(01.03)

Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x minus 3 end quantity plus 5 equals x

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

[tex]y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)[/tex]

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

Answer:

[tex]4x^2+26x-3 = 0[/tex]

Step-by-step explanation:

Given that the total area of Frame and Painting is 45 Sq Fts.

Dimensions of painting are 6 feet and 7 feet. Hence.

Let us assume the uniform thickness of frame is x

Hence the Length of frame with painting = 7+2x

and breadth = 6+2x

Area of the frame = length * breadth

[tex]45=(7+2x)(6+2x)\\45=42+14x+12x+4x^2\\45=42+26x+4x^2\\4x^2+26x+42-45\\4x^2+26x-3=0\\[/tex]

Hence option b is correct.

Answer: B) -  4x^2 + 26x − 3 = 0

Step-by-step explanation:

I got it right :)

For this case we must find the zeros of the following function:

[tex]f (x) = (x-7) (x-3) (x-2)[/tex]

If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:

Thus, the zeros of the function are:

7,3,2

Answer:

Option C

The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

From the question,

We are to determine the zeros of the given function

The given function is

f(x) = (x - 7)(x - 3)(x - 2)

To determine the zeros of this function, we will set f(x) = 0

That is ,

f(x) = (x - 7)(x - 3)(x - 2)  becomes

0 = (x - 7)(x - 3)(x - 2)

∴ (x - 7)(x - 3)(x - 2) = 0

Then,

We can write that

x -7 = 0 OR x - 3 = 0 OR x - 2 = 0

∴ x = 7    OR    x = 3    OR   x = 2

Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

Learn more here: https://brainly.com/question/12488960

Answer:

She has $10 left.

Step-by-step explanation:

There are 13 tags. Every tag is 5$.

13 tags times 5 dollars equals 65 dollars spent.

75 dollars minus 65 dollars spent = 10 dollars left.

Ruby has 10 dollars left.

Ruby is left with 10 dollars. .

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

Ruby had a budget of up to $75 dollar to spend.

Total tags=13

Each tag is $5.

So,

Ruby spent on 13 tags

= 13*5

= $65

Thus, Ruby left with

=75 - 65 dollars

= 10 dollars.

Hence, Ruby has 10 dollars left.

Learn more about graph here:

https://brainly.com/question/16608196

#SPJ2

Answer:

  x + y = -2

Step-by-step explanation:

When you are given the equation of a line in standard form (or close to it, as here), you can make the equation for a perpendicular line through a given point by ...

Here, if we make the left side of the equation be ...

  x + y =

we have done the first part of the above recipe. For the second part, we put the point values in for the variables:

  x + y = (-1) + (-1) = -2

The equation of the perpendicular line is ...

  x + y = -2

Answer:

$3.14

Step-by-step explanation:

Original cost = $2.85

new cost is 110% of original cost

or

new cost is [tex]\frac{110}{100}[/tex] x original cost

= [tex]\frac{110}{100}[/tex] x $2.85

= $3.135

= $3.14 (rounded to nearest cent)

Answer:

D/ 3.14

Step-by-step explanation:

Answer:

No, he did not score 3,

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Step-by-step explanation:

Let x be the score of Skylar,

Since, Wyatt scored 2 times as many goals as Skylar.

So, Wyatt's score = 2x

Thus, total scores = x + 2x = 3x

According to the question,

3x = 15

x = 5

Hence, Skyler have scored 5 goals.

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Final answer:

Skylar could have scored 3 goals because, based on the information provided, they scored 5 goals after solving the equation that evaluates the total goals scored by both Skylar and Wyatt.

Explanation:

To determine if Skylar could have scored 3 goals, given that Wyatt scored 2 times as many goals as Skylar and together they scored 15 goals, we can set up a simple algebraic equation. Let's denote the number of goals Skylar scored as S, which means that Wyatt scored 2S goals.

The total number of goals is the sum of the goals scored by both Skylar and Wyatt, which is S + 2S = 15. This simplifies to 3S = 15. By dividing both sides of the equation by 3, we get S = 5.

Therefore, Skylar could have scored 3 goals because the calculations show that Skylar scored 5 goals.

Answer:

  not really

Step-by-step explanation:

The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.

_____

There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.

No, the solution (6.5,$ 95.25) do not make a sense.

Since, the number of people going for a movie can't be in decimals.

The function h(x) represents the amount of money spent where x is the number of friends at the movies.

The domain of such a function has to be whole numbers.

Because the number of people that go for a movie must exist as a whole they can't exist in decimals.

( i.e. either no one will go.

1 will go.

2 friends will go and so  on)

i.e. the domain is the set of all non-negative integers.

Answer:

-6/5

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

Plug in

Slope = (4 + 2)/(-2 - 3)

Slope = -6/5

Answer:

m = -6 / 5

Step-by-step explanation:

If you are given 2 points (x1, y1) and (x2,y2)

the slope is simply

m = (y2-y1) / (x2-x1)

m = (-2 - 4) / [3 - (-2)]

m = -6 / 5

Answer:

The correct answer is option B.  65

Step-by-step explanation:

To find the measure of <VYX

Central angle of arc VW = 44°

Therefore m<VXY = 44/2 = 22°

And central angle of arc XZ = 86° therefore <XVY = 86/2 = 43

To find the mesure of <XYZ

m<XYZ = m<VXY + m<XVY

  = 22 + 43

 = 65°

Therefore the correct answer is option B. 65°

We can solve this problem using a Pythagorean theorem.

[tex]c^2=a^2+b^2[/tex]

Where a is 7 and b is 4 and c is the hypothenuse we are looking for.

[tex]

c^2=7^2+4^2\Longrightarrow c=\sqrt{49+16}=\boxed{8.06}

[/tex]

The length of the third side is approximately 8.

Hope this helps.

r3t40

Answer:

Step 3

Step-by-step explanation:

when solving by completing the square you are supposed to do (b/2)^2 and then add that to both sides.

In your example (-8/2)^2=16

You are supposed to add sixteen to both sides not 64

Susu forgot to divide 8 by 2 before she raised it to the to the second powerm that is why she got 64, which is incorrect.

Answer:

Step 2

Step-by-step explanation:

Susu is solving the quadratic equation [tex]4x^2 - 8x - 13 = 0[/tex] by completing the square

To apply completing the square method we need to get x^2 alone

Susu added 13 on both sides . So step 1 is correct

When we factor out 4, we divide both terms by 4

[tex]4(\frac{4x^2}{4} -\frac{8x}{2} )=13[/tex]

[tex]4(x^2-2x)=13[/tex]

Susu forgot to divide 8 by 4

So , error in step 2

Answer:

13.75

Step-by-step explanation:

3b + d = 8.75

2b + 2d = 7.50

(3b + d = 8.75) times 2

(2b + 2d = 7.50) times -3

6b + 2d = 17.5

-6b + (-6d) = -22.5

the b's cancel out, 2d - 6d = -4d and 17.5 - 22.5 = -5

-4d = -5 Divide it and d = 1.25

then plug in 1.25 for d.

2b + 2(1.25) = 7.50

2b + 2.5 = 7.50

2b = 5

b= 2.5

3(2.5) + 1.25 = 8.75 ? Yes.

2(2.5) + 2(1.25) = 7.50 ? Yes.

4(2.5) + 3(1.25) = 13.75.

Answer:$2,000

Step-by-step explanation:

Answer:

  B.  that one thing is equal to another.

Step-by-step explanation:

An equation has a "left side", an "equal sign", and a "right side." It shows the left side is equal to the right side (one thing is equal to another).

___

An equation may or may not involve variables and unknown quantities.

Answer:

-77 assuming you meant to write -2x^2+5x-8 instead of -2x^2+5-8

Step-by-step explanation:

You could multiply it out and see...

(-2x^2+5x-8)(4x-9)

(-2x^2)(4x-9)+(5x)(4x-9)+(-8)(4x-9)

-8x^3+18x^2+20x^2-45x-32x+72

-8x^3+38x^2-77x+72

Coefficient of x^3 is -8

Coefficient of x^2 is 38

Coefficient of x is -77

Constant term is 72

Answer:

A

Step-by-step explanation:

Write each parabola in standard form.

f(x) = x²

f(x) = (x − 0)² + 0

For p(x), complete the square.

p(x) = -50 + 14x − x²

p(x) = -(x² − 14x + 50)

p(x) = -(x² − 14x + 49 + 1)

p(x) = -(x² − 14x + 49) − 1

p(x) = -(x − 7)² − 1

The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.

The answer is A.

Answer:

Hi

Step-by-step explanation:

Please make sure you have posted all the information. i will be glad to help however it doesnt seem that all the instructions aare there

Answer: OPTION C.

Step-by-step explanation:

First, it is important to remember the definition of "Suplementary angles".

By definition, two angles are supplementary if they add up 180 degrees.

Therefore, the measure of the supplement angle of 72 degrees can be found by setting up the following expression:

[tex]x+72\°=180\°[/tex]

Being "x"  the measure of the supplement angle of 72 degrees.

Finally, you need to solve for "x":

[tex]x=180\°-72\°\\\\x=108\°[/tex]

This matches with the option C.

Answer:

303.66 in²

Step-by-step explanation:

The area (A) of a trapezoid is

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases

here h = 12.6, a = 19 and b = 29.2, so

A = 0.5 × 12.6 × (19 + 29.2)

  = 0.5 × 12.6 × 48.2 = 303.66 in²

Answer: THIRD OPTION.

Step-by-step explanation:

The area of a trapezoid can be calculated with this formula:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where "h" is the height, "B" is the long base and "b" is the short base.

You can identify that:

[tex]h=12.6in\\B=29.2in\\b=19in[/tex]

Therefore, you need to substitute these values into the formula  [tex]A=\frac{h}{2}(B+b)[/tex] to calculate the area of that trapezoid. This is:

 [tex]A=\frac{12.6in}{2}(29.2in+19in)\\\\A=303.66in^2[/tex]

This matches with the third option.

Answer:

64 people/m^2

Step-by-step explanation:

The population density can be found by diving the number of people by the amount of area

I assume that the answer should be in metre squares or the area should be 1.95 million km^2

124000000/(1.95*1000000)

=63.5897...

=64 people/m^2

Answer:

64M people/km^2

Step-by-step explanation:

To calculate the density of population you just have to divide the population by the area of the country or region that you are calculation, in this case it wouldbe like this:

Density of population= [tex]\frac{124 M}{1.95 km^{2}  }[/tex]

D= [tex]\frac{124 M}{1.95 km^{2}  }[/tex]= 63,58 M[tex]\frac{M}{km^{2} }[/tex]

So rounded to the neares whoel number would be 64 M people per squared kilometer.

Answer:

186655 geese

Step-by-step explanation:

In this question , the next generation is calculated by multiplying the current generation by 2.2. Let's do a simple math;

1st generation = 3

2nd generation= 3×2.2=6.6

3rd generation=6.6×2.2=14.52

4th generation=14.52×2.2=31.94

5th generation=31.94×2.2=70.28

6th generation= 70.28×2.2=154.61

7th generation=154.62×2.2=340.14

8th generation=340.14×2.2=748.31

9th generation=748.31×2.2=1646.28

10th generation=1646.28×2.2=3621.81

11th generation=3621.81×2.2=7967.98

12th generation=7967.98×2.2=17529.55

13th generation=17529.55×2.2=38565.0

14th generation=38565.0×2.2=84843.02

15th generation=84843.02×2.2=186654.64

=186655 geese

OR

If current generation is calculated as the previous generation multiplied by a factor then you should see that this is an exponential function.In this case

Original number of geese=3

Factor of multiplication is =2.2

Exponential function for first generation is =0

How? see here

[tex]1st=3*2.2^0=3*1=3\\\\2nd=3*2.2^1=3*2.2=6.6\\\\3rd=3*2.2^2=3*4.84=14.52[/tex]

So from the above you can derive an expression for 15th generation

You notice for 1st generation , the exponent is 0

For the 2nd generation the exponent is is 1

For the 3rd generation the exponent is 2

Thus for the nth generation the exponent will be n-1

Your expression for nth generation can now be;

[tex]nth=3*2.2^{n-1}[/tex]

For 15th generation

[tex]15th=3*2.2^{15-1} =3*2.2^{14} =186654.63\\\\\\=186655[/tex]

Answer:

A.) 0.20

Step-by-step explanation:

There were 3+6+4+2 beds sold, or 15 beds sold

There were 3 twin beds sold

P(twin) = number of twin/ total

           = 3/15 = 1/5 = .2

Answer:

Option A. 0.20

Step-by-step explanation:

Observations from the given frequency table are :

Total number of beds sold at Cloud Nine Furniture = 3 + 6 + 4 + 2

                                                                                     = 15

Number of twin beds sold = 3

Then, probability that the next bed sold will be a twin bed,

[tex]P=\frac{\text{favorable outcome}}{\text{total number of possible outcomes}}[/tex]

  [tex]=\frac{3}{15}[/tex]

  = 0.20

Therefore, the probability that the next bed sold is a twin bed will be 0.20 or 20%.

Option A. is the correct answer.

Answer:

(x-y)(y-x)

Step-by-step explanation:

because x-y=y-x

Answer:

Step-by-step explanation:

This problem is essentially one of finding the matching mean. The given means are ...

1. It should be no trouble to determine that the largest mean belongs to Cathy.

__

2. The mean is the average of the given 2SD limits, so is ...

  (67,785.08 +83,141.16)/2 = 75,463.12 . . . . matches Amanda

Please note that you only need to work with about 3 significant figures:

  (67.8 +83.1)/2 = 75.45 . . . . close enough to let you select Amanda

__

3. The mean is the average of the given 1SD limits, so is ...

  (70.1 +78.2)/2 = 74.15 . . . . matches Benjamin

Answer:

68% of their data lie  between $70,062.37 and $78,187.37

(1 SD from the mean) Benjamin

had the highest average monthly  commission during the past year Cathy

95% of their data lie between $67,785.08 and $83,141.16

(2 SD from the mean) Amanda

Step-by-step explanation:

Answer:

Step-by-step explanation:

The distributive property lets you multiply each term inside parentheses by a factor outside parentheses. Here, we've gone from 4(x -1) to 4x -4.

The commutative property lets you change the order of elements of a sum or product. Here, we've gone from 3 + ( ) to ( ) + 3.

The associative property lets you move the parentheses from one group of elements of a sum or product to a different group of elements of the same sum or product. Here, we moved the parentheses from the first two terms to the last two terms of the sum.

_____

Comment on these properties in relation to the Order of Operations

The order of operations for evaluating an expression virtually ignores all of these properties, with the possible exception of the distributive property.

For evaluation of numerical expressions, any sum inside parentheses is evaluated to a single number before the multiplication implied by the parentheses is done. Hence the distributive property is not needed. (The distributive property must be used to remove parentheses when literal or mixed expressions are being evaluated.)

Likewise, the associative and commutative properties are ignored, because operations of addition or multiplication are always carried out left-to-right according to the order of operations. In actual practice, the associative and commutative properties can be used to simplify the evaluation of expressions, provided they are used properly and the meaning of the expression is not altered.

Answer:

D. The function is odd because it is symmetric with respect to the origin.

Step-by-step explanation:

We have been given a graph of a function. We are asked to determine whether our given function is odd or even.

We know that a function is even, when it is symmetric with respect to the y-axis.

We also know that a function is odd, when it is symmetric with respect to the origin.

Upon looking at our given graph, we can see that it is symmetric about the origin, therefore, option D is the correct choice.

The function is odd because it is symmetric with respect to the origin.

(Option D)

We will determine whether the function is shown in the graph is even or odd.

Let us recall how to distinguish whether the function graph is included in an even or odd function.

Even Functions

Odd Functions

Generally, the functions that we face are neither even nor odd.

ANSWER

[tex]S.A = 125 {in}^{2} [/tex]

EXPLANATION

The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.

This is given by the formula!

[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]

From the diagram, the base is 5 inches and the height is 10 inches.

We substitute the values to get:

[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]

This simplifies to;

[tex]S.A = 100 + 25[/tex]

[tex]S.A = 125 {in}^{2} [/tex]

Answer:

HL

Step-by-step explanation:

HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.

In the given right triangles MAE and TON,

AM = OT,

EM = NT,

Thus, by the HL postulate,

Δ MAE ≅ Δ TON

First option is correct.

The answer is B.

I tried putting 9 for a and 7 for B. cos(9-7)+cos(9+7) = 2cos(9)cos(7)

[tex]\bf \textit{Product to Sum Identities} \\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}\left[\cfrac{}{}cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)\right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(a)cos(B)=\cfrac{1}{2}\left[\cfrac{}{}cos(a-B)+cos(a-B) \right] \\\\\\ 2cos(a)cos(B)=cos(a-B)+cos(a-B)[/tex]