All of the members of the harvey family are very
tall. their heights are 84 inches, 84 inches, 77
inches, 63 inches, 70 inches, 70 inches and 'x'
inches. if the mean height of the family members
is 75 inches, about how tall is person 'x' ?
77 inches
84 inches
70 inches
63 inches

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}~\hfill \textit{we also know that} \begin{cases} x= 35\\ y = 7 \end{cases} \\\\\\ 7=k(35)\implies \cfrac{7}{35}=k\implies \cfrac{1}{5}=k~\hfill \boxed{y=\cfrac{1}{5}x}[/tex]

Answer: 4/15

Step-by-step explanation:
1. Change 1/3 to 4/3 by multiplying the numerator by 3 and adding one.

2. Multiple 4/3 by 1/5 to get 4/15.

Answer: The median is 6

Step-by-step explanation:

Answer:

C) 312 cm^2

Step-by-step explanation:

To find the total area of the composite figure, you must sum the individual components of the figure.

First, we find the area of the rectange, which is A = l x w = 16 x 12 = 192

Second, we find the area of the first triangle which is also equal to the area of the second triangle, so instead of finding the base times height and dividing by 2, we will simply find the area of base times height and it will work for both trianges.

A = b x h x 1/2 x 2 = 10 x 12 = 120

120 + 192 = 312 cm^2

Answer: (3,3)

Step-by-step explanation:

The expression (-0.3)⁴ is an exponential expression and the value of the expression is 0.0081

The expression is given as:

(-0.3)⁴

Expand the expression

(-0.3)⁴ = (-0.3) * (-0.3) * (-0.3) * (-0.3)

Evaluate the product

(-0.3)⁴ = 0.0081

Hence, the value of the expression is 0.0081

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Answer:

5x + 3x = 28x
8x = 28x
x must be 0

Answer:

No.

Step-by-step explanation:

To find the y value, one must replace x value, meaning that it's a multi step problem and it's not direct because y=exact value is not given

Answer:

5.69

Step-by-step explanation:

22.76/4 = 5.69

Answer:

[tex]y = x^2 - 8x + 38[/tex]

Step-by-step explanation:

Hello!

The standard form of a quadratic is [tex]ax^2 + bx + c[/tex].

To convert the vertex form to standard form, we have to expand the parenthesis and add the constant.

Convert:

The standard form is [tex]y = x^2 - 8x + 38[/tex]

The probability that a student chosen at random will play an instrument other than drums is 31/36.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Total number of elements of sample space is 36.

Based on these results, express the probability that a student chosen at random will play an instrument other than drums as;

31/36

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Answer:

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Answer:

b. more money

Step-by-step explanation:

Randy's original position lets him make:

50*500 = $25,000

The new position will let him make:

$27,500

Therefore,

original position < new position = $25,000 < $27,500

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.

An equation is an expression that shows the relationship  between two or more numbers and variables.

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.

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Answer:

A. -180

Step-by-step explanation:

Edge2022

Answer:B

count 2 and ~1/4 back and you get b

Answer:

Part A: total pizza cost = 2.50s + 2.25t + 18

Part B: 30 dollars

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks"!

Answer:

Part A: 18 + 2.25t + 2.50s

Part B: $30

Step-by-step explanation:

Let t= each additional topping

Let s=each side

First we add the cost of one pizza ($18)

Then we add each additional topping (t) multiplied by its cost (2.25 dollars)

Finally we add each side (s) multplied (2.50 dollars)

Part B:

Plug in 2 for t and 3 for s into the expression from earlier and simplify:

Expression: 18 + 2.25(2) + 2.50(3)

=18+ 4.50 + 7.50

=30

And there you have it- the total cost is $30.

Hope this helps and good luck in your studies :)

Answer:

Step-by-step explanation:

x=(1-sqrt(13))/2=-1.303

x=(1+sqrt(13))/2=2.303

steps

 (2x2 -  2x) -  6  = 0

step 2 pull out like terms

2x2 - 2x - 6  =   2 • (x2 - x - 3)

step 2 continued

3.2     Factoring  x2 - x - 3

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2

     -1    +    3    =    2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

step 3

 2 • (x2 - x - 3)  = 0

Step 4

4.2      Find the Vertex of   y = x2-x-3

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.5000  

Plugging into the parabola formula   0.5000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 0.50 * 0.50 - 1.0 * 0.50 - 3.0

or   y = -3.250

step 4

4.4     Solving    x2-x-3 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -1

                     C   =   -3

Accordingly,  B2  -  4AC   =

                    1 - (-12) =

                    13

Applying the quadratic formula :

              1 ± √ 13

  x  =    —————

                   2

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          x  =  ( 1 ±  3.606 ) / 2

Two real solutions:

x =(1+√13)/2= 2.303

or:

x =(1-√13)/2=-1.303

concluision

x =(1-√13)/2=-1.303

x =(1+√13)/2= 2.303

Answer:

cos(θ) = 3/4

Step-by-step explanation:

Since cos=adj/hyp, the Hypotenous is 24, and the adjacent is 18. We write cos(θ)=18/24, which can be simplified to cos(θ)=3/4.

Answer:

(1) 6

Step-by-step explanation:

Let's start by solving the inequality.

7x +2 > 58

Minus 2 on both sides:

7x > 58 -2

7x > 56

Divide both sides by 7:

x > 56 ÷7

x > 8

This means that the value of x has to be greater than 8. 6 is smaller than 8, and is therefore not in the solution set. Thus, option 1 is the correct answer.

              [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

            Given 7x+2>58, which number is not in the solution set?

      [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer \& how to solve:-}}}\rule{50}{1}[/tex]

        First, subtract 2 on both sides:-

       [tex]\sf{7x > 56}[/tex]

       Now divide by 7 on both sides:-

        [tex]\sf{x > 8}[/tex]

        Henceforth, We conclude that

          [tex]\large\textsf{Numbers greater than 8 make this inequality true}[/tex].

Edit:- Option A (6) is the correct answer, since it's not greater than 8, so it doesn't satisfy the inequality.

[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

Answer:

4ln 2+ln 5

Step-by-step explanation:

Using the Fundamental Counting Theorem, it is found that a simulation with 8 equally likely outcomes would be generated from:

D) A coin and a spinner.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

The total number of equally likely outcomes is given by:

N = 2 x 4 = 8.

Hence option D is correct.

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Answer: The number of miles increases as time increases.

The number of hours causes a change in the number of miles ridden.

The variable h is the independent variable.

The variable m is the dependent variable.

Step-by-step explanation:

Answer:

Step-by-step explanation:

    diameter = 12 cm

                  r =  12 ÷ 2 = 6 cm

                 h = 6 cm

      [tex]\sf \boxed{\text{\bf Volume of cone = $\dfrac{1}{3} \pi r^2h$ }}[/tex]

                                    [tex]\sf = \dfrac{1}{3}*3.14*6*6*6\\\\ = 226.08 \ cm^3[/tex]

To find the surface area, we need to find the slant 'l'

       [tex]\sf l = \sqrt{h^2+r^2}\\\\ =\sqrt{6^2+6^2}\\\\ = \sqrt{36+36}\\\\ =\sqrt{72}\\\\= 8.49 \ cm[/tex]

       [tex]\sf \boxed{\text{\bf Total surface area of cone = $\pi r(r+l)$}}[/tex]

                                                         = 3.14 * 6 * (6 + 8.49)

                                                        = 3.14 * 6 * 14.49

                                                        = 273 cm²

Answer:

the LCM is 6x^2(x-1)^2(x+2)

The logical conclusion to the conditional statements in the question is; hamburger => hands.

Logic deals with the process of arriving at a conclusion based of certain premises. If the premises are true, then the conclusion must be true and vice versa.

Thus, in this case, the logical conclusion to the conditional statements in the question is; hamburger => hands.

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Answer:

The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner

The triangle is congruent with the ASA property.The two triangles are having same sides AB = XY, BC = YZ and CA = ZX and the same angles ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z.

If two triangles are congruent, this means they are the same shape and the same size.

By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

The triangle is congruent by the ASA theorem. Here in the question, we can see in the figure that two angles ∠A = ∠X and ∠B = ∠Y so the third angle must be equal so ∠C = ∠Z.

Since side XY = AB and the three angles are equal so the other two sides will also be equal for the two triangles.

Therefore triangle is congruent with the ASA property.The two triangles are having same sides AB = XY, BC = YZ and CA = ZX and the same angles ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z.

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The given information is,

→ a = -8

→ b = -7

→ c = 6

Let's verify the problem,

→ (a+b) + c = a+ (b+c)

→ (-8 - 7) + 6 = -8 + (-7 + 6)

→ -15 + 6 = -8 - 1

→ -9 = -9

→ [ LHS = RHS ]

Hence, it is equal and verified.