Find the missing side of the triangle. Round your answers to the nearest tenth if necessary.
24 yd
30 yd
35 yd
16 yd
18 yd
38 yd​

Given:

The inequalities are:

[tex]2x-3<7[/tex]

[tex]2x+1>-3x-4[/tex]

To find:

The range of values of [tex]x[/tex] for the given inequalities.

Solution:

We have,

[tex]2x-3<7[/tex]

Adding 3 on both sides, we get

[tex]2x-3+3<7+3[/tex]

[tex]2x<10[/tex]

Divide both sides by 2.

[tex]\dfrac{2x}{2}<\dfrac{10}{2}[/tex]

[tex]x<5[/tex]                      ...(i)

The second inequality is:

[tex]2x+1>-3x-4[/tex]

Subtracting 1 from both sides, we get

[tex]2x+1-1>-3x-4-1[/tex]

[tex]2x>-3x-5[/tex]

Adding [tex]3x[/tex] on both sides, we get

[tex]2x+3x>-3x-5+3x[/tex]

[tex]5x>-5[/tex]

Divide both sides by 5.

[tex]\dfrac{5x}{5}>\dfrac{-5}{5}[/tex]

[tex]x>-1[/tex]            ...(ii)

Using (i) and (ii), we get

[tex]-1<x<5[/tex]

Therefore, the required range is [tex]-1<x<5[/tex].

Answer:

0.0067 = 0.67% probability of selecting at least 3 defective fuses.

Step-by-step explanation:

For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, 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.

A company manufactures fuses. The percentage of non-defective fuses is 95.4%.

This means that 100 - 95.4 = 4.6% = 0.046 are defective, which means that [tex]p = 0.046[/tex]

A sample of 9 fuse was selected.

This means that [tex]n = 9[/tex]

Calculate the probability of selecting at least 3 defective fuses.

This is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

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

[tex]P(X = 0) = C_{9,0}.(0.046)^{0}.(0.954)^{9} = 0.6545[/tex]

[tex]P(X = 1) = C_{9,1}.(0.046)^{1}.(0.954)^{8} = 0.2840[/tex]

[tex]P(X = 2) = C_{9,2}.(0.046)^{2}.(0.954)^{7} = 0.0548[/tex]

Then

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.6545 + 0.2840 + 0.0548 = 0.9933[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.9933 = 0.0067[/tex]

0.0067 = 0.67% probability of selecting at least 3 defective fuses.

Answer:

{2, 4, 6, 8,10}

Step-by-step explanation:

GIven U={1,2,3,.............,10} A={2,4,6,8,10} and B= {1,3,5,7,9);

Required

A-B = AnB'

B' = {2, 4, 6, 8,10}

AnB' are elements common to both A and B'.Hence;

AnB' = A- B = {2, 4, 6, 8,10}

Answer:

The measure of each angle will be 7 degrees. It is because a bisector divides an angle in two equal halves. 14 / 2 = 7

Answer:

[tex]3[/tex] times

Step-by-step explanation:

[tex]5x=15[/tex]

Divide both sides by 5

[tex]x=3[/tex]

Hope this helps

Answer:

9 Times

Step-by-step explanation:

You need to find how many times farther away Amy sets up her target. She used to set it up 5 feet away. Start by finding how many feet away she sets up her target now.

There are 3 feet in a yard, so multiply 15 yards by 3.

15×3=45

Now, Amy sets up her target 45 feet away. She used to set it up 5 feet away. You can use a multiplication fact to find how many times farther away she sets up her target now.

5×9=45

Amy sets up her target 9 times farther away now.

Answer:

∠AEC ≅ ∠BED by vertical angles theorem

Answer:

Answer:

∠AEC ≅ ∠BED by vertical angles theorem

Step-by-step explanation:

Answer:

m = 3 , n = 4

Step-by-step explanation:

Using Section Formula.

[tex]If \ the \ line \ segment \ AB \ where \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \ the \ points \ of \ P \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}[/tex]

   [tex]Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x = -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3[/tex]

  [tex]y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4[/tex]

Answer:

The standard equation is 7x + y = 9

Step-by-step explanation:

Equations given are:  

7x + 3 = 5 and y - 1 = 6

Set both given equations equal to zero, then combine them into one standard form equation

Set the equations to zero by moving the constant from R.H.S to L.H.S

7x + 3 - 5 = 0

7x - 2 = 0 ---- eq 1

y - 1 = 6

y - 1 - 6 = 0

y - 7 = 0 ----- eq 2

We have to combine eq 1 and eq 2

7x - 2 + y - 7 = 0

7x + y - 9 = 0

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

Thus the standard equation is:

7x + y - 9 = 0

7x + y = 9

Thus the standard equation is 7x + y = 9

Answer:

complete the square 2 x + 38 = 0

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Given that DE is parallel to AC then DE divides the sides proportionally, so

[tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex] , substitute values

[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3x = 2(x + 2) ← distribute

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Step-by-step explanation:

is it a question ? please check.

Answer:

Step-by-step explanation:

D.

supplementary.

BC.

D.

3+2=5

Milk =3/5×640 = 384

Curd 2/5×640 = 256

The answer for the following question is 12i.

Answer:

t + u = 10 + 2i

Step-by-step explanation:

t + u

= 4 + 6 + 2i ← collect like terms

= 10 + 2i

Answer:

Is that it's not about the answers and the questions

Answer:

The length of the equal sides of the isosceles triangle with a perimeter of 34 cm perimeter is 12 cm

The length of the equal sides of the isosceles triangle with a perimeter of 82 cm perimeter is 36 cm

The base length of both triangles is 10 cm

Step-by-step explanation:

The given parameters are;

The base length of the triangles are equal

The base length of one of the triangle = The base length of the other triangle

The equal sides of one of the triangles = 3 × The length of the equal sides of the other

The perimeter of the triangles are; 34 cm and 82 cm

Let 'b' represent the base length of each triangle, let 'a' represent the length of an equal side of the smaller triangle with a perimeter of 34 cm and let 'c' represent the length of an equal side of the larger triangle with a perimeter of 82 cm

For the smaller triangle, we have;

b + 2·a = 34..(1)

For the other triangle;

b + 2·c = 82...(2)

Given that the side length of the larger triangle are larger than those of the smaller triangle, and that the side length of the larger triangle is 3 times the side length of the smaller triangle, we get;

c = 3·a

By the substitution method, from equation (2) we get;

b + 2·c = b + 2 × 3·a = b + 6·a = 82

∴ b + 6·a = 82...(3)

Subtracting equation (1) from equation (3) gives;

b + 6·a - (b + 2·a) = 82 - 34 = 48

b - b + 6·a - 2·a = 48

4·a = 48

a = 48/4 = 12

The length of the equal sides of the 34 cm perimeter (smaller) isosceles triangle, a = 12 cm

From c = 3·a, and a = 12, we get;

c = 3 × 12 = 36

The length of the equal sides of the 82 cm perimeter (larger) isosceles triangle, c = 36 cm

From equation (1), we get;

b + 2·a = 34

∴ b + 2 × 12 = 34

b = 34 - 2 × 12 = 10

The base length of both triangles, b = 10 cm

well, let's keep in mind that the SAS postulate, so if one Side and the Angle next to it and the following Side after the angle are equal on both triangles, both triangles are congruent.  Now, we have the angle 30° with sides and 9 and 2x and sides 9 and x + 4, well, the 9's are equal, dohh, you know, if only the 2x  = x + 4, we'd be golden

[tex]2x = x + 4\implies 2x - x = 4\implies \boxed{x = 4}[/tex]

Answer:

[tex]delta = {b}^{2} - 4ac = {p}^{2} - 4 \times 3 \times 3 = {p}^{2} - 36[/tex]

The equation has no real roots if delta <0

that is -6<p<6

Answer:

3

Step-by-step explanation:

3

Answer:

z = -74

Step-by-step explanation:

12 = (2+z) / -6

Multiply each side by -6

-6 * 12 = (2+z)/ -6 * -6

-72 = 2+z

Subtract 2 from each side

-72-2 = 2+z-2

-74 =z

Answer:

this is the answers

Answer:

5

Step-by-step explanation:

AC=AB+BC

so 16=x+1+x+7

which simplifies to 16=2x+8

subtract eight from both sides to get 8=2x

then divide by 2 to get that x=4

AB=x+1, which substitutes into 4+1=5

Answer:

x = 135

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

125 = x-10

Add 10 to each side

125+10 = x

135 =x

Answer:

0.9999

Step-by-step explanation:

One way to calculate the probability that at least one of them need repairs is that we can calculate the opposite (none need repairs) and subtract that from 1 (100%).

The probability that a car does not need repairs is 0.2. To find the probability that six cars all fulfill this 0.2 probability, we can get [tex]0.2^{6} =0.000064[/tex] . This is the probability that none require repairs. The opposite of this is that at least one needs repairs, so 1-0.000064 - 0.999936. Rounded to 4 decimal places, the probability is 0.9999

Solution :

As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis. The first block then should be negative x-axis if r is positive and in the positive x-axis if r is negative.

My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence, which would mean an interference from the above statements, from the drag phase you have given the interference would be positive x-axis.

Answer:

option A

Step-by-step explanation:

22 : 15 + 10hours = 8 : 15

                              8 : 15 + 35 minutes = 8 : 50

Therefore the difference = 10 hours 35 minutes

Answer:

It's well be 2 cause that is the only one thag makes sense

Answer:

Given

To find f(x + 2) substitute x with x + 2 in the given function:

f(x+2)= 4(x + 2)² + 2(x + 2) - 4

         = 4(x² + 4x + 4) + 2x + 4 - 4

         = 4x² + 16x + 16 + 2x

         = 4x² + 18x + 16

f(x+2)