Answer:
156
Step-by-step explanation:
f(x)= 4^(2x) -100
Let x =2
f(2)= 4^(2*2) -100
= 4^4 - 100
= 256 -100
= 156
- If f ( x ) = x² + 2x - 1 and g ( x ) = 3x - 2 , then verify the following :
1. [tex] \large{ \bf{( \frac{f}{g})(2) = \frac{f(2)}{g(2)} }}[/tex]
- Irrelevant / Random answers will be reported! *
Step-by-step explanation:
Hey there!
Given;
f ( x ) = x² + 2x - 1
g ( x ) = 3x - 2
To verify:
[tex]( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} [/tex]
LHS:
[tex] (\frac{f}{g} )(x) = \frac{ {x}^{2} + 2x - 1}{3x - 2} [/tex]
~ Insert "2" instead of "x".
[tex] (\frac{f}{g} )(2) = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} [/tex]
Simplify it;
[tex] \frac{f}{g} (2) = \frac{4 + 4 - 1}{6 - 2} [/tex]
Therefore; (f/g)(2) = 7/4.
RHS:
[tex] \frac{f(x)}{g(x)} = \frac{ {x}^{2} + 2x - 1}{3x - 2} [/tex]
~Insert "2" instead of"x".
[tex] \frac{f(2)}{g(2)} = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} [/tex]
Simplify it.
[tex] \frac{f(2)}{g(2)} = \frac{4 + 4 - 1}{6 - 2} [/tex]
Therefore, f(2)/g(2) = 7/4.
Since (f/g)(2) = f(2)/g(2) = 7/4.
Proved!
Hope it helps!
Step-by-step explanation:
f(x) = x² + 2x - 1 g(x) = 3x - 2Soo :
[tex] \tt( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} [/tex]
[tex] \tt( \frac{ {x}^{2} + 2x - 1 }{3x - 2} )(2) = \frac{ {2}^{2} + 2(2) - 1 }{3(2) - 2} [/tex]
[tex] \tt( \frac{ {2}^{2} + 2(2) - 1}{3(2) - 2} )= \frac{7}{4} [/tex]
[tex] \boxed{ \tt \frac{7}{4} = \frac{7}{4} }[/tex]
Soo true.
Find the equation of this line.
Answer:
[tex]y=-\frac{6}{7} x-\frac{10}{7}[/tex]OAmalOHopeO
0=(x-8)^2-100 Solve the problem using any type of way.
0 = (x-8)^2 -100
Add 100 to both sides
100 = (x-8)^2
Take the square root of both sides
10 = (x-8)
Remove the parentheses
10 = x-8
Add 8 to both sides
18 = x
Answer: x = 18
A dice game involves rolling 2 dice. If you roll a sum of 2, 3, 4, 10, 11, or 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value for the game.
Below is a table for the possible outcomes for rolling two dice.
Answer:
From a glance, -1.67 is the answer.
Step-by-step explanation:
You have a higher probability of losing money than gaining it due to the distribution of probability. Aka: there are more chances to lose than win. As a result, you are expected to lose money. Only -1.67 is the only negative option, which means that we dont even need to do real math since there's already only one choice.
The correct answer is option B which is -1.67 is the answer.
What is probability?Probability 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.
You have a higher probability of losing money than gaining it due to the distribution of probability.
There are more chances to lose than win. As a result, you are expected to lose money. Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.
Therefore the correct answer is option B which is -1.67 is the answer.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ2
Please HELP! ):
The measure of an interior angle of a regular polygon is eight times the measure of one of its exterior angles. How many sides does the polygon have?
If x=(p-3) and y=(p+3),show that xy+9=psquare
Step-by-step explanation:
Answer with explanation is in the attachment
Hope it is helpful to you
Compute the standard deviation of the following set of data to the nearest whole number:
8, 12, 15, 17, 18
14
03
04
13
Answer:
Step-by-step explanation:
The standard deviation is the square root of the variance, and the variance is found by using the mean. So we will do that first. I will use the population variance as opposed to the sample variance since our set of numbers is small.
The mean: 8 + 12 + 15 + 17 + 18 = 70 and divide that by 5 to get
[tex]\bar{x}=14[/tex] and use this to find the variance in the formula:
[tex]s^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex] it is a bit difficult to enter that formula in correctly, but here's how it works mathematically:
[tex]s^2=\frac{(8-14)^2+(12-14)^2+(15-14)^2+(17-14)^2+(18-14)^2}{5}[/tex]
Squaring this ensures us that we don't end up with zero, which would be useless.
[tex]s^2=\frac{36+4+1+9+16}{5}[/tex] so
[tex]s^2=13.2[/tex] which means that the standard deviation is
s = 3.633
(If you do it with n-1 = 4 in the denominator of the variance, you get a standard deviation of 4.062)
Aila wants to solve the equation -2.3 – 5x = 10 – 2x. She uses a graphing program to graph the equations y = -2.3 – 5x and y = 10 – 2x. Use the graph to find the solution of -2.3 – 5x = 10 – 2x. Line graph with 2 lines. X axis ranges from negative 10 to 10; y axis range from 6 to negative 6; both lines cross x, y axes; do not pass through origin; intersect at (negative 4.1, 18.2). Both lines extend from bottom right to upper left quadrants.
Answer:
-4.1
Step-by-step explanation:
Elisa runs a bubble bath for her daughter. The bathtub is 17 inches deep and fills at a rate of 3 inches of water every 5 minutes.
Just after turning on the water, Elisa’s doorbell rings. It’s her neighbor bringing over a package that was mistakenly left on her doorstep. They talk for 26 minutes, then Elisa returns to check on the bathtub. Did the tub overflow while she was talking to her neighbor, or did she return in time?
Answer:
Elisa return in time. :)
Step-by-step explanation:
It is given that the bathtub is 17 inches deep.
The water fills the tub at a rate of 3 inches of water for every 5 minutes.
Elisa spent 26 minutes with neighbor.
Let's find whether the tub overflow or did she return in time.
In 5 minutes water filled is 3 inches
In 10 minutes water filled is 6 inches
In 15 minutes water filled is 9 inches
In 20 minutes water filled is 12 inches
In 25 minutes water filled is 15 inches
In 26 minutes water filled in is 15+1/3 inches , which is same as 15.33 inches.
But the deep of tub is 17 inches.
We could say, she return in time.
Drag the tiles to the correct boxes to complete the pairs.
Find the missing the coordinates.
(2, -2)
(-5, -5)
(2, 1)
(-1, -1)
A(-5, -1), B(1, -1), and C(1, -5) are
three vertices of rectangle ABCD. What
are the coordinates of vertex D?
arrowRight
A(2, 5), B(6, 5), and C(6, 1) are
three vertices of square ABCD. What are
the coordinates of vertex D?
arrowRight
A(2, 3), B(7, 3), and C(7, -2) are
three vertices of square ABCD. What are
the coordinates of vertex D?
arrowRight
A(-1, 4), B(7, 4), and C(7, -1) are
three vertices of rectangle ABCD. What
are the coordinates of vertex D?
arrowRight
Answer:
i think its 24
Step-by-step explanation:
2=2
What are the domain and range of the inequality y < sqrt x+3+1
I don't get it I try to solve it but I just didn't get .
Given:
The inequality is:
[tex]y<\sqrt{x+3}+1[/tex]
To find:
The domain and range of the given inequality.
Solution:
We have,
[tex]y<\sqrt{x+3}+1[/tex]
The related equation is:
[tex]y=\sqrt{x+3}+1[/tex]
This equation is defined if:
[tex]x+3\geq 0[/tex]
[tex]x\geq -3[/tex]
In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.
So, the domain of the given inequality is x>-3.
We know that,
[tex]\sqrt{x+3}\geq 0[/tex]
[tex]\sqrt{x+3}+1\geq 0+1[/tex]
[tex]y\geq 1[/tex]
The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.
So, the domain of the given inequality is y>1.
Therefore, the correct option is A.
Instructions: Find the measure of the indicated angle to the nearest
degree.
?
35
19
?
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and the adjacent side. Therefore, we should use the tangent function.
tan(x) = 19 / 35
x = tan^-1(19/35)
x = 28 degrees
Hope this helps!
Which set of numbers does NOT represent the lengths of the sides of a triangle? A.) (7,5,6)
B.) (9,12,19)
C.) (7,18,11)
D.) (6,8,11)
Answer: B and C
Step-by-step explanation:
the triangle inequality theorem states that any 2 sides of a triangle must be greater than the measure of the third side. now with this rule, let's apply it to all options!
option a:
7 + 5 > 6 .. yes!
6+ 7 > 5 .. yes!
5 + 6 > 7 .. yes!
option b:
9 + 12 > 19 .. yes!
12 + 19 > 9 .. no!
19 + 9 > 12 .. no!
option c:
7 + 11 > 18 .. no!
11 + 18 > 7 .. no!
18 + 7 > 11 .. yes!
option d:
6 + 8 > 11 .. yes!
8 + 11 > 6 .. yes!
11 + 6 > 8 .. yes!
i did this topic years ago so please let me know if there are any mistakes! hope this helped, and good luck! ◝(ᵔᵕᵔ)◜
Find the size of the angles marked by letters in the following diagram.
Answer:
x = 52
y = 19
Step-by-step explanation:
The degree measure of a straight line is (180) degrees. One can use this to find the measure of the angle that is adjacent to the angle with a measure of (142) degrees. Form an equation and solve for the unknown,
142 + (unknown angle) = 180
unknown angle = 38
The inscribed angle theorem states that twice the measure of an angle with its vertex of the circumference (outer edge) of a circle is equal to the measure of the surrounding arc. Therefore, one can state the following:
(2)(unknown angle) = (surrounding arc)
(2)(38) = (surrounding arc)
76 = surrounding arc
The central angles theorem states that the measure of an angle whose vertex is the center of the circle is equal to the measure of the surrounding arc. Therefore, one can state the following:
m<O = (surrounding arc)
m<O = 76
The radius is the distance from the center of the circle to the circumference of the circle. All radii in a circle are congrunet. Therefore the triangle with angle (x) and vertex (O) is an isosceles triangle, as two of its sides are radii, and are thus congruent. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides in an isosceles triangle are congruent. Moreover, the sum of angles in any triangle is (180) degrees. Therefore, one can make the following statement:
m<O + x + x = 180
76 + 2x = 180
x = 52
Finally, one can use the property that the sum of angles in any triangle is (180) degrees to make the following statement:
(x + 19) + (x + y) + (38) = 180
52 + 19 + 52 + y + 38 = 180
161 + y = 180
y = 19
x=52°
y=19°
Answer:
Solution given:
<OCA=19°[base angle of isosceles triangle]
Since ∆AOC is similar to ∆ BOC
y=19°[corresponding angle of a similar triangle are equal]
<OAB=<OBA=x[base angle of isosceles triangle]
again
<A+<B=180°[exterior angle of a triangle is equal to the sum of two opposite interior angle]
x+19+x+19=142°
2x=142°-38°
x=104/2
x=52°
At an amusement park, 63 out of 70 tickets sold were discount tickets.
What percentage of the tickets were discount tickets?
Answer:
90%
Step-by-step explanation:
63/70 = 0.9 = 90%
Answer:
63 out of 70
63×10÷70=9
9%
PLEASEEEE JESUS PLEASE HELP Find an irrational number that is between 4.2 and 4.5.
Explain why it is irrational.
9514 1404 393
Answer:
√20 is not the root of a perfect square
Step-by-step explanation:
4.2^2 = 17.64
4.5^2 = 20.25
The square root of any number between these values that is not a perfect square will be irrational. This includes the roots of the integers 18, 19, or 20.
4.2 < √20 < 4.5
√20 ≈ 4.472135954999579...
_____
Of course, there are an infinite number of possibilities. It is easy enough to check to see if a rational number is a perfect square. (Its square root will have half as many decimal digits.) For example, √18.9225 is 4.35 (rational), but √18.9226 ≈ 4.350011494... is irrational.
Square roots are not the only irrational numbers. Polynomial roots, trig function values, logarithms, exponential functions are only some of the ways that irrational numbers can be specified, along with multiples or other combinations of irrational numbers such as π or e. These will be irrational simply because they cannot be expressed exactly as the ratio of two integers.
Please help 33 points
Answer: it’s 111
Step-by-step explanation:
How many solutions does the system of equations below have? y = – 2x − 6 y = – 2 x + 3 5 one solution one solution two solutions two solutions infinitely many solutions infinitely many solutions no solution
Answer: No solution
Step-by-step explanation:
Given
Pair of lines are
[tex]\Rightarrow y=-2x-6\ \text{and}\ y=-2x+35[/tex]
For lines [tex]a_1x+b_1y+c_1=0\ \text{and}\ a_2x+b_2y+c_2=0[/tex] will be parallel when
[tex]\Rightarrow \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
Rewrite the given lines
[tex]y+2x+6=0\ \text{and}\ y+2x-35=0[/tex]
[tex]\Rightarrow \dfrac{2}{2}=\dfrac{1}{1}\neq\dfrac{6}{-35}\\\\\Rightarrow \dfrac{1}{1}=\dfrac{1}{1}\neq\dfrac{6}{-35}[/tex]
Thus, the given lines are parallel. Therefore, there is no solution for the givebn pair of lines.
HELP ASAP ILL GIVE BRAINLIST
Construct the equation of the graph given. Label the intercept and categorize this graph a horizontal or vertical line.
Answer:
Horizontal line
Step-by-step explanation:
uehdjd
Divide ( 9/11) ÷ (3/2)
Answer:
Its your answer ......
hope it will help u
Can someone help me with this math homework please!
Answer:
1 ) - 0.04
2 ) 1
3 ) - 0.04
4 ) Less of 0.04 gallons of fuel for every 1 mile.
Can someone help me with this math homework please!
Answer:
I believe its (-3,-2)...........
Janes but a small clectric car and recorded the distance it waveled. The table below shows the distance waveled (nt during the st 4 seco
Bapsed Time Distance Traveled
(seconds) feet)
1
62
2
125
3
186
243
Which of the following equations represents the relationship between the distance traveled and the clapsed time?
Of=52-5
52-
+=52
52
Answer:
50
Step-by-step explanation:
Point A is a representation of which number on the number line?
A
B
D
-2
0
2
4
0 -3
0 1
T ♡rt
Which number can each term of the equation be multiplied by to eliminate the fractions before solving ?
-3/4m - 1/2 = 2 + 1/4m
Answer:
4
Step-by-step explanation:
-3/4m - 1/2 = 2 + 1/4m
The denominators are 4 and 2
If we multiply by the least common multiply we can get rid of the fractions
2 and 4 have a least common multiple of 4
I need help what’s the answer I’m trying to pass?
Answer:
11.925
Step-by-step explanation:
What is the volume of this right triangular pyramid?
Height -36
Base:
side 1 -24
side 2 -19
2736 cm³
5472 cm³
8208 cm³
16,416 cm³
Answer:
The answer is 2736 cm³
Answer:
What is the volume of this right triangular pyramid?
2736 cm³
5472 cm³
8208 cm³
16,416 cm³
find an equation of the line with an x intercept of -2 and a slope of 3
I WILL GIVE BRAINLIEST PLEASE HELP
Answer:
y= 3x -6
Step-by-step explanation:
The equation if a line can be written in the form of y= mx +c, where m is the slope and c is the y- intercept.
Given that the slope is 3, m= 3.
Substitute m= 3 into the equation:
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
Given that it has an x- intercept of -2, the line passes through the point (-2, 0). This is because x- intercept is the point at which the line passes through the x- axis, and this occurs at y= 0.
When x= -2, y= 0,
0= 3(-2) -c
0= -6 -c (expand)
c= -6 (+c on both sides)
Thus, the equation of the line is y= 3x -6.
The latest online craze is a new game,khan on seven. You get 100 points for playing the game. In addition,you get 50 points for each seven-letter word you make with the ten letter you receive.sal wants to break the record,and he needs 18,000 or more points to do so
Answer:
how do I get started here
The following points are rotated about the origin through 90° in clockwise direction. Find the new coordinates,
A. A(1,3), B(5,3), and C(3, 1)
B. A' (3,-1), B'(-5, -3), and C (1.-3)
C. A'(3,-1), B (3,-5), and C(1, -3)
D. O A'(3, 1), B'(3,5), and C(1,3)
Answer:
C
Maybe it is B or A as the answer.
Answer:
B.
A'(1,-3), B'(1,-7), C'(-3,-7), D'(-3,-3)
Step-by-step explanation:
study island
