each team plays 9 games
( Team 1 plays team 2 3 times, team 3 3 times, team 4 3 times )
9 x 4 = 36 games total
Write log3 6 as a logarithm of base 2
a. log base 2 of 3 over log base 2 of 6
b. log base 2 of 6 over log base 2 of 3
c. log base 3 of 2 over log base 6 of 2
d. log base 6 of 2 over log base 3 of 2
Final answer:
The expression log3 6 can be converted to a logarithm of base 2 using the change of base formula, which results in log2 6 / log2 3. So the correct option is b.
Explanation:
The student asked how to express log3 6 as a logarithm with a base of 2. To perform this conversion, we can use the change of base formula, which states that logab = logcb / logca for any positive numbers a, b, and c, where a and c are not equal to 1. In this formula, 'c' can be any base, but in our case, we will use base 2 since that's what the question requires.
So, by applying the change of base formula, we can write:
log₃6 = log₂6 / log₂3Therefore, the correct option that represents log3 6 as a logarithm of base 2 is:
(b) log₂6 / log₂3A mountain climber ascends 800 feet per hour from his original position. After 6 hours, his final position is 11,600 feet above sea level. Find the climber's position.
Can anyone help me please? I would really appreciate it! Thank you :D
It takes 1.25 seconds for light to travel from the moon to the earth how many miles away is the moon
A student has some $1 and $5 bills in his wallet. he has a total of 1919 bills that are worth $5959. how many of each type of bill does he hav
What you s 50 percent of 2.98
Answer:
1.49
Step-by-step explanation:
50% of 2.98 is 1.49
Two bags had 100 kilograms of sugar each. after taking out 3 times as much sugar from bag one than bag two, bag one had half as much sugar left as bag two. how much sugar is left in each bag?
According to the given statement, we can get the equation:
50 - 3x = 1/2 (50-x)
where x = amount removed from bag two, 3x removed from bag one
Then we multiply both sides by 2 (to eliminate the ½)
100-6x= 50-x
Add 6x to both sides
100= 50-5x
Then subtract 50 from both sides
50=5x
Lastly, divide by 5
10=x
Therefore 10 kg of sugar was removed from bag 2
further, 3x= 30, so 30 kg of sugar was removed from bag 1.
50-30=20 kg remaining in bag 1.
50-10=40 kg remaining in bag 2.
Answer:
40 kg in the first bag, 80 in the second
Step-by-step explanation:
Classify each number as a Natural number, Whole Number, Integer, Rational Number, or Irrational. (Write all that apply)
a)-40 b)5 c) -14/11 d)√34 e) -√16
A soccer player who is 27 feet from a goal attempted to kick the ball in into the goal. the flight of the ball is modeled by a parabola. the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. the goal has a height of 8 feet. will the soccer ball land in the goal?
Answer:
The ball will land inside the goal.
Step-by-step explanation:
Given : The flight of the ball is modeled by a parabola.
To find : Will the soccer ball land in the goal?
Solution :
Let the equation of the parabola be,
[tex]y=a(x-h)^2+k[/tex]
Where, (h,k) are the vertex of the parabola,
According to question,
A soccer player who is 27 feet from a goal.
Let A be the point where player stand i.e, (27,0)
The height of the goal is 8 feet.
Let B be the point of height of goal i.e, (0,8)
The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.
The distance from goal to the distance 15 feet away from the player is
27-15=12 feet
Let C be the point with maximum height i.e, (12,10)
C is the vertex of the parabola and A is the point on the parabola.
Then, The equation of parabola is
[tex]y=a(x-12)^2+10[/tex]
Point A satisfy the equation,
[tex]0=a(27-12)^2+10[/tex]
[tex]0=a(15)^2+10[/tex]
[tex]a=-\frac{10}{225}[/tex]
Substitute back in equation,
[tex]y=-\frac{10}{225}(x-12)^2+10[/tex]
Now, we find the y-intercept of the equation i.e, x=0,
[tex]y=-\frac{10}{225}(0-12)^2+10[/tex]
[tex]y=-\frac{10}{225}(144)+10[/tex]
[tex]y=3.6[/tex]
If the y-intercept is greater than 8 then the ball will land outside the goal.
If the y-intercept is less than 8 then the ball will land inside the goal.
As 3.6<8
Therefore, The ball will land inside the goal.
Refer the attached figure below.
Final answer:
The soccer ball will not land in the goal due to its maximum height being above the height of the goal.
Explanation:
To determine if the soccer ball will land in the goal, we need to analyze its flight path. From the given information, we know that the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. This indicates that the ball's flight path is modeled by a downward-opening parabola.
Since the soccer player is 27 feet from the goal, we can consider the ball's horizontal distance from the player to the goal as the x-coordinate, and its height above the ground as the y-coordinate.
Based on the given information, the soccer ball will not land in the goal. The ball's maximum height is 10 feet, but the goal has a height of 8 feet. This means that at any point along its flight path, the ball's height will be above the height of the goal.
Which number(s) below belong to the solution set of the inequality?
Check all that apply. x/8<10
A.80
B.96
C.64
D.40
E.32
F.88
A customer ordered fourteen zingers. zingers are placed in packages of four, three, or one. in how many different ways can this order be filled?
The number of different ways this order can be filled is:
13 ways.
Step-by-step explanation:A customer ordered fourteen zingers.
zingers are placed in packages of four, three, or one.
Case-1
If the number of packages of four are: 3
Then 4×3=12 zingers.
a)
So, there will be zero packet of 3.
and 2 packs of 1.
Since, 12+2×1=14
Case-2
If the number of packages of four are: 2
i.e. 4×2= 8 zingers.
a)
If number of packages of 3 are: 2
i.e. 3×2=6
then number of package of 1 have to be 0.
b)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Number of packages of 1 zinger will be: 3
i.e. 8+3+3=14
c)
If number of packages of 3 are: 0
Then number of packets of 1 will be: 6
Case-3
If the number of packages of four are: 1
a)
If number of packages of 3 are: 3
i.e. 3×3=9 zingers.
Hence, number of packets of 1 have to be: 1
b)
If number of packages of 3 are: 2
i.e. 3×2=6 zingers
Then number of packets of 1 have to be: 4
c)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Then number of packets of 1 have to be: 7
d)
If number of packages of 3 are: 0
i.e. 3×0=0 zingers
Then number of packets of 1 have to be: 10
Case-4
If the number of packages of four are: 0
a)
If number of packages of 3 are: 4
i.e. 3×4=12 zingers
Then number of packets of 1 have to be: 2
b)
If number of packages of 3 are: 3
i.e. 3×3=9 zingers
Then number of packets of 1 have to be: 5
c)
If number of packages of 3 are: 2
i.e. 3×2=6 zingers
Then number of packets of 1 have to be: 8
d)
If number of packages of 3 are: 1
i.e. 3×1=3 zingers
Then number of packets of 1 have to be: 11
e)
If number of packages of 3 are: 0
i.e. 3×0=0 zingers
Then number of packets of 1 have to be: 14
There are total 13 ways of doing so.
( 1 from case-1
3 from case-2
4 from case-3
and 5 from case-4
i.e. 1+3+4+5=13 ways )
The order can be filled in 5 different ways by using packages of 4, 3, or 1 zingers.
Explanation:To find the number of different ways the order can be filled, we can use the concept of permutations and combinations. Since zingers can be placed in packages of 4, 3, or 1, we need to find all the possible combinations of these packages that add up to 14.
For packages of 4, we can have 1 package of 4 and 2 packages of 5, for a total of 2 combinations.For packages of 3, we can have 1 package of 3 and 3 packages of 5, for a total of 2 combinations.For packages of 1, we can have 7 packages of 1, for a total of 1 combination.Therefore, the total number of different ways the order can be filled is 2 + 2 + 1 = 5.
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Jacob is ordering custom T-shirts for his soccer team. Long-sleeved shirts cost $15 each and short-sleeved shirts cost $10 each. Jacob can spend at most $250 and he wants to order at least 20 shirts.
Let x represent the number of long-sleeved shirts. Let y represent the number of short-sleeved shirts.
Which inequalities are among the constraints for this situation?
Select each correct answer.
⋅ 15x + 10y ≥ 20
⋅ x + y ≤ 250
⋅ x + y ≥ 20
⋅ 15x + 10y ≥ 250
⋅ 15x + 10y ≤ 250
⋅ x + y ≤ 20
x + y ≥ 20 ( total number of shirts at least 20)
15x + 10y ≤ 250 ( total amount spent no more than $250)
These are the answers.
3. x + y ≥ 20
5. 15x + 10y ≤ 250
Hope this helps and have a wonderful day!
Solve the quadratic equation by completing the square. x^2+6x-6=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
A has $32 more than B, and B has five times as much money as C. If C has d dollars, how much does A have? Answer:
A = B+32
B = 5C
A = 5C+32
C has d dollars so replace d for c
A = 5d+32
One side of a triangle is 4 inches longer than the side that is the base of the triangle. the third side is 6 inches longer than the base. of the perimeter is 34 inches, find the length of each side.
Final answer:
The base of the triangle is 8 inches, one side is 12 inches (base + 4), and the other side is 14 inches (base + 6). Hence, the side lengths of the triangle are 8 inches, 12 inches, and 14 inches, with a total perimeter of 34 inches.
Explanation:
The question describes a triangle with sides of varying lengths relative to what is defined as the base of the triangle. To find the length of each side, we'll use algebra and the fact that the perimeter of the triangle is given as 34 inches.
Let's denote the base as b. According to the problem, one side is 4 inches longer than the base, which would be b + 4 inches. The third side is 6 inches longer than the base, which would be b + 6 inches. The perimeter of a triangle is the sum of all its sides, so we have:
b + (b + 4) + (b + 6) = 34
Combining like terms, we get:
3b + 10 = 34
Subtracting 10 from both sides gives us:
3b = 24
Dividing by 3 gives us the length of the base:
b = 8 inches
Now, we can find the lengths of the other two sides:
b + 4 inches is 12 inches and b + 6 inches is 14 inches.
So, the lengths of the sides of the triangle are 8 inches, 12 inches, and 14 inches.
Find the common ratio for the following sequence
27,9,3,1
Answer:
The common ratio is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given sequence,
27, 9, 3, 1
Since,
[tex]\frac{9}{27}=\frac{3}{9}=\frac{1}{3}[/tex]
Hence, in the given sequence the ratio of a term to its previous term is [tex]\frac{1}{3}[/tex]
Therefore, we can say that,
The common ratio of the given sequence is [tex]\frac{1}{3}[/tex]
A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon. How many yards are on one roll of lace ribbon and one roll of satin ribbon?
Answer:
20 and 30. that's your answer.
Step-by-step explanation:
A recipe calls for 12 ounces of flour, but your scale shows only pounds. The recipe requires __________ pounds of flour. Enter your answer as the decimal number that correctly fills in the blank in the previous sentence. If necessary, round to the nearest hundredth, like this: 42.56 Hint: 1 pound=16 ounces 67 pts
How do i solve this for x
the slope of the line passing through the points (-6,3)and(-6,39) is
The slope of the line passing through points is undefined.
What is slope of a line?The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The line passing through points (x1, y1) is (-6, 3) and (x2,y2) is (-6, 39)
The formula of slope of line is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
⇒ [tex]m=\frac{39-3}{-6-(-6)}[/tex]
⇒ [tex]m=\frac{39-3}{-6+6}[/tex]
⇒ [tex]m=\frac{39-3}{0}[/tex]
⇒ [tex]m=\infty[/tex]
Since x1 = x2, there is no horizontal change. The line passes as a straight line.
Hence we can conclude that the slope of the line passing through points is undefined.
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Julie started solving the equation 3x=4+2(3−x). which is a correct next step?
Answer:
Distribute 2 inside the parenthesis
Step-by-step explanation:
Julie started solving the equation
3x=4+2(3−x)
To simplify any expression we use order of opeation PEMDAS
Always start simplifying the parenthesis
To remove parenthesis we apply distributive property
Distribute 2 inside th4e parenthesis
3x=4+2(3−x)
3x=4+6-2x
So next step is distributing 2 inside the parenthesis
3x=4+6-2x
What what are the rules for addition and subtraction with numbers in scientific notation?
An equation that is true for all real numbers for which both sides are defined is called a(n)
An equation that is true for all real numbers for which the operations are defined is called an identity. It is always true no matter the values of its variables. An example is sin²(x) + cos²(x) = 1
Explanation:An equation that is true for all real numbers for which both sides are defined is called an identity. An identity equation is always true, no matter what values are substituted for its variables. For example, the equation sin²(x) + cos²(x) = 1 is an identity because it is valid for all real numbers x.
Identity equations commonly appear in branches of math such as algebra and trigonometry.
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Attempting to use the regression equation to make predictions beyond the range of the data is called _______.
Which statement is true with respect to the Euclidean approach to geometry?
Answer:
I would think the answer is "axioms are used to prove theorems"
Step-by-step explanation:
Harriet earns the same amount of money each day. Her gross pay at the end of 7 work days is 35h + 56 dollars. Which expression represents her gross pay each day?
Answer:
Daily Payment = 5h+8
Step-by-step explanation:
Here we are given that in seven days the amount Harriet earned is given as
35h+56
It is also given that the amount earned each day is same.
We have to determine the amount earned each day. Total number of days is 7 . Hence in order to find the daily earning we divide the total earning by 7
Daily earning =
[tex]E=\frac{35h+56}{7}\\E=\frac{7(5h+8)}{7}\\E=5h+8[/tex]
Hence answer is 5h+8
x + y = 0 x - y = 8 What is the solution of the system shown?
A; (-8, 12)
B; (8, -12)
C; (8, 12)
Sari has a bag containing 6 half dollars. What is the mass of half dollars in Sari's bag when half dollars weighs 11.34 grams?
1.Given: Triangle PQR with m∠P=(2x)° , m∠Q=(4x)° , and m∠R=(6x)° .
Prove: x = 15
By the triangle sum theorem, the sum of the angles in a triangle is equal to 180°. Therefore, m∠P+m∠Q+m∠R=180° . Using the ,__________ (2x)°+(4x)°+(6x)°=180° . Simplifying the equation gets 12x = 180. Finally, using the division property of equality, .___________
answer to each box to complete
substitution property, distributive property, angle addition postulate, x=12 x=15 x=30
we have
m∠P=[tex](2x)\°[/tex]
m∠Q=[tex](4x)\°[/tex]
m∠R=[tex](6x)\°[/tex]
1) By the triangle sum theorem, the sum of the angles in a triangle is equal to [tex]180\°[/tex]
therefore
m∠P+m∠Q+m∠R=[tex]180\°[/tex]
we know that
Substitution Property of Equality, states that If the values of two quantities are known to be equal, you can replace the value of one quantity with the other
so
2) Using the Substitution Property of Equality
[tex](2x)\°+(4x)\°+(6x)\°=180\°[/tex]
Simplifying the equation gets
[tex](12x)\°=180\°[/tex]
3) using the division property of equality
The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal
[tex](12x)\°/12=180\°/12[/tex]
[tex]x=15\°[/tex]
therefore
the answer is
Part a) Substitution Property of Equality
Part b) [tex]x=15\°[/tex]
Answer:
Part a) Substitution Property of Equality
Part b) x=15
Step-by-step explanation:
Given triangle PQR with
[tex]m\angle P=(2x)^{\circ}[/tex]
[tex]m\angle Q=(4x)^{\circ}[/tex]
[tex]m\angle R=(6x)^{\circ}[/tex]
By the triangle sum property, the sum of the angles of a triangle is equal to [tex]180^{\circ}[/tex]
∴ m∠P+m∠Q+m∠R=180°
Substitution Property of Equality, states that If the values of two quantities are known to be equal, one can replace the value of one quantity with the other
[tex](2x)^{\circ}+(4x)^{\circ}+(6x)^{\circ}=180^{\circ}[/tex]
Simplifying the equation we get
[tex](12x)^{\circ}=180^{\circ}[/tex]
Using the division property of equality
The Division Property of Equality states that division with the same non zero number results that both sides remain equal
[tex]\frac{(12x)^{\circ}}{12}=\frac{180^{\circ}}{12}[/tex]
[tex]x=15[/tex]
Hence, the answer is
Part a) Substitution Property of Equality
Part b) x=15
Define a variable and write an equation for each situation. Solve each equation to answer the question.
A plumber finished three jobs on Tuesday. The first two only cost the owner $45 trip fee because they took very little time to complete. For the third job, the plumber charged the trip fee plus 6 times his hourly rate. If the plumber received a total of $303 for the day, what is the hourly rate?
H = Hourly Rate
for my Equation I made,
5(45)+6h=303
but cant figure out how to solve it
(9th Grade ALG 1)
Plz work out the problem, thnx :-)