Which function has two x-intercepts, one at (0,0) and one at (4,0)?

f(x) = x(x - 4)

f(x) = x(x + 4)

f(x) = (x - 4)(x - 4)

f(x) = (x + 4)(x + 4)

Answer:

Part 1: The polygon ABCDE reflected across y-axis to get the polygon MNOPQ. So, the polygon ABCDE congruent to polygon MNOPQ.

Part 2: The vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3), and Z(-3, 1).

Step-by-step explanation:

Part 1:

The vertices of the polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8), and E(6, 6).

The vertices of the polygon MNOPQ are M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8), and Q(-6, 6).

We need to find the transformation or sequence of transformations that can be performed on polygon ABCDE to show that it is congruent to polygon MNOPQ.

The relation between the vertices of ABCDE and MNOPQ are defined as

[tex](x,y)\rightarrow (-x,y)[/tex]

It means the polygon ABCDE reflected across y-axis to get the polygon MNOPQ. So, the polygon ABCDE congruent to polygon MNOPQ.

Part 2:

If polygon MNOPQ is translated 3 units right and 5 units down, then

[tex](x,y)\rightarrow (x+3,y-5)[/tex]

[tex]M(-2,8)\rightarrow V(-2+3,8-5)=V(1,3)[/tex]

[tex]N(-4,12)\rightarrow W(-4+3,12-5)=W(-1,7)[/tex]

[tex]O(-10,12)\rightarrow X(-10+3,12-5)=X(-7,7)[/tex]

[tex]P(-8,8)\rightarrow Y(-8+3,8-5)=Y(-5,3)[/tex]

[tex]Q(-6,6)\rightarrow Z(-6+3,6-5)=Z(-3,1)[/tex]

Therefore the vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3), and Z(-3, 1).

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:

∠4

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards.

This is ∠4 in the diagram

Answer:

The angle of depression from the light house to the boat is  <4

Step-by-step explanation:

From the figure we can see a light house and a boat.

The angle of depression means that angle from the horizontal downward to an object.

From the figure we can see that, <4 is the angle of depression from the light house to the boat.

Therefore the answer is <a

Answer:

Step-by-step explanation:

1) add the total number of male student

=14

2) divide the number of juniors by the total

2/14 = 1/7 = 0.14285

3)Multiply by 100 to get percentage

0.14285*100=14.285

4)Round

this rounds down to 14%

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:

3/10 or 0.3

Step-by-step explanation:

You have 3 red marbles and 10 marbles in total, so you put how many red marble in the numerator and your total marbles in the denominator.

[tex](f\cdot g)(x)=(9x+1)\cdot x^3=9x^4+x^3[/tex]

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: 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:

Option A is correct.

Step-by-step explanation:

The following matrix represent the augmented matrix

In augmented matrix the left side represent the co-efficient of the variables and right side represent the value of variables.

Since the matrix has been solved and reduced so, the solution of variables x, y and z is written on right side of augmented matrix

The given matrix is:

[tex]\left[\begin{array}{cccc}1&0&5&-2\\0&0&3&0\\0&0&0&-1\end{array}\right][/tex]

Since the last row is all zero and we have a non zero entry for the solution, the matrix is inconsistent.

As the variables have zero values, there cannot be any solution

So, there is no solution.

So, Option A is correct.

Answer:

A) No solution!

Step-by-step explanation:

Edge 2021 :)

Answer:

Step-by-step explanation:

Let s represent the number of Senators in the Congress. Then the number of Representatives is (5s-20) and the total number of members is ...

  s + (5s -20) = 520

  6s = 540 . . . . . . . . . add 20, simplify

  s = 90 . . . . . . . . . . . divide by 6

The number of Senators is 90; the number of Representatives is 430.

_____

You can find the number of Representatives either as 520 -90 = 430 or as 5·90 -20 = 430.

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:

  (x < -1) ∪ (6 < x)

Step-by-step explanation:

Divide by 3

  |2x -5| > 7

"Unfold." That is, put the negative of the constant value on the other side of the absolute value expression, using the same inequality symbol.

  -7 > 2x -5 > 7 . . . . . . . . . . this notation is convenient for expressing the two disjoint inequalities, but is not strictly correct because it is not true that -7 > 7.

Add 5, then divide by 2

  -2 > 2x > 12

  -1 > x > 6 . . . . . . . . . . this should be interpreted as -1 > x OR x > 6. Usually a compound inequality is interpreted as having an AND connector.

The solution is ...

  (x < -1) ∪ (6 < x)

_____

The more correct (and less convenient) way to "unfold" the absolute value is to write it as two distinct inequalities:

Each of these is then separately solved (by adding 5 and dividing by 2) to get ...

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:

B Step 2

Step-by-step explanation:

he was suppose to collect the like terms

5x +x = 5x + 1x

collect the like terms by adding their coefficients

(5 + 1)

add the numbers

(5+1)x = 6x

Answer:

  A.  Step 1

Step-by-step explanation:

The correct result of eliminating parentheses in Step 1 is ...

[tex]\dfrac{5x+10-8+x}{2}[/tex]

Distributing the minus sign in the second term changes the signs of both of the terms in parentheses:

  -(8 -x) = -8 +x

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:

[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 :)

Answer:

6,7,8,9,....

Step-by-step explanation:

the minimum width can be 5 because 9 times 5 is 45 the area using the formula length times width but the question is asking greater than 45 and 9 times any number greater than 5 is greater than 45

Answer:

W > 36

Step-by-step explanation:

i got it right on edgeinuity

Answer:

  x = 5

Step-by-step explanation:

Taking logarithms to the base 5, we get ...

   [tex]\log_x{7}=\log_5{7}[/tex]

Comparing forms gives x = 5.

Answer:

x=5

Step-by-step explanation:

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:

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:

1. 30ft

2. 0.4 min

Step-by-step explanation:

In this question, apply sine law which states that sine Ф= opposite/hypotenuse

The general formulae; is SOHCAHTOA where ;

(SOH) sineФ=opposite/hypotenuse  ; (COH) cosine Ф= adjacent/hypotenuse and (TOA) tan Ф=opposite/adjacent

In the question the height of the two floors is the " c" and the angel at the base is 60° and distance the conveyor travels is the hypotenuse

Hence;

[tex]Sin 60= \frac{26}{H} \\\\\\H=\frac{26}{Sin60} \\\\\\H=30 ft[/tex]

If 75ft=1min

  30ft=?........................simple math

30/75 = 0.4 minutes

Answer:

i) 30 ft

ii) 0.4 min

Step-by-step explanation:

i)

The question will be modeled by a right-angled triangle where-by;

The length of the conveyor belt will represent the Hypotenuse

The vertical distance which is 26 feet high will be the Opposite side to the angle the belt makes the ground which is given as 60 degrees.

The horizontal distance which is the ground will be the Adjacent side to the angle 60 degrees.

Therefore, we have a right angled triangle in which one angle and the length of the opposite side are given. To determine the length of the conveyor belt, the hypotenuse, we use the sine definition of an acute angle;

Remember the mnemonic. SOHCAHTOA

sine 60 = (opposite side)/(hypotenuse)

Hypotenuse = (opposite side)/sin 60

Hypotenuse = 26/sin 60

Hypotenuse = 30.02

The supplies thus travel 30 ft from one end of the conveyor belt to the other.

ii)

The speed of the belt is given as 75 ft/min

The length of the belt has been found to be approximately 30 ft

We are required to determine the time it takes for the supplies to move to the second floor.

Distance, Time and speed are related according to the following equation;

Distance = Time * Speed

Time = Distance/Speed

Time = 30/75

Time = 0.4 min

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:

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:

  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:

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:

The answer in the procedure

Step-by-step explanation:

we have

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

[tex]x^{2}-x-4-2=0[/tex]

[tex]x^{2}-x-6=0[/tex]

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-x-6=0[/tex]

so

[tex]a=1\\b=-1\\c=-6[/tex]

substitute in the formula

[tex]x=\frac{-(-1)(+/-)\sqrt{(-1)^{2}-4(1)(-6)}} {2(1)}[/tex]

[tex]x=\frac{1(+/-)\sqrt{25}} {2}[/tex]

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

[tex]x=\frac{1(+)5} {2}=3[/tex]

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

Answer: b. $407.50

Step-by-step explanation:

Multiply 450 by 0.75= 337.5

add 60: 337.5+60=397.5

add 10: 397.5+10= 407.5

Therefore B) is the correct answer

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

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