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Answer: True

Think of a 3D box. It has 6 faces and the surface area is the total of all six individual rectangular faces. This idea applies to any polyhedron.

Answer:

A. the first possible case is always n = 1

Step-by-step explanation:

Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers

Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0

Therefore, the statement which is not true is that the first possible case is always n = 1

Answer:

G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°

The statement which correctly compares the angles is Angle G is smaller than angle P.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given are two triangles.

Given that,

GK is congruent to PN.

HG is congruent to MP.

Also, given that,

HK = 32 cm and MN = 40 cm

Angle G is opposite to the side HK.

Angle P is opposite to the side MN.

Angles opposite to the greater side will be greater.

So angle P is greater than angle G

Or, angle G is smaller than angle P.

Hence, Angle G is smaller than angle P.

Learn more about Angles here :

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Answer:

Step-by-step explanation:

The equation of blue line A is x = 1.

That of blue line B is y = 4.

Answer:

The corresponding angles theorem works for cases where we have two parallel lines intersecting another line.

Two lines are parallel if, at any point, the distance between these two lines is always the same.

Now, if we look at the image, we can see that the distance between the two horizontal lines changes (is smaller at the right and larger at the left)

Thus, these lines are not parallel.

Then the corresponding angles theorem can not be used here, and we have that:

∠9 ≠ ∠10

Answer:

last one

Step-by-step explanation:

Answer:

let's use Pythagoras theorem,

h²=b²+l²

so,

ad²=ac²+dc²

6²=ac²+3²

36-9=ac²=27

√27 can be written as 3√3,

hence ac= 3√3

Answer:

10

The mean would increase after the outlier is removed

Step-by-step explanation:

An outlier in a dataset is a number that differs significantly from the other data in the set.

In this question, 10 is the number that differs significantly from the other data in the set. Thus, it is the outlier.

Mean = sum of the numbers / total number

Mean including the outlier =  

(93+ 82  + 10  + 61  + 99  + 89  + 84  + 95  + 75  + 98) / 10 = 78.6

Mean without the outlier =

(93+ 82   + 61  + 99  + 89  + 84  + 95  + 75  + 98) / 9 = 86.2

the mean increased after the outlier was removed

Answer:

(x+5)²+(y-4)²=17

Step-by-step explanation:

I think it's safe to assume that the (-5,4) coordinate is in the center

To find the x and y coordinate just flip the signs

which means it would look like

(x+5)²+(y-4)²=?

the question mark is equal to the raidus squared

to find the radius use the distance formula

√((-4+5)²+(8-4)²)= 4.123106

square this to get 17

the final answer is then

(x+5)²+(y-4)²=17

Answer:

[tex]4.2025\pi\:\mathrm{m^2}[/tex]

Step-by-step explanation:

The area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]. In the figure, we're given a diameter of 4.1. All diameters of a circle are exactly 2 times the length of all radii of the circle. Therefore, the radius of the circle is [tex]4.1\cdot \frac{1}{2}=2.05[/tex].

Thus, the area of the circle is [tex]2.05^2\pi=\boxed{4.2025\pi\:\mathrm{m^2}}[/tex]

Answer:

q = -3/8

Step-by-step explanation:

Clearing out the fractions first simplifies this problem.  The LCD here is 8, so we multiply all three terms of 7/8 = q + 1/2 by 8 and simplify the result:

7 + 8q = 4.  

Combining the constants, we get:  8q = 4 - 7, or 8q = -3.

Finally, solve for q:

q = -3/8

Answer:

[tex]x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]

Step-by-step explanation:

[tex]x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]

Answer:

m∠B = 94º

Step-by-step explanation:

Supplementary angles total 180

(8x + 6) + ( 7x + 24) = 180

Combine like terms

15x + 30 = 180

15x = 150

x = 10

m∠B = 7x + 24

m∠B = 7(10) + 24

m∠B = 94º

Answer:

A. (x + 2)²(x - 2)²

Step-by-step explanation:

x⁴ - 8x² + 16 =

(x² - 4)(x² - 4) =

(x - 2)(x + 2)(x - 2)(x + 2) =

(x - 2)²(x + 2)²

Step-by-step explanation:

Simplifying

36 = byx

Solving

36 = bxy

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-1bxy' to each side of the equation.

36 + -1bxy = bxy + -1bxy

Combine like terms: bxy + -1bxy = 0

36 + -1bxy = 0

Add '-36' to each side of the equation.

36 + -36 + -1bxy = 0 + -36

Combine like terms: 36 + -36 = 0

0 + -1bxy = 0 + -36

-1bxy = 0 + -36

Combine like terms: 0 + -36 = -36

-1bxy = -36

Divide each side by '-1xy'.

b = 36x-1y-1

Simplifying

b = 36x-1y-1

Answer:

y = [tex]\frac{36}{bx}[/tex]

Step-by-step explanation:

Given

36 = byx ( isolate y by dividing both sides by bx )

[tex]\frac{36}{bx}[/tex] = y

Answer:

6

Step-by-step explanation:

f(2) = (2 + 1)2

(3)2

6

Answer:

6

Step-by-step explanation:

f(2) = (2+1)*2, f(2) = 3*2 = 6

Step-by-step explanation:

total wood= 45½=22.5 units

cut wood= 8⅞= 7 units

wasted wood= 1/16=0.06

now wood left is,

total wood -cut wood-wasted wood

22.5-7-0.06

15.44 units

Answer:

x = 48°

Step-by-step explanation:

Two sides of the triangle are equal, both 7, Then the 2 base angles are congruent, both 66°

The sum of the 3 angles in the triangle sum to 180° , so

x = 180° - (66 + 66) = 180° - 132° = 48°

Answer:

[tex]{ \tt{x + 66 + 66 = 180}} \\ x = 48 \degree \\ \\ { \boxed{ \bf{or : }}} \\ { \bf{ from \:lamis \: theorem : }} \\ { \tt{ \frac{5.7}{ \sin(x) } = \frac{7}{ \sin(66 \degree) } }} \\ \\ { \tt{x = { \sin }^{ - 1}( \frac{5.7 \times \sin(66 \degree) }{7} ) }} \\ x = 48 \degree[/tex]

Answer:

Option (4)

Step-by-step explanation:

Option (1)

f(x) = 4x⁴- 7x²+ x + 25

Possible rational roots will be,

[tex]\frac{\pm \text{Factors of constant term '25'}}{{\pm \text{Factors of leading coefficient '4'}}}[/tex]

For the given function,

Possible rational roots = [tex]\frac{\pm 1, 5, 25}{\pm 1,2}[/tex]

                                      = [tex]\pm 1, \pm 5, \pm 25, \pm \frac{1}{2},\pm\frac{5}{2},\pm\frac{25}{2}[/tex]

Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.

Option (2)

f(x) = 9x⁴- 7x²+ x + 10

Possible rational roots = [tex]\frac{\pm 1,\pm 2,\pm 5,\pm10}{\pm 1,\pm3,\pm9}[/tex]

Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.

Option (3)

f(x) = 10x⁴- 7x²+ x + 9

Possible rational roots = [tex]\frac{\pm1, \pm3, \pm9}{\pm 1,\pm2,\pm5,\pm10}[/tex]

Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.

Option (4)

f(x) = 25x⁴- 7x²+ x + 4

Possible rational roots = [tex]\frac{\pm 1,\pm2,\pm5}{\pm1,\pm5,\pm 25}[/tex]

                                      = [tex]\pm1,\pm2,\pm5,\pm\frac{1}{5},\pm\frac{1}{25},\pm\frac{2}{5},\pm\frac{2}{25}[/tex]

Therefore, [tex]-\frac{2}{5}[/tex] is the possible rational root.

Option (4) will be the answer.

Mercury is the smallest and fastest planet in the solar system. It is also the closest planet to the sun. It is named after the Roman messenger god Mercury, the fastest Roman god.

Answer:

The radius is 6

Step-by-step explanation:

Arc length ACB = 6 pi

The arc length = fraction of a circle times the circumference

6 pi = 180/360 * 2 * pi *r

6 pi = 1/2 * 2 * pi*r

6 pi =  pi r

The radius is 6

Answer:

y=x+12

Step-by-step explanation:

y=-x+12; is a line with slope m1=-1

to find perpendicular slope of intersecting line take the negative inverse of m1. so -1*(1/(-1))=1=m2

use equation for a line of y=m*x+b and put in the point (-5,7) and solve for b=the y axis intercept

7=1*(-5)+b

7=-5+b

12=b

so

y=x+12

Answer:

9(9m + 3t) = 81m + 27t

Step-by-step explanation:

With brackets with more than one term inside multiplied by a number;

The rule of thumb to know is that with brackets, everything inside must be multiplied by everything outside;

So, in this case, the number 9 must be multiplied by each term inside the brackets:

9 × 9m = 81m

9 × 3t = 27t

So to expand, opening the brackets, you get:

81m + 27t

Answer:

The base is 19.5.

Step-by-step explanation:

The given question is, "The perimeter of a rectangle is 58 and its base exceeds its width by 10, how long is the base?"

Perimeter = 58

Base, l = 10+b

The perimeter of a rectangle is :

P = 2(l+b)

58 = 2(10+b+b)

29 = (10+2b)

29-10 = 2b

19 = 2b

b = 9.5

Base, l = 10 + 9.5

= 19.5

Hence, the base is 19.5.

Answer:

$52

Step-by-step explanation:

Find the cost by plugging in 12 as g and 4 as a into the expression:

3g + 4a

3(12) + 4(4)

36 + 16

= 52

So, the cost will be $52

Answer:

15

Step-by-step explanation:

50 * .30=15

Answer:

[tex](5x - 1)(3x - 1)(x + 2)[/tex]

Step-by-step explanation:

[tex](15 {x}^{3} + 22 {x}^{2} - 15x + 2)[/tex]

Apply Rational Root Theorem, our possible roots will be

plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).

I

I tried root -2 and it work so

If we apply synthetic dividon, we would be left with

[tex]15 {x}^{2} - 8x + 1[/tex]

We can factor this regularly.

Apply AC method that a number

AC will multiply to 15 but add to -8.

The answer are -5 and -3 so we write this as

[tex]15 {x}^{2} - 5x - 3x + 1[/tex]

Factor by grouping

[tex](15x {}^{2} - 5x) - (3x + 1)[/tex]

[tex]5x(3x - 1) - 1(3x - 1)[/tex]

So our factor are

[tex](5x - 1)(3x - 1)(x + 2)[/tex]

Answer:

-2 ≤ n < 8

Step-by-step explanation:

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