Explain why the solution to 3r=2 must be less than 1

Answer:

86

Step-by-step explanation:

Since something minus a negative is just adding, we get 37-(-8)=37+8 or 45. We can do the same with 11-(-30) which is 11+30 or 41. So 45+41=86

Answer:

86.

Step-by-step explanation:

Work out the 'inner' parentheses first:

(37 - (-8)] + [11 - (-30)]

= (37 + 8) + (11 + 30)

Now the outer parentheses:

= 45 + 41

= 86.

Answer:

-1

Step-by-step explanation:

Given equation of line is:

x - y = 8

In order to find the slope of other line we have to convert the given equation in standard form

So,

-y = -x + 8

Multiplying the equation with -1

y = x - 8

The co-efficient of x is the slope of the line.

Here the co-efficient is 1 so the slop of line is 1.

We know that the producct of slopes of perpendicular lines is -1.

Let m2 be the slope of the other line then

1 * m2 = -1

m2 = -1

So the slope of line perpendicular to line x-y = 8 will be: -1 ..

Answer:

C

Step-by-step explanation:

Since the triangle is right with hypotenuse QR

Use Pythagoras' identity to solve for QR

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

QR² = 8² + (8[tex]\sqrt{3}[/tex] )²

       = 64 + 192

       = 256 ( take the square root of both sides )

QR = [tex]\sqrt{256}[/tex] = 16

Final answer:

The length of QR is approximately 2.25 units. Since qr and qs are similar, the length of QR is also approximately 2.25 units.

Explanation:

The length of QR can be determined based on the given information about the vectors near S, R, and T. The vectors near S start at about 6 units away, while vectors near R and T start at about 4 units. Using the equation qr|d² = qs|D², we can find that as|¶R = D² / d² = 36 / 16 = 2.25. Since qr and qs are similar, the length of QR is also approximately 2.25 units.

Answer:

[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]

Step-by-step explanation:

The division problem given to us is [tex](4x^3-3x^2+5x+6)\div (x+6)[/tex].

To perform the synthetic division, we write out the coefficient of the polynomial. We set the linear factor to zero and solve for x, this becomes our divisor. That is [tex]x+6=0\implies x=-6[/tex].

We carry out the synthetic division as shown in the attachment.

The result of the synthetic division is 4   -27   167   -996

The first three terms are the coefficients of the quotient and the last term is the remainder.

Therefore the quotient is [tex]q(x)=4x^2-27x+167[/tex] and the remainder is [tex]r(x)=-996[/tex].

The dividend, the quotient and the divisor are written as

[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]

The correct answer is A

The value of  [tex]f(g(x))=-6x-5[/tex]

Given functions are, [tex]f(x)=-2x-3,g(x)=3x+1[/tex]

We have to find composite function [tex]f(g(x))[/tex].

         [tex]f(g(x))=f(3x+1)\\\\f(g(x))=-2(3x+1)-3\\\\f(g(x))=-6x-2-3\\\\f(g(x))=-6x-5[/tex]

Learn more about the composite function here:

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To find (fxg)(X), you need to multiply the two given functions, apply the distributive property, and then combine like terms. The result for (fxg)(X) is -6x² - 11x - 3.

Step-by-step Explanation:

Therefore, (fxg)(X) = -6x² - 11x - 3.

Answer:

3.6 fl oz

Step- by-step explanation:

Well if one gallon equal 2.4 fl oz that would mean that half of a gallon would be half of that amount. Half of that amount would be 1.2 fl oz. we have now found how much a full gallon needs and how much half a gallon need. Now we add these 2 numbers. 2.4 fl oz + 1.2 fl oz = 3.6 fl oz.

Please give me Brainliest.

Final answer:

To get the correct oil mix for 1.5 gallons of gasoline at a ratio of 2.4 fl oz of oil per gallon, you should add 3.6 fl oz of oil.

Explanation:

To calculate the amount of oil needed for 1.5 gallons of gasoline with a mix ratio of 2.4 fl oz of oil per gallon, you follow these steps:

Determine the amount of oil needed for one gallon of gas, which is 2.4 fl oz.

Multiply this amount by the total gallons of gas. In this case, 2.4 fl oz x 1.5 gallons.

The calculation will be 2.4 fl oz/gallon x 1.5 gallons = 3.6 fl oz of oil.

Therefore, you should add 3.6 fl oz of oil to 1.5 gallons of gasoline to achieve the correct mix ratio.

Answer:

Option c. 30,000

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

y ----> safe load in pounds

x ----> length in feet of a horizontal beam

we have

For [tex]x=15\ feet, y=2,000\ pounds[/tex]

Remember that

[tex]k=y*x[/tex]

substitute

[tex]k=2,000*15=30,000[/tex]

Answer:

The test contains 10 three-point questions and 14 five-point questions

Step-by-step explanation:

Given equations are:

[tex]x+y = 24\\and\\3x+5y=100[/tex]

From 2nd equation we can deduce that x represents number of 3-point questions and y represents number of 5-point questions.

Using the substitution method:

From x+y = 24

y= 24-x

Putting this valu of y in 3x+5y=100

[tex]3x+5(24-x) = 100\\3x + 120 - 5x = 100\\-2x+120=100\\-2x = 100-120\\-2x = -20\\\frac{-2x}{-2} = \frac{-20}{-2}\\ x = 10\\Putting\ the\ value\ of\ x\ in\ x+y=24\\10+y=24\\y = 24-10\\y = 14[/tex]

Hence, the correct answer is:

The test contains 10 three-point questions and 14 five-point questions..

Answer:

They are equivalent

Step-by-step explanation:

x/4 multiplied by y/y equals to xy/4y. Therefore, they are equivalent

92 boxes

1379/15=91.93 but u need a full box so 92

Answer:

92

Step-by-step explanation:

Given:

Number of Paperweights = 1,379

Number of Paperweights that each box can hold = 15

Number of boxes needed = 1379 ÷ 15 = 91.933 boxes

Because 0.933 of a box is of no use to anyone, we simply round this number up to the next whole box and just have the last box partially full.

This gives us 92 boxes.

Answer:

The satisfaction level gained when a customer consumes a product is total utility.It calculated by finding the total sum of utility from consumption.

Marginal utility is the rate of change of total utility and quantity consumed.

Here you apply the expression, Marginal utility=change in total utility/change in quantity consumed

Let, Marginal utility=MU

Total utility=TU

Quantity consumed=QC

Then MU=ΔTU ÷Δ QC

Given the table

Chocolate Candy Bars          Total Utility(utils)          Marginal Utility(utils)

0                                                      0                                 -

1                                                        25                             x

2                                                         y                             17

3                                                      54                                z

4                                                     a                                  b

5                                                      66                                4

6                                                      c                                   -1

Here you have assigned the missing areas with letter, hence finding the real values of the letters;

Apply MU=ΔTU÷ΔQC

[tex]1.17=\frac{y-25}{1}\\\\17=y-25\\\\y=17+25=42\\\\\\2.x=\frac{25-0}{1} \\\\x=25-0=25\\\\\\3.z=\frac{54-42}{1} \\\\z=54-42=12\\\\\\4.\frac{66-a}{1} =4\\\\66-a=4\\\\66-4=a\\a=62\\\\5.b=\frac{62-54}{1} =8\\\\\\6.\frac{c-66}{1} =-1\\\\\\c-66=-1\\\\c=-1+66=65[/tex]

Answers

y=42,x=25,z=12,a=62,b=8,c=65

Replace the letters with the real numbers in filling the table.

Answer:

The smallest number that is in the domain of fog is 3

Step-by-step explanation:

f(x) = [tex]\sqrt{8x}[/tex] (as corrected in comments)

g(x) = x-3

we need to find fog = f(g(x))

For finding f(g(x)) we put the value of g(x) inside the f(x)

f(g(x))=[tex]\sqrt{8(x-3)}[/tex]

The domain of this function is x ≥ 3

because if value of x is less than 3 than the result would be negative and we know √f(x) ≥ 0

So, the smallest number that is in the domain of fog is 3

Answer:

A) Obtuse

Step-by-step explanation:

It is Obtuse due to the angle 115° being in the Triangle. This rules out Acute since the middle angle is not less than 90°. It is not Equiangular since all three angles are not equal. Furthermore it is not a right triangle either since there is no 90° angles. Making it Obtuse.

To classify a triangle based on angle measures, we need to know the specific angles. Triangles can be obtuse, acute, right, or equiangular, and each type has its own unique properties used in various applications across different fields.

To classify the following triangle based on its angle measures, we must first understand the definitions of different types of triangles. A triangle can be classified as:

Considering these definitions, the seeking student must provide the angle measures of their specific triangle to accurately classify it.

Making distinctions between different types of triangles is crucial because each classification has unique properties that are important in various fields such as mathematics, engineering, architecture, and physics. These properties assist in solving problems and understanding the world around us.

For instance, an obtuse triangle may be used in special construction scenarios, while right triangles are essential in trigonometry and geometry, appearing frequently in real-life applications like building and navigation.

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Answer:

d

Step-by-step explanation:

Given the 2 equations

2x - y = 11 → (1)

3x - 2y = 6 → (2)

Multiply (1) by - 2 and adding will eliminate y

- 4x + 2y = - 22 → (3)

Add (2) and (3) term by term

(3x - 4x) + (- 2y + 2y) = (6 - 22)

- x = - 16 ( multiply both sides by - 1 )

x = 16

Substitute x = 16 into (1) or (2) for corresponding value of y

(1) : 32 - y = 11 ( subtract 32 from both sides )

- y = - 21 ( multiply both sides by - 1 )

y = 21

Solution is (16, 21 ) → d

Answer:

It's d. (16,21).

Step-by-step explanation:

2x -  y =  11 .............(1)

3x – 2y = 6...........(2)

Multiply the first equation by -2:

-4x + 2y = -22.......(3)

Adding (2) + (3):

-x = -16

x = 16.

Substitute for x in equation (1):

2(16)  - y = 11

-y = 11-32 = -21

y = 21.

Answer:

Yes

Every straight line can be represented by an equation: y = mx + b.

m=slope

b=y-intercept

(www.math.com/school/subject2/lessons/S2U4L2GL.html)

Answer is:

37 nickels

Answer:

it takes 97 nickels

Step-by-step explanation:

4.85÷0.05=97

Answer:

4.50

Step-by-step explanation:

3 divided by 2 is 1.5, which is equivalent to $1.50. So each drink cost 1.50. 1.50 x 3 = 4.50.

The graph of the equation y = x + 3 is a straight line with a slope of 1 and a y-intercept of 3. This means that for every increase of 1 in x, y increases by 1 and the line crosses the y-axis at y = 3.

The student is asking for the graph of the function g(x)=[x+3]. Please note, the symbol '[' and ']' is usually used to denote the greatest integer function or floor function, but since the context is not very clear, I'll assume that this is a simple linear function y = x + 3.

In such case, the graph of y = x + 3 is a **straight line** with a **slope** of 1 and a y-**intercept** of 3. Remember, the ^ slope is the change in y for every increase of 1 in x, and in this equation, for every increase of 1 in x, y increases by 1 . The intercept is simply where the line crosses the y-axis, and in this case it's at y = 3.

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Answer:

Whats the question?

Step-by-step explanation:

The dots do not form a straight line, there is a small curve.

The dots do move up and to the right which makes it a positive curve.

The answer would be B. nonlinear positive association.

79+(-42/6)-(-24)

first use -42 divide by 6

79 + (-7) - (-24)

then open all the parentheses

79 - 7 + 24

and use 79 minus 7

72 +24

add them together

96

That's how to get it.

Answer:

Step-by-step explanation:

79+(-42 divide 6)- -24

The first step is division

79+(-7)- -24

Then we add and subtract from left to right

72 --24

72+24

96

Answer:

x = 3.133

Step-by-step explanation:

I'm going to take a chance and assume that you meant "ln 11," not "in11."

If I'm right, then we have:

3x-5 = ln 11 + 2.

Adding 5 to both sides yields

3x = ln 11 + 2 + 5, or ln 11 + 7.  Since ln 11 = 2.398,

3x = 2.398 + 7, or    3x = 9.398, and so

x = 3.133.

If this is not what you expected, please ensure that you have copied down the original problem accurately.  Thank you.

Answer:

20

Step-by-step explanation:

If the three numbers are x, x+1, and x+2, then:

x (x+1) (x+2) = 990

x (x² + 3x + 2) = 990

x³ + 3x² + 2x - 990 = 0

(x - 9) (x² + 12x + 110) = 0

Since x must be a whole number, x = 9.  You can also use simple trial and error to find that the three numbers are 9, 10, 11.

The sum is:

9 + 10 + 11 = 20

Answer:

4xy[2xy - x - 3]

Step-by-step explanation:

When finding the Greatest Common Factor [GCF], along with the coefficient, you have to factor out the least degree term possible, which in this case is 4xy. This is because although all terms have y and x, their degrees are not all similar, so we have to go with 4xy.

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

 can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

 must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle

Answer:

Δ = 60

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the discriminant

Δ = b² - 4ac

Given

3x² + 6x = 2 ( subtract 2 from both sides )

3x² + 6x - 2 = 0 ← in standard form

with a = 3, b = 6 and c = - 2

b² - 4ac = 6² - (4 × 3 × - 2) = 36 - (- 24) = 36 + 24 = 60

For this case we have by definition, that the area of a rectangular prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] is the area of the base

h: It's the height

Before finding[tex]A_ {b}[/tex]we convert the mixed numbers to fractions:

length: [tex]2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]

width: 6

Height:[tex]3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}[/tex]

So, we have to:[tex]A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5[/tex]

Finally, the volume is given by:

[tex]V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3[/tex]

Answer:

[tex]47.25 \ ft ^ 3[/tex]

ANSWER

[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]

EXPLANATION

The formula for calculating the volume of a rectangular prism is

[tex]Volume = l \times b \times h[/tex]

Where

[tex]l = 2 \frac{1}{4} ft[/tex]

is the length of the rectangular box,

[tex]w = 6ft[/tex]

is the width and

[tex]h = 3 \frac{1}{2} ft[/tex]

is the height of the rectangular prism.

We plug in the given dimensions into the formula to get:

[tex]Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2} [/tex]

Convert the mixed numbers to improper fraction to get:

[tex]Volume = \frac{9}{4} \times 6 \times \frac{7}{2} [/tex]

Multiply out to get

[tex]Volume = \frac{189}{4} {ft}^{3} [/tex]

Or

[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]

Answer:

Pythagorean Theorem

hypotenuse^2 = side^2 + side^2

16^2 = 7^2 + side ^ 2

256 - 49 = side^2

side x = sq root (207)

207 = 9 * 23 Therefore,

side x = 3 * sq root (23)

answer is A

Step-by-step explanation:

The geometric mean of two numbers is the square root of their product.

sqrt{4 • 12}

sqrt{48}

sqrt{16} •sqrt{3}

4•sqrt{3}.

The geometric mean of 4 and 12 is

4•sqrt{3}.

Answer:

congrats

Step-by-step explanation: