The Groves basketball team did not record how many baskets were made by each player during the last game. Daniel remembers that he made three times as many baskets as Ben. Max knows that he made six more baskets than Ben. Mitchell is sure that he made fewer baskets than Ben. Christion is sure that he made the same number of baskets as Mitchell. Altogether the five players made 40 baskets. How many baskets did each player make?

Answers

Answer 1

Answers:

Ben = 6Max = 12Mitchell = 2Christion = 2Daniel = 18

Each count above refers to the number of baskets made for the given player.

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

Explanation:

For each player, let the following variables represent how many baskets were made

B = BenM = MaxT = MitchelC = ChristionD = Daniel

So for example, if D = 10, then this means Daniel made 10 baskets. Though for now, we're not sure what number replaces D or any given letter.

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

"Daniel remembers that he made three times as many baskets as Ben" tells us that D = 3B is one equation

We know another equation is M = B+6 since Max made six more baskets than Ben

Another equation is C = T because these two students (Christion and Mitchell) made the same number of baskets.

We also know that T < B since Mitchell made fewer baskets compared to Ben.

Altogether the boys made 40 baskets total, so B+M+T+C+D = 40

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

We have these five mathematical statements

D = 3BM = B+6C = TT < BB+M+T+C+D = 40

Let's focus on the last equation

B+M+T+C+D = 40

B+M+T+C+3B = 40 .... plug in D = 3B

4B+M+T+C = 40

4B+M+T+T = 40 .... plug in C = T

4B+M+2T = 40

4B+B+6+2T = 40 .... plug in M = B+6

5B+6+2T = 40

5B+2T = 40-6

5B+2T = 34

Now let's solve for T

5B+2T = 34

2T = 34-5B

2T = -5B+34

T = (-5B+34)/2

T = (-5B)/2 + 34/2

T = -2.5B + 17

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

We've eliminated everything but two variables at this point.

Let's say that x replaced B and y replaces T

We get the equation y = -2.5x + 17

If you graph this equation along with y = x, you'll find that the two equations intersect at roughly (4.857, 4.857)

Since we want T < B, this means we want y < x to be the case. The line y = -2.5x+17 goes downhill as we move from left to right. If x is smaller than 4.857, then x >= y. Otherwise, if x is larger than 4.857, then y < x

Furthermore, looking at a table of values for this equation shows that only (x,y) = (6,2) is a point on y = -2.5x+17 such that both x and y are positive and x is the larger value, and they are both integer coordinates.

All of this means that when B = 6, this pairs with T = 2. No other number pair is possible for these two students.

We then use this to find the other player's basket count

D = 3B = 3*6 = 18M = B+6 = 6+6 = 12C = T = 2

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

So we have the following results

B = 6M = 12T = 2C = 2D = 18

As a check,

B+M+T+C+D = 6+12+2+2+18 = 40

which confirms our answers.

Answer 2

9514 1404 393

Answer:

Ben: 6Daniel: 18Max: 12Mitchell: 2Christion: 2

Step-by-step explanation:

Let x and y represent baskets made by Ben and Mitchell, respectively. Then Daniel made 3x baskets, Max made (x+6) baskets, and Christion made y baskets. The total number is ...

  x + 3x +(x+6) +y +y = 40

  5x +2y = 34 . . . . . . . . . . . subtract 6

The other constraint on the solution is ...

  y < x . . . . . . . . . Mitchell made fewer baskets than Ben

__

We can see that 34 differs from a multiple of 5 by an even number, so (by inspection) we determine that (x, y) = (6, 2) is a solution to the equation. (It is also a solution to the inequality.)

Other possible solutions will require y increase by 5 as x decreases by 2, so those are ...

  (x, y) = {(6, 2), (4, 7), (2, 12), (0, 17)}

The only (x, y) pair that satisfies the inequality is the first one: (x, y) = (6, 2). Hence the numbers of baskets are ...

Ben: 6Daniel: 18Max: 12Mitchell: 2Christion: 2
The Groves Basketball Team Did Not Record How Many Baskets Were Made By Each Player During The Last Game.

Related Questions

Which ordered pair is a solution of y > 2x - 3?

a. (-1, -5)
b. (1, -5)
c. (2, 3)
d. (2, -2)

Answers

Answer:

c. (2,3)

Explanation:

PLEASE HELP

What was similar about Venice and Naples during the Renaissance?

Both were major port cities.
Both were home to the Medici.
Both were weapons-manufacturing cities.
Both were connected to Asian land routes.

Answers

Answer:

Both were major port cities. (A)

Step-by-step explanation:

Answer:

The correct answer is A. Both were major port cities

Step-by-step explanation:

I am 100% sure

PLZ help me with this question

Answers

Answer:

A

Step-by-step explanation:

:))

The answer is A eikenekskwneej

Pls help I’ll brainlest

Answers

Answer:

8

Step-by-step explanation:

Jeremiah bought x toy sets for $20 each and then a video game for $60. Jeremiah spent a total of $220. How may toy sets did he buy?

To find our answer, we can solve the equation:

20x + 60 = 220

        -60    -60

20x = 160

/20    /20

x = 8

Jeremiah bought 8 toy sets!

I hope this helps :)

$13,000 was borrowed from two sources, one that charges 15% simple interest and the other that charges 10% simple interest. If the total interest at the end of 1 year was $1750, how much money was borrowed from each source?

Answers

9514 1404 393

Answer:

$9,000 at 15%$4,000 at 10%

Step-by-step explanation:

Let x represent the amount borrowed at 15%. Then the amount borrowed at 10% is (13000-x). The interest at the end of the year is ...

  0.15(x) + 0.10(13000 -x) = 1750

  0.05x = 1750 -1300 . . . . . . . . . . . . simplify, subtract 1300

  x = 450(20) = 9000 . . . . . . . . . . multiply by 20

$9,000 was borrowed at 15%; $4,000 was borrowed at 10%.

Triangle EFG is dilated by a scale factor of į to form triangle E'F'G'. What is the
measure of side FG?

Answers

The answer is B 36 degreees

What is arctan(−1)?


Negative StartFraction 3 pi Over 4 EndFraction
Negative StartFraction pi Over 4 EndFraction
StartFraction pi Over 4 EndFraction
StartFraction 3 pi Over 4 EndFraction

Answers

Answer: -pi/4 and 3pi/4

Step-by-step explanation:

Whenever you're given an inverse trig function like this, think "tangent of what gives me -1?" There are multiple ways in which you can solve this; knowing how tangent work, guess checking sin/cos to get -1, or using a calculator. The only way tangent can be an integer is if the sine and cosine of the angle are equal.

The only spots on the pi circle where this happens is pi/4, 3pi/4, 5pi/4, and 7pi/4. Answers B and D are correct

Answer:

b

Step-by-step explanation:

just did it on edg 2020

Evaluate: xy+2x^2, if x=0.1 and y=9.8

Answers

Answer: 1

Step-by-step explanation:

[tex](0.1)(9.8)+2(0.1)^2\\0.98+0.02=1[/tex]

Try Photomath! I always use the app for evaluating

19. Eight hot dogs at the baseball park cost $28.
How much does one hot dog cost?
(let h = price of one hot dog)

Answers

Answer:

h= $3.50

Step-by-step explanation:

28 / 8 =

12. Ryan deposited $3,500 in a savings account with
an interest rate of 3% per year. How much simple
interest will he earn in 4 years?

Answers

The answer to this question is 420 dollars

Lara buys bananas for $0.59 per pound. Which expression represents the cost of p pounds of bananas?

Answers

You didn’t include the answer choices but is total=0.59p
No answer choices??! 0.59p

hellppppppooooooppppppppppp​

Answers

Answer:

A

hope i helped

What is 1/3+1/6 I thought it was 36 but my teacher said no so can you help me because I don’t under stand this work pls help I need it now

Answers

Answer:

1/2

Step-by-step explanation:

Given the mathematical expression;

[tex] \frac {1}{3} + \frac{1}{6} = 0 [/tex]

First of all, we would determine the lowest common multiple for 3 and 6.

Lcm = 6

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

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

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

Therefore, 1/3 + 1/6 = 1/2

Convert the fraction to a decimal 5/15

Answers

0.3333 repeating
Explanation:
5/15 simplified is equal to 1/3
1/3 as a fraction is 0.3333 repeating

Write the quadratic equation whose roots are 6 and -6, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)


Answers

Answer:

[tex]2x^2-6[/tex]

Step-by-step explanation:

If a quadratic equation has a root at a certain point, the x value must equal. zero.  If we want to have the function reach 6 and -6 as roots:

x = 6

x - 6 = 0

x = -6

x + 6 = 0

Combining the two we get (x+6)(x-6) which will give us a quadratic equation.

Expanding: [tex]x^2-6x+6x-6 = x^2-6[/tex]

The leading coefficient is the number before the variable with the highest power, which is 2: [tex]2x^2-6[/tex]

helppp!! For the given solid figure, find the value of the variable.

Answers

9514 1404 393

Answer:

  10 cm

Step-by-step explanation:

The diameter of the cylinder is 6 cm, so the length designated 'c' is the hypotenuse of a right triangle with legs 6 cm and 8 cm.

The Pythagorean theorem tells you the hypotenuse is ...

  c^2 = (6 cm)^2 + (8 cm)^2 = 100 cm^2

  c = √(100 cm^2) = 10 cm

The value of c is 10 cm.

_____

You may recognize these numbers as double those of a 3-4-5 right triangle.

What are possible name(s) for the y-coordinate?
A domain
B range
C dependent variable
D independent variable
E input
F output

Answers

Answer:

D. cmdjjcmcjdkxjjskxkxmjxjxkxjmxjddkkxxkxjjsikskkkxksk

Answer:

B. Range C. Dependent Variable F. Output

Step-by-step explanation:

To make an international telephone call, you need the for the country you are calling. The codes for country A, country B, and C are three consecutive integers whose sum is 90. Find the code for each country.

Answers

Answer: 3 consecutive integers

x = 1st integer (country A)

x + 1 = 2nd integer (country B)

x + 2 = 3rd integer (country C)

whose sum is 114

x + (x + 1) + (x + 2) = 114...combine like terms

3x + 3 = 114

3x = 114 - 3

3x = 111

x = 111/3

x = 37 <== country A

x + 1 = 37 + 1 = 38 <==country B

x + 2 = 37 + 2 = 39 <== country C

Step-by-step explanation:

Answer:

29, 30, 31

Step-by-step explanation:

(x) + (x+1) + (x + 2) = 90

3x + 3 = 90

x = 29

(29) + (30) + (31) = 90

The table shows the number of markers in different numbers of boxes.

Answers

Answer:







Explanation:

Answer: 12

Step-by-step explanation: 12+12 = 24 + 12 = 36+12=48+12=60

1) x² + x + 3 = 0 use the discriminant to tell whether the equation has two solution​

Answers

Answer:

The equation does not have any real solutions.

The equation only has two imaginary solutions.

Step-by-step explanation:

Step 1

Use Discriminant to check how many solutions does the equation have.

[tex] \large{D = {b}^{2} - 4ac}[/tex]

Let a = 1, b = 1 and c = 3 from the given equation.

[tex]D = {(1)}^{2} - 4(1)(3) \\ D = 1 - 12 \\ D = - 11[/tex]

Since the value of D is in negative. Therefore, the equation does not have any solutions.

Discriminant

[tex]D > 0 \longrightarrow \sf{two \: \: real \: \: solutions} \\ D = 0 \longrightarrow \sf{one \: \: real \: \: solution} \\ D < 0 \longrightarrow \sf{two \: \: imaginary \: \: solutions} [/tex]

A cellular phone network uses towers to
transmit calls. If the equation of the circular area
transmits by the tower is represented by (x-5)2 +
ly-1)2 = 22. Can you identify if you are inside or
outside of the circular area, if your coordinate
location is (6,0)? How about if your location is
(8,2)?​

Answers

Answer:

Both [tex](6,\, 0)[/tex] and [tex](8,\, 2)[/tex] are inside this circular area.

[tex](6 - 5)^{2} + (0 - 1)^{2} = 2 < 22[/tex].

[tex](8 - 5)^{2} + (2 - 1)^{2} = 10 < 22[/tex].

Step-by-step explanation:

Equation for a circle in 2D, with center [tex](a,\, b)[/tex] and radius [tex]r[/tex]:

[tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex].

Compare this expression with the one from this question:

[tex](x - 5)^{2} + (y - 1)^{2} = 22 = \left(\sqrt{22}\right)^{2}[/tex].

Hence: [tex]a = 5[/tex], [tex]b = 1[/tex], and [tex]r = \sqrt{22}[/tex].

Therefore, [tex]\! (5,\, 1)[/tex] and [tex]\sqrt{22}[/tex] would be the center and the radius of the circle [tex](x - 5)^{2} + (y - 1)^{2} = 22[/tex].

A point is inside a circle if and only the Euclidean distance between that point and the center of that circle is smaller than the radius of the circle. That is the same as requiring that the square of the Euclidean distance between these two points to be smaller than the square of the radius of the circle.

Formula for the Euclidean distance between [tex](x_1,\, y_1)[/tex] and [tex](x_2,\, y_2)[/tex]:

[tex]\displaystyle \sqrt{(x_1 - x_2)^{2} + (y_1 - y_2)^{2}}[/tex].

The square of the Euclidean distance between these two points would be:

[tex]\displaystyle (x_1 - x_2)^{2} + (y_1 - y_2)^{2}[/tex].

Calculate the square of the distance between [tex](6,\, 0)[/tex] and the center of the circle, [tex](5,\, 1)[/tex].

[tex](6 - 5)^{2} + (0 - 1)^{2} = 2[/tex].

The square of this distance is smaller than [tex]22[/tex], the square of the radius of this circle. Hence, the point [tex](6,\, 0)[/tex] is inside this circle.

Similarly, calculate the square of the distance between [tex](8,\, 2)[/tex] and the center of the circle, [tex](5,\, 1)[/tex].

[tex](8 - 5)^{2} + (2 - 1)^{2} = 10[/tex].

The square of this distance is smaller than [tex]22[/tex], the square of the radius of this circle. Hence, the point [tex](8,\, 2)[/tex] is also inside this circle.

Notice that the point [tex](x,\, y)[/tex] is on the 2D circle [tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex] if and only if [tex]x[/tex] and [tex]y[/tex] satisfy the equation of that circle.

On the other hand, [tex](x,\, y)[/tex] is inside this circle if and only [tex]x[/tex] and [tex]y[/tex] satisfy the inequality [tex](x - a)^{2} + (y - b)^{2} < r^{2}[/tex].

Both [tex](6,\, 0)[/tex] and [tex](8,\, 2)[/tex] satisfy the inequality [tex](x - 5)^{2} + (y - 1)^{2} < 22[/tex]. Hence, both points are inside the circle [tex](x - 5)^{2} + (y - 1)^{2} = 22[/tex].

4 cups to 8 pints write each ratio in simplest form

Answers

Answer:

1:4

Step-by-step explanation:

Convert 8 pints into cups which we can do this by 8x2=16 we can do this because 1 pint=2 cups. So know we have 4:16 which we can simplify to 1:4

Hope this helps :)

The cookie recipe had the ratio of oatmeal to raisins as 5 to 1. If 6 cups of oatmeal is required, how
many cups of raisins are needed?

Answers

Answer:

1.2 cups of raisins or 1 and 1/5 cups of raisins. (Same thing) :)

Step-by-step explanation:

6/5 is 1.2. So multiply the 1 by 1.2 as well to get 1.2. This was solved by using proportions.

Hope it helps!

How do u do this one ???

Answers

Girl is that the elpac test!!!

2/3-5/9 find each difference

Answers

Answer:

1/9

Step-by-step explanation:

6-5/9

1/9

Answer:

2/3=6/9 (Equilising denominators using lcm)

Now we have equal denominators, so can subtract.

Therefore,

6/9-5/9

=6-5/9

=1/9

what is the additive inverse of the complex number -8+3i​

Answers

Answer:

8-3i

Step-by-step explanation:

additive inverse of a+bi is -(a+bi)

so -(-8+3i) -- distribute negative through ()

8-3i

3 1/2 + 8 3/4 + 7 5/12 + 1 1/5 = ​

Answers

Answer:

25 3/5

Step-by-step explanation:

i think

Answer:

7/2+35/4+89/12+6/5=210+525+445+72/60=1252/60=313/15

Step-by-step explanation:

an = n2- 5
A) {1, -4, 4, 11, 116...}
B) {1, 2, 3, 4, 5, 6, ...}
C) { -4, 11, 116, 13451,...}
D) { -4, -1, 4, 11, 20,...}

Answers

Answer:

D

Step-by-step explanation:

if to substitute values of n=1;2;3;4;5 into

[tex]a_n=n^2-5[/tex]

then a₁=-4; a₂=-1; a₃=4; a₄=11; a₅=20.

It means the answer {-4, -1, 4, 11, 20,...} is correct.

PLZ ANSWER THESE QUESTIONS IF YOU KNOW ALGEBRA PLZ PLZ PLZ PLZZZZZZZZZZZZ I WILL GIVE BRAINLY AND ALL MY POINTS PLZZ HELP ME
I AM A YOU TUBER I WILL CHEAT IF I HAVE TO

Answers

Answer:

Algebra (from Arabic: الجبر‎ al-jabr, meaning "reunion of broken parts"[1] and "bonesetting"[2]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;[3] it is a unifying thread of almost all of mathematics.[4] It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.[5] For example, in {\displaystyle x+2=5}x+2=5 the letter {\displaystyle x}x is an unknown, but applying additive inverses can reveal its value: {\displaystyle x=3}x=3. In E = mc2, the letters {\displaystyle E}E and {\displaystyle m}m are variables, and the letter {\displaystyle c}c is a constant, the speed of light in a vacuum. Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words.

The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology.

A mathematician who does research in algebra is called an algebraist.

You are making peanut butter and jelly sandwiches. The cost of 4 containers of peanut butter and 7 containers of jelly is $6.95. Eight containers of peanut butter and 6 containers of jelly cost $8.45. Find the cost of each container of peanut butter.


HELPP ME
PLEASEEEEEEEHEHASHEJ

HELPPP

Answers

Answer:

peanut butter cost $0.55

Step-by-step explanation:

j=jelly

p=peanut butter

4p+7j=$6.95

8p+6j=$8.45

solve for p:

8p=8.45-6j

p=(8.45-6j)/8

substitute for p

4(8.45-6j)/8+7j=6.95

reduce

(33.8-24j)/8+7j=6.95

4.225-3j+7j=6.95

4j=6.95-4.225

4j=2.725

j=0.68125

8p+6(0.68125)=8.45

8p+4.0875=8.45

8p=4.3625

p=0.5453

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