Mari is adding (-7) and (-2). She adds their absolute values and says the answer is 9. What did Mari forget?

Answer:  22.8888888889 but rounded 22.9

Step-by-step explanation: This is so because when you turn 23 to ninths you get 207/9 - 1/9 then put into decimal form, 22.8888888889 or 2.9

For the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.

We are given the logarithm expression as:

1 / 4 log₃ 2 + 1 / 4 log₃ x

Now, take 1 / 4 common from the expression:

1 / 4 ( log₃ 2 + log₃ x)

Now, we know that log₃ a + log₃ b = log₃ ( a b)

So, we get that:

1 / 4 ( log₃ ( 2 x) )

1 / 4 log₃ 2 x

Therefore, for the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.

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Answer:

Slope: 2/1

equation: y=2/1x+2

Answer:

11a^2 + 122a + 11

Step-by-step explanation:

First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.

Factor the expression 25-40 x+16 x² is [tex](4x-5)^2[/tex]

On rearranging the equation , we get

   [tex]16x^2-40x+25=0[/tex]        ...(1)

To split the middle term of the quadratic equation, we need to look at the middle term of the quadratic equation under consideration.

Midterm is 40 x  , to split the middle term, use the sum-and-product form which is

" The sum-product form is the product of intermediate terms after splitting and must  equal a × c and the sum must equal b "

    [tex]f(x)=16x^2-40x+25[/tex]

here a = 16 , b = -40 and c = 25

We need to divide into 40x  in two parts

40x = 20x + 20x

The product of the terms is [tex]16\times25=400[/tex]

Now we can rewrite 40x as 20x + 20x

Putting in equation (1) , we get

      [tex]16x^2-(20+20)x+25=0\\\\(16x^2-20x)-(20x-25)=0\\\\4x(4x-5)-5(4x-5)=0\\\\(4x-5)(4x-5)=0[/tex]

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Every conditional has two parts they are hypothesis and conclusion.

The hypothesis is the first part of a conditional statement 'if' and conclusion is the last part of a conditional statement 'then'

According to the given statement every conditional has two parts a hypothesis and a conclusion.

Conditional starts with if and ends with then.It is used to express possible situations.

For example-: if the two angles are complementary then their sum is 90°.

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Answer:

Step-by-step explanation:

The area of the rectangle having three identical circles inside is calculated as: (16√3 + 32) mm².

Area of rectangle = (length)(width)

The image of the three identical circles in the rectangle has been labelled as shown in the diagram attached below.

We need to find the measure of the length and width of the rectangle.

Radius = AB = BD = DF = FG = CD = HI = 2 mm

Length of the rectangle = AB + BD + DF + FG = 2 + 2 + 2 + 2

Length of the rectangle = 8 mm

Width of the rectangle = CD + DH + HI

CD = 2 mm

HI = 2 mm

Use the Pythagorean theorem to find the measure of DH

DH = √(FH² - DF²)

FH = 2 + 2 = 4 mm

DF = 2 mm

Substitute

DH = √(4² - 2²)

DH = √(16 - 4)

DH = √12 = 2√3 mm

Width of the rectangle = CD + DH + HI = 2 + 2√3 + 2

Width of the rectangle = 2√3 + 4

Area = (2√3 + 4)(8)

Area = (16√3 + 32) mm²

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Jack spent first a total of AED 1282.04 and when he bought the box it cost AED 205.96

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the total cost Jack spend before bought the box:

Total cost = (No. drill bits*cost of drill bits) +  (No. washers  *cost of washers ) +  (No. hammers *cost of hammers)

Total cost = (8 drill bits * AED 11.22/ drill bits) + (10 washers * AED 10.11 / washers) + (2 hammers * AED 545.59 / hammers)

Total cost = AED 89.76 + AED 101.1 + AED 1091.18

Total cost = AED 1282.04

Calculating the box cost:

Balance = Paid - (Total cost + box cost)

Balance = Paid - Total cost - box cost

box cost = Paid - Total cost - Balance

box cost = AED 1500 - AED 1282.04 - AED 12

box cost = AED 205.96

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The time it would take Kim running the same distance is 15 minutes.

Ratio is used to show the relationship between two or more numbers. It shows the frequency that one value is contained within other value(s). The sign that is used to represent ratio is :.

Speed = distance / time

The first step is to determine the time spent by Richard running:

(4 x 1/8) / 5 = 1/10 or 10 minutes

The second step is to determine the time spent by Kim running:

(2 x 1/10) / 3 = 1/15 =  15 minutes

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In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

In the right triangle XYZ, angle X and angle Y are complementary angles.

The complementary angle is either of two angles whose sum is 90 degrees

Therefore,

Angle X + Angle Z = 90 degrees

In trigonometry,

sinθ = Opposite side / Hypotenuse

sin z= 36/85

z= [tex]sin^{-1}(\frac{36}{85} )[/tex]

z= 25.06

Then the value of cos z is

cos 25.06 = 77/85

Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

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1) m∠4 + m∠7 = 180° (given)

2) ∠4 is congruent to ∠6 (vertical angles)

3) m∠4 = m∠6 (definition of congruent angles)

4) m∠6 + m∠7 = 180° (substitution)

5) c is parallel to d (converse of same side interior angles theorem)

Answer:

16.3p + (-10)

Step-by-step explanation:

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)

In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.

Now we proceed to check the expression for each case:

(x, y) = (1, - 5)

- 5 + 4 = (3 / 5) · (1 - 2)

- 1 = (3 / 5) · (- 1)

- 1 = - 3 / 5     (FALSE)

(x, y) = (- 8, - 12)

- 12 + 4 = (3 / 5) · (- 8 - 2)

- 8 = (3 / 5) · (- 10)

- 8 = - 30 / 5

- 8 = - 6    (FALSE)

(x, y) = (- 3, - 8)

- 8 + 4 = (3 / 5) · (- 3 - 2)

- 4 = (3 / 5) · (- 5)

- 4 = - 3    (FALSE)

(x, y) = (12, 10)

10 + 4 = (3 / 5) · (12 - 2)

14 = (3 / 5) · 10

14 = 30 / 5

14 = 6     (FALSE)

(x, y) = (7, - 1)

- 1 + 4 = (3 / 5) · (7 - 2)

3 = (3 / 5) · (5)

3 = 3    (TRUE)

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).

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After solving the equation, x = -1 is the value of x in [tex]3^{(-2x)+2} = 81[/tex]

⇒ [tex]3^{(-2x)+2} = 81[/tex]

⇒ [tex]3^{(-2x)+2} = 3^4[/tex]

⇒ -2x + 2 = 4

⇒ -2x = 2

⇒ x = 2/(-2)

⇒ x = -1

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Using the properties of logarithm the value of the expression is   [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]

According to the question the expression that we have been given is

         =  [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75}[/tex]

Now solving it step by step using the properties of logarithm which are

      [tex]log a^{m} = m*loga[/tex] ,  [tex]log \frac{x}{y} = logx - logy[/tex]  and [tex]log_{a} a = 1[/tex]

As √75 is also equal to [tex](75)^{1/2}[/tex]. Thus equating in the equation we get

Therefore ,  

           [tex]= \frac{1}{2}log_{5} 15 - log_{5} 75^{\frac{1}{2} } \\= \frac{1}{2}log_{5} 15 - \frac{1}{2} log_{5}{75} \\[/tex]  

As we can see that 1/2 is common in both the terms we will take out 1/2 common from both terms, by which we get

           [tex]= \frac{1}{2} [log_{5} 15 - log_{5}{75} ] \\= \frac{1}{2} [log_{5} \frac{15}{75} ] \\\= \frac{1}{2} [log_{5} \frac{1}{5} ] \\= \frac{1}{2} [log_{5} 1 - log_{5}{5} ]\\= \frac{1}{2} [0 - 1]\\= -\frac{1}{2}[/tex]

Hence using the properties of logarithm the value of the expression is  [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]

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Answer:

y=-3x-17

Step-by-step explanation:

y=mx+b   (slope-intercept form)           b=y-intercept= (0,?)  m=slope

y=-3x+b  substitute values

y+3x=b isolate b to find b

1+3(-6)=b substitute given ordered pair

-17=b

y=-3x-17

Answer:    14 min

Step-by-step explanation:

After 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90kpx each.

Let after t minutes the scene will have the same amounts rendered.

The linear equation in one variable can be framed as:

540 + 90t = 960 + 60t

After solving the above linear equation in one variable:

90t - 60t = 960 - 540

30t = 420

t = 14 minutes

Thus, after 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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The real square root of the number 0.49 is 0.7

0.49 can also be presented as, 49* [tex]10^{-4}[/tex]

The square root of   49* [tex]10^{-2}[/tex]

= [tex]\sqrt{49}[/tex] * [tex]\sqrt{10} ^{-2}[/tex]

= 7 * [tex]10^{-2}[/tex]

=0.7

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The value of constant  variation is 18.

A key integer with a stable value determined by a clear specification is referred to as a mathematical constant.

connection in mathematics between two variables that may be described by an equation in which the sum of their products equals a constant

Inverse variation is y = k. 1/x

given y = 3

x = 6

So, 3 = k. 1/6

So, the value of k = 18.

We can conclude that the value of constant variation is 18.

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39.16 approx. is the value of x in  [tex]e^{\frac{x}{4} -8}[/tex] = 6 solved by using natural logarithm

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to find x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 using natural logarithm

⇒  [tex]e^{\frac{x}{4} -8}[/tex] = 6

⇒ [tex]\frac{x}{4} - 8[/tex] = ㏑6

⇒  [tex]\frac{x}{4}[/tex] = ㏑6 + 8

⇒ x = ln(1296) + 32

      = 39.16 approx.

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Use natural logarithms to solve each equation.

[tex]e^{\frac{x}{4} -8}[/tex] = 6

-4 is an extraneous solution.

The equation is

[tex](x - 2)^{1/2}[/tex] - [tex](28-2x^{1/4}[/tex] = 0

To know whether the given equation has an extraneous solution or not we need to find the value of x.

[tex](x-2^{1/2}[/tex]= [tex](28-2x)^{1/4}[/tex]

Multiply both sides with the power of 4, and we get

[tex](x- 2)^{2}[/tex] = 28-2x

[tex]x^{2}[/tex] - 4x + 4 = 28-2x

[tex]x^{2}[/tex] - 2x - 24= 0

[tex]x^{2}[/tex]- 6x + 4x -24=0

x(x-6) +4(x-6)=0

(x-6)(x+4) = 0

x = 6 , -4

Now put both the value of x in the equation

x=6

[tex](6-2)^{1/2}[/tex]-[tex](28- 2* 6)^{1/4}[/tex]= 0

[tex]4^{1/2}[/tex]- [tex]16^{1/4}[/tex]= 0

2-2=0

0=0

Now

x = -4

[tex](-4-2)^{1/2}[/tex]-[tex](28-2*-4)^{1/4}[/tex]=0

[tex](-6)^{1/2}[/tex] -[tex]36^{1/4}[/tex]=0

[tex](-6)^{2}[/tex] - [tex]6^{1/2}[/tex]=0

Which is not possible and a negative integer is not present in the square root.

Therefore we get the extraneous solution of the equation which is x= -4, and x = 6 is the solution of the equation.

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The given 4th order polynomial equation only has real solutions,  x = √7  and x = –√7

The given equation is x⁴-14 x²+49 = 0.

This is a 4th degree polynomial equation.

Let p = x².

Then we can write x⁴-14 x²+49 = 0 as:

p²- 14p +49 = 0

This is a quadratic equation.

There are three ways to find the solutions of a quadratic equation:

Notice that p²- 14p +49 = 0 can be written as a perfect square:

(p - 7)² = 0

Hence, it has only single real solution:

p - 7 = 0

p = 7

Substitute p = 7 into p = x², we get:

x² = 7

x = ± √7

The solutions are, therefore,  x = √7  and x = –√7

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The domain of given points are :

IR x ≠ -1 , -2

Points of discontinuity - x = -2 ( non removable / asymptote )

                                         x = -1 ( removable / hole)

x - intercept = -1 , y -  intercept = 1/2

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).

y=x+1/x²+3 x+2

= x+1/x²+2x+x+2

=  x+1/(x+2)(x+1)

The domain of given points are :

IR x ≠ -1,-2

Points of discontinuity - x = -2 ( non removable / asymptote)

                                       x = -1 ( removable / hole)

x-intercept :

0 = x + 1

x = -1

y - intercept :

0+1 / (0+1)(0+2) = 1/2

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The value of a calculated by Noemi is not correct as the correct value is

     a = -1/45

We know that the general form of the quadratic equation is given as

                        y = ax² + bx + c

where, a and b are coefficients of the variable x and c is the constant term.

Now according to the question the path of the golf ball is parabola whose coordinates will be

       (0,0) = origin where it starts

       (60,80) = vertex or the maximum point

       (120,0) = end point

Now putting the value of (x,y) in the above formula to find the value of a,b and c

when (x,y) = (0,0)

       0 = a0² + b0 +c

       c = 0

when (x,y) = (60,80)

      80 = a60² + b60 +c

       80 = 3600a + 60b + 0        (1)

when (x,y) = (120,0)

      0 = a120² + b120 +c

      0 = 14400a + 120b + 0      

       120b = -14400a

          b = -120a

Putting the value of a in equation (1) we get

    80 = 3600a + 60(-120a)

    80 = 3600a - 7200a

    80 = -3600a

     a = - 1/45

 ⇒ b = 8/3

Hence the equation will be         y = -1/45x² + 8/3x

and the value of a calculated by Noemi is not correct as the correct value is a = -1/45

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With an equilateral triangle, only two circles are formed.

What kind of polygon is carved into the circle?

Therefore, with an equilateral triangle, only two circles are formed.

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