Point B is between A and C. If AB = 6 cm and BC = 11 cm, what is AC?

Answers

Answer 1

Since AB and BC are both parts of the same line segment, AB+BC=AC. If you do substitution and some algebra, you get 6+11=17. So the answer is 17 cm. Hope that helped!

Answer 2

AC will equal to 17 since it's a full line segment that contains A & C as endpoints. While b is the midpoint which does not have to be equally dissected. With adding AB & BC together will have the full value of the line segment.

Related Questions

The state of wyoming has roughly the shape of a rectangle that is 3.6 x 102 miles long and 2.8 x 102 miles high. what is the approximate area of wyoming? hint: the area of a rectangle is product of its length and width.

Answers

Assuming a regularly shaped rectangle, the formula for the area is given as:

A = L * W

where L and W are the length and width respectively

A = 3.6 x 10^2 miles * 2.8 x 10^2 miles

A = 100,800 square miles

A = 10.08 x 10^2 miles

Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Step-by-step explanation:

The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]

and height , [tex]H=2.8\times 10^{2}\, miles[/tex]

Area of rectangle , [tex]A=L\times W[/tex]

=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]

=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)

1. A grocer mixes two grades of coffee which sell for 70 cents and 80 cents per pound, respectively. How much of each must he take to make a mixture of 80 pounds which he can sell for 76 cents per pound?

2. How many quarts of pure alcohol must be added to 40 quarts of a mixture that is 35% alcohol to make a mixture that will be 48% alcohol?

3. If a container contains a mixture of 5 gallons of white paint and 11 gallons of brown paint, how much white paint must be added to the container so that the new mixture will be two-thirds white paint?

4. Can the sum of three consecutive odd integers be (a) 25? (b) 45?

5. A tank can be filled in 9 hours by one pipe alone, in 12 hours by a second pipe alone, and can be drained when full, by a third pipe, in 15 hours. How long would it take to fill the tank if it is empty, and if all pipes are in operations?

Answers

1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
[tex] \left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right \\ \\ \Rightarrow \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right \\ \\ \Rightarrow10x=320 \\ \\ \Rightarrow x=32 \\ \\ \Rightarrow y=80-32=48[/tex]
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.

2.) Volume of alcohol in the original mixture
[tex] \frac{35}{100} \times 40=14 [/tex] quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
[tex]\frac{48}{100} \times (40+x)=14+x \\ \\ \Rightarrow19.2+0.48x=14+x \\ \\ \Rightarrow0.52x=5.2 \\ \\ \Rightarrow x=10[/tex]

Therefore, 10 quarts of pure alcohol should be added

3.) Original proportion of white paint in the mixture
[tex]=\frac{5}{5+11}=\frac{5}{16}[/tex]

Let x be the number of gallons of white paint to be added, then
[tex]\frac{5+x}{16+x}=\frac{2}{3} \\ \\ \Rightarrow3(5+x)=2(16+x) \\ \\ \Rightarrow15+3x=32+2x \\ \\ \Rightarrow x=32-15=17[/tex]
Therefore, 17 gallons of white paint should be added.

4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
[tex]x - 2 + x + x + 2 = 25 \\ \\ \Rightarrow3x=25\Rightarrow x=8.33[/tex]
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
[tex]x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15[/tex]
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.

5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
[tex] \frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\ \\ \Rightarrow t= \frac{180}{23} =7.83 [/tex]
Therefore, it will take 7.83 hours to get the tank filled up.

What is the r value of the following geometric sequence?
64, 48, 36. 27

2/3

3/4

5/8

3/8

Answers

It's 3/4 because 48/64=r=3/4

Solve for x and y: 28x-49y=35 and 4x-7y=5

Answers

The answer to your problem is (x,-5/7+4/7x) or 0=0. Infinite Solution

Find S8 for the geometric series 3 + -6 + 12 + -24 +…

Answers

I guess you are asking to find the sum of the first 8 terms. If so, then:
Sum = a₁(1-rⁿ)/(1-r), where a₁ is the 1st term, r=common ratio and n=number of terms:
the 1st term a₁ =3
common ratio r = - 2 (since -6/3 = - 2, and 12/-6 = - 2, etc.)

Sum = 3[(1- (-2)⁸]/(1-2) = 3(1- 256)/(1/2)
Sum = -1530

the sum of the first 8 terms of the series is [tex]$ -255 $[/tex].

To find the sum [tex]$ S_8 $[/tex] of the geometric series [tex]$ 3 - 6 + 12 - 24 + \ldots $[/tex], we need to determine the common ratio [tex]($ r $)[/tex] and the first term [tex]($ a $).[/tex]

The general form of a geometric series is [tex]$ a + ar + ar^2 + \ldots + ar^{n-1} $[/tex], where:

- [tex]$ a $[/tex] is the first term,

- [tex]$ r $[/tex] is the common ratio,

- [tex]$ n $[/tex] is the number of terms.

In our series:

- [tex]$ a = 3 $[/tex] (the first term),

- To find the common ratio [tex]($ r $)[/tex], we can divide any term by its preceding term:

- [tex]$ \frac{-6}{3} = -2 $[/tex]

- [tex]$ \frac{12}{-6} = -2 $[/tex]

- [tex]$ \frac{-24}{12} = -2 $[/tex]

So, [tex]$ r = -2 $[/tex].

Now, [tex]$ S_n $[/tex], the sum of the first [tex]$ n $[/tex] terms of a geometric series, is given by the formula:

[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]

Substituting the values of [tex]$ a $, $ r $[/tex], and [tex]$ n = 8 $[/tex], we get:

[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]

[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]

[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]

[tex]\[ S_8 = -255 \][/tex]

So, the sum of the first 8 terms of the series is [tex]$ -255 $[/tex].

what are the coordinates of a point on the unit circle if the angle formed by the positive x- axis and the radius is 45°??

Answers

On the unit circle, the radius is 1 and the trigonometric ratios are:

sin(angle( = y-coordinate / radius = y-coordinate / 1 = y-coordinate = y

cos(angle) = x-coordinate / radius = x-coordinate / 1 = x

Then:

y = sin(angle) = sin(45°) = √2 / 2

x = cos (angle) = cos (45°) = √2 / 2

=> Answer: (√2 / 2 , √2 / 2), which is the option A)

You will be charged 12.5% interest on a loan of $678. how much interest will you pay on the loan?

Answers

12.5% of 678 =
0.125(678) = 84.75 <==

It is given in the question that

You will be charged 12.5% interest on a loan of $678.

So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125

So we have to find the value of 0.125 of 678.

[tex]0.125*678 = 84.75[/tex]

Therefore the interest that you will have to pay on loan is $84.75 .

How many sides does a polygon have with an interior angle of 108?

Answers

You wanna first find the exterior angle which is 180 - 108 = 72.
360/72 = 5

Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10

Answers

-2x < = 3x + 1 < = 10

split them
-2x < = 3x + 1 3x + 1 < = 10
-2x - 3x < = 1 3x < = 10 - 1
-5x < = 1 3x < = 9
x > = -1/5 x < = 3

solution is : -1/5 < = x < = 3 <==

What is 78% written as a decimal

Answers

Hello there!

78% as a decimal is 0.78
All you have to do is move the decimal place two times to the left.
78%
7.8
0.78 <---- this is your answer, and how to get to it.

I hope this helps!

find the magnitude of 6+2i

Answers

Final answer:

The magnitude of 6 + 2i is 2√10.

Explanation:

To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:

|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10

Therefore, the magnitude of 6 + 2i is 2√10.

in the diagram which pair of angles are corresponding angles

Answers

The answer to that is <3 and <7

C

Answer:

Option C is correct .i.e., ∠3 and ∠7

Step-by-step explanation:

Corresponding angles are the angles that are at the same corner at each Point of Intersection.i.e., if first angle is at the top left corner of one intersection then the angle at the other intersection is also at the top left.

From Given Figure,

Following are pairs of corresponding angles,

∠1 and ∠5

∠2 and ∠6

∠4 and ∠8

∠3 and ∠7

Therefore, Option C is correct .i.e., ∠3 and ∠7

Arrange the functions in ascending order, starting with the function that eventually has the lowest value and ending with the function that eventually has the greatest value.
2x+5
2^x+3
2^x+10
2x
x²+2
x²
PLEASE HELP 20 POINTS PROVIDED

Answers

2^x+10,2^x+3,x²+2,x²,2x+5,2x
2^x is higher than x²+2 because in small numbers for x ,x^2 is bigger but after x=6 the difference between them increases and 2^x becomes more

Susie is paying $558.16 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?

Answers

558.16 x 12 = 6697.92 every year

6697.92 x 30 = 200937.60 total

200937.60-150000 = $50,937.60 total interest paid

Help please:((((((((((((((((

Answers

Answer:

B. The amount spent on grapes compared with the weight of the purchase.

Step-by-step explanation:

Grapes are usually sold at some dollar amount per pound. That dollar amount is the "rate of change," and it is generally constant.

___

In the case of pizza delivery or bus ridership, it is hard to imagine what the "rate of change" might be, as the relationship is probably not a function.

Find all solutions in the interval [0, 2π). 7 tan3x - 21 tan x = 0

Answers

To solve the trigonometric expression we proceed as follows;
7(tan x)^3-21tanx=0
this can be written as:
7(tan x)^3=21tanx
dividing through by 7 we get:
(tan x)^3=tan x
dividing through by tan x we get:
(tanx)^1=1
hence;
tan x=+\-1
when tan x=1
x=45
when tan x=-1
x=-45
Given that our answer should be at the interval [0,2π] the answer:
45=45/180=1/4π

Given a polynomial f(x), if (x + 7) is a factor, what else must be true?

f(0)=7

f(0)=-7

f(7)=0

f(-7)=0

Answers

f(-7)=0

Because that makes the (x+7) factor equal zero and any other factor multiplied by zero also results in zero.

Answer:

f(-7)=0 that is option 4th is correct.

Step-by-step explanation:

If we have given any polynomial then its factor means that value is giving zero of that polynomial

And opposite sign of factor is the zero of the polynomial

For example:

x+a is factor of any polynomial f(x) then f(-a)=0

Similarly, If x+7 is a factor of any polynomial then f(-7)=0

Hence, option 4th is correct.

What is the area of a rectangle with a length of 15 feet and a width of 9 feet?

Answers

Final answer:

The area of a rectangle with a length of 15 feet and a width of 9 feet is 135 square feet.

Explanation:

The area of a rectangle can be found by multiplying its length and width.

In this case, the length is 15 feet and the width is 9 feet.

To find the area, multiply 15 feet by 9 feet:

Area = 15 feet x 9 feet = 135 square feet

Therefore, the area of the rectangle is 135 square feet.

What is a variable?

a.
A variable is an unknown number or value represented by a letter
c.
A variable represents a change in value
b.
A variable always represents the total amount
d.
A variable is always represented by the letter x

Please select the best answer from the choices provided

Answers

A variable is an unknown number or value represented by a letter. If there was an equation x+2=19, then x would be the variable, because it is a letter representing an unknown value
hope this helps:))

A.
A variable is an unknown number or value represented by a letter.

A variable is an unknown number or value represented by a lower case letter.

please help , show your steps , thanks

Answers

5 + 2*SQRT(x) = 15

subtract 5 from each side

2*SQRT(x) = 10

(2*SQRT(x))^2 =10^2

2^2 *x = 100

4x=100

x=400/4

x = 25

Decide if the situation involvesâ permutations, combinations, or neither. explain your reasoning.

Answers

it needs permutations of the order does matter, like 3 people ordering from a coffee shop to see who goes first.

Combinations are when the order doesn't matter, like if you had 3 numbers behind your back and you had to guess the 3 not in order

It needs neither when you don't need to find the amount of choices you have (or something similar) for something

Find the possible value or values of n in the quadratic equation 2n2 – 7n + 6 = 0

Answers

2n^2-7n+6=0

2n^2-4n-3n+6=0

2n(n-2)-3(n-2)=0

(2n-3)(n-2)=0

n=3/2, n=2

Answer:

[tex]n=\frac{3}{2},\,\,n=2[/tex].

Step-by-step explanation:

The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is to factorize the polynomial on the left hand side. To factorize you can do the following:

(1) [tex]2n^2-7n+6[/tex]. The given polinomial

(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex]. Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]

(3) [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.

(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]

(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]

Then the given equation can be written as:

[tex]{(2n-3)(n-2)=0[/tex]

The product of two expression equals zero if and only if one of the expression is zero. From here we have that

[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]

From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].

What is the equation of the following line? Be sure to scroll down first to see all answer options.

Answers

the answer is C y = 1/3x

Answer:

Option C. is the correct option.

Step-by-step explanation:

Equation of line is represented as y = mx + c

where m = slope of the line

c = y - intercept

Since line is passing through origin (0, 0) and a point (6, 2)

Therefore y intercept of the line will be 0.

c = 0

Slope of the line [tex]m=\frac{y-y'}{x-x'}[/tex]

[tex]m=\frac{2-0}{6-0}[/tex]

[tex]m=\frac{2}{3}[/tex]

So the equation will be

[tex]y=\frac{1}{3}x[/tex]

Therefore, option C. is the answer.

The screen aspect of a widescreen tv is 16.9. What are the width and height of a 32 inch tv? Round answer to the nearest tenth of an inch.

Answers

check the picture below.

thus

[tex]\bf 32^2=w^2+\left( \cfrac{9w}{16} \right)^2\implies 32^2=w^2+\cfrac{(9w)^2}{16^2}\implies 32^2=w^2+\cfrac{9^2w^2}{16^2} \\\\\\ 32^2=\cfrac{16^2w^2+81w^2}{16^2}\implies 32^2\cdot 16^2=337w^2 \\\\\\ (32\cdot 16)^2=337w^2\implies \sqrt{(32\cdot 16)^2}=\sqrt{337w^2} \\\\\\ 32\cdot 16=w\sqrt{337}\implies \cfrac{32\cdot 16}{\sqrt{337}}=w\implies \boxed{\cfrac{512}{\sqrt{337}}=w}\\\\ -------------------------------\\\\[/tex]

and we can rationalize that to [tex]\bf \cfrac{512}{\sqrt{337}}\cdot \cfrac{\sqrt{337}}{\sqrt{337}}\implies \boxed{\cfrac{512\sqrt{337}}{337}}[/tex]

thus, its height is [tex]\bf h=\cfrac{9w}{16}\implies h=\cfrac{9}{16}\cdot \cfrac{512\sqrt{337}}{337}\implies \boxed{h=\cfrac{4608\sqrt{337}}{5392}}[/tex]

Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°. Find the height, h, of the lighthouse. Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse. To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations

Answers

Grace has a 45 degree upwards angle, then the height of the lighthouse is 14'.

Case A. Kelly is 26 feet from the lighthouse.
The arcTangent of 14/26 is a 28.3 degree angle.

Case B. But if Kelly stood closer to the lighthouse, i.e. 2 feet away, then her angle is arcTangent of 14/2 = 81.9 degrees

If the lengths of two of the possible sides of a right triangle measure 4 root 15 and 7 root 6 what is the smallest possible length of the third side

Answers

Given that the sides of a right angle measures 4sqrt15 and 7sqrt6, thus the possible size of the third side will be:
using Pythagorean theorem:
c^2=a^2+b^2
c^2=(4sqrt15)^2+(7sqrt16)^2
c^2=4^2*15+7^2*16
c^2=240+784
c^2=1024
hence;
c=sqrt1024
c=32
Th possible third side is 32

A family has two cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. during one particular week, the two cars went a combined total of 675 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?

Answers

car 1 = x

car 2 = y

x+y =40 gallons

x=40-y

15x +20y = 675

15(40-y) +20y = 675

600-15y +20y =675

600+5y = 675

5y=75

y=75/5 = 15 gallons

x=40-15 =25 gallons

Car 1 used 25 gallons

Car 2 used 15 gallons

Help which is the correct function

Answers

It is decreasing in the positive x axis so the exponent will be negative so its either B or D.
when x = 5, y is about 3 . something:-

check for d:- 4*e^(0.05*5) = 3.11

so its D.

A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?

Answers

[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]

Hello!

The number of pairs of shoes each man can repair is its speed times the time.

Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.

Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.

Thus, we can equate:

[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]

That is the speed of the assistant. Then, the speed of the repairman is:

[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]

That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)

3/4 of an hour is 45 minutes and this is the answer.

Final answer:

To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.

Explanation:

To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.

Let's denote the time it takes the repairman to repair one pair of shoes by x hours.

Since the assistant takes twice as long, their time would be 2x hours for one pair.

Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.

Now, we express their combined work rate as the sum of their individual work rates.

The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.

Together, this should equal their combined rate of 2 pairs per hour:

1/x + 1/(2x) = 2

Solving this equation for x, we first find a common denominator and get:

2/2x + 1/2x = 2

3/2x = 2

3 = 4x

x = 3/4

Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.

Help me please!!!!!!

Answers

Let
V1 = volume of the smaller cube (with 1/3 cm sides)
V2 = volume of the box shown

The first volume is
V1 = (1/3)*(1/3)*(1/3)
V1 = 1/27

The second volume is
V2 = (5/3)*(4/3)*(2)
V2 = 40/9

Now divide the two volumes
(V2)/(V1) = (40/9)/(1/27) = (40/9)*(27/1) = 120

Therefore you can fit 120 of the smaller cubes in the larger box shown.

Other Questions