Subtract the following polynomials.
3.1x + 2.8z
4.3x - 1.2z
PLEASE HELP

Answer:

t=(2.5,0)

Step-by-step explanation:

Given that

[tex]t=\frac{1}{2} u+v[/tex]

and

u=(-1,4)

v=(3,-2)

Then,substitute value of u and v in the equation

[tex]t=\frac{1}{2} (-1)+3=-\frac{1}{2}+ (3)=2.5\\\\\\\\t=\frac{1}{2} (4)+-2=2+-2=0\\\\\\t=(2.5,0)[/tex]

Answer:

The answer on edge is C

Step-by-step explanation:

Answer:

7, -4

Step-by-step explanation:

The zeros are just another name for the x intercepts

7, -4

Answer:

The recursive function is;

f(n)=f(n-1)×0.9 for n≥2

After 3 years, 11340 birds will remain.

Step-by-step explanation:

First the native population was 14,000 before decreasing started, hence this is your f(1)

f(1)=14000

⇒A decrease of 10% is similar to multiplying the native value of birds with 90%

New number of birds = native value × 90% ⇒f(1)×0.9

For second year ,  you multiply the value you get after the first decrease by 0.9 to get the new number of birds;

f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600

For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%

f(3)=f(2)×0.9=12600×0.9=11340

Apply the same for the 4th year and above, hence for nth year;

f(n)=f(n-1)×0.9 for n≥2

Answer:

(a^3/7) - 4 + 3

Step-by-step explanation:

We need to translate the words into equations:

The quotient of a number cubed and seven: (a^3/7)

four less than the quotient of a number cubed and seven: (a^3/7) - 4

four less than the quotient of a number cubed and seven, increased by three:

(a^3/7) - 4 + 3

Answer:

400%.

Step-by-step explanation:

The surface area of a 4 cm cube = 6 * 4^2

= 96 cm^2.

The number of 1 cm cubes that can be cut from the larger cube is :

16 * 4 = 64.

The surface area of each of these smaller cubes is 6*1 = 6 cm^2.

The increase in surface area  is a factor of  (6*64) / 96

= 4 = 400%.

Answer:

Sequence 3

-10,-7.5,-5,-2.5,...

Step-by-step explanation:

So f(n+1)=f(n)+2.5 means a term can be found by adding it's previous term to 2.5. That means this is an arithmetic sequence with a common difference of 2.5.

f(n+1)=f(n)+d is the recursive form for an arithmetic sequence with common difference d.

So you are looking for a sequence of numbers that is going up by 2.5 each time.

Let's check sequence 1:

2.5+2.5=5 so not this one because we didn't get 6.25 next.

Let's check sequence 2:

2.5+2.5=5 is what we have for the 2nd term.

5+2.5=7.5 so not this one because we didn't get 10 next.

Let's check sequence 3:

-10+2.5=-7.5 is the 2nd term

-7.5+2.5=-5 is the 3rd term

-5+2.5=-2.5 is the 4th term

Sequence 3 is arithmetic with common difference 2.5 assuming the pattern continues.

Let's check sequence 4 for fun:

-10+2.5=-7.5 is not -25

So we are done. Sequence 3 is the only one that fits term=previous term+2.5 or f(n+1)=f(n)+2.5.

Answer:

Blank 1: 3 is the remainder

Blank 2: not a factor

Step-by-step explanation:

If p(x)=(x-7)(x^2-2x+4)+3, then dividing both sides by (x-7) gives:

[tex]\frac{p(x)}{x-7}=(x^2-2x+4)+\frac{3}{x-7}[/tex].

The quotient is [tex](x^2-2x+4)[/tex].

The remainder is [tex]3[/tex].

The divisor is [tex](x-7)[/tex].

The dividend is [tex]p(x)=x^3-9x^2+18x-25[/tex].

It is just like with regular numbers.

[tex]\frac{11}{3}[/tex] as a whole number is [tex]3\frac{2}{3}[/tex].

[tex]3\frac{2}{3}=3+\frac{2}{3}[/tex] where 3 is the quotient and 2 is the remainder when 11 is divided by 3.

 Here is the division just for reminding purposes:

                        3 <--quotient

                      ----

divisor->  3  |   11  <--dividend

                       -9

                        ---

                         2   <---remainder

Anyways just for fun, I would like to verify the given equation of

p(x)=(x-7)(x^2-2x+4)+3.

I would like to do by dividing myself.

I could use long division, but I have a choice to use synthetic division since we are dividing by a linear factor.

Since we are dividing by x-7, 7 goes on the outside:

         x^3-9x^2+18x  -25

7   |    1     -9        18    -25

    |            7       -14     28

     -------------------------------

          1      -2       4         3

We have confirmed what they wrote is totally correct.

The quotient is [tex]x^2-2x+4[/tex] while the remainder is 3.

If p/(x-7) gave a remainder of 0 then we would have said (x-7) was a factor of p.

It didn't so it isn't.

Just like with regular numbers. Is 3 a factor of 6? Yes, because the remainder of dividing 6 by 3 is 0.

Answer:

The exact probability that the student selected is a junior whose  favorite subject is Math is [tex]\frac{124}{459}[/tex].

Step-by-step explanation:

Let the following events represents by the alphabets A and B.

A: Student selects Math as the favorite subject

B: Student chosen is a junior

The probability that the  student selects Math as the favorite subject is 1/4.

[tex]P(A)=\frac{1}{4}[/tex]

The probability that the student chosen is a junior is

[tex]P(B)=\frac{116}{459}[/tex]

The probability that the student selected is a junior or that the student chooses Math as the  favorite subject is 47/108.

[tex]P(A\cup B)=\frac{47}{108}[/tex]

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

[tex]\frac{47}{108}=\frac{1}{4}+\frac{116}{459}-P(A\cap B)[/tex]

[tex]P(A\cap B)=\frac{1}{4}+\frac{116}{459}-\frac{47}{108}=\frac{31}{459}[/tex]

The exact probability that the student selected is a junior whose  favorite subject is Math is

[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]

[tex]P(\frac{B}{A})=\frac{\frac{31}{459}}{\frac{1}{4}}=\frac{124}{459}[/tex]

Therefore the exact probability that the student selected is a junior whose  favorite subject is Math is [tex]\frac{124}{459}[/tex].

The exact probability that the student selected is a junior whose favourite subject is maths is 124/459

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The probability that the student selects Maths the favourite subject:

P(A) = 1/4

The probability that the student chosen is a junior:

P(B) = 116/459

The probability that the student selected is a junior or that the student chooses maths the favourite subject:

P(A∪B) = 47/108

We know:

P(A∩B) = P(A) + P(B) _P(A∪B)

P(A∩B) = 1/4 + 116/459 - 47/108

P(A∩B) = 31/459

The exact probability that the student selected is a junior whose favourite subject is maths:

P(B|A) = P(A∩B) /P(A)

= (31/459)/(1/4)

= 124/459

Thus, the exact probability that the student selected is a junior whose favourite subject is maths is 124/459

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Answer:

 (4,-7) is the vertex

Step-by-step explanation:

The equation of the parabola is of the form

y= a(x-h)^2 +k

where (h,k) is the vertex

f(x) = -2(x – 4)^2 – 7

  (4,-7) is the vertex

Answer:

The vertex point is (4, -7)

Step-by-step explanation:

Compare withe the general form of the vertex form:

f(x) = a(x - h)^2 + k  where  (h, k) is the vertex.

f(x) = -2(x - 4)^2 - 7.

- so the vertex is (4, -7).

Answer:

Length of the segments will be 10 cm and 45 cm.

Step-by-step explanation:

Let the length of one segment is x.

Then by the statement of this question,

"one segment is 5 cm more than four times the length of another".

Length of other segment = 4x + 5

(4x + 5) - x = 35

4x + 5 - x = 35

3x + 5 = 35

3x = 35 - 5

3x = 30

x = 10 cm

Length of other segment = 4(10) + 5 = 45 cm

Therefore, two segments are of length 10 cm and 45 cm.

Answer:

41F

Step-by-step explanation:

41-32=9

9*5/9=5

Answer:

41 degrees F.

Step-by-step explanation:

C = 5/9(f -  32)

5 = 5/9 (f - 32) Multiply both sides by 9/5:

5 * 9/5 = f - 32

9 = f - 32

f = 9 + 32

= 41.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2y=x+2&\text{subtract x from both sides}\\x-3y=-5\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=2\\x-3y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-y=-3\qquad\text{change the signs}\\.\qquad\boxed{y=3}\\\\\text{put the value of y to the second equation:}\\\\x-3(3)=-5\\x-9=-5\qquad\text{add 9 to both sides}\\\boxed{x=4}[/tex]

Answer:

The answer is ∠C= 20 degree

Step-by-step explanation:

The answer is ∠C= 20 degree

We have given:

AB= 5

AC = 14

and we have to find ∠c to the nearest degree.

So,

We know that:

tan(C)= AB/AC

tan(C)= 5/14

tan(C)= 0.3571

C=20 degree

Thus the answer is ∠C = 20 degree ....

Answer:

12

Step-by-step explanation:

Start by multiplying both sides by 2.

[tex]\frac{1}{2} x+3=\frac{2}{3} x+1\\x+6=\frac{4}{3} x+2[/tex]

Next, multiply both sides by 3.

[tex]x+6=\frac{4}{3} x+2\\3x+18=4x+6[/tex]

Combine like terms.

[tex]3x+18=4x+6\\18=x+6\\12=x[/tex]

Answer:

a)

i) Mean = 72

ii) Median = 72

iii) Mode = 72

b)

69, 70, 71, 72, 72, 72, 73, 74, 75

Step-by-step explanation:

a. To find mean, median and mode

It is given that all the 9 students get 72 marks.

Therefore the data set be,

72, 72, 72, 72, 72, 72, 72, 72 72

i) mean = (sum of data)/(total number of data)

 = (9 * 72)/9 = 9

ii) Median - Central data in the data set when arranging ascending or descending order

72, 72, 72, 72, 72, 72, 72, 72 72

Median = 72

iii) Mode - Most repeating data in the data set

Here mode = 72

b). To find a data set

69, 70, 71, 72, 72, 72, 73, 74, 75

Here Mean, mode and median are all 72

Answer:

g(x) will eventually exceed f(x) because g(x) is an exponential function.

Step-by-step explanation:

From the first table we can observe the following patterns:

[tex]f( - 1) = {( - 1)}^{2} - 6 = - 5[/tex]

[tex]f(0) = {( 0)}^{2} - 6 = - 6[/tex]

[tex]f( 1) = {( -1)}^{2} - 6 = - 5[/tex]

[tex]f(2) = {( 2)}^{2} - 6 = - 2[/tex]

In general,

[tex]f(x) = {x}^{2} - 6 [/tex]

From the second table we can observe the following pattern:

[tex]g( - 1) = {6}^{ - 1} = \frac{1}{6} [/tex]

[tex]g(0) = {6}^{ 0} = 1[/tex]

[tex]g(1) = {6}^{1} = 6[/tex]

[tex]g(2) = {6}^{2} = 36[/tex]

In general,

[tex]g( x) = {6}^{ x} [/tex]

Conclusion:

Since the f(x) represents a quadratic function and g(x) represents an exponential function, g(x) will eventually overtake f(x).

The correct answer is C.

Answer: C.

Step-by-step explanation:

Go it right on my test

Answer:

x = sqrt( 4^2 + 7^2)

Step-by-step explanation:

They want the equation to solve the triangle

We can use the Pythagorean theorem

a^2 + b^2 = c^2

where a and be are the legs and c is the hypotenuse

4^2 + 7^2 = x^2

Take the square root of each side

sqrt(4^2 + 7^2) = sqrt(x^2)

sqrt( 4^2 + 7^2) = x

Answer:

[tex]\large\boxed{x=\sqrt{7^2+4^2}=\sqrt{65}}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=7,\ leg=4,\ hypotenuse=x[/tex]

Substitute:

[tex]x^2=7^2+4^2\to x=\sqrt{7^2+4^2}[/tex]

[tex]x=\sqrt{49+16}\\\\x=\sqrt{65}[/tex]

Answer:

[tex]\large\boxed{7\sqrt2}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (-3, 2) and (4, -5). Substitute:

[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]

Answer:

4 and 11

Step-by-step explanation:

Lets call the smallest n

And the other one n+7

Then,

n.(n+7)=44

n²+7n=44

Subtract 44 from both sides.

n²+7n-44=44-44

n²+7n-44=0

Factorize the equation.

n²+11n-4n-44=0

n(n+11)-4(n+11)=0

(n+11)(n-4)=0

n+11=0 , n-4=0

n=-11 , n=4

n=4 is the only positive solution, so the numbers are:

4 and 11....

Answer:

The two integers are: 4 and 11.

Step-by-step explanation:

We are given that one positive integer is 7 less than another. Given that the product of two integers is 44, we are to find the integers.

Assuming [tex]x[/tex] to be one positive integer and [tex]y[/tex] to be the other, we can write it as:

[tex]x=y-7[/tex] --- (1)

[tex]x.y=44[/tex] --- (2)

Substituting x from (1) in (2):

[tex](y-7).y=44[/tex]

[tex]y^2-7y-44=0\\\\y^2-11y+4y-44=0\\\\y(y-11)+4(y-11)[/tex]

y = 11

Substituting y = 11 in (1) to find x:

[tex]x=11-7[/tex]

x = 4

Answer:

[tex]\large\boxed{a_{10}=\dfrac{3}{110}}[/tex]

Step-by-step explanation:

Put n = 10 to the equation [tex]a_n=\dfrac{3}{n(n+1)}[/tex]

[tex]a_{10}=\dfrac{3}{10(10+1)}=\dfrac{3}{10(11)}=\dfrac{3}{110}[/tex]

For this case we have the following sequence:

[tex]a_ {n} = \frac {3} {n (n + 1)}[/tex]

We must find the value of[tex]a_ {10}[/tex], then, substituting [tex]n = 10[/tex] in the formula we have:

[tex]a_ {10} = \frac {3} {10 (10 + 1)}\\a_ {10} = \frac {3} {10 * 11}\\a_ {10} = \frac {3} {110}[/tex]

ANswer:

[tex]a_ {10} = \frac {3} {110}[/tex]

Answer:

55/73

Step-by-step explanation:

Soh Cah Toa gives us our definitions for the trigonometric ratios: sine, cosine, and tangent.

That is the first part means sine is opposite / hypotenuse.

The second part means cosine is adjacent / hypotenuse.

The last part means tangent is opposite / adjacent.

No matter what angle you are looking to label the right triangle from, the hypotenuse will always be the same.  The hypotenuse is the side opposite the 90 angle.  Opposite meaning not touching; across from.

The other two terms are adjacent and opposite and depending on what angle you are looking from these change.

Adjacent means touching (exclude the hypotenuse from this).

Opposite means across from; not touching.

So from Z:

The side that has measurement 55 is opposite to Z.

The side that has measurement 48 is adjacent to Z.

The hypotenuse is the side that has measurement 73.

So from Y:

The side that has measurement 48 is opposite to Y.

The side that has measurement 55 is adjacent to Y.

The hypotenuse is the side that has measurement 73.

We don't label are triangle with respect to the 90 degree, X.

Anyways we asked to find sin(Z).

[tex]\sin(Z)=\frac{\text{opposite to }Z}{\text{ hypotenuse}}=\frac{55}{73}[/tex]

Answer:

$ 254.85

Step-by-step explanation:

Total amount invested = $ 560

Interest rate = r = 4.8% = 0.048

Time in years = t = 8 years

The formula for compound interest is:

[tex]A =P(1+\frac{r}{n})^{nt}[/tex]

Here,

A is the total amount accumulated after t years. P is the amount invested initially and n is the compounding periods per year. Since in this case compounding is done annually, n will be 1. Using the values in the above formula, we get:

[tex]A=560(1+\frac{0.048}{1})^{8} = \$ 814.85[/tex]

Thus, the total amount accumulated after 8 years will be $ 814.85

The amount of interest earned will be:

Interest = Amount Accumulated - Principal Amount

Interest = $ 814.85 - $ 560 = $ 254.85

By the end of 8 years, $ 254.85 would be earned in interest.

Answer:

[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

===============================================

We have the points (2, -1) and (5, -3). Substitute:

[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]

We have the equation:

[tex]y=-\dfrac{2}{3}x+b[/tex]

Put the coordinates of the point (2, -1):

[tex]-1=-\dfrac{2}{3}(2)+b[/tex]

[tex]-1=-\dfrac{4}{3}+b[/tex]     add 4/3 to both sides

[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]

Finally:

[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]

Answer:

A. 12 mm

Step-by-step explanation:

May I have brainliest please? :)

Answer: A: 12 mm

Step-by-step explanation:

^^

Answer:

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Step-by-step explanation:

The formula for the perimeter of a rectangle is [tex]P=2L+2W[/tex].

If the width is [tex]W=12\:units[/tex] and the length is [tex]L=18\:units[/tex], then the perimeter becomes:

 [tex]P=2\times 12+2\times 18[/tex].

 [tex]\implies P=24+36[/tex].

 [tex]\implies P=60[/tex].

Therefore the answer is

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Answer:

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Step-by-step explanation:

The formula for the perimeter of a rectangle is .

If the width is  and the length is , then the perimeter becomes:

 .

 .

 .

Therefore the answer is

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Ok.

So an hour contains 60 minutes.

The fraction is therefore,

[tex]\dfrac{33}{60}=\boxed{\dfrac{11}{20}}[/tex]

Hope this helps.

r3t40

Answer:

33 minutes is 11/20 of an hour.

Explanation:

So we know that 30 minutes is equal to half an hour. 30÷60 = 0.5

0.5 as a fraction is equal to 1/2.

Now let's use that same method for 33.

33÷60= 0.55.

0.55×100== 55.

55 as a fraction would be 55/100.

Let's convert that to its simplest form.

55÷5 = 11

100÷5 = 20

33 minutes is 11/20 of an hour.

Answer:

P = 1 3  

Q = 1 6 8 3

Step-by-step explanation:

through factorization of 21879

Answer:

Step-by-step explanation:

When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.

Let A= [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right][/tex]

     B= [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

Then the augmented matrix is(A|B)

Note that a vertical line is used to separate te columns of A from the columns of B

(A|B) [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

This is a simple example of augmented matrix....

Answer:

An augmented matrix refers to a matrix formed by appending the columns of two matrices.

The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.

If we have the system

[tex]2x+3y=5\\x-4y=9[/tex]

The two maxtrix involved here are

[tex]\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right][/tex]

However, to solve the system using matrices, we have to formed an augmented matrix

[tex]\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right][/tex]

So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.

Answer:

Max is 4.

Step-by-step explanation:

Maximum means it has a highest point and what is the highest point.

Minimum means it has a lowest point and what is the lowest point.

It doesn't have a minimum because it keeps going down forever and ever.

It does have a maximum because it does stop at the top. The y-value that is stops at is 4 so the max is 4.