Answer:
f(x) = [tex]e^{x}[/tex]
Step-by-step explanation:
The only function that has it;s derivative equal to the function is the exponential function.
That is f(x) = f'(x) = [tex]e^{x}[/tex]
Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 40%.
Answer:
20 pts
Step-by-step explanation:
50 points corresponds to a 100% grade. How many points (x) correspond to a 40% grade?
x 40%
------------ = ---------
50 pts 100%
Then 100x = 2000, and so x = 20.
A score of 20 points would correspond with a test score of 40%.
Answer:
A score of 20 points would correspond with a test score of 40%.
Step-by-step explanation:
x 40% How many points (x) correspond to a 40% grade?
------------ = ---------
50 pts 100% 50 points corresponds to a 100% grade.
100x = 2000 divide both sides by 100
x = 20
Apollo Spas services 105 hot tubs. If each hot tub needs 165 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?
Apollo Spas would require approximately 17.325 liters of muriatic acid to service all 105 hot tubs.
Explanation:The student is looking to find out the total amount of muriatic acid, noted in liters, required to service all hot tubs. The problem states Apollo Spas needs to service 105 hot tubs, with each one requiring 165 mL of acid.
Firstly, we need to multiply the number of hot tubs by the amount of acid each one needs: 105 hot tubs * 165 mL/hot tub = 17325 mL.
However, the student needs the amount in liters, not milliliters. To convert mL to L, we need to divide the total mL by 1000 because there are 1000 mL in a liter. Therefore, 17325 mL / 1000 = 17.325 L.
So, Apollo Spas will need 17.325 liters of muriatic acid to service all 105 hot tubs.
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A bag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue
Follow below steps;
The probability of drawing a blue marble from the bag:
Calculate the total number of marbles in the bag: 3 red + 4 white + 5 blue = 12 marbles.
Calculate the probability of drawing a blue marble: Number of blue marbles / Total number of marbles = 5 / 12 = 5/12.
What is the solution to x – 10 > – 12?
Answer:
x>-18
Step-by-step explanation:
Ali has a 64 gram bar of chocolate. on day 1 he eats half of his chocolate. on day 2 he eats half of what is left. he does the same each day.
a. when will he have only 1 gram left?
b. how much would a bar of chocolate need to weigh to last All 14 days?
Answer:
A: Day 6
B: 8196 grams (He will become obese for sure)
Step-by-step explanation:
Part A:
As you can infer from the problem, Ali halves his bar everyday, regardless of how the bar is.
Day 1= 32 grams left
Day 2= 16 grams left
Day 3= 8 grams left
Dat 4= 4 grams left
Day 5= 2 grams left
Day 6=1 gram left
He will have one gram left on Day 6
Part B:
This part is basically vice versa. Instead on halving, we need to be doubling. I will do Part a in reverse until Day 14 comes
Day 1= 1
Day 2= 2
Day 3= 4
Day 4= 8
Day 5= 16
Day 6= 32
Day 7 = 64
Day 8= 128
Day 9= 256
Day 10= 512
Day 11= 1024
Day 12= 2048
Day 13= 4096
Day 14= 8192
He will need 8192 grams of chocolate!!!
The number of days when he has only 1 gram left will be 6. And the chocolate needs to weigh to last All 14 days will be 1/256 grams.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
Ali has a 64 grams bar of chocolate.
On day 1 he eats half of his chocolate.
And on day 2 he eats half of what is left.
He does the same each day.
Then the value of a is 64 grams and b is 1/2.
y = 64 · (1/2)ⁿ
Where n is the number of days.
The number of days when he has only 1 gram left will be
1 = 64 · (1/2)ⁿ
1/64 = (1/2)ⁿ
(1/2)⁶ = (1/2)ⁿ
n = 6
The number of days when he has only 1 gram left will be 6.
The chocolate needs to weigh to last All 14 days will be
y = 64 · (1/2)¹⁴
y = 64 · (1/16384)
y = 1/256 grams
The chocolate needs to weigh to last All 14 days will be 1/256 grams.
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Which one should I choose?
Answer:
A
Step-by-step explanation:
The answer is A as the height starts at 36 and decreases by 9 inches vertically every 12 inches it goes down horizontally.
If you turn this into an equation, you get y = -(9/12)x+36.
Then, you simplify this to y = -(3/4)x+36, which is A.
The function that models the height y railing in inches according to the horizontal distance in inches x, from the top of the stairs is [tex]y = -\frac{3}{4} x \ + \ 36[/tex]. (Option A).
How to calculate the equation for the stairs?The function that models the height y railing in inches according to the horizontal distance in inches x, from the top of the stairs is calculated as follows;
The general equation of a line;
y = mx + c
where;
m is the slope of the functionc is the y - interceptIf the stairs decreases by 9 inches vertically every 12 inches it goes down horizontally, then the slope becomes;
m = (0 - 9)/(12 - 0)
m = - 3/4
The y - intercept becomes the initial vertical height = 36
The equation that models the problem becomes;
[tex]y = -\frac{3}{4} x \ + \ 36[/tex]
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Solve the equations. 2x+4y+3x=6
5x+8y+6z=4
4x+5y+2z=6
Answer:
b. (x, y, z) = (-8, 10, -6)
Step-by-step explanation:
The easiest way to do this one is to try the answers to see which works.
2(-8) +4(10) +3(-6) = -16 +40 -18 = 6
5(-8) +8(10) +6(-6) = -40 +80 -36 = 4
4(-8) +5(10) +2(-6) = -32 +50 -12 = 6
The answers of choice B work in the given equations.
___
In case you don't have answers to select from, you generally solve this sort of problem using elimination. You can also use Cramer's rule, a graphing calculator, an on-line equation solving tool, or any of a variety of other methods.
Here, we can find the variable x by subtracting twice the first equation from the second:
(5x +8y +6z) -2(2x +4y +3z) = (4) -2(6)
x = -8
This is sufficient to identify the correct answer choice.
We can substitute this into the last two equations to get ...
-40 +8y +6z = 4 . . . . 8y +6z = 44
-32 +5y +2z = 6 . . . . 5y +2z = 38
Subtracting the first of these from 3 times the second gives ...
3(5y +2z) -(8y +6z) = 3(38) -(44)
7y = 70 . . . . . . . simplify
y = 10 . . . . . . . . divide by 7
Substituting this into the second of the above equations, we have ...
5(10) +2z = 38
25 +z = 19 . . . . . . divide by 2
z = -6 . . . . . . . . . . subtract 25
_____
The choice of the combinations to use to eliminate variables can be ad hoc (as here), or it can be made according to some rules (as in Gaussian elimination).
My personal choice for solving systems like this is to use the matrix functions of a graphing calculator.
Which function below is the inverse of f(x)=x^2-36
X^2/36
+- 6 square root of x
1/x^2-36
+- square root of x+36
Answer:
+- square root of x+36
Step-by-step explanation:
f(x) = x^2 -36
y = x^2 -36
Exchange x and y
x = y^2 -36
Solve for y
Add 36 to each side
x+36 = y^2 -36+36
x+36 = y^2
Take the square root of each side
±sqrt(x+36) = y
±sqrt(x+36) = f^-1(x)
Solve by factoring
[tex]4m {}^{2} - 31m - 45 = 0[/tex]
A.-5/4,9
B.9,-5
C.31,-41
D.45,4
Answer:
A. -5/4, 9
Step-by-step explanation:
The solution is in the picture
Answer:
A
Step-by-step explanation:
Given
4m² - 31m - 45 = 0
Consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term
product = 4 × - 45 = - 180 and sum = - 31
The factors are - 36 and + 5
Use these factors to split the m- term
4m² - 36m + 5m - 45 = 0 ( factor the first/second and third/fourth terms )
4m(m - 9) + 5(m - 9) = 0 ← factor out (m - 9) from each term
(m - 9)(4m + 5) = 0
Equate each factor to zero and solve for m
m - 9 = 0 ⇒ m = 9
4m + 5 = 0 ⇒ 4m = - 5 ⇒ m = - [tex]\frac{5}{4}[/tex]
Please help with this question
Answer:
Many possible answers, including
Major Arc: JKM
Minor Arc: JM
Step-by-step explanation:
The answers you selected in this photo are correct. But let's see why.
A major arc is an arc that is bigger than a minor arc.
They are defined using a starting point and an ending point. In this case, you have many reference points (J, K, L and M), and none is identified in the question. However, the answers shown indicate they're using point J as starting point and M as ending point.
If you look at the positions of J and M on the diagram, you see you can take two routes to join them... the shortest route is the minor arc (going counter-clockwise direction from J to M). While the other route, going clockwise passes through the points K and L is much longer.... and forms the major arc.
That major arc could be identified as JKM, JLM or JKLM, since it starts at J, ends in M, but passes through points K and L, in that order.
PLZZZZ HELP!!!! Amit solved the equation
+420 for x using the steps shown below. What was Amit's error?
420
19 (420) -- A20 (420)
X= 175
Amit should have multiplied both sides of the equation by i
12
Amit should have multiplied both sides of the equation by
The product of 17 and 420 is not equal to 175.
20 hould have been the value of y
Answer:
Option D.
Step-by-step explanation:
We will solve the given equation and compare it with the solution of Amit's solution.
[tex]\frac{5}{12}=-\frac{x}{420}[/tex]
We will multiply by (-420) on both the sides of the equation.
[tex]\frac{5}{12}(-420)=-\frac{x}{420}(-420)[/tex]
-175 = x
By comparing the solutions we find that the product of [tex]\frac{5}{12}[/tex] and (-420) should have been the value of x, while Amit multiplied the equation by (420).
Therefore, Option D. is the correct option.
1
Solve for x.
(x - 4)(x - 4) = 0
A.
-16
B.
-4
C.
4
D.
16
Reset Next
Answer:
x = {4, 4}
Step-by-step explanation:
(x - 4)(x - 4) = 0 has two real, equal roots: x = 4 and x = 4. Notice that subbing 4 for x in this equation results in a TRUE equation.
The value of x in (x - 4)(x - 4) = 0 is x = (4, 4) repeated roots.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given (x - 4)(x - 4) = 0.
∴ Either (x - 4) = 0 or (x - 4) = 0.
x - 4 = 0 ⇒ x = 4 or x - 4 = 0 ⇒ x = 4.
So, x = (4, 4).
This is a case when a quadratic equation has real repeated roots.
The vertex of this graph of this quadratic equation just touches the x-axis.
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what is the simplified form of 7 radical x^5 x 7 radical x^5
Answer:
the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]
Step-by-step explanation:
We need to find the simplifies form of
[tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex]
We need to find product of above terms
We can write as
[tex](7*7)(\sqrt{x^5}*\sqrt{x^5})\\(7^2)((\sqrt{x^5})^2)\\49\,x^5[/tex]
So, the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]
Choose the equation and the slope of the line that passes through (5,-3) and
is perpendicular to the x-axis.
Answer:
x = 5; the slope is undefined
Step-by-step explanation:
A line perpendicular to the x-axis is a vertical line.
In a vertical line, every point has a different y-coordinate and the same x-coordinate. Since you want a line that is vertical and passes through the point (5, -3), then every point on the line must have x-coordinate 5 no matter what its y-coordinate is. The slope of a vertical line is undefined.
Answer: The equation is x = 5; the slope is undefined
Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:
f(t) = 300(0.946)t
Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?
Clara's body eliminated the antibiotic faster than Heidi's body.
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.
Clara's body eliminated the antibiotic at one-fourth of the rate at which Heidi's body eliminated the antibiotic.
Answer:
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Answer:
Option. B is the answer.
Step-by-step explanation:
Clara is taking a medicine for a common cold. Table that shows the amount f(t) that was present in Clara's body after time t is
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Now we will find the explicit formula of geometric sequence.
f(1) = 236.5
and f(2) = 223.73
Therefore, common ratio of the sequence = [tex]\frac{f(2)}{f(1)}=\frac{223.73}{236.5}[/tex]=0.946
So the equation will be f(t) = [tex]236.5(0.946)^{t}[/tex]------(1)
At the same time Heidi was administered 300 mg of same medicine of the same sample.
Amount of medicine in her body f(t) after time t is shown by the equation
f(t) = [tex]300(0.946)^{t}[/tex]----(2)
By comparing these equations 1 and 2, we find common ratio is same as (0.946), which reflects the rate of elimination of the antibiotic was same for both Clara and Heidi.
Option B is correct.
which of the following are solutions to the following equation?
3x^2-48=0
A. 4
B. -4
C. 4sqr3
D. -4sqr3
Answer:
A and B
Step-by-step explanation:
We can add 48 to both sides of the equation to get
3x^2 = 48
Dividing by 3 on both sides,
x^2 = 16
Taking the square root of both sides,
x = +/- 4
So A and B are our answers.
Answer: Option A and Option B
[tex]x=4[/tex] and [tex]x=-4[/tex]
Step-by-step explanation:
We must find the solutions of the following equation
[tex]3x^2-48=0[/tex]
Add 48 on both sides of the equality
[tex]3x^2-48+48=48[/tex]
[tex]3x^2=48[/tex]
Divide both sides of equality by 3
[tex]\frac{3}{3}x^2=\frac{48}{3}[/tex]
[tex]x^2=16[/tex]
Apply the square root on both sides of the equation
[tex]x=\±\sqrt{16}[/tex]
[tex]x=4[/tex] and [tex]x=-4[/tex]
simplify (6x2 - 3 + 5x3) - (4x3 - 2x2 - 16
Answer:
x^3 +8x^2 +13
Step-by-step explanation:
(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)
Distribute the minus sign
6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16
Combine like terms
x^3 +8x^2 +13
Answer:
Simplify (6x2 − 3 + 5x3) − (4x3 − 2x2 − 16).
its (C) -------> x^3 + 8x2 + 13
Step-by-step explanation:
Mr. Turner earned $40,000 last year. This year he estimates that he will earn 12% more money. How much does he estimate that he will earn.
Answer:
$44,800
Step-by-step explanation:
Original salary : $40,000
12% of original salary = 12% x 40,000 = 0.12 x 40,000 = $4,800
New salary = $40,000 + $4,800 = $44,800
PLEASE HELP! I don’t understand
Answer:
sqrt(2-sqrt(3))/2
Step-by-step explanation:
sin(15)=sin(30/2)=sqrt(1-cos(x))/sqrt(2)=(1-sqrt(3)/2)/sqrt(2)
Again we don't like compound fractions so multiply top and bottom inside sqrt( ) by 2.
sin(15)=sqrt(2-sqrt(3))/sqrt(4)
simplify
sin(15)=sqrt(2-sqrt(3))/2
Answer:
[tex]\frac{\sqrt{2-\sqrt{3} } }{2}[/tex]
Step-by-step explanation:
[tex]sin(\frac{u}{2} =\sqrt[+]{\frac{1-cosu}{2} } =\sqrt{\frac{1-cos30^0}{2} } \\=\sqrt{(\frac{1-\frac{\sqrt{3} }{2)} }{2} } \\=\sqrt{\frac{2-\sqrt{3} }{4} } \\=\sqrt{\frac{2-\sqrt{3} }{\sqrt{4} } } \\=\sqrt{\frac{2-\sqrt{3} }{2} } \\[/tex]
what is the point-slope form of a line with slope -4 that contains the point (-2,3)
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=-4[x-(-2)]\implies y-3=-4(x+2)[/tex]
Answer: [tex](y-3)=(-4)(x+2)[/tex]
Step-by-step explanation:
We know that the equation of a line in point-slope form that is passing through a point (a,b) and has slope m is given by :-
[tex](y-b)=m(x-a)[/tex]
Then, the point-slope form of a line with slope -4 that contains the point (-2,3) :-
[tex](y-3)=(-4)(x-(-2))\\\\\Rightarrow\ (y-3)=(-4)(x+2)[/tex]
Hence, the point-slope form of a line with slope -4 that contains the point (-2,3) is [tex](y-3)=(-4)(x+2)[/tex]
Jenny biked 3 miles less than twice the number of miles Marcus biked. Jenny biked a total of 4 miles. Write an equation to determine how many miles Marcus biked. A.3 + 2x = 4 B.4 = 2x − 3 C.x − 4 = 2(3) D.x over four = 2(3)
Answer:
Option (B) 4 = 2x - 3
Step-by-step explanation:
Let distance travel by Marcus be "x" miles
Then, according to question
Distanced travelled by Jenney will be
twice of "x" minus 3.
Distance travelled by Jenny = 2x - 3.
Also, it is given that Jenny has travelled 4 miles.
then, 4 = 2x - 3. So, here option (B) is the correct option.
Answer:
B
Step-by-step explanation:
What equation can be used to solve for c?c = (5)cos(35o) c = 5/cos(350), c = (5)sin(35o) c =
Answer:
c = 6.1 in
Option B.
Step-by-step explanation:
Your full question can be found in the image below
Since we are dealing with a right triangle, we can use a great number of properties,
We know that
cos(35°) = Adj cathetus / Hypotenuse
cos(35°) = 5 in / c
c = 5 in / cos(35°)
Option B.
c = 5 in / 0.82
c = 6.1 in
Answer:
D. c=5/sin(35°)
Step-by-step explanation:
got it right on edge
The length of one of the legs in a right triangle is 3 inches . If the hypotenuse is 10 inches long what the length of the other leg
Answer:
9.5 inches
Step-by-step explanation:
We are given that in a right angled triangle, one leg is 3 inches long while the hypotenuse is 10 inches long. We are to find the length of the other leg.
For this, we will use the Pythagoras Theorem.
Assuming x to be the length of the other leg.
[tex] 1 0 ^ 2 = 3 ^ 2 + x ^ 2 [/tex]
[tex]100=9+x^2[/tex]
[tex]x^2=91[/tex]
[tex]\sqrt{x^2} =\sqrt{91}[/tex]
x = 9.5
Answer:
9.53 inches
Step-by-step explanation:
In a right angles triangle, the sum of the squares of the two legs (a and b) equals the square of the the hypotenuse.
a²+b²=c²
Substituting for the values provided in the question we get the following:
3²+b²=10²
b²=10²-3²
b²=91
b=9.53 inches.
Elise and her dad are planning to attend the state fair. An adult ticket is $21.00. The price of an adult ticket is $10.00 more than two thirds the price of a student ticket. Write an equation to determine how much Elise will pay for a student ticket. A)two thirdsx + 21 = 10 B)two thirdsx − 21 = 10 C)two thirdsx + 10 = 21 D)two thirdsx − 10 = 21
Answer:
C. two thirds x + 10 = 21
Step-by-step explanation:
Given
Price of adult ticket = $21.00
Let x be the price of student ticket
Then
two third of the student ticket will be:
[tex]\frac{2}{3} x[/tex]
The statement $10.00 more than two third of student ticket:
[tex]\frac{2}{3} x+10[/tex]
As we are given in the question that the adult ticket price is $21.00 and the second explanation is th equation formed by the given statement
So, both will be equivalent
[tex]\frac{2}{3} x+10 = 21[/tex]
Solving this equation for x will give us the price for the student ticket.
Hence,
C. two thirdsx + 10 = 21 is the correct answer ..
Answer:
C
Step-by-step explanation:
What is the value of x in the equation 1.5(х + 4) — 3 = 4.5(х – 2)?
A 3
B 4
C 5
D 9
Answer:
B.4
Step-by-step explanation:
1.5(x+4) - 3 = 4.5( x-2)-----------------------open brackets on both sides
1.5 x +6 -3= 4.5x- 9.................................collect like terms
3+9 = 4.5 x- 1.5x
12=3x..................................divide by 3 both sides to get x
12/3=x
x=4
ANSWER
x=4
EXPLANATION
The given equation is
[tex]1.5(x + 4) - 3= 4.5(x - 2)[/tex]
Multiply through by 10
[tex]15(x + 4) - 30= 45(x - 2)[/tex]
We expand to get:
[tex]15x + 60 - 30= 45x - 90[/tex]
Group similar terms to get;
[tex]15x - 45x = - 90 - 60+ 30[/tex]
[tex] - 30x = - 120[/tex]
[tex] x= 4[/tex]
Factor the expression below x^2-12x+36
Answer:
(x-6)^2
Step-by-step explanation:
x^2-12x+36
What two numbers multiply to 36 and add to -12
-6 * -6 = 36
-6 + -6 = -12
(x-6) (x-6)
(x-6)^2
Select the correct answer.
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
A.
Q(1, 11)
B.
R(2, 4)
C.
S(4, -4)
D.
T(9, -2)
Reset Next
Answer:
Option B R(2,4) is correct
Step-by-step explanation:
The equation of the circle is:
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
Where r = radius
a and b are coordinates of the center of circle.
To check which point lies on a circle, we need to verify the equation
[tex](x-6)^2 + (y-1)^2 = (5)^2[/tex]
We will check for each option.
Option A Q(1,11)
x=1 and y =11
[tex](1-6)^2 + (11-1)^2 = 25\\(-5)^2 + (10)^2 = 25\\25 + 100 = 25\\125 \neq 25[/tex]
So, Option A is incorrect
Option B R(2,4)
x =2 and y = 4
[tex](2-6)^2 + (4-1)^2 = 25\\(-4)^2 + (3)^2 = 25\\16 + 9 = 25\\25 = 25[/tex]
Option B is correct.
Option C S(4,-4)
x =4 and y =-4
[tex](4-6)^2 + (-4-1)^2 = 25\\(-2)^2 + (-5)^2 = 25\\4 + 25 = 25\\29 \neq 25[/tex]
Option C is incorrect
Option D T(9,-2)
x =9 and y =-2
[tex](9-6)^2 + (-2-1)^2 = 25\\(3)^2 + (-3)^2 = 25\\9 + 9 = 25\\18 \neq 25[/tex]
Option D is incorrect.
Answer:
B.
Step-by-step explanation:
The general equation of a circle is [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] where (h,k) is the center and r the radius. In this case, the general equation of the circle with radius 5 and center at (6,1) is [tex](x-6)^{2}+(y-1)^{2} = 5^{2}[/tex], so the point that satisfies the equation will be in the circle.
A. [tex](1-6)^{2}+(11-1)^{2} = 25+100 = 125[/tex] this option is not correct.
B. [tex](2-6)^{2}+(4-1)^{2} = 16+9= 25[/tex] this option is correct so is the answer.
what is the y-intercept of the function f(x)=5•(1/6)x
Answer:
y intercept = 5
Step-by-step explanation:
f(x)=5•(1/6)^x
The y intercept is when x =0
Let x =0
f(0)=5•(1/6)^0
= 5* 1 = 5
The y intercept is 5
If the question is
f(x)=5•(1/6)x
although I have never seen the question written this way
The y intercept is when x =0
Let x =0
f(0)=5•(1/6)0
= 5* 0 = 0
The y intercept is 0
Which description from the list below accuratley describe the relationship between ABC and DEF check all that apply.
Answer:
B. Similar
D. Same Shape
Step-by-step explanation:
In the given triangles:
∠A ≅ ∠D = 22°
∠B ≅ ∠E = 120°
∠C ≅ ∠F = 38°
Hence using the AAA axiom of geometry
Triangle ABC and DEF are similar.
More over due to the similarity of angles the triangles also have same shape.
One more thing, that can be observed is that
DE = 2* AB
EF = 2*BC
DF = 2*AC
The sides of triangle ABC are scaled with a factor of 2 which makes it similar to DEF ..
Hence,
Option B and Option D are correct ..
Answer with explanation:
Given two triangles ΔABC and ΔDEF
⇒Ratio of Sides
[tex]\rightarrow \frac{AB}{DE}(\frac{5}{10})=\frac{BC}{EF}(\frac{3}{6})=\frac{AC}{DF}(\frac{7}{14})=\frac{1}{2}[/tex]
⇒Comparison of Angles
→∠A=∠D=22°
→∠B=∠E=120°
→∠C=∠F=36°
⇒As length of corresponding sides are Proportional ,as well as corresponding Angles of two triangles are same.So Two Triangles are similar either by SSS Similarity or AA Similarity or S AS Similarity.
→If Triangles are similar then they are congruent also.
→The description which accurately describe the relationship between ΔABC and ΔDEF is:
→ Option B: Similar
FIRST GETS BRAINLIEST
Use roots or exponents to solve the each equation. Write fractions in the simplest form
Answer:
8, 36, 81, 11, 7, 1000
Step-by-step explanation:
A
Lets start with number one.
x^2 = 64.
That means that x times x equals 64.
To find x's value, simply find the square root of 64, which is 8.
So x = 8.
For the second one, the square root of x is 6.
That means that 6 x 6 = x
6 x 6 = 36.
So, x = 36.
B
For the third one, the square root of x is 9.
That means that 9 x 9 = x
9 x 9 = 81
So, x = 81.
For the fourth one, x^2 = 121
That means x times x = 121
To find x's value, simply find the square root of 121, which is 11
So, x = 11.
C
For the fifth one, x^3 = 343.
That means that x times x times x = 343
To find x's value, simply find the square root of 343, which is 7.
So, x = 7.
For the sixth and last one, the cube root of x is 10.
That means 10 x 10 x 10 = x.
10 x 10 x 10 = 1,000
So, x = 1,000
I hope this helps! :)