Answer:
t=84
Step-by-step explanation:
Malin's answer is $\frac{t-6}{6}$. Shawn's answer is $\frac{t+7}{7}$. We know these are equal, so we have the equation
$$\frac{t-6}{6} = \frac{t+7}{7}.$$
To eliminate denominators from the problem, we multiply both sides by $6\cdot 7$:
$$\frac{6\cdot 7\cdot (t-6)}{6} = \frac{6\cdot 7\cdot (t+7)}{7},$$
then simplify to get
$$7\cdot (t-6) = 6\cdot (t+7).$$
The parentheses are important here! For example, the parentheses on the left side of the equation tell us that it is $t-6$, not just $t$, which is multiplied by $7$.
Now we expand using the distributive property:
7t - 7\cdot 6 &= 6t + 6\cdot 7;\\
7t - 42 &= 6t + 42.
Adding $42$ to both sides gives
$$7t = 6t + 84,$$
then subtracting $6t$ from both sides gives $t=\boxed{84}$.
(We can check that starting from $t=84$, Malin and Shawn do indeed get the same final answer -- namely, $13$.)
Urgent!
18. A tennis ball is launched straight upward with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:
4.9t2 + 24.5t + 117.6 = 0
-4.9t2 - 24.5t + 117.6 = 0
-4.9t2 + 24.5t - 117.6 = 0
4.9t2 + 24.5t - 117.6 = 0
-4.9t2 + 24.5t + 117.6 = 0
19. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)
t = 8 seconds
t = 4 seconds
t = 3 seconds
t = -3 seconds
The ball will never reach the ground.
20. Using the same equation, determine when the ball is at a height of 49 meters.
Step-by-step explanation:
18.
the last one.
-4.9t² + 24.5t + 117.6 = 0
the ball starts at 117.6 meters height. then, during the first seconds the thrust upwards is adding height, until finally, with more and more seconds passing, gravity will win with a vengeance and pulls the ball down faster and faster than any other force in any other direction.
19.
the general solution for a quadratic equation
y = ax² + bx + c
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -4.9
b = 24.5
c = 117.6
t = (-24.5 ± sqrt(600.25 - -4×4.9×117.6))/-9.8 =
= (-24.5 ± sqrt(600.25 + 2304.96))/-9.8 =
= (-24.5 ± sqrt(2905.21))/-9.8 = (-24.5 ± 53.9)/-9.8
t1 = (-24.5 + 53.9)/-9.8 = -3
t2 = (-24.5 - 53.9)/-9.8 = 8
a negative time does not make any sense, so the real solution is : the ball reached the ground after 8 seconds.
20.
now the equation is
-4.9t² + 24.5t + 117.6 = 49
but this is quickly transformed again into a "= 0" equation :
-4.9t² + 24.5t + 68.6 = 0
t = (-24.5 ± sqrt(600.25 - -4×4.9×68.6))/-9.8 =
= (-24.5 ± sqrt(600.25 + 1344.56))/-9.8 =
= (-24.5 ± sqrt(1944.81))/-9.8 = (-24.5 ± 44.1)/-9.8
t1 = (-24.5 + 44.1)/-9.8 = -2
t2 = (-24.5 - 44.1)/-9.8 = 7
again, negative time does not make sense.
the ball will be at 49 m height after 7 seconds.
can someone please help me i need to show the working out too
Answer:
(1) x=15/2
(2) x=1
Step-by-step explanation:
(1) 4x−1 /2 =x+7
2x+ −1 /2 =x+7(Distribute)
2x+ −1 /2 =x+7
Step 2: Subtract x from both sides.
2x+ −1 /2 −x=x+7−x
x+ −1 /2 =7
Step 3: Add 1/2 to both sides.
x+ −1 /2 + 1 /2 =7+ 1 /2
x= 15 /2
(2) 3x+2=( 2x+13)/ 3
3x+2= 2 /3 x+ 13 /3 (Distribute)
3x+2= 2 /3 x+ 13 /3
Step 2: Subtract 2/3x from both sides.
3x+2− 2 /3 x= 2 /3 x+ 13 /3 − 2 /3 x
7 /3 x+2= 13 /3
Step 3: Subtract 2 from both sides.
7 /3 x+2−2= 13 /3 −2
7 /3 x= 7 /3
Step 4: Multiply both sides by 3/7.
( 3 /7 )*( 7 /3 x)=( 3 /7 )*( 7 /3 )
X=1
what are 4 quarts in one gallon but in a
fraction form
Answer:
4 Quarts = 1 Gallon
Step-by-step explanation:
1 is an integer and not a fraction. However, it can be expressed as a fraction in rational form as 1/1. So a possible answer is 1/1 gallon. I don't know for sure though its my best guess.
plz help answer will mark brainiest
Answer:
4/3 litres of water is enough to water 2/5 of the plants
Assuming the number of plants in the house is an unknown variable, take the value as x.
Thus, 4/3 litres is enough to water 2x plants in the house.
x = 4/3 ÷ 2
= 2/3 litres
Amount of water for all the plants = 5x = 5 × 2/3
= 10/3 litres
Thus, 10/3 litres of water is necessary to water all the plants in the house.
helllp meeeeeeeeeeeeeeee
If 2 inches are equivalent to 5 centimeters, how many square centimeters are in one square inch
Answer:
there are 6.45 or 6.5 square cm in one square inch
Step-by-step explanation:
In the diagram below, PQ and RS are parallel. Based on the angle measures in the diagram, what is the value of X?
Answer:
x would be equal to 70 grades
Step-by-step explanation:
The angle QRS is equal to 180 - 130 = 50 grades.
We add up that with the other 60 grades on the left, and we encounter ourselves with a simple equation:
60 + x + 50 = 180
x = 70
Hope this was helpful
point:(-5,1); slope: -
4
write in point-slope form:
Answer:
y-1=-4(x+5)
Step-by-step explanation:
y-y1=m(x-x1)
y-1=-4(x-(-5))
y-1=-4(x+5)
Answer: y - 1 = -4(x + 5)
Step-by-step explanation:
The point-slope formula is y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ( [tex]x_1[/tex], [tex]y_1[/tex]) is a point on the graph.
Using the formula, we will plug in our known values to write our equation.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (1) = (-4)(x - (-5))
y - 1 = -4(x + 5)
However, in the picture the slope is [tex]\frac{1}{4}[/tex], so we would write it as;
y - 1 = [tex]\frac{1}{4}[/tex](x + 5)
A construction crew is paving a road. The crew has already paved 1,000 square feet and can pave at a rate of 300 square feet of road per hour. The function f(x) = 300x + 1,000 represents this situation.
What is f(3), and what does it represent?
900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
900 square feet;, f, (3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
900 square feet; , f, (3) represents the total number of square feet the construction crew has paved after 3 hours.
1,900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
1,900 square feet;, f, (3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
Answer:
1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
The function of the construction crew is an illustration of a linear function
The value of f(3) is 1900, and f(3) represents the total number of square feet paved after working for 3 hours
The function is given as:
To calculate f(3), we substitute 3 for x
Multiply 300 and 3
Add 900 and 1000
This means that the value of f(3) is 1900.
And it represents the total number of square feet paved after working for 3 hours
1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
Which statement is true about this equation? 3(-y 7) = 3(y 5) 6.
The statement that is true about the equation 3(-y + 7) = 3(y + 5) + 6 is;
Statement A; The equation has one solution, y = 0
The given equation is;
3(-y + 7) = 3(y + 5) + 6
Expanding the brackets gives us;
-3y + 21 = 3y + 15 + 6
-3y + 21 = 3y + 21
Using subtraction property of equality, subtract 21 from both sides to give;
-3y = 3y
Using addition property of equality, add 3y to both sides to give;
-3y + 3y = 3y + 3y
6y = 0
Using division property of equality, divide both sides by 6 to get;
y = 0
Read more about factorization at; https://brainly.com/question/11000698
The missing statements are;
A. The equation has one solution, y = 0.
B. The equation has one solution, y = -1.
C. The equation has no solution.
D. The equation has infinitely many solutions.
Someone help me out on this math question?
Answer:
A. discrete
B. discrete
C. continuous
D. continuous
Step-by-step explanation:
When things are expressed in terms of whole numbers, the value is discrete. This is the case for A and B.
__
When the variable can have any rational or irrational value, it is a continuous variable. This is the case for C and D.
Rotation 180 counterclockwise around the origin of the point (-3,-7)
Answer: (3 , 7)
Step-by-step explanation: When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative. Since x and y are already negative, they become positive due to the double negative rule.
Which expression represents the expanded version of the expression below?
4x(3x+7)
Answer:
X is just a variable.
Step-by-step explanation:
2x- 5 >18 +x
necesito ayuda pliss
necesito con resolución
Answer:
x > 23
Step-by-step explanation:
2x - 5 > 18 + x
x - 5 > 18
x > 23
brainliest pls
Apple + Orange = $20
Apple is twice the price of the orange
How much does the apple cost?
Answer:
Step-by-step explanation:
let price of Orange=x
price of Apple=2x
x+2x=20
3x=20
x=20/3
cost of Apple=2x=2×20/3=40/3=$13 1/3
Shameka buys a blue garden hose that is 16.5 feet long and a green garden hose that is 14.75 feet long. How many feet of garden hose does she buy?
Help please?
Answer:
21.25 feet
Step-by-step explanation:
16.5 feet
+14.75
=21.25 feets
what is the area of a oblong with a base of 7cm and a height of 4 cm
Answer: 7*4 is 28 square centimeters...
Does anyone know how to solve this? Please helppp, I’m so confused
Answer:
y = 65 degree
x = 50 degree
Step-by-step explanation:
I believe that’s right
The two angles in the isosceles triangle are 50 and 65 degrees .
An isosceles triangle has two equal sides and two equal angles.
Consider that the one angles in the triangle is x degrees and the bottom angle is 65 degrees.
Then we have:
65 = y
(The sum of all angles in a triangle is 180 degrees.)
Then Simplifying the equation:
65 + 65 + x = 1802
x = 180 - 65 - 65
x = 50 degrees
Therefore, the two angles in the isosceles triangle are 50 and 65 degrees .
Learn more about angles here;
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What is th eslope of the graph if it has these coords?
(1,2) and (3,-1)
a box of snacks contained 20 individual packages. the newly designed box contains 28 individual packages by what percent did the individual packages increase
Answer:
40%
Step-by-step explanation:
increased amount = 28 - 20 = 8
to get the percentage we have to divide the increased amount by original amount which will be 8/20 = 0.4
0.4 is 40%
The percentage increase is given as:
= [ (Final value - Initial value) / Initial value] x 100
The percentage increase in the number of individual packages is 40%
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Number of initial individuals packages = 20
Number of final individuals packages = 28
The percentage increase is given as:
= [ (Final value - Initial value) / Initial value] x 100
The percentage increase in the number of individual packages:
= [(28 - 20) / 20] x 100
= (8/20) x 100
= 40%
We can cross-check:
100% = 20 packages
140% = 140/100 x 20 packages
140% = 28 packages.
Thus,
The percentage increase in the number of individual packages is 40%
Learn more about percentages here:
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What is the measurement of pie?
Answer: 3.14159
Step-by-step explanation:
Please help me please please please
Answer:
Perpendicular bisector
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
i don't know but I think question 1 is 64
Your little brother wants hot chocolate ot be 150 degrees, but you accidentally heated the water to 175 degrees. If after 5 minutes the temperature is 165 and the temperature in your house is 70 degrees, how long will your little brother have to wait to drink his hot chocolate?
Answer:
12.5 minutes
Step-by-step explanation:
it takes 5 minutes to cool 10 degrees
after ten minutes it would be 20 degrees less
then after 2.5 minutes it would be 5 degrees less
so it would take you 12.5 minutes to get 25 degrees less
We know that in 5 minutes, the temperature of the hot chocolate decreased by 10 degrees. We also know that the temperature is fixed at 70 degrees. Now, using the info given, let's solve!
=> 5 minutes = 10 degrees decrease=> 1 minute = 2 degrees decrease=> 1 minute x 12.5 = 2 x 12.5 degrees decrease=> 12.5 minutes = 25 degrees decreaseConclusion:Therefore, my little brother will have to wait for 12.5 minutes to drink his hot chocolate.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
The expression below represents the perimeter of a square in centimeters.
4(6+2.5)
What is the square's perimeter?
Answer:
34
Step-by-step explanation:
4(8.5) = 34
Here is a balanced Hanger. Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and x represents the weight of each square. Select all equations that represent the hanger
Answer:
4x+2.5+2.5+3+3=2x+2.5+3+3+3 AND 4x+5+6=2x+2.5+6
Step-by-step explanation:
Triangle NLM is reflected over the line segment as
shown, forming triangle ABC. Which congruency
statement is correct?
NLM - CAB
NLM -CBA
NLM - BCA
NLM - BAC
Triangle NLM is reflected over the line segment as shown, forming triangle ABC then the correct congruency statement is NLM ≅ CAB
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Triangle NLM is reflected over the line segment and form the triangle ABC.
Triangle NLM is reflected over the line segment to form triangle ABC. This means that the corresponding sides and angles of the two triangles are congruent.
The reflection over a line segment preserves the orientation of the triangle, so the order of the letters in the names of the triangles should remain the same.
Therefore, triangle NLM is reflected over the line segment as shown, forming triangle ABC then the correct congruency statement is NLM ≅ CAB
To learn more on Triangles click:
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a) Write an equation for the line of best fit.
Y=-0.007x+13.713
5. The data below shows the population of a city,
In millions of people, since 1950.
Year Population
1950 1.75
1960 1.68
1970
1.52
1980
1.16
TO
b) Estimate the population of the city in 2020.
1990
1.04
2000
0.98
Answer
Step-by-step explanation:
In millions of people, since 1950
what is 0.75 greater than 9
Answer: 9.75
Step-by-step explanation: i just added
Answer:
less
Step-by-step explanation:
Please quickly answer number 17&18 I will give brainliest
Answer: 17) 150°C 18) 17 minutes
Step-by-step explanation:
x represents time in minutes and y represents temperature in Celsius
17) y=10x+30
y=10(12)+30
y=120+30
y=150 - Therefore, the water temperature will be 150°C after 12 minutes
18) 200=10x+30
10x+30=200
10x+30-30=200-30
10x=170
x=17 - Therefore, the water temperature will reach 200°C after 17 minutes