Answer:
He can have 6 friends eat cake
Step-by-step explanation:
If each friend can eat 1/6 of the cake, we need to find how many friend can have a piece
1/6 * f = 1 cake
Multiply each side by 6
6*1/6 * f = 1 *6
f = 6
He can have 6 friends eat cake
Answer:
6 friends can have a piece of cake.
Step-by-step explanation:
Each friend eats 1/6 of the cake.
There are six 1/6's in a unit.
6 friends can have a piece of cake.
What is one method to find the measure of angle B?
Answer:
A is the right one
Step-by-step explanation:
it is right on edge
We find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
BCD is a right angle triangle
We have to find the angle B from the triangle
BD is the hypotenuse which is √89
DC is the opposite side of angle B
We can find angle B by using sine function.
Or we can find the length of BC by using pythagorean theorem
then find the tanB function
tanB=8/BC
Hence, we find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC
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A plant has a initial height of 1 inch and grows at a constant rate of 3 inches each month. A second plant that also grows at a constant rate has an initial height of 4 inches and is 28 inches taller after 1 year. After how many months are the plant the same height?
Answer: that would be 3 months.
Step-by-step explanation:
In an airplane 35% of the passengers are children they’re 140 children on the airplane how many passengers are on the airplane
Answer:
there are 49 passengers
Step-by-step explanation: 35%=0.35
0.35*140= 49
Can someone pls help me find the lowest common denominator of
x³y⁴
Step-by-step explanation:The Lowest Common Denominator of fractions is the Least Common Multiple of their denominators. That is, you want to find the LCM of ...
x³ · yx · y⁴Find the highest power of each of the factors, and multiply those together.
The highest power of x is x³. The highest power of y is y⁴. So, the LCM of these expressions is ...
... x³y⁴
_____
Then the two fractions are ...
... 3y³/(x³y⁴) . . . and . . . 7x²/(x³y⁴)
The table shows formulas for the recommended heart rates during exercise for a person who is "a" years old. Write and solve a compound inequality to determine the heart rate range for a 16 year old person.
Answer:
102 ≤ heart rate ≤ 183.6
Step-by-step explanation:
... lower limit ≤ heart rate ≤ upper limit
Put 16 where "a" is and do the arithmetic.
... lower limit = 0.5(220 -16) = 102
... upper limit = 0.9(220 -16) = 183.6
Then the inequality is ...
... 102 ≤ heart rate ≤ 183.6
_____
Comment on the problem
There is nothing to "solve" here. One only needs to evaluate the limits.
In this Compound Inequality question, The recommended heart rate range for a 16 year old person, according to the provided formulas, is between 102 and 183.6 beats per minute.
Given that the age 'a' is represented by 16 years, we can simply substitute this value into the two given formulas to find the recommended heart rate range.
The lower limit of the heart rate is given by the formula 0.5 x (220 - a) and the upper limit is given by the formula 0.9 x (220 - a).
For the lower limit, substituting a = 16, we get 0.5 x (220 - 16) = 102 beats per minute. Similarly, for the upper limit, we get 0.9 x (220 - 16) = 183.6 beats per minute.
Therefore the range of the heart rate for a 16 year old person is 102 to 183.6 beats per minute.
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my sides are all the same length. my area is 9 square meters. what is the length of one of my sides?
Answer:
3
Step-by-step explanation:
if the length and width is 3, 3 times 3 is 9
please help me asap!
Answer:
d 31 degrees
Step-by-step explanation:
We can use the formula
<C = 1/2 (arc AE - arc BD)
Let substitute in what we know
ARC AE = 120
ARC BD = 58
<C = 1/2 (120 - 58)
<c = 1/2(62)
<c = 31
An apartment complex offers 15 apartments with a view of the river, 8 with two bedrooms, and 6 that have both selections. How many only have a view of the river?
Answer:
9
Step-by-step explanation:
Otf the 15 that have a view of the river, 6 have both selections.
The remaining 9 only have a view of the river.
Math true or false
Septima investing money into two different accounts at the same time. the system of inequalities represent the balance of each account where x represents the number of years the money has been invested.
Math! Please help! Please explain your answers.
Answer:
FalseFalseTrueStep-by-step explanation:
Since the given expression represents the account balance, the initial amount (when x=0) is $500 in Account A, and $100 in Account B. (Less money was invested in account B.)
The growth rate of each account is $1.03 per year.* (The growth rate ($/year) is identical for each account.)
The total of the initial amounts invested is $500 +100 = $600.
_____
* Comment on growth rate
Since the account balance is shown as greater than or equal to the given expression, there appears to be the possibility that adjustments are made to the account balance by some means other than the growth predicted by this inequality. For example, if the balance in Account A is $900 at the end of 1 year, the inequality will still be true, but the extra $398.97 will be in addition to the $1.03 growth predicted by this expression.
This means we really cannot say what the growth rates of the accounts might be, except that it is a minimum of $1.03 per year in each account.
_____
Comment on the expressions
More usually, we would expect to see an account balance have the equation a = 400·1.03^x. That is, the interest rate would be 3% and it would be compounded annually. The expression 400 + 1.03x is very unusual in this situation.
Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
Answer:
75 ft
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.
For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.
[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]
So putting in the given values to get:
[tex]cos 20=\frac{x}{80} \\\\x= cos 20*80\\\\x=75.17[/tex]
Therefore, the value of x is the closest to 75 ft.
Choose all of the unit vectors
To choose unit vectors, one must understand that they have a magnitude of one and are directed along the axes in space. For any point P or S, the unit vectors are (i_p, j_p, k_p) or (i_s, j_s, k_s) respectively, each with a magnitude of one.
Explanation:To determine which vectors are unit vectors, you must know that a unit vector has a magnitude (length) of one and indicates direction in space. The given information states that for a point P in space, the unit vectors are (î_p, â_p, k_p). Each of these vectors has a magnitude of one and points in the direction of increasing x, y, and z coordinates, respectively. Similarly, for point S, you have (i_s, j_s, k_s), also with a magnitude of one.
The special types of unit vectors such as î (i-hat), â (j-hat), and k (k-hat) are always of magnitude one and are parallel to the x, y, and z axes, respectively. The vector dê, represents a vector of length d pointing in the positive x-direction, implying dê is also a unit vector if d equals one.
Therefore, in the context provided, all options (a), (b), (c), and (d) are correct if their vectors have a magnitude of one and adhere to the rules to be considered unit vectors.
The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining 1 3/4 miles to the lookout. The trail the hikers will use to return from the lookout is 1/2 mile shorter than the trail they will use to go to the lookout. Each hiker will bring 1/4 gallon of water for each mile to and from the lookout. Determine the total distance, in miles, each hiker will hike? and Determine the total number of gallons of water each hiker will bring ?
Answer:
7 miles1 3/4 gallonsStep-by-step explanation:
The distance to the lookout is the sum of distances before and after the rest stop:
... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi
The distance from the lookout is 1/2 mile shorter, so is ...
... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi
Then the total hike is ...
... total distance = "to" distance + "from" distance
... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi
... total distance = 7 mi
The water each hiker will bring is ...
... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal
Each hiker will hike a total of 7 miles, and they will need to bring 1.75 gallons of water for the entire trip.
First, we need to determine the total distance each hiker will travel:
Initial hike to rest: 2 milesRemaining hike to the lookout: 1 3/4 miles or 1.75 milesTotal distance to the lookout: 2 + 1.75 = 3.75 milesThe return trail is described as 1/2 mile shorter than the trail to the lookout. Therefore:
Return trail distance: 3.75 - 0.5 = 3.25 milesSumming up the distances:
Total hiking distance: 3.75 + 3.25 = 7 milesCalculating Total Water Needed:
Each hiker brings 1/4 gallon of water per mile:
Total miles hiked: 7 milesWater needed per mile: 1/4 gallonTotal water needed: 7 * 1/4 = 1.75 gallonsThus, each hiker will hike a total of 7 miles and will need to bring 1.75 gallons of water for the entire trip.
the average temperature in Alaska in January is -9°F in February it is -16°F which month has the coldest temperature
Answer:
February
Step-by-step explanation:
February is colder by 7°F
-9 - 7 = -16
~
Answer:February
Step-by-step explanation:
If you see the number line below -16 is more far than -9
-------------------------------------------------------------------------------------------------
' ' '
-16 -9 0
Which expressions are equivalent to 70 × 5.3
Answer:
35 x 10.6, 140 x 2.65 and 371 x 1
Step-by-step explanation:
Convert theta= 3pi/4 to rectangular form.
A. y= -1
B. y= 1
C. y= x
D. y= -x
E. x= -1
[tex]\theta=\dfrac{3\pi}{4}=\pi-\dfrac{\pi}{4}\\\\y=\tan\theta x\\\\y=\left(\tan\dfrac{3\pi}{4}\right)x\\\\y=\left(\tan\left(\pi-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(\tan\left(-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(-\tan\dfrac{\pi}{4}\right)x\\\\y=-1x\\\\\boxed{y=-x}\to\boxed{D.}[/tex]
Answer:
If you are doing it on edge it is x+y=0
Step-by-step explanation:
x+y=0 when you solve for y it equals -x( y=-x)
Barney works as a car salesman and earns $175 for every car that he sells. He has fixed expenses of $3100 every month. He has laid out his projected variable expenses as well as his projected car sales for the first 6 months of next year.
. EXPENSES VARIABLE CARS SOLD
january 2,600 32
feb 3,200 36
march 1,600 26
may 800 22
which month will barney sell enough cars to pay for all his monthly expenses ?
feb
Step-by-step explanation:When the number of cars needed to be sold to meet fixed plus variable expenses is subtracted from the number of cars projected to be sold, the result is negative for all months listed except February. In that month, Barney covers is expenses.
We have computed ...
... (expected car sales) - (needed car sales)
where ...
... (needed car sales) = (variable expenses + fixed expenses)/(income per car sold)
For January, this calculation gives ...
... 32 - (2600 +3100)/175 = 32 -32.571 = -0.571
That is, Barney does not project he will sell enough cars to pay his January expenses.
In February, the result is 0, which means he will sell enough cars in February to pay all his monthly expenses.
suppose y varies directly with x. if y= 24 when x = 4, what is y when x = 9?
Answer: y=54
Step-by-step explanation: so 24/4 is 6 soooo 9*6=54 ez
Answer:
y =54
Step-by-step explanation:
We can use the equation y =kx
If we know y and x we can solve fork
24 = k*4
24/4 = k
6 =k
y = 6x
Substitute in 9
y =6*9
y =54
The diameter of a hydrogen atom 0.000000000106 meter. write this diameter in scientific notation
The Diameter of Hydrogen Atom in Scientific Notation is :
✿ 1.06 × 10⁻¹⁰ Meters
Answer:
1.06 x 10-10 mStep-by-step explanation: I just solve it.
find each side length,round to the nearest tenth if necessary 11.
We can use a modified form of the Pythagorean Theorem to find the length of x, also known as side b.
Pythagorean Theorem:
a^2 + b^2 = c^2
We can fill in the values of a^2 and c^2, and then solve for b.
14^2 + b^2 = 25^2
196 + b^2 = 625
Subtract 196 from both sides.
b^2 = 429
√ both sides.
b = 20.7
The value of x, or b, is equal to 20.7.50 POINTS FOR CORRECT ANSWER @PlatoNation
REPORTED IF INCORRECT
Answer:
About 2614 years.
Step-by-step explanation:
We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:
[tex]N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}[/tex]
and we can solve for t:
[tex]0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}[/tex]
The estimated age of the bird skeleton is 2614 years.
Which of the following functions is graphed below ?
See the attachment
Step-by-step explanation:The solid dot on the right-hand portion of the curve means the function is defined for x ≥ 2. Choices A and C have that condition.
The function is linear for x ≥ 2, so matches selection C, not A.
If GF is a midsegment of CDE, find CD.
A. 3.4
B. 6.8
C. 13.6
D. 14
Answer:
C
Step-by-step explanation:
Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:
[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}[/tex]
We can now cross multiply and solve for CD:
[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}[/tex]
Since GF is a midsegment of CDE, CD is double of CF. So we can write:
[tex]CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0[/tex]
By using quadratic formula [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:
[tex]\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2[/tex]
Since the expression for CD is [tex]\frac{15x^2+16x+3.2}{2x+3}[/tex] , we plug in [tex]x=2[/tex] into this expression to find value of CD:
[tex]\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6[/tex]
The correct answer is C
Answer:
C. 13.6
Step-by-step explanation:
We have been given that GF is a mid-segment of CDE.
Since we know that mid-segment of a triangle is half the length of its parallel side.
We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:
[tex]GF=\frac{1}{2}ED[/tex]
Let us substitute given value of GF and ED to find our x.
[tex]2x+3=\frac{1}{2}(5x+4)[/tex]
Multiply both sides of equation by 2.
[tex]2*(2x+3)=2*\frac{1}{2}(5x+4)[/tex]
[tex]2*(2x+3)=5x+4[/tex]
[tex]4x+6=5x+4[/tex]
[tex]6=5x+4-4x[/tex]
[tex]6=x+4[/tex]
[tex]6-4=x[/tex]
[tex]2=x[/tex]
We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.
[tex]\frac{CF}{GF}=\frac{CD}{ED}[/tex]
Substitute given values.
[tex]\frac{3x+0.8}{2x+3}=\frac{CD}{5x+4}[/tex]
Upon substituting x=2 in our equation we will get,
[tex]\frac{3*2+0.8}{2*2+3}=\frac{CD}{5*2+4}[/tex]
Let us simplify our equation.
[tex]\frac{6+0.8}{4+3}=\frac{CD}{10+4}[/tex]
[tex]\frac{6.8}{7}=\frac{CD}{14}[/tex]
[tex]14*\frac{6.8}{7}=CD[/tex]
[tex]2*6.8=CD[/tex]
[tex]13.6=CD[/tex]
Therefore, CD equals 13.6 and option C is the correct choice.
A rectangle has a length of 4 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. What is the value of x?
Final answer:
To find the value of x in a rectangle with a length of 4 inches, set up the equation 2(4 + x) = 4x and solve for x. The value of x is 4 inches.
Explanation:
To find the value of x, we need to set up an equation using the given information. The perimeter of a rectangle is equal to twice the length plus twice the width. The area of a rectangle is equal to the length times the width. So, we can set up the equation: 2(4 + x) = 4x. Next, solve the equation for x:
8 + 2x = 4x
8 = 4x - 2x
8 = 2x
4 = x
Therefore, the value of x is 4 inches.
Which inequality represents the graph shown below?
Answer:
2<x<∞
Step-by-step explanation:
The arrow has a filled in circle at around the 2.5 mark which allows us to deduce that the number 2 is not included in the inequality but almost all the numbers after 2 i.e. (2.1,2.2,2.3,2.4,2.4... etc ) are included. This gives us our lower bound.
The arrow goes to positive infinity. Which gives us our upper or left bound.
Answer:
r>(greater than or equal to)2.5
Step-by-step explanation:
△ABC @ △DEF. Find the measures of the given angles or the lengths of the given sides
BC = 3z + 2, EF = z + 6
Answer:
BC = EF = 8
Step-by-step explanation:
Assuming you mean BC ≅ EF, then ...
... 3z +2 = z +6
... 2z = 4 . . . . . . . . add -2-z
... z = 2 . . . . . . . . . divide by 2
BC = EF = 2+6 = 8
The question is about finding the measures of given sides and angles in similar triangles. By setting up a proportion between the given sides BC and EF, we can solve for the variable 'z'. This 'z' can then be used to find the sides and angles of the triangles.
Explanation:In the case of the problem, we're dealing with the concept of similar triangles in geometry. Since △ABC is similar to △DEF, this means that the corresponding sides are in proportion, and corresponding angles are equal.
Given that BC = 3z + 2 and EF = z + 6, we can write a proportion: BC/EF = 3z+2 / z+6, because the lengths of the corresponding sides of these two similar triangles should be in ratio.
Then you can solve this equation for the variable 'z', which will give us the values for sides BC and EF. If necessary, you can also find the measure of the angles using the values of 'z'.
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Which ordered pairs lie on the graph of the exponential function f(x)=−3^(x−1) +2 Select each correct answer.
(−1, 2)
(1, 1)
(0, 0)
(4,−25)
(1, 1), (4, -25)
Step-by-step explanation:You can evaluate the function to see.
f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2
f(1) = -3^(1-1) +2 = -1 +2 = 1
f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0
f(4) = -3^(4 -1) +2 = -27 +2 = -25
_____
Or, you can graph the points and the curve.
Answer:
(1, 1), (4, -25)
Step-by-step explanation:
help please !!!
What is the recursive rule for an=−3n+1 ?
an=
a1=
To find a1, put 1 in the given equation and evaluate.
... a1 = -3·1 +1
... a1 = -2
Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...
... a[n] = a[n-1] - 3
Find the discriminant and determine how many solutions the equation has and if they are imaginary or real. Please show all work.
y = 4x^2 - 5x + 1
Answer:
as discriminant = 9, it has two real solutions.
Step-by-step explanation:
for eqn ax^2 + bx + c, discriminant = b^2 - 4ac
y = 4x^2 - 5x + 1
discriminant = (-5)^2 - 4(4)(1)
= 25 - 16
= 9
as discriminant > 0, it has two real solutions.
Answer:
Discriminant = 9 and the equation has two real solutions
Step-by-step explanation:
For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.
If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.
In this case, y = 4x^2 - 5x + 1.
So its discriminant = -5^2 - 4*4*1
= 9 so it has two real solutions.
A jetski rental company charges a $50 deposit, plus $25 per hour to rent a jetski. This can be represented by the formula T = 25h + 50, where T is the total cost, and h is the number of hours rented. If the deposited is changed to $40 and the hourly rate is changed to $35, how much more money will the company make on a hour of rental?
Answer:
None, the answer will be the same
Step-by-step explanation:
Select the correct answer. What is the mode of this data set? {41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
The mode is the number in the set that appears the most.
In the given data set, the number 45 is listed twice while all the other numbers are only listed once.
The mode is 45.
Answer:
45
Step-by-step explanation:
The value which appears most often or has the highest frequency in a data set is said to be the mode.
Here we are given the following data set:
{41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
For this data set, we can see that the number / element 45 has occurred the most often which is twice. So the mode of this data set will be 45.