Find the value of x.
A. About 57.6
B. About 42.6
C. About 12.6
D. About 27.6

Answer:

D

Step-by-step explanation:

for you to find x you first have to find the adjacent of the 45° angle you can do that by using the other triangle.using the sin ratio

sin60=opposite/hypotenuse

sin60=a/7√3

a=10.5

then after you have found the adjacent you can use the cos ratio

cos45=adjacent/hypotenuse

cos45=10.5/x

cos45x/cos45=10.5/cos45

x=14.849

which is the same as 21√2 over 2

I hope this helps

Answer:

D

Step-by-step explanation:

Using sine ratio in left right angled triangle to find the altitude a of the large triangle which is common to both right triangles and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2a = 21 ( divide both sides by 2 )

a = [tex]\frac{21}{2}[/tex]

Using the cosine ratio in the right side triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{a}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = [tex]\sqrt{2}[/tex] a = [tex]\sqrt{2}[/tex] × [tex]\frac{21}{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → D

Step-by-step explanation:

1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n

make the 3rd term an improper fraction

1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n

multiply equation by 30, cancel the denominators, resulting in:

6n + 6(51) = 6(152) - 5n

6n + 306 = 912 - 5n

6n + 5n = 912 - 306

11n = 606 is the number

n = 606/11

n = 55 1/11

Answer:

68

Step-by-step explanation:

let unknown number be x

⅕x + 5½= 30⅖ - ⅙x

⅕x + 11/2= 152/5 - ⅙x

collect like terms

⅕x+⅙x= 152/5 - 11/2

[tex] \frac{11}{30}x = \frac{249}{10} [/tex]

cross multiply

30 * 249=(11 * 10)x

7470=110x

x=7470/110

x= 68

Answer:

16.8 or  16 whole 4/5

Step-by-step explanation:

14 divided by 5/6

take reciprocal

14 x 6/5

84/5

16.8

Answer: True

Step-by-step explanation:

The number is going down in a way that cannot be written as a straight line so it is a nonlinear.

(5,-8) after a 180 degree counterclockwise rotation about the origin is (-5,8)

Answer: (3, 18)

Step-by-step explanation: Where the lines corss the x does not go over 10 so the only other option is a 3. If you cut the box hori in half in you mind, the top half being 15-20 and the bottom half bring 10-14, then you can see the lines cross on the top half. Meaning it’s at 18 not 12.

answer =

=3a²-16ab+13b²

=3a²-(13+3)ab+13b²

=3a²-13ab-3ab+13b²

=a(3a-13b)-b(3a-b)

=(3a-13b)(a-b)

Answer:

even I got confused in question no. j

no worry rest all are solved .

all the questions are solved by middle term splitting method .

Answer:

No, because 6² + 8² ≠ 12²

Step-by-step explanation:

In a right angled triangle,

Perpendicular² + Base² = Hypotenuse² (pythagoras theorem)

But in the given triangle; 6² + 8² ≠ 12²

36 + 64 ≠ 144

100 ≠ 144

Perpendicular² + base² ≠ hypotenuse²

Thus the given triangle is not right angled.

Answer:

15

Step-by-step explanation:

Sum of 'n' terms formula is given by:-    

s=n/2(2a+(n-1)d)  

s=13/2[2xa+(13-1)5]    

s=13/2(2xa+12x5)    

s=13/2(2a+60)    

585=13/2(2a+60)    

585 x (2/13) = 2a + 60

90 = 2a + 60  

90-60 = 2a

30 = 2a

a = 15

Answer:

22.08 cm

Step-by-step explanation:

Area = pi*r^2*(angle/360)

r=11.04, d=22.08

Answer:

37.5 miles

Step-by-step explanation:

Distance covered in 4 hours = 150 miles

Distance covered in 1 hour = 150/4 = 37.5 miles

Answer:

72.35%

Step-by-step explanation:

246/340 = .723529

Just multiply it by 100 to get the percentage

.723529 x 100 = 72.3529

Answer:

H=A/B

Step-by-step explanation:

Using the rules of Algebra we can divide both sides by B to isolate H on one side. Now we can find H in terms of A, and B. H=A/B

Answer:

Below

Step-by-step explanation:

You can rearrange this equation to solve for H ....

    H = A / B

I did this by using a rearranging pyramid!

Hope this helped!

Answer:

50

Step-by-step explanation:

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

= 3^3 + (12) + 2^2 + (3 + 2)^5

= 3^3 + 12 + 2^2 + (5)^5

= 9 + 12 + 2^2 + 5^5

= 9 + 12 + 4 + 5^5

= 9 + 12 + 4 + 25

= 50

Answer:

Step-by-step explanation:

Answer:

undefined, you cannot divide by zero

Step-by-step explanation:

Answer:

hjk

Step-by-step explanation:

Answer:

Im not sure what is in the algebra 1 module 4 but for algebra 1 you should study how to graph equations, solve system of equations with substitution and elimination. those topics, at least for e, have been a little tricky

Step-by-step explanation:

Answer:

-1/8

Step-by-step explanation:

(-1/2) ^3

(-1/2)(-1/2)(-1/2)

-1/8

Answer:

a open and close switch and a condentation out put.

Answer:

9(1 +6)

Step-by-step explanation:

9 = 9 * 1

54 = 9 * 6

9 + 54 = (9*1 ) + (9*6)      {9 is common in both terms}

           = 9*(1 + 6)

Answer:

Step-by-step explanation:

I am not sure if you are asking for the graph of

√(x-16) that has a x intercept at (16,0)

or

√ x -16 that has a y intercept at (0, -16)

Answer:

A is the answer I pretty sure

Answer:

i think the answer is 502 m2

Answer: 50%

Step-by-step explanation:

From the question, we're given the information that Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world and that it rises 450 ft over a horizontal distance of 1,000 ft.

Therefore, the percentage grade of this hill will be calculated as the height over the length and this will be:

= 450/1000 × 100

= 45%

= 0.45

= 0.5 to nearest tenth

= 50% to nearest tenth.

Answer:

let the polynomial be

f(x)=x³+2kx+2

is divided by

g(x)=x+2

hence

(x+2) is a factor of f(x)

so comparing with x-a we get a=-2

so

f(a)=0

f(-2)=(-2)³+2*-2*k+2

0=-8-4K+2

4k=-6

K=-6/4

k=-3/2

again

when divided by x+1

g(x)=x+1

hence

x+1 is a factor

so a=-1

f(-1)=-(1)³+2*-1*k+2

0=-1-2k+2

0=1-2k

k=1/2

The value of k is 1/2 when divided by x+1

and

K =-3/2 when divided by x+2

Answer:

-2 <= x <= 1/3

Step-by-step explanation:

it is the same as for equations.

the solution for a square equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

our parameters here are

a = 3

b = 5

c = -2

so,

x = (-5 ± sqrt(25 - -24))/6 = (-5 ± sqrt(49))/6 = (-5 ± 7)/6

x1 = (-5 + 7)/6 = 2/6 = 1/3

x2 = (-5 - 7)/6 = -12/6 = -2

since we are looking for smaller or equal, points of 0 will be part of the solution.

now we need to check each side of these points on the x-axis, if they are true or not to the inequality.

left of -2 : let's pick -3

3×(-3)² + 5×-3 -2 = 3×9 - 15 - 2 = 27 - 15 -2 = 10

this is NOT <= 0, so this interval does not fit.

similar, right of 1/3 : let's pick 1

3×1² + 5×1 - 2 = 3 + 5 - 2 = 6

this is NOT <= 0, so this interval does not fit either (as expected, as normally either both sides fit, or both fail).

lastly, in the middle between -2 and 1/3 : let's pick 0

3×0² + 5×0 - 2 = -2

this IS <= 0, so the interval between -2 and 1/3 fits.

Answer:

This is called system of equations.

Step-by-step explanation:

This combines two equations and then lines them up to a system.

Answer:

Step-by-step explanation:

  matrix

     or

vector geometry