Why is x^4 - 16 when factored not just (x^2 + 4) (x^2 - 4)?

Answer:

A. 8.9x + 1.66

Step-by-step explanation:

5.3x - 8.14 + 3.6x + 9.8 =

= 5.3x + 3.6x - 8.14 + 9.8

= 8.9x + 1.66

Answer: A. 8.9x + 1.66

Answer:

I'll make the answer short.

Step-by-step explanation:

It's (A) 8.9x + 1.66

5.3x − 8.14 + 3.6x + 9.8

group the numbers on one side and the x's on the other

5.3x + 3.6x - 8.14 + 9.8

solve

8.9x +  1.66

So the answer (A)

Answer:

[tex] - 5 \sqrt{ - 2} [/tex]

Step-by-step explanation:

We can write sq root (- 18) as = sq root [3 x 3 x (-2)]

Similarly sq root ( - 8) = sq root [2 x 2 x (-2)]

2 sq root [2 x 2 x (-2)] - 3 sq root [3 x 3 x(-2)]

We simply,

2 x2 sq root (-2) - 3 x 3 sq root (-3)

4 sq root (-2) - 9 sq root (-2)

Bcoz sq root (-2) is common in bot term so

So

Sq root (-2) (4-9)

-5 sq root (-2) answer

Answer:

8 cm apart

Step-by-step explanation:

First, let's consider our unit rate.

1 cm = 50 km

Next, divide 400 km (the distance between two cities) by 50 (the unit rate).

400/50 = 8 km

There you go! The two cities are 8 km apart!

Hope this helps you and maybe earns a brainliest!!

Bye!

If two cities are 400 km apart. Then the length of distance between the cities on this map will be 8cm.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The scale on a map indicates that 1 cm represents 50 km.

Then the scale factor will be 1/50.

If two cities are 400 km apart.

Then the length of distance between the cities on this map will be

⇒ 400 x (1/50)

⇒ 8 cm

More about the dilation link is given below.

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Answer:

B) (2,0) and (0,-4)

Step-by-step explanation:

The answer to the system of equations is where the two intersect on the graph, in this case on the points (2,0) and (0,-4)

Answer:

61°

Step-by-step explanation:

Given:

∆MNO,

Side MO (n) = 18

MN (o) = 6

m<O = 17°

Required:

m<N

Solution:

Using the sine rule, [tex] \frac{sin N}{n} = \frac{sin O}{o} [/tex] , solve for N.

Plug in the values of M, n, and m

[tex] \frac{sin N}{18} = \frac{sin 17}{6} [/tex]

Cross multiply

[tex] 6*sin(N) = sin(17)*18 [/tex]

[tex] 6*sin(N) = 0.292*18 [/tex]

Divide both sides by 6

[tex] \frac{6*sin N}{6} = \frac{0.292*18}{6} [/tex]

[tex] sin N = \frac{0.292*18}{6} [/tex]

[tex] sin N = \frac{5.256}{6} [/tex]

[tex] sin N = 0.876 [/tex]

[tex] N = sin^-1(0.876) [/tex]

[tex] N = 61.16 [/tex]

m<N ≈ 61°

Answer:

Step-by-step explanation:

We can make use of the identities ...

  [tex]\cos{\alpha}-\cos{\beta}=-2\sin{\dfrac{\alpha+\beta}{2}}\sin{\dfrac{\alpha-\beta}{2}}\\\\\sin{\alpha}+\sin{\beta}=2\sin{\dfrac{\alpha+\beta}{2}}\cos{\dfrac{\alpha-\beta}{2}}[/tex]

These let us rewrite the equation as ...

  [tex]0=\cos{\theta}-\cos{2\theta}+\cos{3\theta}-\cos{4\theta}\\\\0=-2\sin{\dfrac{\theta+2\theta}{2}}\sin{\dfrac{\theta-2\theta}{2}}-2\sin{\dfrac{3\theta+4\theta}{2}}\sin{\dfrac{3\theta-4\theta}{2}}\\\\0=2\sin{\dfrac{\theta}{2}}\left(\sin{\dfrac{3\theta}{2}}+\sin{\dfrac{7\theta}{2}}\right)\\\\0=4\sin{\dfrac{\theta}{2}}\sin{\dfrac{3\theta+7\theta}{4}}\cos{\dfrac{3\theta-7\theta}{4}}\\\\0=4\sin{\dfrac{\theta}{2}}\sin{\dfrac{5\theta}{2}}\cos{\theta}[/tex]

The solutions are the values of θ that make the factors zero. That is, ...

  θ = 2πk . . . . for any integer k

  θ = (2/5)πk . . . . for any integer k (includes the above cases)

  θ = π(k +1/2) . . . . for any integer k

Answer:

7.8 cm

Step-by-step explanation:

Let's find the volume of the water bottle first. The radius is 5.5/2 = 2.75 cm

V = πr²h = 3.14 * 2.75² * 20 = 474.925 cm³

If we call the minimum side length of the cube as x we can write:

x³ = 474.925 because the volume of the cube is x * x * x = x³

x ≈ 8 cm

Answer:

Step-by-step explanation:

f(x)=-5x+5

f(-5)=-5(-5)+5

f(-5)=25+5=30

Answer:

Step-by-step explanation:

X = -5 ( Given)

Now,

[tex]f(x) = - 5x + 5[/tex]

plugging the value of X

[tex] = - 5 \times ( - 5) + 5[/tex]

Calculate the product

[tex] = 25 + 5[/tex]

Calculate the sum

[tex] = 30[/tex]

Hope this helps...

Good luck on your assignment ....

Answer:

Hi, the Answer is 0.75.

Step-by-step explanation:

it is 0.75 because if you look on the graph, and you calculate the 3/4 slope between the two, 3/4= 0.75

Answer:

A) 0.75 meters per hour

Step-by-step explanation:

Answer:

We have 2 rational solutions

0 irrational solutions

0 complex solutions

Step-by-step explanation:

a^2 + 8a + 12 = 0

Using the discriminant

b^2 -4ac where ax^2 + bx+ c

so a =1  b = 8 and c = 12

8^2 -4(1)*12

64 - 48

16

Since the discriminant is greater than 0, we have 2 real solutions

since we can take the square root of 16, we have rational solutions

We have 2 rational solutions

Since this is a quadratic equations, there are only 2 solutions so there are

0 irrational solutions

0 complex solutions

Answer:

2 Rational Solutions

0 Irrational Solutions

0 Complex Solutions

Step-by-step explanation:

The discriminant of the quadratic formula is the name given to the portion underneath the radical (or the square root)"

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

Discriminant = D = b²-4ac

If D is less than 0 you have two complex solutions.

If D is equal to 0 you'll have one real solution.

If D is bigger than 0 you'll get two real solutions.

So here we have:

a=1

b=8

c=12

Which means D=64-4(1)(12)=64-48=16>0

D is bigger than 0, so you'll have two real solutions. And since 16 is a perfect square, they'll both be rational numbers.

Answer:

1286 meters long

Step-by-step explanation:

421,808 divided by the width of the plot gives you 1,286 meters for the width.

A diameter splits a circle in half and has an arc measure of 180 degrees

WZ = 180

You are given WX = 32

So ZWX = 180 + 32 = 212

The answer is 212

Answer:

B. 212

Step-by-step explanation:

An arc degree is the same as its corresponding angle degree. So we need to find m∠ZWX:

m∠WCR = 148° because of Supplementary Angles

m∠ZCR = m∠XCW = 32° because of Vertical Angles Theorem

m∠ZWX = m∠WCR + m∠ZCR + m∠XCW = 212°

Since our angle measure is 212°, our arc degree measure is also 212°

Answer:

The constant of proportionality in the inverse variation is -3000

Step-by-step explanation:

Given that the initial value of the car was X, after owning the car for 3 years the value is $15,000 and the value after 5 years was $9,000 we have;

At  year 3, value of car = $15,000

At year 5, value of car = $9,000

Rate of change of car value with time = Constant of proportionality

Rate of change of car value with time = (15000 - 9000)/(3 - 5) = -3000

The constant of proportionality = -3000

Therefore;

y - 15000 = -3000 × (x - 3)

y = -3000x + 9000 + 15000 = -3000·x + 24000  

The value of the car, y with time,x is, y = -3000·x + 24000

Answer:

[tex] \boxed{\sf Length \ of \ the \ rectangle = 16 \ in} [/tex]

Given:

Perimeter of rectangle = 48 in

Length = Twice the width

To Find:

Length of the rectangle

Step-by-step explanation:

Let width of the rectangle be 'w'.

So,

Length of the rectangle = 2w

[tex]\sf \implies Perimeter \ of \ rectangle = 2(Length + Width \\ \\ \sf \implies 48 = 2(2w + w) \\ \\ \sf \implies 48 = 2(3w) \\ \\ \sf \implies 48 = 6w \\ \\ \sf \implies 6w = 48 \\ \\ \sf \implies \frac{ \cancel{6}w}{ \cancel{6}} = \frac{48}{6} \\ \\ \sf \implies w = \frac{48}{6} \\ \\ \sf \implies w = \frac{8 \times \cancel{6}}{ \cancel{6}} \\ \\ \sf \implies w = 8 \: in[/tex]

Width of the rectangle (w) = 8 in

Length of the rectangle = 2w

= 2 × 8

= 16 in

Step-by-step explanation:

sin 46°= a/12.8

a = sin46° * 12.8 = 9.20

cos59°=b/16.8

b = cos59°*16.8 = 8.65

Answer:

Step-by-step explanation:

First Question

To find a we use sine

sin ∅ = opposite / hypotenuse

a is the opposite

12.8 is the hypotenuse

sin 46 = a / 12.8

a = 12.8 sin 46

Second question

To find b we use cosine

cos∅ = adjacent / hypotenuse

b is the adjacent

16.8 is the hypotenuse

cos 59 = b / 16.8

b = 16.8 cos 59

Hope this helps you

Answer:

The circumference of circle is 14π cm.

Step-by-step explanation:

Given that the formula of circumference is C = 2×π×r where r represents radius of circle. In this case, diameter of circle is 14cm so the radius will be 7cm. Then, you have to substitute the value into the formula :

[tex]c = 2 \times \pi \times r[/tex]

[tex]let \: r = 7[/tex]

[tex]c = 2 \times \pi \times 7[/tex]

[tex]c = 14\pi \: \: cm[/tex]

Answer:

14[tex]\pi[/tex]

units = cm

Step-by-step explanation:

circumference = 2 x [tex]\pi[/tex] x r

c = 2 x [tex]\pi[/tex] x 7   - it's 7 because the diameter is 14 and radius is half the diameter

c = 14 x [tex]\pi[/tex]

c = 43.98229715

in terms of pi c = 14 [tex]\pi[/tex]

units = cm

Answer:

BA=BC

Step-by-step explanation:

Answer:

v=11/5 or v=2.2

Step-by-step explanation:

The wording of this question is a little confusing but if it says what I think it does (5/3v+4=8-1/3) then this is the answer.

Answer:

y = -(x - 2)^2.

Step-by-step explanation:

Vertex form is a(x - b)^2 + c   where  a is a constant and (b, c) is the vertex.

Here b = 2 and c = 0

So we have:

y = a( x - 2)^2 + 0

When x = 4 y = -4 so:

-4 = a( 4 - 2)^2

a = -4/2^2 = -1

So the required equation is

y = -(x - 2)^2.

Answer:

C = n + 2

Step-by-step explanation:

Well looking at the line on the graph we can see that the y intercept is 2 because the y intercept is the point in the line that touches the y axis.

And the slope is how fat away each points are from each other on a line so we can find the slope by using two points on the line, we can use (1,3) and (2,4).

So we set up the formula like this [tex]\frac{y^2-y^1}{x^2-x^1}[/tex].

And now we gotta plug in the numbers and solve so the answer is 4-3 = 1 and 2-1 = 1 so the slope is 1.

And we can’t write that as just n.

So the answer is C = n + 2.

For proof look at the image below.

Answer:

B, C=n+1

Step-by-step explanation:

Rlly late answer lol, the slope of the equation is 1 so it must be

C=n+b b is the y intercept, the y intercept is (0,2)

So the answer is C=n+1

Answer:

[tex]\boxed{-3}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation is determined by the constant equation [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept of the line.

Therefore, we can use the equation given and implement it to find your slope.

[tex]y=-3x[/tex]

Our equation does not have a y-intercept, [tex]b[/tex]. Therefore, it can just be inferred as [tex]+0[/tex].

Because we do have a [tex]m[/tex], we can then find out what our slope is: [tex]\boxed{-3}[/tex].

Answer:

Malik substituted 60 for y instead of x.

Step-by-step explanation:

According to the given situation the computation of error that Malik make first when solving the equation is shown below:-

First, we will find the value of x

[tex]\frac{2}{5} x - 4(60) = 10[/tex]

[tex]\frac{2}{5} x = 10 + 240[/tex]

[tex]\frac{2}{5} x = 250[/tex]

x = 625

Now, we have

[tex]\frac{2}{5} x - 4 y = 10[/tex]

we will solve the above equation, to find the value of y

24 - 4y = 10

4y = 24 - 10

4y = 14

[tex]y = \frac{14}{4}[/tex]

[tex]y = \frac{7}{2}[/tex]

So, from the above calculation, the correct option is

Malik substituted 60 for y instead of x.

Answer:

D on EDGE

Step-by-step explanation:

Answer:

-270

Step-by-step explanation:

Here, we want to know the coefficient of the fourth term.

The coefficients according to pascal triangle for the expansion is 1 5 10 10 5 1

So the expansion looks as follows;

1[(-x)^5(-3)^0] + 5[(-x)^4(-3)^1)] + 10[(-x)^3(-3)^2) + 10[(-x)^2(-3)^3] + ...........

So the fourth term we are dealing with is

10[(-x)^2(-3)^3)]

So the value here is

10 * x^2 * -27

= -270 x^2

So the coefficient is -270

Answer:

13/t

Step-by-step explanation:

you add the numerators, because the denominators are the same variable.

Answer:

83.85%

Step-by-step explanation:

Given that:

Mean (μ) = 65 months, Standard deviation (σ) = 6 months.

The empirical rule states that about 68% of the data falls within one standard deviation (μ ± σ), 95% of the data falls within two standard deviation (μ ± 2σ) and 99.7% of the data falls within three standard deviation (μ ± 3σ).

For the question above:

68% of the data falls within one standard deviation (μ ± σ) = (65 ± 6) = (59, 71) i.e between 59 months and 71 months

95% of the data falls within one standard deviation (μ ± 2σ) = (65 ± 12) = (53, 77) i.e between 53 months and 77 months

99.7% of the data falls within one standard deviation (μ ± 3σ) = (65 ± 18) = (47, 83) i.e between 47 months and 83 months

The percentage of cars that remain in service between 47 and 59 months = (68% ÷ 2) + (99.7% ÷ 2) = 34% + 49.85 = 83.85%

Answer:

Most likely height after 8 weeks

y(8) =  7.4 cm

Step-by-step explanation:

The regression line can be represented by

y = (4/5)x + 1  for x (#weeks) between 0 and 5.

Eight weeks exceeds the experimental range, so the best possible guess is to apply the regression line using x=8

Most probable height after 8 weeks

y(8) =  (4/5)*(8)+1 = 7.4 cm

5.2 cm height of plant after 8 weeks.

The equation of a line can be formed with the help of the slope of the line and a point on the line. Let us understand more about the slope of the line and the needed point on the line, to better understand the formation of the equation of a line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.(The equation of the line is  y = mx + b)

According to the question,

The equation of the line is:

y = mx + b

The slope is 3/5. The y-intercept is given 1.

y = 3/5x + 1

Put x as 7, to find where point y lies.

y = 3/5(7) + 1

y = 21/5 + 1

y = 4.2 +1

y = 5.2 cm

hence, 5.2 cm height of plant after 8 weeks.

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Answer:

ABC≅DEF ASA POSTULATE

There must be two angles and one side of ABC congruent to DEF

Step-by-step explanation:

Answer:

BC=EF

Step-by-step explanation:

Process of elimination and I just took the test so trust me.