Answer:
D. 5
Step-by-step explanation:
AC = AB + BC
Substituting what we know
3x+20 = 12 + 5x-2
Combining like terms
3x+20 = 10 +5x
Subtract 3x from each side
3x+20-3x = 10 +5x-3x
20 = 10+2x
Subtract 10 from each side
20-10 = 10-10 +2x
10 = 2x
Divide by 2
10/2 =2x/2
5 =x
Use the substitution method to solve the system of equations. Choose the
correct ordered pair
x + 2y = 12
y = x + 3
O A. (5,8)
O B. (5,2)
O C. (2,1)
O D. (2,5)
Answer:
D. (2,5)
Step-by-step explanation:
For X:
2+2(5)=12
2+10=12
For Y:
5=2+3
Answer:
D
Step-by-step explanation:
Given the 2 equations
x + 2y = 12 → (1)
y = x + 3 → (2)
Substitute y = x + 3 into (1)
x + 2(x + 3) = 12 ← distribute and simplify left side
x + 2x + 6 = 12
3x + 6 = 12 ( subtract 6 from both sides )
3x = 6 ( divide both sides by 3 )
x = 2
Substitute x = 2 into (2) for corresponding value of y
y = 2 + 3 = 5
Solution is (2, 5 ) → D
Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting
the null hypothesis?
The Z-statistic is less than 0.
The z-statistic lies in the critical region.
The Z-statistic lies outside the critical region.
The z-statistic is greater than 0.
Answer:
The z-statistic lies in the critical region
Step-by-step explanation:
When a hypothesis test is performed, the decision to reject or not reject the null hypothesis is made on basis of following observations:
If the z-statistic falls in the critical or rejection region, there is enough evidence to reject the Null HypothesisIf the z-statistic falls outside the critical or rejection region, there is not enough evidence to reject the Null Hypothesis.In the given statement Zachary rejects the Null Hypothesis, this means the z-statistic she calculated must have been inside the critical or rejection region. Hence the correct answer would be:
The z-statistic lies in the critical region
Answer: b) The z-statistic lies in the critical region.
ed21
An elevator at a department store must carry fewer than 17 people at a time. An elevator operator is present in the elevator at all times. If x customers can travel in the elevator with the elevator operator, which inequality represents this situation? A. x + 1 < 17 B. x > 18 C. x + 1< 16 D. x < 17 E. x + 1 > 18
Answer:
A. x+ 1 < 17
Step-by-step explanation
Customers = x persons
Operator = 1 person
Total = x + 1 persons
Total persons must be less than 17.
The inequality is
x + 1 < 17
A research company wants to test the claim that a new multivitamin helps to improve short term memory. State the objective of the experiment, suggest a population, determine the experimental and control groups, and describe a sample procedure.
(SHOW WORK)
Answer:
I would think that you would want to have the multivitamin and then a placebo, then conduct an experiment testing the results of the multivitamin and observe the effects on both groups taking the medicine.
Step-by-step explanation:
your control group would be the placebo and your experimental group would be the multivitamin...
Answer with explanation:
Objective of the experiment:
The Multivitamin made by research company is beneficial or not for abolishing short term memory.
Population
The population can be chosen from the largest city hospital where people are suffering from short term memory loss.
Suppose 100 people are suffering from short term memory loss.
Experimental and control group
Suppose 40 people are being tested that is in experimental group and 60 people are in Control group.
Sample Procedure
After selecting 40 people in the experimental group , and then providing them Multivitamin for few days ,and then checking whether it is helping them to attain their memory or not is the procedure.
which mapping diagrams represent functions (choose all that apply)
which mapping diagrams represent relations that are not functions (choose all that apply)
in mapping diagram D what is the domain
in mapping diagram D what is the range
Answer:
A) function
B) not function
C) not function
D) function
D has domain {1,3,5} and range {2,4,6}.
Step-by-step explanation:
So for a mapping diagram to show a function there can only be at most one line segment coming from a number in the first circle.
So let's look at the problems:
A) There is one segment coming from 2. (2 to 1)
There is one segment coming from 4. (4 to 3)
There is one segment coming from 6. (6 ro 5).
So this is a function.
The domain is the first numbers: {2,4,6}.
The range is the second numbers: {1,3,5}.
B) There is two segments coming from 1. So it is over with, this is not a function.
The domain is the first numbers: {0,1,4}.
The range is the second numbers: {-2,-1,0,1,2}.
C) There is two segments coming from a. So it is over with, this is not a function.
The domain is the first numbers: {a,b,c}.
The range is the second numbers: {4,5,6,7}.
D) There is one segment coming from each 1, 3, and 5. So this is a function.
The domain is the first numbers: {1,3,5}.
The range is the second numbers: {2,4,6}.
Factor completely 3x² − x − 4.
20 for the top answer
Answer:
[tex](3x-4)(x+1)[/tex]
Step-by-step explanation:
This is in the form [tex]ax^2+bx+c[/tex].
If your wish is to factor by grouping, then you goal is too look for two numbers that multiply to be [tex]ac[/tex] and adds up to be [tex]b[/tex].
Then once you find those numbers you replace b with those numbers. Then the factor by grouping can be done.
So you have [tex]a=3,b=-1,c=-4[/tex]
[tex]ac=3(-4)[/tex]
[tex]b=-1[/tex]
The numbers that we need are already present since -4+3 is -1.
So replace -1 in
[tex]3x^2-1x-4[/tex]
with (-4+3)
[tex]3x^2-4x+3x-4[/tex]
Now group the first two terms together and group the last two terms together:
[tex](3x^2-4x)+(3x-4)[/tex]
Factor what you can from both pairs:
[tex]x(3x-4)+1(3x-4)[/tex]
Notice you have two terms: x(3x-4) and 1(3x-4). These terms have a common factor of (3x-4) so factor that out of our expression like so:
[tex](3x-4)(x+1)[/tex]
Check with foil if you like:
First: 3x(x)=3x^2
Outer: 3x(1)=3x
Inner: -4(x)=-4x
Last: -4(1)=-4
----------------------Add together:
3x^2-x-4
Answer: [tex]=(3x-4)(x+1)[/tex]
Step-by-step explanation:
Given the polynomial [tex]3x^2- x -4[/tex]
We can observe that it is written in this form:
[tex]ax^2+bx+c[/tex]
To factor completely, we need to follow these steps:
- Rewrite the term "b" as the sum of two terms whose product be [tex](3)(-4)=-12[/tex] and whose sum be -1:
[tex]=3x^2+(-4+3)x-4[/tex]
- Applying Distributive property, we get:
[tex]=3x^2-4x+3x-4[/tex]
- Make two groups of two terms each:
[tex]=(3x^2-4x)+(3x-4)[/tex]
- Factor out "x" from the first group and 1 from the second group:
[tex]=x(3x-4)+1(3x-4)[/tex]
- Factoring out [tex](3x-4)[/tex], we get:
[tex]=(3x-4)(x+1)[/tex]
Including scholarships and financial aid, Mark has $37,000 to spend on
college. If the total cost of his college education is _____, he will have
enough resources to pay.
A. $43,000
B. $40,000
C. $46,000
D. $34,000
Answer:
D
Step-by-step explanation:
The answer is anything less than $37,000 because that is how much he has to spend. D. $34,000 is the only answer less than that, so D is the correct answer.
in diagram below, ab and bc are tangent to o. what is the measure of abc.
A. 46
B.67
C.42
D.92
help FAST please!!!!
Check the picture below.
Answer:
Option A. will be the answer.
Step-by-step explanation:
It is given in the diagram attached, AB and BC are the tangents to circle O.
We have to find the measure of ∠ABC.
By the theorem,
Measure of ∠ABC which inscribed within the tangents will be [tex]=\frac{1}{2}(arcADC-arcAC)[/tex]
[tex]=\frac{1}{2}(226-134)[/tex]
[tex]=\frac{1}{2}(92)[/tex]
= 46°
Option A. will be the answer.
Quinton has an average resting heart rate of 70 beats per minute. When he runs, his heart rate increases by fewer than 50 beats per minute. If b represents his heart rate while running, which statements about the scenario are true? Check all that apply.
The inequality b=70<50 can be used to represent the situation.
The inequality b-50<70 can be used to represent the situation.
The graph of the solution set will be shaded to the left.
A possible value for b is 120.
A possible value for b is 140.
Answer:
1st and 3rd statements are true: 1) The inequality b=70<50 can be used to represent the situation and 2) The graph of the solution set will be shaded to the left.
Step-by-step explanation:
Lets look at this question step by step.
Quinton has an average resting heart rate of 70 beats per minute so heart rate = 70His heart rate increases by fewer than 50 beats per minute so heart rate = <50 or 70<50B represents heart rate while running, so 70 is the average resting heart and after running the heart rate is b = 70<50.Therefore, the first statement is true; The inequality b=70<50 can be used to represent the situation.
The inequality b-50<70 can be used to represent the situation.This cannot be true because as heart rate increases, it gets lesser than 50 so in this case, 50 is greater than 70 not lesser than 70.
Moreover, if we take 50 to the right side, it will be 70 + 50 = 120 which is wrong because b is supposed to be less than 50.
The graph of the solution set will be shaded to the left.This is true because b<50 and whenever there is a less than sign, the graph is shaded to the left.
A possible value for b is 120.A possible value for b is 140.These two statements cannot be true as be is supposed to be less than 50.
!!
Answer:
1 and 3
Step-by-step explanation:
pls give other person brainliest, they explained it very well:)
Which function represents the following graph?
00
Answer:
[tex]\large\boxed{y=\sqrt[3]{x+3}+3}[/tex]
Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
===========================================
The original graph ( y = ∛x) shifted 3 units to the left and 3 units up.
Therefore, the new equation is:
y = ∛(x + 3) + 3
is the grouping method to factor 5x^3+15x^2-2x-6
Answer:
[tex](x+3)(5x^2-2)[/tex]
Step-by-step explanation:
[tex]5x^3+15x^2-2x-6[/tex]
The grouping method means you are going to group some terms together and then factor what you can out of each pair to hopefully make the expression you started with factorable.
Let's try it.
[tex]5x^3+15x^2+-2x-6[/tex]
I like to insert a + in front of the last two terms if it isn't already one. I think it makes it less confusing.
I'm going to group the first two terms together and I'm going to group the last two terms together like so:
[tex](5x^3+15x^2)+(-2x-6)[/tex]
Now I'm going to factor what I can out of each pairing.
[tex]5x^2(x+3)+-2(x+3)[/tex]
(*I always factor out negative number if the first term in the second pair has a negative on it.)
Now notice in each pairing, there is a common factor of (x+3) so I can factor that out.
The expression then becomes:
[tex](x+3)(5x^2-2)[/tex]
Final answer:
Yes, the grouping method can be used to factor the polynomial 5x³ + 15x² - 2x - 6, resulting in (x + 3)(5x² - 2) as the factored form.
Explanation:
The question is asking if we can use the grouping method to factor the polynomial 5x³ + 15x² - 2x - 6. Factoring by grouping is a technique where we group terms that have common factors and then factor each group individually.
To apply the grouping method to this polynomial, we would look for groups of terms that have common factors and try to factor out those common factors. Let's group the first two terms and the last two terms:
Group 1: 5x³ + 15x²
Group 2: -2x - 6
Factoring out the greatest common factor from each group, we get:
Group 1: 5x² (x + 3)
Group 2: -2 (x + 3)
Now, we can factor out the common binomial factor (x + 3):
(x + 3)(5x² - 2)
This is the factored form of the polynomial using the grouping method.
what does x² - 5x equal
Answer:
x(x-5)
Step-by-step explanation:
We cannot solve this expression because there is no equals sign.
We can,however simplify the expression
x^2 -5x
Factor out an x
x(x-5)
Triangle XYZ is reflected across the y-axis. Then its image is rotated 90° about the origin. What are the
coordinates of the final image of point X under the composition of transformations?
• (-3,2)
• (3,2)
• (2-1)
0 (-2,-3)
None of the other answers are correct
Help me
Answer:
(- 3, 2 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
X has coordinates X(- 2, 3 ), hence
X'(2, 3 ) ← after reflection in the y- axis
Under a rotation about the origin of 90°
a point (x, y ) → (- y, x )
Hence
X'(2, 3 ) → X''(- 3, 2 ) ← final image point
The correct option will be option A: The final image point of X will be (-3,2).
What is reflection?The reflection about an axis is the transformation of the picture about an axis so that distance of every point from the axis before and after reflection will remain the same.
Here the coordinate of point X in triangle XYZ is (-2,3).
First, the triangle XYZ is reflected about the y-axis.
As we know, the reflection of the point of coordination (x,y) after reflection about the y-axis will be (-x,y).
(x,y)→(-x,y)
So the point X of coordination (-2,3) after reflection about the y-axis will be (2,3).
Then the reflected point is rotated about the origin.
As we know the rotation of the point of coordination (x,y) after rotation about origin will be (-y,x).
(x,y)→(-y,x)
So the point of coordination (2,3) after rotation about the origin will be (-3,2).
Therefore The final image point of X will be (-3,2).
Learn more about reflection
here: https://brainly.com/question/1908648
#SPJ2
Lexi and Maria had $250 altogether. After Lexi spent 2/5 of her money and Maria spent $40 they had the same amount of money left. How much more money did Lexi have in the beginning.
Answer:
The amount of money that Lexi had at the beginning was $131.25
Step-by-step explanation:
Let
x -----> amount of money that Lexi had at the beginning
y -----> amount of money that Maria had at the beginning
we know that
x+y=250 -----> equation A
(1-2/5)x=y-40
(3/5)x=y-40
y=(3/5)x+40 ----> equation B
substitute equation B in equation A and solve for x
x+(3/5)x+40=250
(8/5)x=250-40
(8/5)x=210
x=210*5/8
x=$131.25
Joyce had business cards made through a printing company. They charge an initial fee of $12 and $3.99 for each box of 100 business cards. If Joyce needs 5 boxes, how much will she be charged?
Answer:
$31.95
Step-by-step explanation:
The total cost is the initial fee plus the cost of the boxes.
12 + 5×3.99 = 31.95
2354 bdxbdbdbht55675443t35222222222222222222222222
A rectangular flower bed is to be 8 m longer than it is wide. The flower bed will have an area of 84 m squared
What will it's dimensions be?
Answer:
6m wide
14m long
Step-by-step explanation:
Let the length be represented by L.
Let the width be represented by W.
We are given we want the length to be 8 m longer than it's width.
So we want L=8+W.
The area of the rectangle is 84 m squared, this means that LW=84.
So I'm going to substitute L=8+W into LW=84.
LW=84
(8+W)W=84 (L=8W)
So we are going to solve (8+W)W=84 for W.
(8+W)W=84
Distribute:
8W+W^2=84
Rearrange left hand side using commutative property:
W^2+8W=84
Subtract 84 on both sides:
W^2+8W-84=0
Now to factor a quadratic with leading coefficient 1 (assuming it isn't prime) is to find two numbers that multiply to be c=-84 and add up to be b=8.
I'm going to play with factor pairs that multiply to be -84
c=-84=4(-21)=12(-7)=6(-14)
So the number we are looking for is -6 and 14 since -6(14)=-84 and -6+14=8.
The factored form of our equation is:
(W+14)(W-6)=0
This means we need to solve both W+14=0 and W-6=0.
W+14=0
W=-14 (I subtracted 14 on both sides)
W-6=0
W=6 (I added 6 on both sides)
The solution W=-14 makes no sense.
W=6 is the solution for the width. That is the width is 6 m long.
Now the length is 8 more than the width so the length is 14 m long.
Answer:
6m wide and 14m long
Step-by-step explanation:
If a rectangular flower bed is to be 8 m longer than it is wide and the flower bed will have an area of 84 m squared, its dimensions will be 6m wide by 14m long.
L = length
W = Width
Factor completely 21x3 + 35x2 + 9x + 15. (3x − 5)(7x2 − 3) (3x − 5)(7x2 + 3) (3x + 5)(7x2 − 3) (3x + 5)(7x2 + 3)
Answer:
(7x^2+3)( 3x+5)
Step-by-step explanation:
21x^3 + 35x^2 + 9x + 15.
We will do factor by grouping
Rearranging the terms so I have the terms with a factor of 3 first and 5 last
Factor a 3x from the first two terms and 5 from the last two terms
21x^3 + 9x + 35x^2+ 15
3x(7x^2 +3) +5(7x^2+3)
Now factor out a (7x^2+3)
(7x^2+3)( 3x+5)
Answer:
Cubic = (3x + 5)(7x^2 + 3)
Step-by-step explanation:
If you make up two groups of 2, you might be able to factor this using the distributive property. Let's try it.
First group: 21x^3 + 35x^2 Take out 7x^2 as a common fact
First group: 7x^2(3x + 5)
Second group: 9x + 15 The HCF is 3
Second group: 3(3x + 5)
Now put your factors together in one long string.
Cubic = group 1 + group 2
Cubic = 7x^2 (3x + 5) + 3(3x + 5)
Note: If you had something like 7x^2 * y + 3 *y then you should see that the factors are y* (7x^2 + 3). So to solve the cubic, you should observe that (3x + 5) is a common factor.
Let y = 3x + 5
y(7x^2 + 3) Now substitute back for the y.
Cubic = (3x + 5)(7x^2 + 3)
Anthony purchased 6 fruit bars and 3 chocolate-nut bars for a camping trip. He spent $4.12 on the bars. Anthony wrote the following equation: 6x+3y=4.12 . What did he define as the variable x?
Answer:
He defined variable x as the cost of each fruit bar.
Step-by-step explanation:
6 is the amount of fruit bars Anthony has, so 3y must be for the chocolate-nut bars. So the only thing that makes sense is if variable x is the cost of each fruit bar.
Answer:
A cost a friut bar
Step-by-step explanation:
just finished the test and that was correct have a great day or night!
Square lMNO is shown in the diagram below what are the coordinates of the midpoint of a diagonal LN
Answer:
The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
answer (4)
Step-by-step explanation:
* Lets explain how to find the midpoint of a line
- The coordinates of the midpoint of a line whose endpoints are (x1 , y1)
and (x2 , y2) are [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ LMNO is a square
∵ The coordinates of point L are (-6 , 1)
∵ The coordinates of point N are (1 , 8)
- Let the coordinates of point L are (x1 , y1) , the coordinates of point
N are (x2 , y2) and the coordinates of the midpoint of LN are (x , y)
∴ x1 = -6 , x2 = 1 and y1 = 1 , y2 = 8
- Use the rule of the midpoint above to find the midpoint (x , y)
∵ [tex]x=\frac{-6+1}{2}=\frac{-5}{2}=-2\frac{1}{2}[/tex]
∵ [tex]y=\frac{1+8}{2}=\frac{9}{4}=4\frac{1}{2}[/tex]
∴ The coordinates of the midpoint are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
* The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]
Answer:
The answer should be D the fourth one
Step-by-step explanation:
witch numbers belong to the equation 6x <= 66
A 11
B 53
C 9
D 12
E 50
F 7
plz explain i need to know how this works lol
Answer:
A 11
C 9
F 7
Step-by-step explanation:
6x≤ 66
Divide each side by 6
6x/6 ≤ 66/6
x ≤ 11
Any number less than or equal to 11 is a solutions
A 11 yes
B 53 no
C 9 yes
D 12 no
E 50 no
F 7 yes
5xy-25x square+50x-10y
Answer:
the answer is 5(y-5x) (x-2)
Step-by-step explanation:
Answer:
[tex]5(x - 2)(y - 5x)[/tex]
Explanation
We want to factorize:
[tex]5xy - 25 {x}^{2} + 50x - 10y[/tex]
The factors have been grouped already. We now factor the GCF from each group to get:
[tex]5x(x- 5x) - 10(y - 5x)[/tex]
We factor further to obtain:
[tex](5x- 10)(y - 5x)[/tex]
We can still factor 5 to obtain:
[tex]5(x - 2)(y - 5x)[/tex]
please answer also if you answer this one please answer my other one it basically the same
Answer:
D is the correct answer.
Step-by-step explanation:
Step 1: Write the data
Total number of songs = 100
Total ratio = 1
Total percentage = 100%
Ratio of jazz songs = 1/4
Percentage of jazz songs = 1/4 x 100 = 25%
Ratio of pop songs = 1 - 1/4 = 3/4
Percentage of pop songs = 3/4 x 100 = 75%
Step 2: Match the statement.
The correct statement is D; 25% are Julian's songs are jazz because 1/4 = 25/100 and 75% are pop because 3/4 = 75/100.
!!
Beth is designing a business card. She makes a scale drawing of her old business card by using the scale factor 5/4. Her scale drawing is 2 1/2in by 5in rectangle.
The print shop says the scale drawing is a reduction of the original card because the original card must be 3 1/8in by 6 1/4in. Which explains the print shop’s error?
A. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 2in by 4in
B. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 3 3/4in by 6 1/4in
C. The scale factor is a fraction so the scale drawing is an reduction, and the original card is 2in by 4in
D. The scale factor is a fraction so the scale drawing is an reduction, and the original card is 3 3/4in by 6 1/4in
Answer:
The correct option is A.
Step-by-step explanation:
It is given that Beth makes a scale drawing of her old business card by using the scale factor 5/4.
If the scale factor is less than 1, then it represents compression and if the scale factor is greater than 1, then it represents enlargement.
Since the scale factor is greater than 1 so the scale drawing is an enlargement.
Let the initial dimension of business card is a by b.
Her scale drawing is [tex]2\frac{1}{2}[/tex] in by 5 in rectangle. Multiply each dimension by reciprocal of scale factor to find the dimension of original card.
[tex]a=2\frac{1}{2}\times \frac{4}{5}=\frac{5}{2}\times \frac{4}{5}=2[/tex]
[tex]b=5\times \frac{4}{5}=4[/tex]
The dimension of original card is 2 in by 4 in.
Therefore the correct option is A.
Answer: A
Step-by-step explanation:
without actually performing the long division state whether 17 / 3125 will have a terminating decimal expansion or a non-terminating decimal expansion
Answer:
It is terminating decimal expansion.
Step-by-step explanation:
17/3125 is a terminating decimal expansion.
REASON:
If the factors of the denominator are in the form of 2^n 5^m then the rational number is a terminating decimal expansion otherwise it is recurring. Here n and m are non negative integers.
Proof:
Lets have a look on the solution of the given term.
17/1325
We will break the denominator in the factors:
If we multiply 5 five times than it will give us 1325.
17/1325 = 17/5^5 * 2^0 = 17/2^0 * 5^5
We know that any number with exponent zero = 1
∴ 2^0 = 1
So it satisfies our explanation that the factors of the denominator are in the form of 2^n * 5^m and n and m are non negative integers.
Thus this term has a terminating decimal expansion....
Answer:
Two of the most important characteristics of seawater are temperature and salinity – together they control its density, which is the major factor governing the vertical movement of ocean waters. The temperature of seawater is fixed at the sea surface by heat exchange with the atmosphere.
Step-by-step explanation:
plz mark as brainliest..
What is the sum of the geometric sequence −1, 6, −36, ... if there are 6 terms? (1 point) −39,991 6,665 −6,665 39,991
Answer:
=6665
Step-by-step explanation:
The sum of a geometric series is given by:
Sn=a(1-rⁿ)/(1-r)
Sn is the sum of the first n terms, r is the rate and n is the number of terms.
r the quotient between any two consecutive numbers.
r=6/-1= -6
Sn=-1(1-(-6)⁶)/(1--6)
=46655/7
=6665
Sum of the first six terms=6665
Given the Arithmetic sequence A1,A2,A3,A4 45, 51, 57, 63 What is the value of A34?
Answer:
Value of A(34) = 219
Step-by-step explanation:
A1, A2,A3,A4,45,51,57,63 are in Arithmetic sequence
Common difference in this Arithmetic sequence = 63 - 57 = 06
so, A4 = 45 - 6 = 39
A3 = 39 - 6 = 33
A2 = 33 - 6 = 27
A1 = 27 - 6 = 21
First term of Arithmetic sequence = 21
Common difference = 06
Using general term of Arithmetic sequence,
A(n) = First term + (n - 1) common difference
A(34) = 21 + (34 - 1) 6
A(34) = 21 + 33 × 6
A(34) = 21 + 198
A(34) = 219
Value of A(34) = 219
Reflect the given the coordinate points over the line y=x. F(−5,−3) G(−5,−2) H(−2,−2) F′( , ) G′( , ) H′( , )
Answer:
[tex]F'(-3,-5),G'(-2,-5),H'(-2,-2)[/tex]
Step-by-step explanation:
The given points are: F(−5,−3) G(−5,−2) H(−2,−2)
The mapping for reflection in the line [tex]y=x[/tex] is [tex](x,y)\to (y,x)[/tex].
We just have to swap the coordinates of the preimage to obtain the image
[tex]F(-5,-3)\to F'(-3,-5)[/tex].
[tex]G(-5,-2)\to G'(-2,-5)[/tex].
[tex]H(-2,-2)\to H'(-2,-2)[/tex].
Therefore the image points are
[tex]F'(-3,-5),G'(-2,-5),H'(-2,-2)[/tex]
Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
A. f is concave down from x = –3 to x = 0.
B. f is decreasing from x = –1.5 to x = 1.5.
C. f has a relative maximum at x = 1.
D. None of these is true.
Answer:
C. f has a relative maximum at x = 1.
Step-by-step explanation:
A. False. f(x) is concave down when f"(x) is negative. f"(x) is the tangent slope of the graph, f'(x). So f(x) is concave down between x = -1.5 and x = 1.5.
B. False. f(x) is decreasing when f'(x) is negative. So f(x) is decreasing in the intervals x < -3 and 1 < x < 2.
C. True. f(x) has a relative maximum where f'(x) = 0 and changes from + to -.
6 radians is the same as ____°.
Round to the nearest hundredth of a degree.
Answer:
343.77°
Step-by-step explanation:
1 radian = [tex]\frac{180}{Pi}[/tex]°
6 radians will be;
6 × [tex]\frac{180}{Pi}[/tex]° =343.7746771 °
Or 343.77° (rounded up to nearest hundredth)
Answer:
343.77
Step-by-step explanation:
You roll a number cube three consecutive times. What is the probability that you roll an even number the first two times and a 3 the last time?
Answer:
1/24.
Step-by-step explanation:
Probability(Rolling an even number)
= 3/6 = 1/2.
Probability(Rolling a 3) = 1/6.
Required Probability = 1/2 * 1/2 * 1/6
= 1/24.
The probabilities are multiplied because the 3 events are independent.
Answer:
1/24
Step-by-step explanation:
A die has 6 faces with numbers 1 through 6. Three faces have even numbers, and 3 faces have odd numbers.
Each roll of the die can result in 6 different outcomes.
The total number different outcomes of rolling a die 3 times is 6 * 6 * 6 = 216.
There are 3 possible even number outcomes on the first roll, and another 3 possible even number outcomes on the second roll. The third roll needs to be a 3, so there is one single desired outcome of the third roll.
Total number of desired outcomes: 3 * 3 * 1 = 9
probability(even, even, 3) = 9/216 = 1/24