The sum of three numbers is 108. The second number is four times greater than the first number, and the third number is 18 more than the first. Find the largest of the three numbers.

Answer:

18

Step-by-step explanation:

2a+3b

2•3+3•4

6+12

18

Answer:

2124+272cd

Step-by-step explanation:

Answer:

5x+3x+6>14

8x>14-6

8x>8

divide both sides by 8

x>1

Answer:

C.$150

Step-by-step explanation:

The sales man told her that he would sell it to he for ⅓ of the marked price.

Given:

Marked Price= $450

⅓

Required:

⅓ of the marked price or $450

Formula:

⅓*$450

Solution:

⅓ of $450

⅓*$450

$450/3

$150

Hope this help ;) ❤❤❤

Answer:

A.180

Step-by-step explanation:

Answer: 8 students per team and 4 pencils each student

Step-by-step explanation:

Answer:

Both C and D

Step-by-step explanation:

Answer:

It makes the calculation easy and quick.

Step-by-step explanation:

When you multiply as it is given:

Using the commutative property makes it much easier:

Answer:

see below.

Step-by-step explanation:

its a commutative property of multiplication.

it doesn't matter in order or not... the result will always be the same.

form your example 5×87×2, if you use a calculator it doesn't matter which number you start.

say 2 x 87 x 5 = 870

or 87 x 5 x 2 = 870

or 5 x 2 x 87 = 870

see the results are all the same no matter which way you go.

Answer:

x= -1/3 or -2

Step-by-step explanation:

3x^2 +3x= -2x +2-4

3x^2 + 5x +2=0

by factorization method

3x(x+2) 1(x+2)=0

(3x+1)(x+2)

Answer:

x3(x+1)= –2(x-1)–4

3x^2+3x=–2x+2-4

3x^2+3x+2x=2-4

3x^2+5x=–2

3x^2+5x+2=0

3x^2+3x+2x+2=0

3x(x+1)2(x+1)=0

(3x+2)(x+1)=0

3x+2=0 or x+1=0

3x=–2 or x=–1

x=–2/3 or –1

Step-by-step explanation:

–remove brackets by multiplication

–form a quadratic equation

–and then solve either by means of quadratic formula or factorisation method

Answer:

I think your suppose to multiply the lengths together then you multiply the width together and the add those two

Step-by-step explanation:

srry if i am wrong lol

Answer:

For Khan: A-Only (2,5)

Step-by-step explanation:

Answer:8

Step-by-step explanation: she makes $100 a day so you would subtract that from the total (276) then you would divide the remainder (176) by the amount she makes an hour (22) then you would end up with 8 hours

Answer:

8 hours

Step-by-step explanation:

For $22=1 hour

For $1=1/22 hours

For $176=176/22 hours=8 hours

And she gets also $100 extra

So for $276 she works 8 hours.

Answer:

If you need to evaluate the equation, the answer would be x=19/16.

Step-by-step explanation:

Answer:

-3,5,-10,16

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

[tex](3x-1)(3x+1)=9x^{2}-1[/tex] [tex]=\frac{9x^{2} }{9}-\frac{1}{9}=[/tex] [tex]x^{2} -\frac{1}{9}[/tex]

[tex](x-1/3)(x+1/3)=x^{2} -\frac{1}{9}[/tex]

Answer:

20/3

Step-by-step explanation:

5/k=15/20

5/k=3/4

5 x 4/3 = k

k=20/3

Answer:

Step-by-step explanation:

it is given by the formula=4× 90/ n

where n = number of sides

exterior angle= 4 x 90/13

=360/13=[tex]27.7[/tex]°

The value of x in the expression will be 100.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that FG = (2x) meters, GH = 1,000 meters, and FH = 1,200 meters,

The value of x will be calculated by making an equation for the line segment below:-

FG + GH = FH

2X+1000=1200

2X = 1200 - 1000

2X = 200

X = 100 meters

2X + 1000= 1200

Therefore, the value of x in the expression will be 100.

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Answer:

Step-by-step explanation:

[tex]2 . 4x =\\2 \times 4x\\\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8\\\\= 8x[/tex]

Answer:

I think a spinner is not a type of probability model.

I am not sure tho

Option (c) A spinner is not a probability model

A probability model is a mathematical representation of a random phenomenon.

Here,

In systematic list, the outcomes for an event can be listed in an organized or systematic way to make sure that none of the possible outcomes is missed out.

In area model, area models can be used to represent simple probabilities.

A probability tree diagram is used to represent the probability of occurrence of events without using complicated formulas.

But spinner is not a probability model.

Hence, option (D) Spinner is not a probability model

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Answer: two-column

Step-by-step explanation:

Answer:

two-column proof

Step-by-step explanation:

quizlet

Answer: Answer is in the steps

Step-by-step explanation:

If the system of equations have the same slope and same y-intercepts then it means that they have infinitely many solutions.

if the system of equations have the same slope but different y-intercepts it means that they have no solution because they will never intersect but will always form parallel lines.

If the system of equations have different slopes and different y-intercepts or have same y-intercepts and different slopes it means that they have exactly on solution.

Answer:

14

Step-by-step explanation:

Since gaining fourteen pounds means going in a positive direction, we can say the gain of fourteen pounds numerically as 14.

Answer:

5 quarters and 3 nickels

Step-by-step explanation:

x = nickels

y = quarters

x + y = 8

x(0.05) + y(0.25) = 1.40

3 + 5 = 8

3(0.05) + 5(0.25) = 1.40

0.15 + 1.25 = 1.40

1.25 + 0.15 = 1.40

Answer:

a) [tex]a = 2[/tex] and [tex]b = -4[/tex], b) [tex]c = -10[/tex], c) [tex]f(-2) = -\frac{5}{3}[/tex], d) [tex]y = -\frac{5}{2}[/tex].

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex].

Denominator

i) [tex](x+2)\cdot (x-1) = 0[/tex] Given

ii) [tex]x^{2} + x-2 = 0[/tex] Factorization

iii) [tex]2\cdot x^{2}+2\cdot x -4 = 0[/tex] Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that [tex]a = 2[/tex] and [tex]b = -4[/tex]

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) [tex]c\cdot x - 5\cdot x^{2} = 0[/tex] Given

ii) [tex]x \cdot (c-5\cdot x) = 0[/tex] Distributive Property

iii) [tex](-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0[/tex] Distributive and Associative Properties/[tex](-a)\cdot b = -a\cdot b[/tex]/Result

As we know, this polynomial has [tex]x = -2[/tex] as one of its roots and therefore, the following identity must be met:

i) [tex]\left(x -\frac{c}{5}\right) = (x+2)[/tex] Given

ii) [tex]\frac{c}{5} = -2[/tex] Compatibility with addition/Modulative property/Existence of additive inverse.

iii) [tex]c = -10[/tex] Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of [tex]c[/tex] is -10.

c) We can rewrite the rational function as:

[tex]f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}[/tex]

After eliminating the removable discontinuity, the function becomes:

[tex]f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)[/tex]

At [tex]x = -2[/tex], we find that [tex]f(-2)[/tex] is:

[tex]f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right][/tex]

[tex]f(-2) = -\frac{5}{3}[/tex]

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward [tex]\pm \infty[/tex]. That is:

[tex]y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}[/tex] Given

[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right][/tex] Modulative Property

[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right][/tex] Existence of Multiplicative Inverse/Definition of Division

[tex]y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)[/tex]   [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]

[tex]y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)[/tex]   [tex]\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}[/tex]/[tex]x^{m}\cdot x^{n} = x^{m+n}[/tex]

[tex]y = -\frac{5}{2}[/tex] Limit properties/[tex]\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0[/tex], for [tex]n \geq 1[/tex]

The horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex].

Using asymptote concepts, it is found that:

a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.

b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.

c) Simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex].

d) The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]

-------------------------

Item a:

[tex]2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4[/tex]

[tex]2x^2 + ax + b = 2x^2 - 2x - 4[/tex]

Thus a = 2, b = -4.

-------------------------

Item b:

[tex]-2c - 5(-2)^2 = 0[/tex]

[tex]-2c - 20 = 0[/tex]

[tex]2c = -20[/tex]

[tex]c = -\frac{20}{2}[/tex]

[tex]c = -10[/tex]

-------------------------

Item c:

With the coefficients, the function is:

[tex]f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}[/tex]

At x = -2:

[tex]-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}[/tex]

Thus, simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex]

-------------------------

Item d:

The horizontal asymptote of a function is:

[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]

Thus:

[tex]y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}[/tex]

The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]

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Answer:

-13

Step-by-step explanation:

Answer:

x = [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex] = [tex]\frac{x-1}{4}[/tex] ( cross- multiply )

3(x - 1) = 8

3x - 3 = 8 ( add 3 to both sides )

3x = 11 ( divide both sides by 3 )

x = [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Angle A = 4x + 12 = 4(15) + 12 = 72°.

Acute is for angles that are less than 90°.

Obtuse is for angles that are between 90° and 180°, not inclusive.

Right is for angles that are 90°

Hence the answer is acute.

The angle is an acute angle

An acute angle is an angle that is less than 90 degrees

An obtuse angle is an angle that is greater than 90 degrees and less than 180 degrees

In order to determine which type of angle it is, solve for angle A

4x + 12

4(15) + 12

60 + 12 = 72

The angle is acute because it is less than 90 degrees

Please check the attached image for an image of an acute angle

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Answer:

24

Step-by-step explanation:

We are given segment XZ and point Y. First, draw a number line. Draw X and Z on either side of the number line. We know that Y is between X and Z since there are the distances of XY and YZ. To find XZ, add the distance of XY and YZ, which are respectively 7 and 17. Adding 7 and 17, we get 24 as the answer.

The value of XZ is 24.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment XZ, where the length of line segment XZ refers to the distance between its endpoints, X and Z.

Given that a line segment XZ and point Y that lies on XZ

XY = 7 and YZ = 17

Here XZ = XY + YZ

X_____________Y_______________Z

⇒ XZ = XY + YZ

Substitute the values of  XY = 7 and YZ = 17, we get

⇒ XZ = 7 +  17

Apply the addition operation in the above equation,  

⇒ XZ = 24

Therefore, the value of XZ is 24.

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