Which polynomial could have the following graph?



y = (x + 3)(x - 1)(x - 5)
y = (x - 3)(x + 1)(x + 5)
y = -(x + 3)(x - 1)(x - 5)
y = -(x - 3)(x + 1)(x + 5)

Answer:

Figure M

Step-by-step explanation:

Figure P has vertices at points (-2,4), (-2,8), (-6,8) and (-6,6).

Consider figure M with vertices (-4,-4), (-4,-8), (-8,-8) and (-8,-6).

1. Translate figure M 2 units to the right. This translation has the rule:

(x,y)→(x+2,y),

so

2. Reflect the translation image figure M across the x-axis according to the rule

(x,y)→(x,-y)

Thus,

Answer:

C.

Step-by-step explanation:

If f(c)=0 then (c,0) is on the graph.

In general, if f(a)=b then (a,b) is on the graph.

By factor theorem if f(c)=0 then x-c is a factor.

If x-c is a factor then x-c will divide f(x) evenly.  We know this because the remainder will be 0 because we know x-c is a factor of f.

The only choice that I have said in this whole thing that is true is C.

Answer:  The correct option is

(C) x-c is a factor of f(x).

Step-by-step explanation:  Given that for a function f(x), f(c) = 0.

We are to select the true statement from the given options.

We have the factor theorem as follows :

Factor theorem :  If p(a) = 0 for a polynomial function p(x), then (x-a) is a factor of p(x).

According to the given information, we have

f(c) = 0.

Therefore, (x-c) is a factor of f(x).

Thus, (C) is the correct option.

Answer:

D

Step-by-step explanation:

the question not give enough explanation and clue

For this case we have that the sum of the internal angles of a quadrilateral is 360 degrees.

In the figure they only give us the measure of an angle. We can not say that the angles C and D or E and F are the same because they do not say it.

Thus, we do not have enough information to solve the problem.

Answer:

Option D

Answer:

Option B is correct.

Step-by-step explanation:

Nico surveyed 300 new car buyers at the auto mall and found that 75% of the buyers were shopping for the same model of a car they have owned before.

This is 225 customers out of 300.

When people are satisfied with their car's current company and brand and model, they can prefer the same thing again for the same better experience. But this is not 100% proven. We can only say that there may be a link between the two things.

Hence, the conclusion that can be drawn here is :

B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.

The conclusion of the given study is that; Option B

We are told that;

Number of new cars Nico surveyed = 300

Percentage of buyers that surveyed the new cars = 75% .

Thus, number of customers surveying this cars = 75% * 300 = 225 customers

If people are satisfied with their car's current company and brand and model,it means that they can also prefer the same thing again for the same better experience. Thus, the conclusion is that;

B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.

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Answer:

[tex]\large\boxed{f(x)=(x+1)^2-4}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================[/tex]

[tex]\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4[/tex]

Answer:

Nina's rate in miles per hour is 2.7 miles/hour

Nina bikes faster

Step-by-step explanation:

we know that

1 hour=3,600 seconds

1 mile=5,280 feet

Convert feet to miles

63,360 feet=63,360/5,280=12 miles

Convert seconds to hours

3,400 sec=3,400/3,600=0.94 hours

Find Nina's rate in miles per hour

12/0.94=12.7 miles/hour

Sophia's rate in miles per hour is 10 miles/hour

Compare the rates

12.7 miles/hour > 10 miles/hour

therefore

Nina bikes faster

Answer:

12.7 mph

Nina

Step-by-step explanation:

Answer:

x = 1/2

Step-by-step explanation:

The equation in correct format is:

[tex]log_{5}(25)=x[/tex]

We have to solve this logarithmic equation to find the value of x. This can be done by using the rules of logarithm i.e the power rule and same base rule shown below:

[tex]log(a)^{b}=b \times log(a)\\\\log_{a}(a)=1[/tex]

Using these rules on our equation, we get:

[tex]log_{5}(25)=x\\\\log_{5}(5^{\frac{1}{2} })=x\\\\ \frac{1}{2} log_{5}(5)=x\\\\ \frac{1}{2} (1)=x\\\\ x=\frac{1}{2}[/tex]

Thus the value of x would be 1/2

Answer:

Step-by-step:

Write in exponential form

Simplify the expression

Swap sides

Step-by-step explanation:

ΔACX is an isosceles triangle, so ∠AXC = ∠XAC.  We'll call the measure of this angle x°.

∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180.  That means ∠BXC = 180 − x.

ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB.  We'll call the measure of this angle y°.

Angles of a triangle add up to 180, so:

y + y + (180 − x) = 180

2y = x

y = x/2

∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.

x + y = 90

x + x/2 = 90

3/2 x = 90

x = 60

Therefore, ∠AXC = ∠XAC = 60°.

Step-by-step explanation:

Step-by-step explanation:

To answer the question you have t the square of the differences.

So this means that (x-3)^2= x^2-9x+9

Next youmultiply 3 on both sides which says…

x^2-9x+9=27

x^2-9x=18

So, x equals

9/2+3/2 square root 17

OR

9/2-3/2 square root 17

Answer:

x=2 or x=5

Step-by-step explanation:

0−(x^2−7x+10)

=x^2−7x+10−(x^2−7x+10)

−x^2+7x−10=0

(−x+2)(x−5)=0

−x+2=0 or x−5=0

x=2 or x=5

Answer:

x = 2 or x = 5

Step-by-step explanation:

Several ways to do this.. but i'll use completing the square:

x²-7x +10 = 0

x²-7x  = -10   (take the x coefficient , divide that by two and then square the result and add it back to both sides)

x² - 7x   + ( -7/2 )²  = -10 + ( -7/2 )²  (simply the left side using the property (a + b)² = a² + 2ab + b² )

[x  + (-7/2)]² = -10 +  ( -7/2 )²

[x - (7/2)]² = -10 +  ( 49/4 )

[x - (7/2)]² = 9/4

x - (7/2) = ±√(9/4)

x - (7/2) = ±(3/2)

x = (7/2) ± (3/2)

x = 2 or x = 5

Geometric sequence--

The sequence is said to be geometric if each of the term of the sequence is obtained by multiplying the preceding term of the sequence by a fixed constant.

This fixed constant is known as  a common ratio and is denoted by r.

i.e. the sequence is given by:

                 a,ar,ar²,ar³,.....

The graph which represents the geometric sequence is attached to the answer.

Since the table of values are as follows:

          x             y

          1              1

          2             2

          3             4

          4             8

i.e. the sequence 1,2,4,8

form a geometric sequence.

Since the common ratio of the sequence is: 2 with first term as: 1

(first term is: 1

second term is: 1×2=2

Third term is: 2×2=4

and fourth term is: 4×2=8 )

Answer:

It's B. Second Graph.

Step-by-step explanation:

Answer:

25/81

Step-by-step explanation:

1000³ = (10³)³ = 10⁹ = 2⁹ × 5⁹

For a factor to be a perfect square, the exponents must be even.  For example:

2⁰ × 5⁰, 2⁰ × 5², 2² × 5⁰, etc.

There are 5 even exponents between 0 and 9 for each 2 and 5.  So the number of perfect square factors is 5×5 or 25.

The total number of factors is 9×9 or 81.

So the fraction of positive integer factors that are perfect squares is 25/81.

25/81 is the fraction of the positive integer factors of 1000^3,

1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9

Perfect square factors have even exponents.

There are 5 even exponents between 0 and 9 for each 2 and 5.

Number of perfect square factors: 5x5 =25

Total number of factors: 9x9 =81

Fraction: 25/81

To learn more about perfect Square refer,

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C or QR

Step-by-step explanation:

Answer:

Length = x-5

Step-by-step explanation:

Length= Area/width

Length = x³-5x²+3x-15/ x²+3

Re-arrange the numerator:

Length=x³+3x-5x²-15/x²+3

Take common from the numerator:

Length=x(x²+3) -5(x²+3)/x²+3

Length=(x²+3)(x-5)/x²+3

Length = x-5

Thus the answer is x-5 ....

Answer:

7+16= 23

23*2=46. ..........

Answer:4.95

Step-by-step explanation:

so you multiply (13*8) because its k*t and then the bottom of the formula is 13+8 because its k+t so 13*8 equals 104 and 13+8 is 21 then you divide 104/21=4.95

Answer: OPTION A

Step-by-step explanation:

It is important to remember the "Angle Addition Postulate" in order to solve this exercise.

You have this larger angle:

 [tex]\angle AVB[/tex]

According to the "Angle Addition Postulate", if the point "C"  is in the interior of [tex]\angle AVB[/tex], then the measure of this angle can be obtained by adding the angle [tex]\angle AVC[/tex] and the angle [tex]\angle CVB[/tex].

You can observe in the figure that:

 [tex]m\angle AVC=39\°\\\\\mangle CVB=23\°[/tex]

Then you get that:

[tex]m\angle AVC+m\angle CVB=m\angle AVB\\\\39\°+23\°=62\°[/tex]

Therefore, the correct answer is Option A.

Answer:answer is actually C

Answer:

The measurements of the interior angles of the triangles are 45°-90°-45°

Step-by-step explanation:

we know that

A square is a quadrilateral with 4 equal sides and 4 interior angles of 90 degrees

The diagonal of a square bisect the square into two congruent isosceles right triangles

The two congruent legs of each isosceles right triangle is equal to the length side of the square

The measure of the base's angles of each isosceles right triangle is equal to 45 degrees, because the diagonal bisect the right angle of the square

therefore

The measurements of the interior angles of the triangles are 45°-90°-45°

Answer:

Sample Explanation:

Since the triangle shares an angle with the original square, the triangle has a right angle. Since the triangle has two angles that are congruent, the equation for the measures of all three angles is 90 + 2x = 180, and I found that x = 45. The angles in the triangle are 90°, 45°, and 45°.

Step-by-step explanation:

Finding Unknown Angle Measures  Assignment

Finding Unknown Measurements

Explanation

Answer

First option: 1/3x = y - 3

[tex]\dfrac{1}{3}+x=\dfrac{1}{12}\\\\\dfrac{4}{12}+x=\dfrac{1}{12}\\\\x=-\dfrac{3}{12}=-\dfrac{1}{4}[/tex]

Answer:

1/4

Step-by-step explanation:

The LCD here is 12.  Subtract 1/3, or 4/12, from 7/12, to obtain the missing fraction.  7/12 - 4/12 = 3/12, or 1/4.  The missing fraction is 1/4.

Answer:

7/15

Step-by-step explanation:

first recognise that 3/3 is a whole pizza and so is 5/5.

Secondly make all the numbers to have the same denominator

So times both denominators of the fractions together; 5x3=15

Now find 1/3 of 15. Do this by dividing 15 by 3. This equals 5.

So 1/3 is equal to 5/15

Now do the same for 1/5. 15 divided by 5, this equals 3.

So 1/5 is equal to 3/15

Now that we know that the whole pizza is 15/15

We minus 1/3 from 15.

15-5=10.  So we now have 10/15 left.

now we know that 'x' is representative of the amount of pizza Tom gave to his bother.

10/15 - 3/15 = x

x = 7/15

So out of the whole pizza (15/15), tom ate 5/15 and was left with 3/15 meaning he gave 7/15 to his brother.

Final answer:

Tom ate 1/3 of the pizza and was left with 1/5 of it, so he gave away 2/15 of the pizza to his brother.

Explanation:

The question is asking which fraction of a pizza Tom gave to his brother. To find out, we know Tom ate 1/3 of the pizza and ended up with 1/5 of it. The fraction that Tom gave his brother is the difference between what he had after eating and what he was left with, thus:

1/3 - 1/5 = (5 - 3) / 15

So, 2/15 of the pizza was given to Tom's brother.

Answer:

≈ 523.6 in³

Step-by-step explanation:

The volume (V) of a sphere is

V = [tex]\frac{4}{3}[/tex] π r³ ← r is the radius

here diameter = 10, hence r = 5, so

V = [tex]\frac{4}{3}[/tex] π × 5³

  = [tex]\frac{4}{3}[/tex] π × 125

  = [tex]\frac{4\pi (125)}{3}[/tex] ≈ 523.6 ( to 1 dec. place )

Answer:

1055.04

Step-by-step explanation:

Cylinder

h = 16 cm

r = 5 cm

Volume = ?

Formula

V=pi * r^2 * h

Solution

V = pi r^2*h

V = 3.14 * 5*5*16

V = 1256 cm^3

Cone

h = 12 cm

r = 4 cm

Formula

V = (1/3) pi r * r * h

Solution

V = (1/3) 3.14 * 4 * 4 * 12

V = (1/3) 602.88

V = 200.96

Answer

Volume of unoccupied region = Cylinder - Cone

Volume of unoccupied region = 1256 - 200.96

Volume of unoccupied region = 1055.04

You will have to round it to the number of digits required.

Answer:

y = - 34

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 51 when x = 3

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-51}{3}[/tex] = - 17

y = - 17x ← equation of variation

When x = 2, then

y = - 17 × 2 = - 34

Final answer:

To find the value of y when x = 2 in a direct variation relationship, determine the constant of variation first and then substitute the given values to find the unknown.

Explanation:

The relationship given is that y varies directly with x. To find y when x = 2, you can use the direct variation formula.

First, find the constant of variation by using the values given: y = kx. Plug in y = -51 and x = 3 to find k.

Once you have k, solve for y when x = 2 using y = kx.

Therefore, when x = 2, y = -34.

Answer:

-1/8

Step-by-step explanation:

(-2)^-3

The negative exponent means it's the inverse.

1 / ((-2)^3)

-2 cubed is -8.

1 / (-8)

So the simplified answer is -1/8.

Answer:

-8

Step-by-step explanation:

=(-2)^-3

= -2 ×-2 ×-2

= -8

Answer:

True

Step-by-step explanation:

Since 1 km is 1000 metres that is the correct ratio to use

1 : 1000

( × 10 to get 10 km )

10 : 10000

Answer:

Step-by-step explanation:

Let's actually do the work:

10 km     1000 m

--------- * --------------- = 10^4 m

    1            1 km

Answer:  TRUE

Answer:

6.5

Step-by-step explanation:

For this case we must perform a conversion of milliliters to ounces.

By definition we have to:

1 US liquid ounce equals 29.5735 milliliters. Then, making a rule of three:

1 oz. ---------> 29.5735 milliliters

x -------------------> 650 milliliters

Where "x" represents the number of oz equivalent to 650 mL.

[tex]x = \frac {650 * 1} {29.5735}\\x = 21.9791[/tex]

Thus, 650 mL equals 21.9791 oz.

Answer:

650 mL equals 21.9791 oz.

Answer:

a. x = t, y = -[tex]\frac{3}{2}t[/tex] + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The answer is a. x = t, y = -3/2t + 5/2

The parametric equations of the line with the equation 3x + 2y = 5 is mathematically given as

x=t

y = (5-3t)/2

Question Parameter(s):

the line with the equation 3x + 2y = 5.

Generally, the equation for the equation in slope-intercept  is mathematically given as

 y = 3x -5/ 2

Therefore

y = (5-3t)/2

While

x=t

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Answer:

3x over x+1 MULTIPLIED by 1 over x+1 Letter choice will be A On ingenuity  

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]\frac {\frac {3x} {x + 1}} {x + 1}[/tex]

Applying double C we have:

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

Finally, an equivalent expression is:

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

Answer:

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