Answer:
Their point of intersection will always be on the line y = x.
Step-by-step explanation:
We have a function f(x) and its inverse is the function f⁻¹(x).
The domain and range of a function replaces each other for the inverse of that function.
So if f(x) and f⁻¹(x) are inverse of each other
and f(a) = b
then a = f⁻¹(b)
Another example to make it clear is that
f(5) = 25
f⁻¹(25) = 5
The function and its inverse will intersect each other at the point where f(x) = f⁻¹(x) which is only possible when a = b.
Hence, a function and its inverse will always intersect at a point on the line x=y.
a coin is tossed two times find the probability of getting (1 . exactly one head (2.at least one head (3. at most one head
[tex]|\Omega|=2^2=4[/tex]
1.
[tex]|A|=2\\P(A)=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
2.
[tex]|A|=3\\P(A)=\dfrac{3}{4}[/tex]
3.
[tex]|A|=3\\P(A)=\dfrac{3}{4}[/tex]
How many solutions does the equation 4s + 8 = 3 + 5 + 4s have? (5 points) Two None One Infinitely many
Answer:
Infinitely many
8
Step-by-step explanation:
First, you subtract by 4s both sides of equation.
4s+8-4s=3+5+4s-4s
Then, simplify.
8=3+5
Same thing like order of operations.
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
Add the numbers from left to right.
3+5=8
8=8 is true
8 is the correct answer.
Infinitely many is the correct answer.
The given equation has no solution.
As the given equation is:
[tex]4s+8=3+5+4s\\[/tex]
So, if we simplify we get;
[tex]8=3+5+4s-4s[/tex] (subtracting 4s from both sides of the equation)
Now, on adding we get;
[tex]8=8[/tex]
So, LHS=RHS.
Therefore, there is no variable for which we can find the solution.
Hence option(b) none is the correct answer
What's an equation in math?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in maths when you do not know the exact number in a calculation. Many professionals use equations every day, including air traffic controllers, architects, computer programmers and carpenters.
What is an equation example?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
What is the best definition for equation?Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account. An example of an equation is 2+2 = 3+1.
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Kite ABCD is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis. What is the location of point a after the transformations are complete? (5,-1), (-5,1), (-5,-1), (5,1)
Answer:
(-5, 1)
Step-by-step explanation:
We are given a kite on the graph which is rotated 180° clockwise about the origin and then reflected over the Y axis followed by reflection over the X axis.
We are to find the coordinates of point A after the complete transformation.
A (-5, 1)
When a point is rotated 180° clockwise about the origin, the signs of its coordinates change.
A (-5, 1) ---> A' (5, -1) - after clockwise rotation of 180 degrees about origin
Then this point A' is reflected over the Y axis where the y coordinate remains the same but x coordinate changes its sign.
A' (5, -1) ---> A'' (-5, -1) - after reflection through y axis
Now this point A'' is reflected over the X axis where the x coordinate remains the same while y coordinates changes its sign.
A'' (-5, -1) ---> A''' (-5, 1) - after complete transformation
Answer:(-5, 1)
Step-by-step explanation:
Please help. The survey data, and question is in the picture provided.
Answer:
[tex]\frac{83}{186}[/tex]
Step-by-step explanation:
In probability, "OR" means "+" and "AND" means "*".
The total amount of people is:
32 + 54 + 78 + 112 + 96 = 372
Number of diabetic patients are 54
Number of eye patients are 112
Since we want "OR", we will add the two probabilities:
P(diabetic or eye problem) = 54/372 + 112/372 = 83/186
Whatis the value of the expression
4(x + y)
when x= 6 and y= 24?
Answer:
120
Step-by-step explanation:
Evaluate the expression by substituting the given values into it
4(6 + 24) = 4 × 30 = 120
The number of lattes sold daily for two coffee shops is shown in the table:
Lattes
12
52
57
33
51
15
46
45
Based on the data, what is the difference between the median of the data, including the possible outlier(s) and excluding the possible outlier(s)?
48.5
23
8.4
3
Answer:
The Answer would be D) 3
In △ABC, a=26, b=19, and c=17.2. Identify m∠C rounded to the nearest degree.
The figure shows triangle A B C. The length of segment A B is c units. The length of segment A C is b units. The length of segment B C is a units.
Answer:
41°
Step-by-step explanation:
∠C is opposite of side c.
Using law of cosines:
c² = a² + b² − 2ab cos C
17.2² = 26² + 19² − 2(26)(19) cos C
cos C = 0.750
C ≈ 41°
Answer:
The answer is 41 degrees
Find 12% less than 60
Answer:
52.8
Step-by-step explanation:
First we need to find 12% of 60
12% * 60
.12 * 60
7.2
We want less than which means subtract
60-7.2
52.8
Which shows how to solve the equation 3/4x=6 for x in one step?
Well going off what I know (you don't have the equations up)
You have to isolate x
3/4x = 6
(4) 3/4x = 6 *multiplying by 4 cancels the fraction.
3x = 24
Divide by 3
X = 6
Answer:
[tex]x = 8[/tex]
Step-by-step explanation:
Let multiply each side by 4/3:
[tex]\frac{4}{3}\cdot \frac{3}{4} \cdot x = 6\cdot \frac{4}{3}[/tex]
[tex]x = 8[/tex]
True or false? Many triangular shapes can be circumscribed about a given circle
Answer:
False.
Because Only one circle can be circumscribed about a given triangle.
Final answer:
The statement that many triangular shapes can be circumscribed about a given circle is true, as an infinite number of triangles can be formed by connecting any three distinct points on the circumference of the circle.
Explanation:
The statement "Many triangular shapes can be circumscribed about a given circle" is true. By definition, a circumscribed triangle is one that surrounds a circle, touching the circle exactly at its perimeter at three points.
Given a circle, you can indeed construct infinite triangles that circumscribe the circle, as for any set of three points on the circumference of the circle, a unique triangle can be formed.
In mathematical terms, three points determine one of these curves; that is, through any three points not in a straight line on a circle's circumference, we can draw a unique triangle which will circumscribe the circle.
Since there are an infinite number of points on a circle's circumference, we can choose an infinite number of triplets of points, each producing a different circumscribed triangle.
What are the coordinates of the center and length of the radius of the circle whose equation is X^2+6x+4y=23?
The center of the circle is (-3, -9/2) and the radius is sqrt(41)/2.
Explanation:To find the coordinates of the center and length of the radius of the circle, we need to rewrite the equation of the circle in the standard form (x-h)^2 + (y-k)^2 = r^2. First, complete the square for the x and y terms by adding and subtracting the necessary constants:
x^2 + 6x + 4y = 23
x^2 + 6x + 9 + 4y + 9 = 23 + 9 + 9
(x + 3)^2 + (y + 9/2) = 41/4
Therefore, the center of the circle is (-3, -9/2) and the radius is sqrt(41/4), which simplifies to sqrt(41)/2.
If p(x) = x2 + 7x + 3 is divided by x + 4, the remainder is
On Election Day, the temperature was 56°F in Durkeeville. Over in Tindertown, the temperature was 48°F. What was the difference in temperature between the two places?
Answer:
The difference is 8 F
Step-by-step explanation:
The difference means subtract
56-48 = 8
The difference is 8 F
(x-1)(x+20)
May I know the work to this
[tex](x-1)(x+20)=x^2+20x-x-20=x^2+19x-20[/tex]
If 75 is 25% of a value, what is the value?
Since 25% of something is also 1/4 of something, multiply 25% by 4 to get the full value.
Since 75 is 25 percent, multiply 75 by 4.
75*4=300
The value is 300.
Hope this helps!
Find the average rate of change from x = 3 to x = 15 for the function f(x) = 0.01(2)x and select the correct answer below
Plug values in function.
f(3) = 0.01(2)(3)
f(3) = 0.06
f(5) = 0.01(2)(5)
f(5) = 0.10
Average rate of change formula: f(b) - f(a) / b - a
Plug in.
0.10 - 0.06 / 5 - 3 = 0.04 / 2 = 0.02
Average rate of change: 0.02
Answer:
The Average rate of change: 0.02
Step-by-step explanation:
Great Question, First to be able to figure out the average rate of change for the function we need to plug each value for x given into the function and get an output value
[tex]f(3) = 0.01(2)(3)[/tex]
[tex]f(3) = 0.06[/tex]
[tex]f(15) = 0.01(2)(15)[/tex]
[tex]f(15) = 0.3[/tex]
Now that we have both outputs for the values of x given to us in the question, we can use the rate of change formula from the picture below to find the Rate of Change of these two values of x.
[tex]\frac{0.3-0.06}{15-3} = r[/tex]
[tex]\frac{0.24}{12} = r[/tex]
[tex]0.02 = r[/tex]
So Now we see that The Average rate of change: 0.02
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Solve (x-3)^2 = 49. Select the values of x
Answer:
x = -4, 10
Step-by-step explanation:
We take the square root and use the fact of "plus-minus" and find two values of x. The process of solving this equation is shown below:
[tex](x-3)^2 = 49\\\sqrt{(x-3)^2}=\sqrt{49}\\ x-3=+-7\\x=3+7=10\\x=3-7=-4[/tex]
Hence the two values of x are -4 and 10
Note: both (-7)^2 and (7)^2 are 49 . So we took "plus-minus" values of [tex]\sqrt{49}[/tex]
Answer: -4 and 10
Step-by-step explanation:
b and c
the second and and the third option
the middle two
Please help... For what value of x would the quotient (2x2 +3x-4)/(x+ 4) not make sense?
Answer:
-4 or A
Step-by-step explanation:
If x was -4 then you would be dividing by zero and it would not be possible.
Which property was used to write the equation in step 2?
Answer:
Distributive property.
For this case we have that by definition, the distributive property establishes that:
[tex]a (b + c) = ab + ac[/tex]
So, if we have:
[tex]5 (x-7) = 55[/tex]
When applying distributive property to the terms within the parenthesis we have:
[tex]5x-35 = 55[/tex]
The distributive property was used to write the second step.
Answer:
Distributive property
X Y
2 6
5 15
8 24
What is the ratio of x to y? (Write it in simplest form)
Answer:
⅓
Step-by-step explanation:
Whether you divide by ⅓ [X ÷ ⅓] or multiply by ⅓ [Y × ⅓], the ratio is similar. It never varies.
1/3
Divide the 2 lowest values by each other.
6/2=1/3
Hope this helps!
5.Find the roots of the parabola given by the following equation.
2x2+ 5x - 9 = 2x
6.Solve the inequality and graph the solution on a number line.
–3(5y – 4) ≥ 17
Answer:
Part 5) The roots are x=-3 and x=1.5
Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)
Step-by-step explanation:
Part 5) Find the roots of the parabola given by the following equation
[tex]2x^{2} +5x-9=2x[/tex]
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2}+5x-2x-9=0[/tex]
[tex]2x^{2}+3x-9=0[/tex]
so
[tex]a=2\\b=3\\c=-9[/tex]
substitute in the formula
[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-9)}} {2(2)}[/tex]
[tex]x=\frac{-3(+/-)\sqrt{81}} {4}[/tex]
[tex]x=\frac{-3(+/-)9} {4}[/tex]
[tex]x=\frac{-3(+)9} {4}=1.5[/tex]
[tex]x=\frac{-3(-)9} {4}=-3[/tex]
therefore
The roots are x=-3 and x=1.5
Part 6) Solve the inequality and graph the solution on a number line.
[tex]-3(5y-4)\geq 17[/tex]
Solve for y
[tex]-15y+12\geq 17[/tex]
Subtract 12 both sides
[tex]-15y\geq 17-12[/tex]
[tex]-15y\geq 5[/tex]
Multiply by -1 both sides
[tex]15y\leq -5[/tex]
Divide by 15 both sides
[tex]y\leq -1/3[/tex]
The solution is the interval -----> (-∞, -1/3]
All real numbers less than or equal to negative one third
The solution on a number line is the shading area below of the line y=-1/3 (close circle)
The graph in the attached figure
Write 0.0002507 in scientific notation.
Answer:
2.507* 10^-4
Step-by-step explanation:
0.0002507
We need to have one number to the left of the decimal
We move the decimal 4 places to the right
Since we moved the decimal to the right, the exponent on the power of 10 is negative
2.507* 10^-4
625 kids play sports. If there are 125 kids on each team, how many sports are there?
Answer:
5 sports
Step-by-step explanation:
To find the number of sports, take the total number of kids and divide by the number of teams
625/125 = 5
There are 5 sports
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to find the number of sports were there, we have to divide!}[/tex]
[tex]\bullet\ \text{625 kids play sports}[/tex]
[tex]\bullet\ \text{125 kids on each team}[/tex]
[tex]\text{625 will be our numerator (or front number)}[/tex]
[tex]\text{125 will be our denominator (or back number)}[/tex]
[tex]\dfrac{625}{125}=625\div125=5[/tex]
[tex]\boxed{\boxed{\bf{Your\ answer:5}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Part of the population of 7000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected
Answer:
1120
Step-by-step explanation:
8/50=x/7000
50x=56000
Divide 50 on both sides
1120
Answer:
1120
Step-by-step explanation:
8/50=x/7000
50x=56000
Divide 50 on both sides
1120
15p!!what is the percent of change from 134 to 106? round to the nearest percent!
Answer:
The answer is 21%.
Step-by-step explanation:
1) divide 134 by 106
106/134 is about 0.79
2) Multiply by 100 to find the percentage
0.79(100)= 79%
3) Subtract 79% from 100% to find the percentage difference
100%-79%= 21%
Therefore, the percent of change between 134 and 106 is 21%.
Hope this helps!
If DH = 4x - 2 and FH = x + 28, find the value of x for which DEFG must be a parallelogram.
6
10
7
8
Answer:
The answer for this question is B (10) I have shown a step by step explaination for you to understand how I got this answer
Step-by-step explanation:
4x-2=x+28
-x -x
3x-2=28
+2 +2
3x=30
3x/3 = 30/3
x=10
The value of x for which DEFG must be a parallelogram is Option(B) 10 .
What is a parallelogram ?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
How to find the value of x for which the figure is a parallelogram ?As we know that for a parallelogram, the opposite adjacent sides are always parallel and equal in length.
Therefore, for DEFG to be a parallelogram, the sides DH and FH must be equal in length.
We have, DH = FH
⇒ 4x - 2 = x + 28
⇒ 3x = 30
∴ x = 10
Thus, the value of x for which DEFG must be a parallelogram is Option(B) 10 .
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The length of a rectangle is 8 1/2
inches and the width
3 1/4
inches. What is the ratio, using whole numbers, of the length to the width?
13:34
34:13
17:13
1311
Answer:
34/13
Step-by-step explanation:
The length-to-width ratio here is:
8.5 / 3.25
which can be reduced by dividing numerator and denominator both by 0.25:
8.5/0.25
--------------- = 34/13
3.25/0.25
HOW do you solve this?
What could be the side lengths of a right triangle?
A. 27, 35, 43
B. 26, 34, 42
C. 25, 33, 41
D 24, 32, 40
Answer:
you just need memorize some of the side lengths of right triangle, or you can use this formula to calculate: a^2 + b^2 = c^2
For example, you need memoreize this group of side lengths of right triangle: 3 , 4 , 5
and in your options, there is a group is same as 3, 4 , 5 but it's 8 times bigger.
The answer is:
D. 24, 32, 40
Answer:
D.
Step-by-step explanation:
In a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side.
The law to observe here is the Pythagorean theorem where;
[tex]a^2+b^2=c^2\\[/tex]
where a and b are the two shorter sides where as c is the longest side/hypothenuse
In this question the last option is correct.How?
Lets take a=24 and b=32, what is c?
You apply;
[tex]a^2+b^2=c^2\\\\24^2+32^2=c^2\\\\\\576+1024=1600\\\\c^2=1600\\\\c=\sqrt{1600} =40[/tex]
Hence option D is correct where ;
[tex]24^2+32^2=40^2[/tex]
Convert the radian measure to degree measure. Use the value of π found on a calculator, and round answers to two decimal places.
eleven pi divided by four
Answer: 495 degrees
Step-by-step explanation:
[tex]\frac{11\pi }{4}[/tex] · [tex]\frac{180}{\pi }[/tex]
[tex]\frac{1980}{4}[/tex]
495 degrees
F (- 12) = 2/3(-12)+7
F (- 12) = 2/3(-12)+7
F (- 12) = 2(-4) + 7
F(-12) = -8 + 7
F(-12) = -1