Answer:
True
Step-by-step explanation:
In general, when you compose a function [tex]f(x)[/tex] with its inverse [tex]f^{-1}(x)[/tex], you always get the identity function:
[tex]f(f^{-1}(x))=x[/tex]
The limitation [tex]-1\leq x \leq 1[/tex] is necessary because the arcsin function wouldn't be defined otherwise.
The statement 'sin(sin^-1 x) = x' is true for all real numbers x.
The statement 'sin(Sin^-1 x)=x for -1<=x<=1' is true. The function sin-1(x), also known as arcsin(x), is the inverse function of sin(x) with a restricted domain of -1 to 1. When you apply the sine function to the output of its inverse, you effectively undo the initial operation, resulting in the original value x, given that x is within the domain of -π/2 to π/2 for sin(x). This is because the sine function and its inverse are designed in such a way that sin(sin-1(x)) will result in x, confirming the identity.
He model below can be used to find the quotient of one over two divided by one over six. What is the quotient?
1/2÷1/6
=
1/2*6/1
=
6/2
=
3
Answer:
Quotient would be 3.
Step-by-step explanation:
The model below can be used to find the quotient of one over two dividend by one over six.
We will rewrite the problem :
[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{6}[/tex]
As we know when we divide the two fractions, we must invert the second fraction and put the sign of multiplication in place of division sign and multiply.
So now we can write the problem as :
[tex]\frac{1}{2}[/tex] × [tex]\frac{6}{1}[/tex]
= [tex]\frac{6}{2}[/tex]
= 3
Quotient would be 3.
Bethany sells roses and petunias. The expression 3r+2.5p3r+2.5p3, r, plus, 2, point, 5, p gives the cost (in dollars) of r roses and p petunias. What is the cost of 7 roses and 8 petunias?
The side of a square is 12 feet. What is the area of the square? A) 12 sq. Ft. B) 24 sq. Ft. Eliminate C) 48 sq. Ft. D) 144 sq. Ft.
Answer:D) 144
Step-by-step explanation:12*12=144
Answer:
the answer is 144
Step-by-step explanation:
Please help me if you can!
Here is your answer
[tex]<b>z= 20 degrees</b>[/tex]
REASON:
[tex]<font color="blue" size=5>Concept used</font>[/tex]: The sum of adjacent angles of a parallelogram is 180 degrees.
So, in above given figure
[tex] 2z+16+124=180 [/tex] (measures of adjacent angles)
[tex]2z+140=180 [/tex]
[tex] 2z=180-140 [/tex]
[tex]2z=40 [/tex]
[tex]z= 40/2 [/tex]
[tex]z= 20 [/tex]
HOPE IT IS USEFUL
You have a job as a teacher with a starting salary of $37,185. You will receive a 6% raise every year. How much will you salary be after 5 year?
if it is asking for compound interest your answer should be 49761.9
At what x-values do the graphs of the functions y=cos 2x and y=1-sin^2x intersect over the interval 0 < x < pi
_ _
Answer:
No solution.
Step-by-step explanation:
The given functions are
[tex]y=\cos2x[/tex] and [tex]y=1-\sin^2x[/tex].
To find the point of intersections of the graphs of the two functions: we equate them and solve for [tex]x[/tex].
[tex]\cos2x=1-\sin^2x[/tex]
Recall the double angle identity; [tex]\cos2x=cos^2x-sin^2x[/tex]
Apply this identity to obtain;
[tex]cos^2x-sin^2x=1-\sin^2x[/tex]
[tex]\Rightarrow cos^2x=1[/tex]
[tex]\cos x=\pm1[/tex]
[tex]x=0\:or\:x=\pi[/tex]
if the interval is [tex]0\le x\le \pi[/tex], then the two graphs intersect at [tex]x=0\:or\:x=\pi[/tex]
But [tex]x=0\:and\:x=\pi[/tex] does not belong to the open interval [tex]0\:<\:x\:<\:\pi[/tex]
No point of intersection.
PLEASE HELP! I AM NEED IT DESPERATELY!!
Write the equation of the line in point-slope form.
Answer:
y= -2x/3+8
Step-by-step explanation:
find 2 points: (0,8) and (6,4)
substitute in y=ax+b
8=0a+b
b=8
4=6a+b
4=6a+8
6a=-4
a=-2/3
Jerome solved the equation below by graphing.
log2(x) + log2(x-2) = 3
Which of the following shows the correct system of equations and solution?
Answer:
B. x = 4
Step-by-step explanation:
I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:
[tex]\log_bm+\log_bn=\log_bmn[/tex]
Using this law, we can combine and rewrite our initial equation as
[tex]\log_2(x\cdot(x-2))=3\\\log_2(x^2-2x)=3[/tex]
Remember that logarithms are simply another way of writing exponents. The logarithm [tex]\log_28=3[/tex] is just another way of writing the fact [tex]2^3=8[/tex]. Keeping that in mind, we can express our logarithm in terms of exponents as
[tex]\log_2(x^2-2x)=3\rightarrow2^3=x^2-2x[/tex]
2³ = 8, so we can replace the left side of our equation with 8 to get
[tex]8 = x^2-2x[/tex]
Moving the 8 to the other side:
[tex]0=x^2-2x-8[/tex]
We can now factor the expression on the right to find solutions for x:
[tex]0=(x-4)(x+2)\\x=4, -2[/tex]
The only option which agrees with our solution is B.
Answer:
The answer is:
[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]
Step-by-step explanation:
We are given a logarithmic expression as:
[tex]\log_2 x+log_2 (x-2)=3[/tex]
As we know that:
[tex]\log_a x=\dfrac{\log x}{\log a}[/tex]
Hence, we get the logarithmic expression as follows:
[tex]\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}=3[/tex]
We know that we can get the system of equations as follows:
[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}[/tex]
and
[tex]y_2=3[/tex]
Hence, when we plot the graph for this system of equations we see that the point of intersection of the graph is: (4,3)
Hence, the solution is the x-value of the point of intersection of the two equations.
Hence, x=4 is the solution.
Hence, the correct option is:
[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]
A 5.5-foot-tall woman walks at 4 ft/s toward a street light that is 27.5 ft above the ground. what is the rate of change of the length of her shadow when she is 16 ft from the street light? at what rate is the tip of her shadow moving?
The scenario involves differentiating a proportional relationship between the woman's distance from a streetlight and the length of her shadow to determine the rate of change of the shadow's length and the speed of the shadow's tip.
Explanation:The question involves finding the rates of change in the scenario where a woman walks toward a streetlight and the effects on her shadow's length and speed. Let's denote the distance between the woman and the streetlight as x, the length of her shadow as y, and her height as h. The streetlight's height is given as H. Using similar triangles, we can establish the relationship (H - h) / y = H / (x + y). Differentiating both sides with respect to time, t, allows us to calculate the rates of change we're interested in.
To find the rate of change of her shadow's length when she is 16 feet from the streetlight, we can take dh/dt as 0 since her height is constant, dx/dt as -4 ft/s because she is walking towards the light and substitute into the derived equation after differentiating. Similarly, we calculate the rate at which the tip of the shadow is moving by adding the rate of the woman's movement to the rate of change of the shadow's length.
Solve: 3x(x + 4) + 3(x + 4) = 0 A) 0 and -4 B) -1 and 4 C) -1 and -4 Eliminate D) 1 and 4
Answer:
The answer is C) -1 and -4
Step-by-step explanation:
Sorry i don't have the step by step explanation but that's the answer
g A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes (P = 0.287). This conclusion implies that the maximum difference in GPAs between male and female scholarship athletes is 0.287. the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287. the GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes. the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287
Answer:
the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287
Step-by-step explanation:
When conducting hypothesis tests, the P value tells you the probability of the results happening by random chance. That's why we usually test against a very low alpha level, usually 1% or 5%.
Here P = 28%, so there is a 28% chance that if we take a sample of athletes, about 1 out of 4 times there won't be a significant difference in GPA between males and females.
∠A and ∠B supplementary and vertical angles. What is m∠B
135
90
180
45
Answer:
90°
Step-by-step explanation:
Supplementary means they add to 180°. Vertical angles are congruent, so they must both be 180°/2 = 90°.
Answer:
90
Step-by-step explanation:
Did the Geometry quiz 2021
Plz click the Thanks button!
<Jayla>
Given that DE = 75 inches what is the length of EF ?
Answer:
61.19 inchesStep-by-step explanation:
Use the sine law:
[tex]\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}[/tex]
We have:
[tex]DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788[/tex]
Substitute:
[tex]\dfrac{75}{0.9659}=\dfrac{EF}{0.788}[/tex] cross multiply
[tex]0.9659EF=(75)(0.788)[/tex]
[tex]0.9659EF=59.1[/tex] divide both sides by 0.9659
[tex]EF\approx61.19[/tex]
The length of the EF is 61.19 inches if the DE = 75 inches option fourth is correct.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have:
DE = 75 inches
By using the sin law:
sin52/EF = sin75/DE
sin52/EF = sin75/75
sin52/EF = 0.0128
EF = 61.185 ≈ 61.19 inches
Thus, the length of the EF is 61.19 inches if the DE = 75 inches option fourth is correct.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ2
Choose Yes or No to tell if the fraction 4 9 49 will make each equation true. 63 × □ = 28 63×□=28 18 × □ = 8 18×□=8 96 × □ = 42 96×□=42 36 × □ = 16 36×□=16
Answer:
YES
YES
NO
YES
Step-by-step explanation:
Assuming that the value is [tex]\dfrac{4}{9}[/tex].
Let's take each of the equations and check if the fraction makes the equation true.
When multiplying a whole number to a fraction, it is the same as multiplying the whole number to the numerator and dividing the total by the denominator.
[tex]63*\dfrac{4}{9}=28[/tex]
[tex]\dfrac{63*4}{9}=28[/tex]
[tex]\dfrac{252}{9}=28[/tex]
[tex]28=28[/tex] YES
[tex]18*\dfrac{4}{9}=8[/tex]
[tex]\dfrac{18*4}{9}=8[/tex]
[tex]\dfrac{72}{9}=8[/tex]
[tex]8=8[/tex] YES
[tex]96*\dfrac{4}{9}=42[/tex]
[tex]\dfrac{96*4}{9}=42[/tex]
[tex]\dfrac{384}{9}=42[/tex]
[tex]42.67=42[/tex] NO
[tex]36*\dfrac{4}{9}=16[/tex]
[tex]\dfrac{36*4}{9}=16[/tex]
[tex]\dfrac{144}{9}=16[/tex]
[tex]16=16[/tex] YES
Answer:
yes
yes
no
yes
hope this helps!!
what is the value of the constant in the equation that relates the height and width of this rectangle?
would appreciate any help i could get :)
Answer:
Option C. [tex]2.5[/tex]
Step-by-step explanation:
we know that
In the rectangle of the figure
[tex]\frac{H}{W}=\frac{25}{10}=2.5[/tex]
so
[tex]H(W)=2.5W[/tex]
The constant is equal to [tex]2.5[/tex]
Answer:
2.5
Step-by-step explanation:
David sold 6 apple trees. He sold 5 of the apple trees to max. What fraction of the apple trees did david sell to max
Answer:
wouldn't it be 6/5 or 5/6 or 1.2
Step-by-step explanation:
Find the area of a parallelogram that has a base of 24 feet and a height of 12 feet
you're answer would be two hundred eighty eight
Answer:
288
Explanation:
Hope this helps
Simplify the expression (4x − 3)(x + 5).
A. 4x2 − 17x + 15
B. 4x2 − 17x − 15
C. 4x2 + 17x + 15
D. 4x2 + 17x − 15
D using the foil method
Answer: [tex]4x^2+17x-15[/tex]
Step-by-step explanation:
To simplify the given expression we need to apply the distributive property in algebra.
The distributive property is given by :
[tex]a(b+c)=ab+ac[/tex]
The given expression:
[tex](4x- 3)(x + 5)\\\\=(4x-3)x+(4x-3)5\ \ \ \ \text{By distributive property}\\\\=4x^2-3x+20x-15\\\\=4x^2+(-3+20)x-15\ \ \ \text{Combining like terms}\\\\=4x^2+17x-15[/tex]
Kendall is buying a home for $119,000. She is making a 12% down payment and financing the rest with a 20-year loan at a 4.5% interest. What is her monthly mortgage payment?
Answer:
$455.97
Step-by-step explanation:
119000 × 0.12 = 14280
119000 - 14280 = 104720
104720 × 1.045 = 109432.4
109432.4/(20×12)
109432.4/240
455.97 a month
Answer:
$662.46
Step-by-step explanation:
Solve the equation (linear equation)
[tex]8^{2x+7} = (\frac{1}{32})^{3x}[/tex]
Answer: [tex]x=-1[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
Therefore, you can rewrite the left side of the equation has following:
[tex](\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}[/tex]
Descompose 32 and 8 into its prime factors:
[tex]32=2*2*2*2*2=2^5\\8=2*2*2=2^3[/tex]
Rewrite:
[tex](\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}[/tex]
Then:
[tex](\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}[/tex]
As the base are equal, then:
[tex]-3(2x+7)=5(3x)[/tex]
Solve for x:
[tex]-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1[/tex]
A party store sells large plates in packs of 12 and small plates in packs of eight. In order to have an equal number of both, what is the least amount of large plaate packs that would have to be purchased?
Answer:
The least amount of large plate packs that would have to be purchased is 24.
Step-by-step explanation:
To do this we have to find first multiplication of 8 that is equally divided by 12.
A person can buy large packs of plates in multiple of 12 only.
A person can buy {1,2,3,4,5,6,7,8,...}packs of plates and will purchase
{12,24,36 ,48,60,72,84,96,...}large plates.
A person can buy small packs of plates in multiple of 8 only.
A person can buy {1,2,3,4,5,6,7,8,9,10,11,12...}packs of plates and will purchase..
{8,16,24,32,40,48,56,64,72,80,88,96,...}small plates
Now we have to keep in mind that one has to purchase equal amount of plates..
A person can buy {24,48,72,96} plates and hence least amount of large plate packs that would have to be purchased is 24....
What is the graph of the function x^2-9x+20 over x-4
Answer:
a straight line: y = x -5, with a hole at (4, -1)
Step-by-step explanation:
The rational function can be simplified to ...
[tex]f(x)=\dfrac{x^2-9x+20}{x-4}=\dfrac{(x-5)(x-4)}{(x-4)}\\\\f(x)=x-5\qquad\text{$x\ne 4$}[/tex]
The graph of this is a straight line, with a hole at x=4, where the function is not defined.
One geometry question need this as soon as possible please!
simplify :7x + 3x - 5 + 8x + 5 = 180
x = 10
True or false (Picture provided)
The answer is: True.
Why?A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.
So:
[tex]sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx[/tex]
Then, evaluating we have:
[tex]\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}[/tex]
Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for [tex]sec^{2}x-1=\frac{cosx}{cscx}[/tex] and the answer is true.
Have a nice day!
Given that the points (-5,7), (5,7),(5,1), and (-5,1) are vertices of a rectangle, how much stronger is the width than the length
Answer:
4 units
Step-by-step explanation:
The sides of the rectangle are parallel to the axes, so it is a simple matter to subtract coordinate values to find the dimensions.
Along the line y=7, the rectangle extends from -5 to 5, so has width 10.
Along the line x=5, the rectangle extends from 1 to 7, so has length 6.
The width is 10 - 6 = 4 units more than the length.
Answer: width=7 length =9
9-7=2
2 is the answer
HELPPPPPPPPPPPPPPP ONNNNNNNNNNN MATHHHHHHHH
a. The ratio of boys to girls in a class is 6 to 5 . What is the ratio of girl s to all the students in the class? b. If the ratio of boys to girls in a class is m:n, what is the ratio of girl s to all the students in the class? c. If five elevenths of the class are girls, what is the ratio of girls to boys? a. The ratio, in simplest form, of the number of girl s to the total number of students is 5 :11 . b. The ratio, in simplest form, of girl s to all the students in the class is nothing :nothing . c. The ratio, in simplest form, of girls to boys is nothing :nothing.
Answer:
a. Ratio of girls to all students 5:11
b. Ratio of girls to all students n:m+n
c. Ratio of girls to boys 5:6
Step-by-step explanation:
In order to find each of these, we simply need to look at these as a comparison of two data points.
a. In this example, we are looking for girls to all students. We already who there would be 5 girls in the comparison. Then we need to find the whole amount, which is girls + boys (6 + 5 = 11)
5:11
b. In this example, we are looking for girls to all students. We already who there would be n girls in the comparison. Then we need to find the whole amount, which is girls + boys (m + n)
n:m+n
c. In this example, we are looking for girls to boys. We already who there would be 5 girls in the comparison. Then we need to find the boys amount, which is whole - girls (11 - 5 = 6)
5:6
Final answer:
The ratio of girls to all students in a class with a boy-girl ratio of 6 to 5 is 5 to 11. The general ratio of girls to all students with a boy-girl ratio expressed as m:n is n:(m+n). Lastly, if five elevenths of the class are girls, then the ratio of girls to boys is 5 to 6.
Explanation:
Understanding Ratios in a Classroom Setting
The ratio of boys to girls in a class is initially given as 6 to 5. To find the ratio of girls to all the students in the class, the sum of the parts of the ratio must first be calculated, which is 6 (boys) + 5 (girls) = 11 (total students).
Therefore, the ratio of girls to the total number of students is 5 to 11. This is because for every 11 students, 5 are girls. If the ratio of boys to girls is expressed as m:n, then the ratio of girls to all students will be n:(m + n).
For a scenario where five elevenths of the class are girls, the ratio of girls to boys needs to be determined. As five elevenths represent the girls, six elevenths must represent the boys, since they sum up to the whole, which is one (or 11/11). Therefore, the ratio of girls to boys is 5:6.
After 2 years, $600 deposited in a savings account with simple interest had earned $120 in interest. What was the interest rate?
Answer:
300%
Step-by-step explanation:
600 / 120 = 300
What is the volume of a cylinder whose base has a diameter of 10 and whose height is 12?
the answer is 942.because the formula is V=Bh. V=pir2h. so V= 3.14×5squared×12. so 3.14×25×12. 25×12=300. and 3.14×300=942
What is the equation of the horizontal asymptote? f(x)=4⋅2^x−5
Question options:
y=0
y=4
y=−5
y=2
ANSWER
[tex]y = - 5[/tex]
EXPLANATION
The horizontal asymptote of a general exponential function,
[tex]f(x) = a {(b)}^{x} + c[/tex]
is y=c.
The given exponential function is
[tex]f(x) = 4{(2)}^{x} - 5[/tex]
By comparing the given function to
[tex]f(x) = a {(b)}^{x} + c[/tex]
we have c=-5, therefore the horizontal asymptote is
[tex]y = - 5[/tex]