raise each side of the equation as the power of the base of the log, 0.98 = log x

Answer:

[tex]\large\boxed{f(x)-g(x)=x^2-4x+13}[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2-4x-3\\\\g(x)=(x-4)(x+4)=x^2-4^2=x^2-16\qquad\text{used}\ a^2-b^2=(a-b)(a+b)\\\\f(x)-g(x)=(2x^2-4x-3)-(x^2-16)\\\\=2x^2-4x-3-x^2-(-16)\\\\=2x^2-4x-3-x^2+16\qquad\text{combine like terms}\\\\=(2x^2-x^2)-4x+(-3+16)\\\\=x^2-4x+13[/tex]

Answer:

A: Day 6

B: 8196 grams (He will become obese for sure)

Step-by-step explanation:

Part A:

As you can infer from the problem, Ali halves his bar everyday, regardless of how the bar is.

Day 1= 32 grams left

Day 2= 16 grams left

Day 3= 8 grams left

Dat 4= 4 grams left

Day 5= 2 grams left

Day 6=1 gram left

He will have one gram left on Day 6

Part B:

This part is basically vice versa. Instead on halving, we need to be doubling. I will do Part a in reverse until Day 14 comes

Day 1= 1

Day 2= 2

Day 3= 4

Day 4= 8

Day 5= 16

Day 6= 32

Day 7 = 64

Day 8= 128

Day 9= 256

Day 10= 512

Day 11= 1024

Day 12= 2048

Day 13= 4096

Day 14= 8192

He will need 8192 grams of chocolate!!!

The number of days when he has only 1 gram left will be 6. And the chocolate needs to weigh to last All 14 days will be 1/256 grams.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

Ali has a 64 grams bar of chocolate.

On day 1 he eats half of his chocolate.

And on day 2 he eats half of what is left.

He does the same each day.

Then the value of a is 64 grams and b is 1/2.

y = 64 · (1/2)ⁿ

Where n is the number of days.

The number of days when he has only 1 gram left will be

1 = 64 · (1/2)ⁿ

1/64 = (1/2)ⁿ

(1/2)⁶ = (1/2)ⁿ

n = 6

The number of days when he has only 1 gram left will be 6.

The chocolate needs to weigh to last All 14 days will be

y = 64 · (1/2)¹⁴

y = 64 · (1/16384)

y = 1/256 grams

The chocolate needs to weigh to last All 14 days will be 1/256 grams.

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Answer:

the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]

Step-by-step explanation:

We need to find the simplifies form of

[tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex]

We need to find product of above terms

We can write as

[tex](7*7)(\sqrt{x^5}*\sqrt{x^5})\\(7^2)((\sqrt{x^5})^2)\\49\,x^5[/tex]

So, the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]

Answer:

Simply Put:

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 200 and 350 is 50

Divide both terms by the GCF, 50:

200 ÷ 50 = 4

350 ÷ 50 = 7

The ratio 200 : 350 can be reduced to lowest terms by dividing both terms by the GCF = 50 :

200 : 350 = 4 : 7

Therefore:

200 : 350 = 4 : 7

Step-by-step explanation:

Answer:

B.4

Step-by-step explanation:

1.5(x+4) - 3 = 4.5( x-2)-----------------------open brackets on both sides

1.5 x +6 -3= 4.5x- 9.................................collect like terms

3+9 = 4.5 x- 1.5x

12=3x..................................divide by 3 both sides to get x

12/3=x

x=4

ANSWER

x=4

EXPLANATION

The given equation is

[tex]1.5(x + 4) - 3= 4.5(x - 2)[/tex]

Multiply through by 10

[tex]15(x + 4) - 30= 45(x - 2)[/tex]

We expand to get:

[tex]15x + 60 - 30= 45x - 90[/tex]

Group similar terms to get;

[tex]15x - 45x = - 90 - 60+ 30[/tex]

[tex] - 30x = - 120[/tex]

[tex] x= 4[/tex]

The conversion from 2000 Swiss francs to Dutch guilders requires a historical exchange rate which is not provided. The Dutch guilder is obsolete since 2002, and precise conversions cannot be made without the rate from the time period when both currencies were in use.

To convert 2000 Swiss francs to Dutch guilders, you would need to know the specific exchange rate between the Swiss franc and the Dutch guilder at the time of the conversion. Unfortunately, as of today, the Dutch guilder is no longer in use, as the Netherlands adopted the euro as its currency in 2002. However, if you were to convert currencies similar to how holders of dollars are willing to exchange $2,500 for euros or vice versa, you would need the specific exchange rate from Swiss francs (CHF) to Dutch guilders (NLG) during the time when both currencies were in use.

Without historical exchange rate data, it is impossible to provide an exact number of Dutch guilders you would receive for 2000 Swiss francs. If you have a specific date in mind, you could find the historical exchange rate for that date and then calculate the conversion using this formula:

Amount in Swiss francs * Exchange rate (CHF to NLG) = Amount in Dutch guilders

Remember, when performing historical currency conversions, it's essential to use the correct exchange rate from the time period in question.

Answer:

Clara's body eliminated the antibiotic at the same rate as Heidi's body.

Answer:

Option. B is the answer.

Step-by-step explanation:

Clara is taking a medicine for a common cold. Table that shows the amount f(t) that was present in Clara's body after time t is

t (hours)      1             2           3            4             5

f(t) (mg)   236.5   223.73   211.65    200.22   189.41

Now we will find the explicit formula of geometric sequence.

f(1) = 236.5

and f(2) = 223.73

Therefore, common ratio of the sequence = [tex]\frac{f(2)}{f(1)}=\frac{223.73}{236.5}[/tex]=0.946

So the equation will be f(t) = [tex]236.5(0.946)^{t}[/tex]------(1)

At the same time Heidi was administered 300 mg of same medicine of the same sample.

Amount of medicine in her body f(t) after time t is shown by the equation

f(t) = [tex]300(0.946)^{t}[/tex]----(2)

By comparing these equations 1 and 2, we find common ratio is same as (0.946), which reflects the rate of elimination of the antibiotic was same for both Clara and Heidi.

Option B is correct.

Answer:

general, factored, and vertex form.

general: y=ax^2+b^2+c

Factored: y=(x+a)(x+b)

Vertex: y=a(x-h)^2+k

Step-by-step explanation:

Answer:

x = 5/6 , y = 8/5

Step-by-step explanation:

Solve the following system:

{12 x + 15 y = 34 | (equation 1)

{5 y - 6 x = 3 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{12 x + 15 y = 34 | (equation 1)

{0 x+(25 y)/2 = 20 | (equation 2)

Multiply equation 2 by 2/5:

{12 x + 15 y = 34 | (equation 1)

{0 x+5 y = 8 | (equation 2)

Divide equation 2 by 5:

{12 x + 15 y = 34 | (equation 1)

{0 x+y = 8/5 | (equation 2)

Subtract 15 × (equation 2) from equation 1:

{12 x+0 y = 10 | (equation 1)

{0 x+y = 8/5 | (equation 2)

Divide equation 1 by 12:

{x+0 y = 5/6 | (equation 1)

{0 x+y = 8/5 | (equation 2)

Collect results:

Answer:  {x = 5/6 , y = 8/5

Answer:

B. Similar

D. Same Shape

Step-by-step explanation:

In the given triangles:

∠A ≅ ∠D = 22°

∠B ≅ ∠E = 120°

∠C ≅ ∠F = 38°

Hence using the AAA axiom of geometry

Triangle ABC and DEF are similar.

More over due to the similarity of angles the triangles also have same shape.

One more thing, that can be observed is that

DE = 2* AB

EF = 2*BC

DF = 2*AC

The sides of triangle ABC are scaled with a factor of 2 which makes it similar to DEF ..

Hence,

Option B and Option D are correct ..

Answer with explanation:

Given two triangles ΔABC and ΔDEF

 ⇒Ratio of Sides

[tex]\rightarrow \frac{AB}{DE}(\frac{5}{10})=\frac{BC}{EF}(\frac{3}{6})=\frac{AC}{DF}(\frac{7}{14})=\frac{1}{2}[/tex]

⇒Comparison of Angles

→∠A=∠D=22°

→∠B=∠E=120°

→∠C=∠F=36°

⇒As length of corresponding sides are Proportional ,as well as corresponding Angles of two triangles are same.So Two Triangles are similar either by SSS Similarity or AA Similarity or S AS Similarity.

→If Triangles are similar then they are congruent also.

→The description which accurately describe the relationship between ΔABC and ΔDEF is:

→ Option B: Similar

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= - 4x² - 6x - 1 + (- x² - 5x + 3) ← remove parenthesis

= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms

= - 5x² - 11x + 2 → C

Answer:

The angular velocity of Earth is π/12 radians per hour.

The angular velocity of Earth is 2π radians per day.

Step-by-step explanation:

A full circumference of a circle (as the Equator line on Earth) is 2π radians.

Since the planet does a full revolution in 24 hours... that means it makes a full turn in a day.

So, we can see that in a day, the planet rotates 360 degrees... or 2π radians per day!

Now, if you want to find the angular velocity per HOUR... you divide that by 24... so  2π/24 = π/12 radians

So, we can also say it does π/12 radians per hour.

Answer:

a and d on ed

Step-by-step explanation:

Answer:

$44,800

Step-by-step explanation:

Original salary : $40,000

12% of original salary = 12% x 40,000 = 0.12 x 40,000 = $4,800

New salary = $40,000 + $4,800 = $44,800

Answer:

20 pts

Step-by-step explanation:

50 points corresponds to a 100% grade.  How many points (x) correspond to a 40% grade?

     x            40%

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

50 pts       100%

Then 100x = 2000, and so x = 20.

A score of 20 points would correspond with a test score of 40%.  

Answer:

A score of 20 points would correspond with a test score of 40%.  

Step-by-step explanation:

    x            40%           How many points (x) correspond to a 40% grade?

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

50 pts       100%          50 points corresponds to a 100% grade.  

100x = 2000                divide both sides by 100

x = 20

Answer:

The perimeter of the rectangle is 10 + 2x.

Step-by-step explanation:

The formula for the perimeter of a rectangle is 2(l + w) where l = length and w = width because you add up the length of all the sides.

So we can plug in our givens into the formula and simplify:

2(5 + x)

So the perimeter is: 10 + 2x

Notice that we cannot simplify the expression further because there is an unknown (the length).

Answer:

2x + 10

Step-by-step explanation:

A rectangle has opposite sides equal

2(5 + x)

2x + 10

Use two pints on the graph to find the slope:

(0,0) and (5,1)

Slope = Change in Y over the change in x.

Slope = (1-0) / (5-0) = 1/5 = 0.20

The slope of the given equation is 0.25 which is greater than 0.20.

The unit rate is greater in the equation.

Answer:

y = - 5x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = - 5 and b = - 7, hence

y = - 5x - 7 ← equation of line

Since b equals the y-intercept, we automatically know that the answer will be in slope-intercept form which is y = mx + b where m equals slope and b equals the y-intercept.

Given.

m = –5, b = –7

Slope intercept formula.

y = mx + b

Plug in m = -5 and b = -7.

y = -5x - 7 ← Choice C

Answer:

Step-by-step explanation:

Two lines that are parallel have the same slope but different y intercepts.

So you could have any equation that satisfies y = 8x + b. The only value that b cannot have is 7. All other values including 0 are fine.

So here are a couple of examples.

y = 8x     b = 0

y = 8x + 92

y = 8x + 1/2

y = 8x + pi

y = 8x - 13

7 = 8x - pi

Answer:

Many possible answers, including

Major Arc: JKM

Minor Arc: JM

Step-by-step explanation:

The answers you selected in this photo are correct. But let's see why.

A major arc is an arc that is bigger than a minor arc.

They are defined using a starting point and an ending point.  In this case, you have many reference points (J, K, L and M), and none is identified in the question.  However, the answers shown indicate they're using point J as starting point and M as ending point.

If you look at the positions of J and M on the diagram, you see you can take two routes to join them... the shortest route is the minor arc (going counter-clockwise direction from J to M).  While the other route, going clockwise passes through the points K and L is much longer.... and forms the major arc.

That major arc could be identified as JKM, JLM or JKLM, since it starts at J, ends in M, but passes through points K and L, in that order.

Answer:

38.68        

Step-by-step explanation:

First we need to find the markdown

markdown = original price * markdown rate

               = 45.50 * 15%

               = 45.50 * .15

               = 6.825

Then we need to find the sale price  

sale price = original price- markdown

                = 45.50 - 6.825

                =38.675

Rounding to the nearest cent

               = 38.68

The sale price is 38.68          

Answer:

8, 36, 81, 11, 7, 1000

Step-by-step explanation:

A

Lets start with number one.

x^2 = 64.

That means that x times x equals 64.

To find x's value, simply find the square root of 64, which is 8.

So x = 8.

For the second one, the square root of x is 6.

That means that 6 x 6 = x

6 x 6 = 36.

So, x = 36.

B

For the third one, the square root of x is 9.

That means that 9 x 9 = x

9 x 9 = 81

So, x = 81.

For the fourth one, x^2 = 121

That means x times x = 121

To find x's value, simply find the square root of 121, which is 11

So, x = 11.

C

For the fifth one, x^3 = 343.

That means that x times x times x = 343

To find x's value, simply find the square root of 343, which is 7.

So, x = 7.

For the sixth and last one, the cube root of x is 10.

That means 10 x 10 x 10 = x.

10 x 10 x 10 = 1,000

So, x = 1,000

I hope this helps! :)

Answer: Infinitely Many Solutions

Step-by-step explanation:

Substitute y into the second equation:

2(-2x-6)=-4x-12

Then you get -4x-12=-4x=-12. Since this is 0=0 it would make it infinitely many solutions.

There are infinitely many solutions to the given system. The equations in the system are y = -2x - 6 and 2y = -4x - 12.

For a system of linear equations, there are three types of solutions. They are,

Infinitely many solutions are there for a system if they both are equal on both sides while solving. (their graphs intersect at all the points)

Given the system of equations as

y = -2x - 6

2y = -4x - 12

Using substitution method, substituting first equation into the second equation,

2( -2x -6) = -4x - 12

⇒ -4x -12 = -4x - 12

Thus, both sides are equal, and the given system has infinitely many solutions.

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Answer:

x>-18

Step-by-step explanation:

Answer:

Step-by-step explanation:

The easiest to solve for is y in the second equation.   Just subtract 3x from both sides, obtaining y = -3x + 9.

The value of x = 1 and y = 6. The easiest to solve for is y in the second equation.

Let the equations be

2x + 4y = 26 ......(1)

3x + y = 9 ........(2)

From (2), we get

3x + y = 9

y = -3x + 9 .......(3)

then substitute the value of y in (1), then we get

2x + 4y = 26

2x + 4(-3x + 9) = 26

Simplifying the above equation, we get

2x - 12x + 36 = 26

-10x + 36 = 26

-10x = 26 - 36

-10x = -10

Then the value of x = 1

Substitute the value of x in (3), then we get

y = -3x + 9

Simplifying the equation, we get

y = -3(1) + 9

y = -3 + 9

y = 6

The value of x = 1 and y = 6.

Therefore, the correct answer is option (d) The easiest to solve for is y in the second equation.

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Answer:  The correct options are

(A) DEF.

(C) FED.

Choices:

A. DEF B. DFE C. FED D. EFD

Answer:

FED and DEF

Step-by-step explanation:

vertex is the middle letter

Follow below steps;

The probability of drawing a blue marble from the bag:

Calculate the total number of marbles in the bag: 3 red + 4 white + 5 blue = 12 marbles.

Calculate the probability of drawing a blue marble: Number of blue marbles / Total number of marbles = 5 / 12 = 5/12.

Answer:

C≈37.7 or 36

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

2x3.14x6=36

Step-by-step explanation:

Answer:

(5,0) and (5,-2)

Step-by-step explanation:

we know that

If two points are on the line x=5, then the x-coordinates of the points must be equal to 5

therefore

The coordinates of two points that are on the line x=5 are

(5,0) and (5,-2)

[tex](f-g)(x)=3x+10-(2x-4)=3x+10-2x+4=x+14[/tex]