Must write and solve using a system of linear equation.
* 10. You have 39 math and science problems for homework. You
have 15 more math problems than science problems. Use the
model to write a system of linear equations. How many problems
do you have in each subject?

Given:

[tex]f(x)[/tex] is continuous, [tex]f(3)=1,f(1)=6,f(6)=-2,f(-2)=3[/tex].

To find:

The value of [tex]\lim_{x\to 6^+}f(x)[/tex] and [tex]\lim_{x\to -2^-}f(x)[/tex].

Solution:

If a function f(x) is continuous at [tex]x=c[/tex], then

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

It is given that the function [tex]f(x)[/tex] is continuous. It means it is continuous for each value and the left-hand and right-hand limits are equal to the value of the function.

The function is continuous for 6. So,

[tex]\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)[/tex]

[tex]\lim_{x\to 6^+}f(x)=f(6)[/tex]

[tex]\lim_{x\to 6^+}f(x)=-2[/tex]

The function is continuous for -2. So,

[tex]\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)[/tex]

[tex]\lim_{x\to -2^-}f(x)=f(-2)[/tex]

[tex]\lim_{x\to -2^-}f(x)=3[/tex]

Therefore, [tex]\lim_{x\to 6^+}f(x)=-2[/tex] and [tex]\lim_{x\to -2^-}f(x)=3[/tex].

Answer:

ddXvffggf

Step-by-step explanation:

vvzgsgygsv gdhvsysgvs gsvysvvs6sg he's) v gateways tsgsyysgd Yacc subs USB GA t gsd

Answer:

-1.833 ; we do not reject the Null.

Pvalue = 0.0409 ; We do not reject the Null

There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13

Step-by-step explanation:

H0 : μ = 13

HA : μ < 13

Test statistic :

(xbar - μ) ÷ s/sqrt(n)

(12.8 - 13) ÷ 0.5/sqrt(21)

-0.2 / 0.1091089

= - 1.833

The critical value at α = 0.01 ; df = 21 - 1 = 20 = 2.528

-1.833 > - 2. 528 (left tailed test) ; Hence we do not reject the Null.

Test statistic :

Pvalue from Test statistic at DF = 20 ; α = 0.01

Pvalue = 0.0409

Pvalue > α

0.0409 > 0.01 ; Hence, we do not reject H0.

There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13

Answer:

the area is 50

Step-by-step explanation:

Answer:

its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs

Answer:

If you share 7 apples equally with 3 people, then there are 2 1/3 apples per person.

The number 2 represents the number of whole apples each individual gets.

The denominatior, 3, represents how many times an apple will have to be split to divide equally

The numerator, 1, represents how many 3rds each person gets.

Answer:

117.8097 [tex]in^{2}[/tex]

Step-by-step explanation:

Depending on how you're math is going there are two ways to solve this,  find the are by the arc or just figure out the whole cookie and divide by 6.   Let's try the latter is seems easier to say.    I mean easier for me to say.  

area of a circle is pi * r^2

the diameter is 30 inches so the radius is half of that or 15 inches

then the whole cookie is

pi*15^2 = 706.858 [tex]in^{2}[/tex]

now divide by 6 or each piece

706.858 [tex]in^{2}[/tex] / 6 = 117.8097 [tex]in^{2}[/tex]

now eat your cookie  :p  

Answer:

x=12

Step-by-step explanation:

Using angle sum property

[tex]\\ \sf\longmapsto x+43+73+70=180[/tex]

[tex]\\ \sf\longmapsto x+43+143=180[/tex]

[tex]\\ \sf\longmapsto x+186=180[/tex]

[tex]\\ \sf\longmapsto x=180-186[/tex]

[tex]\\ \sf\longmapsto x=-6[/tex]

Option C is correct

Sum of angles of any triangle is 180°

Option C

Answer:

bro that is easy its 15*1/2

Step-by-step explanation:

Answer:

The inverse is  

y =  1 /3 x  −  2 /3

Step-by-step explanation:

Answer:

12 minutes

Step-by-step explanation:

The Hot tap fills 1/30th of the bath in 1 minute. The cold tap fills 1/20th of the bath in one minute. In one minute both taps together will fill (1/30 + 1/20) of the bath, which is 5/60ths or 1/12th of the bath. Since it takes one minute to fill 1/12th of the bath, it’ll take 12 minutes to fill the bath

Answer: [tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]

Step-by-step explanation:

Given

Function is  [tex]f(x)=mx+b[/tex]

[tex]f(-2)=3[/tex]

[tex]\therefore 3=m(-2)+b\\\Rightarrow b-2m=3\quad \ldots(i)[/tex]

[tex]f(4)=1\\\therefore 1=4m+b\quad \ldots(ii)[/tex]

from (i) and (ii) we get

[tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]

Answer:

Volume=[tex]4x^3-44x^2+112x[/tex]

Step-by-step explanation:

Let x denotes the length of the side of each cut

After Cutting square length will be=8-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)

After cutting square width will be=14-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)

Height = x

Volume=Length*width*Height

Volume=(8-2x)*(14-2x)*x

On solving we will get:

Volume=[tex]4x^3-44x^2+112x[/tex]

Answer:

40

Step-by-step explanation:

This is asking you to plug in the value of h(5) into g(x). First solve for h(5)

x^2-3 = h(x)

5^2-3= 22

h(5) = 22

h(5) is 22. So now, plug that into g(x).

g(h(5)) = 2(22)-4

44-4=40

(g.h)(5) is 40.

Answer:

$46.08

Step-by-step explanation:

Hi,

She gets 48 (1.35) when she sells 48 muffins. That equals 64.8.

But she pays 48 (.39) to make them. That equals 18.72.

64.8 - 18.72 = 46.08

She makes $46.08

I hope this helps :)

Answer:

9

Step-by-step explanation:

9514 1404 393

Answer:

  270 miles

Step-by-step explanation:

For h hours of driving the distance d is covered:

  h = 2 +d/54

Solving for d, we find the distance covered in h hours is ...

  d = 54(h -2)

In 7 hours, the distance they traveled is ...

  d = 54(7 -2) = 270 . . . miles

They traveled 270 miles on the first day.

Answer:

300cm

Step-by-step explanation:

scale 1:200 means 1cm on drawing represent 200cm on ground so 15cm will be 15×200 which is 3000cm

9514 1404 393

Answer:

  1. attendance (y), time (x)

  2. 1,2: increasing; 3: constant; 4: decreasing

  3. attendance increases, remains constant, then decreases

  4. increasing; pre-heating the oven

Step-by-step explanation:

It is always difficult to read the mind of the author of questions like these. Usually, specific wording is expected. If your curriculum material has examples you can copy from, you should do that.

__

1. The variables and what they stand for are listed on the axes of the graph. The y-variable stands for attendance. The x-variable stands for time. It isn't clear whether the desired answer is "y and x" or "attendance and time".

__

2. The graph slopes upward in intervals 1 and 2. It can be described as "increasing."

The graph remains level in interval 3. It can be described as "constant."

The graph slopes downward in interval 4. It can be described as "decreasing."

__

3. The attendance is adequately described in question 2. Attendance increases, remains constant, then decreases. It isn't clear how general or specific the answer is supposed to be.

__

4. The graph of the function is "increasing." We don't know if the indicated temperature is the temperature of the bread, the oven, or the room containing the oven. If we assume the indicated temperature is that of the oven, we expect an increase during the oven pre-heat interval.

If the indicated temperature is that of the bread, then the increase would be following insertion of the bread into the oven.

Answer:

0.4% or in decimal form 0.004

Step-by-step explanation:

took the test and got it right!

Answer:

d ≈ 45 ft

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Define

Circumference C = 141.3 ft

Step 2: Solve for d

Answer:

x(2x+3)

Step-by-step explanation:

Answer:

X= -2

2. x = 1/2 = 0.500

Step-by-step explanation:

Answer:

it is 36 inches

Step-by-step explanation:

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.

  x = 16/4

  x = 4