simplify the following ；giving your answers in index form

Answer:

(x + 5) (x^2 -3)

Step-by-step explanation:

[tex]x^{3} +5x^{2} - 3x - 15[/tex]

Do the grouping:

[tex]x^{3} +5x^{2} - 3x - 15 = (x^{3} +5x^{2}) + (-3x - 15)[/tex]

Then factor out [tex]x^{2}[/tex] in the first and −3 in the second group.

[tex]x^{2}(x+5) - 3(x+5)[/tex]

Factor out the common term x + 5 by using the distributive property.

Polynomial [tex]x^{2}-3[/tex] is not factored in since it does not have any rational roots, thus getting the following:

[tex](x+5)(x^{2} -3)[/tex]

Answer:

the fourth option (x+5)(x²-3)

Step-by-step explanation:

the "-15" tells us we need a 3 and a 5 with different signs.

that eliminates the first and the second options.

and the "5x²" tells us it has to be +5, as there is only one part in the whole multiplication that delivers a x² term (5×x²).

it is also confirmed for the same reasons by "-3x" that the other number has to be -3.

Answer:

22.5 degrees and 67.5 degrees

Step-by-step explanation:

complementary angles add up to 90°

x + 3x = 90°

4x = 90

90/4 = x

x = 22.5

The first angle is 22.5

The second angle is 3 times as much

22.5 x 3 = 67.5

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Answer:

f(5) = 22

Step-by-step explanation:

Substitute x = 5 into f(x) for image , that is

f(5) = 3(5) + 7 = 15 + 7 = 22

Answer:

-163.64..................

Median- is the middle value whereby the values are place in order (ascending)

$9.25 is the median of these prices

Answer:

a)

There are 6 planes - 5 faces of the pyramid and one base, which overlaps with the plane X.

b)

Collinear points are the points on the same line:

c)

The intersection of planes X and HGD is the line section HG.

a:-

This is a pentagonal pyramid

B:-

C:-

HG is the intersection line

Answer:

p and q value is 70 deg and r,s,t and u is 110 deg

Step-by-step explanation:

I. If half circle = 180°

 when p = q = 70°

 so r = s = t = u = 180 - 70 = 110°

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

Gordon will use 5/6 of the bag of cheese to make the entire recipe.

Step-by-step explanation:

We are given that Gordon makes 4/5 of a recipe with 2/3 bag of cheese.

And we want to determine what fraction of the bag of cheese Gordon will use to make the entire recipe.

We can write the following ratio:

[tex]\displaystyle \frac{\dfrac{2}{3}\text{ bag of cheese}}{\dfrac{4}{5}\text{ recipe}}[/tex]

Find the unit rate. Multiply both layers by 5/4:

[tex]\displaystyle \frac{\dfrac{2}{3}\text{ bag of cheese}}{\dfrac{4}{5}\text{ recipe}}\times \frac{\dfrac{5}{4}}{\dfrac{5}{4}}[/tex]

Multiply:

[tex]\displaystyle \frac{\dfrac{5}{6}\text{ bag of cheese}}{1 \text{ recipe}}[/tex]

In conclusion, Gordon will use 5/6 of the bag of cheese to make the entire recipe.

Step-by-step explanation:

For x-intercept:

put y=0

0=-1/4 x -15

1/4x=-15

x=-15×4

x=-60

points(-69,0)

For y-intercept:

put x=0

y=-1/4(0)-15

y=-15

points(0,-15)

This line will never pass through first quadrant.

Note:if you need to ask any question please let me know.

The line will never pass through first quadrant.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given line:

y= -1/4 x-15

Now, the x-intercept:

0=-1/4 x -15

1/4x=-15

x=-15×4

x=-60

and the y-intercept will be

y=-1/4(0)-15

y=-15

Hence, the line will never pass through first quadrant.

Learn more about intercept here:

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Step-by-step explanation:

2x+y and 18x+9y

=2x+18x=9y2

=2x"=9y"

Answer:

about 15.08

Step-by-step explanation:

Angle BAC + Angle CAH = 180 (they are supplenmentary angles), which means (12x+4)+(x-20)=180

solve:

13x-16=180

13x=196

x≈15.08

Answer:

12x+4 + x-20 = 180

13x = 196

x = 15.08

Step-by-step explanation:

Answer:

150 + 150 = 300

Step-by-step explanation:

50x = 30y  

x + y = 8

~~~~~~~~~~~~~~~

x = 8 - y

50(8-y) = 30y

400 - 50y = 30y

400 = 80y

y = 5

x= 3

[tex]\frac{28}{9}[/tex]   liters do they drink in 4 days.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the question

John's family drinks 7/9 of milk a day.

Liters do they drink in 4 days: X

Using unitary method

X = [tex]\frac{7}{9} \times4[/tex]

X = [tex]\frac{28}{9}[/tex]

[tex]\frac{28}{9}[/tex]   liters do they drink in 4 days.

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Answer:

33 miles did the car travel on each gallon of gas

Answer:

c. {1/15,16,1/17,18}

Step-by-step explanation:

please follow me

Answer:

[tex]{ \sf{set \:A \: and \: B }}[/tex]

Step-by-step explanation:

S'(7,-4)

T'(7,-3)

U'(2,-7)

V'(2,-9)

Answer:

35

Step-by-step explanation:

Because,

when we take the maximum values of marbles in a jar ,

that is each jar contains 10 marbles

then the total number of marbles in 3 jars is 30

so , the value 35 is not possible.

Thank you

Answer:

About 76.5 ft.

Step-by-step explanation:

Draw a diagram of a right triangle.  The shorter leg represents the height of the main entrance of the library, which is 8 ft.  The longer leg won't matter in this case.  The hypotenuse is what we're trying to find, so mark it as x.  We know there's a 6° angle of elevation, so the 30° angle of the triangle will be 6° in this case.  Now we have to use trig.  Think of Soh Cah Toa.  The 6° is opposite from 8 and the hypotenuse is x.  So, the equation to find x would be:

sin (6°) = 8/x

Multiply both sides by x

sin (6°) * x = 8

Divide both sides by sin (6°)

x = 8/sin (6°)

When putting it into a calculator, your answer should be 76.534, which rounds to 76.5 ft.

Answer:

Associative property of multiplication

Answer:

The correct answer is B 60 - 5 x 4 = 20 x3 = 60

Answer:

60 ways

Step-by-step explanation:

5P3 = 5!/[3!(5-2)!]

= 5!/(3!2!)

= 5 × 4 × 3

= 60

Answer:

x = 3+y/2

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

17+2a=-13

2a=-30

a=-15

Answer:

1,000 pencils  

Step-by-step explanation:  

First, there are 10,000 cents in $100.  

So divide 10,000 by 10.  

1,000.

I hope this helps!  

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Answer:

5.

Step-by-step explanation:

Distance = √(2-6)^2 + (-2-(-5)^2)

= √(16 + 9)

= √25

= 5.

Hello ;)

We can calculate the distance between two points by knowing their coordinates.

Here is the formula :

Let two points [tex]A(x_{A};y_{A})[/tex] and [tex]B(x_{B};y_{B})\\[/tex]

The distance between those two points is given by using this formula :

[tex]AB^{2} =(x_{B}-x_{A})^{2} +(y_{B}-y_{A})^{2}[/tex]

Now, we can use this formula in your exercice.

(2 - 6)² + (-2 - (-5))²

= (-4)² + 3²

= 16 + 9

= 25

Do not forget to do the square root of 25 ;)

So we obtain : [tex]\sqrt{25}=5[/tex]

The distance between points (6 ; -5) and (2 ; -2) is 5 units of lengh.

Hi :)

6

6 is a whole number

6 is an integer

and 6 is a natural number

Answer:

Natural number is 6 here

Whole number is 6 too and so is integer. 4.9 and (-1/2) are a rational number while pi is an irrational number

Therefore, a linear equation in two variables has infinitely many solutions. Thus, y = 3x + 5 has infinitely many solutions. Hence (iii) is the correct answer.

Answer:

a

Step-by-step explanation:

Answer:

Distance cannot be negative because no matter which direction you travel, you will never travel negative units.

Step-by-step explanation:

Distance cannot be negative in the same way that when you put a car in reverse, the odometer does not go backwards.

If you have a mailbox 30 feet east of your house and a park 30 feet west of your house, you can think of it like a number line: your house is 0, the park is -30 and the mailbox is 30. But, if you walk to your park, you have not walked -30 feet.