Write the expression in simplest form.

Answer:

f(-5)=17

Step-by-step explanation:

Took the quiz.

The remainder theorem is an easy way of calculating the remainder from polynomial division.

The conclusion of remainder theorem, here is that: [tex]f(-5) = 17[/tex]

We have:

[tex]\frac{f(x)}{x + 5}[/tex] and a remainder of 17

The general rule of the remainder theorem is that:

For [tex]\frac{f(x)}{x + a}[/tex] and a remainder of b

It means:

[tex]f(-a) = b[/tex]

By comparing

[tex]\frac{f(x)}{x + a}[/tex] and [tex]\frac{f(x)}{x + 5}[/tex]

It means:

[tex]a = 5[/tex] and [tex]b = 17[/tex]

So:

[tex]f(-a) = b[/tex] becomes

[tex]f(-5) = 17[/tex]

Hence, the conclusion is that:

[tex]f(-5) = 17[/tex]

Read more about remainder theorems at:

https://brainly.com/question/13416073

Answer:

just learn the sin value of all the degrees

the cos values are opposite to the sin values example sin 30 degree = cos 60 degrees. and sin 45 and cos 45 remains same . use the same logic for tan and cot and also for sec and cosec . tan values are sin degrees / cos degrees

Your question has been heard loud and clear.

This is a right triangle , which means it has a hypotenuse ( longest side of the triangle)

X is the length of the hypotenuse. We need to find x.

By Pythagoras theorem ,

Side^2+side^2= Hypotenuse^2

2.5^2+3^2= x^2

= 6.25+9=x^2

15.25=x^2

So , x = root of 15.25 =  3.9

Therefore , x= 3.9

Thank you

Answer:

[tex]\huge \boxed{\mathrm{3.91 \ m}}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

The hypotenuse length of the right triangle is not given.

We can use Pythagorean theorem to solve for the hypotenuse.

[tex]c=\sqrt{a^2 +b^2 }[/tex]

c is the hypotenuse length of the right triangle.

a and b are the legs of the right triangle.

[tex]x=\sqrt{3^2 +2.5^2 }[/tex]

Evaluate and solve for x.

[tex]x=\sqrt{9+6.25}[/tex]

[tex]x=\sqrt{15.25}[/tex]

[tex]x= 3.905125...[/tex]

Answer:

The perimeter of the rectangle is 10.5p + 10.7q - 3.8r

Step-by-step explanation:

The perimeter of the triangle is calculated by adding the values of the three sides.

In this case, the values of the individual sides are expressed algebraically.

We can still add them, however, taking into consideration like terms.

Perimenter of triangle = (4.1p+4.4q) + (6.4p-5.1r) + (1.3r+6.3q)

Perimeter = 4.1p + 6.4p + 4.4q + 6.3q -5.1r + 1.3r

Now we have grouped them, we can add the different groups separately

Perimeter = 10.5p + 10.7q - 3.8r

Therefore, the perimeter of the rectangle is 10.5p + 10.7q - 3.8r

Answer:

Step-by-step explanation:

The area is given by the product of length and width.

  A = LW

  209 = (4x +3)(4x -5)

  209 = 16x^2 -8x -15

  224 = 16x^2 -8x

You could rearrange and use the quadratic formula at this point, but we elect to "complete the square".

  14 = x^2 -(1/2)x

  14 +1/16 = x^2 -1/2x +(1/4)^2 . . . . . add the square of half the x-coefficient

  (x -0.25)^2 = 14.0625

  x = 0.25 ± 3.75 . . . . . . take the square root; add 0.25

Only positive values of x are useful here, so we have

  x = 4

Then the dimensions are ...

  length = 4x +3 = 4(4) +3 = 19 . . . feet

  width = 4x -5 = 16 -5 = 11 . . . feet

Answer:

A

Step-by-step explanation:

a. CD = [tex]\sqrt{13}[/tex], EF = [tex]\sqrt{13}[/tex], CD≅EF

If [tex](x_{1}, y_{1})[/tex] & [tex](x_{2}, y_{2})[/tex] are co-ordinates of two points then the distance between this two points = [tex]\sqrt{(x_{2}- x_{1}) ^{2}+ (y_{2}- y_{1} )^{2} }[/tex]

Here, Point C = (0, 4) & Point D = (3, 2)

Then CD = [tex]\sqrt{(3-0)^{2} +(2-4)^{2} }[/tex] = [tex]\sqrt{3^{2} +(-2)^{2} }[/tex] = [tex]\sqrt{9+4}[/tex] = [tex]\sqrt{13}[/tex]

And Point E = (-2, 1) & Point F = (-4, -2)

Then EF = [tex]\sqrt{((-4)-(-2))^{2}+ ((-2)-1)^{2} }[/tex]= [tex]\sqrt{(-2)^{2} +(-3)^{2} }[/tex]= [tex]\sqrt{4+9}[/tex]= [tex]\sqrt{13}[/tex]

We know that, if two line segment have same length, they are congruent.

Here CD = EF = [tex]\sqrt{13}[/tex]

Since CD & EF have same length, so CD is congruent to EF.

Learn more about congruence of two lines here :

https://brainly.com/question/15580358

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Answer:

34. E 2 1/2

36. C 6cm

Step-by-step explanation:

34. ABC's triangle has 4, as it is equivalent to ADE's triangle's 10. I added 4 and 6 because the whole triangle shown is ADE. Then I did 10/4.

36. The reasoning is that on the other side, there is 9cm and 6cm which is equivalent to AB and 4cm

It goes like: 9/6 = AB/4

9 times 4 equals 36, and 36 divided by 6 is 6. Therefore the answer is 6cm.

Answer:

which one should we solve and you are from my school now a secondary school it is Michael in jss3 daisy meet me tomorrow but which questions should I solve

Answer:

The answer is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question

r = 3 inches

So the volume of the sphere is

[tex]V = \frac{4}{3}( {3)}^{3} \pi[/tex]

[tex]V = \frac{4}{3} \times 27\pi[/tex]

[tex]V = 4 \times 9 \times \pi[/tex]

We have the final answer as

Volume = 36 π cubic inches

Hope this helps you

Answer:

36pi cubic inches.

Step-by-step explanation:

Just took the Pre-Test on Edg (2020-2021)!!

Answer:

In general direct variation suggests that two variables change in the same direction. as one variable increases the other also increases and as one decreases the other also decreases.

Step-by-step explanation:

i hope this helps.

Answer:

4-6=-2

4.

rotational - no

reflectional - yes

angle - 90° (vertical)

5.

rotational - no

reflectional - yes

angle - 90° (vertical)

6.

rotational - omnidirectional

reflectional - yes

angle - 90° (vertical)

aswell as (horizontal)

Hi there! :)

Answer:

[tex]\huge\boxed{n = -2}[/tex]

5n + 6 = -3n - 10

Solve for n:

Add 3n to both sides:

5n + 3n + 6 = -3n + 3n - 10

8n + 6 = -10

Subtract 6 from both sides:

8n + 6 - 6 = -10 - 6

8n = -16

Divide both sides by 8:

8n/8 = -16/8

n = -2.

Answer:

n= -2

Step-by-step explanation:

Answer:

8.125 Litres

Step-by-step explanation:

Given:

Initial volume of hand sanitizer in the storage = 12 litres

Volume of dispensers:

350 ml

600 ml

475 ml

580 ml

650 ml

720 ml and

500 ml

To find:

Volume of sanitizer left after filling all the dispensers = ?

Solution:

The volume of sanitizer left can be calculated by subtracting sum of volumes of all the dispensers from the Initial total volume of the storage cabinet.

First of all, let us convert them into the same units i.e. litres.

We know that 1 Litre = 1000 ml

So,

350 ml = 0.350 Litres

600 ml = 0.600 Litres

475 ml = 0.475 Litres

580 ml = 0.580 Litres

650 ml = 0.650 Litres

720 ml = 0.720 Litres

500 ml = 0.500 Litres

Total volume of dispensers = 0.350 + 0.600 + 0.475 + 0.580 + 0.650 + 0.720 + 0.500 = 3.875 Litres

Let us subtract the total volume of dispensers from the initial volume of storage cabinet to find the volume remaining the storage cabinet.

Volume that remain in the storage cabinet = 12 - 3.875 = 8.125 Litres

Answer:

Step-by-step explanation:

The expression for the lateral area of a cylinder is given as

AL=2πrh

where r is the radius of the circular surface of the cylinder

and h represents the height of the cylinder

while the constant π has a value of 3.142

Now upon substitution we can solve for the lateral area and the unit for the lateral area is (units)^2 i,e cm^2, mm^2 or m^2 etc.

Answer:

the answer is .009 rounded to the nearest thousandths

Answer:

x+5

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{x+5}[/tex]

Step-by-step explanation:

Let the number be x.

5 more than x.

The verbal phrase to algebra:

x + 5

Answer:

x= 8.4

Step-by-step explanation:

y=0.8

4x + 8y =40

4x + ( 8 x 0.8) = 40

4x + (6.4)  =40

4x = 40 - 6.4

4x = 33.6

x = 8.4

Answer:

The value of x in this equation is -1.3

Step-by-step explanation:

8.8 + 7.8x = -7.9 - 5.5x

Subtract 8.8 on both sides of the equation.

7.8x = -16.7 - 5.5x

Add 5.5x on both sides of the equation.

13.3x = -16.7

Divide 13.3 on both sides of the equation. Don't forget to round to the nearest tenth.

x = -1.3

Answer:

x = -1.3

Step-by-step explanation:

8.8 + 7.8x = -7.9 - 5.5x

Add 5.5x to each side

8.8 + 7.8x+5.5x = -7.9 - 5.5x+ 5.5x

8.8+13.3x = -7.9

Subtract 8.8 from each side

8.8 + 13.3x - 8.8 = -7.9 - 8.8

13.3x = -16.7

Divide by 13.3

x = -16.7/13.3

x =-1.255639098

Rounding to the nearest tenth

x = -1.3

growth

Step-by-step explanation:

3 (.25)= .75

multiply 3 into the .25 and it's a positive number so it's increasing

Let present age of women be x.

Then,Present age of her daughter be y.

According to the question,

Two years ago,

Woman age = x - 2

Her daughter age = y - 2

Woman was 7 times old as her daughter. [ Given ]

x - 2 = 7 ( y - 2 )

=> x - 2 = 7y - 14

=> x - 2 + 14 = 7y

=> x + 12 = 7y ....( i )

After Three years ,

Woman age = x + 3

Her daughter age = y + 3

she would be 4 times old as the girl. [ Given ]

x + 3 = 4 ( y + 3 )

=> x + 3 = 4y + 12

=> x = 4y + 12 - 3

=> x = 4y + 9....( ii (

Now,

★ Putting the value of x = 4y + 9 from equation ( ii ) in equation ( i ),we get

x + 12 = 7y

=> 4y + 9 + 12 = 7y

=> 21 = 7y - 4y

=> 21 = 3y

=> 3y = 21

=> y = 21/3

=> y = 7

And,

x = 4y + 9

★ Putting the value of y in equation ( ii ), we get

x = 4 × 7 + 9

x = 28 + 9

x = 37

Hence, the present age of women is 37 years and her daughter age is 7.

Answer:

l=(P-2W)/2 (first answer choice lol)

Step-by-step explanation:

Answer:

dihdvsjhvbsuhdsvubhjvdhbdsvhbdsvhbkvdshbds

Step-by-step explanation:

DJ CUCRACH AAE SLAHTI8AOS

Hi there! Hopefully this helps!

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First we need to substitute the value of the variable into the expression.

[tex]b^{2}+3(2x-y)[/tex] = [tex]3^{2} + 3 (2(4)-5)[/tex] .

Now we need to solve [tex]3^{2} + 3 (2(4)-5)[/tex].

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

[tex]3^{2} + 3 (2(4)-5)[/tex]

First, calculate 3 to the power of 2 and get 9.

[tex]9+3(2\times 4-5)=18[/tex]

Multiply 2 and 4 to get 8.

[tex]9+3(8-5) =18[/tex]  

Subtract 5 from 8 to get 3.    

[tex]9+3\times 3 =18[/tex]  

Multiply 3 and 3 to get 9.

[tex]9+9 =18[/tex].

Answer:

one angle : 6x=6(90/11)=540/11 (49.1 rounded to the nearest tenth)

other angle=5(90/11)=450/11 (41 degrees rounded to the nearest ones)

Step-by-step explanation:

ratio of the angles 6:5

when you draw diagonal inside a rhombus it creates four right angled triangle

one angle=90

6x+5x=90 ( the other angles is complimentary)

11x=90

x=90/11

one angle : 6x=6(90/11)=540/11 (49.1 rounded to the nearest tenth)

other angle=5(90/11)=450/11 (41 degrees rounded to the nearest ones)

Answer:

Kelly earns more.

Step-by-step explanation:

Find how much Luna makes first.

24hx8days=192 hours

Then put the 192 hours into groups of 4.

192h/4h=48

Now, we take 48 x 500 to find how much Luna makes.

48x$500=$24000

Now, we have found how much Luna makes. Now, we find how much Kelly makes.

24hx10d=240h

Then put the 240 hours in groups of three.

240h/3h=80

Now, we take 80x$490

80x$490=$32900

(disclaimer: This method is what i use, i always come up with them takes me super long)

Answer:

500 - 2a = 340

500 - 2a - 500 = 340 - 500

-2a = -160

-2a/-2 = -160/-2

a = 80

Step-by-step explanation:

Answer:

From the RHS:

Cot^4θ-tan^4θ

=(cos^2θ/sin^2θ)*(cos^2θ/sin^2θ)-(sec^2-1)*(sec^2-1)

=(1-sin^2θ)/(sin^2(θ))*(1-sin^2θ)/(sin^2(θ))-(sec^4θ+2sec^2θ+1)

=(cosec^2θ-1)*(cosec^2θ-1)-sec^4θ+2sec^2θ-1

=cosec^4θ-2cosec^2θ+1-sec^4θ+2sec^2θ-1

=cosec^4θ-2cosec^2θ-sec^4θ+2sec^2θ

=LHS

Step-by-step explanation:

Answer:  see proof below

Step-by-step explanation:

Use the following Pythagorean Identities:

sec²A = tan²A + 1

csc²A = 1 + cot²A

Use group factoring:  a(x + y) + b(x + y) = (a + b)(x + y)

Proof LHS → RHS

Given:                    2sec²Ф      - sec⁴Ф             -     2csc²Ф       + csc⁴Ф

Pythagorean:        2(tan²Ф + 1) - (tan²Ф + 1)²    +   -2(1 + cot²Ф) + (1 + cot²Ф)²

Group Factoring:   (tan²Ф + 1)(2 - tan²Ф - 1)     +    (1 + cot²Ф)(-2 + 1 + cot²Ф)

Simplified:               (tan²Ф + 1)(1 - tan²Ф)           +    (1 + cot²Ф)(cot²Ф - 1)

Multiplied:               tan²Ф - tan⁴Ф + 1 - tan²Ф   +    cot²Ф - 1 + cot⁴Ф - cot²Ф

Simplified:                                         1  - tan⁴Ф   +    cot⁴Ф - 1

                                                    =      - tan⁴Ф  +  cot⁴Ф  

                                                    =        cot⁴Ф  - tan⁴Ф    

cot⁴Ф  - tan⁴Ф = cot⁴Ф  - tan⁴Ф    [tex]\checkmark[/tex]

Answer: Many people mistakenly give credit to Leonardo da Vinci for inventing scissors. Although da Vinci was brilliant, scissors were around for a long time before him. Some historians believe scissors were invented in the Middle East as long as 3,000-4,000 years ago.

Step-by-step explanation: Leonardo da Vinci

Scissors of the kind used today are believed to have been first made in 1 A.D in Rome. Some historians believe that Leonardo da Vinci is the inventor, for he had used it for cutting canvas. Although this view has not been widely accepted, Da Vinci helped to spread the popularity of scissors.

Hope this helps^^

Answer:

Apparently he isnt....

Answer: The measure of angle 1 is 39 degrees,the measure of angle 2 is 78 degrees and the measure of angle 3 is 63 degrees.

Step-by-step explanation:

We will represent the measure of angle 1 by x because it is unknown.

It says that the measure of angle 2 is twice angle 1   so we could represent that as  2x  and the measure of angle 2  is 15 less than angle 3 and we could also represent that by  2x - 15.

Now we know they all add up to 180 so add them up and set them equal to 180 and solve for x.

x + 2x + 2x -15 = 180  

5x - 15 = 180

      +15   +15

5x = 195

x = 39  

If x is equal to 39 then the measure of angle 1 is 39 degrees and the measure of angle 2 is twice that so 2(39) = 78   which also gives us the measure of angle 2 as 78.

For angle 3 it says that it has to be 15 less than the measure of angle so  subtract 15 from  78 to find the measure of angle 3.

78 - 15 = 63   The measure angle 3 is 63 degrees. Now add the measures all together to see if they equal 180 degrees .

Check:

39 + 78 + 63 = 180

  180 = 180