The angle A of a triangle ABC is 20% less than the sum of other two angles. If angle C is [tex]\frac{2}{3}[/tex] times angle B, then find the value of angle B.

Answer:

no..........................

Answer:

D

Step-by-step explanation:

sin theta is equal to perpendicular by hypotenuse

here perpendicular is equal to 15 and base is equal to 8 therefore hypotenuse will be equal to 17

on putting on putting the value of perpendicular by hypotenuse we get 15 by 17 as sin theta

Answer:

Step-by-step explanation:

hypotenuse = √(15²+8²) = √289 = 17

sinθ = (leg opposite θ)/hypotenuse = 15/17

Answer: 19/3

Step-by-step explanation:

[tex]4x+3-x-5=30-3x\\\\3x-8=30-3x\\\\6x-8=30\\\\6x=38\\\\x=\frac{19}{3}[/tex]

Answer:

Average speed = [tex]\frac{(x+y)}{2}[/tex] miles per hour

Step-by-step explanation:

Formula to calculate the average speed of an object is,

Average speed = [tex]\frac{\text{Total distance covered}}{\text{Time taken to cover this distance}}[/tex]

If I travel with the speed of x mph for t hours,

Total distance covered = Speed × Time

                                       = [tex]x\times t[/tex]

                                       = [tex]xt[/tex] miles

Similarly, if I travel with the speed y mph for t hours,

Total distance covered = [tex]yt[/tex] miles

Total distance covered by me = [tex](xt+yt)[/tex] miles

Total time taken to cover this distance = [tex]t+t[/tex]

                                                                 = [tex]2t[/tex] hours

Therefore, expression for the average speed will be,

Average speed = [tex]\frac{xt+yt}{2t}[/tex]

                          = [tex]\frac{(x+y)t}{2t}[/tex]

                          = [tex]\frac{x+y}{2}[/tex] miles per hour

Answer:

<BAC = 36degrees

Step-by-step explanation:

Find the diagram attached

The sum of the interior angle is equal to the exterior. Hence;

<B + <C = <DAB

6x+40 + x+20 = 180 - 3x

7x+60 = 180 - 3x

7x+3x = 180 - 60

10x = 120

x = 120/10

x = 12

Get <BAC

<BAC = 180 - (180-3x)

<BAC = 180-180+3x

<BAC = 3x

<BAC = 3(12)

<BAC = 36degrees

Answer:

there are 6 units

hope this help

Answer:

Step-by-step explanation:

This is a volume problem as indicated by the exponent on the unit feet. Cubed is a volume thing, whereas squared is an area thing, etc.

The volume for a box-shaped microwave is

V = l x w x h and we are given the length and the width, but those are in inches and they need to be in feet. That's the tricky part here...catching the inconsistency in the units!

18 inches = 1.5 ft and

14 inches = 7/6 feet

Filling in:

1.75 = 1.5 x 7/6 x h and

1.75 = 1.75h so

h = 1 foot

Answer:

0.7744 = 77.44% probability of getting two good coils when two coils are randomly selected

Step-by-step explanation:

For each coil, there are only two possible outcomes. Either it is good, or it is not. Since the coil taken is replaced, the probability of choosing a good coil on a trial is independent of any other trial, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

88 out of 100 are good:

This means that [tex]\pi = \frac{88}{100} = 0.88[/tex]

Find the probability of getting two good coils when two coils are randomly selected.

This is P(X = 2) when n = 2. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.88)^{2}.(0.12)^{0} = 0.7744[/tex]

0.7744 = 77.44% probability of getting two good coils when two coils are randomly selected

Answer:

60

Step-by-step explanation:

5x + 10y = 800

y = 50

5x + 10(50) = 800

5x + 500 = 800

5x = 300

x = 60

Answer: 60

Step-by-step explanation:

If x = small vehicles and if y = large vehicles and y = 50, then substitute and solve for x. So,

5x + 10(50) = 800

5x + 500 = 800

5x = 300

x = 60

So, the number of small vehicles is 60.

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Answer:

Step-by-step explanation:

If the product of 2 integers is -12, then that equation looks like this:

xy = -12

If the sum of those same 2 integers in 1, then that equation looks like this:

x + y = 1

Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us

x = 1 - y and plug that into the first equation in place of x to get:

(1 - y)y = -12 and

[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:

[tex]-y^2+y+12=0[/tex] and the 2 values for y are

y = -3 and y = 4. Let's see what happens when we solve for x.

If xy = -12 and y is -3:

x(-3) = -12 so

x = 4

If xy = -12 and y is4:

x(4) = -12 so

x = -3

So it looks like the 2 integers are -3 and 4

Answer:

114

Step-by-step explanation:

114

Answer:

no .... 20% is .2 not .02

Step-by-step explanation:

Answer:

Traversable because it has exactly two odd nodes

Step-by-step explanation:

There is a rule that says it is traversable if it has exactly 2 odd nodes. The are other rule where it can be traversable is if has no odd nodes.

Also if we let the starting point be D and the ending point be B we can travel the network in such way that each edge is only traveled once which is the definition that the network is traversable.

So I will do this by starting at D, then travel to A using the outside edge, then travel to back to D using inside edge, then travel to C, then travel to B, then travel to A using outside edge, and then back to B from A using inside edge.

Answer: 11 units

Step-by-step explanation:

Use the distance formula: [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

[tex](x_{1}, y_{1})=(-5, 6)\\(x_{2}, y_{2})=(6, 6)\\\\\sqrt{(6-(-5)^{2}+(6-6)^{2}} =\sqrt{(11)^{2}+(0)^{2}} =\sqrt{121+0}=\sqrt{121}=11[/tex]

The length of the line is 11 units.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

Given that, endpoints are (-5,6) and (6,6) of the line segment.

The length= √(6+5)²-(6-6)²

                  =11 units

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Answer:

17.5

Step-by-step explanation:

as the triangles are similar, when oriented in the same direction they have the same angles, and the lengths of all sides of DEF are the lengths of the sides of ABC but multiplied by the same scaling factor f for all sides.

so, we see that

A ~ D

B ~ E

C ~ F

and therefore

AB ~ DE

BC ~ EF

CA ~ FD

that means

DE = AB × f

EF = BC × f

FD = CA × f

we know DE and AB.

so,

4 = 10 × f

f = 4/10 = 2/5

and now we know

EF = 7 = BC × f

BC = 7/f = (7/1) / (2/5) = (5×7)/(2×1) = 35/2 = 17.5

Answer:

17.5

Step-by-step explanation:

Answer:

[tex]{ \bf{15x + 30 = 180}}[/tex]

Answer:

Step-by-step explanation:

by considering  2 + 3 = 95

3² = 9

2 + 3 = 5      

by considering  4 + 5 = 259

5² = 25

4 + 5 = 9  

by considering  6 + 7 = 4913

7² = 49

6 + 7 = 13  

by considering  8 + 9 = ????

9² = 81

8 + 9 = 17  

∴ 8 + 9 = 8117

Answer:   [tex]\huge\boxed{x=3\frac{1}{3} \quad ;\quad y=-3}[/tex]

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol+\ \left \{ {{6x+4y=8} \atop {-4y=12}} \right. \Longrightarrow\\\\\\ 6x+ 4y\!\!\!\!\!\diagup-4y\!\!\!\!\!\diagup=12+8 \\\\6x=20 \\\\x=\frac{20}{6} =\frac{10}{3} =3\frac{1}{3} \quad ; \quad y=-3[/tex]

Answer:

2a(b+c)

Step-by-step explanation:

Find HCF (2a)

Then factorise

Answer:

2a(b+c)

.............

Answer:

slope= 1/2

y-intercept= 0,7

Answer:

slope = 1/2 or 0.5, the y-intercept is (0,7)

Step-by-step explanation:

Step-by-step explanation:

Length of a rope is 5 meter. it means the rope is 5 meter long..

Answer:

The answer is "6000".

Step-by-step explanation:

It seems to be a total of 30 buddies there. Every column has 10 seats so that the 10 pals are now in a row. Of all the other 20 buddies, 10 are on the following row. And we have ten friends remaining and that they are sitting in the next row.

Therefore the possibility of sitting is:

[tex]30 \times 20 \times 10 = 6000[/tex]

Answer:

6, -5 and 6. Assume the leading coefficient of f(x) is 1. Write the equation of the cubic polynomial in standard form.

Answer:

70%

Step-by-step explanation:

Finding each side :-

Finding area of unshaded region :-

Overall area :-

Finding percentage :-

Answer:70%

Step-by-step explanation:

Answer: b

Step-by-step explanation:

The inverse of a function can be determined graphically by reflecting the graph over line y =x, the correct option is D.

An inverse of a function can be determined by interchanging variables in the function, y is interchanged by x in an f(x,y) function and then the equation is solved for y to determine the inverse of a function.

The equation is y = 2x+3

The inverse of a function is determined graphically the graph will be reflected in the line y =x.

The graph is attached with the answer.

Therefore, the correct option is D.

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Answer:

[tex]\boxed {\boxed {\sf D. \ 16}}[/tex]

Step-by-step explanation:

We are given the following equation and asked to solve for 2x+1.

[tex]\sqrt {2x+1}=4[/tex]

We want to isolate the entire expression of 2x+1. Notice that it is under the square root. If we want to isolate it, we have to perform the inverse operation. The inverse of a square root is a square, so we square both sides of the equation.

[tex](\sqrt{2x+1} )^2= (4)^2[/tex]

[tex]2x+1=(4)^2[/tex]

[tex]2x+1=16[/tex]

We could continue solving for x, then plug the answer back into the expression 2x+1. However, hopefully you notice that we already found the answer!

We only had to do one step to find the answer, but you could complete many other steps to get the same answer:

[tex]2x+1-1=16-1\\2x=15\\2x/2=15/2\\x= 7.5[/tex]      (Solve for x)

[tex]2x+1\\2(7.5)+1\\15+1\\16[/tex]                   (Plug the answer in for x)

The value of 2x+1 is 16 and the correct answer is 16.