Answer:
The inequality to show how many hours of television Julia can still watch this week can be given as:
⇒ [tex]x+1.5\leq 5[/tex]
where [tex]x[/tex] represents he number of hours of television that Julia can still watch this week
On solving for [tex]x[/tex], we get
[tex]x\leq3.5[/tex]
Thus, Julia can still watch no more than 3.5 hours of television this week.
Step-by-step explanation:
Given:
Julia is allowed to watch television no more than 5 hours a week.
She has already watched 1.5 hours
To write and solve an inequality to show how many hours of television Julia can still watch this week.
Solution:
Let the number of hours of television that Julia can still watch this week be = [tex]x[/tex]
Number of hours already watched = 1.5
Total number of hours of watching television this week would be given as:
⇒ [tex]x+1.5[/tex]
It is given that Julia is allowed to watch no more than 5 hours of television in a week.
Thus, the inequality can be given as:
⇒ [tex]x+1.5\leq 5[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 1.5
[tex]x+1.5-1.5\leq 5-1.5[/tex]
[tex]x\leq3.5[/tex]
Thus, Julia can still watch no more than 3.5 hours of television this week.
W
13. one-third the sum of eleven and p
We can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have one-third the sum of eleven and [p].
We can model the given question as -
y = (1/3)(11 + p)
Therefore, we can model the statement "one-third the sum of eleven and [p]" as y = (1/3)(11 + p)
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Convert to scientific notation
Answer:
5.7* 10 to the power of 4
Answer:
57,000 = 5.7 × 10⁴Step-by-step explanation:
[tex]\text{The scientific notation}:\\\\a\times10^k\\\\\text{where}\\\\1\leq a<10,\ k\in\mathbb{Z}\\\\================================[/tex]
[tex]57,000=5.7\times10000=5.7\times10^4\\\\-----------------------\\\\57000=5\underbrace{7000}_{\leftarrow4}=5\times10^4[/tex]
Lucas says his twin baby brothers have a total weight of 15 and one eighth pounds. jackson 6 and one fourth pounds and jeremy weighs 8 and seven eighths pounds. explain how you can use estemation to tell if the total weight is reasonable
By rounding each brother's weight to the nearest whole number and adding these, we get an estimate of 15 pounds. The actual total weight, 15 and one eighth pounds, is close to this estimate, indicating that Lucas' claim about his brothers' weight is reasonable. This demonstrates how estimation can be used to quickly verify the validity of a claim.
Explanation:Estimation is a valuable mathematical tool that can be used to assess the reasonableness of a solution. In the case of Lucas' twin baby brothers' weight, you can use rounding to estimate their total weight. Let's start by rounding each brother's weight to the nearest whole number. In this scenario, Jackson, who weighs 6 and one fourth pounds could be estimated to weigh 6 pounds, and Jeremy, who weighs 8 and seven-eighths pounds, could be estimated to weigh roughly 9 pounds.
Adding these together gives a total of 15 pounds. The actual weight of the twins, 15 and one eighth pounds, is very close to this estimation, indicating that Lucas' claim about his brothers' weight is reasonable. This approach makes effective use of estimation as a means to quickly and simply verify a given claim's feasibility.
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Which point is on the line y = -2x + 3?
(-2,-1)
(3, -3)
(3, 3)
(-3,-9)
Answer:
Hence (3, -3) is on the given line y = -2x + 3
Step-by-step explanation:
For a point on the Line, It must Satisfy the Equation of a line
Therefore for
[tex]y=-2x+3[/tex]
For (-2,-1)
Substitute x = - 2 and y = -1 in above equation
Left Hand Side = y
= -1
Right Hand Side = -2 × (-2) +3
= 4 +3
= 7
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (-2,-1) is NOT on the given line
For (3, -3)
Substitute x = 3 and y = -3 in above equation
Left Hand Side = y
= -3
Right Hand Side = -2 × (3) +3
= -6 +3
= -3
Left Hand Side = Right Hand Side
Satisfied
Hence (3, -3) is on the given line y = -2x + 3
For (3, 3)
Substitute x = 3 and y = 3 in above equation
Left Hand Side = y
= 3
Right Hand Side = -2 × (3) +3
= -6 +3
= -3
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (3,3) is NOT on the given line
For (-3,-9)
Substitute x = -3 and y = -9 in above equation
Left Hand Side = y
= -9
Right Hand Side = -2 × (-3) +3
= 6 +3
= 9
Left Hand Side ≠ Right Hand Side
Not Satisfied
Hence (-3,-9) is NOT on the given line
Only the point (3, -3) lies on the line y = -2x + 3. None of the other points satisfy the equation.
To determine which point lies on the line y = -2x + 3, we need to substitute the coordinates of each point into the equation:
(-2, -1): Substitute x = -2 into y = -2x + 3:
y = -2(-2) + 3 = 4 + 3 = 7. Since y = -1, this point does not lie on the line.
(3, -3): Substitute x = 3 into y = -2x + 3:
y = -2(3) + 3 = -6 + 3 = -3. Since y = -3, this point lies on the line.
(3, 3): Substitute x = 3 into y = -2x + 3:
y = -2(3) + 3 = -6 + 3 = -3. Since y = 3, this point does not lie on the line.
(-3, -9): Substitute x = -3 into y = -2x + 3:
y = -2(-3) + 3 = 6 + 3 = 9. Since y = -9, this point does not lie on the line.
The only point that satisfies the equation is (3, -3).
Complete question:
Which point is on the line y = -2x + 3?
A. (-2,-1)
B. (3, -3)
C. (3, 3)
D. (-3,-9)
9 cm
3 cm
AB is parallel to DC.
AD = 9 cm, DC = 3 cm. Angle BCD = 35°
Angle ABD = 90°
Calculate the size of angle BAD.
Give your answer correct to one decimal place.
Answer:
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Step-by-step explanation:
i) AD = 9 cm
ii) DC = 3 cm
iii) ∠BCD = 35°
iv) Since AB is parallel to DC and ∠ABD = 90° then we can conclude that ∠BDC = 90°.
v) [tex]\frac{BD}{DC} = \frac{BD}{3\hspace{0.1cm}cm} = tan(35)[/tex] = 0.6128 ∴ BD = 3 [tex]\times[/tex] 0.6128 = 1.84 cm
vi) ∴ sin(∠ BAD ) = [tex]\frac{BD}{AD}[/tex] ⇒ sin(∠ BAD ) = [tex]\frac{1.84}{9}[/tex] = 0.2044
∴ ∠BAD = [tex]sin^{-1}[/tex](0.2044) = 11.8°
Answer:
Step-by-step explanation:
Two communications companies offer calling
plans. With Company X, it costs 35¢ to connect
and then 5¢ for each minute. With Company Y,
it costs 15¢ to connect and then 4¢ for each
minute.
Write and simplify an expression that represents
how much more Company X charges than
Company Y, in cents, for n minutes.
Answer:
(20 + n)¢
Step-by-step explanation:
With Company X, it costs 35¢ to connect and then 5¢ for each minute.
So, for n minutes of calling the company X charges, C(x) = (35 + 5n)¢
Again, With Company Y, it costs 15¢ to connect and then 4¢ for each minute.
So, for n minutes of calling the company Y charges, C(y) = (15 + 4n)¢.
Therefore, the company Y charges for n minutes of calling less than company X is [(35 + 5n) - (15 + 4n)]¢ = (20 + n)¢ (Answer)
To find how much more Company X charges than Company Y for n minutes, subtract the cost of Company Y from the cost of Company X. The expression to represent the difference in charges is 0.2 + 0.01n.
Explanation:To find how much more Company X charges than Company Y, we need to subtract the cost of Company Y from the cost of Company X for n minutes.
Let's denote the cost of Company X as CX and the cost of Company Y as CY.
For Company X, the cost is $0.35 to connect and $0.05 for each minute. So, the cost of CX for n minutes is given by CX = 0.35 + 0.05n.
Similarly, for Company Y, the cost is $0.15 to connect and $0.04 for each minute. So, the cost of CY for n minutes is given by CY = 0.15 + 0.04n.
To find the difference in charges, we subtract CY from CX:
Company X charges (CX - CY) = (0.35 + 0.05n) - (0.15 + 0.04n) = 0.2 + 0.01n
For the function f defined by f(x)=3x2−2x+5 find f(−x),−f(x) , and −f(−x).
Step-by-step explanation:
[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]
The answers are:
[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]
Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].
f(−x):
Replace x with −x in the function:
[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]
Simplify this expression:
[tex]f(-x)=3 x^2+2 x+5[/tex]
−f(x):
Multiply the entire function f(x) by −1:
[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(x)=-3 x^2+2 x-5[/tex]
−f(−x):
Replace x with −x in the function f(x) and then multiply the whole expression by −1:
[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]
Simplify this expression:
[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]
Distribute the negative sign:
[tex]-f(-x)=-3 x^2-2 x-5[/tex]
Question:
For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).
Louis wants to carpet the rectangular floor of his basement.The basement has a area 432 square feet,The width of the basement is 1/3 its length.What's the length of Louis's basement.
Answer:
36 ft
Step-by-step explanation:
Let L represent the length of Louis's basement. The area is the product of length and width, so is ...
A = L(L/3)
432 = L²/3 . . . . . fill in area value
1296 = L² . . . . . . multiply by 3
36 = L . . . . . . . . . take the square root
The length of Louis's basement is 36 feet.
The cube root of 0.000004913 is
Answer:
[tex]\sqrt[3]{0.000004913}=0.017[/tex]
Step-by-step explanation:
Cubic Root
The cubic root of a number N is M, if
[tex]M^3=N[/tex]
It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.
Let's compute
[tex]M=\sqrt[3]{0.000004913}[/tex]
The argument can be expressed in scientific notation as
[tex]0.000004913= 4913\ 10^{-9}[/tex]
The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.
[tex]4913=17*17*17=17^3[/tex]
Thus our number is
[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]
We have then
[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]
Which of the following functions has the same horizontal asymptote as the function graphed below?
f(x)=-3^x+2 +2
f(x)=2^x-3
f(x)=3^x+2 -2
f(x)=2^x+2 -3
Answer:
The functions which has the same horizontal asymptote y = -3 as given in the graph are,
f(x) = [tex]2^{x} - 3[/tex] and
f(x) = [tex]2^{(x+2)} -3[/tex]
Step-by-step explanation:
The function that is graphed has horizontal asymptote as y = -3 .
As x → -∞ f(x) → - 3 for the second and fourth function. Hence the functions which has the same horizontal asymptote y = -3 as given in the graph are,
f(x) = [tex]2^{x} - 3[/tex] and
f(x) = [tex]2^{(x+2)} -3[/tex]
(3-20i)-(14+6i)-(8-2i)
Because there are parentheses we distribute the negative signs:
3 - 20i + (-14) - 6i + (-8) + 2i
Next combine like terms:
3 + (-14) + (-8) and -20i - 6i + 2i
-19 -24i
NEED HELP ASPA PLS HELP WITH THIS
SEE IMAGE FOR A, B, C, D REFERENCE
A- 3
B- 3
C- 6
D- 3x+6
On the board you should have 6 of the orange + tiles and 3 of the orange x tiles.
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number. (5 points)
Time (year) Population
0 40
1 62
2 96
3 149
4 231
Answer:
The population of moose after 12 years will be 7,692
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
y ----> population of moose
x ----> the time in years
a is the y-intercept or initial value
b is the base of the exponential function
we have
[tex]a=40[/tex] ----> the y-intercept is given in the table (value of y when the value of x is equal to zero)
substitute
[tex]y=40(b^x)[/tex]
Find the value of b
For x=1, y=62
substitute in the equation
[tex]62=40(b^1)\\b=62/40\\b=1.55[/tex]
therefore
[tex]y=40(1.55^x)[/tex]
What will be the population of moose after 12 years?
For x=12 years
substitute in the exponential equation
[tex]y=40(1.55^{12})[/tex]
[tex]y=7,692[/tex]
what is the quotient of m^6/5 divided by 5/m^2
Answer:
[tex]\large\boxed{\dfrac{m^8}{25}}[/tex]
Step-by-step explanation:
[tex]\dfrac{m^6}{5}\div\dfrac{5}{m^2}\\\\\text{Divide by a fraction is the same as multiply by its reciprocal}\\\\=\dfrac{m^6}{5}\times\dfrac{m^2}{5}=\dfrac{m^6\times m^2}{5\times5}\\\\\text{use}\ a^n\times a^m=a^{n+m}\\\\=\dfrac{m^{6+2}}{25}=\dfrac{m^8}{25}[/tex]
What is 967 divided by 60 equals???
Answer:
16.11(6)
Step-by-step explanation:
967/60=16 7/60
In Connecticut, there is a tax charge of $0.84 on a $14 dinner bill. Find the tax rate in
Connecticut. (Tax rates are based on cents per one dollar.)
What is the equation to solve this?
Explanation: Calculation of the general sales taxes of Connecticut State for 2019 ... combined rates mentioned above are the results of Connecticut state rate (6.35%). There is no county sale tax for Connecticut. There is no city sale tax for the Connecticut cities. ... The Connecticut's tax rate may change depending of the type of purchase.
Answer:
0.84+1.00=1.84 +14=15.
If there are 12 people sitting at a round table how many different pairs of people can have conversations assuming they can all talk to each other?
Answer: 6
Step-by-step explanation: 12/2 because a pair is 2 people and there are 12 people in total.!
The number of different pairs of people who can have conversations at a round table with 12 people is 66. This is calculated using the combination formula C(n, 2).
The student asks about the number of different pairs of people who can have conversations at a round table with 12 people, assuming that everyone can talk to each other. The problem is a combinatorial one and can be solved by using the formula for combinations. The formula for the number of combinations of pairs from a set of n items is [tex]C(n, 2) = \frac{n! }{2! * (n - 2)!}[/tex], where n! (n factorial) is the product of all positive integers up to n, and C denotes the combination.
To find how many different pairs can have conversations, we plug in n = 12 into the combination formula:
[tex]C(12, 2) = \frac{12! }{2! * (12 - 2)!} = \frac{12 * 11}{2 * 1} = 66[/tex]
So, there are 66 different pairs of people that can have conversations at a round table with 12 people.
How do I find the area
Answer:
For the smaller rectangle: 9 x 19.8 = 178.2
For the bigger rectangle: 27 x 10.8 = 291.6
Square root of one hundred and twenty three
round 2.7364 to the nearest thousandths
Answer:
2.736
Step-by-step explanation:
5 it more --> round up
4 or less --> leave it how it is
Answer:
i think its 2.74
Step-by-step explanation:
Substitution for {2x-3y=11 and -x + 2y = -6
Step-by-step explanation:
-x+2y=-6
x-2y=6
x=2y+6
substitute in 2x-3y=11 gives us 2(2y+6)-3y=11
4y+12-3y=11
y=-1
-x+2(-1)=-6
-x=-4
x=4
a _____ angle has the same measure as its arc.
Answer:
central
Step-by-step explanation:
greetings the correct answer is central odyssey ware
What is the measure of AC?
Answer:
AC = 52.8
Step-by-step explanation:
33/20 = 1.65
12*1.65 = 19.8
BA = 19.8
CB + BA = AC
33 + 19.8 = 52.8
Answer:
AC = 52.8
Step-by-step explanation:
Since BE is parallel to CD and intersects the 2 sides of the triangle then it divides those sides proportionally, that is
[tex]\frac{BC}{AB}[/tex] = [tex]\frac{DE}{AE}[/tex], substituting values
[tex]\frac{33}{AB }[/tex] = [tex]\frac{20}{12}[/tex] ( cross- multiply )
20AB = 396 ( divide both sides by 20 )
AB = 19.8
Thus
AC = AB + BC = 19.8 + 33 = 52.8
what conclution can be drawn about lines AB and CD?
Answer:
Step-by-step explanation:
they are both equal
Answer: They are not parallel because the two given alternate interior angles are not congruent
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Answer:
[tex] - 10 \div 9 = \frac{ - 10}{9} [/tex]
[tex]10 \div ( - 9) = \frac{10}{ - 9} [/tex]
[tex] - ( - 10 \div ( - 9)) = - (10 \div 9) = - \frac{10}{9} [/tex]
[tex] - \frac{10}{9} = \frac{10}{ - 9} = - \frac{10}{9} [/tex]
A and B are the correct choices.
7x + 3x + 5 - 2x + 7. Select all that are equivalent.
a. 2x + 6
b. 10X + 12 - 2x
c. 12x + 12
d. 8x + 12
Answer:
d 8x+12
Step-by-step explanation:
7x+3x+5-2x+7
combine 7x+3x-2x=8x
and 5+7=12
8x+12
Answer:
Step-by-step explanation:
7x+3x-2x=8x
5+7=12
8x+12
Input the expression x +9/2
Answer:um where is the constant
Step-by-step explanation:
The expression 'x + 9/2' involves adding a variable 'x' to the fraction 9/2. In an example situation, if you substitute x with the number 5, the result would be 9.5. Remember, x can represent any number.
Explanation:The expression you provided is x + 9/2. In mathematics, this is an algebraic expression which comprises of a variable x and a fraction 9/2. It means that you're adding the x variable to the fraction 9/2. For example, if you were to substitute x with a number, let's say 5, the answer would then be 5 + 9/2 = 9.5. It's important to remember that variables can represent any number, and in this case, the variable is x.
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What is the quotient when the decimal number 10 and 6/10 is divided by four hundredths
A) 265
B) 265.2
C) 26.25
D) 26.52
Answer:
Step-by-step explanation:
10 and 6/10 = 10.6
4 hundredths = 4/100 = 0.04
10.6 / 0.04 = 265 <==
Find the product. Simplify your answer.
(4z–1)(z–3)
Answer: 4z (to the 2 power) - 13z + 3
Step-by-step explanation:
2x-7 divided by 6x squared -37x+56
Answer:
the 6.192# melebulated by 59 and devide it by 597 your answere is 64
Step-by-step explanation: