61/6 to mixed number

Answer: 9

The steps are in the picture

Answer:

8x² + 5x - 3

Step-by-step explanation:

Given

(3x² - 2) + (5x² + 5x - 1)

Since both parenthesis are distributed by 1 just remove them, that is

3x² - 2 + 5x² + 5x - 1 ← collect like terms

= (3x² + 5x²) + 5x + (- 2 - 1)

= 8x² + 5x - 3

Step-by-step explanation:

multiply the 1 1/2 by 2 to get 3.

find the closest number that is divisible by 3

3*7 is 21.

We now have to multiply 7 by 2 since we did that to our mixed number to get a whole number.

There is still a 1 1/2 left over. Simply add 1 to 14.

Answer:

15 servings

Step-by-step explanation:

Given,

Total number of cups = [tex]22\frac{1}{2}[/tex]

The number of cups required for each serving = [tex]1\frac{1}{2}[/tex]

Thus,

[tex]\text{The number of servings}=\frac{\text{Total cups}}{\text{cups required for each serving}}[/tex]

[tex]=\frac{22\frac{1}{2}}{1\frac{1}{2}}[/tex]

[tex]=\frac{\frac{45}{2}}{\frac{3}{2}}[/tex]

[tex]=\frac{45}{3}[/tex]

= 15

The volume of a rectangular prism is found by multiplying its length, width, and height. Given the dimensions as 1 3/4 ft by 1 3/4 ft by 2 1/4 ft, when converted to improper fractions and multiplied together, we find that the volume of the suitcase is 220.5 cubic feet.

The subject of the student's question is focused on the mathematical concept of volume, specifically the volume of a rectangular prism. To find the volume of the suitcase, we need to multiply the length, width, and height of the suitcase. Given that the suitcase's dimensions are 1 3/4 ft by 1 3/4 ft by 2 1/4 ft, we first convert these mixed numbers into improper fractions (7/4 ft by 7/4 ft by 9/4 ft). Then, we multiply them together:

Volume = Length x Width x Height.
Volume = (7/4 ft) x (7/4 ft) x (9/4 ft) = 220.5 ft³.

The volume of the rectangular prism (suitcase) is 220.5 cubic feet.

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Answer:

Are there any options for this question?

Step-by-step explanation:

I cant answer it without options.

being [tex]x^{2} +5x+6[/tex] the answer is (x-3)(x-2)

begin [tex]x^{2} -5x+6[/tex] the answer is (x+3)(x+2)

1. [tex]x^{2} +5x+6[/tex]

second grade formala is used

[tex]x= \frac{-b±\sqrt{b^{2} } -4ac}{2a}\\ x=\frac{-5±\sqrt{5^{2} } -4.1.6}{2} \\ x= \frac{-5±1}{2} \\ x_{1} =-3  \\  x_{2} =-2[/tex]

Answer:

see explanation

Step-by-step explanation:

Consider the differences in the terms

2 - (- 1) = 2 + 1 = 3

7 - 2 = 5

14 - 7 = 7

The differences are 3, 5, 7 ← increasing in steps of 2

Thus the next 2 differences should be 9 and 11

Then the next 2 terms are

14 + 9 = 23

23 + 11 = 34

Answer:

The value of x is 2

Step-by-step explanation:

* Lets explain how to find a distance between 2 points

- If the endpoints of a segment are [tex](x_{1},y_{1})[/tex] and

 [tex](x_{2},y_{2})[/tex] is [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

- Triangle ABC has a perimeter of 12 units

∵ The perimeter of any triangle is the sum of lengths of its sides

∴ P Δ ABC = AB + BC + AC

* Lets find the length of the three sides

∵ A = (x , 2) , B = (2 , -2) , C = (-1 , 2)

∵ [tex]AB=\sqrt{(2-x)^{2}+(-2-2)^{2}}[/tex]

∴ [tex]AB=\sqrt{(2-x)^{2}+(-4)^{2}}[/tex]

∴ [tex]AB=\sqrt{(2-x)^{2}+16}[/tex]

∵ [tex]BC=\sqrt{(-1-2)^{2}+(2--2)^{2}}[/tex]

∴ [tex]BC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]

∴ [tex]BC=\sqrt{9+16}[/tex]

∴ [tex]BC=\sqrt{25}[/tex]

∴ BC = 5

∵ [tex]CA=\sqrt{(x--1)^{2}+(2-2)^{2}}[/tex]

∴ [tex]CA=\sqrt{(x+1)^{2}+(0)^{2}}[/tex]

∴ [tex]CA=\sqrt{(x+1)^{2}}[/tex]

- The √ is canceled by power 2

∴ CA = (x + 1)

∵ AB + BC + CA = 12

∴ [tex]\sqrt{(2-x)^{2}+16}[/tex] + 5 + (x + 1) = 12

- Add 5 and 1

∴ [tex]\sqrt{(2-x)^{2}+16}[/tex] + 6 + x = 12

- subtract 6 and x from both sides

∴ [tex]\sqrt{(2-x)^{2}+16}[/tex] = (6 - x)

- To cancel (√ ) square the two sides

∴ (2 - x)² + 16 = (6 - x)²

- Simplify the two sides

∴ [(2)(2) + (2)(2)(-x) + (-x)(-x)] + 16 = (6)(6) + (2)(6)(-x) + (-x)(-x)

∴ 4 - 4x + x² + 16 = 36 - 12x + x²

- Subtract x² from both sides

∴ 20 - 4x = 36 - 12x

- Add 12x to both sides and subtract 20 from both sides

∴ 12x - 4x = 36 - 20

∴ 8x = 16

- Divide both sides by 8

∴ x = 2

* The value of x is 2

Answer:

[tex]\boxed {\sf x=66^o}[/tex]

Step-by-step explanation:

Apply the properties of a triangle:-

Where, the sum of all internal angles of a triangle is always equal to 180°.

[tex]\sf 90^o+x+24^o=180^o[/tex]

Combine like terms.

[tex]\sf x+90+24=180^o[/tex]

Add numbers.

[tex]\sf x+114=180^o[/tex]

Subtract 114 from both sides.

[tex]\sf x+114-114=180-114[/tex]

[tex]\sf x=66^o[/tex]

the answer is 2,220

you first aline 185 × 12 like so 185

× 12

then you need to multiply everything

Hey!

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Solution:

I would assume that the iron intake is combined between breakfast and lunch. So 8.25mg is too meals worth of iron. So all we have to do is subtract.

15 - 8.25 = 6.75

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Answer:

6.75mg are still needed for his daily intake.

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Hope This Helped! Good Luck!

Answer:2 to 4%

Step-by-step explanation:

your odds are 1/30 then your persentage would be 3 percent so your range of 20 to 30 students would be 2 to 4 percent chances

Final answer:

The estimated probability of a specific student's name being drawn from a class of 20-30 students is 4% or 1 in 25.

Explanation:

The probability of a specific student's name being drawn from a class with a number of students between 20 and 30 can be estimated by taking the inverse of the average of the maximum and minimum possible number of students. We calculate the average by adding 20 (the minimum) to 30 (the maximum) and dividing by 2, resulting in an average class size of 25 students.

To estimate the probability of drawing any one student's name, we take the inverse of 25, which is 1/25 or 0.04. Thus, the estimated probability is 4% that any particular student would be chosen in a random draw from a class size between 20 and 30 students.

Answer:

1+2x=13

Step-by-step explanation:

the sum of= +

one=1

products of a number and 2= 2x

equals= =

thriteen=13

Put them all together:

1+2x=13

Answer:

3 whole number, 9/20

because if you multiply 20 by 3 and add it by 9 you get 69, so when you divide the 69/20, you get 3.45

Answer:

Step-by-step explanation:

The first step is to take p on both sides:

[tex]A - p = p + p*r*t - p[/tex]

On the right hand side, cancel p and -p, since [tex]p-p=0[/tex]. The equation will be:

[tex]A - p = p*r*t[/tex]

Then, divide both sides of the equation by p*t:

[tex]\frac{A-p}{p*t} = \frac{p*r*t}{p*t}[/tex]

On the right hand side, p*t can be cancelled:

[tex]\frac{A-p}{p*t} = r[/tex]

Answer:

r=A-p     (the line is the bar so this is a-p over pt)

    pt

Step-by-step explanation:

P + Prt = A

P r t=A −P            isolate the term which contains  r

P rt=A−P

divide pt by each side

Answer:

= 10x² + 9x³

Step-by-step explanation:

I'm assuming you mean question 19

3x² + 5x³ + 7x² + 4x³    (rearrange to group like terms)

=3x² + 7x² + 5x³ + 4x³  (factor out common powers)

= (3+7)x² + (5+4)x³

= 10x² + 9x³

Every kilogram is 1,000 grams, but you want 10 kilograms. You can multiply 1,000 10 times (you can also add 1,000 10 times,) giving you the answer > 10,000.

Hope this helped!

Nate

[tex]\huge\boxed{\text{10,000 grams}}[/tex]

One kilogram is made up of [tex]\text{1,000}[/tex] grams. You can remember this because the Greek root "kilo" means "thousand."

So, just multiply [tex]\text{10} \times \text{1,000}[/tex] to get [tex]\boxed{\text{10,000 grams}}[/tex].

Answer:

The perimeter of quadrilateral ABCD is 27.48 units

Step-by-step explanation:

we know that

The perimeter of quadrilateral ABCD is the sum of its four length sides

so

[tex]P=AB+BC+CD+AD[/tex]

we have

A(-5, 4),B(0,3),C(4,-1) and D(4,-5)

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

Substitute in the formula

[tex]d=\sqrt{(3-4)^{2}+(0+5)^{2}}[/tex]

[tex]d=\sqrt{(-1)^{2}+(5)^{2}}[/tex]

[tex]AB=\sqrt{26}\ units[/tex]

Find the distance BC

Substitute in the formula

[tex]d=\sqrt{(-1-3)^{2}+(4-0)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]

[tex]BC=\sqrt{32}\ units[/tex]

Find the distance CD

Substitute in the formula

[tex]d=\sqrt{(-5+1)^{2}+(4-4)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]

[tex]CD=4\ units[/tex]

Find the distance AD

Substitute in the formula

[tex]d=\sqrt{(-5-4)^{2}+(4+5)^{2}}[/tex]

[tex]d=\sqrt{(-9)^{2}+(9)^{2}}[/tex]

[tex]AD=\sqrt{162}\ units[/tex]

Find the perimeter

substitute the values

[tex]P=\sqrt{26}+\sqrt{32}+4+\sqrt{162}=27.48\ units[/tex]

see the attached figure to better understand the problem

Answer:

Step-by-step explanation:

[tex]\frac{11}{7} * \frac{7}{33}[/tex]

[tex]\frac{11 * 7}{7 * 33}[/tex]

[tex]\frac{1}{3}[/tex]

[tex]0.333[/tex]

Answer:

6 ≤ x < ∞

Step-by-step explanation:

The value of x cannot be less than 6 because that would make the term in the square root part negative. There is no real square root of a negative vale.

Final answer:

A real world situation that can be represented by the quotient -85/15 is paying off a credit card debt.

Explanation:

A real world situation that can be represented by the quotient -85/15 is the following:

Suppose you owe $85 on your credit card and you make monthly payments of $15. You want to know how many months it will take for you to pay off your debt completely.

To find the answer, you divide the amount you owe ($85) by the monthly payment ($15):

-85/15 = -5.67

This means it will take approximately 5.67 months to pay off your debt.

Answer:

c

Step-by-step explanation:

Its c because 10/3.69=0.369 then you tomes that by twelve and itequals 4.428 round that up and its 4.43.

Answer:

y = 6

Step-by-step explanation:

Given

6y - 2 = 34 ( add 2 to both sides )

6y = 36 ( divide both sides by 6 )

y = 6

Answer:

y = 6

Step-by-step explanation:

6y - 2 = 34

+2         +2

6y = 36

---    -----

6      6

y = 6

Answer:

4 is the highest common factor

Answer:

The highest common factor is 4

Step-by-step explanation:

Factors of 24 are { 1,2,3,4,6,8,12.......}

And factors of 76 are{ 1,2,4,19......)

from the two factors,

common factor ( C. F ) ={1,2,4}

and from the common factors, the highest is 4

Therefore 4 is the highest common factor for 24 and 76.

Answer:

[1, 4]; 1 = m

Step-by-step explanation:

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so in this case, the coordinates are [1, 4]. Now, the rate of change [slope] is 1 because an invisible coefficient is always assumed to be 1.

I am joyous to assist you anytime.

Answer:

The slope of the line is 1 and it passes through the point (1,4).

Step-by-step explanation:

If a line passes through a points [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is

[tex]y-y_1=m(x-x_1)[/tex]            .... (1)

The given equation of line is

[tex]y-4=(x-1)[/tex]                .... (2)

We need to find the slope and the coordinates of a point on the given line.

On comparing (1) and (2) we get

[tex]m=1[/tex]

[tex]x_1=1[/tex]

[tex]y_1=4[/tex]

Therefore, the slope of the line is 1 and it passes through the point (1,4).

Answer:

1. The railroad built towns along the railroad.

and

3. The railroad recruited settlers to form new.

Step-by-step explanation:

I just took it

The railroad facilitate population growth in the interior of the country by  The railroad built towns along the railroad, The railroad recruited settlers to form new.

A population is a complete set of a group of individualists, whether that group constitutes a nation or a group of groupings with a common characteristic. In data point, a population is the pool of individuals from which a statistical sample is drawn for a study. As we see, different countries have different populations.

The construction of the transcontinental railroad boosted Western economic development and population growth. For both persons and commodities, railroad businesses offered superior transportation. Additionally, they sold the property to settlers, which prompted a Westward migration. New railroads benefited the industry.

Therefore, option (A) is correct

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Answer:

The coordinates of Z are (2,7)

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]Y=(\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]

we have

X(-10,9),Y(-4,8)

Let

(x2,y2) ----> the coordinates of Z

substitute the values

[tex](-4,8)=(\frac{-10+x2}{2} ,\frac{9+y2}{2})[/tex]

Solve for x2

[tex]-4=(-10+x2)/2\\-8=-10+x2\\x2=10-8\\x2=2[/tex]

Solve for y2

[tex]8=(9+y2)/2\\16=9+y2\\y2=16-9\\y2=7[/tex]

therefore

The coordinates of Z are (2,7)

Answer:  The required co-ordinates of Z are (2, 7).

Step-by-step explanation:  Given that Y is the midpoint of XZ  and the co-ordinates of X are (-10, 9) and the of Y are (-4, 8).

We are to find the co-ordinates of Z.

Let (a, b) represents the co-ordinates of the point Z.

We know that

the co-ordinates of the midpoint of a line segment with endpoints (x, y) and (z, w) are given by

[tex]\left(\dfrac{x+z}{2},\dfrac{y+w}{2}\right).[/tex]

So, according to the given information, we have

[tex]\left(\dfrac{-10+a}{2},\dfrac{9+b}{2}\right)=(-4,8)\\\\\\\Rightarrow \dfrac{-10+a}{2}=-4\\\\\Rightarrow -10+a=-8\\\\\Rightarrow a=-8+10\\\\\Rightarrow a=2[/tex]

and

[tex]\dfrac{9+b}{2}=8\\\\\Rightarrow 9+b=16\\\\\Rightarrow b=16-9\\\\\Rightarrow b=7.[/tex]

Thus, the required co-ordinates of Z are (2, 7).

Answer:

50 hours.

Step-by-step explanation:

First I found how how much the man was paid in a week for the base 40 hours which was 384. Then i subtracted that from the wage from the week so i could just have the overpay amount which was 144. I then multiplied 9.6 by 1.5 to get the hourly pay for overtime and god 14.4 dollars an hour. Lastly, i divided 144 by 14.4 and got 10 extra hours which got me to my answer of 50 hours because i added the 40 initial hours.

Final answer:

In this case, the man worked 10 hours of overtime.

Explanation:

The question pertains to calculating the regular and overtime pay of a man who earns $9.60 per hour for a standard 40-hour work week and time and a half for any hours worked beyond that. To find how many hours of overtime he worked when he earned $528.00 in a week, we need to use mathematical equations.

First, we calculate the man's regular weekly pay for 40 hours: 40 hours × $9.60/hour = $384.00. Since his total pay is $528.00, the overtime pay is $528.00 - $384.00 = $144.00.

Overtime pay is time and a half, so the overtime rate is $9.60/hour × 1.5 = $14.40/hour. We then divide the total overtime pay by the overtime rate: $144.00 / $14.40/hour = 10 hours of overtime work.

Thus, the man worked 10 hours overtime in addition to his regular 40 hours to make a total of $528.00.

Answer:

300, 600, 300.

Step-by-step explanation:

324:  The tens digit is 2 so we do nothing to the hundreds digit so its 300.

558:  The tens digit is 5 so we round up the 5 . So it is 600.

In a similar way 256 becomes 300.

Answer:

300, 600, 300

Step-by-step explanation:

When you round a number up by the nearest 100. The digit in the tens place must be equal to or more than 5.

For example: 250 is rounded up to 300, but 240 can not be rounded up to 300.

When you have a number like 240, it can only be rounded down to 200

324 is rounded down to 300 because the tens place digit is less than 5

558 is rounded up to 600 because the tens place digit is higher than 5.

256 is rounded up to 300 because the tens place digit is 5.