What is the arc length of a quarter circle with a radius of 6 inches?

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:

[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:

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:

[tex]\large\boxed{C.\ 75<x<110\ and\ 0<y\leq50}[/tex]

Step-by-step explanation:

x - the temperature

y - the number of people

the temperature is between 75 degrees and 110 degrees:

75 < x < 110

the room for 50 people:

0 < y ≤ 50

Answer:

C

Step-by-step explanation:

We know x is more than 75

75<x

and there is room for 50 people and we have to use y

0<y<110

  _^

The only possible answer is C hope this helps :)

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:

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]

The expression will be    [tex]\[ (-125) \cdot c^3 \][/tex]

The exponential form of the expression [tex]\((-5)(-5)(-5) \cdot c \cdot c \cdot c\)[/tex] can be calculated as follows:

First, simplify the multiplication of the negative numbers:

[tex]\[ (-5)(-5)(-5) = (-125) \][/tex]

Next, simplify the multiplication of the variables:

[tex]\[ c \cdot c \cdot c = c^3 \][/tex]

Now, combine the results:

[tex]\[ (-125) \cdot c^3 \][/tex]

The final exponential form of the expression is:

[tex]\[ (-125) \cdot c^3 \][/tex]

Here's a step-by-step explanation of the calculation:

1. Multiply the negative numbers:

[tex]\[ (-5)(-5) = 25 \][/tex]

  Multiply 25 by -5 again:

[tex]\[ 25 \cdot (-5) = -125 \][/tex]

2. Multiply the variables:

[tex]\[ c \cdot c = c^2 \]\\ Multiply \(c^2\) by c again:\\ \[ c^2 \cdot c = c^3 \][/tex]

3. Combine the results:

[tex]\[ (-125) \cdot c^3 \][/tex]

That's the final exponential form of the given expression.

Complete Question:

What is the exponential form of the following expression

(-5)(-5)(-5) •c•c•c

[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

Step-by-step explanation:

A = P (1 + r)^t

Given that P = $1,200,000, r = 0.1037, and t = 5:

A = $1,200,000 (1 + 0.1037)^5

A = $1,965,334.41

Round as needed.

Answer:

The forecasted sales for 2004 is $1965281.

Step-by-step explanation:

The annual sales in 1999 were = $1,200,000

Let geometric mean growth rate = r

we have now p = $1,200,000,

r = 10.37% or 0.1037

t = 5:

We have the formula Amt= [tex]p(1+r)^{t}[/tex]

Amt =[tex]1200000(1+0.1037)^{5}[/tex]

Solving this we get;

[tex]1200000\times1.63777=1965324[/tex]

A = $1,965,324

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:

$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:

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:

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:

10 ≥ ⅛c + ¼d

Step-by-step explanation:

They budgeted up to 10 gallons of water, meaning that it CANNOT exceed 10. When turned around, you will see that everything is less than or equal to 10.

I am joyous to assist you anytime.

Complete question:

A small kennel has budgeted to provide 10 gallons of water for its animals. Each cat receive one eight of a gallon per day and each dog receives one fourth of a gallon per day . Which inequality correctly represent the scenario.

a. 10 < -1/8c - 1/4d

b.  10 ≤  1/8c + 1/4d

c  10 ≥ -1/8c - 1/4d

d. 10 ≥ 1/8c + 1/4d

Answer:

d. 10 ≥ 1/8c + 1/4d

Step-by-step explanation:

The kennel was budgeted to provide 10 gallons of water for its animals. The cat receives  1/8 of a gallon per day and each dog receive 1/4 of a gallon per day.

Since 10 gallons was budgeted for the animals the sum of the a gallon per day for the cat and dog will most likely not exceed 10 gallons. The animals will most likely consume less than the budgeted value or equals to the budgeted value.    

note that the sum of 1/8 of a gallon  for the cat and 1/4 of a gallon for the dog should be either less than 10 or equals to 10. This means  10 ≥ 1/8c + 1/4d .

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:

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

[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:

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

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:

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.

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:

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

[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:

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( - 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.

the name of the plane is C. plane EGF

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:

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.

https://brainly.com/question/15513632

#SPJ3

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