PLEASE HELP! Urgent!!!
Which of the following expressions represents the area of the composite figure ( i said 18 pi + 35 and it said it was wrong)
Answers
Answer:
[tex]\frac{9}{2}\pi +35[/tex]
Step-by-step explanation:
The area of trapezoid is given by the formula:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]
Where
A is the area
b_1 is base 1
b_2 is base 2, and
h is the height
Looking at the figure, base 1 is the left line which goes from y = 3 to y = 3, so 6 units. Also, base 2 is the right line which goes from y = -3 to y =5, so 8 units.
The height is the horizontal distance in the middle, which goes from x = -2 to x = 3, so 5 units. Hence area of trapezoid is:
[tex]A=\frac{1}{2}(b_1+b_2)h\\A=\frac{1}{2}(6+8)*5\\A=35[/tex]
Now, area of semicircle is:
[tex]A=\frac{\pi r^2}{2}[/tex]
Where
A is the area
r is the radius
Looking at the figure, the diameter (twice radius) goes from y = -3 to y = 3, so 6 units. But radius is half of that, so 3 units. Hence area of semicircle is:
[tex]A=\frac{\pi r^2}{2}\\A=\frac{\pi (3)^2}{2}\\A=\frac{9}{2} \pi[/tex]
Total area of the figure is [tex]\frac{9}{2}\pi +35[/tex]
Related Questions
Solve: ^3 sqrt x^2-8=2
Answers
Answer:
∛x²-8 = 2
-2∛x² = 2
∛x² = 2+2
x² = 4³
x = √64
x = 8
Answer:
C. x = –4 or x = 4
Step-by-step explanation:
B. s = 7 (for the second one)
Find the slope of the line that contains the points (4,-3) and (-4,1). is it undefined?
Answers
[tex]\huge{\boxed{-\frac{1}{2}}}[/tex]
We can find the slope with [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are both points.
Plug in the values. [tex]\frac{1-(-3)}{-4-4}[/tex]
Simplify. [tex]\frac{1+3}{-4-4}[/tex]
Add/subtract. [tex]\frac{4}{-8}[/tex]
Simplify. [tex]\boxed{-\frac{1}{2}}[/tex]
Answer:
No.
The slope of the line is -1/2.
Step-by-step explanation:
I'll give you a hint, to solve slope of the line use [tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\displaystyle \frac{1-(-3)}{(-4)-4}=\frac{4}{-8}=\frac{4\div4}{-8\div4}=\frac{1}{-2}=-\frac{1}{2}[/tex]
The slope of the line is -1/2, which is our answer.
I hope this helps!
Which statements are always true regarding the diagram?
Select three option. (Picture included)
m<5+m<3=m<4
m<3+m<4+m<5=180
m<5+m<6=180
m<2+m<3=m<6
m<2+m<3+m<5=180
Answers
Answer:
m∠5+m∠6=180°
m∠2+m∠3=m∠6
m∠2+m∠3+m∠5=180°
Step-by-step explanation:
Verify each option
case A) we have
m∠5+m∠3=m∠4 ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
This equation is true when m∠2=m∠3
therefore
Is not always true
case B) we have
m∠3+m∠4+m∠5=180° ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
This option is not true
case C) we have
m∠5+m∠6=180°
we know that
m∠5 and +m∠6 are supplementary angles
so
Their sum is always 180 degrees
therefore
This option is always true
case D) we have
m∠2+m∠3=m∠6 -----> equation A
we know that
m∠5+m∠6=180° ----> by supplementary angles
m∠6=180°-m∠5 ----> equation B
substitute equation B in equation A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Remember that the sum of the interior angles of a triangle must be equal 180 degrees
therefore
This option is always true
case E) we have
m∠2+m∠3+m∠5=180°
Remember that the sum of the interior angles of a triangle must be equal 180 degrees
therefore
This option is always true
Answer:
CDE
Step-by-step explanation:
p (a) =0.60, p(b) = 0.25, and p(a and b) =0.15 what is p(a or b) ?
a.) 0.40
b.) 0.85
c.) 0.70
d.) 0.75
Answers
Answer:
C is the correct option
Step-by-step explanation:
To find the probability of P(a or b) we will use the formula:
P(a or b)= P(a)+ P(b) - P(a-b)
Now put the given values in the formula:
P(a or b)= 0.60+0.25-0.15
P(a or b)=0.85 - 0.15
P(a or b)= 0.70
Thus the correct option is C....
Answer: Option C
[tex]P (A\ or\ B) = 0.70[/tex]
Step-by-step explanation:
If A and B are events that are not mutually exciting, then it is true that:
[tex]P (A\ or\ B) = P (A) + P (B) - P (A\ and\ B)[/tex]
In this case we know [tex]P(A)[/tex], [tex]P(B)[/tex] and we also know [tex]P (A\ and\ B)[/tex]
[tex]P(A)=0.60[/tex]
[tex]P(B) = 0.25[/tex]
[tex]P(A\ and\ B)=0.15[/tex]
Therefore we have that:
[tex]P (A\ or\ B) = 0.60 + 0.25 - 0.15[/tex]
[tex]P (A\ or\ B) = 0.60 + 0.1[/tex]
[tex]P (A\ or\ B) = 0.70[/tex]
Which simplifications of the powers of i are correct? There may be more than one correct answer. Select all correct answers.
A) i^6=1
B) i^18=1
C) i^7=-i
D) i^16=1
Answers
Answer:
Option C and D are correct options
Step-by-step explanation:
The correct options are C and D.
We know that i = √-1
i² = -1
i³ = -i
and i^4 = 1
Lets solve the options one by one:
i^6 =1
Break the power:
i² *i ² * i² = (-1)(-1)(-1)
= -1
Therefore A is wrong
B) i^18 = 1
Lets break the power:
i²* i² *i² *i²*i²*i²*i²*i²*i²
put the value of i^2
= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)(-1)
= -1
Therefore option B is incorrect.
C) i^7 = -i
= i² * i² *i² *i
=(-1) (-1) (-1) * √-1
= - √-1
We know that √-1 = i
So,
- √-1 = -i
Therefore option C is correct.
D) i^16 = 1
= i² * i² * i² * i² * i² * i² *i² *i²
= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)
= 1
Therefore option D is correct.
Thus option C and D are correct option....
Answer: Option C and Option D
Step-by-step explanation:
Remember that by definition we have to:
[tex]i=\sqrt{-1}[/tex] and [tex]i^2=-1[/tex]
So for the option A we have to:
[tex]i^6=(\sqrt{-1})^2*(\sqrt{-1})^4\\\\i^6=-1*(-1)^2\\\\i^6=-1[/tex]
Option A is false
So for the option B we have to:
[tex]i^{18}=(i^6)^3[/tex]
We know that [tex]i^6=-1[/tex]
So
[tex]i^{18}=(-1)^3[/tex]
[tex]i^{18}=-1[/tex]
Option B is false
So for the option C we have to:
[tex]i^7=(i)^6*i^1[/tex]
[tex]i^7=-i[/tex]
Option C is true
Finally for the option D we have to:
[tex]i^{16}=(i^4)^4[/tex]
[tex]i^{16}=((-1)^2)^4[/tex]
[tex]i^{16}=(1)^4[/tex]
[tex]i^{16}=1[/tex]
Option D is true
2x2 + 14x- 4 = - x2 + 3x
Answers
first, lets solve by factoring:
Let's solve your equation step-by-step.
2x2+14x−4=−x2+3x
Step 1: Subtract -x^2+3x from both sides.
2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)
3x2+11x−4=0
Step 2: Factor left side of equation.
(3x−1)(x+4)=0
Step 3: Set factors equal to 0.
3x−1=0 or x+4=0
x=
1
3
or x=−4
we can also solve using the quadratic formula:
2x2+14x−4=−x2+3x
Step 1: Subtract -x^2+3x from both sides.
2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)
3x2+11x−4=0
Step 2: Use quadratic formula with a=3, b=11, c=-4.
x=
−b±√b2−4ac
2a
x=
−(11)±√(11)2−4(3)(−4)
2(3)
x=
−11±√169
6
x=
1
3
or x=−4
lastly, we can complete the square.
2x2+14x−4=−x2+3x
Step 1: Add x^2 to both sides.
2x2+14x−4+x2=−x2+3x+x2
3x2+14x−4=3x
Step 2: Subtract 3x from both sides.
3x2+14x−4−3x=3x−3x
3x2+11x−4=0
Step 3: Add 4 to both sides.
3x2+11x−4+4=0+4
3x2+11x=4
Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x2+11x
3
=
4
3
x2+
11
3
x=
4
3
Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.
Then we need to add (b/2)^2=121/36 to both sides to complete the square.
Add 121/36 to both sides.
x2+
11
3
x+
121
36
=
4
3
+
121
36
x2+
11
3
x+
121
36
=
169
36
Step 6: Factor left side.
(x+
11
6
)2=
169
36
Step 7: Take square root.
x+
11
6
=±√
169
36
Step 8: Add (-11)/6 to both sides.
x+
11
6
+
−11
6
=
−11
6
±√
169
36
x=
−11
6
±√
169
36
x=
1
3
or x=−4
Answer:
x=
1
3
or x=−4
Final answer:
The equation [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex] is a quadratic equation, which can be solved by standard methods such as factoring, completing the square, or applying the quadratic formula and then validated by substituting the solutions back into the original equation.
Explanation:
To solve the quadratic equation, [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex], first combine like terms by getting all terms on one side of the equation, resulting in [tex]3x^2 + 11x - 4[/tex] = 0. This is a standardized quadratic equation [tex]ax^2[/tex] + bx + c = 0. To find the solutions for this equation, you can either factorize it, complete the square or use the quadratic formula, (-b ± √([tex]b^2[/tex] - 4ac)) / (2a). After finding the roots (values for x), verify them by plugging them back into the original equation to ensure they satisfy it.
Please help I’m stuck!
Answers
Answer:
1. the value of x can equal 25
the shortest length can equal 7
the longest length can equal 30
2. 2x+2.1=7.5
Step-by-step explanation:
Given:
1.
A scalene triangle with sides y, 4y and x
and perimeter,p= 60cm
As per perimeter formula:
p= sum of all sides
Putting values we get
60=x+4y+y
60=x+5y
so correct options are
the value of x can equal 25
the shortest length can equal 7
the longest length can equal 30
2. An isosceles triangle with sides y=2.1, x and x
and perimeter,p = 7.5
As per perimeter formula:
p= sum of all sides
Putting values we get
7.5=2.1 + x +x
7.1=2.1+2x !
Look at the diagram below. If JM = LM, then angles JKM are congruent.- From Apex
True or False
Answers
Answer:
The answer to this question is True
Answer: true
Step-by-step explanation:
An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed with a mean equal to 13.00 and a standard deviation equal to 0.2 seconds. What percentage of players on the team run the 100-meter dash in 13.30 seconds or faster? (Round your answer to two decimal places.)
Answers
Answer:
6.68%
Step-by-step explanation:
First find the z-score:
z = (x − μ) / σ
z = (13.30 − 13.00) / 0.2
z = 1.50
Look the value up in a z-score table, or use a calculator.
P(z>1.50) = 1 − 0.9332
P(z>1.50) = 0.0668
6.68% of players on the team run the 100 meter dash in 13.30 seconds or faster.
complete the point slope equation of the line through(-1,-10)and(5,2).
y-6=
Answers
Answer:
y - 6 = 2(x - 7)Step-by-step explanation:
The point-slope of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the poinys (-1, -10) and (5, 2). Substitute:
[tex]m=\dfrac{2-(-10)}{5-(-1)}=\dfrac{12}{6}=2[/tex]
Put the value of the slope and the coordinateso f the point (5, 2), to the equation of a line:
[tex]y-2=2(x-5)[/tex]
In the question we have y - 6 = ...
Therefore
[tex]y-2=2(x-5)[/tex] subtract 4 from both sides
[tex]y-6=2(x-5)-4[/tex] use the distributive property
[tex]y-6=2x-10-4[/tex]
[tex]y-6=2x-14[/tex] distributive
[tex]y-6=2(x-7)[/tex]
Suppose that you want to design a cylinder with the same volume as a given cylinder, but you want to use a different radius and height. In general
terms, how can you changer and h to produce the same wolume for both cylinders?
Answers
volume of a cylinder = pi×r^2×h
Answer:
I can increase r and decrease h, or I can decrease r and increase h.
Step-by-step explanation:
answer given in edmentum
Figure ABCD is transformed to figure , as shown: Which of the following sequences of transformations is used to obtain figure from figure A'B'C'D?
Answers
You need a picture deficiencies did that for 20 characters
Which of the following polynomials has a remainder of -11 when divided by x+1? A. −2x3+4x2+3x−2 B. 3x3+6x−2 C. x3−2x2−4x+1 D. 4x3+2x2+5
Answers
Answer:
B. 3x3+6x−2
Step-by-step explanation:
When you divide 3x3+6x−2 by x+1 we get a remainder of -11.
Helena uses a free online account to store digital photos and videos. She uploads 650 photo and video files from her phone to the account. The average size of each photo is 4 megabytes and the average size of each video is 9 megabytes. The total upload size was 2,925 megabytes. Which system of equations can be used to determine the number of photo files, p, and the number of video files, v, Helena uploaded from her phone?
p + v = 650 and 4v + 9p = 2,925
p = 650 – v and 4p + 9v = 2,925
4v = 650 – 9p and 13(p + v) = 2,925
9v + 4p = 650 and v + p = 2,925
Answers
Answer:
p = 650 – v and 4p + 9v = 2,925 , Its B
https://brainly.com/question/3605037
Answer:
b
Step-by-step explanation:
There are 200 counters in a bag.
50 of them are taken out and have a dab of white paint placed on them.
These 50 marked counters are now put back in the bag which is given
a good shake to ensure even distribution of the marked counters.
80 counters are now taken out of the bag.
About how many of them would you expect to be marked with a
dab of white paint?
Answers
We could expect about 20 of the counters taken out to have white paint
Out of those 80 counters, 20 counters may have a white dab on them.
Given to usTotal number of counters in the bag = 200
counters that have a white dab = 50
counters that are now taken out of the bag = 80
Let's first take the ratio of counters that have a white dab to the total number of counters in the bag.
The ratio of bag[tex]\rm{=\dfrac{counters\ that\ have\ a\ white\ dab}{Total\ number\ of\ counters\ in\ the\ bag}[/tex]
[tex]=\dfrac{50}{200} = \dfrac{1}{4} = 0.25[/tex]
Therefore, the ratio of counters that have a white dab to the total number of counters in the bag is 0.25.
80 countersAs the bag is given a good shake to ensure even distribution of the marked counters.
Those 80 counters will follow the same ratio of the bag, so, the number of tokens with white dab will be,
Number of tokens taken out x ratio of the bag
= 80 x 0.25
= 20
Hence, out of those 80 counters, 20 counters may have a white dab on them.
Learn more about ratio:
https://brainly.com/question/1504221
based only on the information given in the diagram which congruence theorems or postulates could be given as reason why ABC=DEF
Answers
Answer:
HL
SAS
SSS
Step-by-step explanation:
Since these are right triangles, and you have the two hypotenuses are congruent to each other and two legs that are also congruent to each other, then HL can be applied.
For HA to work we must have been given something else about one of those angle (besides the 90 degree one).
Since you have two corresponding sides that are congruent, then the 90 degree angles in both are congruent, and then the sides right after that 90 degree angle are also congruent to each other, so SAS can be applied.
We can't use AAS. We only know something about one angle per each triangle due to the markers.
LA? Needed another angle besides the 90 degree one.
All three corresponding sides are congruent. The markers tell us this. So we can apply SSS.
Answer:
HL
SAS
SSS
Step-by-step explanation:
I really need help with this
Answers
Answer:
[tex]\frac{1}{x^2y^6}[/tex]
Step-by-step explanation:
We are given [tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex]
First rule I'm going to use is [tex](m^rn^p)^s=m^{r \cdot s}n^{p \cdot s}[/tex].
This gives us:
[tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex] is
[tex](x^2y^6) \cdot (x^{-4}y^{-12})[/tex].
Now pair up the bases that are the same:
[tex](x^2x^{-4}) \cdot (y^6y^{-12})[/tex].
Add the exponents when multiplying if the bases are the same:
[tex]x^{-2} \cdot y^{-6}[/tex]
Now usually teachers don't like negative exponents.
To get rid of the negative exponents just take the reciprocal:
[tex]\frac{1}{x^2} \cdot \frac{1}{y^6}[/tex]
[tex]\frac{1}{x^2y^6}[/tex]
Identify the mapping diagram that represents the relation and determine whether the relation is a function. {(–3, –6), (–1, –6), (5, –6), (8, –6)} Which of the following is true?
Answers
Answer:
This relation is a function.
Step-by-step explanation:
A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.
We have
{(-3, -6), (-1, -6), (5, -6), (8, -6)}
x = -3 → y = -6
x = -1 → y = -6
x = 5 → y = -6
x = 8 → y = -6
YES. This relation is a function.
/each x has one value of y/
Answer: Yes, it is a function
Step-by-step explanation:
solve the equation -9x+1=-x+17
Answers
Answer:
x=-2
Step-by-step explanation:
-9x+1=-x+17
Add 9x on both sides:
1=8x+17
Subtract 17 on both sides:
-16=8x
Divide both sides by 8:
-2=x
Check x=-2!
-9x+1=-x+17 with x=-2
-9(-2)+1=-(-2)+17
18+1=2+17
19=19
19=19 is a true equation so x=-2 is correct.
Answer: b
Step-by-step explanation:
need help with 1-5 , please!!!!!!
Answers
Answer:
1)
[tex] \frac{26 + 16 + 11 + 13 + 24}{5} = \frac{90}{5} = 18[/tex]
2)
[tex] \frac{51 + 20 + 32 + 18 + 45 + 8}{6} = \frac{174}{6} = 29[/tex]
3)
[tex] \frac{17 + 39 + 15 + 42 + 37 + 61 + 19 + 40}{8} = \frac{270}{8} = 33.75[/tex]
4)
[tex] \frac{62 + 21 + 18}{3} = \frac{101}{3} = 33.67[/tex]
5)
[tex] \frac{9.2+8.6+9.4+9.2}{4} = \frac{36.4}{4} = 9.1[/tex]
Which of the following inequalities matches the graph?
[tex]x > - 3[/tex]
[tex]x < - 3[/tex]
[tex]y > - 3[/tex]
[tex]y < - 3[/tex]
which one is it 1,2,3,or 4 one
Answers
Answer:
y < -3Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
x ≤ a or x < a - the region below the horizontal line x = a
x ≥ a or x > a - the region above the horizontal line x = a
y ≤ a or y < a - the region on the left side of the vertical line y = a
y ≥ a or y > a - the region to the right of the vertical line y = a
=========================================
We have dotted line (<, >).
The vertical line (y).
The region on the left side of the vertical dotted line y = -3
The tax on a property with an assessed value of $67,000 is $975. Using a proportion, find the tax on a property with an assessed value of $96,000
Answers
Answer:
1,440
Step-by-step explanation:
1.5 percent of 96k
TIME REMAINING
01:54:53
O
At a grocery store, blueberries come packaged in 8-ounce containers for $2.80 At a farmer's market, blueberries cost $4.20
for 14 ounces. There are 16 ounces in one pound. Which statement accurately compares the cost of blueberries?
Answers
$0.30 (farmer's market) < $0.35 (grocery store), the farmer's market offers blueberries at a lower price per ounce.
To compare the cost of blueberries from a grocery store and a farmer's market below:-
Cost of blueberries at the grocery store:
Price for an 8-ounce container: $2.80 Price per ounce = [tex]\frac{2.80}{8} = 0.35[/tex]Therefore, the cost is $0.35 per ounce.
Cost of blueberries at the farmer's market:
Price for a 14-ounce container: $4.20 Price per ounce = [tex]\frac{4.20}{14} = 0.30[/tex]Therefore, the cost is $0.30 per ounce.
Thus,
The cost of blueberries at the grocery store is $0.35 per ounce.The cost of blueberries at the farmer's market is $0.30 per ounce.Write the domain and range of the function using interval notation.
Answers
Answer:
Domain [-5,3)
Range [0,2]
Step-by-step explanation:
Domain is where the function exists for the x's.
The graph starts at x=-5 and ends at x=3. The graph includes what happened at x=-5 but not at x=3. Since there are no breaks in the graph, the graph exists for x values bigger that or equal to -5 but less than 3.
The domain is [-5,3) in interval notation.
Range is very similar except it is for the y values. So the graph starts at y=0 and stops at y=2. It includes something happening at both and there are no breaks between y=0 and y=2.
The range in interval notation is [0,2].
The values are (x = -5) and (x = 3). But the graph includes what happened at (x = -5) but not (x = 3), therefore, the domain is [-5,0). The values are (y = 0) and (y = 2) and the graph includes what happened at (y = 0) and (y = 2), therefore, the range is [0,2].
Domain is nothing but the value of x in the equation (y = f(x)) and range is nothing but the value of y in the equation (y = f(x)).
So, from the given graph there are two values of 'x' at which the graph of the function gets started and ends.
The values are (x = -5) and (x = 3). But the graph includes what happened at (x = -5) but not (x = 3). Therefore, the domain of the given graph is:
[tex]x\; \epsilon\;[-5,3)[/tex]
Similarly, there are two values of 'y' at which the graph of the function gets started and ends.
The values are (y = 0) and (y = 2) and the graph includes what happened at (y = 0) and (y = 2). Therefore, the range of the given graph is:
[tex]y\; \epsilon\;[0,2][/tex]
For more information, refer to the link given below:
https://brainly.com/question/2263981
Plz help!!!!!!!!!
Pre-calulus
Answers
Answer:
1
Step-by-step explanation:
We are to find the value of the following:
[tex] log _ 3 5 \times log _ { 2 5 } 9 [/tex]
[tex] \log _ { 3 } 5 \times \log _ { 2 5 } 9 =\dfrac{1}{\log_{5}3}\times\log_{25}9=\dfrac{1}{\log_{5}3}\times\log_{5^2}9=\dfrac{1}{\log_{5}3}\times\dfrac{1}{2}\log_{5}9[/tex]
[tex] \dfrac { 1 } { \log _ { 5 } 3 } \times \dfrac { 1 } { 2 } \log_ { 5 } 9 = \dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}3^2=\dfrac{1}{\log_{5}3}\cdot\dfrac{2}{2}\log_{5}3=\dfrac{1}{\log_{5}3}\cdot\log_{5}3=\dfrac{\log_{5}3}{\log_{5}3}=[/tex] 1
Answer:
The value is: 1
Step-by-step explanation:
Use the Change of base formula. This is:
[tex]log_a(x)=\frac{log_b(x)}{log_b(a)}[/tex]
Using base 10:
[tex]log_3(5)*log_{25}(9)=\frac{log(5)}{log(3)}*\frac{log(9)}{log(25)}[/tex]
We know that:
[tex]9=3^2\\25=5^2[/tex]
And according to the logarithms properties:
[tex]log(x)^n=nlog(x)[/tex]
Then, we can simplify the expression:
[tex]=\frac{log(5)}{log(3)}*\frac{log(3)^2}{log(5)^2}=\frac{log(5)}{log(3)}*\frac{2log(3)}{2log(5)}=\frac{log(5)}{log(3)}*\frac{log(3)}{log(5)}=\frac{log(5)*log(3)}{log(3)*log(5)}=1[/tex]
write the equation of the lines that passes through the points (-3, -2) and (0, -3)
Answers
Answer:
[tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
To find the slope of a line using two points, employ the use of the slope formula.
[tex]\frac{y_{2}-y_{1}}{x_{2}- x_{1}}[/tex]
Your y1 term is -2, your y2 term is -3.
Your x1 term is -3, your x2 term is 0.
[tex]\frac{-3-(-2)}{0-(-3)} \\\\\\\frac{-3+2}{0+3} \\\\\frac{-1}{3} \\[/tex]
Solve and graph the absolute value inequality: |2x + 4| > 14.
number line with open circles on negative 9 and 5, shading going in the opposite directions.
number line with open circles on negative 9 and 5, shading in between.
number line with closed circles on negative 9 and 5, shading going in the opposite directions.
a number line with open circles on negative 5 and 5, shading going in the opposite directions.
Answers
Answer:
"number line with open circles on negative 9 and 5, shading going in the opposite directions."
Step-by-step explanation:
Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.
|u|>14 means that the number u has to be greater than 14 or less than -14. These numbers I describe just now all have a distance greater than 14 from 0.
So |u|>14 implies u>14 or u<-14.
But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.
2x+4>14
Subtract 4 on both sides:
2x >10
Divide both sides by 2:
x >5
2x+4<-14
Subtract 4 on both sides:
2x <-18
Divide both sides by 2:
x <-9
So our solution is x>5 or x<-9.
Graphing!
~~~~~~~O O~~~~~~~~
-----------(-9)---------------------------------(5)---------------
So we shaded to the right of 5 because our inequality says x is bigger than 5.
We shaded to the left of -9 because our inequality says x is less than -9.
how do you calculate this
Answers
Answer:
Step-by-step explanation:
Josh has to drive at least 6 hours. d≥ 6 Answer 2
Amelia walking 35 min or less b ≤ 35 Answer 3
Nancy < 35 hours = part time y < 35 Answer 1
Sarah at least 6 hours math f > 6 Answer 4
6 friends are going to sit together in a rollercoaster that has 6 seats. In how many different arrangements can they sit?
Answers
Answer:
36
Step-by-step explanation:
I think it may be 36. I did 6×6, but I'm not fully positive
There are 720 different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster.
To calculate the number of different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster, we can use the concept of permutations.
Since each friend occupies one seat and no two friends can occupy the same seat, we have 6 choices for the first seat, 5 choices for the second seat, 4 choices for the third seat, and so on until 1 choice for the last seat.
So, the total number of arrangements is the product of these choices:
[tex]\[ 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
2. Find the distance between -18 and 8
using the ruler postulate.
Answers
Step-by-step explanation:
1 1-5 Measuring Segments Find the distance between two points using the Ruler Postulate Determine the length of a segment using the Segment Addition Postulate.
Answer:
26.
Step-by-step explanation:
We are asked to find the distance between -18 and 8 using the ruler postulate.
The ruler postulate states that the distance between two pints on a ruler is the absolute value of the difference between the numbers shown on ruler.
So the distance between -18 and 8 would be [tex]|-18-8|=|-26|=26[/tex].
Therefore, the distance between -18 and 8 is 26.