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Yolanda is 4 years younger than 3 times her daughter's age. The sum of their ages is 88 What is Yolanda's daughter's age?

The graph of the inequality expressions is added as an attachment

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expressions are given as

y ≥ 2

x + y ≤ 4

y ≤ 2x + 2

Next, we interpret each inequality expression

First expression: y ≥ 2

The inequality symbol in the above inequality expression is ≥

This implies that the inequality expression is a greater than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the upper part is shaded

Second expression: x + y ≤ 4

The inequality symbol in the above inequality expression is ≤

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Third expression: y ≤ 2x + 2

The inequality symbol in the above inequality expression is ≤

This implies that the inequality expression is a less than or equal to and the inequality symbol implies that the bottom part is shaded

See attachment for the graph of the inequality expressions

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-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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Answer:

170 minutes

Step-by-step explanation:

So if there was two 45 min work outs in a week and she left those 10 mins early that was two 35 min work outs and then there was 4, 30min work outs and she left those 5 mins early so 4, 25min workouts so its 35+35+25+25+25+25.

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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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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Answer:

3g=x-2

Step-by-step explanation:

3g+2=x then, move 2 to the other side(nb*change to negative) then it will be 3g=x-2 finally divide both sides by 3 then it will be g=x-2

3

Answer:

10 2/5 inches

Step-by-step explanation:

Since P=2L+2W, we can flip it to find the length. For example, we could minus 2L from both sides to get P-2L=2W.

We already know that W is 4.5, and P is 29.4.

Plugging that in, we get 29.4-2L=9. Again we can flip the perimeter, and -29.4 on both sides. This would make -2L=-20.4.

For our last flip, we divide the -2 from both sides to finally get L=10.2 (or 10 1/5 if you want) inches.

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:

270

Step-by-step explanation:

(∛9)³ × (√30)²

9 × 30 = 270

I hope this helps!

Answer:

Answer:

270

Step-by-step explanation:

(∛9)³ × (√30)²

9 × 30 = 270

Step-by-step explanation:

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:

x = 0

Step-by-step explanation:

x + 2 - 0.5x = 1 + 0.5x +1

    2 - 0.5x = 2 + 0.5x

-0.5 - 0.5x = 2 - 2

          -1x = 0

      -1x/-1 = 0/-1

            x = 0

Answer:

Step-by-step explanation:

Solve X + 2 - 0.5 x = 1 + 0.5 x + 1 : The answer is: X = 2X

The expression given tests on indices. The expression can be written in index form as a^m. Thus, b√a =  a^(1/b) From the power rule of indices, a^m x a^n = a^(m+n).

√11(4√11)

11^1/2 ( 11^1/4)

11 ^(1/2+1/4)

11^3/4

4√11^3

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Answer:

It can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.

Step-by-step explanation:

It is given that we need to rectify whether 0.6 divided by 30 = 0.02 or not.

Firstly, let us understand how does simplification work;

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Now, let us understand what exactly is arithmetic;

According to the assertions, it deals with a number of operations in mathematics. Addition, subtraction, multiplication, and division are the four main arithmetic operators.

Now, let us equate the given condition that is;

=> 0.6 can also be expressed as 6/10

Now, let us divide the above numbers with each other as given in the question;

=> (6/10) ÷ 30

=> 6/300

On dividing both the numbers with each other we get;

=> 0.02 which can be expressed as 2/100

Therefore, it can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.

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Answer:

Step-by-step explanation:

The equation of the required line parallel to the given line is y = -x - 10.

Slope can be defined as the rate of change.

According to the given question we have to write an equation of a line parallel to the line y = - x - 1 that goes through the point (-2,-8).

We know that lines are parallel because of the same slope they have.

So, the required line also have a slope(m) = -1.

∴ The equation of the required line in slope intercept form can be written as y = mx + b.

Putting the value of given points (-2, -8) in (x,y) t evaluate y intercept b.

So, - 8 = (-1)(-2) + b.

- 8 = 2 + b.

b = -10.

∴The equation of the required line in slope intercept form is  y = -x -10.

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Answer:

D.

Step-by-step explanation:

x=2 1/3

That is the answer

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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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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12

Step-by-step explanation:

n + (2/3)n = 2n - 4

(5/3)n = 2n - 4

(5/3)n - 2n = -4

(-1/3)n = -4

n = 12

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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Answer: w = -32

Step-by-step explanation:

Start isolating the variable by getting rid of 3/4. You can do this by multiplying by its reciprocal.

That leaves us with 3/4 times -27

The product is -32.

Hope this helps!

Answer:

2 2/4 because i just know the answer

The value of logarithm as the quotient of two common logarithms is [tex]\frac{Log 140}{Log5}[/tex]. Because [tex]Log_{a}(b)=Log\frac{b}{a}[/tex]

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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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:

$37.96

Step-by-step explanation:

$9.49 x 4 = $37.96

A) The roots of the graph f(x) are;  x = -2 and x = -1

B) The value of the function at f(0) is; 2

a) We want to find f(0) of the graph.

Now, f(0) simply refers to the y-values when x = 0.

This is the point at which the graph crosses the y-axis

From the graph we can see that the value here is 2. Thus;

f(0) = 2

b) To find the roots of f(x) , we simply find the points at which the plot crosses the x-axis.

From the graph, the roots are at x = -2 and x = -1

Thus, the roots of the equation are x = -2 and x = -1

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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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