To bowl two games costs $7 and to bowl four games it costs $14. What equation can be written to show the relationship between the cost, c, and the number of games, g, bowled?
If you divide 7 by 2 it equals 3.5 meaning each game is 3.5 dollars. So you can find how much any number of games would be by using this equation g (3.5) = c For example, if there were 3 games then you would do 3 (3.5) = c and the cost would be 10.5 dollars.
Final answer:
The relationship between the cost and the number of games bowled can be represented by the equation c = 3.5g, where c is the total cost and g is the number of games bowled.
Explanation:
To determine the relationship between the cost (c) and the number of games (g) bowled, we need to find a formula that connects these two quantities based on the information provided. Given that bowling two games costs $7 and bowling four games costs $14, we can see that the cost is directly proportional to the number of games bowled. This means for every game bowled, there is a fixed rate being paid.
Let's break down the information given:
2 games = $7
4 games = $14
From this, we can see that each game costs $3.50 because $7 divided by 2 equals $3.50. Therefore, the relationship between the cost and the number of games can be represented by the equation:
c = 3.5g
Where c represents the total cost and g represents the number of games bowled. This equation can be used to calculate the cost for any number of games bowled.
Select Equal or Not Equal to correctly classify each statement.
Only the second row is equal. The first row can't be equal because it says -2=-1/2
onsider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36 Step 1 ⇒ 3x − 12 + 5x = 9x − 36 Step 2 ⇒ 3x + 5x − 12 = 9x − 36 Step 3 ⇒ 8x − 12 = 9x − 36 Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36 Step 5 ⇒ 0 − 12 = x − 36 Step 6 ⇒ −12 = x − 36 Step 7 ⇒ −12 + 36 = x − 36 + 36 Step 8 ⇒ 24 = x + 0 Step 9 ⇒ 24 = x Which property yields Step 6? A) Additive Inverse Property B) Additive Identity Property C) Addition Property of Equality D) Commutative Property of Addition
3(x - 4) + 5x = 9x - 36 Given
(3)(x) + (3)(-4) + 5x = 9x - 36 Distributive Property
3x - 12 + 5x = 9x - 36
(3x + 5x) - 12 = 9x - 36 Combine like terms
8x - 12 = 9x - 36
8x - 8x - 12 = 9x - 8x - 36 Subtraction Property of Equality
0 - 12 = x - 36 Additive Identity Property
-12 = x - 36
-12 + 36 = x - 36 + 36 Addition Property of Equality
24 = x
Answer: Additive Identity Property
Answer:Additive Identity Property
Step-by-step explanation:
Best estimate for 61/7
I would say the best estimate would be 9 because the real answer is 8.71 and if you round that to the 1 place the answer would be 9.
Which number sentences show how to solve the problem?
The truck driver loaded 72 crates of eggs. There are 36 eggs in each crate. The driver will make 6 deliveries and unload the same number of eggs at each delivery stop.
How many eggs will the driver unload at each stop?
Choose all answers that are correct.
72 ÷ 6 = 12 and 12 × 36 = 432
72 ÷ 6 = 12 and 12 × 12 = 144
72 ÷ 36 = 2 and 2 × 72 = 144
72 × 36 = 2,592 and 2,592 ÷ 6 = 432
72 ÷ 6 = 12 and 12 × 36 = 432 and 72 × 36 = 2,592 and 2,592 ÷ 6 = 432
27 pounds of recyclable trash is what percentage of the barrel of 53 pounds of trash
50.94339623 percent boiii
Answer:
50.9%
Step-by-step explanation:
We are asked to find 27 pounds of recyclable trash is what percentage of the barrel of 53 pounds of trash.
We need to find 27 is what percent of 53. We can represent this information in an equation as:]
[tex]\frac{27}{53}\times 100[/tex]
[tex]0.5094339\times 100[/tex]
[tex]50.94339\%\approx 50.9\%[/tex]
Therefore, 27 pounds of recyclable trash is 50.9% of the barrel of 53 pounds of trash.
a house is valued £210 000, correct to 2 significant figures, what is the lowest possible value of the house and the highest possible value of the house?
The lowest possible value of the house is £205000 and highest possible value is £214999.99...
Given that:
The house is valued £210000, correct to 2 significant figures.
Since its correct to 2 significant figures, thus there is error of approx 10000 range in £210000
The lowest possible number that would round up to 2 significant numbers to £210000 is £205000 since any value lower than that would look like £204..... which won't round up to £21..... but £20....
Similarly, the highest possible number that would round up to 2 significant figures to £210000 is £214999.999... since any real number bigger than that would make starting digit of the number as £215.... and thus 2 significant figure rounding will lead to £22....
Thus, the lowest possible value of the house is £205000 and highest possible value is £214999.99...
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Jk has endpoints J(-1, 10) and K(-5, 2). MN had the endpoints M(9, -7) and N(1, -3). is JK congruent to MN?
Answer:
It's true that [tex]JK \cong MN[/tex]
Step-by-step explanation:
If the lengths of two line segments are equal, then they are said to be congruent to each other.
[tex]JK[/tex] has endpoints as [tex]J(-1, 10)[/tex], [tex]K(-5,2)[/tex] and [tex]MN[/tex] has endpoints as [tex]M(9,-7), N(1,-3)[/tex]
Formula for finding the length of line segment: [tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}[/tex] , where [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] are two endpoints.
So, the length of [tex]JK = \sqrt{(-1-(-5))^2+(10-2)^2}= \sqrt{(4)^2+(8)^2}= \sqrt{16+64}= \sqrt{80}[/tex]
and the length of [tex]MN=\sqrt{(9-1)^2+(-7-(-3))^2}= \sqrt{(8)^2+(-4)^2}= \sqrt{64+16}= \sqrt{80}[/tex]
As, the lengths of [tex]JK[/tex] and [tex]MN[/tex] are equal, so we can say that, [tex]JK[/tex] is congruent to [tex]MN[/tex].
To determine if JK is congruent to MN, use the distance formula to find the lengths of the line segments. If the lengths are equal, then the segments are congruent.
Explanation:To determine if JK is congruent to MN, we need to compare the lengths of these line segments. The formula for finding the length of a line segment with endpoints (x1, y1) and (x2, y2) is the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
For JK: d = sqrt((-5 - (-1))^2 + (2 - 10)^2) = sqrt((-4)^2 + (-8)^2) = sqrt(16 + 64) = sqrt(80).For MN: d = sqrt((1 - 9)^2 + (-3 - (-7))^2) = sqrt((-8)^2 + (4)^2) = sqrt(64 + 16) = sqrt(80).Since the lengths of JK and MN are equal (sqrt(80) = sqrt(80)), we can conclude that JK is congruent to MN.
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(6,-2),(r,-6),m=4 find the value of r so that the line passes through each pair of points has a given slope
r = 5
calculate the slope m using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with ( x₁, y₁ ) = (6, - 2 ) and (x₂, y₂ ) = (r, - 6)
m = [tex]\frac{-6+2}{r-6}[/tex] = [tex]\frac{-4}{r-6}[/tex] = 4
cross multiply
4(r - 6 ) = - 4
4r - 24 = 4 ( add 24 to both sides and divide by 4 )
4r = 20
r = [tex]\frac{20}{4}[/tex] = 5
The value of r so that the Slope of a line passes through the points (6,-2) and (r,-6) with a slope of 4 is 7.
In mathematics, the slope of a line through two points can be determined using the formula m = (y2 - y1) / (x2 - x1), where m is the slope, (x1, y1) and (x2, y2) are the coordinates of two points on the line.
In your case, the given points are (6, -2) and (r, -6) and the slope (m) is given to be 4. So, insering these values in the formula, you get: 4 = (-6 - (-2)) / (r - 6).
By simplifying the above equation, we find that r = 7.
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The total area of both plots of land is?
You have 2x^2 + 9x -9 and 3x^2 -2x +14
To find total area add the two polynomials together by combining the like terms.
2x^2 + 3x^2 = 5x^2
9x + -2x = 9x-2x = 7x
-9 + 14 = 5
Total area = 5x^2 + 7x + 5
Help me please , and thank you .
Remark
There is a 4 year difference between Sal and Carrie. Carrie is the older. She is going to occupy 1 side of the equation. The other side is Sal and the 4 years.
Let Sal = S
Let Carrie = C
Carrie = Sal + 4
Equation
C = S + 4
Samuel and Leticia are playing a game. After the first round of the game, Samuel's score was -19 and Leticias score was 21. The score with the greater absolute value wins each round. Who won the first round? Explain
Answer: Leticia won the first round
==============================================================
Your teacher is basically asking "which value is further from zero on the number line?". The value -19 is 19 units away from zero; while 21 is 21 units away from zero.
See the attached image below. Each "space" is a distance of 1
Absolute value measures distance along the number line. Distance is never negative. In terms of notation, you would say
|-19| = 19 and |21| = 21
The outputs 19 and 21 are then compared. We see that 21 is larger, so therefore, Leticia has the higher score and she won the first round.
what is the greatest common factor of 16y^3 z^3 and 56y^4z
Answer:
8y^3z
Step-by-step explanation:
8, y^3 and z are common to both expressions. Thus, the GCF is 8y^3z.
what's the value of y
(3y +10) /4 = 2y
Multiply both sides by 4:
4(3y +10) = 4(2y)
12y +40 = 8y
Subtract 40 from each side:
12y = 8y -40
Subtract 8y from each side:
4y = -40
Divide both sides by 4:
y = -40 / 4
y = -10
The answer is A. -10
An= -6+7n calculate A30
[tex]a_n=-6+7n\\\\a_{30}\to \text{substitute n = 30}\\\\a_{30}=-6+(7)(30)=-6+210=214[/tex]
DOES ANYONE KNOW THE ANSWER??!
The answer might be c
Record the product 51 times 77
the answer is 128 because 51 + 77= 128
The product is 3927.
Estimate by rounding. 121÷42
Answer:
2.88095238095
Step-by-step explanation:
What is the fifth term of a number pattern that begins with 32 and adds 5? A. 47 B. 42 C. 52 D. 57
The answer you want would be C.52
Reason: 32+5= 37 that is the 1st and 2nd term. 37+5=42 thatis the 3rd term. 42+5=47 that's the 4th term. And 47+5=52 that's the 5th term.
Hope it helps!!
Teaser) What is the measure of the angle between the minute and the hour hands, when they show 3:05 PM?
If it were 3:00 precisely then it would be 90 degrees.
The minute hand moves 360 degrees per hour so 5 minutes makes it 30 degrees closer to the hour haned.
The hour hand moves 360 degrees per 12 hours (720 minutes) so 5 minutes make it move 2.5 degrees further from the minute hand.
90 degrees -30 degrees + 2.5 degrees = 62.5 degrees
Answer:
30° angle between the minute and the hour hands, when they show 3:05 PM.
Step-by-step explanation:
Given : 3:05 PM
To find : What is the measure of the angle between the minute and the hour hands.
Solution : We have given clock that showing time 3:05 PM
We know that clock make the complete angle that is 360 degree.
We know 1 hour = 60 minute.
So, angle formed by 60 minute = 360 °.
Angle formed by 1 minute = [tex]\frac{360}{60}[/tex].
Angle formed by 1 minute = 6°.
According to question :
At 3:05 pm
Total minute between minute hand and hour hand is 5.
So. Angle formed by 5 minute = 5 * 6 .
Angle formed by 5 minute = 30° .
Therefore, 30° angle between the minute and the hour hands, when they show 3:05 PM.
5 /9 of students at a school are girls. If there are 4041 students at the school, how many are boys?
i bleieve the answer is 1796
Out of 4041 students in a school where 5/9 are girls, the number of boys in the school will be 1796.
Explanation:In this mathematics problem, we are looking to find the number of boys in a school where we know the total number of students (4041) and the proportion that are girls (5/9). To start, you can determine the number of girls in the school by multiplying the total number of students by the proportion of students that are girls (4041 * 5/9 = 2245). Taking this number of girls away from the total number of students gives us the number of boys: 4041 - 2245 = 1796. So, out of 4041 students, 1796 of them are boys.
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during his first year as a pilot, rob flies 6,692 miles. he flies 16,429 miles the second year and 24,211 miles the third year. he wants to estimate how many more miles he flew in the third year than the first and second year combined. which shows one way rob could estimate?
First years flies = 6,692 miles ≈7000 miles.
Second year flies = 16,429 miles ≈ 16000.
Third year flies = 24,211 miles ≈ 24000
Total number of miles flies in first and second year = 7,000miles +16,000 miles
Number of more miles he flew in the third year than the first and second year combined = Number of miles flies in third year - Total number of miles flies in first and second year
Number of more miles he flew in the third year than the first and second year combined 24,000 - (7,000+16,000)
Therefore, 24,000 - (7,000+16,000) estimation of how many more miles he flew in the third year than the first and second year combined.
A washer and a dryer cost $800 combined. The washer costs $50 less than the dryer. What is the cost of the dryer?
This is what I think:
#1: 800 - 50 = 750
#2: 800 divided by 2 = 400 - 50 = $350
i think the dryer costs 450$ and the washer 350$
The temperature was -3 C last night. It is now -4 C. What was the change in temperature
-1 C, that's the only logical answer I can think of. Or does it have to be in F?
The change in temperature is a decrease of 1°C, which is calculated by subtracting the initial temperature from the final temperature.
The question involves calculating the change in temperature from -3°C to -4°C. To find the change in temperature, you subtract the initial temperature from the final temperature. In this case, the change would be:
-4°C - (-3°C) = -4°C + 3°C = -1°C.
So the change in temperature is a decrease of 1°C.
Let n be the smallest composite number such that it can be written as the product of two positive integers that differ by 10. How many distinct prime factors does n have?
Answer: n has two distinct prime factors 2 and 3.
Step-by-step explanation:
As given the smallest composite number such that it can be written as the product of two positive integers that differ by 10.
i.e. if first number be x then the other number be x+10 and n=x(x+10), where n must be composite number.
So after putting the values of x by positive integer
1) x=0 then n=0(10+0)=0...which is not a composite number.
2) x=1 then n=1(1+10)=11..... which is not a composite number.
3)x=2 then n=2(2+10)=24......which is a composite number.
so our n=24 and we know that 24=2×2×2×3
Therefore its distinct prime factors are 2 and 3.
Answer:
2
Step-by-step explanation:
Solution:
The smallest pair of numbers that differ by 10 is 1 and 11; however, they multiply to 11 which is not composite. We try the next pair up: 2 and 12, which multiply to 24 which is composite, so [tex]$n=24$[/tex]. [tex]$24$[/tex] factors as [tex]$2^3 \cdot 3$[/tex], so it has [tex]$\boxed{2}$[/tex] prime factors: 2 and 3.
Hope this helped! :)
if the mean of a symmetrical distribution is 56, which of the values could be the median of the distribution 56,14,28,42
First you want to organize the numbers in order to find the median so it should look like this: 14, 28, 42, 56. Then you want to find the one in the middle. But oh wait there are TWO in the middle so add 42 and 28 up 70 then divide it by 2 which equals your median of 35.
Answer: 56
Step-by-step explanation: Apex
Which of the following is an arithmetic sequence? a.2,4,16,32 b.2,3,7,1, c.3,0,-3,-6 d.5,-5,5,-5
Answer:
c apex im positive
Step-by-step explanation:
Option C of the following is an arithmetic sequence. 3,0,-3,-6 is the correct arithmetic sequence.
What is a sequence?A sequence is a collection of items that have been arranged in a logical order, with members appearing either before or after each other. A series is a collection of sequences.
3,0,-3,-6 is the correct arithmetic sequence.
d is the common difference of the series;
3,0,-3,-6
d=0 - 3= - 3 - 0 = -6 - (-3)
d= - 3
An arithmetic sequence has an equal common difference in each progressive term.
Hence, option C of the following is an arithmetic sequence.
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Simplify. 8√200-3√162
53√2
using the ' law of radicals '
√a × √b = √ab
simplifying the radicals
√200 = √( 100 × 2 ) = √100 × √2 = 10√2
√162 = √( 81 × 2 ) = √81 × √2 = 9√2
8(10√2 - 3(9√2) = 80√2 - 27√2 = 53√2
Complete the synthetic division problem below 2|1 7 -18 WHATS is the quotient polynomial form? a x+7 b x+9 c x-9 d x-7
Answer:
x+9
Step-by-step explanation:
Synthetic division calc on Mathaway
The quotient is x+9 and the remainder is 0 if the synthetic division problem is 2|1 7 -18.
What is synthetic division?In the case of dividing by a linear factor, synthetic division is a shorthand, or quicker, technique of polynomial division.
W have:
2 | 1 7 -18
2 | 1 7 -18
__________
1
2 | 1 7 -18
____2×1 = 2______
1 7+2 = 9
2 | 1 7 -18
______2___2×9=18___
1 9 -18+18 = 0
The quotient is x+9, and the remainder is 0.
Thus, the quotient is x+9 and the remainder is 0 if the synthetic division problem is 2|1 7 -18.
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Need help Finding the side length X.
Because the 2 triangles are similar, find the ratio of 2 known sides.
Side XY = 10
Side AB = 25
25 / 10 = 2.5
This means the larger triangle is 2.5 times larger than the smaller one.
Now find the side of the smaller triangle, that would be the same side as X on the larger triangle and multiply that by 2.5.
XZ is the same side as AC
So X = 6 x 2.5
X = 15