find the limit as x approaches 0 of x/sin3x
A cab charges $1.45 for the flat fee and $0.55 for each mile. Write and solve an inequality to determine how many miles Ariel can travel if she has $35 to spend. please help!
Solve. 3t < –15 (1 point)
t < –5
t > –5
t < –45
t > –45
The solution to the inequality 3t < –15 is t < –5, attained by dividing both sides by 3.
Explanation:The student's question involves solving an inequality, specifically 3t < –15. To solve for t, we need to isolate t on one side of the inequality. This can be done by dividing both sides of the inequality by 3. The solution to the inequality is:
Divide both sides by 3: t < –5Therefore, the correct answer to the inequality 3t < –15 is t < –5. The other options such as t > –5, t < –45, and t > –45 are incorrect.
Identify the expression as a numerical expression or a variable expression. For a variable expression, name the variable.
1 × 12
A. numerical expression
B. variable expression; a is the variable.
C. variable expression; there is no variable.
D. variable expression; l is the variable.
which equation is equivalent to
2x + 4a = 10
A. x= 5/4a
B. x= 5 + 2a
C. x= 10 - 4a
D. x=5 - 2a
An equation is equivalent to 2x + 4a = 10 will be D. x=5-2a.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
In all answers we are solving for x. That means x needs to be by itself.
2x + 4a = 10
Subtract 4a;
2x = 10 - 4a
Divide by 2;
x = 5 - 2a
D. x=5-2a
Therefore, an equation is equivalent to 2x + 4a = 10 will be D. x=5-2a.
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write a polynomial function with rational coefficients so that p(x)=0 has the given roots: -5 and 3i
The polynomial with rational coefficients and roots -5 and 3i will be [tex]p(x)=x^3+5x^2+9x+45=0[/tex].
Given information:Polynomial p(x)=0 has the roots: -5 and 3i
It is required to write a polynomial with rational coefficient and the given roots.
The polynomial has a complex root 0+3i. So, there will be one more root of the polynomial which is 0-3i.
Now, the roots of the polynomial are
[tex]\alpha =-5\\\beta=0+3i\\\gamma=0-3i[/tex]
So, the required polynomial can be written as,
[tex](x-\alpha)(x-\beta)(x-\gamma)=(x-(-5))(x-(0+3i))(x-(0-3i))\\=(x+5)(x-3i)(x+3i)\\=(x+5)(x^2-(3i)^2)\\=(x+5)(x^2+9)\\=x(x^2+9)+5(x^2+9)\\=x^3+5x^2+9x+45[/tex]
Therefore, the polynomial with rational coefficients and roots -5 and 3i will be [tex]p(x)=x^3+5x^2+9x+45=0[/tex].
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if AB is congruent to ED and BC is congruent to DC, how is AC congruent to EC
example of why division is not associative.
Division is not associative, as if you look at one of the operands to a nest of divisions, the result will vary either in proportion to it or inversely to it depending on whether it's to the right of an odd or even number of divisions. And the basic associative law changes the number of operations the rightmost operand is to the right of by 1.
BC ___ AC
Choose the relationship symbol that makes the statement true.
Answer:
BC≅AC
Step-by-step explanation:
From the given figure, triangle ABC is such that ∠CAB=∠CBA=70°, therefore the sides of the triangle that are AC and BC will be congruent to each other as if two angles of the same triangle are equal then the sides opposite to those angles are also equal to each other, therefore
BC is congruent to AC that is BC≅AC.
8 is 15% of what number?
15% of 18.95 is what number?
what percent of 64 is 326?
10% of what number is 40?
Solve log11 (y + 8) + log11 4 = log11 60. what is y?
Answer:
The value of y is 7.
Step-by-step explanation:
The given equation is
[tex]log_{11}(y+8)+log_{11}4=log_{11}60[/tex]
[tex]log_{11}[(y+8)4]=log_{11}60[/tex] [tex][\because log_ax+log_ay=log_axy][/tex]
[tex]log_{11}(4y+32)=log_{11}60[/tex]
Equating both sides.
[tex]4y+32=60[/tex]
[tex]4y=60-32[/tex]
[tex]4y=28[/tex]
Divide both sides by 4.
[tex]y=7[/tex]
Therefore the value of y is 7.
Malia works at a movie theater and is paid hourly. One month, she earned $388.80. The total amount she earns can be found using the equation y = 8.1x, where x is the number of hours she works and y is the total amount she earns in dollars. Bill works at a golf course and is also paid hourly. The table shows the total amount he is paid for different numbers of hours worked. The number of hours:18, 28, 35. Total number earned:144.90, 225.40, 281.75. How do the units compare?
Answer:
Malia's unit rate is greater than Bill's by $0.05.
Step-by-step explanation:
Consider the provided information.
The total amount she earns can be found using the equation y = 8.1x, where x is the number of hours she works and y is the total amount she earns in dollars.
The unit rate, when written as a fraction, has a denominator equal to one.
The unit price of Malia is $8.1
For Bill works:
Number of hours Total amount earned
18 $144.90
28 $225.40
35 $281.75
Unit price would be:
[tex]\dfrac{144.90}{18}=\dfrac{y}{x}\\\\8.05=\dfrac{y}{x}\\\\y=8.05x[/tex]
Hence, unit price of Bill is $8.05
Malia's unit rate is 8.1 whereas Bill's unit rate is 8.05,
Thus, Malia's unit rate is greater than Bill's by 8.10-8.05=0.05.
Use one transformation to solve n-4.6=2.98
what is point O on MN called if MO=ON
A horizontal pull A pulls two wagons over a horizontal frictionless floor, the first wagon is 500N, the second is 2000 N. The tension in the light horizontal rope connecting the wagons is.
the options are:
a) equal to A, by Newton’s third law.
b) equal to 2000 N.
c) greater than A.
d) less than A.
During a 52 week period, a company paid overtime wages for 19 weeks and hired temp help for 11 weeks. During 5 weeks, the company paid overtime AND hired temp help. If an auditor randomly examined the payroll for only one week, whats the probability that the payroll for that week contained overtime wages or temp help wages? ...?
The probability that the payroll for one week contained overtime wages or temporary help is [tex]\boxed{\frac{10}{13}}[/tex].
Further explanation:
It is given that during a [tex]52[/tex] week period, a company paid overtime wages for [tex]19[/tex] weeks and hired temporary help for [tex]11[/tex] weeks.
During [tex]5[/tex] weeks, the company paid overtime and hired temporary help.
Calculation:
A company paid overtime wages for [tex]19[/tex] weeks and [tex]5[/tex] weeks during the [tex]52[/tex] week period.
Therefore, the probability of overtime wages [tex]P(O)[/tex] is calculated as follows:
[tex]\begin{aligned}P(O)&=\dfrac{19}{52}+\dfrac{5}{52}\\&=\dfrac{19+5}{52}\\&=\dfrac{24}{52}\end{aligned}[/tex]
The probability of overtime wages is [tex]\frac{24}{52}[/tex].
The same company hired temporary help for [tex]11[/tex] weeks and [tex]5[/tex] weeks during the [tex]52[/tex] week period.
Therefore, the probability of temporary help [tex]P(H)[/tex] is calculated as follows:
[tex]\begin{aligned}P(H)&=\dfrac{11}{52}+\dfrac{5}{52}\\&=\dfrac{11+5}{52}\\&=\dfrac{16}{52}\end{aligned}[/tex]
The probability of temporary help is [tex]\frac{16}{52}[/tex].
Now, the combined probability [tex]P[/tex] that the payroll for one week contained overtime wages or temporary help is calculated by adding the probabilities of overtime wages and temporary help as follows:
[tex]\begin{aligned}P&=\dfrac{24}{52}+\dfrac{16}{52}\\&=\dfrac{24+16}{52}\\&=\dfrac{40}{52}\\&=\dfrac{10}{13}\end{aligned}[/tex]
The probability that the payroll for one week contained overtime wages or temporary help is [tex]\boxed{\dfrac{10}{13}}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, events, outcome, sample, experiment, equally likely, random, complementary events, joint probability, independent events, mutually exclusive events, conditional probability.
The perimeter of a rectangle is 96 ft. The ratio of its length to its width is 5 : 3. What are the dimensions of the rectangle?
Yen calculates the product 5/8 times 24/25. before he multiples he
Answer:
[tex]\frac{1}{1} \times \frac{3}{5}[/tex]
Step-by-step explanation:
The complete question is
Yen calculates the product 5/8 x 24/25. before he multiplies, he simplifies all the factors. what does the problem look like after he simplifies the factors?
The given product is
[tex]\frac{5}{8} \times \frac{24}{25}[/tex]
Then, Yen simplifies and the problem looks like
[tex]\frac{1}{1} \times \frac{3}{5}[/tex]
Because, we simplified 5 with 25 and 8 with 24.
Therefore, the result of the product is
[tex]\frac{3}{5}[/tex]
A kite, flying 50 feet high in the air is attached by a string to a stake in the sand. How long is the string to the nearest tenth of a foot?
a) 50.0 feet
b) 70.7 feet
c) 86.6 feet
d) 100.0 feet ...?
Answer:
the answer is b) 70.7 feet
Step-by-step explanation:
thank you for amazing answers on the board.
1. The figure attached is a regular octagon with radii and an apothem drawn. What is the measure of angle 1?
A. 22.5 degrees
B. 45 degrees
C. 60 degrees
D. 67.5 degrees
lottie needs a driver. Drive A is offering his services for an initial $200 in addition to $80 per hour. Driver B is offering this service for an intal $230 and an addition of $70 per hour When will the two drivers charge the same amount
Driver A and Driver B will charge the same amount after 3 hours of service.
Explanation:The subject of this question is a problem involving linear equations, a topic in mathematics. Specifically, it pertains to the intersection point of two linear functions, representing the costs charged by the two drivers over time. Let's denote the driving time as 't' (in hours) and the total cost as 'C' to solve it.
Driver A's cost function could be formulated as C = 200 + 80t, while Driver B's as C = 230 + 70t.
To find out when both drivers will charge the same amount, set these two equations equal to each other:
200 + 80t = 230 + 70t
This simplifies to 10t = 30 after subtracting 200 from both sides and 70t from both sides. Finally, dividing by 10 gives us t = 3.
Therefore, both drivers would charge the same amount after 3 hours of service.
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What is half of 9 1/2 inches?
As per linear equation, the half of 9(1/2) inches is 4(3/4) inches or 4.75 inches.
What is a linear equation?A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.
The given measurement is 9(1/2) inches.
Therefore, the half of the given measurement is
= [9(1/2) ÷ 2] inches
= [19/2 ÷ 2] inches
= 19/4 inches
= 4(3/4) inches
= 4.75 inches
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Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?
He is correct. The angles share a common vertex so they are a linear pair.
He is correct. The angles share a common ray so they are a linear pair.
He is incorrect. Angle ORP does not have a linear pair shown on the diagram.
He is incorrect. Ray RO and ray RL are not opposite rays.
Answer: D is the answer
Maple Grove wants to include two types of maple trees, the namesake of the city,for their parks.Two varieties of maple trees have been selected.One variety costs $80 per tree; the other more colorful variety costs $85 per tree. The tree budget must not exceed $75,000. Citizens want more of the colorful $85 trees than the others if possible.
Let x be the number of $80 trees and y the number of $85 trees. Which system of inequalities represents the situation?
Options:
80x+85y>= 75,000 x<=y
80x+85y>=75,000 x>=y
80x+85y<=75,000 x>=y
80x+85y<=75,000 x<=y ...?
Given that f(x) = 3x + 1 and g(x) = the quantity of 4x plus 2
divided by 3, solve for g(f(0)).
2
6
8
9
Find parametric equations for the tangent line at the point (cos(3pi/6),sin(3pi/6), (3pi/6))
on the curve x=cost, y= sint, z=t
x(t)=?
y(t)=?
z(t)=?
Pleasee help x.x 1. Solve the system by elimination-
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5
2.Solve using substitution-
x-y-z=-8
-4x+4y+5z=7
2x+2z=4
Thanks for any help :o
Inez has 699 pennies and 198 nickels estimate how many more pennies than nickels she has.
Scientists are studying the temperature on a distant planet. Let
y
represent the temperature (in degrees Celsius). Let
x
represent the height above the surface (in kilometers). Suppose that
x
and
y
are related by the equation
y=41-3x
.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
what is the temperature on the surface of the planet?
what is the temperature change for each kilometer we go up from the surface?
Answer:
The temperature on the surface of the planet is 41 °C.The tempearture decreases 3 °C when the height increases 1 km.Step-by-step explanation:
The given equation is
[tex]y=41-3x[/tex]
Where [tex]x[/tex] is the height above the surface and [tex]y[/tex] is the temperature in degrees Celsius.
Now, the temperature on the surface can be find when the height above the surface is zero, that is [tex]x=0[/tex]. So, we replace this value and solve for [tex]y[/tex]
[tex]y=41-3x=41-3(0)\\y=41[/tex]
Therefore, the temperature on the surface of the planet is 41 °C.
The second question is about the constant rate of change of the given relation, which is also the slope of the linear expression. That constant rate of change is always the coefficient of variable [tex]x[/tex]. Therefore, the ratio of change is [tex]r=-3[/tex]. Which means the tempearture decreases 3 °C when the height increases 1 km.
The decreasing behaviour is deduct from the ratio of change, when it's negative, that means the function decreases, like in this case.
Evaluate the function as indicated determine its domain and range.
2x+1 , X<0
FX=
2x+2 ,X>or equal to 0
a. F(-1) b.f(0) c.F(2) d.F(t^2+1) ...?