What is a division expression for Two bottles of juice are divided equally among six people.

The value of  [tex]3log_{4}(2)+log_{5}(512)[/tex]  is about 5.376

Step-by-step explanation:

Let us revise some rules of logarithm

∵ The expression is [tex]3log_{4}(2)+log_{5}(512)[/tex]

- By using the 1st rule in the first term

∵ [tex]3log_{4}(2)=log_{4}(2)^{3}[/tex]

∵ 2³ = 8

∴ [tex]log_{4}(2)^{3}=log_{4}(8)[/tex]

- By using the second rule

∵ [tex]log_{4}(8)=\frac{log(8)}{log(4)}=1.5[/tex]

∵ [tex]log_{5}(512)=\frac{log(512)}{log(5)}=3.876[/tex]

- Add the two answers

∴  [tex]3log_{4}(2)+log_{5}(512)[/tex] = 1.5 + 3.876

∴  [tex]3log_{4}(2)+log_{5}(512)[/tex] = 5.376

The value of  [tex]3log_{4}(2)+log_{5}(512)[/tex]  is about 5.376

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Answer:A ($139.26)

Step-by-step explanation:

Answer:

4(x-1)units

Step-by-step explanation:

In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.

Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where

L is the length(shorter side) and x is the breadth (longer side).

According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,

L = x-2

Substituting L = x-2 into the formula of perimeter of a rectangle we have,

P = 2(x-2) + 2x

P = 2x-4+2x

P = 4x-4

P = 4(x-1)

The perimeter of the rectangle will be 4(x-1)units

Answer:4 divided by  x hours

Step-by-step explanation:

The number of hours that Daniel gets paid for on each paycheck will be 4x.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Every 4 weeks, Daniel receives a paycheck. He puts in x hours a week at work.

The number of hours that Daniel gets paid for on each paycheck is given as,

⇒ 4 · x

⇒ 4x

The number of hours that Daniel gets paid for on each paycheck will be 4x.

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Answer:

The slope of y=4-2x is -2.

Answer:

Multiply or divide 7.3 times or divided by 71.54

Height of the prism is 9.8 cm

Given that;

Triangular prism base area = 7.3 square cm

Volume of prism = 71.54 cubic cm

Find:

Height of the prism

Computation:

Height of the prism = Volume of prism / Triangular prism base area

Height of the prism = 71.54 / 7.3

Height of the prism = 9.8 cm

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By using mental math and breaking down the numbers into parts, you find that 2,100 more people attended the baseball game on Thursday than on Friday.

The subject of this problem is subtraction. To find out how many more people attended the baseball game on Thursday than on Friday, you need to subtract the number of people who attended on Friday from the number who attended on Thursday. In math terms, this would be 13,450 (Thursday's attendance) - 11,350 (Friday's attendance).

To make this easier using mental math, you might notice that both numbers end in 50. You could subtract these separately: 13,000 - 11,000 = 2,000 and 450 - 350 = 100. Adding these results together, you get 2,000 + 100 = 2,100.

So, the answer is that 2,100 more people attended the baseball game on Thursday than on Friday.

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Answer:

The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].

Step-by-step explanation:

We have to choose from options the exponential function which has a simplified base of 4∛4 i.e. ∛(256).

Now, the exponential function in the option III will be the answer.

The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].

So, the base is [tex](\sqrt[3]{16} )^{2}[/tex] = [tex]\sqrt[3]{16^{2}} = \sqrt[3]{256} = 4\sqrt[3]{4}[/tex]. (Answer)

The general formula of an exponential function is [tex]f(x) = a(b)^{x}[/tex] , where b is called the base of the function.  

The function that has a simplified base of (4∛4) is;

Option C; 4(∛16)^(2x)

From the general formula of an exponential function, we know that;

f(x) = a(b)^(x)

Now, we have;

f(x) = (4∛4)^(x)

Thus, looking at the options, option C is correct because;

In 4(∛16)^(2x), the base is (∛16)² and when we simplify it, we will get 4³(√4) because;

(∛16)² = √(16^(⅔))

>> 256^(⅓)

>> 4∛4

This is the same as our initial value.

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Answer:

[tex]y = - x-1[/tex]

Step-by-step explanation:

The line a passes through th points (-1,0) and (0,-1)

The equation of line which is passes through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

[tex](y-y_1)= \frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Therefore the equation of line which passes through the points (-1,0) and (0,-1)

is

[tex]y-0=\frac{-1-0}{0-(-1)} [x-(-1)][/tex]       [ [tex]x_1 = -1, y_1= 0[/tex] [tex]x_2 = 0[/tex]  and [tex]y_2 = -1[/tex]]

[tex]\Leftrightarrow y = -1 (x+1)[/tex]

[tex]\Leftrightarrow y = - x-1[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Harry's solution is incorrect.

Harry can first substitute (30) for t. He can the multiply 1/3 by (30) to get a product of (10). Since 15 (≠) equal to (10), Harry's solution is (not) correct.

Step-by-step explanation:

Given:

Equation = [tex]\frac{1}{3}(t) =15[/tex]

Solution of the equation = [tex]30[/tex]

Lets check the equation whether both sides of the equation gives same result by plugging the values of t = 30.

⇒ [tex]\frac{1}{3}(t) = 15[/tex]

⇒ [tex]\frac{1}{3}(30) = 15[/tex]

⇒ [tex]\frac{30}{3} =15[/tex]

⇒ [tex]10=15[/tex]

We know that 10 ≠ 15 so the solution is incorrect.

According to the question :

Harry can first substitute (30) for t. He can the multiply 1/3 by (30) to get a product of (10). Since 15 (≠) equal to (10), Harry's solution is (not) correct.

Harry's solution is incorrect.

Answer:

0.5

Step-by-step explanation:

Answer:

C)

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

2-8x=10   subtract both sides by 2

-8x=8   divide both sides by -8

x=-1

Answer:

x = -1

Step-by-step explanation: 2 - 8x = 10

-2. -2

-8x. 8

Divide -8. -8

x = -1

Step-by-step explanation:

3 5/6 = 3 × 6 + 3 = 23 = 23/6

1 2/4 = 1 × 4 + 2 = 6 = 6/4

23 × 6 = 138

6 × 4 = 24

138/24÷2=68/12÷2=34/6÷2=17/3

since 17 and 3 are prime numbers we cannot simplify any further but 17/3 is an improper fraction so we convert it back to a mixed fraction

3÷17=5 R2 = 5 2/3

Answer:

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Answer:

-17

Step-by-step explanation:

-4 - 3 - 10 = -17

To solve the given system of linear equations, we use the elimination method to find the solution, which is (x, y) = (-1, 1).

The student is asking how to find the solution to a system of linear equations:

x + 5y = 4

3x - 7y = -10

To solve this system, one can use the method of elimination.

Multiply the first equation by 3 and the second equation by 1 to align the coefficients of x.

The resulting equations are:

3x + 15y = 12

3x - 7y = -10

Subtract the second equation from the first to eliminate x:

22y = 22

Divide by 22 to find y:

y = 1

Substitute y = 1 into the original first equation:

x + 5(1) = 4

Solve for x:

x = -1

The solution to the system is (x, y) = (-1, 1).

Answer:

4

Step-by-step explanation:

15 = 7 - /2x/

Subtract 7 from both sides ( if it was negative you would add it)

(15-7) = (7 - 7) -/2x/ now the seven is no longer there

8 = -/2x/

Now divide 2 from both sides

( 8 / 2 ) = - /(2 / 2)x/

4 = -/x/

4 = -x

Now the two is no longer there but the x would still be there because you divided it by 2 and not 2x

To solve the equation 15 = 7 - |2x|, consider two cases: 2x ≥ 0 and 2x < 0. In case 1, x = -4. In case 2, x = 4.

To solve the equation 15 = 7 - |2x|, we need to eliminate the absolute value. To do this, we can consider two cases: when 2x is positive and when 2x is negative.

Case 1: 2x ≥ 0

In this case, the equation becomes 15 = 7 - 2x, which simplifies to 2x = -8. Solving for x, we get x = -4.

Case 2: 2x < 0

In this case, the equation becomes 15 = 7 + 2x, which simplifies to 2x = 8. Solving for x, we get x = 4.

Therefore, the solution to the equation 15 = 7 - |2x| is x = -4 or x = 4.

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Answer:

[tex]\frac{5x^{2} }{6}[/tex]

Step-by-step explanation:

Given: Base of triangle= [tex]\frac{5x}{3}[/tex]

           Height of triangle= x

Now, finding the area of triangle.

We know area of triangle= [tex]\frac{1}{2} \times base\times height[/tex]

Subtituting the value of base and height in the formula.

⇒[tex]Area\ of\ triangle= \frac{1}{2} \times \frac{5x}{3} \times x[/tex]

Solving it to find area of triangle

∴ [tex]Area\ of\ triangle= \frac{5x^{2} }{6}[/tex]

Hence, area of triangle is [tex]\frac{5x^{2} }{6}[/tex]

Answer:

A=5x^2/6

Step-by-step explanation:

Answer:

car C gets the best gas mileage

Step-by-step explanation:

Final answer:

To find the car with the best gas mileage, the miles driven are divided by the gallons used for each car. Car A gets 25 MPG, Car B gets 28 MPG, Car C gets 31 MPG, and Car D gets 20 MPG. Car C has the best gas mileage with 31 MPG.

Explanation:

The student's question is about calculating and comparing the gas mileage (miles per gallon or MPG) of different cars to determine which one is the most fuel-efficient. To answer this, we calculate the MPG for each car by dividing the number of miles driven by the gallons of gas used and then compare the results.

Car A: 200 miles / 8 gallons = 25 MPG

Car B: 28 miles / 1 gallon = 28 MPG

Car C: 279 miles / 9 gallons = 31 MPG

Car D: 140 miles / 7 gallons = 20 MPG

Upon comparison, Car C has the highest MPG at 31 miles per gallon, making it the most fuel-efficient car among those listed.

Answer:

A, B, and C are true

Step-by-step explanation:

Using the Factor Theorem to find the function, the correct statement is:

The function is positive on (0,∞).

The Factor Theorem states that a polynomial function with roots

x1, x2,...xn  is given by:

f(x) = a(x-x1)(x-x2).....(x-xn)

In which a is the leading coefficient.

here, we have,

The described roots means that:

x1 = 0, x2 = x3= x4 =x5 = 2

Hence the function is:

f(x) = x(x - 2)^4

(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:

The function is positive on (0,∞).

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Answer:b = 81

Step-by-step explanation:

perimeter = 2(l+b)

344= 2(91 + b)

344 =182 + 2b

344 -182 =2b

162 = 2b

b = 162/2

b= 81

Answer:

perimeter = 2(l+b)

344= 2(91 + b)

344 =182 + 2b

344 -182 =2b

162 = 2b

b = 162/2

b= 81

Step-by-step explanation:

Week 1: 4.23

———————

Week 2: 8.46

Week 4: 16.92

Week 6: 25.38

Week 8: 33.84

Week 10: 42.30

Week 12: 50.76

I can’t draw a graph on here but it’s basically a straight line.

Equation: y=4.23x

y is the amount of money she has at x weeks

Answer:

week one 4.23

week 2 8.46

week 3 12.

Step-by-step explanation:

Answer:

The number of acres of corn planted was 230 and the number of acres of wheat planted was 140

Step-by-step explanation:

Let

c ----> the number of acres of corn

w ----> the number of acres of wheat

we know that

Farmer Brown planted corn and wheat on 370 acres of his land

so

[tex]c+w=370[/tex] -----> equation A

The cost and planting and harvesting corn,c,is $280 per acre

The cost of planting and harvesting wheat,w,is $135 per acre

The Farmer Brown's total cost was $83,300

so

[tex]280c+135w=83,300[/tex] ----> equation B

solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (230,140)

see the attached figure

therefore

The number of acres of corn planted was 230 and the number of acres of wheat planted was 140

Farmer Brown planted 230 acres of corn and 140 acres of wheat.

To determine how many acres of corn and wheat Farmer Brown planted, we can set up a system of equations. Let x be the number of acres of corn and y be the number of acres of wheat. From the given information, we have the following equations:

Cost of planting and harvesting corn: 280x

Cost of planting and harvesting wheat: 135y

Total cost: 280x + 135y = 83,300

We also know that the total number of acres planted is 370 acres, so we have the equation:

x + y = 370

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

From the second equation, we can solve for x in terms of y: x = 370 - y

Substitute this expression for x in the first equation:

280(370 - y) + 135y = 83,300

Simplify and solve for y:

103,600 - 280y + 135y = 83,300

-145y = -20,300

y = 140

Substitute the value of y back into the second equation:

x + 140 = 370

x = 230

Therefore, Farmer Brown planted 230 acres of corn and 140 acres of wheat.

Answer:

3,840 calories

Step-by-step explanation:

a = an avocado's calories

Given: 1/2a = 160 calories

Multiply both sides of the equation by 2

a = 320 calories

We need to find the amount of calories in a dozen (12) avocados so multiply both sides of this equation by 12

12a = 3,840 calories

Hope this helps :)

Answer:

B. of the AAS congruence theorem.

Step-by-step explanation:

Triangles TSR and QRS share side SR

SR=RS

Angle TSR and Angle QRS are right angles, so

∠S= ∠R

Angle T Is-congruent-to Angle Q, so

∠T= ∠Q

From these data, we have one congruent side and two congruent angles. The possible congruence theorem that we can apply will be either ASA or AAS. In the ASA theorem, the congruence side must be between the two congruent angles.

The congruence side required for the ASA theorem for this triangle is ST = RQ. It is wrong because the congruent side we have is SR=RS. The correct option is the AAS theorem.

y=a.(X-x1)(X-x2)

x1 and x2 are x-intercepts

x1=-3

x2=1

other points: (-1,8) and (0,5)

y=a.(x+3).(x-1)

a=-2

f(x)= -2.(x+3)(x-1)

The equation is [tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]

Given the quadratic equation in the form \(y =[tex]a \cdot (X - x_1)(X - x_2)\), where \(x_1\) and \(x_2\)[/tex]represent the x-intercepts, and the given x-intercepts are[tex]\(x_1 = -3\) and \(x_2 = 1\).[/tex]

Using the given x-intercepts [tex]\(x_1 = -3\) and \(x_2 = 1\)[/tex], the equation becomes [tex]\(y = a \cdot (x + 3)(x - 1)\).[/tex]

We are also provided with two other points: (-1, 8) and (0, 5).

We can substitute the point (-1, 8) into the equation to solve for \(a\):

[tex]When \(x = -1\) and \(y = 8\):\[8 = a \cdot ((-1) + 3)((-1) - 1)\]\[8 = a \cdot (2)(-2)\]\[8 = -4a\]\[a = -2\][/tex]

Therefore, the value of \(a\) is -2.

Substituting [tex]\(a = -2\) into the equation \(y = a \cdot (x + 3)(x - 1)\), we get:\[y = -2 \cdot (x + 3)(x - 1)\][/tex]

[tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]

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Answer:

  [tex]0.\overline{1}[/tex]

Step-by-step explanation:

The fraction reduces to 1/9. Since you're familiar with the decimal equivalents of fractions with denominators less than 10, you know this has the decimal equivalent:

  1/9 = 0.11111111...(repeating)

_____

Even if you're not familiar with the equivalent of 1/9, you probably know that ...

  1/3 = 0.33333...(repeating)

and

  2/3 = 0.66666...(repeating)

Of course, 1/3 = 3/9, so dividing 0.333... by 3, we get 1/9 = 0.111....

_____

The attachment shows the long division. It gets boring quickly.

Final answer:

The equivalent decimal of the fraction 5/45 is approximately 0.1111

Explanation:

To find the equivalent decimal of the fraction 5/45, we can start by simplifying the fraction. Since both the numerator (5) and the denominator (45) are divisible by 5, we can reduce the fraction to 1/9.

To convert this simplified fraction into a decimal, we divide 1 by 9.

1 ÷ 9 = 0.111...

The decimal 0.111... means that the 1 repeats indefinitely, which is known as a repeating decimal.

If we want to convert this repeating decimal into an approximation with a specific number of decimal places, we could round it. For example, we could say 0.111... is approximately 0.111 when rounded to three decimal places.