Step-by-step explanation:
24x³ ÷ 14x²
= 2 × 2 × 2 × 3 × x × x × x / 7 × 2 × x × x
= (2 × x × x) ( 2 × 2 × 3 × x) / (2 × x × x) x 7
= 12x / 7
The height of an object launched into the air can be modeled by the graph shown.
When does the object return to the ground?
Answer:
9 seconds
Step-by-step explanation:
right side of the graph touches the x axis at 9
In ADEF, f= 33 inches, ZF=140° and ZD=5°. Find the length of e, to the nearest 10th
of an inch.
The length of e is 29.53 inches.
what is Sine Law?In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".
Given:
f= 33 inches
<F= 140, <D = 5
Now,
<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35
Using Sine law
sin F / f = sin E/ e
sin 140 / 33 = sin 35 / e
0.642/ 33 = 0.573 / e
0.0194 e= 0.573
e= 29.53 inches
Hence, the length of e is 29.53 inches.
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Find the measure of the supplement of an angle that measures 72º.
O 18°
O 36°
O 72°
O 108°
Find the equation, function and describe. (100 points)
X
1
2
3
4
5
6
7
Y
5
2.5
1.6667
1.25
1
.83333
.71429
Answer:
257890 is the function of the equation
Step-by-step explanation:
mark me BRAINLIEST
Work this problem
9.215 -627
Answer:
−617.785
Step-by-step explanation:
Calculate the circumference of a circle with a radius of 8 inches.
To calculate the circumference of a circle, you can use the formula:
\(\displaystyle C=2\pi r\)
Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.
Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:
\(\displaystyle C=2\pi (8)\)
Simplifying the expression:
\(\displaystyle C=16\pi \)
Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.
Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
a bit of help please?
The value of x for the chord is:
x = 12
How to find the value of x for the chord of the circle?A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
Recall that: If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords.
Using the above principle, we can say:
3 * x = 4 * 9
3x = 36
x = 36/3
x = 12
Thus, the value of x for the chord is 12.
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7/10 = y/100
what is y?
Answer:
7/10= y/ 100
Well the answer is
y=70
solve the following by multiplying by the inverse of the fractional coeffident 2/5t=20
Answer:
t=1/50
Step-by-step explanation:
2/5t=20
2=100t
2/100=t
t=1/50
Estimate 6,976 + 3,983 + 13,560 by first rounding each number to the nearest thousand.
Answer:
Step-by-step explanation:
The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000, 3,983 rounded to the nearest thousand is 4,000, 13,560 rounded is 14,000.
7,000 + 4,000+ 14,000 = 25,000
The solids are similar. Find the missing dimension.
Answer:
i need the picture
Step-by-step explanation:
To find the missing measure of similar solids, set up a proportion of corresponding dimensions. Then, cross multiply and divide. To find the surface are of similar solids, set up a ratio of surface area equal to the squared ratio of given linear measures. Then cross multiply and divide.
What value of x will make the triangle congruent
Answer:
x = 3/5 = 0.6
Step-by-step explanation:
By the ASA Triangle Congruence Theorem, the two given triangles are congruent (vertical angles are congruent). Because we know that corresponding parts of congruent triangles are congruent, we can write the following equation: 7x - 3 = 2x. Now we can solve:
7x - 3 = 2x
-3 = -5x
3/5 = x
Gary is working on a school project. He calculated the total cost of the project to be $102.47,
where the project cost is based on the percentage of the project work that was finished. He
finished 16 of the project in the first week, 6.25% of the project in the second week, and 2 of the
project in the third week. If Gary took another week to finish all of the remaining project work,
approximately how much did the project work he finished in the last week cost?
Answer:
Percent Complete is a measure based on duration and Percent Work Complete is based on work. The two fields are calculated as follows: Percent Complete = Actual Duration/Duration (PC=AD/D) Percent Work Complete = Actual Work/Work (PWC=AW/W)
Step-by-step explanation:
Solve the equation square root 2x – 7 + x = 5 algebraically, and justify the solution set
Answer: \(x=4\)
Step-by-step explanation:
\(2x-7+x=5\)
Group like terms:
\(\left(2x+x\right)-7=5\)
Simplify the arithmetic:
\(3x-7=5\)
Add 7 to both sides:
\(3x-7+7=5+7\)
Simplify the arithmetic:
\(3x=5+7\)
Simplify the arithmetic:
\(3x=12\)
Divide both sides by 3:
\(\frac{3x}{3}=\frac{12}{3}\)
Simplify the fraction:
\(x=\frac{12}{3}\)
Find the greatest common factor of the numerator and denominator:
\(x=\frac{4\cdot 3}{1\cdot 3}\)
Factor out and cancel the greatest common factor and the answer will be:
\(x=4\)
Use the Product Property for Exponents to explain why x · x = x2.
Whenever there is no exponent on a variable,
you can give it an exponent of 1.
So we can rewrite the x's in this problem as x¹.
When we multiply two terms together
with like bases, we add their exponents.
So now just add their exponents to get x².
In 1990, a total of $641 billion was spent on food and drinks in a particular country. In 2003, the total spent was $1016 billion.
(a) Find the equation of the exponential function that can be used to model the total 7 spent (in billions of dollars) on food and drinks in this country as a
function of the number of years t since 1990. (Round your decimal value to four decimal places.)
x
T=
(b) Use your model to predict the amount spent (in billions of dollars) in 2000. (Round your answer to the nearest integer.)
billion dollars
(c) What is your prediction for the total sales of food and drink (in billions of dollars) in 2018? (Round your answer to the nearest Integer.)
billion dollars
(d) Estimate when the total sales will reach $2 trillion if this exponential trend continues. (Round your answer to two decimal places.)
t=
Part(a),
The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:
\(T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x\)
Part(b),
The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).
Part(c),
The predicted total sales of food and drink in 2018 is 1756 billion dollars
Part(d),
If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.
(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:
\(T = a \times b^t\)
where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.
Using the given information, we can set up two equations:
T(0) = 641 (total spent in 1990)
T(13) = 1016 (total spent in 2003, which is 13 years after 1990)
Substituting these values into the exponential function, we get:
\(641 = a \timrd b^0\) => a = 641
\(1016 = a b^{13\) => \(b = (\dfrac{1016}{641})^{\frac{1}{13}\)
Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:
\(T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x\)
(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:
\(T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10\) ≈ 964
Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).
(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:
\(T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28\) ≈ 1756
Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).
(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):
\(2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t\)
\(ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})\)
\(t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}\)
t = 32.72
Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.
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Suppose that $4500 is placed in an account that pays 19% interest compounded each year.
Assume that no withdrawals are made from the account.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
Answer:
a) 5355
b) 6372.45
Step-by-step explanation:
4500 * 1.19 = 5355
5355 * 1.19 = 6372.45
Marry collected 16.2 pounds of cans for the recycling center on Monday. On Tuesday, he collected 11.8 pounds. If the recycling center gives her $0.40 per pound how much money will she earn for both days of recycling?
If the recycling center gives Marry $0.40 per pound money she will earn for both days of recycling is $11.20
What information is given in the question?
Marry collected 16.2 pounds of cans for the recycling center on Monday.
On Tuesday, she collected 11.8 pounds.
The recycling center gives her $0.40 per pound.
According to the given question:
To find how much money she will earn for both days of recycling, calculate money earned on Monday and Tuesday. Then add the amount to get the amount earned on both days.
Money earned by Marry on Monday = 16.2 x 0.40 = $6.48
Similarly, money earned by Marry on Tuesday = 11.8 x 0.40 = $4.72
Therefore, Total money earned by Marry for both days
= 6.48 + 4.72
= $11.20
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Three students that share a townhouse find that their electric bill for October is $2.23 less than the September bill. The
total of both bills is $292.43, and each bill is split evenly among the roommates. How much did each owe in September?
Answer:
$47.48
Step-by-step explanation:
Let x = the amount owed Sept.
x + x - 2.23 = 292.43 Combine like terms
2x -2.23 = 292.43 Add 2.23 to both sides
2x - 2.23 + 2.23 = 292.43 + 2.23
2x = 294.66 Divide both sides by 2
\(\frac{2x}{2}\) = \(\frac{294.66}{2}\)
x = 147.33 this is the bill for September
Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.
Total:
147.33 + 145.10 = 292.43
292.43 ÷ 3 = 97.48 This is what each will owe rounded to the nearest penny.
PLEASE ANSWERING THIS QUESTION!
By completing the square, the expression \(\sf{x^2-12x+101}\) equals (x+A)^2+B
where A = (Blank)
and B = (Blank)
Show your work!
Do not spam answers!
Explain your answer!
Thanks!
The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65
A = -6 and B = 65
Completing the squareFrom the question, we are to express the given expression in the form (x + A)^2+B by completing the square
The given expression is
x² -12x + 101
Using the completing the square method
x² -12x + 101
Divide the coefficient of x by 2 and then square it
The coefficient of x is -12
Dividing by 2, we get
-12/2 = -6
Squaring
(-6)²
Now, add and subtract this value from the expression
x² -12x + (-6)² + 101 - (-6)²
Then, we can write that
(x - 6)² + 101 - (-6)²
(x - 6)² + 101 - 36
(x - 6)² + 65
Thus,
The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65
By comparison,
A = -6
and
B = 65
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belle de correct answer.
Consider the expression below.
9+4(x + 2) - 3x
Select the term that best describes "3" in the given expression.
OA.
variable
OB. exponent
OC.
constant
OD
coefficient
Answer:
B
Step-by-step explanation:
3 in the expression is part of -3x called the coefficient of the variable. See the definitions below to distinguish the difference between each term:
A.
variable - an unknown value represented with a letter
B.
coefficient - a number written with a variable denoting how many
C.
constant - a number without a variable denoting how much
D.
exponent - a number written on a base denoting how many times to multiply the base by itself
P = kQ
a) direct
b) inverse
c) joint variation
PLEASE HELP!! WILL MARK BRAINIEST!!
what number represents the same amount as 2 hundreds + 12 tens + 6 ones ?
Answer:
326
Step-by-step explanation:
The value of the given expression is 326.
Given:
The given expression 2 hundreds + 12 tens + 6 ones.
To find:
The value of the given expression.
Explanation:
The numeric form of given expression is:
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
Therefore, the value of the given expression is 326.
NEED HELP!! I"LL GIVE YOU BRAINLIEST!! Find the value of b. a = 3 and c =12
Answer: b = 11.62
Step-by-step explanation:
We can use this formula to solve for b:
\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)
\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)
\(b^2= \sqrt{144-9}\)
= 11.61895004
We can round that to 11.62.
Hope this helped!
i need help its worth 30 points i have no clue how to do it and i have 5 mins left
Answer:
B
Step-by-step explanation:
what is 7 1/2 divided by 5 5/8
Answer:
1.33
Step-by-step explanation:
9514 1404 393
Answer:
4/3
Step-by-step explanation:
If you're familiar with decimal equivalents (or even if you're not), you can use your calculator to compute the quotient:
7.5/5.625 = 1.333333333...
The rational number equivalent of the result is 4/3.
__
If you like to work directly with the rational numbers, you can write the ratio as ...
(7 1/2)/(5 5/8) = (7 4/8)/(5 5/8) = (60/8)/(45/8) = 60/45 = 4/3
you are helping your sister plan her sweet 16. the venue you want to host it at charges $75 for every 3 guest as well as a rental deposit of $200 write an equation to determine the total party cost
Answer:
y = 25x + 200
Step-by-step explanation:
y = the total cost of the party
x = the number of guests
75/3 = 25
25 is the cost per guest.
Helping in the name of Jesus.
Please please look at the picture and answer the question thank you
Solve the following for θ, in radians, where 0≤θ<2π.
−7cos2(θ)+4cos(θ)+6=0
Select all that apply:
1.07
3.96
0.31
2.32
1.68
2.43
Answer:correct answers are 3.96
2.32
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
-7u^2 + 4u + 6 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -7, b = 4, and c = 6. Substituting these values, we get:
u = (-4 ± sqrt(4^2 - 4(-7)(6))) / 2(-7)
u = (-4 ± sqrt(136)) / (-14)
u = (2 ± sqrt(34)) / 7
Therefore, either:
cos(θ) = (2 + sqrt(34)) / 7
or:
cos(θ) = (2 - sqrt(34)) / 7
Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:
θ = arccos((2 + sqrt(34)) / 7)
θ = arccos((2 - sqrt(34)) / 7)
Using a calculator, we find:
What's another name for qualitative variables?
Answer:
A qualitative variable, also called a categorical variable, is a variable that isn't numerical.