Mathematics High School

A 10​-foot piece of string is cut into two pieces so that the longer piece is 1 footfoot longer than twice the shorter piece. If the shorter piece is x feet​ long, find the lengths of both pieces.

Answers

Answer 1

shorter piece = x

longer piece = 2x+1

3x+1 =10

3x=9

x = 9/3=3

short piece = 3 feet

 long piece = 2*3+1 = 7 feet


Related Questions

Two angles are supplementary one angle measure 12 more than the other find the measures

Answers

We have a + b = 180 and a = 12 + b;
Then, 12 + b + b = 180;
12 + 2b = 180;
2b = 168;
b = 84;
a = 12 + 84;
a = 96;

Not sure ^^^^^^^^^^^

Answers

To factor the trinomial, use slip and slide.
y^2-7y-30
(y-10)(y+3)
(y-5)(2y+3)
If you divide out y-5, you are left with 2y+3
B

Which of the following represents the set of possible rational roots for the polynomial shown below 2x^3+5x^2-8x-20=0

Answers

The questioner wants us to list all possible roots by applying the Rational Roots theorem

factors of constant term (-20) = +/- 1, +/-2, +/-5, +/-10, +/-20 WE call these factors p.

factors of leading coefficient (2) = +/- 1, +/-2 (call these q)

then possible roots are p/q = +/-1/1, +/- 1/2 , +/- 5/1 , +/- 5/2 and so on.

The possible rational roots are given by the ratio of the constant term to the leading coefficient. That is [tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on and this can be determined by using the arithmetic operations.

Given :

Polynomial Equation -- [tex]2x^3+5x^2-8x-20=0[/tex]

The following steps can be used in order to determine the rational roots of the given polynomial equation:

Step 1 - Write the given polynomial equation.

[tex]2x^3+5x^2-8x-20=0[/tex]

Step 2 - The coefficient of [tex]x^3[/tex] is 2. So the factors of 2 are [tex]\pm[/tex]1, [tex]\pm[/tex]2.

Step 3 - The constant term of the given polynomial is -20 and the factors of the constant term are  [tex]\pm[/tex]1,  [tex]\pm[/tex]2,  [tex]\pm[/tex]5,  [tex]\pm[/tex]10,  [tex]\pm[/tex]20.

Step 4 - The rational roots are given by the ratio of the constant term to the leading coefficient. That is,

[tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on.

For more information, refer to the link given below:

https://brainly.com/question/12254880

Collinear points are not necessarily coplanar.. true or false

Answers

I believe the correct answer is true. Collinear points are not necessarily coplanar. Points are considered to be collinear when the points lie on a single line. They are considered to be coplanar when these points are located on the same plane. It is possible that collinear points are not coplanar when these points on the line are not on the same plane. For instance, the line formed by the points is perpendicular to a plane so it is possible that only a point can be found in the plane or no points can be found in the plane. If points are collinear, then it does not follows that they are coplanar.
Answer:

The given statement is a false statement.            

Step-by-step explanation:

Collinear Points--

Two or more points are said to be collinear if they lie on a straight line.

Coplanar--

Set of points are said to be coplanar if they lie on the same plane.

If the set of points are collinear then we may get a line such that it will contain all these points and as we know that line always lie in a plane also there may be infinite number of planes which may contain the same line.

So, all the points on the line will also lie in the same plane.

Yes, collinear points are necessarily coplanar.

What is the measure of (arc) BC?

A. 55

B. 110

C. 48

D. 96

Answers

Angle BAC is the inscribed angle, therefore it is equal to half the arc AB  ⇒

arc AB = 2*48 = 96°

Answer:

(D)[tex]96^{\circ}=(arc)BC[/tex]

Step-by-step explanation:

It is given from the figure that m∠BAC=48° and arcAC=110°.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Now, using the above property, we have

[tex]m{\angle}BAC={\frac{1}{2}}(arc)BC[/tex]

Substituting the given values, we get

[tex]48^{\circ}=\frac{1}{2}(arc)BC[/tex]

[tex]96^{\circ}=(arc)BC[/tex]

Thus, the measure of the arc BC is 96 degrees.

Hence, option D is correct.

What is 5.75% of $6,000? (Express answer as dollars as cents.)

Answers

6000*0.0575=345
Final answer: $345.00

Answer:

The answers are:

345 dollars

34500 cents

Step-by-step explanation:

In order to determine the answers, we have to know about the percentage notation. For any "x" value that is expressed as x%, it is the same that:

x%=[tex]\frac{x}{100}[/tex]

So, first we determine the value in dollars and then we determine the value in cents, where:

1 dollar=100 cents

In dollars $:

=5.75%*$6000

=[tex]\frac{5.75}{100}[/tex]*$6000

=$345.00

In cents c:

=5.75%*6000*100

=[tex]\frac{5.75}{100}[/tex]*6000*100

=34500.00 cents

The number of new cars purchased in a city can be modeled by the equation where C is the number of new cars and t is the number of years since 1958. C = 26t^2 + 168t + 4208. In what year will the number of new cars reach 15,000? a. 2026 b. 1993 c. 1970 d. 1976 Solve using the quadratic formula. HELP PLZ!

Answers

C(t)=26t^2+168t+4208, and we wish to know when C(t)=15000

26t^2+168t+4208=15000

26t^2+168t-10792=0

They want you to use the quadratic formula...

For a quadratic of the form ax^2+bx+c=0, the quadratic formula is:

x=(-b±√(b^2-4ac))/(2a), in this case we have:

x=(-168±√1122368)/52, since x>0

x≈17.14

1958+17.14≈1975.14

So by 1976 the number of new cars will reach 15000.

Final answer:

To determine when the number of new cars reaches 15,000, the quadratic equation 26t^2 + 168t + 4208 = 15,000 is solved for t and then added to 1958.

Explanation:

To find the year when the number of new cars reaches 15,000, we need to set the equation C = 26t^2 + 168t + 4208 equal to 15,000 and solve for t, where t is the number of years since 1958.

First, set up the equation: 15,000 = 26t^2 + 168t + 4208.

To solve for t, we subtract 15,000 from both sides to get the quadratic equation: 0 = 26t^2 + 168t - 10,792.

Next, we use the quadratic formula [tex]t = (-b \pm \sqrt{b^2 - 4ac}) / (2a)[/tex], where a = 26, b = 168, and c = -10,792.

Plugging the values into the quadratic formula, we get the two possible solutions for t. After calculating the roots, we discard any negative value as it would not make sense in the context of time since 1958. The positive year will give us the answer we need.

Adding the positive value of t to 1958, we obtain the year in which the number of new cars purchased will reach 15,000.

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

A(n) = 12 + (n – 1)(3)


A.12, 21, 39

B. 0, 9, 27

C. 12, 24, 42

D. 3, 24, 27

Answers

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference} \end{cases}\\\\ -------------------------------\\\\[/tex]

[tex]\bf A(n)=12+(n-1)(3)\qquad \begin{cases} n=n^{th}\ term\\ 12=\textit{first term's value}\\ 3=\textit{common difference} \end{cases} \\\\\\ n=1,4\ and\ 10\implies \begin{cases} A(\underline{1})=12+(\underline{1}-1)(3)\\ A(\underline{4})=12+(\underline{4}-1)(3)\\ A(\underline{10})=12+(\underline{10}-1)(3) \end{cases}[/tex]

What information can be used to compare linear relationships?

Answers

Line graphs are used to display data or information that changes continuously over time. hope that helped

Sample Response:

Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.

Thirty pounds of a salt-water solution contains fifteen percent salt. How much salt is in the water?
1.5 lb
3 lb
4.5 lb

(I came up with 2 answers and I need someone with the same answer, the two options that I came up with is 1.5 lb. or 4.5lb.

Answers

30 lbs x 0.15 = 4.5 lbs

answer
4.5 lb
30 x .15=?---------------

(-3,1) perpendicular to y=2/5x-4

Answers

(-3, 1)             y = 2/5x - 4 
 x₁  y₁              slope (m) = 2/5x

Since the equation we are looking for is perpendicular to y = 2/5x - 4, we need to find the opposite reciprocal slope. We have to flip the slope upside down and turn it negative.

2/5 ⇒ 5/2 ⇒ -5/2

So far, we have the equation y = -5/2.

Now, we need to find the y intercept by plugging in the given point into point slope form, which is...

y - y₁ = m(x - x₁) 

The subscripts in the y and x are just the x and y in (-3,1). They are just placeholders, not exponents.

y - 1 = -5/2(x + 3)
 y - 1 = -5/2x - 15/2
   + 1               +     1
------------------------------
 y = -5/2x - 13/2 ⇒ final equation


Colby took out a sinlge payment loan for $550 that charged a $60 fee. How much does he have to pay by the time the loan reaches maturity?

Answers

He has to pay by the time the loan reaches maturity
550+60=610

Answer:

Step-by-step explanation610:

Please help! Thanks (:

Answers

Move the decimal 5 spots to the left to get the final answer of 0.0000416

So the answer is choice B

Note: there are four zeros between the decimal point and the digit '4' in the value 0.0000416

WILL GIVE A BRAINLIEST!!

Find the range of the parent function below.

y=1/x

A.
all real numbers
B.
all real numbers except 0
C.
all positive numbers
D.
all negative numbers

Answers

(the Domain of the function is clearly all Real numbers - {0})

The Range is the set of all values that the function can take.

let c be any value in the range. So c=1/x for some x in the domain, 

and so x=1/c.

For example, is c=10 in the range of the function?
yes, for x=1/10, f(1/10)=1/(1/10)=10.

Consider again x=1/c, the only value of c that cannot be in the Range is c=0, because to produce 0 in the range, x would need to be 1/0, which is undefined.


Answer: 

B.
all real numbers except 0

Jessica deposits $2000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 2 years?

Answers

$2000 x 0.03 x 2 = $120
answer

interest will  be $120 in the first 2 years

A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?

Answers

6 x 4 x 10 x 10 = 2400 possible outcomes

Answer:

2400

Step-by-step explanation:

Given : The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each.

To Find: If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?

Solution:

No. of faces of first die = 6

No. of faces of second die = 4

No. of faces of third die = 10

No. of faces of fourth die = 10

Now we are supposed to find the the number of possible outcomes exist.

So, Number of possible outcomes if all the dice are thrown together :

= [tex]6 \times 4 \times 10 \times 10[/tex]

=[tex]2400[/tex]

Hence there are 2400 possible outcomes if all the dice are thrown together and their combination dictates a certain outcome of the game.

if y varies inversely as x, and y=20 as x=3, find y for the x value 4

Answers

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{cases} y=20\\ x=3 \end{cases}\implies 20=\cfrac{k}{3}\implies 20\cdot 3=k\implies 60=k \\\\\\ thus\qquad \boxed{y=\cfrac{60}{x}}\\\\ -------------------------------\\\\ now\qquad x=4\qquad y=\cfrac{60}{4}[/tex]

True or false the difference of two numbers is less than either of those two numbers

Answers

The difference of two numbers is not always less at either of the two numbers. (especially for negative numbers)

Take fo example, 40 - 30 = 10.
Here the difference is less than both two numbers.

But in 40 - 15 = 25
Here the difference is less than one of the numbers but greater than the other number.

Now consider, -3 and -5, their difference is given by (-3) - (-5) = -3 + 5 = 2.
Here, 2 is greater than both -3 and -5.

Therefore, The difference of two numbers is not always less than either of those two numbers.

Your answer is False.

How many different pizzas can be ordered if the restaurant offers 15 different toppings and there is no limit to
the number of toppings on the pizza?

Answers

Final answer:

Using the formula for combinations with repetition, with 15 different toppings and no limit on the number of toppings per pizza, we find that there can be 32,768 different possible pizzas.

Explanation:

The question you're asking relates to combinations with repetition, a topic in combinatorics, a branch of mathematics. Given 15 different pizza toppings and the possibility of choosing any number of these toppings for a single pizza (including the possibility of a pizza with no toppings at all), we're essentially looking at how many different pizzas can be created.

To calculate the total number of different pizzas that can be ordered, we use the formula for combinations with repetition, which is (n+r-1)C(r), where 'n' is the number of toppings to choose from (15 in this case), 'r' is the number of toppings chosen, and 'C' represents the combination function. Since there's no limit to the number of toppings, 'r' can vary from 0 (a pizza with no toppings) to 15 (a pizza with all the toppings). However, because the question allows any number of toppings and we consider repetitions, the calculation simplifies to 2ⁿ, where n is the number of toppings.

Therefore, calculating this gives us 2¹⁵, which equals 32,768 different possible pizzas. This includes every combination from no toppings at all to a pizza with all 15 toppings.

The graph of a linear equation contains the points (4,1) and (-2,-11). Which point also lies on the graph?
A. (1,1)
B.(1,-5)
C.(1,-2)
D.(1,-7)

Answers

Answer:

Option B is correct.

(1 , -5) lies on the graph.

Step-by-step explanation:

Given the points (4,1) and (-2 , -11)

First find the linear equation for the given points.

Equation of line for two points [tex](x_1, y_1)[/tex] and  [tex](x_2, y_2)[/tex]

is given by:   [tex]y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)[/tex]

Substitute the given points (4,1) and (-2 , -11)  in above equation to find the equation of line:

[tex]y-1=(\frac{-11-1}{-2-4})(x-4)[/tex]

or

[tex]y-1=(\frac{-12}{-6})(x-4)[/tex]

or

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

Using distributive property on RHS ( i.e,  [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex] )

we have;

y -1 = 2x-8

Add 1 to both sides of an equation;

y-1+1 = 2x-8+1

Simplify:

y = 2x -7

Therefore, the equation of line for the given point is: y =2x - 7     ....[1]

To find which points lies on the graph ( i.e, Line)

Substituting the given options in equation [1] we have;

A . (1,1)

Put x =1 and y =1

[tex]1 = 2\cdot 1 -7 = 2-7[/tex]

1 = -5 which is not true.

Similarly

B. for (1, -5)

[tex]-5= 2\cdot 1 -7 = 2-7[/tex]

-5 = -5 which is true.

C. for (1, 2)

[tex]2= 2\cdot 1 -7 = 2-7[/tex]

2 = -5 which is not true.

And

D.  For (1 , -7)

[tex]-7= 2\cdot 1 -7 = 2-7[/tex]

-7 = -5 which is also not true.

Therefore, the only point which lies on the  line graph [1] is; (1 ,-5)



In a hospital ward, there are 12 nurses and 4 doctors. 3 of the nurses and 2 of the doctors are male. If a person is randomly selected from this group, what is the probability that the person is female or a doctor? @IMStuck @TheSaint905621 @Compassionate @phi @math&ing001 @acxbox22

Answers

13/16
Because there are all together there are 16 people, 4 are doctors and 9 are female nurses. So add 9 and 4 are you get 13 since the question is asking for females or doctors.

Answer:  

[tex]\bf \textbf{Probability that the person is female or a doctor = }\frac{13}{16}[/tex]

Step-by-step explanation:

Number of nurses in the hospital = 12

Number of doctors in the hospital = 4

Number of male nurses = 3

Number of male doctors = 2

Number of male persons = 5

So, Number of female persons = 16 - 5 = 11

Number of female doctors = 4 - 2 = 2

So, Probability that the person is female or a doctor = Probability that a person is female + Probability that a person is doctor - Probability that a person is female doctor

[tex]\implies\text{Probability that the person is female or a doctor = }\frac{11}{16}+\frac{4}{16}-\frac{2}{16}\\\\\implies\bf \textbf{Probability that the person is female or a doctor = }\frac{13}{16}[/tex]

Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: ∠F ∠ F is supplementary to ∠G ∠ G and ∠G ∠ G is supplementary to ∠H ∠ H . Conjecture: ∠F ∠ F is supplementary to ∠H ∠ H .

Answers

Given the symbols were duplicated when written, I will re-write the statement:

Given: ∠F is supplementary to ∠G  and ∠G is supplementary to ∠H . Conjecture: ∠F is supplementary to ∠H .

It is False.

Definition: two angles are supplementary if, and only if, they add up 180°.

=>

∠F is supplementary to ∠G => ∠F = 180° - ∠G => ∠G = 180° - ∠F

∠G is supplementary to ∠H => ∠G = 180° - ∠H

=> 180° - ∠F = 180° - ∠H 

=> ∠F = ∠H,

Then, you have gotten the two angles are equal, and they will be supplementary only if ∠F = ∠ G = 90°, because 90° + 90° = 180°. In any other case, they are  not supplementary.

This is a counter example:

∠G = 60°

∠F is supplementary to ∠G => ∠F = 180° - G = 180° - 120°


∠H = 30°

∠G is supplementary to ∠H => ∠G = 180° - H = ∠G = 180° - 30° = 150°

Then, ∠H + ∠F = 150° + 120° = 270° ≠ 180° => they are not supplementary.

determine whether the sequence converges or diverges. if it converges give the limit.

48, 12, 3, 3/4, ...

Answers

The sequence converges.
The limit of the sequence is 0.

-------------------------------------------------------------

This is a geometric sequence with the first term a = 48 and r = 1/4 = 0.25 as the common ratio. Since |r| < 1, this means that the terms are steadily getting smaller and smaller. The terms will approach 0 but not actually get there.

Note: if you added up all the terms of this infinite sequence, then the sum would be S = a/(1-r) = 48/(1-0.25) = 64

Final answer:

The provided sequence is a geometric sequence that converges to 0 because its common ratio's absolute value is less than 1.

Explanation:

The sequence provided is 48, 12, 3, 3/4, suggesting a pattern where each term is divided by 4 to get the next term (this is a common ratio r = 1/4). This type of sequence is known as a geometric sequence, and to determine if it converges, we can apply the ratio test.

In a geometric sequence, successive terms approach zero if |r| < 1. Since the absolute value of the common ratio here is less than 1, the terms of the sequence will get progressively smaller and approach zero. Therefore, we can conclude that this geometric sequence converges, and the limit is 0.

How to solve and why the answer is (A)

Answers

[tex]\dfrac{1}{2}x^2+mx=5\\ \dfrac{1}{2}x^2+mx-5=0\\\\ \Delta=m^2-4\cdot\dfrac{1}{2}\cdot(-5)=m^2+10\\ \sqrt{\Delta}=\sqrt{m^2+10}\\\\ x=\dfrac{-m\pm\sqrt{m^2+10}}{2\cdot\dfrac{1}{2}}=-m\pm\sqrt{m^2+10}[/tex]

For the graphed function f(x) = (2)x + 2 + 1, calculate the average rate of change from x = −1 to x = 0. graph of f of x equals 2 to the x plus 2 power, plus 1. (6 points) −2 2 3 −3

Answers

Next time you should write the correct form of equation because it affects greatly the answer. I believe the correct form would be:

f (x) = 2 * x^2 + 1

where the second 2 is a power of x

The average rate of change is also defined as the slope of the equation. Therefore:

average rate of change = slope

Where slope is:

m = (y2 – y1) / (x2 – x1) = [f (0) – f (-1)] / (x2 – x1)

 

Calculating for f (0): x2 = 0

f (0) = 2 * 0^2 + 1 = 1

Calculating for f (-1): x1 = -1

f (-1) = 2 * (-1)^2 + 1 = 3

 

Substituting the known values to the slope equation:

average rate of change = (1 – 3) / (0 – 1)

average rate of change = -2 / -1

average rate of change = 2

 

Answer: 2

Answer:

I believe the proper form of this question is actually... as I have also come across this question.

"For the graphed function f(x) = (2)^(x + 2) + 1, calculate the average rate of change from x = −1 to x = 0."

Step-by-step explanation:

the y2 - y1/ x2 - x1, will actually be (-1,3) and (0,5).

This means you will get a 5 + 1 (because subtracting a -1 is the same as adding 1) over 0 - 3.

Next you have 6/-3 which will give you a answer of -2

Now I do believe the proper answer is actually 2 because the graph shows a chart that is growth, not decay, but the math gives a -2 which is confusing.

Suppose that some country had an adult population of about 50 million, a labor-force participation rate of 60 percent, and an unemployment rate of 5 percent. how many people were unemployed?

Answers

60% of 50 mill......0.6(50 mill) = 30 mill...this is the labor force participation
unemployment rate of 5%....0.05(30 mill) = 1.5 mill

 1.5 million were unemployed <==

** if the unemployment rate is 5%, that means 5% of the labor force, not the entire adult population because some of the adult population might be too old or disabled and cant participate in the labor force. The labor force is people that are able to work.

Based on the labor force participation rate, the number of unemployed people is 1.5 million people.

The unemployed rate is based on the labor force participation rate and not the adult population.

The labor force is 60% and in absolute value this is:

= 60% x 50 million people

= 30 million people

The unemployment rate is 5% of this:

= 5% x 30 million

= 1.5 million people

In conclusion, there are 1.5 million unemployed people

Find out more at https://brainly.com/question/3672142.

Consider the system of linear equations.

7x+16y=-2
9x-4y=22

To use the linear combination method and addition to eliminate the y-terms, by which number should the second equation be multiplied?

A. -4
B. -1/4
C. 1/4
D. 4

Answers

by 4  becuase this will change the -4y to -16y , then adding the 2 equations will eliminate y.

D

To use the linear combination method and addition to eliminate the y-terms, the second equation should be multiplied by 4.

What is equation?

An equation is like a relationship between two or more variables. It is expressed in equal to form. Equation of two variables looks like: ax+ by=c.

It is solved to find the value of variables.

How to solve equation?

The given equations are 7x+16y= -2 and 9x-4y=22 and we have to solve using linear combination method.

First we have to change  -4y to -16y because after we have to do addition so we will multiply the second equation by 4 which makes the equation as under:

36x-16y=88

Adding equation 1 and 2

7x+16y+36x-16y=-2+22

42x=20

x=20/42

x=10/21

Put the value of x in 7x+16y=-2

7(10/21)+16y=-2

10/3+16y=-2

16y=-2-10/3

16y=-16/3

y=-1/3

Hence to solve the equations we need to first multiply second equation by 4 which is option D.

Learn more about equation at https://brainly.com/question/2972832

#SPJ2

A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $14. For 5 pounds of jelly beans and 6 bounds of trail mix, the total cost is $28. Find the cost for each pound of jelly beans and each pound for trail mix.

Answers

3j+2t=14  subtract 2t from both sides

3j=14-2t  divide both sides by 3

j=(14-2t)/3

...

5j+6t=28, using j found above in this equation yields.

5(14-2t)/3+6t=28  perform indicated multiplication on left side

(70-10t+18t)/3=28  multiply both sides by 3

70-10t+18t=84  combine like terms on the left side

70+8t=84  subtract 70 from both sides

8t=14 divide both sides by 8

t=$1.75, and since j=(14-2t)/3

j=(14-2(1.75))/3

j=$3.50

So a pound of trail mix costs $1.75 and a pound of jelly beans costs $3.50.

Kwamee created a coffee blend for his cafe by mixing Kona beans and Fuji beans.Kona beans cost $11 per pound and Fuji beans cost $7.50 per pound.He bought a total of 23 pounds of coffee beans and it cost $197. Write a system of equations that can be used to determine how many pounds of Kona and Fuji beans Kwamee bought.

Answers

Let's use K for Kona and F for Fuji.  The system of equations has to be a balanced system.  For example, you can't mix the number of pounds of beans with the cost for each because pounds and dollars are different and you can only combine like terms...pounds with pounds and dollars with dollars.  So let's start with the number of pounds.  Since we don't know how much of each he bought we have the 2 unknowns, F and K, but we DO know that he bought 23 pounds total. So the first equation is
K + F = 23
Now let's see what we can do with the dollars. Again, we don't know how much he bought of each kind of coffee, but we do know that Kona beans cost $11 per pound and that Fuji beans cost $7.50 per pound, and we know that he spent a total of $197. So let's set that up:
11K + 7.50F = 197
Those are your 2 equations. It doesn't say you need to solve them, so you're done.

The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 9 miles. The length BC of the triangle is labeled as 6 miles. This length BC is also the length of an irregular gray shaded shape. Which of the following options is closest to the distance (in miles) between points A and B? 6.71 miles 7.35 miles 8.66 miles 10.82 miles.

Answers

6.71 miles

use the Pythagorean theorem 

6^2 + x^2 = 9^2

36 + x^2 = 81
81-36= 45 

square root of 45 is approximately 6.71 miles

Answer:

6^2 + x^2 = 9^2

36 + x^2 = 81

81-36= 45

square root of 45 is approximately 6.71 miles

Step-by-step explanation:

Using the theram theroy is very important to know the fulma and steps

Other Questions
How is light used in photosynthesis reddit? A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram? Predict what might happen if the broad ligament and other supporting ligaments were damaged by infection or injury Before world war 1 France and Russia had a military alliance this meant that each country promised to support the other in the event of war in 1914 Germany declared war on Russia by the end of the year both French and Russia troops were battling the German military Which type of substance is an environmental contaminant that causes harm to living organisms? Air bags are designed to __________. A. cushion impact in a collision B. work without passengers having to buckle up C. deploy at a harmless speed for passengers sitting within ten inches D. All of the above Este pas est situado en Sudamrica y su capital es La Paz. Investigators are most likely to use the case history method when they study Hope is desperate for the new designer purse that she saw while window shopping at her local mall. she knew every girl in school would covet her bag and wish to be like her. when she walked in, she whipped out her credit card, and purchased the $5,000 bag. this kind of purchasing is called: question 50 options: 1) conspicuous consumption 2) popular consumerism 3) designer consumerism 4) credit card consumerism Assume that y varies inversely with x. If y=12 when x=5, find y when x=3 The A) democratic B) populist C) RebublicanParty emphasized the role of ordinary or common citizens. Low voter turnout and political apathy endanger ________. if H(x)=4x-8 and j(x) = -x solve h{j(3)} five friends go out to lunch and they decide to split the bill evenly the bill comes out to 57.25 how much does each person owe? Les films policiers sont _____ films intressants. The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam? The way that the conflict in a story is resolved often reveals the storystheme.climax.plot.setting. What should the title of an essay give hints about? PLEASE HELP!!!!!During the Cold War Era, the Soviet Union believed one political party should be represented during governmental elections, while the United States argued - a minimum of six political parties must be included - elections should include multiple candidates and political parties - elections should be free of influence by political parties - a maximum of two political parties could participate in electionsWhat was the goal of the Berlin Airlift?- To assist citizens of East Germany who wanted to move to West Germany- To keep the people of West Berlin alive after the Soviet Union tried to starve them- To rescue military troops being held as prisoners by Soviet Union troops in East Berlin- To transfer as many citizens as possible from communist East Berlin into West Berlin A woman is admitted at 24 weeks' gestation with rupture of membranes, maternal fever, and premature labor.the care team offers the parents counseling.what is likely to be helpful Steam Workshop Downloader