write a polynomial f(x) of lowest degree that satisfies the given conditions. Zeros: -4, multiplicity 1; 3 multiplicity 2; and f(0)=-108

Answer:

  7.2224

Step-by-step explanation:

The value of the summation is given by the formula ...

  Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.

Your sum has first term and ratio ...

  a1 = 2(0.6) . . . . . summation term for n=1

  r = 0.6

So the sum is ...

  [tex]\displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112[/tex]

Then the value of the entire given expression is ...

  [tex]\displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}[/tex]

_____

A calculator can help you find the value.

Answer:

Step-by-step explanation:

a.

[tex]2^3*2^{-3}=2^0\\b.\\\frac{2^3}{2^5} =2^{-2}\\c.\\2^{-3}*5^{-3}=10^{-3}[/tex]

Answer:

scale factor is 3/2

Step-by-step explanation:

to find scale factor, new image divided by original image.

Make sure you rotate the image on the right so it matches the image on the left. 3 corresponds to 9/2 and 5 corresponds to 15/2.

[tex]\frac{9}{2}[/tex] ÷ [tex]\frac{3}{1} \\[/tex]

[tex]\frac{9}{2}[/tex] × [tex]\frac{1}{3}[/tex]

[tex]\frac{9}{6}[/tex]

reduce

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Using distance formula,

Let the distance between point E and F = ef,

[tex]ef = \sqrt{{(7 - 1)}^{2} + {(2 - 9)}^{2} } \\ ef = \sqrt{85} \\ = 9.219544457[/tex]

Answer:

C

Step-by-step explanation:

3/5 + 2/5 + 4/5 = 1 4/5 or 9/5

Answers are c !!!

Step-by-step explanation:

if you added them you would get c I think hope this helps!!

Answer: The answer is B:350

Step-by-step explanation:

edge

Answer:

B

Step-by-step explanation:

Got it right

Answer:

(-1, -1)

Step-by-step explanation:

x - y = 0      ------>     x = y

2x + 3y = -5

2(y) + 3y = -5

5y = -5

y = -1

x - (-1) = 0

x = -1

The solution to this system is (-1, -1). To solve graphically, plot both functions and you will see that they intersect at (-1, -1).

I hope this helps!

Let's complete

Rule following=4n

#2

The rule is 4n

#3

Let's see

Answer:

  a)  |sec(θ)|

  b) 2cot(2x)

Step-by-step explanation:

Trig identities are used to simplify these expressions. Several are used:

__

  [tex]\sqrt{1-\tan(180^\circ-\theta)\cot(90^\circ-\theta)}=\sqrt{1-(-\tan(\theta))\tan(\theta)}\\\\=\sqrt{1+\tan^2(\theta)}=\sqrt{\sec^2(\theta)}=\boxed{|\sec(\theta)|}[/tex]

__

  [tex]\dfrac{\cos(2x)\tan(x)}{\sin^2(x)}=\dfrac{\cos(2x)}{\sin^2(x)}\cdot\dfrac{\sin(x)}{\cos(x)}=\dfrac{\cos(2x)}{\sin(x)\cos(x)}\\\\=\dfrac{\cos(2x)}{\left(\dfrac{\sin(2x)}{2}\right)}=2\dfrac{\cos(2x)}{\sin(2x)}=\boxed{2\cot(2x)}[/tex]

Answer:

true

Step-by-step explanation:

(-3)^22 -> to the power of an even number -> answer is positive

(-2)^33 -> to the power of an odd number -> answer is negative

positive # > negative #

Answer:

True

Step-by-step explanation:

First let's compare them.

-3 raised to an even power will give a positive number.

-2 raised to an odd power will give a negative number.

Therefore, (-3)²² > (-2)³³ is a true statement.

Answer:

In a right triangle, we know that there is one 90 degree angle and two acute angles. The angle sum theorem states that the sum of all angles in a triangle equal 180 degrees. For this reason, we know that these two acute angles must equal 90 degrees or be complementary angles to add up with the 90 degree right angle and equal 180.

I hope this helps!

Answer:

In a right triangle, the angle opposite the hypotenuse is always 90 degrees. The angle sum theorem states that the sum of the interior angles of a triangle is 180 degrees.  Therefore, the other two angles sum to 90 degrees, which means they are complementary.  They are also acute angles, since they are each less than 90 degrees.

The plane HGD contains at least three points

The three points on the plane are H, G and D

Coplanar points are at least three points that are in the same plane

The name of the plane is given as:

Plane = HGD

The above means that points H, G and D are on the plane HGD

Hence, the three points on the plane are H, G and D

Read more about coplanar points at:

https://brainly.com/question/1593959

Answer:

Option D, The distributions are somewhat similar

Step-by-step explanation:

Step 1:  Determine the means-to-MAD ratio

Data Set 1 → Mean = 173.5, MAD = 3.9

Data Set 2 → Mean = 161.2, MAD = 4.1

[tex]Ratio = \frac{Mean\ of\ 2 - Mean\ of\ 1}{MAD\ of\ 2 - MAD\ of\ 1}[/tex]

[tex]Ratio = \frac{161.2 - 173.5}{4.1 - 3.9}[/tex]

[tex]Ratio = \frac{-12.3|}{0.2}[/tex]

[tex]Ratio = -61.5[/tex]

Step 2:  Determine if the distributions are similar or not

Since the MAD of set 2 is somewhat similar to MAD of set 1, the distributions are somewhat similar.

Answer:  Option D, The distributions are somewhat similar

Answer:

B. 3x³ - 5x² + 3x - 3

Step-by-step explanation:

8x³ - 2x² + 5x - 7 - 5x³ - 3x² - 2x + 4 <== combine like terms

3x³ - 5x² + 3x - 3

Hope this helps!

the answers are as follows:

• -15

• -7

• 5

• 13

• 21

Answer: C (third choice)

Step-by-step explanation:

Square roots cannot hold negative x values as it will create an imaginary number.

Therefore the starting value of x must be starting at 0 and then moving to infinity

Answer:

c

Step-by-step explanation:

a=1

-2a + 3 < 9 − 3a

5a − 4a + 6 < 8

2a + 3 > 10 − 3a

a=2

-4 + 3a + 8 < 16

14 + 5a < 12a + 1

3a − 2a + 1 > 2

Answer:

2√2 / (5√2 + 7)

Step-by-step explanation:

Given :

Expanding

Answer:

[tex]-14\sqrt{2}+20[/tex]

Step-by-step explanation:

[tex]\textsf{Substituting}\quad x=1+\sqrt2\quad\textsf{into}\quad\left(\dfrac{x-1}{x}\right)^3[/tex]

[tex]\implies \left(\dfrac{(1+\sqrt2)-1}{(1+\sqrt2)}\right)^3[/tex]

[tex]\implies \left(\dfrac{\sqrt2}{1+\sqrt2}\right)^3[/tex]

[tex]\textsf{Apply exponent rule}:\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}[/tex]

[tex]\implies \dfrac{(\sqrt2)^3}{(1+\sqrt2)^3}[/tex]

Expand numerator:

[tex](\sqrt{2} )^3=\sqrt{2}\sqrt{2}\sqrt{2}=2\sqrt{2}[/tex]

Expand denominator:

[tex]\begin{aligned}(1+\sqrt2)^3 & = (1+\sqrt2)(1+\sqrt2)(1+\sqrt2)\\ & =(1+\sqrt2)(1+2\sqrt{2}+2)\\ & =1+2\sqrt{2}+2+\sqrt{2}+2\sqrt{2}\sqrt{2}+2\sqrt{2}\\ & = 7+5\sqrt{2}\end{aligned}[/tex]

[tex]\implies \dfrac{(\sqrt2)^3}{7+5\sqrt2}[/tex]

Substituting expanded numerator and denominator:

[tex]\implies \dfrac{2\sqrt{2}}{7+5\sqrt2}[/tex]

[tex]\textsf{Mulitply by conjugate :}\quad\dfrac{7-5\sqrt2}{7-5\sqrt2}[/tex]

[tex]\implies \dfrac{2\sqrt{2}(7-5\sqrt2)}{(7+5\sqrt2)(7-5\sqrt2)}[/tex]

[tex]\implies \dfrac{14\sqrt{2}-20}{49-50}[/tex]

[tex]\implies \dfrac{14\sqrt{2}-20}{-1}[/tex]

[tex]\implies -14\sqrt{2}+20[/tex]

keeping in mind that the solution to a system of equations is where the graphs of the equations meet or intersect, Check the picture below.

The number of miles planned on Saturday is 19 milea

This means the sequence where the difference between one term and the next term is a constant.

In this case, the following information are illustrated:

Sunday: 1 miles

Monday: 4 miles

Tuesday: 7 miles

Wednesday : 10 miles

Thursday: 13 miles

Friday: 16 miles

As we can see there's a difference of three between them. This can be seen as:

= 4 miles - 1 mile

= 3 miles

Therefore, the number planned on Saturday will be:

= Friday + 3 miles

= 16 miles + 3 miles

= 19 miles

Learn more about sequence on;

brainly.com/question/6561461

#SPJ1

The dimension of the rectangle is 40meters by 20meters

The perimeter of a figure is the sum of all the external sides of the figure

The formula for calculating the perimeter of rectangle = 2(l+w)

If the length is 20 meters longer than the width, then;

l = 20 + w

Substitute

120 = 2(20+2w)

60 = 20 + 2w

30 = 10 + w

w = 20 meters

Since l = 20  + w

l = 20 + 20

l = 40 meters

Hence the dimension of the rectangle is 40meters by 20meters

Learn more on perimeter of figure here: https://brainly.com/question/22447290

Answer:

Step-by-step explanation:

Let the distance Brenda walked is B and distance John walked is J.

We have

and

Comparing the two equations we see

It means 2y + 4 is the distance walked by John

Correct answer choice is D

The set of data that might produce one of more gaps on thr histogram are:

A histogram is a graphical representation of data such that the data is organized by data points into user-specified ranges.

The categories of people highlighted above will cause gaps because there is an increased likelihood that their ages will vary greatly or be distanced from the mean.

Learn more about Histograms at:

https://brainly.com/question/2962546

Answer:

  $100

Step-by-step explanation:

Debbie's earnings are found by multiplying her commission rate by her sales:

  0.25 × $400 = $100

Debbie earns $100 commission on her sales.

Answer:

See below ↓↓

Step-by-step explanation:

Plan 1

Plan 2

Part A

Equating them

⇒ 127x = 363 + 94x

⇒ 33x = 363

⇒ x = 11 months [They will be same at this point]

Part B

⇒ Plan 1 : 127(24) = $3048

⇒ Plan 2 : 363 + 94(24) = 2256 + 363 = $2619

⇒ I would recommend Plan 2 as it costs less for the time period of 2 years

Step-by-step explanation:

Just times all the number for every question like the first one, 4×4×4=64(units)

=64ft

Same for the rest

Answer:

the answer is 66.67%

Step-by-step explanation:

54.90-18.30=36.60

36.60÷54.90×100=66.666666666... or 66.67%