Find the remainder of (h4+ h² - 2) /(h+3).

Answer:

[tex]-2\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\textsf{Given expression}: \quad(\sqrt{3}+1)(\sqrt{3}-3)[/tex]

[tex]\textsf{Use the FOIL method to expand}\quad(a+b)(c-d)=ac-ad+bc-bd:[/tex]

[tex]=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}+1(-3)[/tex]

[tex]=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}-3[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{a}=a:[/tex]

[tex]=3-3\sqrt{3}+\sqrt{3}-3[/tex]

[tex]\textsf{Collect like terms}:[/tex]

[tex]=3-3-3\sqrt{3}+\sqrt{3}[/tex]

[tex]\textsf{Combine like terms}:[/tex]

[tex]=0-2\sqrt{3}[/tex]

[tex]=-2\sqrt{3}[/tex]

Answer:

a. 5

b. 1

c. 2

d. -28

e. 10.4

f. 11.41

g. 8003

h. 1

Answer:

Step-by-step explanation:

left to right

63 33 28 88 55 120 24 24 2 90

48 28 40 50 72 30 60 99 12 20

18 16 81 9 42 32 62 40 22 66

18 8 60 6 49 108 110 27 121 80

36 35 20 24 44 36 54 96 132 12

56 144 77 30 72 36 70 16 15 14

45 21 25 84 10 100 40 12 120 54

64 30 27 60 24 36 121 10 18 18

Answer:

t = 3

Step-by-step explanation:

Given: 9t - (2t - 4) = 25

Distributive property: a(b + c) = ab + ac

1. Distribute '-' or '-1'

9t + -1(2t) + -1(-4) = 25

9t - 2t + 4 = 25

2. Combine like terms

7t + 4 = 25

3. Subtract 4 from both sides

7t + 4 - 4 = 25 - 4

7t = 21

4. Divide both sides by 7 to isolate the variable

7t ÷ 7 = 21 ÷ 7

t = 3

Learn more about the distributive property and equations here:

Answer:

There are 9 geese and 18 horses.

Step-by-step explanation:

Step 1: Make equations.

g ... number of geese

h ... number of horses

First equation: There are 27 animals in the barn.

g + h = 27

Second equation: There are 90 legs in all.

We know geese have two legs and horses 4.

2g + 4h = 90

Step 2: Solve the system of equations.

g + h = 27 (first equation)

2g + 4h = 90 (second equation)

Let's express g in terms of h in first equation.

g + h = 27

g = 27 - h

Now let's substitute g in second equation with g in first equation.

2g + 4h = 90

2(27 - h) + 4h = 90

And solve for h.

54 - 2h + 4h = 90

54 + 2h = 90

2h = 90 - 54

2h = 36

h = 18

Let's substitute the value of h back to first equation to get g.

g = 27 - h

g = 27 - 18

g = 9

Answer:

See below ~

Step-by-step explanation:

Blue inequality

Red Inequality

Answer:

See below

Step-by-step explanation:

Find the equation of the blue line....the blue shaded area is LESS than or EQUAL to this SOLID line

Blue line =    y = -x+4        so   y <= -x+4

Red line  =    y = 1/4 x              y > 1/4x     (dotted line says line is not included so the inequality is >   NOT ≥   )

Answer:

(-1 , -5)

Hope this helped you! I would appreciate a Brainliest, if you wouldnt mind!

Answer:

Step-by-step explanation:

The equation is solved by starting with the given equation, then performing inverse operations to undo what is done to the variable.

__

The equation shown is the same as the given equation.

  reason: given

The equation shown has the "-5" term missing. That happens when +5 is added to both sides of the equation. -5 +5 = 0, and 0 added to anything leaves the value unchanged.

  reason: addition property of equality

The equation shown has the "-6" coefficient of 'a' missing. That happens when the equation is multiplied by the multiplicative inverse of -6. That is, it is divided by -6.

  reason: division property of equality

_____

Additional comment

As we have noted in Step 3, division is the same as multiplication by the multiplicative inverse. The definition of multiplicative inverse tells you that the product of a number and its inverse is 1. The identity element property for multiplication tells you that multiplying by 1 leaves the value unchanged.

  (1/(-6))(-6a) = 1a = a

So, the reason for Step 3 could also be "multiplication property of equality."

Answer:

C=12

Step-by-step explanation:

The interior angle of a polygon is 360.

So just add them all up.

(3c-29)+(127)+(c+43)+(c+43)+(2c+36)+(c+44)=360

Combine like terms

8c+264=360

Simplify

8c=96 .  Divide both sides by 8

C=12

Step-by-step explanation:

number 2)

3√2/3√4=

=3√2/3×2

=3√2/6

=3√2/6 ×3/3

=1√2/2

=√2/2

Answer:

x(1,2) = -5 ± √61) / (-2)

Step-by-step explanation:

The ABC formula of quadratic equation states

x(1,2) = (-b ± √b^2 - 4ac) / 2a

-x^2 + 5x + 9 = 0

a = -1

b = 5

c = 9

Thus x(1,2) = (-b ± √b^2 - 4ac) / 2a

= (-5 ± √(-5)^2 - 4*(-1)*9) / 2*(-1)

= (-5 ± √25+36) / (-2)

= (-5 ± √61) / (-2)

Answer:X is equal to -4 twice

Step-by-step explanation:

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:

2x² + 8x - x² + 16 = 0

Simplifying further, we get:

x² + 8x + 16 = 0

This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.

We can solve this equation by factoring it:

(x + 4)(x + 4) = 0

This gives us two solutions:

x + 4 = 0 or x + 4 = 0

x = -4 or x = -4

Therefore,

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

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Answer:

(8w + 7)(7w + 9)

Step-by-step explanation:

56w² + 121w + 63

consider the factors of the product of the coefficient of the w² term and the constant term which sum to give the coefficient of the w- term

product = 56 × 63 = 3528 and sum = 121

After much trial and error the factors are + 49 and + 72

use these factors to split the w- term

56w² + 49w + 72w + 63 ( factor first/second and third/fourth terms )

= 7w(8w + 7) + 9(8w + 7) ← factor out (8w + 7) from each term

= (8w + 7)(7w + 9) ← in factored form

Answer:

degrees like in angles. from 0 to 180

nwcggov

Answer:

  8 feet

Step-by-step explanation:

The length can be found using the volume formula with the known values. The resulting equation can be solved for the unknown value.

__

  V = LWH . . . . . volume of a prism is the product of its dimensions

  108 ft³ = l×(3 ft)×(4.5 ft) . . . . . known values filled in

  l = 108 ft³/(13.5 ft²) = 8 ft . . . . . . divide by the coefficient of length

The length of the prism is 8 feet.

Answer:

8ft

Step-by-step explanation:

Answer:

Mean:  The sum of all data values divided by the total number of data values.

Median: The middle value when all data values are placed in order of size.  If there is an even number of data values, the median is the mean of the middle two values.

Mode: The most frequently occurring data value.

-------------------------------------------------------------------------------------------------

Question 3

[tex]\textsf{Mean}=\dfrac{69 + 70 + 71 + 73 + 74 + 75 + 76 + 76 + 76 + 86}{10}=74.6[/tex]

Ordered data values:  69, 70, 71, 73, 74, 75, 76, 76, 76, 86

Median = (74 + 75) / 2 = 74.5

Mode = 76

-------------------------------------------------------------------------------------------------

Question 4

[tex]\textsf{Mean}=\dfrac{3 + 5 + 5 + 5 + 6 + 6 + 7 + 8 + 8}{9}=5.9\: \sf (nearest \:tenth)[/tex]

Ordered data values:  3, 5, 5, 5, 6, 6, 7, 8, 8

Median = 6

Mode = 5

-------------------------------------------------------------------------------------------------

Question 5

[tex]\begin{aligned}\textsf{Mean} & =\dfrac{11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 16 + 16 + 17 + 18 + 19 + 20 + 23}{15}\\ & =15.5 \: \sf (nearest\:tenth)\end{aligned}[/tex]

Ordered data values:  11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 18, 19, 20, 23

Median = 15

Mode = 12, 13, 14, 16

Answer:

see explanation

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the median is the middle value of a set of data. If there is no exact middle value then it is the average of the values on either side of the middle.

the mode is the value that occurs most often in the data set

A data set can have more than 1 mode

------------------------------------------------------------------------

(3)

(a)

mean = [tex]\frac{74+73+75+76+71+69+70+76+76+86}{10}[/tex] = [tex]\frac{746}{10}[/tex] = 74.6

(b)

Arrange the data in ascending order

 69  70  71  73  74  75  76  76  76  86

                              ↑ middle

median = (74 + 75) ÷ 2 = 149 ÷ 2 = 74.5

(c)

mode = 76

(4)

(a)

mean = [tex]\frac{6+8+8+5+6+7+5+3+5}{9}[/tex] = [tex]\frac{53}{9}[/tex] ≈ 5.9 ( to 1 dec. place )

(b)

3  5  5  5  6  6  7  8  8

                 ↑ middle

median = 6

(c)

mode = 5

(5)

(a)

mean = [tex]\frac{12+13+18+23+14+17+14+16+13+16+15+19+11+20+12}{15}[/tex] = [tex]\frac{233}{15}[/tex]  ≈ 15.5 ( to 1 dp )

(b)

11  12  12 13  13  14  14  15  16  16  17  18  19  20  23

                                      ↑ middle

median = 15

(c)

the mode is multimodal

modes are 12, 13, 14, 16

Answer:

Exterior angle = sum of opposite interior angles

Step-by-step explanation:

Answer:

^2x2√3+2x√2-^2x2√3-2x√2

Step-by-step explanation:

Answer:

<6 and <16 are alternate exterior angles.

Answer:

X = 10.09

Step-by-step explanation:

Answer:

See below for answers and explanations

Step-by-step explanation:

If we check x=5:

[tex]f(5)=-(5)^3+7(5)^2-7(5)-15\\f(5)=-125+7(25)-35-15\\f(5)=-125+175-50\\f(5)=50-50\\f(5)=0[/tex]

So [tex]x=5[/tex] is indeed a zero

If we check x=3:

[tex]f(3)=-(3)^3+7(3)^2-7(3)-15\\f(3)=-27+7(9)-21-15\\f(3)=-27+63-36\\f(3)=36-36\\f(3)=0[/tex]

So [tex]x=3[/tex] is also indeed a zero

If we check x=-1:

[tex]f(-1)=-(-1)^3+7(-1)^2-7(-1)-15\\f(-1)=1+7+7-15\\f(-1)=8+7-15\\f(-1)=15-15\\f(-1)=0[/tex]

So [tex]x=-1[/tex] is also indeed a zero

End Behavior

Since the degree of [tex]-x^3[/tex] is odd [tex](3)[/tex] and the leading coefficient is negative [tex](-1)[/tex], the end behavior of function [tex]f[/tex] is as follows:

Answer:

Step-by-step explanation:

2.2:

[tex]3^2(6)(3.14) = 169.56 in^3[/tex]

3.3

[tex]9^2(5)(3.14) = 1287.4 un^3[/tex]

Answer:

[tex]f(-3) = -3 + 8 \\= 5\\f(0) = 0 + 8 \\= 8\\f(5) = 5 + 8 \\= 13[/tex]

Step-by-step explanation:

All we need to do is plug in the x-values.

if

[tex]f(x) = x + 8[/tex]

then

[tex]f(-3) = -3 + 8 \\= 5\\f(0) = 0 + 8 \\= 8\\f(5) = 5 + 8 \\= 13[/tex]

hope this helped!!

Hey there!

12w = 102

DIVIDE 12 to BOTH SIDES

12w/12 = 102/12

SIMPLIFY IT!

w = 102/12

w = 102 ÷ 6 / 12 ÷ 6

w = 17 / 2

w = 8 1/2

Therefore, your answer should be:

w = 17/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

      Find the slope of the line that passes through (10, 7) and (3, 15).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

We can find the slope using the following formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with numbers:-

[tex]\boxed{\frac{15-7}{3-10}}[/tex]

[tex]\bigstar[/tex] On simplification,

[tex]\boxed{\frac{8}{-7}}[/tex]

[tex]\bigstar[/tex] The slope is

[tex]\boxed{-\frac{8}{7}}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

400 centimeters

Step-by-step explanation:

hope this helps. have a nice day

Answer:

Step-by-step explanation:

i hope these help

Answer:

498

Step-by-step explanation:

dI'd the math

The equation that represents the value of collection after 6 years is $420 + 54.6(6).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given data provided by the question,

The worth of the vintage collection = is $420

The price of the collection appreciates per year = by 13%

The price appreciates per year = 420 × 13/100 = $54.6.

So, the equation for n years is,

$420 + $54.6(n)

Where n is the number of years.

$420 + $54.6(6) = $747.6

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The percent of change in the number of points she scored between the first and second tests  = 4.878 %

If the data is decreasing,

Decrease = Original Number - New Number.

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100.

Given that:

The score of first Math test = 82

The score of second Math test = 78

Changes occurs in marks by=78-82

                                               =-4

So, there is decrease in marks.

We have to find the decrease percentage:

Decrease%= [tex]\frac{change \;in \;value}{Original\; value} *100[/tex]

                   = [tex]\frac{4}{82} *100[/tex]

                   = 0.04878 * 100

                  = 4.878 %

There is 4.88% decrease in Olivia's score.

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