A triangle has sides measuring 5 inches and 8 inches. If x represent the length in inches of the third side , which inequality gives the range of possible values for x ?

Answer: A. 4

The largest exponent in the polynomial tells us the max number of roots, x intercepts, or zeroes of the function. In this case, that happens to be 4. This is the degree of the polynomial. It is considered a quartic polynomial. It is also a trinomial since it has 3 terms (3x^4, x^2 and 1)

Answer:

ITs A

Step-by-step explanation:

The highest degree is 4 ( 3x^4)  so the maximum number of zeroes is 4.

The answer is: 6,641.40$

Explanation:

Six thousand= 6,000

Six hundred= 600

Forty one= 41

Forty cents: .40

Now add all of these together:

6,000

+  600

+      41

+          0.40

Which will give you 6,641.40$

I hope this helps! :)

-LizzyIsTheQueen

Answer:

$1808263    

Step-by-step explanation:

We're given with the below information:-

Initial price of the building = Principal amount (P) = $590000

Rate of interest (r) = 14% = 0.14

Time in years (t) = 2020 - 2012 = 8

The formula to calculate the final amount where interest is continuously  compounded each year is :-

[tex]A = Pe^{rt}[/tex]                              [e is the mathematical const = 2.71828]

Plugging in the values of P, e, r, and t in the above formula, we get

[tex]A = 590000*2.71828^{0.14*8}[/tex]

=> A= 1808262.6

=> A = $1808263     (rounded off to the nearest whole dollar)

So, she expect to sell the building in 2020 for an amount of $1808263

Answer:\

180000

Step-by-step explanatii took

Answer: 2x + y

Step-by-step explanation:

logₐ(3) = x

logₐ(5) = y

logₐ(45) = logₐ(3²· 5)

             = logₐ(3)² + logₐ(5)

             = 2 logₐ(3) + logₐ(5)

             = 2     x      +   y        substituted given values (stated above)

Step-by-step explanation:

Here we make use of the laws of logarithms:

log_a(PQ) = log_a(P)+log_a(Q)

which implies the following corollary

log_a(P^2) = log_a(P)+log_a(P) = 2log_a(P)

Notice how the log of a product is reduced to the sum of the log of the factors.  (Advantage is taken of this fact in the use of logarithm tables before the wide-spread use of electronic calculators (pre-70's) )

So substituting

x=log_a(3)

y=log_a(5)

we have

log_a(45) = log_a(3^2 * 5) = log_a(3^2) + log_a(5)=2log_a(3)+log_a(5)

=2x+y

Answer:

1) 3

2) {x = 9 or x = -1}

3) (b) The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]

Step-by-step explanation:

Problem 1

3 - 2 [tex]\frac{\sqrt{11} }{2} + \sqrt{11}[/tex]

i) Cancelling out the 2's from the top and bottom of the middle term, we get

3 - [tex]\sqrt{11} + \sqrt{11}[/tex]

ii) Cancelling out -[tex]\sqrt{11}[/tex] and +[tex]\sqrt{11}[/tex], we get

3 as the simplified form

Problem 2

x-1 = [tex]\sqrt{6x+10}[/tex]

Our first goal is to get rid off the radical on the right side

i) Squaring both sides, we get

[tex](x-1)^{2}[/tex]=[tex](\sqrt{6x+10})^{2}[/tex]

ii) (x-1)*(x-1) = 6x+10

iii) Applying the distributive property (a+b)(c+d) = ac+ad+bc+bd to the left side of the equation, we get

(x)(x)+(x)(-1)+(-1)(x)+(-1)(-1) = 6x+10

=> [tex]x^{2}[/tex]-x-x+1 = 6x+10

=> [tex]x^{2}[/tex]-2x+1 = 6x+10

iv) Subtract 6x from both sides, we get

[tex]x^{2}[/tex]-2x+1-6x = 6x+10-6x

v) Cancelling out 6x and -6x from the right side, we get

[tex]x^{2}[/tex]-2x-6x+1 = 10

=> [tex]x^{2}[/tex]-8x+1 = 10

vi) Subtracting 10 from both the sides, we get

[tex]x^{2}[/tex]-8x+1-10 = 10-10

vii) Cancelling out 10 and 10 from the right side, we have

[tex]x^{2}[/tex]-8x-10+1 = 0

=> 1[tex]x^{2}[/tex]-8x-9 = 0

viii) Coefficient of the first term = 1

Multiplying the coefficient of the first term and the last term, we get

1*(-9) = -9

We need to find out two such factors of -9 which when added should give the middle term -8

So, -9 and +1 are the two factors of -9 which when added gives us the middle term -8

ix) Rewriting the middle term, we get

[tex]x^{2}[/tex]-9x+x-9 = 0

x) Factoring out x from the first two terms and factoring out 1 from the last two terms, we get

x(x-9)+1(x-9)=0

xi) Factoring out x-9 from both the terms, we get

(x-9)(x+1)=0

xii) Either x-9=0 or x+1=0

xiii) Solving x-9=0, we get x=9

xiv) Solving x+1=0, we get x= -1

So, solution set {x = 9 or x = -1}

Problem 3

5 − 3i

a) In order to graph the complex number 5-3i, we need to move right by 5 units on the real axis and then move down by 3 units on the imaginary axis.

See figure attached

b) A complex number is in the form of z= a+ bi

i) Comparing 5-3i with a+bi, we get a=5 and b = -3

The modulus is given by

|z| = [tex]\sqrt{a^{2}+b^{2} }[/tex]

ii) Plugging in a=5 and b=-3, we get

|z| = [tex]\sqrt{5^{2}+(-3)^{2} }[/tex]  

iii) |z| = [tex]\sqrt{25+9} [/tex]

iv) |z| = [tex]\sqrt{34}[/tex]

The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]

Answer:

A 0.2 L water was filled into the bottle from faucet each seconds.

Step-by-step explanation:

Unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or  6 miles per hour, they are called unit rates.

Given the statement: A 2 liter bottle is filled completely with water from a faucet in 10 seconds.

⇒ In 10 sec  a  2L bottle  is completely filled with water  from a faucet.

Unit rate per second =  [tex]\frac{2}{10} = \frac{1}{5} = 0.2 L[/tex]

Therefore, 0.2 L water was filled into the bottle each seconds.

Answer:

0.2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition y = 2 when x = 10

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

y = [tex]\frac{1}{5}[/tex] x ← equation of variation

when x = 40, then

y = [tex]\frac{1}{5}[/tex] × 40 = 8 → A

The value of y when x = 40 with the same proportion will be 8 thus option (A) is correct.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

If y varies directly with x.

y ∝ x

y = kx

k = y/x

Thus, k will be the same for both conditions.

2/10 = y/40

1/5 = y/40

40/5 = y

8 = y

Hence "The value of y when x = 40 with the same proportion will be 8 ".

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Answer: b

Step-by-step explanation:

NOTE:

hypothesis : If two lines intersect at right angles

conclusion: then the two lines are perpendicular

Answer:

15 students joined the radio-controlled model club

Step-by-step explanation:

The students joining the  radio-controlled model club were divided into three equal groups i.e

a) Radio-controlled boat group

b) Radio-controlled car group

c) Radio-controlled airplane group

10 new students joined the Radio-controlled airplane group  and the new sum of students in this group is 15.

This implies that there were 5 students in Radio-controlled airplane group  before the joining of 10 new students.

In the starting, the three groups have equal number of students which means that Radio-controlled boat group, Radio-controlled car group, Radio-controlled airplane group  have 5 students in each group. Thus, In the beginning there were total 15 students who joined the radio-controlled model club

Answer:

7.15x + 3.55y + 20 = weekly income

Step-by-step explanation:

7.15x + 3.55y + 20 = weekly income

Answer:

12 years will it take for light from the star to reach Earth.

Step-by-step explanation:

As per the given statement: A certain star is 1.135 × 10^14 km away from Earth. If light travels at 9.4607 × 10^12 km per year.

⇒Speed of light travel = [tex]9.4607 \times 10^{12}[/tex] km per year

and Distance of a certain star from the Earth = [tex]1.135 \times 10^{14}[/tex] km

To find how long will it take for light from the star to reach Earth.

Using Formula:

[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]

or

[tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]

Substitute the given values we have;;

[tex]\text{Time} = \frac{1.135 \times 10^{14}}{9.4607 \times 10^{12}}[/tex]

Simplify:

Time = 11.9969981 year ≈ 12 years

therefore, 12 years will it take for light from the star to reach Earth.

Answer:

1.  16

2.  -4

Step-by-step explanation:

First factor the expression

lim x→1  (x^3 + 5x^2 + 3x-9)/(x-1)

lim x→1  (x-1) (x+3)^2/(x-1)

Canceling the x-1  in the top and bottom

lim x→1   (x+3)^2

Let x=1

lim x→1   (1+3)^2 = 4^2 = 16

2.  lim x→0 (x^2 -6x+8) /(x-2)          

First factor the expression

    lim x→0 (x-4) (x-2) /(x-2)        

Canceling the x-2  in the top and bottom

lim x→0 (x-4)

Let x=0

lim x→0   (0-4) = -4

Filling in the table

x     -.1      -.01       -.001     .001     .01     .1

f(x) -4.1  -4.01    -4.001   -3.999   -3.99  -3.9

I know this isn't helpful, but I REALLY need help on this question...

Given: f(x) = x^2 + 7x + 10. From the Rational Root Theorem, we know p=10 and q=1. List all potential roots using the ratio p/q.

Adam has 6,000 points.

Let's use algebra to solve this problem. Let's assume that Adam's points are represented by 'x'. According to the problem, Nick has 20% more points than Adam, so Nick's points can be represented as 'x + 20% of x' or '1.2x'. Given that Nick has 7,200 points, we can set up the equation 1.2x = 7,200 and solve for 'x'. Divide both sides of the equation by 1.2 to isolate 'x' and find that Adam has 6,000 points.

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Answer:

2. 9

3.12 p^4 - 1/2 p^3 -8p^2 + 2p

Step-by-step explanation:

The degree of the polynomial is found by taking the number of the highest exponent.  We add the exponent when there is more than one variable in a term

5m^6n^3 =  degree (6+3)  = 9

3m^4n^2 = degree (4+2) = 6

So the polynomial is degree 9

Standard from is written from largest exponent to smallest exponent

12 p^4 - 1/2 p^3 -8p^2 + 2p

C it the answer because since heads hit 14 times it haves a higher percent of hitting heads again.

Answer:

x=6

Step-by-step explanation:

If ABCD is a parallelogram, then AB = CD

AB=CD

10x-15 = 6x+9

Subtract 6x from each side

10x-6x -15 = 6x-6x+9

4x-15 = 9

Add 15 to each side

4x-15+15 = 9+15

4x = 24

Divide by 4 on each side

4x/4 =24/4

x=6

Look at the picture.

The equation:

10x - 15 = 6x + 9       add 15 to both sides

10x = 6x + 24      subtract 6x from both sides

4x = 24    divide both sides by 4

Answer:

Option d is correct.

Domain = all real number

range = positive real numbers

Step-by-step explanation:

Given the function: [tex]y=f(x) = a^x[/tex]

Domain of the function is all real numbers except where the expression is undefined.

In this case, there is no real number that makes the expression undefined.

Domain of f(x) = [tex](-\infty , \infty)[/tex] = {a | a∈R}

Range is the set of all valid  f(x) values.

[tex](0,1) \cup (1, \infty)[/tex]

[tex]\{y | y\neq 1 , y>0\}[/tex]

Therefore, Domain is all real number and the range of function is positive real number

For [tex]f[/tex] to be differentiable, it must be continuous, so we need to have

[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3^+}f(x)=f(3)[/tex]

By its definition, [tex]f(3)=3^2=9[/tex]. The one-sided limits are

[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3}x^2=9[/tex]

[tex]\displaystyle\lim_{x\to3^+}f(x)=\lim_{x\to3}mx+b=3m+b[/tex]

so we require [tex]3m+b=9[/tex].

In order for [tex]f[/tex] to be differentiable at [tex]x=3[/tex], we also need to have [tex]f'(3)[/tex] exist, which requires that [tex]f'[/tex] also be continuous at [tex]x=3[/tex]. First, compute the derivatives of all pieces of [tex]f[/tex]:

[tex]f'(x)=\begin{cases}2x&\text{for }x<3\\?&\text{for }x=3\\m&\text{for }x>3\end{cases}[/tex]

[tex]f'[/tex] is continuous at [tex]x=3[/tex] if

[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3^+}f'(x)=f'(3)[/tex]

The one-side limits are

[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3}2x=6[/tex]

[tex]\displaystyle\lim_{x\to3^+}f'(x)=\lim_{x\to3}m=m[/tex]

so we need to have [tex]m=6[/tex], and moreover [tex]f[/tex] will be differentiable if we set [tex]f'(3)=6[/tex].

So with [tex]m=6[/tex], we must have [tex]3m+b=9\implies b=-9[/tex].

For the piecewise function f(x) = x^2 when x <= 3 and mx + b when x > 3, values m = 6 and b = -9 ensure differentiability at x = 3.

To make the piecewise function f(x) differentiable at x = 3, we need the two pieces, x^2 and mx + b, to smoothly connect at x = 3. This requires the values of m and b to ensure continuity of both function values and derivatives.

First, evaluate both pieces at x = 3:

x^2 when x <= 3 and mx + b when x > 3

For continuity, set these expressions equal to each other:

3^2 = m * 3 + b

This yields 9 = 3m + b. To ensure differentiability, the derivatives of both pieces must also match at x = 3:

f'(x) = 2x when x <= 3 and f'(x) = m when x > 3

For continuity of derivatives, set the derivatives equal to each other at x = 3:

2 * 3 = m

This gives m = 6. Substituting m = 6 into the continuity equation 9 = 3m + b gives b = -9.

Therefore, the values m = 6 and b = -9 make the piecewise function f(x) differentiable at x = 3.

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Answer:

The period is [tex]\pi[/tex].

Step-by-step explanation:

The answer is determined by finding the length of 1 cycle of the function. Trig functions sine and cosine have a wavy form. One starts and ends int he middle - sine. The other starts above and stops above- cosine. Regardless of the function, the period will be the same because the period asks "how fast does this function complete 1 wave?"

If cosine we start at one of the top points, trace the graph till we reach the same y-value again. The period is the time or difference in x-values. For instance if I started at the x-value [tex]\frac{\pi }{2}[/tex] and ended at [tex]\frac{3\pi }{2}[/tex] then I'd subtract them.

[tex]\frac{3\pi }{2}[/tex]-[tex]\frac{\pi }{2}[/tex]=[tex]\frac{2\pi }{2}[/tex]=[tex]\pi[/tex]

The period is [tex]\pi[/tex].

Answer:

The function that represents the cost in cents of ‘d' dozen gumballs is y = 10d .

Step-by-step explanation:

As given

If 30 gumballs can be purchased for 3 dollars .

i.e

30 gumballs = $3

Now find out the cost of one  gumballs .

[tex]1\ gumballs = \$ \frac{3}{30}[/tex]

[tex]1\ gumballs = \$ \frac{1}{10}[/tex]

[tex]1\ gumballs = \$\ 0.1[/tex]

As 1 dollar = 100 cents

[tex]1\ gumballs = 0.1\times 100\ cents[/tex]

[tex]1\ gumballs = \frac{1\times 100}{10} \ cents[/tex]

1 gumballs = 10 cents

Thus the cost of one gumball is 10 cents .

As d = dozen gumballs.

Let us assume that the cost for ‘d' dozen gumballs = y

Than the function becomes

y = 10d

Therefore the  function that represents the cost in cents of ‘d' dozen gumballs is y = 10d .

Answer: Correct Option is "C"

( - ∞ , 3) U (3, ∞ )

Step-by-step explanation:

The function f/g is defined as

( x + 8) / (x -3)

Domain of the function is the set of values which the independent variable can assume.

Clearly in the above function x cannot assume the value 3, otherwise the function would become undefined.

So domain of the function is

( - ∞ , 3) U (3, ∞ )

Hope it helps.

Thank you.

Answer:

X=3

Step-by-step explanation:

We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship.  This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.

The input value is [tex]\boxed{x =  3}.[/tex] Option (d) is correct.

Further explanation:

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

Given:

The options are as follows,

(a). [tex]x =  - 3[/tex]

(b). [tex]x = -1[/tex]

(c). [tex]x = 1[/tex]

(d). [tex]x = 3[/tex]

Explanation:

The functions are [tex]f\left( x \right){\text{ and }}g\left( x \right).[/tex]

It has been observed from the graph that the line of the functions [tex]f\left( x \right){\text{ and }}g\left( x \right)[/tex] intersects each other at [tex]x = 3.[/tex]

The input value is [tex]\boxed{x =  3}[/tex]. Option (d) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (d) is not correct.

Option (d) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Relation and Function

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.

Answer:

If the shape is a square,then it is a rectangle.

Step-by-step explanation:

The hypothesis of the statement is the one which follows after if,

If the shape is a square.

The conclusion of the statement is the sentence that follows after then,

Then it is a rectangle.

The statement 'All squares are rectangles' translates into an if-then form as 'If a shape is a square, then it is a rectangle'. The hypothesis is 'a shape is a square' and the conclusion is 'it is a rectangle'.

The geometrical statement 'All squares are rectangles' can be translated into an if-then form as follows: 'If a shape is a square, then it is a rectangle'. In this statement, the hypothesis is 'a shape is a square' and the conclusion is 'it is a rectangle'. This means that if we start with a shape and it happens to be a square (which is our condition or hypothesis), then it must also necessarily be a rectangle (which is our end result or conclusion). This is because all the properties of a rectangle - having all angles being 90 degrees and opposite sides being equal - are also properties of a square.

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Answer:

<T = 83

Step-by-step explanation:

In a parallelogram  <M = < P   and < N = <T  (opposite angles are congruent)

We also know that <M + <N = 180  ( consecutive angles are supplementary)

<M + <N = 180

6x+10  + 5x+10.5 = 180

Combine like terms

11x+20.5 = 180

Subtract 20.5 from each side

11x +20.5-20.5 = 180-20.5

11x = 159.5

Divide each side by 11

11x/11 = 159.5/11

x=14.5

We can find <N

<N = 5x+10.5

    = 5(14.5)+105

   =72.5 +10.5

   = 83

<N = <T = 83

Answer:

7x + 9

Yes they are equivalent

Step-by-step explanation:

The first expression given to us is

2x + 3 + 5x + 6

Let us call it equation (i)

Now we have to find equivalent expression to it

the given equation is 2x + 3 + 5x +6

similar terms are terms involving x and not involving x

so solving the equation gives

2x + 5x + 3 +6

= 7x + 9

Now we have two equations one is

2x + 3 +5x + 6              ...............(i)

Other is

7x + 9                            ..............(ii)

To check they are equivalent or not

Put x = 3 in equation (i)

2(3)+3+5(3)+6= 6 + 3 + 15 + 6

                      =30

Now put x=3 in second equation

7(3)+9=21 + 9

          =30

As the answer of both the equations are 30 so they are equivalent

To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, the expression can be simplified to 7x + 9. Substituting x with 3 in both expressions shows that they have the same value, which is 30.

To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, we add the coefficients of the like terms. In this case, the like terms are the terms with the same variable, which is x. So, 2x + 3 + 5x + 6 simplifies to 7x + 9. To show that this expression is equivalent to the original expression, we can substitute x with 3. So, when we replace x with 3, both expressions 2x + 3 + 5x + 6 and 7x + 9 result in the same value, which is 30.

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Answer:

A

Step-by-step explanation:

Your first step is to figure out what f(x) is. You should start with x = 0. f(x) has a value of - 4.  That only tells you that whatever x is or what it is coupled with, the constant term is - 4.

What you know so far is that y = x something - 4

Now go to work on some of the other numbers. It really doesn't look linear so don't try it.

What happens when x = 16? Somehow f(x) winds up being 0. What can cause that?

First of all it can't be y = ax - 4. We've already establish the constant must be  - 4

What about y = ax^2 - 4

That cannot be either. y = 16^2*a - 4  ?? y = 256ax  - 4. No other value will fit the bill.

By looking at g(x) you get the idea that y = a*sqrt(x) - 4 might have something to do with f(x). The most obvious value for a = 1, so try it first.

Now try some of the other values.

And that's what the table says.

The red graph is y = sqrt(x) - 4

The blue graph is y = 4*sqrt(x) - 8

Answer

It looks like A is the answer.

g(x) has a y intercept of - 8

f(x) has a y intercept of - 4

==============

The two intercepts are not equal. If they were they would start from the same point.   B is incorrect

==============

C is wrong. the x intercepts are distinct points. One is 4 and the other is 16 I think.

0 = sqrt(x) - 4

4 =  sqrt(x)                Square both sides.

16 = x                         This is the x intercept of the red line

The other intercept = 4 (Blue line). I'll leave you to work it out. Leave a not if you can't.

========================

A and D can't  both be true. Since A is true, D can't be.

Answer:

In quadrilateral LMNO, LO ∥ MN.

ML ∥ NO

LO ≅ MN

Answer:

1 & 3 is correct on edg.

Answer:g hvt

Step-by-step explanation:

Answer:

P =44 + 4xy

Step-by-step explanation:

To find the perimeter of a triangle, add up the three sides

P = 29+15+4xy

P =44 + 4xy