Use Rearranging Formulae

M = 2(r - p) find R

M = 2 ( r - p) find P ​

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

[tex](3x + 1)(x + 4)[/tex]

[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]

Multiply it by x.

[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]

[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

[tex]x = 5[/tex]

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

[tex]1 - 2 - 5 + 6 = 0[/tex]

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

[tex] {x}^{2} - x - 6[/tex]

We can then factor this into

[tex](x - 3)(x + 2)[/tex]

So our roots or factors is

[tex](x - 1)(x - 3)(x + 2)[/tex]

Answer:

Step-by-step explanation:

x² + y² + 42x + 38y - 47 = 0

Put the equation into standard (center-radius) form:

regroup terms

(x²+42x) + (y²+38y) = 47

complete the squares:

(x²+42x+21²) + (y²+38y+19²) = 47 + 21² + 19²

(x+21)² + (y+19)² = 849

center at (-21,-19)

radius = √849 units

The general form of the equation for a circle with radius √849 units is:

(x-h)² + (y-k)² = 849

where the (h,k) is the center.

Step-by-step explanation:

Hey there!

Given;

[tex]1st \: expn = 26 {m}^{4} {n}^{2} [/tex]

= 2*13 m⁴ n²

2nd expn = m² n

Therefore, greatest common factor is; m²n.

Hope it helps!

Answer:

There are 8 bottles in each box.

Step-by-step explanation:

Victor has 12 boxes with 'n' number of water bottles in each box.

A dozen is same as 12.

Now, 12 boxes and each with 'n' number of bottles. Total number of bottles in '12' boxes is 12n bottles.

Now, it is removing 12(a dozen) bottles from 12n bottles which gives 84.

So, 12n -12=84

Add both sides 12

12n= 96

Divide both sides by 12

n=8

So, there are 8 bottles in each box.

Answer:

The equation of the circle is given by:

(x-a)^2+(y-b)^2=r^2

where:

(a,b) is the center  of the circle

given that the center of our circle is (2,3) with the radius of 5, the equation will be:

(x+2)^2+(y+3)^2=5^2

expanding the above we get:

x^2+4x+4+y^2+6y+9=25

this can be simplified to be:

x^2+4x+y^2+6y=25-13

x^2+y^2+4x+6y=12

Answer:

[tex]\sf\longrightarrow \boxed{\sf x^2+y^2-4x-6y-12=0}[/tex]

Step-by-step explanation:

Here we are given the radius of circle as 5cm and the centre of the circle is (2,3) . We need to find the equation of the circle. Here we can yse the Standard equation of circle to find the equation .

Standard equation of circle :-

[tex]\sf\implies \green{ (x - h )^2+(y-k)^2 = r^2 }[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow ( x - 2 )^2 + ( y - 3)^2 = 5^2 [/tex]

Simplify the whole square ,

[tex]\sf\longrightarrow x^2 + 4 -4x + y^2+9-6y = 25[/tex]

Rearrange and add the constants ,

[tex]\sf\longrightarrow x^2 + y^2 -4x -6y +13 = 25 [/tex]

Subtract 25 on both sides ,

[tex]\sf\longrightarrow x^2 +y^2-4x-6y+13-25=0[/tex]

Simplify ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x^2+y^2-4x-6y-12=0}}[/tex]

Answer:

D

Step-by-step explanation:

We are given the two functions:

[tex]f(x) = 5x^2-x+1 \text{ and } g(x) = -3x[/tex]

And we want to find:

[tex](f \circ g)(1)[/tex]

Recall that this is equivalent to:

[tex]=f(g(1))[/tex]

Evaluate g(1):

[tex]g(1) = -3(1) = -3[/tex]

Substitute:

[tex]=f(-3)[/tex]

Evaluate f(-3):

[tex]f(-3)=5(-3)^2-(-3)+1=49[/tex]

Therefore:

[tex](f \circ g)(1) =49[/tex]

Our answer is D.

Answer:

49

Step-by-step explanation:

ƒ(x) = 5x2 – x + 1 and g(x) = –3x

(ƒ ∘ g)(1)

First find g(1) = -3(1) = -3

Then find f(g(1) = f(-3)

f(-3) = 5(-3)^2 - (-3) +1 = 5(9) +3+1 = 45+4 = 49

Angle ECD and Angle FDC are same-side interior angles. They lie on the same side of the transversal and are on the inside of the two parallel lines. Same-side interior angles are supplementary, meaning that they add up to 180.

(40x + 15) + (5x + 30) = 180

45x + 45 = 180

45x = 135

x = 3

Angle ECD = 40(3) + 15 = 120 + 15 = 135

Angle FDC = 5(3) + 30 = 15 + 30 = 45

Hope this helps!

Answer: is 3

Step-by-step explanation:

Very easy man !!!

Answer:

21x+4

Step-by-step explanation:

X’s: 21x

#’s: 4

So it will be 21x+4

Answer:

i) 2160

ii) 1800

Step-by-step explanation:

so, the retailer sold the item for 2052, if I understand the problem description correctly.

and with this sale price, he actually made a loss of 5%.

so, 2052 are actually only 95% of what he himself paid the wholesaler for it.

2052 = 95%

1% = 2052/95 = 21.60

100% (the whole price the retailer paid to the wholesaler) = 21.60 × 100 = 2160

so, now, these 2160 have the wholesaler a profit from his perspective of 20%.

that means this price includes the 20% profit margin.

2160 = 120%

1% = 2160 / 120 = 18

100% (the price the wholesaler originally paid) = 18 × 100 = 1800

Answer:

16ml is the answer.......mmmm...

Answer:

-3 =x

Step-by-step explanation:

The angles are corresponding angles and corresponding angles are equal if the lines are parallel

2x+9 = 7x+24

Subtract 2x from each side

2x+9-2x = 7x+24-2x

9 = 5x+24

Subtract 24 from each side

9-24 = 5x

-15 = 5x

Divide by 5

-15/5 = 5x/5

-3 =x

Answer:

[tex]1[/tex]

Step-by-step explanation:

Step 1:  Find the value

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

[tex]9 - (4)(2)[/tex]

[tex]9 - 8[/tex]

[tex]1[/tex]

Answer:  [tex]1[/tex]

the correct answer is BBBBBBBBB

Answer:

-64x^3 +64x^2-20x+10

Step-by-step explanation:

simplify, distribute

(btw, the little arrow sign means a exponent)

Answer:

The ratio 450 : 200 can be reduced to lowest terms by dividing both terms by the GCF = 50 :

450 : 200 = 9 : 4

Therefore:

450 : 200 = 9 : 4

basically 9/4

Step-by-step explanation:

Answer: 1⅓ batch of cookies

Step-by-step explanation:

From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.

Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:

= 4/3

= 1⅓ batch of cookies

Answer:

245 cm³

Step-by-step explanation:

Volume of a triangle = length x width x height / 3

7 x 7 x 15 = 735

735/3 = 245

volume of a triangle =length×width height 3

7×7×15=735

735/3=24

Answer:

Following are the solution to the given question:

Step-by-step explanation:

For question 1:

Calculating the speed between A and B:

[tex]Time\ (t)= 1 \ hours\\\\Distance\ (d)= 10 \ km\\\\V=\frac{d}{t}=\frac{10}{1}= 10 \ kmph[/tex]

For question 2:

Calculating the speed between B and C:

[tex]Time\ (t)= (2-1)=1 \ hours\\\\Distance\ (d)= (15-10)= 5\ km\\\\V=\frac{d}{t}=\frac{5}{1}= 5 \ kmph\\[/tex]  

For question 3:

In this the speed between A and B is the double to speed between B and C.

Answer:

32 years

Step-by-step explanation:

8x12 because there are 12 inches in a foot

8x12=96

96/3

96/3=32

Answer:

32 years

Step-by-step explanation:

y = years

1 foot  = 12 inches

12 × 8 = 96

Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.

3y

3 × 10 = 30

3 × 20 = 60

3 × 30 = 90

3 × 31 = 93

3 × 32 = 96

It will take the pine tree 32 years to grow 8 feet, or 96 inches.

Answer:

2875

Step-by-step explanation:

Answer:

B. False

Step-by-step explanation:

There is not enough information to make that conclusion. The two statements are completely unrelated, so the transitive property cannot be used. None of the given statements say that ABC is congruent to MNO or PQR. That means that nothing can be assumed about DEF. To use the transitive property you would need proof that ABC=MNO or ABC=PQR. But neither of those statements are there so the answer is false.

Answer:

true

Step-by-step explanation:

a pe c

Answer:

x = 7.535 and y = 0.307

Step-by-step explanation:

Given that,

Two equations,

2x + 3y = 8 ...(1)

x – 5y = 6....(2)

Multiply equation (2) by -2.

-2x + 10y = -12....(3)

Now, adding equations (1) and (2),

2x + 3y -2x + 10y = 8-12

13y = 4

y = 0.307

Put the value of y in equation (2).

x – 5(0.307) = 6

x = 6 + 1.535

x = 7.535

So, the solutions of the given equation are x = 7.535 and y = 0.307.

Answer:

Hundreds

Step-by-step explanation:

It is the third number in this bigger one, going from the left you can see it's in the hundreds place.

Answer:

Circles have equations such as: (x -h)² + (y -k)² = radius²

You need terms raised to the power of 2

Step-by-step explanation:

The values of x between which the relative maximum occurs is between the x-values; -1 and 1

The known parameters;

The table of the partial set of the polynomial values is presented as follows;

[tex]\begin{array}{rcr}\mathbf{x}&&\mathbf{g(x)}\\-2&&-14\\-1&&-2\\0&&0\\1&&-4\\2&&-6\\3&&2\end{array}[/tex]

From the table above, we have that g(x) is maximum (g(x) = 2) when x = 3

Method;

Define and find the relative maximum

The relative maximum of a function, is given by a point where the graph of the function changes direction from 'continuously' increasing values of the function before the point to 'continuously' decreasing values of the function after the point

From the table, at x = -2, -1, 0, g(x) = -14, -2, 0, and is therefore, increasing

Where, x = 0, 1, 2, we have g(x) = 0, -4, -6, therefore, g(x) is decreasing

The maximum value of g(x), in the region where g(x) changes from increasing to decreasing is g(x) = 0, which is given between the x-values of -1 and 1

Therefore, the relative maximum is most likely to occur between the values of x = -1, and x = 1, which is the option -1 and 1

Learn more about relative maximum here;

https://brainly.com/question/2321623

Answer:

100-35=65

15*0.65=9.75

so the price now is 9.75

Hope This Helps!!!

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

see this attachment

Answer:

46°

Step-by-step explanation:

arcsin(5/7)

Answer:

504 cm²

Step-by-step explanation:

Let the length and the width of the rectangle be L cm and W cm respectively.

Perimeter= 2(L +W)

2(L +W)= 108

L +W= 108 ÷2

L +W= 54

L= 54 -W -----(1)

[tex] \frac{L}{W} = \frac{7}{2} [/tex]

Cross multiply:

2L= 7W -----(2)

Substitute (1) into (2):

2(54 -W)= 7W

Expand:

108 -2W= 7W

+2W on both sides:

9W= 108

Divide both sides by 9:

W= 108 ÷9

W= 12

Substitute W= 12 into (1):

L= 54 -12

L= 42

Area of rectangle

= length ×width

= LW

= 42(12)

= 504 cm²

Answer:

[tex]4x^3-2x^2+5x-6+\frac{1}{x}[/tex] is a polynomial

Step-by-step explanation:

a polynomial is a set of numbers with multiple terms that are not simplify able

[tex]9x^7y^{-3} z[/tex] is not a polynomial because its actually one term, there is no addition/subtraction of different terms.

-13 is a single number, so not a polynomial

13x^-2 is also a single number, not a polynomial