how much is 2 plus 3

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 2^{\frac{3}{4}} \right)^2\implies 2^{\frac{3}{4}\cdot 2}\implies 2^{\frac{3}{2}}\implies \sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2}\implies 2\sqrt{2}[/tex]

Answer:

Isolate the variables in all cases. Note the equal sign, what you do to one side, you do to the other.

a) 3x = 18

Isolate the variable, x. Divide 3 from both sides:

(3x)/3 = (18)/3

x = 18/3

x = 6

b) 2x = 9

Isolate the variable, x. Divide 2 from both sides:

(2x)/2 = (9)/2

x = 9/2

x = 4.5

c) (x/5) = 7

Isolate the variable, x. Multiply 5 to both sides:

(x/5)(5) = (7)(5)

x = 7 * 5

x = 35

d) x/2 = 6.5

Isolate the variable, x. Multiply 2 to both sides:

(x/2)(2) = (6.5)(2)

x = 6.5 * 2

x = 13

~

a) 3x = 18

x = 6

____________

b) 2x = 9

x = 4.5

____________

c) (x/5) = 7

x = 35

____________

d) x/2 = 6.5

x = 13

____________

Have a great day!

Answer:

[tex]f^{-1}[/tex] (x ) = [tex]\frac{x+6}{5}[/tex]

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject, that is

y = 5x - 6 ( add 6 to both sides )

y + 6 = 5x ( divide both sides by 5 )

x = [tex]\frac{y+6}{5}[/tex]

Change y back into terms of x

[tex]f^{-1}[/tex] (x ) = [tex]\frac{x+6}{5}[/tex]

Answer:

Around 6 - 7 months.

Step-by-step explanation:

Most months have varied number of days. If they were 30 days in each month, there would be a little less than 7 months that it would take to complete the pills.

[tex]\bf \begin{array}{ccll} x&y\\ \cline{1-2}\\ 2&\stackrel{2\cdot 7}{14}\\\\ 4&\stackrel{4\cdot 7}{28}\\\\ x&x\cdot 7 \end{array}~\hspace{7em}y=7x[/tex]

Answer:

y = 7x

Step-by-step explanation:

A direct variation is of the form

y = kx where k is the constant of variation

We have the point (2,14)

Substituting this in

14 = k*2

Divide each side by 2

14/2 =2k/2

7 =k

The direct variation equation is y = 7x

Answer:

Option C. 32°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the measure of arc AB

we know that

The semi-inscribed angle measures half that of the arc comprising

so

74°=(1/2)[arc AB]

arc AB=(2)(74°)=148°

step 2

Find the measure of arc BCDA

we know that

arc BCDA+arc AB=360°

substitute the given value

arc BCDA+148°=360°

arc BCDA=360°-148°=212°

step 3

find the measure of angle m

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

m=(1/2)[arc BCDA-arc AB]

substitute

m=(1/2)[212°-148°]=32°

Answer:

[tex]y + 2 = - (x - 4)[/tex]

Step-by-step explanation:

The graph passes through: (0,2) and (2,0)

The slope is

[tex] \frac{0 - 2}{2 - 0} = - 1[/tex]

The equation of the line in point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

The graph passes through (4,-2).

We substitute the slope and this point to get:

[tex]y - - 2 = - 1(x - 4)[/tex]

[tex]y + 2 = - (x - 4)[/tex]

The first option is correct

Answer:

1)all numbers less than -5 and greater than 5

Step-by-step explanation:

We are given

x<-5

and

x>5

So

Looking at both the inequalities one by one, The solution will consist of all the numbers that are less than -5 and greater than 5. The numbers between -5 and 5 will be excluded from the solution..

Hence,

1)all numbers less than -5 and greater than 5

is correct ..

The intersection of the sets {X|X<-5} and {x|x>5}, which represents numbers that fulfill both conditions, results in no real numbers, or the empty set.

The solution set of the given intersection of the two sets {X|X<-5} and {x|x>5} is defined as the set of numbers that fulfill both conditions: numbers less than -5 and numbers greater than 5.

However, there are no real numbers that can be both less than -5 and greater than 5 at the same time. Therefore, when these two sets intersect, the result is an empty set.

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[tex]\large\boxed{7.68\,\text{per hour}}[/tex]

In this question, we're trying to find how much you made per hour.

We can answer this question using the information given in the question.

Important information:

With the information above, we can solve the question.

We would simply divide 230.40 by 30 in order to find how much you made per hour.

Lets divide:

[tex]230.40\div30=7.68[/tex]

When you're done dividing, you should get 7.68

This means that you made 7.68 per hour.

For this case you must find the payment per hour, for this we must make a division. We divide the payment of the week between hours worked, then:

[tex]\frac {230.40} {30} = 7.68[/tex]

Thus, the hourly payment was $7.68

Asnwer:

$7.68

Answer:

29.97 square feet

Step-by-step explanation:

Given

The length of rectangle = 9 ft

The width of rectangle = 40 in

We have to bring the length and width in same unit. As the area is required in square feet so we will convert width in feet

The width will be divided by 12 to be onverted into feet

So,

Width = 40/12 = 3.33 feet

Now

Area = Length * width

= 9 * 3.33

= 29.97 square feet ..

Answer:

Area of rectangle = 30 square feet

Step-by-step explanation:

We are given that a rectangle is 9 feet long and 40 inches wide and we are to find its area in square feet.

For this, we will covert the width of the rectangle to feet and then find the area.

We know that:

[tex]\frac{1 foot}{x} =\frac{12 inches}{40}\\x=3.3 feet[/tex]

So width in feet is 3.3 feet.

Area of rectangle = [tex]9 \times 3.33[/tex] = 30 square feet

For this case we have that by definition, the area of a trapezoid is given by:[tex]A = \frac {(B + b) * h} {2}[/tex]

Where:

B: It is the major base

b: It is the minor base

h: It's the height

According to the data we have:

[tex]B = 10ft\\b = 5ft\\h = 4ft[/tex]

Substituting:

[tex]A = \frac {(10 + 5) * 4} {2}\\A = \frac {15 * 4} {2}\\A = \frac {60} {2}\\A = 30[/tex]

So, the area of the figure is [tex]30 \ ft ^ 2[/tex]

ANswer:

Option D

Answer:

D 30 ft^2

Step-by-step explanation:

This figure is a trapezoid

The area of a trapezoid is given by

A = 1/2 (b1+b2) *h  where b1 and b2 are the lengths of the top and bottom

A = 1/2( 10+5) * 4

   = 1/2 (15)*4

   = 1/2(60)

   = 30 ft^2

Answer:

$60 a month is the answer

Step-by-step explanation:

$200 down payment leaves you with $300's to pay still. Divide the $300's by 5 and that leaves you with $60 a month.

Answer:

22

Sarah's age is best represented by M-24 or as the question used x-24 where the mother's age is best represented by M where the question used x.

Step-by-step explanation:

We are given that Sarah (S) is 24 years younger than her mother (M).

So S=M-24.

We are given that Sarah (S) and her mom's age adds up to 68.

So S+M=68.

We are going to solve this system by substitution since one of the variables is solved for. I'm going to plug first equation into second like so:

(M-24)+M=68   I replaced S with M-24.

M+M-24=68      Put like terms together.

2M-24  =68       Combined the like terms.

2M      =  92      Added 24 on both sides.

 M      = 92/2    Divided 2 on both sides.

 M      = 46        Simplified the 92/2.

So her mother's age is 46.

We know that S=M-24 so S=46-24=22.

Sarah is 22 years old.

Answer:

Part one: r5 = 41.5 m , r6 = 42.75 m , r7 = 44 m , r8 = 45.25  

Part two: Max ran 399.34 m in lane one

Part three: The distance in lanes 3 and 7 are 415.04 m and 446.46 m

Part four: Max ran in the three laps 1260.84 m around the track

Step-by-step explanation:

* lets explain how to solve the problem

- The school track has eight lanes

- Each lane is 1.25 meters wide

- The arc at each end of the track is 180° , that means the arc at each

 end is a semi-circle

- The distance of the home straight for all lanes is 85 m

- The radius of the first lane is 36.5 m

∵ The width of each lane is 1.25

∴ The radius of the second lane = 36.5 + 1.25 = 37.75

- That means the radius of each lane increased by 1.25 then the

  previous lane

∴ The radius of each lane = the radius of the previous lane + 1.25

# Part one:

∵ The radius of the 4 lane is 40.25

∴ The radius of the 5th lane = 40.25 + 1.25 = 41.5 m

∴ The radius of the  6th lane = 41.5 + 1.25 = 42.75 m

∴ The radius of the  7th lane = 42.75 + 1.25 = 44 m

∴ The radius of the  8th lane = 44 + 1.25 = 45.25 m

* r5 = 41.5 m , r6 = 42.75 m , r7 = 44 m , r8 = 45.25  

- The length of each lane is the lengths of the 2 end arcs and  2

   home straight distance

∵ The arc is a semi-circle

∵ The length of the semi-circle is πr

∴ The length of the 2 arcs is 2πr

∵ The length of the home straight distance is 85 m

∴ The length of each lane = 2πr + 2 × 85

∴ The length of each lane = 2πr + 170

# Part two:

- Max ran around lane one

∵ The radius of lane one = 36.5 m

∵ The distance of each lane = 2πr + 170

∴ The distance of lane one = 2π(36.5) + 170 = 399.34 m

* Max ran 399.34 m in lane one

# Part three:

- We will chose lanes 3 and 7

∵ The distance of each lane = 2πr + 170

∵ The radius of lane 3 = 39

∵ The radius of lane 7 is 44

∴ The distance of lane 3 = 2π(39) + 170 = 415.04 m

∴ The distance of lane 7 = 2π(44) + 170 = 446.46 m

* The distance in lanes 3 and 7 are 415.04 m and 446.46 m

# Part four:

- To find the total distance that Max ran in the 3 laps ad the answers

  in part two and part three

∵ Max ran 399.34 m in lane one

∵ Max ran 415.04 m in lane three

∵ Max ran 446.46 m in lane seven

∴ The total distance of the 3 lanes = 399.34 + 415.04 + 446.46

∴ The total distance of the 3 lanes = 1260.84

* Max ran in the three laps 1260.84 m around the track

The magnitude of a vector is found by applying the Pythagorean theorem to the horizontal and vertical changes. The formula to calculate the magnitude is given by A = sqrt(x^2 + y^2) where x and y are the vector’s horizontal and vertical displacements respectively.

The magnitude of a vector is calculated by forming a right triangle using the horizontal (x) and vertical (y) changes as the triangle's legs. The magnitude of the vector is the hypotenuse of this right triangle. This relationship is captured by the Pythagorean Theorem which states that the square of the hypotenuse (i.e. the magnitude of vector A) is equal to the sum of the squares of the other two sides (the vector's components or changes).

So, the formula for finding the magnitude of the vector (A) is:

Where x is the horizontal displacement or change, and y is the vertical displacement or change.

For example, if you have a vector with an x component of 3 and y component of 4, you could compute the magnitude as follows:

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To find the magnitude of a vector with horizontal change x and vertical change y, use the Pythagorean theorem: |v| = sqrt(x^2 + y^2).

To find the magnitude of a vector with horizontal change x and vertical change y, you can use the Pythagorean theorem. The magnitude (|v|) of the vector is given by the square root of the sum of the squares of the horizontal and vertical changes:

|v| = sqrt(x^2 + y^2)

For example, if x = 3 and y = 4, the magnitude of the vector would be:

|v| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.

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Answer: The midpoint of segment PQ is the number 2.5

note: 2.5 as a fraction is 5/2; as a mixed number 2.5 converts to 2&1/2

============================================================

Explanation:

Apply the midpoint formula to get the midpoint of -8 and 6

We simply add up the values and divide by 2 and we get (-8+6)/2 = -2/2 = -1

So point Q is at -1 on the number line, which is exactly halfway from R to P

Focus on just points P and Q now. Apply the midpoint formula again

Q = -1

P = 6

(Q+P)/2 = (-1+6)/2 = 5/2 = 2.5

So the midpoint of segment PQ is 2.5

The decimal 2.5 can be written as the mixed number 2&1/2, showing that this new point is exactly halfway between 2 and 3.

Answer:

C

Step-by-step explanation:

Person A bought 3 tickets for 191

The price per ticket is 191/3 =63.67

Person B bought 5 tickets for 309

The price per ticket is 309/5 =61.80

Person C bought 8 tickets for 435

The price per ticket is 435/8 =54.38

The lowest price per ticket is 54.38

Person C paid the lowest price per ticket

Answer:

the first one x value is between 2 and 3, and the y value is between -4 and -5

Step-by-step explanation:

Multiply the first equation for 4 and second equation by 3

y=1/4x-5 (x4) Then, 4y= x-20

y=-1/2x-3 (x3) Then, 2y=-x-6

From the fist equation we organize the equation as y= (x-20)/4

and we add this value of y on the second equation

2((x-20)/4)=-x-6  the number 4 goes to the other side multiply x-6 and number 2 on the other side multiply x-20

Then, 2x -40= -4x-24 then we put x in one side and numbers on the other

2x+4x = -24+40

Then. 6x = 16 then x= 2.66  => x is between 2 and 3

Then this value of X goes to the first equation y = (2.66-20 )/ 4

y= - 4.33 the value y is between -4 and -5

Answer:

A: The x-value is between 2 and 3, and the y-value is between –4 and –5.

Step-by-step explanation:

Answer:

d (-5,0)

Step-by-step explanation:

x-coordinate moves a point left or right from the origin.

y-coordinate moves a point down or up form the origin.

So we don't want any down or up, so we want y to be 0.

If a point is located on the x-axis, then the y-coordinate is 0.  

d is the only point that sits on the x-axis. I know this because it's y-coordinate is 0.

(0,8) is actually a point sitting on the y-axis.

Answer:

(D) (-5,0)

Step-by-step explanation:

Answer:

90.6

Step-by-step explanation:

I think you have the first line incorrect. You show below that 10 students scored 90, so the first line is that 2 students scored 100, not 90. The line with the score of 90 is missing the number of students, but we can find it out. Call that number x for now.

Two students scored 100 each                                2

x students scored 95 on each test                         x

ten students scored 90 on each test                    10

three students score  80 on each test                    3

and one student scored 70                                 +   1

                                                                            x + 16

There are x + 16 students accounted for. The total number of students is 25.

x + 16 = 25

x = 9

9 students scored 95 on each test.

Now add up all the points scored by all students.

Two students scored 100 each  (2 * 90)                200

9 students scored 95 on each test (9 * 95)          855

ten students scored 90 on each test (10 * 90)     900

three students score  80 on each test (3 * 80)      240

and one student scored 70 (1 * 70)                      +  70

Sum of all points:                                                  2245

Now we find the average grade by dividing the sum of the points by the number of students.

average = sum/number = 2265/25 = 90.6

Answer:

all numbers greater than or equal to -1

Step-by-step explanation:

Let's find the vertex.

Since the function is in factored form, I'm going to find the zeros.

The average of the zeros will give me the x-coordinate of the vertex.

I can then find the y-coordinate of the vertex by using the equation

y=(x-4)(x-2).

Also the parabola is open up since the coefficient of x^2 is positive (or 1 in this case).

So the range has something to do with the y's. It is where the function exist for the y-values.

So the range for this one since the parabola is open up will be of the form

[y-coordinate of vertex , infinity).

So let's begin.

The zeros can found by solving (x-4)(x-2)=0.

This means we need to solve both x-4=0 and x-2=0.

x-4=0 gives us x=4

x-2=0 gives us x=2

Now the average of our x-intercepts (or zeros) is (4+2)/2=6/2=3.

So the x-coordinate of the vertex is 3. To find the y-coordinate of the vertex we are going to use y=(x-4)(x-2) where x=3.

Plug in:  y=(3-4)(3-2)=(-1)(1)=-1.

So the range is [tex][-1,\infty)[/tex]

or all numbers greater than or equal to -1

Answer:

all real numbers greater then or equal to -1

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

Line 1: 2

Line 2: 2 * 2 - 1 = 3

Line 3: 2 * 3 - 1 = 5

Line 4: 2 * 5 - 1 = 9

Line 5: 2 * 9 - 1 = 17

Line 6: 2 * 17 - 1 = 33

Answer:

[tex]f( - 10) = 2(-10)+1[/tex]

which is then equal to-19

[tex]f(2)=2^2 \\ [/tex]

which is then equal to 4

[tex]f(-1)=1^2 \\ [/tex]

which is then equal to 1

[tex]f(8)=3-8 \\ [/tex]

which is then equal to -5

Answer:

In the explanation:

Step-by-step explanation:

f(-10) means we need to find the piece so that x is also satisfied.

So we have x=-10 here.  Which of your pieces satisfy that?

Well [tex]-10 \le -5[/tex] so the first piece.  

[tex]f(-10)=2(-10)+1=-20+1=-19[/tex].

f(2) means we find the piece so that x is also satisfied.

So we have x=2 here. Which of your pieces satisfy that?

Well [tex]-5<2<5[/tex] so the second piece.

[tex]f(2)=(-2)^2=4[/tex].

f(-5) means we use the piece that satisfied x=-5.

-5 equals -5 and the equals -5 part is included in the first piece.

[tex]f(-5)=2(-5)+1=-10+1=-9[/tex]

f(-1) means use the piece so that x=-1 is satisfied.

-1 is between -5 and 5 so use [tex]x^2[/tex]

[tex]f(-1)=(-1)^2=1[/tex]

f(8) means use the piece so that x=8 is satisfied.

9 is greater than 5 so we use the third piece.

[tex]f(8)=3-8=-5[/tex]

It looks like you have all the answers and you are trying to figure out why.

Let's do another problem.

What piece would you use if I asked you to evaluate:

f(-2)?

x=-2 satisfies the [tex]-5<x<5[/tex] so we use the [tex]x^2[/tex]

[tex]f(-2)=(-2)^2=4[/tex]

f(-6)?

x=-6 satisfies the [tex]x \le -5[/tex] so we use the [tex]2x+1[/tex]

[tex]f(-6)=2(-6)+1=-12+1=-11[/tex]

f(7)?

x=7 satisfies [tex]x \ge 5[/tex] so we use [tex]3-x[/tex]

[tex]f(7)=3-7=-4[/tex]

I will post the answers here after you had time to think about it.

Answer:

45

Step-by-step explanation:

Here are two ways of solving this problem.

Method 1:

Term 1 is 2.

Term 2 is 3.

Term 3 is 4.

Each term is 1 more than the term number.

The 44th term is 45.

Method 2:

Using the hint

Find the common difference: 5 - 4 = 1

The common difference is 1.

1st term + (common difference)(desired term - 1)

2 + 1(44 - 1) = 2 + 43 = 45

Answer: 45

Answer:

x1/2

Step-by-step explanation:

Simplify the following:

(3 x1)/6

Hint: | In (x1×3)/6, divide 6 in the denominator by 3 in the numerator.

3/6 = 3/(3×2) = 1/2:

Answer:  x1/2

For this case we have the following expression:

[tex](x ^ {\frac {1} {6}}) ^ 3[/tex]

We have that by definition of properties of powers it is fulfilled that:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Now we have to, by applying the property:

[tex](x ^ {\frac {1} {6}}) ^ 3 = x ^ {\frac {3} {6}}[/tex]

Simplifying:

[tex]x ^ {\frac {3} {6}} = x ^ {\frac {1} {2}}[/tex]

Answer:

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

Answer:

slope = [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (6, 9)

m = [tex]\frac{9-4}{6-2}[/tex] = [tex]\frac{5}{4}[/tex]

Answer:

y = - 10x - 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here slope m = - 10, hence

y = - 10x + c ← is the partial equation

To find c substitute (- 1, 4) into the partial equation

4 = 10 + c ⇒ c = 4 - 10 = - 6

y = - 10x - 6 ← equation of line

Answer:

The measure of angle A is 51 degrees

Answer:

The measure of an angle A=[tex]1^{\circ}[/tex].

Step-by-step explanation:

We are given that an angle [tex]95^{\circ}[/tex] and two sides are 7  in and 9 in in a given figure.

We have to find the value of measurement of angle A.

To find the measurement of angle A we apply sine law.

Sine law:[tex]\frac{a}{sin \alpha}=\frac{b}{sin\beta}=\frac{c}{sin \gamma}[/tex]

Where  side a is opposite to angle [tex]\alpha[/tex]

Side b is opposite to angle [tex]\beta[/tex]

Side c is opposite to angle[tex] \gamma[/tex]

We are given an angle 95 degrees and opposite side of given angle is 9 in and the angle A is opposite to side 7 in.

Substituting the values then we get

[tex]\frac{9}{sin 95^{\circ}}=\frac{7}{sin A}[/tex]

[tex]\frac{9}{0.683}=\frac{7}{sin A}[/tex]

[tex] sin A=\frac{7\times 0.683}{9}[/tex]

[tex] sin A=\frac{4.781}{9}=\frac{4781}{9000}[/tex]

[tex] sin A=0.531[/tex]

[tex] A= sin^{-1}(0.531)[/tex]

[tex] A=0.56^{\circ}[/tex]

[tex] A= 1^{\circ}[/tex]

Hence, the measure of an angle A=[tex]1^{\circ}[/tex].

Answer:

y^18

Step-by-step explanation:

(y^2)^5 x y^8

Assuming the x is multiplication

We know (a^b)^c = a^(b*c)

(y^2)^5 = y^(2*5) = y^10

We are multiplying this by y^8

We know a^b * a^c = a^(b+c)

y^10* y^8 = y^(10+8) = y^18

Assuming the x is a variable

We know (a^b)^c = a^(b*c)

(y^2)^5 = y^(2*5) = y^10

We are multiplying this by y^8

We know a^b * a^c = a^(b+c)

y^10* y^8 = y^(10+8) = y^18

This is multiplies by x

x y^18

Answer:

[tex]\Huge \boxed{xy^1^8}[/tex]

Step-by-step explanation:

Exponent rule: [tex]\displaystyle (a^b)^c=a^b^c[/tex]

[tex]\displaystyle y^2^\times^5[/tex]

Multiply.

[tex]\displaystyle 2\times5=10[/tex]

[tex]\displaystyle y^1^0^+^8[/tex]

Add.

[tex]\displaystyle 10+8=18[/tex]

[tex]\large \boxed{xy^1^8}[/tex], which is our answer.