3 = 17

Answer:

I cant Really type the thing out, i posted a screen shot

Step-by-step explanation:

We need to find distance they travel as a function of time. This simply means that x is the function of time. The destination is 120 miles away, this is irrelevant for the question that is currently being asked. However, we know that they have already travelled 20 miles and are going 50 miles and hour. So lets plug in what we have.

50 is our rate of change, so we match that with the x.

20 is our constant, the distance already travelled.

This means our function is:

f(x) = 50x + 20

This means our answer is D) f(x) = 50x + 20

Lets also plug in 120 to solve how much further they need to travel before arriving.

120 is our f(x) as it is the final distance travelled.

120 = 50x + 20

120-20 = 50x

100 = 50x

100/50 = x

2 = x

This means that they need to travel 2 hours in addition to the 20 miles they have already gone.

I hope I've helped! :)

The two consecutive integers between which the solution is located are 1 and 2

The two consecutive integers between which the solution is located are 2 and 3

Given the expressions x^2 = 3 and x^2 = 5

For the equation

x^2 = 3

Take the square root of both sides

x = ±√3

x = 1.732

Hence the two consecutive integers between which the solution is located are 1 and 2

For the expression

x^2 = 5

x = ±√5

x= 2.24

The two consecutive integers between which the solution is located are 2 and 3

learn more on roots here:https://brainly.com/question/12501796

Answer:

1. 1,2       2. 2,3

Step-by-step explanation: