Answer:10 to the 2nd power
Step-by-step explanation:
The train station clock runs too fast and gains 5 minutes every 3 days.
How many minutes and seconds will it have gained at the end of 4 days?
Answer:
first find the average per day. 5/3= 1 & 2/3... 2/3 of a minute is 40 is 60/3=20 seconds. so 4 days would be the full 5 minutes plus another 1 minute and another 40 seconds.. so by day 4 it would be 6 min and 40 seconds.
What is the center and radius for the circle with equation 2x2 - 8x + 2y2 +12y + 14 = 0?
A A
(2,-3); r = 6
B
00
(293); r = 16
(-2,3); r = 6
0
D
(-2,3); r = 16
Answer:
[tex](2,\, -3)[/tex].
[tex]r = \sqrt{6}[/tex].
Step-by-step explanation:
Let [tex](a,\, b)[/tex] denote the center of this circle. Let [tex]r[/tex] ([tex]r > 0[/tex]) denote the radius of this circle. The equation of this circle would be:
[tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex].
Expand to obtain an equivalent equation:
[tex]x^{2} + (- 2\, a) + y^{2} + (- 2\, b) + (a^{2} + b^{2} - r^{2}) = 0[/tex].
Since this equation and the given equation describe the same circle, their corresponding coefficients should match.
Notice that the coefficients of [tex]x^{2}[/tex] and [tex]y^{2}[/tex] in this equation are both [tex]1[/tex]. However, the corresponding coefficients in the given equation are both [tex]2[/tex]. Thus, divide both sides of the given equation by [tex]2\![/tex] to match the coefficients of the [tex]x^{2}[/tex] and [tex]y^{2}[/tex] terms:
[tex]x^{2} + (- 4\, x) + y^{2} + 6\, y + 7 = 0[/tex].
Coefficients of [tex]x^{2}[/tex] and [tex]y^{2}[/tex] are now matched after the division.Coefficients of [tex]x[/tex] should match: [tex](-4) = (-2\, a)[/tex], such that [tex]a = 2[/tex].Coefficients of [tex]y[/tex] should match: [tex]6 = (-2\, b)[/tex], such that [tex]b = (-3)[/tex].The constants should also match. Thus:
[tex]a^{2} + b^{2} - r^{2} = 7[/tex].
Substitute in [tex]a = 2[/tex] and [tex]b = (-3)[/tex]; given that [tex]r > 0[/tex], the value of [tex]r[/tex] would be:
[tex]r = \sqrt{2^{2} + 3^{2} - 7} = \sqrt{6}[/tex].
NO LINKS!! A quarterback tosses a football to a receiver 40 yards downfield. The height of the football, f(x), in feet, can be modeled by f(x)= -0.0.25x+x+6, where x is the ball's horizontal distance, in yards, from the quarterback. What is the ball's maximum height and how far from the quarterback does this occur?
Answer:
Maximum height = 16 yards
This occurs 20 yards from the quarterback.
Step-by-step explanation:
Given function: [tex]f(x)=-0.025x^2+x+6[/tex]
To find the maximum (turning point), differentiate the function:
[tex]f('x)=-0.05x+1[/tex]
Set the derivative to zero and solve for [tex]x[/tex]:
[tex]\implies f'(x)=0[/tex]
[tex]\implies -0.05x+1=0[/tex]
[tex]\implies 0.05x=1[/tex]
[tex]\implies x=20[/tex]
Substitute found value of [tex]x[/tex] into the function to find the maximum height:
[tex]f(20)=-0.025(20)^2+(20)+6=16[/tex]
Therefore, the maximum height is 16 yards.
This occurs 20 yards from the quarterback.
The maximum height of the football can be 16 yards and this occurs 20 yards from the quarterback. The concepts of differentiation are used to solve this problem.
Differentiation is a fundamental mathematical concept that is generally used to obtain the rate of change or slopes of a line.
It is given that the height of the football is modeled as the following function:
f(x) = -0.025x² + x + 6
where x is the ball's horizontal distance (in yards) from the quarterback.
To obtain the maximum height of the ball, the equation is needed to be differentiated and set equal to zero as follows:
[tex]\dfrac{d}{dx}f(x) = 0\\\dfrac{d}{dx}(-0.025x^2+x+6)=0\\-0.025\times2x +1 = 0\\-0.05x+1 = 0\\x = \dfrac{1}{0.05}\\x = 20[/tex]
Substitute this value of x in f(x) to find the maximum height,
f(20) = -0.025(20)² + 20 + 6
f(20) = -0.025 × 400 + 26
f(20) = -10 + 26
f(20) = 16
Therefore, the maximum height is 16 yards and this occurs 20 yards from the quarterback.
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The complete question is as follows:
A quarterback tosses a football to a receiver 40 yards downfield. The height of the football, f(x), in feet, can be modeled by f(x) = -0.025x²+x+6, where x is the ball's horizontal distance, in yards, from the quarterback. What is the ball's maximum height and how far from the quarterback does this occur?
1 All sides are congruent. Paralelogram Rhombus Rectangle Square
Answer:
Rhombus
Square
Step-by-step explanation:
Rhombuses and squares have sides that are always congruent.
for function f(x) =-3x+3 find f(0).
Answer:
f(0)=3
Step-by-step explanation:
f(0) = -3 x 0 + 3
f(0)=3
2 ft is equal to how many meters?
Answer:
2 feet is equal to 0.609 meters
One meter is equal to roughly 3.281 feet.
So two feet is less than one meter.
To find how many meters a certain amount of feet is, you divide by 3.281
2 ÷ 3.281 = 0.609
2 feet is equal to 0.609 meters
Answer:
0.61 meter
Step-by-step explanation:
Determine if true:
3x5+8=23
Answer:
True
Step-by-step explanation:
3x5=15
15+8=23
23=23
Answer:
True
Step-by-step explanation:
3 x 5 = 15
15 + 8 = 23
zearn lesson really hard
Answer:7541
Step-by-step explanation:
all you have to do is add the bottom
how do you calculate Ending Inventory if beginning inventory is 15000 the purchases is 24,000 and the cost of good sold is 23,000.
NO LINKS!!! Draw and solve each triangle.
1. a= 3, b= 4, C= 40°
2. a= 3, c= 2, B=110°
3. a= 12, b= 13, , c= 5
4. a= 5, b= 8, c = 9
The missing values are highlighted in bold, which are approximate to four decimal places (with the exception of B = 90 in problem 3).
Lowercase letters a,b,c are side lengths; Uppercase letters A,B,C are angles opposite the sides mentioned.
The drawings are shown below.
==========================================================
Explanation:
Problem 1
Use the Law of Cosines to solve for side c
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 3^2 + 4^2 - 2*3*4*cos(40)
c^2 = 6.61493337
c = sqrt(6.61493337)
c = 2.57195128
c = 2.5720
Now apply the Law of Sines to find angle A
sin(A)/a = sin(C)/c
sin(A)/3 = sin(40)/2.57195128
sin(A) = 3*sin(40)/2.57195128
sin(A) = 0.74976647
A = arcsin(0.74976647)
A = 48.57015285
A = 48.5702
Once we know two angles of a triangle, we can then subtract their sum from 180 to get the third missing angle.
A+B+C = 180
B = 180 - (A+C)
B = 180 - (48.57015285+40)
B = 91.42984715
B = 91.4298
-----------------------------------
Problem 2
Like with the previous problem, we can use the Law of Cosines to solve for the missing side.
b^2 = a^2 + c^2 - 2*a*c*cos(B)
b^2 = 3^2 + 2^2 - 2*3*2*cos(110)
b^2 = 17.10424172
b = sqrt(17.10424172)
b = 4.13572747
b = 4.1357
Now use the Law of Sines to find angle A
sin(A)/a = sin(B)/b
sin(A)/3 = sin(110)/4.13572747
sin(A) = 3*sin(110)/4.13572747
sin(A) = 0.68164014
A = arcsin(0.68164014)
A = 42.9719427
A = 42.9719
Then we can wrap things up like so
A+B+C = 180
C = 180 - (A+B)
C = 180 - (42.9719427+110)
C = 27.0280573
C = 27.0281
-----------------------------------
Problem 3
Use the Law of Cosines to find angle A.
a^2 = b^2 + c^2 - 2*b*c*cos(A)
12^2 = 13^2 + 5^2 - 2*13*5*cos(A)
144 = 194 - 130*cos(A)
-130*cos(A) = 144 - 194
-130*cos(A) = -50
cos(A) = (-50)/(- 130)
cos(A) = 0.38461538
A = arccos(0.38461538)
A = 67.38013505
A = 67.3801
We could use the Law of Cosines to find angle B, but I'll use the Law of Sines instead.
sin(A)/a = sin(B)/b
sin(B) = b*sin(A)/a
sin(B) = 13*sin(67.38013505)/12
sin(B) = 0.99999999998574
sin(B) = 1
B = arcsin(1)
B = 90
It turns out we have a 5-12-13 right triangle (though usually c is the longest side instead of b).
Now we could use the Law of Cosines to find angle C, but the steps shown below are much quicker in my opinion that don't involve any trig functions.
A+B+C = 180
C = 180 - (A+B)
C = 180 - (67.38013505 + 90)
C = 22.61986495
C = 22.6199
-----------------------------------
Problem 4
The steps will basically be identical to problem 3, but with different numbers of course.
First we need the Law of Cosines to find angle A.
a^2 = b^2 + c^2 - 2*b*c*cos(A)
5^2 = 8^2 + 9^2 - 2*8*9*cos(A)
25 = 145 - 144*cos(A)
-144*cos(A) = 25 - 145
-144*cos(A) = -120
cos(A) = (-120)/(-144)
cos(A) = 0.83333333
A = arccos(0.83333333)
A = 33.55730976
A = 33.5573
Now use the Law of Sines to find angle B.
sin(A)/a = sin(B)/b
sin(B) = b*sin(A)/a
sin(B) = 8*sin(33.55730976)/5
sin(B) = 0.88443328
B = arcsin(0.88443328)
B = 62.18186103
B = 62.1819
Lastly,
A+B+C = 180
C = 180 - (A+B)
C = 180 - (33.55730976 + 62.18186103)
C = 84.26082921
C = 84.2608
-----------------------------------
Side notes:
The phrasing "solve the triangle" means to find all three sides and all three angles.Each answer is approximate with the exception of B = 90 in problem 3.Intermediate calculations were done to eight decimal places. The final answers are to four decimal places. In the first two problems, we can prove only one triangle is possible due to the SAS triangle congruence theorem.For the last two problems, only one triangle is possible because of the SSS triangle congruence theorem.I used GeoGebra to make each triangle shown below.pls help me find the awnser
Answer:
I have no clue thats why is got this app
Answer:
57 units³
Step-by-step explanation:
Volume = length • width • height
Fill in the numbers:
V = 3 4/5 • 2 1/2 • 6
I am making them into improper fractions to make it easier:
V = 19/5 • 5/2 • 6
Multiplying the length and the width:
V = 95/10 • 6
Multiplying the height in:
V = 57
at a stationery store 6 pens were sold at $20. Mr. wong bought pens for his 36 students. each student got 2 pens. how much did he spend altogether?
Answer:
[tex](20 \div 6) \times (36 \times 2) = 3.30 \times 72 = 237.60[/tex]
HOPE IT HELP!!this season the baseball team won 3/5 of its games. assuming there’s no ties, what is the ratio of games won to games lost
Answer:
3:2
Step-by-step explanation:
if they won 3/5 games, then the other 2 were lost so the ratio would be 3:2
What % of people surveyed
were 6-10 and 21-25 years old
Add total people:
5 + 20 + 40 + 30 + 20 = 115 people
Add people 6-10 to 21-25 = 20 + 20 = 40
Divide the two age ranges by total people:
40/115 = 0.34782609
Multiply by 100 to get percent:
0.34782609 x 100 = 34.782609% Round off as needed
Change 288 square inches to feet
[tex]______________________________________________[/tex]
[tex]\huge\rm{ANSWER:}[/tex]
2 square feet[tex]\huge\rm{GIVEN:}[/tex]
Change 288 square inches to feet
(Keep in mind that 1 feet equals 12 inches)
[tex]\huge\rm{SOLUTION:}[/tex]
Follow these steps to convert to square feet.
Step 1: Convert an inch to a square inch.
If 1 feet equals 12 inches, then
1 square feet equals (12) inches equals 144 square inches
As a result, 144 square inches equals one square feet.
Step 2: Using the unitary method, we obtain
288 square inches = 288/144 square feet.
288 square inches = 2 square feet
As a result, 288 square inches equals 2 square feet.
[tex]______________________________________________[/tex]
What is the answer for X+8
Answer: the answer is x+8= 1
out of 30 students in a class,5 said they ride there bikes to school. based on these relusts, how many of the 600 students ride there bike to school
Answer:
125 students ride their bike to school
Step-by-step explanation:
We can set a proportion.
5 / 32 = x / 800
where x is the number of students out of 100 who ride their bikes.
Cross multiply.
32x = 4000
Divide both sides of the equation by 32.
x = 125
125 students out of 800 students ride their bikes to school.
Find the missing angle measure of the triangle.
Answer:
58
Step-by-step explanation:
65 + 57 = 122
A triangle is 180 degrees
180 - 122 = 58
58 is the missing measurement
Solve for x .
A) 48
B)42
C)47
D) 44
Answer:
B. 42.
Step-by-step explanation:
x/35 = 30/25
25x = 30*35
x = (30*35)/25
= 1050/25
= 42.
Choose the angles that are coterminal with -225° with -45° -125° -225° -495° 45° 135° 225° 495°
Answer:
-225°, 135°, 495°
Step-by-step explanation:
Adding or subtracting multiples of 360° will give angle values that are coterminal with a given angle.
-225° -360° = -595° (not on the list)
-225° +0·360° = -225°
-225° +360° = 135°
-225° +2·360° = 495°
Angles -225°, 135°, 495° are coterminal with -225°.
Diane, Henry, and Abdul have a total of $82 in their wallets. Diane has $8 less than Henry. Abdul has 3 times what Henry has. How much does each
Answer:
let's suppose
Diane: D= H – 8
Henry: H
Abdul: A = 3H
D+H+A=82
D=10
H=18
A=54
A bag of marbles contains five red marbles three green marbles and six yellow marbles what is the probability of randomly choosing a marble that is green
Numbers x and y both squared and added
And ASAP pls
Nira here :)
Answer:
2x² + 4y²
according to your given information.......
Find the radius of the cylinder with the given volume
WILL GIVE BRAINLIEST
Answer:
6.71 mm
Step-by-step explanation:
Find radius R
Volume = πR²H
4500π = πR²*100
R² = 45
so R = √45 = 3√5 = 6.71 mm
Pls help me solve part a and part b
26. Let S = (-1,0,2,4,7). Find f(S) if
a) f(x)= 1.
b) f(x)=2x + 1.
c) f(x) = x/5
. d) f(x)=(x2 + 1)/3).
Answer:
d.f(x)=(×2 +1)/3).
Step-by-step explanation:
I think that was my answer
3 ounces cost $273
Find the unit rate
Answer:
$91 per ounce
Step-by-step explanation:
If 3 ounces cost $273, we can divide both sides by 3 to find the unit rate. To make this clearer, we use the variable [tex]x[/tex] for ounces. Then, we have the equation
[tex]3x=273[/tex].
Dividing both sides by 3, we have
[tex]x=91[/tex].
The cost of one ounce is $91.
select the correct form for 562,932 I want the correct form
Answer: five hundred sixty-two thousand nine hundred thirty-two
Step-by-step explanation: Student instructed to give the word form of a given value.
Answer:
The correct word form is:
Five hundred sixty-two thousand nine hundred thirty-two.
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Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Look at VSW and ZTSW in the image below.
Which of the following is the best description for this pair of angles?
O complementary
O supplementary
O acute
O straight
Answer:
Supplementary
Step-by-step explanation:
VSW and TSW combine and make 180. Complementary is when they make up to 90
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
Infinetly many (d)
Step-by-step explanation:
The graphs are the same, so they will all have the same solutions.
hope this helps!
ibrahim