Think of a number, divide it by 5 and then add 27 to the result. The resulting number is half of the original number. What was the original number?
(Answer with work please)
find the formula for the graph of function f(x) given in the graph above
The given graph is scaled form of trigonometric function graph.
The formula for the graph function f(x) is given by:
[tex]f(x) = -2sin(\dfrac{x}{4})[/tex]
How to find the formula for f(x) for given graph?Note down the properties one by one.
Firstly its a periodic function.
Secondly, the maximum value of the function is 2 and minimum value is -2
Thirdly the function assumes maximum or minimum value when it reaches to [tex]2 \pi n; n \in \mathbb Z[/tex]
Fourthly, the graph from the center to right side goes down then up then down then up and so on.
If you've seen graph of sine function, then you'd know that the graph is periodic(repeating same values after some interval), the maximum and minimum values being 1 and -1 and maximum or minimum values are achieved when input is [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex]
Plus, the graph from center to right goes up then down then up then down and so on.
Transforming sine graph to make the given graph:First we need down then up instead of up and down. Since down is negative output in its graph and up is positive, thus we will negate the value of sine function.
[tex]-sin(x)[/tex] will have flipped mountains and valley's in comparison to that of sin(x).
Now since the maximum and minimum values are needed to be 2 and -2 instead of 1 and -1, thus we will scale the output with factor of 2.
[tex]-2sin(x)[/tex] will have maximum and minimum as 2 and -2 respectively.
We need the graph to be maximum or minimum at x = [tex]2 \pi n; n \in \mathbb Z[/tex] and not at x = [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex]. Thus, we will scale down the input of -2sin(x) so that it treats [tex]2 \pi n; n \in \mathbb Z[/tex] as if it was given [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex].
The scaling needs to be by 1/4 since [tex]\dfrac{1}{4} \times 2\pi n = \dfrac{n\pi}{2}[/tex]
Thus, the resultant function is [tex]-2sin(\dfrac{x}{4})[/tex]
The below plotted graph shows graph of sin(x) (in red) and that of [tex]-2sin(\dfrac{x}{4})[/tex] (in blue).
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Alex wants to start an IRA that will have $1,250,675 in it when he retires in 30 years. How much should he invest semiannually in his IRA to do this if the interest is 4.5% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.
Answer:
$9828.44
Step-by-step explanation:
The semi annual payment is such that the future value of the annuity due is equal to the desired amount when he retires.
The formula to calculate future value of an annuity due periodic payment of M for time period T for given periodic return r,
A=[tex]\frac{M(1+r)^{T+1}-(1+r)}{r}[/tex]
in this question there are 30*2= 60 payments and the semi annual rate= 4.5/2= 2.25%
putting values we get
1250675= [tex]\frac{M(1+2.25%)^{60+1}-(1+2.25%)}{2.25%}[/tex]
on solving we get M= $9828.44
Alex needs to invest $9828.44 semiannually in his IRA
Which of the following is a situation in which an equation cannot be solved using the quadratic formula? A.) The coefficient of the x^2 term is zero B.) The right hand side of the equation is zero C.) The coefficient of the x term is zero D.) The degree of the polynomial is 2
Final answer:
An equation cannot be solved using the quadratic formula if the coefficient of the [tex]x^{2}[/tex] term is zero, as this makes it a linear equation, not a quadratic. So, option A is correct.
Explanation:
The situation in which an equation cannot be solved using the quadratic formula is when the coefficient of the [tex]x^{2}[/tex] term is zero (A). An equation is only quadratic if it is of the form a[tex]x^{2}[/tex] + bx + c = 0, where 'a' is not equal to zero. If 'a' is zero, the equation is not a quadratic equation but a linear one, and the quadratic formula cannot be applied. The quadratic formula, 'x' equals minus 'b', plus-or-minus the square root of 'b' squared minus four 'a' 'c', all over two 'a', requires a nonzero 'a' value because the denominator of the formula includes '2a'. If 'a' is zero, the formula would involve division by zero, which is undefined.
Option B is incorrect because having zero on the right-hand side of the equation does not affect the use of the quadratic formula. Likewise, option C is incorrect because the equation can still be quadratic even if the coefficient of the x term ('b') is zero; the equation becomes a pure quadratic equation. Option D suggests the polynomial is already of degree 2, which is the correct type of equation to apply the quadratic formula.
The equation x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b
Answer:
Step-by-step explanation:
Alright, let get started.
The given equation is : [tex]x^2-1x-90=0[/tex]
This is a quadratic equation.
The standard form of a quadratic equation is : [tex]AX^2+BX+C=0[/tex]
Comparing the given equation with standard one, the values of A ,B and C are :
A is 1
B is -1
C is -90
Since a and b are the roots of the equation, so the formula for sum of roots a+b will be = [tex]\frac{-B}{A}[/tex]
a+b=[tex]-\frac{-1}{1} =1[/tex]
hence a+b will be 1 : Answer
Hope it will help :)
Which of the following best describes the square root property of equality
if they have two quantities that are equal to the same things, then they would be equal to each others.
Heather drove at a constant rate. She traveled miles in 3 hours. How far did Heather travel in 1 hour?
The distance travelled for 1 hours will be h / 3 miles
She travels at a constant rate. Therefore, the speed is the same for any journey or distance covered.
Speedspeed = distance / timeIf she travels h miles in 3 hours the rate will be as follows;
rate = h / 3 miles per hourTherefore, if she travels 1 hour at the same rate , the distance travel can be computed as follows;
h / 3 = d / 1Therefore,
cross multiply
h = 3d
d = h / 3
The distance travelled for 1 hours will be h / 3 miles
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I don't understand how 251/4 divided by (-3/8)= -502/3
Using the PEMDAS rule, the correct result is -502/3.
We have,
Using the order of operations (PEMDAS) and simplifying the fractions, we have:
251/4 ÷ (-3/8)
= 251/4 × (-8/3) (since dividing by a fraction is the same as multiplying by its reciprocal)
= -502/3
Therefore,
The correct result is -502/3.
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As part of a traffic safety campaign a speed detector was used to record speed in the entrance driveway to the Jefferson High School parking lot. The box and whisker plot shows the results.
HELP ME PLEASE ASAP
The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamall‘s house. How much farther from school is Tonyas house than Jamall‘s house? Explain how you can use a quick picture to solve the problem.
The answer is 2.37 miles. The possible explanation for this is I can illustrate 3.65 using 3 squares for ones, 6 lines for tenths, and 5 circles for hundredths. I would now then reform 1 tenth as 10 hundredths. Then, I would subtract 8 hundredths from 15 hundredths. Then, I would take away 2 tenths from 5 tenths. Last, I would deduct 1 from 3.
Find the exact circumference of a circle with an area equal to 36 sq. in.
1) 12
2) 18
3) 324
Answer:
The answer would be option 1) 12
Answer:
The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].
Step-by-step explanation:
The area of a circle when we know the circumference is
[tex]A=\frac{C^2}{4\pi }[/tex]
We know the area [tex]A=36 \:{in^2}[/tex], we plug this value into the above equation and we solve for C the circumference.
[tex]36=\frac{C^2}{4\pi }\\\frac{C^2}{4\pi }=36\\\frac{C^2\cdot \:4\pi }{4\pi }=36\cdot \:4\pi \\\\C^2=144\pi \\C=\sqrt{144\pi }\\C=12\sqrt{\pi }[/tex]
The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].
Maricella plots two ordered pairs on the grid below.
Answer:
B. [tex](0,-10)[/tex]
Step-by-step explanation:
We have been given an image of a line segment on coordinate plane. We are asked to find the y-intercept of line, is the line segment is extended to cross both the axes.
We will find the equation of line in slope-intercept form: [tex]y=mx+b[/tex], where,
m = Slope of line,
b = The y-intercept.
We will find slope of our given line using the coordinates of our given points (6,2) and (8,6).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{6-2}{8-6}[/tex]
[tex]m=\frac{4}{2}[/tex]
[tex]m=2[/tex]
Now, we will substitute [tex]m=2[/tex] and coordinates of point (8,6) in slope-intercept form of equation.
[tex]6=2*8+b[/tex]
[tex]6=16+b[/tex]
[tex]6-16=16-16+b[/tex]
[tex]-10=b[/tex]
Since y-intercept of our given line is [tex]-10[/tex], which is at [tex]x=0[/tex], therefore, option B is the correct choice.
What is the equation of this line in standard form? −6x+11y=13 −6x+7y=−17 −6x+11y=−13 −11x+6y=−13 Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points begin ordered pair negative four comma negative one end ordered pair and begin ordered pair one and begin fraction one-half end fraction comma, two end ordered pair
Answer:
What is the equation of this line in standard form?
6x−11y=−13
is the answer
In how many ways can the letters BEACH be rearranged
A basketball court is shaped like a rectangle. It has a perimeter of 288 feet. The width of the court is 50 feet. What is the length of the court? Use the following formula to help you decide: Pr = 2l + 2w where Pr is the perimeter of a rectangle, l is the length, and w is the width
using the given formula, fill in the numbers where they belong
perimeter = 288
width = 50
so Pr = 2l + 2w becomes
288 = 2l +2(50)
288 = 2l +100
subtract 100 from each side
188 =2l
divide both sides by 2
l = 188 /2
l = 94
length = 94 feet
Maricella plots two ordered pairs on the grid below.
Answer: (0,-10)
Step-by-step explanation:
The equation of a line (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
From the given graph , the line is passing through (6,2) and (8,6) is given by :_
[tex](y-6)=\dfrac{6-2}{8-6}(x-8)\\\\\Rightarrow\ y-6=\dfrca{4}{2}(x-8)\\\\\Rightarrow\ y-6=2(x-8)\\\\\Rightarrow\ y=2(x-8)+6[/tex]
To find the y intercept put x =0 , we get
[tex]y=2(0-8)+6=-16+6=-10[/tex]
Hence, the y-intercept of the graph : (0,-10)
If f(x) = f(x)g(x), where f and g have derivatives of all orders, show that f'' = f ''g + 2f 'g' + fg''.
P (1.23 < z < 3.24) =
The value of the P (1.23 < z < 3.24) is 0.49 after using the Z table and concept of the probability.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
P (1.23 < z < 3.24)
As we know, from the normal distribution, It's the probability curve of a continuous distribution that's most likely symmetric around the mean.
On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
From the Z curve:
P (1.23 < z < 3.24) = 0.49
Thus, the value of the P (1.23 < z < 3.24) is 0.49 after using the Z table and concept of the probability.
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Which equation shows how the properties of numbers extend to negative whole numbers by the commutative property of addition?
A) -2 + 4 = 4 + (-2)
B) -2(4) = 4(-2)
C) (-2 + 4) + 3 = -2 + (4+3)
D) -2(4+3) = (-2 x 4) + (-2 x 3)
Please help!
Action movies make up 85% of Devon’s movie collection. If he has 20 movies, how many action movies are in Devon’s collection ? Explain your reasoning to classmate
Use cross products to determine whether the points a, b, and c are collinear.
bo has 23 video games for sale he plans to donate the money he makes from each sale to a local charity what is the least amount of money in whole dollars bo should charge for each game in order to raise 100$
Answer: $5
Step-by-step explanation:
Let x be the least charge for each video game.
Given : Total games for sale =23
The required minimum amount needed to raise by selling video games =$100
Then the required inequality:
Total games × x ≥ Required minimum amount
i.e. [tex]23x\geq100[/tex]
Divide 23 from both sides , we get
[tex]x\geq 4.34782608696\approx5[/tex]
Hence, Bo should Charge $5 for each game in order to raise 100$.
Rectangles ABCD and EFGH are similar. The perimeter of rectangle ABCD is 5 times greater than the perimeter of rectangle EFGH. What is the relationship between the areas of the rectangles?
A. The area of rectangle EFGH is 25 times greater than the area of rectangle ABCD.
B. The area of rectangle EFGH is 5 times greater than the area of rectangle ABCD.
C. The area of rectangle ABCD is 25 times greater than the area of rectangle EFGH.
D. The area of rectangle ABCD is 5 times greater than the area of rectangle EFGH.
Answer:
Step-by-step explanation:
Thank you
A student solved the problem below by first dividing 20 by 10. What mistake did the student make? A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?
Answer:
Step-by-step explanation: The student divided the number of wins by the number of losses.
The student should have divided the number of wins by the total number of games.
The student should have first added 20 and 10 to find that there were a total of 30 games.
Answer:
SAMPLE RESPONSE: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.
Step-by-step explanation:
other answer: The student divided the number of wins by the number of losses.
The student should have divided the number of wins by the total number of games.
The student should have first added 20 and 10 to find that there were a total of 30 games.
Find the three consecutive integers whose sum is 171
171 / 3 = 57
56 + 57 +58 = 171
the 3 numbers are 56, 57 & 58
If a flower is 6.5 cm wide, its width expressed in millimeters is x mm, where x is
A unit of measure is the actual unit in which the associated values are measured. If a flower is 6.5 cm wide, its width expressed in millimeters is 65 mm,
What is Unit of Measurement?A Unit of measure is the actual unit in which the associated values are measured.
Unit of Measurement is used as a standard for measurement of the same kind of quantity. The weight is measured in kilograms, grams. The kilogram is unit of mass. litres is the unit of measuring liquids and length is measured in different units, feet, inches, meters, kilometers, centimeters.
We know that 1 centimeter = 10 milli meters.
So if a flower is 6.5 cm wide, its width expressed in millimeters is x mm
We need to find the value of x.
6.5 cm = 6.5×10
=65
So 6.5 cm in millimeters is 65 mm.
Hence if a flower is 6.5 cm wide, its width expressed in millimeters is 65mm.
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Convert the following temperatures from K to °C.
100 K = °C
273 K = °C
6 K = °C
143°C = K
573°C = K
we know that
The formula to convert K to C is equal to
[tex]\° C =\°K - 273.15\°[/tex] --------> equation [tex]1[/tex]
and
The formula to convert C to K is equal to
[tex]\° K =\°C +273.15\°[/tex] --------> equation [tex]2[/tex]
case a) [tex]100\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =100\°- 273.15\°=-173.15\°[/tex]
therefore
the answer Part a) is
[tex]\° C =-173.15\°[/tex]
case b) [tex]273\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =273\°- 273.15\°=-0.15\°[/tex]
therefore
the answer Part b) is
[tex]\° C =-0.15\°[/tex]
case c) [tex]6\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =6\°- 273.15\°=-267.15\°[/tex]
therefore
the answer Part c) is
[tex]\° C =-267.15\°[/tex]
case d) [tex]143\° C[/tex]
convert to K
substitute in the equation [tex]2[/tex]
[tex]\° K =143\°+ 273.15\°=416.15\°[/tex]
therefore
the answer Part d) is
[tex]\° K =416.15\°[/tex]
case e) [tex]573\° C[/tex]
convert to K
substitute in the equation [tex]2[/tex]
[tex]\° K =573\°+ 273.15\°=846.15\°[/tex]
therefore
the answer Part e) is
[tex]\° K =846.15\°[/tex]
The Soup Shack usually makes tomato soup with 9 tomatoes for every 12 cups of soup. Today, they made 8 cups of soup with 6 tomatoes. How does today's soup compare to the usual recipe?
Answer: We compare today's soup to the usual recipe by using "Unitary Method".
Step-by-step explanation:
Since we have given that
The Soup Shack makes tomato soup with 9 tomatoes for every 12 cups of soup.
For every 12 cups of soup , 9 tomatoes is needed
For every 1 cup of soup , the number of tomato is needed is given by
[tex]\frac{9}{12}=\frac{3}{4}[/tex]
Today, they made 8 cups of soup with 6 tomatoes ,
For 8 cups, 6 tomatoes are used .
For 1 cup, number of tomato is used is given by
[tex]\frac{6}{8}=\frac{3}{4}[/tex]
So, we can see that both the soup has same quantity .
∴ We compare today's soup to the usual recipe by using "Unitary Method".
When more than one function has the same name they are called ________ functions?
Z varies inversely with the product of x and y. When x=2 and y =4 z=0.5 what is the value of x=4 and y=9