5. Use the law of Cosines to find each missing sides. Round to the nearest tenth

Answer:

B is correct.

Answer:

Three linear equations that has a unique solution (1,2,-1) are:-

x+ y+ z =2

2x + y + 3z = 1

x+ 2y+ z  = 4

Step-by-step explanation:

Linear equations in three variables:-

If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0)

then ax + by + cz = r is called a linear equation in three variables. (The

“three variables” are the x, the y, and the z.)

The numbers a, b, and c are called the coefficients of the equation. The

number r is called the constant of the equation.

so from from above explanation we can write 3 linear equations with three variables as.

x+ y+ z =2

2x + y + 3z = 1

x+ 2y+ z  = 4

Now to check if the given point (1,2,-1) is solution or not  these equations must satisfy this point,

x+ y+ z =2

1+ 2- 1 = 2

   2= 2

2x + y + 3z = 1

2×1 +2 - 3×1 = 1

     1=1

x+ 2y+ z  = 4,

1+ 2×2 -1 = 4

    4=4  

therefore all three equations satisfies the given point

hence these are the three linear equation having point (1,2, -1) as the unique solution

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Answer:

4

Step-by-step explanation:

2L=w

32=LxW

so you put the 2L as the w

which is 32=Lx2L

32=2L^2

16=L^2

4=L

*To find the width you input 4 as L*

So 8=W

The shortest side would be 4

The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home is 40.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

For the given data the table can be made as shown below. The marginal distribution of tenure in counts can be calculated as,

Owns home = 71 + 5 = 76

Rents home = 13 + 27 = 40

Hence, The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home is 40.

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Answer:

Point Form:

(9,12)

Equation Form:

x = 9

y = 12

Step-by-step explanation:

Answer:

[tex]\fbox{x = 9, y = 12}[/tex]

Step-by-step explanation:

[tex]\textsf {Let's solve by substitution.}[/tex]

[tex]\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}[/tex]

[tex]\textsf {Substitute for x in the first equation of the system.}[/tex]

[tex]\implies \mathsf {-5(2y-15)+4y=3}[/tex]

[tex]\implies \mathsf {-10y+75+4y=3}[/tex]

[tex]\implies \mathsf {-6y=-72}[/tex]

[tex]\implies \textbf {y = 12}[/tex]

[tex]\implies \mathsf {x = 2(12) - 15}[/tex]

[tex]\implies \mathbf {x = 9}[/tex]

[tex]\textsf {The solution is : x = 9, y = 12}[/tex]

Answer:

288

Step-by-step explanation:

First position choice:   4 numbers

Second                         6 numbers

Third                             6

Fourth                           6

       TOTAL 4 digit numbers   4 * 6 * 6 * 6 = 864 combos

             2 out of 6 of these will end in 3 or 5  (thus making an odd number)

                    864 * 2/6 = 288 such numbers

Answers for different section are given below;

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, given function;

  f(x) = -x² - 4x + 6

1.    If we take -1 common from the given function, we get

                     f(x) = -1 (x² + 4x - 6)

                    f(x) = -1 (x² + 4x) + 6

     Thus, first block contains -1 and second block contains 4.

2.   Then we add half of the coefficient of x², (b/2)², inside the bracket and subtract it outside a times, a(b/2)².

                f(x) = -1 ( x² + 2. 2x + 2²) +2² + 6

                f(x) = -1 ( x² + 4x + 2²) +4 + 6

Thus, first block contains -1, second block contains 4, third block contains 4, and fourth block contains 4.

3. Then we factorize the bracket and simplify outside the bracket;

               f(x) = -1 (x + 2)² + 10

Thus, first block contains -1, second block contains 2 and third block contains 10.

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Answer:

0.4706

Step-by-step explanation:

Using trigonometric formulas we know:

[tex]sin(x) = \frac{opposite}{hypotenuse}[/tex]

Here, our opposite is the side opposite to the angle A, which in this case is the line BC which is equal to 8.

The hypotenuse is the diagonal line, which in this case is AB, and this is equal to 17.

Therefore,

[tex]sinA = \frac{8}{17} =0.4706[/tex]

Our final answer is 0.4706.

Answer:

8/17= 0.4706 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

Your classmate says that there is not enough information to determine whether the two triangles below are congruent. Is your classmate correct?

yes it is

The two triangles are congruent triangles by RHS theorem of congruent triangles

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔMLJ

Let the second triangle be represented as ΔLJK

Now , the measure of ∠MLJ = 90°

The measure of ∠LJK = 90°

The measure of side MJ = measure of side LK

So , the two sides of the triangles are similar and they have a common hypotenuse

Therefore , the triangles are congruent by right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Hence , the triangles are congruent

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Answer:

Volume = (1/2)[tex]x^{3}[/tex]           [(1/2)x^3]

Step-by-step explanation:

The volume of a right rectangular prism is given by:

Volume = (length)*(width)*(height)

Volume = (x)*(x)*((1/2)x)

Volume = (1/2)[tex]x^{3}[/tex]

The greatest common factor for the numerical part will be 2.

The greatest common factor, as the name implies, is the greatest among all common factors among the quantities given.

We can factorize the quantities in the smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could.

Those will together compose GCF(The greatest common factor).

Given;

[tex]6x^2-8+22[/tex]

Since the expression contains both numbers and a variable part.

For numerical parts 6, -8, 22

The factors are

6 = -6, -3. -2, -1,1, 2, 3 , 6

8 = -8, -4, -2, -1,1, 2, 4, 8

22 = -22, -11, -2, -1,1, 2, 11, 22

The greatest common factor for the numerical part will be 2.

The number part does not contain any common variable factor.

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Answer:

Side b is approximately 4.00064cm or since the question asked for the answer to be up to one decimal point, your answer should be 4 cm

Step-by-step explanation:

First of all, this triangle isn't a right triangle. This can be proven if we assume that the triangle is a right triangle. If it is a right triangle, since, one of its angle is 30 degrees, we can find the last unknown angle to = 60 degrees. Therefore, using the side ratios of a 30-60-90 triangle, and since side b is the smallest side (because it has the smallest angle facing it), its length is one half the length of the hypotenuse, therefore making its length 4. However, the 30-60-90 ration also states that, in this case, side b * sqrt(3) should be equal to the side tha measure 7cm, which is clearly not true. Therefore, proving that this triangle isn't a rigt tirangle.

So now, let's get to solving the question. Since we found out that this isn't a right triangle, we have to use the law of cosines which states

a^2 = b^2 + c^2 - 2bc*cos(A) where A is the angle facing side a

If we do this, it comes to the solution that a is approximately 4.00064cm.

Therefore, side b measures to 4.00064cm.

Answer:

Kathy and Lilly

Step-by-step explanation:

Because they both are nearest to the leader distance of 5 meters

Answer:

Y + 15 = 30

Y = 30 - 15

Y = 15

15 is not equal to 20

False

Answer:

x=9

Step-by-step explanation:

Answer:

x = [tex]\frac{1}{2}[/tex] , x = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

(2x - 1)(3x + 4) = 0

equate each factor to zero and solve for x

2x - 1 = 0 ( add 1 to both sides )

2x = 1 ( divide both sides by 2 )

x = [tex]\frac{1}{2}[/tex]

and

3x + 4 = 0 ( subtract 4 from both sides )

3x = - 4 ( divide both sides by 3 )

x = - [tex]\frac{4}{3}[/tex]

So

And

Coplanar points are those that are all in the same PLANE. The other point that lies on line AC is B.

Collinear Points: Points are collinear if they are all in the same straight line.

Coplanar points: Coplanar points are those that are all in the same PLANE.

A.) Another way to label KF is F K.

B.) The other point that lies on line AC is B.

C.) Yes, Any two points can form a line, thus, A and D are colinear.

D.) Coplanar points are those points that lie in the same place. Although D and K lie on the same plane,j; the point E does not lie on the same plane. Thus, points E, D, and K are not coplanar points.

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Answer:

b. 66

c.56

a 0

Step-by-step explanation:

????????????????????????

Answer:

C

Step-by-step explanation:

you need to re arrange like terms

Answer:

No

Step-by-step explanation:

First solve both equations:

1) 9x = 5x + 4

Simplifying

9x = 5x + 4

Reorder the terms:

9x = 4 + 5x

Solving

9x = 4 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.

9x + -5x = 4 + 5x + -5x

Combine like terms: 9x + -5x = 4x

4x = 4 + 5x + -5x

Combine like terms: 5x + -5x = 0

4x = 4 + 0

4x = 4

Divide each side by '4'.

x = 1

Simplifying

x = 1

2) 14x = 4

14x = 4 (divide both sides by 14 to get x)

14x/14 = 4/14

x = 0.285714285714

As you can see, the value of x in the second equations is less than one, therefore making these algebraic equations not equivalent.

Answer:

No

Step-by-step explanation:

9x=5x+4 and 14x=4

9x= 5x+4

Subtract 5x from each side

9x-5x = 5x+4-5x

4x= 4

The equations are not the same

Answer:

y = 7+2x

Step-by-step explanation:

4x = 5 - 2y __(1)

y - 2x = 7 __(2)

From eq (2) ,

y = 7 + 2x

Hence, we can substitute (7+2x) in place of y in the first equation.

Answer:

Step-by-step explanation:

According to the first statement, "Three years ago, Dedrick's age was a third of Francisca's age":

D - 3 = (1/3) * (F - 3)

According to the second statement, "In 13 years, Francisca's age will be twice Dedrick's age":

F + 13 = 2 * (D + 13)

Now, we have a system of two equations. We can solve these equations to find their current ages.

Step 1: Solve the first equation for D in terms of F:

D - 3 = (1/3) * (F - 3)

3D - 9 = F - 3

3D = F + 6

D = (F + 6) / 3

Step 2: Substitute the expression for D into the second equation:

F + 13 = 2 * ((F + 6) / 3 + 13)

Step 3: Solve for F:

F + 13 = 2 * ((F + 6) / 3 + 13)

F + 13 = 2 * (F + 6 + 39)

F + 13 = 2 * (F + 45)

F + 13 = 2F + 90

F - 2F = 90 - 13

-F = 77

F = -77

Step 4: Find D using the expression we found earlier:

D = (F + 6) / 3

D = (-77 + 6) / 3

D = -71 / 3

Now, we have found their ages, but we encounter a problem. Both Francisca and Dedrick's ages are coming out as negative, which is not meaningful in this context. It suggests that there might be an error in the initial information provided or in the equations derived from it.

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Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:

Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC

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The expression -4 (-11 + 4n) – 3(- 2n + 9) is equivalent to the expression 17 — 10n.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ -4 (-11 + 4n) – 3(- 2n + 9)

On simplifying, we have

⇒ 44 – 16n + 6n – 27

⇒ 17 — 10n

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The volume of the prism as given with dimensions is; 840cm³.

The prism given in the task content can be further subdivided to be represented by two rectangular prisms as follows;

First prism = 10cm by 6cm by 8cm.

Second prism = 5cm by 12cm by 6cm

Hence, the volume of the prism is; (10×6×8) + (5×12×6) = 840cm³.

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Answer: 43.5

Step-by-step explanation:

[tex]A=\frac{1}{2}(8)(12)(\sin 65^{\circ}) \approx \boxed{43.5}[/tex]

Answer:

Check all of them

Step-by-step explanation:

If you are on Edg, just check all of them.

Answer:

Irrational

Step-by-step explanation:

Answer:

  b, c

Step-by-step explanation:

A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.

__

A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.

The value of f(0) is 2, so the y-intercept is 2.

The given function is defined for all values of x, so its domain is all real numbers.

The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.

The function has a stationary point at x=0, so is not decreasing over its entire domain.

_____

Additional comment

The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.

Answer:

A.

Step-by-step explanation:

Only table A shows a direct proportion between time and distance, so the answer is A.