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2 years ago

Quiz

Mathematics

2 answers:

Serjik [45]2 years ago

8 0

Answer:

Step-by-step explanation:

5^2 = 25 5^3 = 125 them two added together equals 150

6^2 = 36 so 36 plus 36 equals 72

150-72=78

Alex777 [14]2 years ago

7 0

Answer:

1829

Step-by-step explanation:

D - E
(5² x 5³) - (6² x 6²)
(25×125) - (36×36)
3125 - 1296
1829

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1)cot a/2 -tan a/2 = 2 cot a 2) cot b/2 + tan b/2= 2 cosec b prove

VladimirAG [237]

1)

LHS = cot(a/2) - tan(a/2)

= (1 - tan^2(a/2))/tan(a/2)

= (2-sec^2(a/2))/tan(a/2)

= 2cot(a/2) - cosec(a/2)sec(a/2)

= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))

= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)

= 2[(1+cos(a) -1)/sin(a)]

=2cot a

= RHS

2.

LHS = cot(b/2) + tan(b/2)

= [1 + tan^2(b/2)]/tan(b/2)

= sec^2(b/2)/tan(b/2)

= 1/sin(b/2)cos(b/2)

using product to sums

= 2/sin(b)

= 2cosec(b)

= RHS

8 0

3 years ago

Find the distance between the 2 points (6, - 4) and (2, - 7). Please show me how you found it.

Serga [27]

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 6}}\quad ,&{{ -4}})\quad 
% (c,d)
&({{ 2}}\quad ,&{{ -7}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[2-6]^2+[-7-(-4)]^2}\implies d=\sqrt{(2-6)^2+(-7+4)^2}$

5 0

3 years ago

State whether the lines are parallel, perpendicular,or neither.

cluponka [151]

Answer:

Please check the explanation.

Step-by-step explanation:

Two lines are parallel if their slopes are equal.

Two lines are perpendicular if the product of their slope is -1

We also know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

Given the lines

y = 6х - 3

Comparing with y=mx+b, the slope of y = 6х - 3:

m₁=6

y = - 1/6x + 7

Comparing with y=mx+b, the slope of y = - 1/6x + 7:

m₂=-1/6

m₁ × m₂ = -1

6 × - 1/6 = -1

-1 = -1

Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.

y = 3x + 2

Comparing with y=mx+b, the slope of y = 3x + 2:

m₁=3

2y = 6x - 6

simplifying to write in slope-intercept form

y=3x-3

Comparing with y=mx+b, the slope of y=3x-3:

m₂=3

As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.

i.e. m₁ = m₂ → 3 = 3

Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.

8x - 2y = 3

simplifying to write in slope-intercept form

y = 4x - 3/2

Comparing with y=mx+b, the slope of y = 4x - 3/2:

m₁=4

x + 4y = - 1

simplifying to write in slope-intercept form

y=-1/4x-1/4

Comparing with y=mx+b, the slope of y=-1/4x-1/4:

m₂=-1/4

m₁ × m₂ = -1

4 × - 1/4 = -1

-1 = -1

Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.

3x+2y = 5

simplifying to write in slope-intercept form

y = -3/2x + 5/2

Comparing with y=mx+b, the slope of y = -3/2x + 5/2:

m₁=-3/2

3y + 2x = - 3

simplifying to write in slope-intercept form

y = -2/3x - 1

Comparing with y=mx+b, the slope of y = -2/3x - 1:

m₂=-2/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

y - 5 = 6x

simplifying to write in slope-intercept form

y=6x+5

Comparing with y=mx+b, the slope of y=6x+5:

m₁=6

y - 6x = - 1

simplifying to write in slope-intercept form

y=6x-1

Comparing with y=mx+b, the slope of y=6x-1:

m₂=6

As the slopes of y - 5 = 6x and y - 6x = -1 are equal.

i.e. m₁ = m₂ → 6 = 6

Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.

y = 3х + 9

Comparing with y=mx+b, the slope of y = 3х + 9:

m₁=3

y = -1/3x - 4

Comparing with y=mx+b, the slope of y = 1/3x - 4:

m₂=1/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

8 0

2 years ago

Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloo

DaniilM [7]

$149.60 that's what he will have left

6 0

3 years ago

PLEASE HELP VERY URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

diamong [38]

Q1. Look at the picture.

$C.\\y=-\dfrac{1}{3}x+3\\\\y=2x-4$

Q2. Look at the picture.

$A.\ 4-t$

Q3.

Put the value of x = 2 to the equation 3x + y = 5:

$3(2)+y=5$

$6+y=5$ subtract 6 from both sides

$y=-1\\\\F.\ -1$

Q4.

$\left\{\begin{array}{ccc}n=3m-11&(*)\\2m+3n=0&(**)\end{array}\right$

Substitute (*) to (**):

$2m+3(3m-11)=0$ use distributive property

$2m+(3)(3m)+(3)(-11)=0$

$2m+9m-33=0$ add 33 to both sides

$11m=33$ divide both sides by 11

$m=3$

Put the value of m to (*):

$n=3(3)-11\\\\n=9-11\\\\n=-2$

$C. (3,\ -2)$

Q5.

w - width

3w - length

24 in - the sum of length and width

The equation:

$w+3w=24$

$4w=24$ divide both sides by 4

$w=6\ in$

$3w=3(6)=18\ in$

$J.\ 18\ inches$

7 0

3 years ago

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