A linear function and an exponential function are shown below.

Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?

Answer:

Step-by-step explanation:

=> x + 3x + 3y + 3z = 21

=> 4x + 3y + 3z = 21

=> 4x + 3y + 3z - 3y = 21 - 3y

=> 4x + 3z = 21 - 3y

=> 4x + 3z - 3z = 21 - 3y - 3z

=> 4x = 21 - 3y - 3z

[tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]

[tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]

Given :

To Find :

Solution :

[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]

Adding the like terms :

[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]

Transposing 3y to the other side which then becomes negative :

[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]

Now, Transposing 3z to the other side which then becomes negative :

[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]

Dividing both sides by 4 :

[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]

Therefore, the value of x = 21 – 3y – 3z/4

Answer:

14,001

Step-by-step explanation:

old machine: 1,100+.12x

new machine: 1,520+.09x

if you plug in 14,000 for x, you get

old machine: 2,780

new machine: 2,780

therefore, you need 1 over 14,000 for it to be worth it because

if you plug in 14,001 for x, you get

old machine: 2,780.12

new machine: 2,780.09

which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)

hope this helps!

Answer:

C 43

Step-by-step explanation:

happy holidays

Answer:

Since the two triangles are similar, the two medians AC and FH are in proportion. The proportionality rate is [tex]k=\frac{48}8=6[/tex]. That is the same ratio of the sides., so AD is k times the corresponding side FG, or [tex]\overline {AD} = k\overline{FG} = 6\times 9 = 63[/tex]

[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation:

Answer:

use pemdas(order of the operations)and you'll get the answer 27!!

Step-by-step explanation:

[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]

Answer: It is D

Step-by-step explanation:

Answer:

255,340,000(1.61)= $411097400

Step-by-step explanation:

multiply the total amount of bottles by $1.61, since it costs $1.61 per bottle.

Answer:

carbon take x(1)+4(-2)=0

x(1)-8=0

x(1)=8

x=8

[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]

[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]

Answer:

$8x + $12y = $120

Step-by-step explanation:

x = amount of juice

y = amount of pizza

$120 = his total money

Answer:

I’d say 84.68%

Answer:

Step-by-step explanation:

Parallel lines have identical slopes

y = 3x + b

add in the desired point

10 = 3(2) + b

b = 4

B.  y = 3x + 4

Answer:

Definetly t = 4n

Step-by-step explanation:

OK so

Tomatoes = 2 3/8 = 19/8 (turned into improper fraction)

Asparagus = 1 1/4 =5/4

Potatoes = 2 7/8 = 23/8

Total vegetables used =

19/8 + 5/4 + 23/8 = 42/8 + 5/4 = 42+10/8 =52/8

Answer is 52/8 = 6.5

Answer : 52/8 pounds were used altogether

See picture for solution.

Answer:

See below

Step-by-step explanation:

Dilation of 4

Z (0, -1) Z' (0, -4)

X (1, -1) X' (4, -4)

Answer:

WT = 63

Step-by-step explanation:

Given Δ SDE is similar to Δ SWT then the ratio of corresponding sides are in proportion, that is

[tex]\frac{WT}{DE}[/tex] = [tex]\frac{ST}{SE}[/tex] , substitute values

[tex]\frac{5x+3}{56}[/tex] = [tex]\frac{4x-3}{40}[/tex] ( cross- multiply )

56(4x - 3) = 40(5x + 3) ← distribute parenthesis on both sides

224x - 168 = 200x + 120 ( subtract 200x from both sides )

24x - 168 = 120 ( add 168 to both sides )

24x = 288 ( divide both sides by 24 )

x = 12

Then

WT = 5x + 3 = 5(12) + 3 = 60 + 3 = 63

Answer:

15.7 cm to nearest 10th

Step-by-step explanation:

Circumference = 2 pi r = 2 pi 2.5

= 5 * pi

= 15.708 cm.

So basically what you have to do is first identify all of the sides or angles that equal eachother then you can see if you did a side side and side in a row etc, like 44 would be SAS because the vertical angles would be inbetween the two sides. 46 would be SSS because after you make the line in the middle for reflexive property you can see that there are three sides in a row. If this didnt help i recommend looking on Khan Academy

Answer:

Freezer B has 8 more cubic feet than Freezer A.

Step-by-step explanation:

Volume of Freezer A = 8 * 4 * 2 = 64 ft^3.

Volume of Freezer B = 6 * 4 * 3 = 72 ft^3.

72 - 64 = 8 ft^3.

Answer:

Freezer B has 8 more cubic feet than Freezer A.

Step-by-step explanation:

Answer:

(cotA − 1) (cotB − 1) = 2

Step-by-step explanation:

A+B= π/4 = 180°/4 = 45°

A+B=45°

∴ cot(A+B)=cot45°

∴ cotBcotA−1 / (cotB+cotA) = 1

⇒cotB + cotA = cotBcotA = 1

⇒cotB + cotA − cotBcotA + 1 = 0

⇒cotBcotA − cotB − cotA − 1 = 0

⇒cotBcotA − cotB − cotA − 1 + 2 = 0+2

⇒cotBcotA − cotB − cotA + 1 = 2

⇒cotB(cotA − 1) (cotA − 1) = 2

⇒(cotA − 1) (cotB − 1) = 2

Proved

Answer:

1) -3/4

2) (6, 0), (0, -4)

3) connect (0,-2) and (8,0) together

Step-by-step explanation:

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

2) x = 0 -3y=12 y = -4, y= 0 2x =  12 x = 6, x intercept = (6, 0) y intercept = (0, -4)

3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line

#1

#2

Inetercept form x/a+y/b=1

x inetercept at 6 and y intercect at -4

#3

Graph attached

Answer:

Look at images below ^^

Step-by-step explanation:

I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.

Answer:

y=7

Step-by-step explanation: