Which two operations are needed to write the expression that represents “five less than the quotient of a number and three”?

Step-by-step explanation:

first distribute the 5.

10x-40=90

then get rid of the 4o and add it to 90

10x=130

then divide by 10 to get x alone

x= 13

Answer:

x = 13

Step-by-step explanation:

5(2x - 8) = 90       Divide by 5 on both sides

2x - 8 = 18            Add 8 to both sides

    + 8  + 8

2x = 26               Divide by 2 on both sides

x = 13

Final answer:

The rectangle's width is found to be 7.3 cm, and the length is approximately 10.47 cm, both measured to three significant figures. This was determined by setting up equations based on the given perimeter and the relationship between the rectangle's length and width.

Explanation:

To find the dimensions of the rectangle, we need to set up an equation based on the given perimeter and the relationship between length and width.

Let's denote the width of the rectangle as w centimeters. According to the problem, the length l is 3 1/6 cm longer than the width, so l = w + 3 1/6 cm. The perimeter P of a rectangle is given by the formula P = 2l + 2w. Substituting the given perimeter 15 1/3 cm and the expression for l into the formula, we get:

15 1/3 = 2(w + 3 1/6) + 2w

To solve, first convert the mixed numbers to improper fractions:

46/3 = 2((6w + 19)/6) + 2w

Multiply through by 6 to clear the fractions, resulting in:

92 = 4w + 19 + 6w

Combine like terms and solve for w:

92 = 10w + 19

73 = 10w

w = 7.3 cm

Now that we have the width, calculate the length:

l = w + 3 1/6

l = 7.3 + 3 1/6

l = 7.3 + 19/6

l = 7.3 + 3.1667

l = 10.4667 cm

So the width of the rectangle is 7.3 cm, and the length is approximately 10.47 cm, to three significant figures.

Answer:

x = 45/7

Step-by-step explanation:

Write as an algebraic equation.

Look at each part in the word question : 0.7 of what number is 4 1/2

"0.7 of what number" can be written as 0.7x

The word "is" means equals.

0.7x = 4 1/2     <= The equation, using 'x' to represent the number.

To find the number, isolate 'x'.

0.7x = [tex]4\frac{1}{2}[/tex]    Convert mixed fraction to improper fraction

0.7x = [tex]\frac{(4*2)+1}{2}[/tex]     Multiply the whole number by the denominator and add it to the numerator

0.7x = [tex]\frac{9}{2}[/tex]     Now isolate 'x'

0.7x/0.7 = [tex]\frac{9}{2}/0.7[/tex]     Divide both sides by 0.7

x = [tex]\frac{9}{2}/0.7[/tex]     Simplify right side

x = [tex]\frac{9}{2}/\frac{7}{10}[/tex]     Rewrite 0.7 as a fraction

x = [tex]\frac{9}{2}*\frac{10}{7}[/tex]     To divide, you multiply a flipped fraction

x = [tex]\frac{9*10}{2*7}[/tex]     Multiply across the top and across the bottom

x = 90/14      Reduce to lowest terms. Top and bottom are divisible by 2

x = 45/7        Answer

Answer:

Therefore , Equation of Line Passing through A with slope 1/3 is

[tex]x-3y=-12[/tex]

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( 3 , 5)

[tex]Slope = m =\dfrac{1}{3}[/tex]  

To Find:  

Equation of Line Passing through A with slope 1/3 =?  

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e Equation in point - slope form

[tex](y-y_{1})=m(x-x_{1})[/tex]

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 3 , 5) we get

[tex](y-5)=\dfrac{1}{3}(x-3)\\\\3y-15=x-3\\x-3y=-15+3=-12[/tex]

Therefore , Equation of Line Passing through A with slope 1/3 is

[tex]x-3y=-12[/tex]

Answer:

8(2x+7y)

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Part one is always the ones 'in these: ( )'. 12/3=4 4*2=8. So now it is 8^2+8-7. 8^2 is 8*8=64. 64+8-7=64+1=65

Start by working inside the parentheses which are these things ( )

The things inside the ( ) is "12 divided by 3 times 2"

Division comes first so 12 divided by 3 = 4.

4 times 2 = 8

So now we have 8^2 + 8 - 7

In PEMDAS, Exponents come before addition and subtraction, so 8^2 is 64.

64 + 8 = 72

Lastly is subtraction

72 - 7 = 65

65 is your answer.

Answer:19.7

Step-by-step explanation:

Sin‐(7.5/22.3) on your calculator

The answer to 3 significant figures is 19.7

The question seeks to find the size of angle YZX in a triangle but lacks the necessary information to provide an accurate answer. By using the sum of the angles in a triangle (180 degrees), we could find the angle YZX if we had the other two angle measurements.

Your question is a mathematical one, specifically within the study of geometry, but it seems to be missing information needed to provide a specific answer. Determining the size of Angle YZX would depend on other given angles or measurements within the triangle. For example, if we know the other two angles, we could calculate Angle YZX by subtracting the sum of the other two angles from 180 (as the total degrees in a triangle is 180). Furthermore, the number of significant figures doesn't affect the calculation of an angle, it only refers to how precise your final answer should be represented. In this case, the answer should be given to three significant figures. Let's say that the value of Angle YZX was calculated to be 123.456 degrees, then presenting this to three significant figures would result in 123 degrees.

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ANSWER=  square root(-1) =  i

STEP-BY STEP EXPLANATION:

Imaginary number. An imaginary number is the square root of a negative real number. (The square root of a number is a second number that, when multiplied by itself, equals the first number.)

Answer:

$39.50

Step-by-step explanation:

Multiply 7.9 by 5 to get 39.5

Answer:

if 10 of them costs $7.90 then 50 would cost $39.50.

there are two different ways of doing this:

1. you could divide $7.90 by 10 which would get you $0.79 (the price of one frozen juice bar) then multiply $0.79 by 50 to get $39.50 (the price of 50 frozen juice bars)

or

2. you could just take $7.90 and multipy it by 5 (b/c 10 x 5 is 50)

The principal to be deposited is $ 11874.6594

Solution:

Given is a simple interest problem

Principal = ?

Simple Interest = $ 2179

[tex]Rate = 3\frac{2}{3} \% = \frac{11}{3} \% = 3.67 \%[/tex]

Number of years = 60 months = [tex]\frac{60}{12} = 5 \text{ years }[/tex]

The simple interest is given by formula:

[tex]Simple\ Interest = \frac{p \times n \times r}{100}[/tex]

Where, "p" is the principal and "r" is the rate of interest and "n" is the number of years

[tex]2179 = \frac{p \times 3.67 \times 5}{100}\\\\217900 = 18.35p\\\\p = \frac{217900}{18.35}\\\\p = 11874.6594[/tex]

Thus the principal to be deposited is $ 11874.6594

Answer:

slope = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m = [tex]\frac{-3-0}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

Answer:

60%

Step-by-step explanation:

so u have 15 players.....6 of them are in 8th grade....meaning (15 - 6) = 9 are not in 8th grade

percent of the team not in 8th grade...

9/15 = 0.6 = 60% <===

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point on a line

We have

[tex](-6,\ 3)\to x_1=-6,\ y_1=3,\ m=\dfrac{5}{2}[/tex]

Substitute:

[tex]y-3=\dfrac{5}{2}(x-(-6))\\\\y-3=\dfrac{5}{2}(x+6)[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]y-3=\dfrac{5}{2}(x+6)[/tex]         use the distributive property

[tex]y-3=\dfrac{5}{2}x+\dfrac{5}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3[/tex]

[tex]y-3=\dfrac{5}{2}x+15[/tex]           add 3 to both sides

[tex]y=\dfrac{5}{2}x+18[/tex]

Convert to the standard form:

[tex]Ax+By=C[/tex]

[tex]y=\dfrac{5}{2}x+18[/tex]              multiply both sides by 2

[tex]2y=5x+36[/tex]              subtract 5x from both sides

[tex]-5x+2y=36[/tex]          change the signs

[tex]5x-2y=-36[/tex]

Answer:

The solution set can be given as:

[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\frac{1}{2x+6}[/tex]

To find the domain of the function in set notation.

Solution:

For the function [tex]f(x)[/tex] to exist the denominator must be ≠ 0

We have the denominator [tex](2x+6)[/tex] which  cannot be = 0.

Thus, we can find the domain of the function using the above relation.

The function [tex]f(x)[/tex] will not exist when:

[tex]2x+6=0[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 6.

[tex]2x+6-6=0-6[/tex]

[tex]2x=-6[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}=\frac{-6}{2}[/tex]

∴ [tex]x=-3[/tex]

Thus, the function will not exist at [tex]x=-3[/tex]. This means it has all real number solutions except -3.

The solution set can be given as:

[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]

Answer:

3 slices each

Step-by-step explanation:

18 people ÷ 6 pizzas = 3 slices each

18÷6=3

To find the total amount of water needed to water all the plants in the house, the amount of water for a part of the plants is used to set up a proportion. After cross-multiplying and calculating, it is determined that 10/3 liters or approximately 3.33 liters of water is required.

If 4/3 liters of water is enough for 2/5 of the plants, then the amount of water required for all the plants can be found by setting up a proportion. We use cross-multiplication to solve for the unknown amount of water needed to water all the plants.

First, we express the given information as a fraction:

(4/3) liters

(2/5) plants

Next, we solve for the total water required (let's call it x):

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

We cross-multiply to solve for x:

4/3 * 1 = x * (2/5)

Multiplying both sides by the reciprocal of (2/5), which is (5/2), to isolate x, we get:

(4/3) * (5/2) = x

Now we calculate:

x = (4 * 5) / (3 * 2) = 20/6 = 10/3 liters

Therefore, 10/3 liters of water, or approximately 3.33 liters, is necessary to water all the plants in the house.

Answer:

4x+60 or 4(x+15)

Step-by-step explanation:

1/2x+4x-1/2x+60

1/2x-1/2x+4x+60

4x+60

Answer: It’s 4(x+60)

Step-by-step explanation: hope this helps

Answer:

6-k

Step-by-step explanation:

Difference means subtraction.

Answer:

$52

Step-by-step explanation:

90-38

total amount subtracted by the amount she had

Answer:

  {-1, -1/3, 1/3, 1}

Step-by-step explanation:

The possible rational roots are ...

  ±(divisor of constant)/(divisor of leading coefficient)

Here, that means the rational roots are ...

  ±p/q where p ∈ {1}, and q ∈ {1, 3}

That is, they can be ±1/1 or ±1/3. Arranged from smallest to largest, they are ...

  -1, -1/3, 1/3, 1

_____

A graph shows the roots to be -1 (multiplicity 2) and (+1/3). Then the function factors as ...

  f(x) = (3x -1)(x +1)²

To find the possible rational roots of the function f(x) = 3x^3 + 5x^2 + x - 1, we can use the Rational Root Theorem. The p/q list of possible rational roots is ±1/1, ±1/3, ±1/3, ±1/1.

To find the possible rational roots of the function f(x) = 3x^3 + 5x^2 + x - 1, you can use the Rational Root Theorem. According to the theorem, the possible rational roots are all the possible fractions that can be formed by dividing a factor of the constant term (-1) by a factor of the leading coefficient (3).

Step 1: Find the factors of the constant term (-1), which are ±1.

Step 2: Find the factors of the leading coefficient (3), which are ±1 and ±3.

Step 3: Write out all the possible fractions using the factors found in steps 1 and 2 as p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The p/q list of possible rational roots for the function f(x) = 3x^3 + 5x^2 + x - 1 is ±1/1, ±1/3, ±1/3, ±1/1.

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Answer:

B

Step-by-step explanation:

∠ FDG = ∠ CDB = 50° ( vertical angles are congruent ), thus

∠EDG = 90° - ∠ FDG = 90° - 50° = 40° → B

Answer:

no bro

Step-by-step explanation:

because copy has same shape

Final answer:

A photocopy is not a dilation; dilations change size while maintaining shape, while photocopies replicate the original image at the same scale.

Explanation:

When you make a photocopy of an image, it is not considered a dilation. A dilation involves resizing an image while maintaining its shape, whereas a photocopy reproduces the original image at the same scale.

A dilation in physics refers to a transformation that changes the size of an object, typically without altering its shape. Examples of dilations can be seen in various optical processes such as lens systems and camera projections.

Photocopying is a replication process that duplicates an image onto another surface with the same proportions and characteristics as the original, making it distinct from a dilation.

Answer:

Step-by-step explanation:

8x - 20.....factor a 4 out

4(2x - 5) <=== this one is correct...not 100% sure who wrote it

8x - 20...factor out a 2

2(4x - 10) <==== this is correct

8x - 20....factor out a -2

-2(-4x + 10) <==== this is correct

8x - 20....factor out a -4

-4(-2x + 5).....nobody did this one......but somebody tried....that person didn't factor correctly

Final answer:

Craig, Ester, and Lisa wrote correct expressions equivalent to 8x - 20. Ali's expression is incorrect due to improper distribution of the negative sign, resulting in an expression equivalent to 8x + 20, rather than 8x - 20.

Explanation:

The expressions provided by the students need to be equivalent to 8x - 20. We can factor out a common factor or distribute and combine like terms to check the equivalence of each expression:

For the incorrect expression (-4)(2x + 5), Ali likely distributed the negative incorrectly. Ali should have distributed the negative sign across the terms inside the parenthesis, producing -8x - 20, which is equivalent to 8x + 20, and not 8x - 20.

Answer:

2.15

Step-by-step explanation:

The easiest way to convert a percentage to a decimal is to simply add a decimal on the number (If the number does not already have one), then move that decimal two places to the left.

We can do that like so:

1: Remove the percentage sign: 215% -> 215

2: Add a decimal at the end of the number: 215.

3: Move the decimal two places to the left: 2.15

So 215% converted to a decimal would be 2.15

Answer:

Step-by-step explanation:

Final answer:

The original dimensions of the cardboard sheet are 12 inches by 12 inches, which is calculated by setting up an equation using the provided volume of the open-top box and the size of the squares cut from each corner.

Explanation:

Solving for the Original Dimensions of the Cardboard Sheet

To solve this problem, we need to find the original dimensions of the square sheet of cardboard that will create an open-top box with a volume of 128 cubic inches after 2-inch squares are cut from each corner and the sides are folded up. Since the volume of the box (V) is given by the formula V = length x width x height, we first denote the original side length of the cardboard as x inches. After cutting out 2-inch squares from each corner, we will fold up the sides, which means the new length and width of the box will be (x - 4) inches (since we lose 2 inches on each side). The height of the box will be 2 inches, which is the size of the square cut out from each corner. Therefore, the volume of the box can be expressed as 2(x - 4)^2.

To find the value of x, we solve the equation 2(x - 4)^2 = 128. Simplifying, we get (x - 4)^2 = 64. Taking the square root of both sides, we have x - 4 = 8. Adding 4 to both sides gives us x = 12. So, the original dimension of the cardboard is 12 inches by 12 inches.

Answer: D. 2500

Step-by-step explanation:

If total expense is $5000 and the spend 20% on food

30% on housing

Which make is 50% on both hosing and food leaving 50% on other expenses

Which makes half of the total budget

50/100* $5000 =$2500

Answer:

D

Step-by-step explanation:

Answer: [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0

Step-by-step explanation:

Since the zeros of the polynomials are -3 , 4 and 1 , then the equation will be in the form:

(x+3)(x-4)(x-1) = 0

Expanding (x+3)(x-4) , we have

[tex]x^{2}[/tex] - 4x + 3x - 12

⇒[tex]x^{2}[/tex] -x - 12

combining with (x-1) , we have

([tex]x^{2}[/tex] -x - 12) ( x -1 ) = 0

expanding , we have :

[tex]x^{3}[/tex] - [tex]x^{2}[/tex]-[tex]x^{2}[/tex] + x - 12x + 12 = 0

⇒[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0

Answer:

D negative four

Step-by-step explanation:

Answer:

d) y= -4

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{6}[/tex] hour or [tex]10[/tex] minutes

Step-by-step explanation:

Lisa:

Rate = 10 mph

Time = t hours

Distance = x miles

[tex]x=10\cdot t[/tex]

Jen:

Rate = 4 mph

Time = t hours

Distance = x - 1 miles

[tex]x-1=4\cdot t[/tex]

Hence,

[tex]10t-1=4t\\ \\10t-4t=1\\ \\6t=1\\ \\t=\dfrac{1}{6}\ hour[/tex]

Answer:

Step-by-step explanation: the sender below is not correct