Solve for x: 2 over 5 (x − 4) = 2x. (1 point)

The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).

Step-by-step explanation:

Given Equation:

           [tex]\log _{x} 36=2[/tex]

As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:

           [tex]b^{y}=a[/tex]

Then, the base b logarithm of x is equal to y

           [tex]\log _{b}(x)=y[/tex]

Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,

            [tex]b^{y}=a[/tex]

            [tex]x^{2}=36[/tex]

When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]

Answer:D

Step-by-step explanation:

i got it right

Answer:

The food at the fast food restaurant of chicken nuggets is  having higher unit price.

Step-by-step explanation:

Given:

A fast food restaurant had 5 boxes of chicken nuggets for $33.95.

A competing restaurant had 4 boxes of chicken fingers for $26.96.

Now, to get the food which has a higher unit price.

So, to get the unit price we use unitary method:

In, a fast food restaurant:

5 boxes of chicken nuggets cost for = $33.95.

Thus, 1 box of chicken nuggets cost for = [tex]\$33.95\div 5 = \$6.79.[/tex]

In a competing restaurant:

4 boxes of chicken fingers cost for = $26.96.

Thus, 1 box of chicken fingers cost for = [tex]\$26.96 \div 4 = \$6.74.[/tex]

Now, as comparing the prices of both restaurant the price of chicken nugget in fast food restaurant is $6.79 per box which is higher than the price of chicken fingers cost of $6.74 per box in competition restaurant.

Therefore, the food at the fast food restaurant of chicken nuggets is  having higher unit price.

Answer:

[tex]105.84\ cm^2[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=21.2/2=10.6\ cm[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (10.6)^{2}[/tex]

[tex]A=112.36\pi\ cm^2[/tex]

step 2

Find the area of a sector

Remember that

The area of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector with a central angle of 108 degrees

[tex]\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]33.708(3.14)=105.84\ cm^2[/tex]

Answer: 12 small candles and 16 large candles.

Step-by-step explanation:

Notice that an small candle costs $4 and a large candle costs $6.

Let be "s" the number of small candles you sold and "l" the number of large candles you sold.

Set up a System of equations:

[tex]\left \{ {{4s+6l=144} \atop {s+l=28}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the second equation by -4.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{4s+6l=144} \atop {-4s-4l=-112}} \right.\\.......................\\2l=32\\\\l=16[/tex]

- Substitute the value of "l" into the second equation and solve for "s":

[tex]s+16=28\\\\s=12[/tex]

Answer:

The number of each coin she have are 17 dimes and 14 nickels.

Step-by-step explanation:

Given:

A coin collector has 31 dimes and nickels with a total face value of $2.40.

Now, to find each does she have.

Let the number of dimes be [tex]x[/tex].

Let the number of nickels be [tex]y[/tex].

So, total number of coins are:

[tex]x+y=31[/tex]

[tex]x=31-y.............(1)[/tex]

Value of a dime = 10 cents

Value of a nickel = 5 cents

Total face value = 240 cents

(1$ = 100 cents.  $2.40×100 =240 cents)

Now, total value of coins:

[tex]10x+5y=240[/tex]

Putting the equation (1) in the place of [tex]x[/tex]:

[tex]10(31-y)+5y=240[/tex]

[tex]310-10y+5y=240[/tex]

[tex]310-5y=240[/tex]

Moving variables on one side and the numbers on other:

[tex]310-240=5y[/tex]

[tex]70=5y[/tex]

Dividing both sides by 5 we get:

[tex]14=y[/tex]

The number of nickels = 14.

Now, putting the value of [tex]y[/tex] in equation (1) we get:

[tex]x+y=31[/tex]

[tex]x+14=31[/tex]

Subtracting both sides by 14 we get:

[tex]x=17.[/tex]

The number of dimes = 17.

Therefore, the number of each coin she have are 17 dimes and 14 nickels.

Answer:

y-5=4(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=4(x-(-3))

y-5=4(x+3)

The bug's speed is approximately 5.33 meters per minute, which is closest to option (2).

To find the bug's speed in meters per minute, we need to convert its speed from inches per second to meters per minute.

First, let's convert the bug's speed from inches per second to inches per minute:

[tex]\[3.5 \text{ inches per second} \times 60 \text{ seconds per minute} = 210 \text{ inches per minute}\][/tex]

Now, let's convert inches to meters:

[tex]\[210 \text{ inches} \times \frac{2.54 \text{ centimeters}}{1 \text{ inch}} \times \frac{1 \text{ meter}}{100 \text{ centimeters}} = 5.33 \text{ meters per minute}\][/tex]

So, the bug's speed is closest to option (2) 5.33.

Complete Question:

There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then which of the following is closest to its speed in meters per minute?

(1) 3.86

(3) 6.25

(2) 5.33

(4) 7.19

Answer:

4/15 cocoa would be left if we made cookies

Step-by-step explanation:

4/6- 2/5

= 4(5)- 2(6)/30

= 20-12/30

=8/30

=4/15

After making the cookies using 2/5 cup of cocoa from the initial 4/6 cup, you would subtract 12/30 cup from 20/30 cup to find that you would have 4/15 cup of cocoa left.

To determine how much cocoa you would have left after making the cookies using 4/6 cup of cocoa and using 2/5 cup for the recipe, you would need to subtract the amount used from the initial amount. To perform the subtraction, you first need to have the quantities expressed with a common denominator. The least common denominator for 6 and 5 is 30.

Convert 4/6 cup to an equivalent fraction with a denominator of 30: (4 × 5) / (6 × 5) = 20/30 cup.

Convert 2/5 cup to an equivalent fraction with a denominator of 30: (2 × 6) / (5 × 6) = 12/30 cup.

Now you can subtract the amount of cocoa used for the cookies from the total amount you have:

Remaining cocoa = Initial amount - Amount used = 20/30 cup - 12/30 cup.

Remaining cocoa = (20 - 12) / 30 = 8/30 cup of cocoa.

To simplify this, divide both the numerator and denominator by their greatest common divisor, which is 2:

Remaining cocoa = 4/15 cup. So you would have 4/15 cup of cocoa left after making the cookies.

Answer:

y=1/2x-5/4

Step-by-step explanation:

y=2x+5/2

x=2y+5/2

2y=x-5/2

y=1/2x-(5/2)/2

y=1/2x-(5/2)(1/2)

y=1/2x-5/4

Answer:

405.224

Step-by-step explanation:

Answer:

It's B.

Step-by-step explanation:

Have a good day.

Answer:

x-intercept - x = 1/2y - 3.15

y-intercept - y = 2x + 6.3

Step-by-step explanation:

For x,

-6x + 3y = 18.9

-6x = -3y + 18.9

x = -3y/-6 + 18.9/-6

x = 1/2y - 3.15

For y,

-6x + 3y = 18.9

3y = 6x + 18.9

y = 6x/3 + 18.9/3

y = 2x + 6.3

Answer:

The number of weeks Marla will take to paint all the pots is  5 weeks and 3 days .

Step-by-step explanation:

Given as :

The number of pots Marla will paint = 48 pots

The number of pots she plans to paint each week = 9 pots

Let The number of weeks Marla needs to paints all pots = n weeks

Now, According to question

The number of weeks = [tex]\dfrac{number of pots Marla will paints}{\textrm The number of pots Marla will paints each week}[/tex]

Or , n = [tex]\dfrac{48}{9}[/tex]

∴ n = 5.3

So The number of weeks =  n = 5 weeks and 3 days

Hence The number of weeks Marla will take to paint all the pots is  5 weeks and 3 days . Answer

Answer:

32 cars

Step-by-step explanation:

we know that he can paint 12 cars in 3 weeks.

that means that he can paint 4 cars per week.

4cars x 8weeks = 32 cars in 8 weeks

Answer:

Step-by-step explanation:

12 cars in 3weeks

Then in 1week he will paint= 12/3 car

= 4 cars

so in 8weeks = 4 × 8 cars

= 32cars

Answer:

None. Wanda's work is correct.

Step-by-step explanation:

The first is correct.

Answer:

Wanda converted the percent to a decimal incorrectly. It should be 0.73

Step-by-step explanation:

It has to be move two decimal place.

The student is probably asking about the cube root function multiplied by 3, which is an increasing function and is defined for all real numbers, including negative values.

The phrase 'f(x)=3 square root x' seems to be a typo. Assuming this refers to the cube root function, such as 'f(x) = 3 √x,' then this function represents the cube root of 'x' multiplied by 3. To graph this function, start by plotting points, taking the cube root of various values of 'x' and scaling these by 3.

The graph will pass through the origin and rise less steeply than a linear function; it will be an increasing function for all 'x' as the cube root of a real number is always real. This also means that the function will be defined for all real numbers, including negatives, as cubing can produce both positive and negative results.

The solution for y in 2x − 5y ≤ 15  is [tex]y \geq \frac{2x}{5} - 3[/tex]

Solution:

Given that we have to find solution for given inequality for y

2x − 5y ≤ 15

Let us solve above equation for "y"

[tex]2x - 5y \leq 15[/tex]

Add -2x on both sides

[tex]-2x + 2x - 5y\leq 15 - 2x\\\\-5y \leq 15 - 2x[/tex]

Divide by -5 on both sides

Remember that You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number, we must flip the sign

[tex]\frac{-5y}{-5} \geq \frac{15}{-5} - \frac{2x}{-5}\\\\y \geq -3 + \frac{2x}{5}\\\\y \geq \frac{2x}{5} - 3[/tex]

Thus solution for "y" is found

Answer:

b

Step-by-step explanation:

Answer:

121x2 + 36y2

Step-by-step explanation:

= (4x + 4)(x + 1)

= 4(x + 1)(x + 1)

= 4(x + 1)2 and is hence the fully factored form

not sure bout the rest though...... it may have mistakes in the question forms.

Polynomials given to us can be factored except 121x² + 36y²,

so we can say that 121x² + 36y² is factored completely.

Factorization of a polynomial is the method by which we write the given polynomial as a product of two or more factors, which when multiplied gives back the same Polynomial.

We will analyze all the given polynomial.

∴ After checking all the options, we can say that 121x² + 36y² was completely factored.

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Answer: 700 adults and 1500 children

Step-by-step explanation:

Let the number of adults be x and the number of children be y , then

x + y = 2200 ........................... equation 1

4x + 1.5y = 5050 ............................ equation 2

solving the system of linear equation by substitution method , from equation 1 make x the subject of the formula , that is

x = 2200 - y ....................... equation 3

substitute x = 2200 - y into equation 2 , that is

4 ( 2200 - y ) + 1.5y = 5050

8800 - 4y + 1.5y = 5050

8800 - 2.5y = 5050

2.5y = 8800 - 5050

2.5y = 3750

y = 3750/2.5

y = 1500

substitute y = 1500 into equation 3 , we have

x = 2200 - y

x = 2200 - 1500

x = 700

Therefore , 700 adults and 1500 children entered

Answer:

The net pay of her will be $4702.21

Step-by-step explanation:

The State Tax plus Social Security Taxes plus Medicare takes (3 + 6.2 + 1.45) = 10.65% from Jessica's monthly gross pay.

If the gross pay is $5660 then the after the above deduction the remaining pay will be [tex]5660(1 - \frac{10.65}{100}) = 5057.21[/tex] dollars.

Now, again there is a deduction of $355 from her payment each month.

Therefore, the net pay of her will be = $(5057.21 - 355) = $4702.21 (Answer)

From 2 hours to 4 hours she traveled 7 miles.

7 miles  / 2 hours = 3.5 miles per hour.

The slope is 3.5 , which is 3.5 miles per hour, which is how fast she is walking.

Answer:

The answer can be calculated by doing the following steps;

Step-by-step explanation:

The Reminder is 0 and (x -2) is the factor of polynomial p(x).

Polynomials are mathematical articulations that comprise of factors and coefficients. In other cases, variables are referred to as indeterminates. We can perform math activities like expansion, deduction, increase, and furthermore sure number types for polynomial articulations yet not division by factor.

Given polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4

to divide by (x - 2)

We choose long division and look for what will multiply with (x-2) to make the polynomial

(x - 2)(-4x³) = -4x⁴ + 8x³

We subtract this from the original -4x⁴ + 6x³ + 8x² - 6x - 4 - (-4x⁴ + 8x³)

this leaves -2x³ + 8x² - 6x - 4

repeat the same process

(x - 2)(-2x²) = -2x³ + 4x²

subtract this from -2x³ + 8x² - 6x - 4 we get

-2x³ + 8x² - 6x - 4  - (-2x³ + 4x²) = 4x² - 6x - 4

again repeat the process

(x - 2)(4x) = 4x² - 8x

subtract this from 4x² - 6x - 4 we get

4x² - 6x - 4 - (4x² - 8x) = 2x - 4

repeat again

(x - 2)(2) = 2x - 4

subtract this from 2x - 4 we get

2x - 4  - (2x - 4) = 0

Hence the reminder of  polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4 is 0 and (x - 2) is factor of p(x).

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Answer:

26.5%

Step-by-step explanation:

Increasing  Percentages

When sequential percentages increasing are computed, each increase applies to the previous result, instead of the first quantity. That is why sometimes the final results may be confusing. For example, increasing 10% and then 15% will not be the same as increasing a total of 25%.

The average test scores of RSM students first increased by 10%. It means that some quantity C increased by

[tex]10C/100=0.1C[/tex]

Now the average test scores are

[tex]C+0.1C=1.1C[/tex]

A new increasing occurred by 15%, and the previous quantity must be multiplied by 1.15, so the final average test scores are

[tex]1.15(1.1C)=1.265C[/tex]

It means that the total increasing was [tex]100(1.265-1)=26.5\%[/tex]

Answer:

26.5%

Step-by-step explanation:

IM SMART! :D

Answer:

x= -15

Step-by-step explanation:

3x+10=2x-5

3(-15)+10=2(-15)-5

-45+10=-30-5

-35=-35

Each side of the angle is equal, that's how i knew the two were supposed to be equal. <3 Hope this helps!

(I found the picture.)

Answer:

17

Step-by-step explanation:

L 3x + 10 5875 =90 2x - 5 x=_17 5 5 - x =17 Use the image to answer questions 6-7. 125 Given that Xll Y use the figure below to answer questions 8 - 11. -40-40 normal Unit 2: Equations & Exponents Directions: 1. Solve each problem.

Answer:

Ic² + b²l = 13 units.

Step-by-step explanation:

We have to evaluate the expression Ic² + b²l with unknowns b and c and having the values of b and c respectively - 3 and - 2.

Now, Ic² + b²l

= I(- 2)² + (- 3)²l {Putting the values of b and c}

= I4 + 9l  

= I13l

= 13 units.

Therefore, Ic² + b²l = 13 units. (Answer)

Answer:

Step-by-step explanation:

143.17

round the bill to the nearest $ 10..

that would make it $ 140

a 10% tip......its the same thing as multiplying by 0.1

and when u multiply any number by 0.1 ur actually starting at the decimal ( or the end of the number) and move one space to the left.

examples :

10% of 245 = 24.5

10% of 5010 = 501

10% of 76 = 7.6

10% of 88.5 = 8.85 .....if there is a decimal, start at the decimal

so.....10% of 140

start at the end of the number and move 1 space to the left...

ur answer is 14 <==

Answer:

Adverage of 20 mph

30 1/5 = 30.2

2/3 = .6667

30.2 x .6667 = 20.13

Answer:

45.3 miles/hour

Step-by-step explanation:

the information we have is:

distance:

[tex]d=30\frac{1}{5}miles=30.2miles[/tex]

time:

[tex]t=\frac{2}{3} hour[/tex]

the formula for the average speed is:

[tex]v=\frac{distance}{time} =\frac{d}{t}[/tex]

substituting all the known values we get:

[tex]v=\frac{30.2miles}{2/3hour} =\frac{3(30.2miles)}{2hour}= 45.3miles/hour[/tex]

the average speed in miles per hour is: 45.3

Answer:

6 1/2

Step-by-step explanation:

So basically 8 2/3 is equally to 26/3 so 45 minutes is 45/60.

45/60=3/4

26/3*3/4=6 1/2

Jordan, with a speed of 8 2/3 miles per hour, will cover a distance of 6.5 miles in a 45 minute bike ride.

First, we need to understand that Jordan is biking at a speed of 8 2/3 miles per hour. This means in 1 hour, or 60 minutes, he covers that distance. If we want to know how much he covers in a different timeframe - 45 minutes in this case - we have to adjust proportionally.

As a step-by-step calculation, first change 8 2/3 to a decimal, which equal to 8.67.

To find out how far Jordan bikes in 45 minutes, you need to multiply his speed (8.67 mph) by the time in hours. Since 45 minutes is 0.75 of an hour (45/60), the mathematical calculation will be:

Distance = Speed x Time = 8.67 miles/hour x 0.75 hour = 6.5 miles

Therefore, Jordan will bike 6.5 miles in 45 minutes.

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