During a sale, a dress decreased in price from $90 to &63. What was the percent of decrease?
how to simplify expression by distribution 3(2y-7)
Choose the solution for the equation.
d3=284? need help asap
Answer:
the answer is A
Step-by-step explanation:
ttm
Write five numbers that round to 360 When rounded to the nearest 10.
Kevin is solving this problem. 737 × 205 What are the partial products Kevin will need to solve the problem? A. 3,685 and 147,400 B. 3,685 and 14,740 C. 3,685 and 1,474 D. 3,685 and 7,370 and 147,400
the answer is A
700 x 5 = 3500
30 x 5 = 150
7 x 5 = 35
3500 + 150 +35 = 3685
700 x 200 = 140,000
30 x 200 = 6000
7 x 200 = 1400
140000 + 6000 + 1400 = 147400
What is the domain of y = sec(x)?
The domain of y = sec(x) is all real numbers except for values where the cosine function is zero.
Explanation:The domain of y = sec(x) is all real numbers except for values where the cosine function is equal to zero. Since the secant function is the reciprocal of cosine, it is undefined when cosine is zero.
So, the domain of y = sec(x) is all real numbers except for values of x where cos(x) = 0.
For example, if we consider the unit circle, the cosine function is equal to zero at π/2 and 3π/2. Therefore, the domain of y = sec(x) would exclude these values.
The domain of [tex]\( y = \sec(x) \)[/tex] is all real numbers except [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex], [tex]\( n \)[/tex] integer.
Let's find the domain of [tex]\( y = \sec(x) \)[/tex].
The secant function, [tex]\( \sec(x) \)[/tex], is defined as the reciprocal of the cosine function, [tex]\( \cos(x) \)[/tex]. So, [tex]\( \sec(x) = \frac{1}{\cos(x)} \).[/tex]
The cosine function is defined for all real numbers, except where the denominator becomes zero, because division by zero is undefined.
So, to find the domain of [tex]\( \sec(x) \)[/tex], we need to find where [tex]\( \cos(x) \)[/tex] is not zero.
The cosine function has a range between -1 and 1. It equals zero at [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x = -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
So, the domain of [tex]\( \sec(x) \)[/tex] is all real numbers except where [tex]\( \cos(x) = 0 \)[/tex]. Therefore, the domain of [tex]\( \sec(x) \)[/tex] is [tex]\( x \neq \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x \neq -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
In interval notation, the domain of [tex]\( \sec(x) \)[/tex] is:
[tex]\[ (-\infty, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \infty) \][/tex]
A circular fountain has a circular walkway surrounding it with a width of 7 ft. The total area taken up by the walkway is 693π ft^2. Find the diameter of the pool.
Car rental at Q.T. Rental is $22 per day plus an initial deposit of $36.Which expression shows how much it will cost to rent a car for d number of days?
Answer:
The expression is Price = 36 +22*d where d is each day that pass.
Step-by-step explanation:
The inicial 36 are the independant term since it's not related to how many days the car is rented. 22 is the slope since it depends on the days the car is rented.
Given the following triangle, if a = 12 and ∠B = 48°, find b to the nearest whole number.
Answer:
The value of b nearest whole number is, 13.
Step-by-step explanation:
We know an [tex]\angle B=48^{\circ}[/tex] and the side adjacent to it i.e, a=12.\
In a right triangle BCA ,
the tangent(tan) of an angle is the length of the opposite side divided by the length of the adjacent side.
i.e, [tex]\tan B=\frac{opposite}{Adjacent}=\frac{b}{a}[/tex]
Substitute the value of a=12 and [tex]\angle B=48^{\circ}[/tex] to solve for b in above expression:
[tex]\tan 48^{\circ}=\frac{b}{12}[/tex]
we have the value of [tex]\tan 48^{\circ}=1.110613[/tex]
then, [tex]1.20012724=\frac{b}{12}[/tex]
On simplify we get,
[tex]b=1.110613 \times 12=13.327356[/tex]
Therefore, the value of b nearest whole is, 13
At an aquarium, 6 out of 18 deliveries are plants. Out of 15 deliveries in one week,how many are plants?
The sum of two consecutive even integers equals 6426?
If the minimum value of the function y = cos θ + d is –5, the value of d is...
The value of d, when the function is at its minimum is -4.
What is a Function?A function is a law that relates two variables namely, a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as an input and range is all the value that a function can have.
The function is of various types, logarithmic, exponential, quadratic, radical etc.
The function is y = cos [tex]\rm \theta[/tex] + d
The minimum value of the function, y = cos [tex]\rm \theta[/tex] + d is -5.
The minimum value is the lowest value of the function.
The minimum value of cos [tex]\rm \theta[/tex] is at 180 degree equals to -1
Substituting the value in the equation.
-5 = - 1 + d
d = -5 +1
d = -4
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Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?
The conjugate of the given complex number is:
[tex]2+8i[/tex]
Step-by-step explanation:We know that any complex number is written in the form of:
[tex]z=a+ib[/tex]
where a and b are real numbers.
The conjugate of the complex number is given by:
[tex]\bar z=\bar {a+ib}\\\\i.e.\\\\\bar z=a-ib[/tex]
Here we are given that:
We have a complex number such that the real part of a complex number is 2 and it's imaginary part is -8.
i.e.
a=2 and b= -8
i.e. the complex number is:
[tex]z=2+(-8)i[/tex]
Hence, the conjugate of this number is:
[tex]\bar z=2-(-8)i\\\\i.e.\\\\\bar z=2+8i[/tex]
Can two numbers have a GCF that is bigger than their LCM? Explain how you know?
1. An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line. How many different ways can they sit if the elf and the dwarf insist on sitting next to each other?
a. 6 ways
b. 48 ways
c. 36 ways
d. 12 ways
e. 24 ways
2. How many ways can you order a hamburger of you can order it with or without cheese, lettuce, tomatoes, pickles, or onions?
a. 10
b. 32
c. 64
d. 5
Final answer:
In this question, the arrangements of characters sitting together and the options for hamburger toppings are explored using permutations and combinations in Mathematics for High School.
Explanation:
(1) When the elf and the dwarf insist on sitting next to each other, treat them as one entity. Then, there are 4 entities: {elf & dwarf}, hobbit, wizard, man. This gives 4! ways to arrange them, and the elf and dwarf can be arranged within their entity in 2! ways.
So, the total ways are 4! x 2! = 48 ways.
(2) For the hamburger order, since you can choose to include/exclude each topping independently, there are 2 options for each topping (with or without).
Hence, the total ways to order the hamburger are 2⁵ = 32 ways.
What is the value of a?
In a survey of 3450 registered voters who reside in California, 1789 were found to be republican. Construct a confidence estimate for the true percentage of republicans among registered voters in California. Use a confidence level of 95%.
A triangle has a perimeter of 10x+2. Two sides have lengths of 5x and 2x+9. What is the length of the 3rd side?
FIND THE FOLLOWING USING THE GIVEN TRIANGLE...PLEASE HELP ME SUCK AT MATH...SOS!!! ASAP!!!!
perimeter = 20 +20 +24 = 64 feet
area = 12^2 + x^2 = 20^2
144 + x^2 = 400
x^2 = 256
x = sqrt(256) = 16 feet
area = 1/2 x 16 x 24 = 192 square feet
cost = 192 x $2 = $384
How long will it take a bird traveling at an average speed of 12 miles per hour to travel 202 miles while flying south for winter?
Answer:
16 50 min
Step-by-step explanation:
Mateo is constructing an equilateral triangle inscribed in a circle with center P. He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle. What is his next step?
when I make macaroni and cheese for my brother and me, I use 2 2/3 tablespoons of butter. how much butter will I n need to make my macaroni and cheese dish for Thanksgiving dinner if 15 people are attending?
on a certain planet, objects weight about 7/12 of what they weigh on earth. an object weights 13 5/12 pounds on the planet. solve the equation 7/12 w= 13 5/12 for w to find the objects weight on earth in pounds.
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is negative and the value of b is zero. Where could point P be located on the coordinate plane?
Select one or more:
Quadrant I
Quadrant II
Quadrant IV
Quadrant III
x-axis
y-axis
Answer:
X-axis.Step-by-step explanation:
Givens
We have point which coordinates are (a,b)The value of a is negative.The value of b is zero.Now, remember that all coordinates with the form (a,0), represents points on the x-axis, because the y-coordinate is zero.
In this case, we have negative horizontal coordinates and a null vertical coordinate, like (-a,0).
This points is on the x-axis, because y-value is null. Actually, it's on the negative part of x-axis, because its horizontal coordinate is negative.
Therefore, the right answer is x-axis.
Shelley spent 17 minutes washing dishes. She spent 38 minutes cleaning her room. Explain how you can use mental math to find how long Shelley spent on the two tasks.
A car uses 25L of petrol to travel 280km. What is the rate of petrol usage in kilometres per litre?
The rate of petrol per liter is 11.2 liter
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
In 25l car travels = 280km
For finding rate of petrol per liter we have to divide as
Rate of petrol = 280/25
Rate of petrol = 11.2 liter
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The rate of petrol usage for the car is 11.2 kilometers per litre, calculated by dividing the distance travelled, 280km, by the amount of petrol used, 25L.
The question asks to find the rate of petrol usage in kilometers per litre for a car that uses 25L of petrol to travel 280km. To calculate the fuel efficiency, you divide the distance travelled by the amount of petrol used.
Step-by-step calculation:
Distance travelled = 280 km
Amount of petrol used = 25L
Fuel efficiency (km/L) = Distance travelled / Amount of petrol used
Fuel efficiency = 280 km / 25L = 11.2 km/L
Therefore, the car's fuel efficiency is 11.2 kilometers per litre.
Carlos is putting money into a savings account. He starts with $750 in the savings account, and each week he adds $40 . Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Carlos has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 11 weeks.
Equation:
Total amount of money after 11 weeks:
Final answer:
The equation relating the total amount of money S in Carlos's savings to the number of weeks W he adds money is S = 750 + 40W. By substituting W with 11, we find that after 11 weeks, Carlos will have $1,190 in his savings account.
Explanation:
The question involves creating a linear equation to represent the relationship between the total amount of money S in Carlos's savings account and the number of weeks W he has been adding money. The equation can be written as S = 750 + 40W, where 750 represents the initial amount and 40 is the amount added each week. To find the total amount of money after 11 weeks, substitute W with 11:
S = 750 + 40(11) = 750 + 440 = 1190
Therefore, after 11 weeks, the total amount of money in the savings account would be $1,190.
Using the given zero, find all other zeros of f(x).
-2i is a zero of f(x) = x4 - 32x2 - 144
a) 2i, 12, -12
b) 2i, 6i, -6i
c) 2i, 6, -6
d) 2i, 12i, -12i
Answer:
c) 2i, 6, -6Step-by-step explanation:
The given function is
[tex]f(x)=x^{4}-32x^{2} -144[/tex]
The given zero to this function is
[tex]x=-2i[/tex]
Remember that a function has so many roots as its grade dictates. So, in this case, the function grade is four, which means it has four solutions.
Now, the given function is an imaginary number, which happens in pairs, that means the second root must be [tex]x=2i[/tex], because a function can have complex roots as pairs, 2, 4, 6,... many solutions.
The other two solutions are 6 and -6, because if we replace them into the function, it will give zero.
[tex]f(6)=6^{4}-32(6)^{2} -144=0\\f(-6)=(-6)^{4}-32(-6)^{2} -144=0[/tex]
Therefore, the other three solutions missing are: c) 2, 6, -6.
(The image attached shows the real solutions).
Use the number 913,256. Write the name of the period that has the digits 913.
The Grand Prix Formula 1 race this weekend is in Singapore. The race consists of 61 laps around a 5.067 km long track. At 225 miles per hour, how long will it take to go around once?