Answer:
Numbers less than 1/9.
Step-by-step explanation:
We are given a number [tex]a[/tex] and that it is less than -3.
That is [tex]a<-3[/tex].
What is the range of possibles for [tex]\frac{1}{a^2}[/tex]?
So if [tex]a<-3[/tex] then [tex]a^2>9[/tex].
*I knew to flip inequality here because if I square any number less than -3 it was going have a value bigger than 9.
If [tex]a^2>9[/tex], then [tex]\frac{1}{a^2}<\frac{1}{9}[/tex].
*When taking reciprocal flip the inequality.
Let's do a test:
Let's see if we pick a number less than -3 that we get a result that is less than 1/9 after we find the reciprocal of the square of the number we choose.
Let's pick -4.
-4 is less than -3
Square -4, you get 16 and 16>9.
The reciprocal of 16 is 1/16 and 1/16<1/9.
So 1/16 is a number less than 1/9.
Final answer:
The range of possible values for 1/a squared is all positive numbers greater than 0.
Explanation:
The range of possible values of 1/a squared can be determined by considering the range of values for a. Since a is a number less than -3, it means that a is a negative number less than -3. To find the range of possible values for 1/a squared, we need to consider the range of possible values for a squared. Since a squared is the square of a negative number, it will always be positive. Therefore, the range of possible values for 1/a squared is all positive numbers greater than 0.
Which represents a perfect cube?
8.8.8
8+8+8
9.9.9.9
9+9+9+9+9
Answer:
8.8.8.
Step-by-step explanation:
8.8.8 = 8^3 = 512 Perfect cube.
8+8+8 =24
9.9.9.9 = 6561
9+9+9+9+9 = 45.
None of the others are perfect cubes.
Answer:A 8.8.8
Step-by-step explanation:i did the quiz
HELPPPP WILL NAME BRAINIEST
Answer:
Triangle APB is an isosceles triangle ⇒ 3rd answer
Step-by-step explanation:
* Lets explain the how to solve the problem
- ABCD is a square
∴ AB = BC = CD = AD
∴ m∠A = m∠∠B = m∠C = m∠D = 90°
- DPC is equilateral triangle
∴ DP = PC = DC
∴ m∠DPC = m∠PCD = m∠CDP = 60°
- In the Δs APD , BPC
∵ AD = BC ⇒ sides of the square
∵ PD = PC ⇒ sides of equilateral triangle
∵ m∠ADB = m∠BCP = 30° (90° - 60° = 30) ⇒ including angles
∴ Δs APD , BPC are congregant ⇒ SAS
- From congruent
∴ AP = BP
∴ Triangle APB is an isosceles triangle
Which graph represents the solution set of the inequality x+2 greater than or equal to 6
Answer:
4 ≤ x
4
●→
Step-by-step explanation:
There is no illustration, it looks something like this.
What is the midpoint of the segment shown below?
Answer:
A
Step-by-step explanation:
Calculate the midpoint using the midpoint formula
[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5)
midpoint = [ 0.5(- 1 + 5), 0.5(5 + 5) ]
= [ 0.5(4), 0.5(10) ] = (2, 5 ) → A
Answer:
The answer would be A 2,5
Step-by-step explanation:
Find the value of x.
A. 1.1
B. 6.6
C. 8.8
D. 5.5
Answer:
B. 6.6Step-by-step explanation:
AC is a midsegment of the trapezoid DFBE.
The formula of a midsegment of trapezoid is:
[tex]m=\dfrac{a+b}{2}[/tex]
a, b - bases of a triangle
We have
a = x, b = 4.4, m = 5.5
Substitute:
[tex]5.5=\dfrac{x+4.4}{2}[/tex] multiply both sides by 2
[tex]11=x+4.4[/tex] subtract 4.4 from both sides
[tex]6.6=x\to x=6.6[/tex]
[tex] - 3 + 5i \div - 3 - 4i[/tex]
Answer:
[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex] given you are asked to simplify
[tex]\frac{-3+5i}{-3-4i}[/tex]
Step-by-step explanation:
You have to multiply the numerator and denominator by the denominator's conjugate.
The conjugate of a+bi is a-bi.
When you multiply conjugates, you just have to multiply first and last.
(a+bi)(a-bi)
a^2-abi+abi-b^2i^2
a^2+0 -b^2(-1)
a^2+-b^2(-1)
a^2+b^2
See no need to use the whole foil method; the middle terms cancel.
So we are multiplying top and bottom of your fraction by (-3+4i):
[tex]\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}[/tex]
So you will have to use the complete foil method for the numerator. Let's do that:
(-3+5i)(-3+4i)
First: (-3)(-3)=9
Outer:: (-3)(4i)=-12i
Inner: (5i)(-3)=-15i
Last: (5i)(4i)=20i^2=20(-1)=-20
--------------------------------------------Combine like terms:
9-20-12i-15i
Simplify:
-11-27i
Now the bottom (-3-4i)(-3+4i):
F(OI)L (we are skipping OI)
First:-3(-3)=9
Last: -4i(4i)=-16i^2=-16(-1)=16
---------------------------------------------Combine like terms:
9+16=25
So our answer is [tex]\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:
[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex]
When solving -1/5 (x − 25) = 7, what is the correct sequence of operations?
A:Multiply each side by negative one over five , add 25 to each side
B:Multiply each side by 5, subtract 25 from each side
C:Multiply each side by negative one over five , subtract 25 from each side
D;Multiply each side by −5, add 25 to each side
Answer:
It is C. Multiply each side by negative one over five , subtract 25 from each side.
Hope this helped you! :3
Answer:
D;Multiply each side by −5, add 25 to each side
Step-by-step explanation:
-1/5 (x − 25) = 7
To solve this equation, we will first multiply both-side of the equation by -5
-5 × -1/5(x-25) =7 × 5
(At the left-hand side of this equation, the 5 we multiplied will cancel the 5 at the denominator, leaving us with just '1' since negative multiply by negative is positive), Hence our equation becomes;
(x - 25) = 35
x - 25 = 35
Then the next thing to do is to add 25 to both-side of the equation in other to get the value of your x
x -25 + 25 = 35 + 25
x=60
Therefore, option D is the correct sequence of operation to follow to enable you solve the equation.
What is the greatest common factor of 8x and 40y
Answer:
The GCF of both the terms is 8....
Step-by-step explanation:
Given:
What is the greatest common factor of 8x and 40y.
The GCF of 8x and 40y is 8.
We will use the method of prime factorization to find the greatest common factor.
The prime factorization of 8x is:
8x = 2*2*2*x
The prime factorization of 40y is:
40y = 2*2*2*5*y
Therefore the common factors in both the terms are 2*2*2 which becomes 8
Thus the GCF of both the terms is 8....
Answer:
8
Step-by-step explanation:
Which expression is equivalent to log3(x + 4)?
log3 - log(x + 4)
log12 + logx
log3 + log(x + 4)
log 3/log(x+4)
Answer:
log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.
Step-by-step explanation:
By the logarithm product rule, for two nonzero numbers [tex]a[/tex] and [tex]b[/tex],
[tex]\log{(a \cdot b)} = \log{(a)} + \log{(b)}[/tex].
Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.
For example, [tex]3(x + 4)[/tex] is the number in the logarithm [tex]\log{[3(x + 4)]}[/tex]. Since [tex]3(x + 4)[/tex] is a product of the two numbers [tex]3[/tex] and [tex](x + 4)[/tex], the logarithm [tex]\log{[3(x + 4)]}[/tex] can be split into two. By the logarithm product rule,
[tex]\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}[/tex].
However, [tex]\log{(x + 4)}[/tex] cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.
Answer:
c
Step-by-step explanation:
for the level 3 course, examination hours cost twice as much as workshop hours and workshop hours cost twice as much as lecture hours. how id the lectures cost per hour? Total cost level 3 =$528
Answer:
The lectures cost is $7.33 per hour
Step-by-step explanation:
* Lets explain how to solve the problem
- For the level 3 course the examination hours cost twice as much
as workshop hours
- The workshop hours cost twice as much as lecture hours
- There are examination hours , workshop hours and lecture hours
- There are 3 hr for examination, 24 hr for workshops and 12 hr
for lectures
* Let the cost of the lecture hours is $x per hour
∴ The cost of the lecture hours is x per hour
∵ The cost of workshop hours is twice the cost of lecture hours
∴ The cost of the workshop hours is 2(x) = 2x per hour
∵ The cost of examination hours is twice the cost of workshop hours
∵ The cost of the workshop hours is 2x
∴ The cost of examination hours is 2(2x) = 4x per hour
- The cost of the level 3 is the sum of the costs of the lecture hours,
workshop hours and examination hours
∵ There is 12 hours for lectures
∵ There is 24 hours for workshops
∵ There is 3 hours for examination
∵ The total cost of level 3 = 12(x) + 24(2x) + 3(4x)
∴ The total cost of level 3 = 12 x + 48 x + 12 x
∵ The total cost of level 3 = $528
∴ 12 x + 48 x + 12 x = 528
∴ 72 x = 528 ⇒ divide both sides by 72
∴ x = 7.33
∵ x is the cost of the lecture hours per hour
∴ The lectures cost is $7.33 per hour
Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) = 18 f (n + 1) = f(n) + 6 f (n + 1) = 2f(n) f (n + 1) = f(n) + 2 f (n + 1) = 1.5f(n)
Answer:
f(n + 1) = f(n) + 2
Step-by-step explanation:
A recursive formula gives any term in the sequence from the previous term.
the n th term of an arithmetic sequence is
f(n) = f(1) + (n - 1)d ← d is the common difference
Given
f(1) = 6 and
f(4) = 12, then
f(1) + 3d = 12, that is
6 + 3d = 12 ( subtract 6 from both sides )
3d = 6 ( divide both sides by 3 )
d = 2
To obtain a term in the sequence add 2 to the previous term, hence
f(n + 1) = f(n) + 2 ← recursive formula
Answer:
c
Step-by-step explanation:
its c
-8(5x+5)+9x(10x+9)=20
[tex]-8(5x+5)+9x(10x+9)=20\\-40x-40+90x^2+81x-20=0\\90x^2+41x-60=0\\\\\Delta=41^2-4\cdot90\cdot(-60)=1681+21600=23281\\\\x=\dfrac{-41\pm \sqrt{23281}}{2\cdot90}=\dfrac{-41\pm \sqrt{23281}}{180}[/tex]
The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original
number. What is the original number?
Answer:
It's 53.
Step-by-step explanation:
Let the number be xy so the digits are x and y, so:
x + y = 8...........(1)
Reversing the 2 digits we have the number 10y + x and this equals
10x + y - 18 so we have the equation:-
10x + y - 18 = 10y + x
9x - 9y = 18
x - y = 2...........(2) Adding equations (1) and (2) we have:
2x = 10
x = 5
and y = 8 - 5 = 3.
So the original number is 53.
We can check this as follows
Original number is 53 so the reverse is 35 .
53 - 35 = 18 which checks out.
Use the graph of f(x) to evaluate the following:
The average rate of change of f from x=0 to x=4 is_____.
Give your answer as an integer or reduced fraction
Answer:
-5/4
Step-by-step explanation:
The average rate of change of f from x=0 to x=4 is_____.
This means we are being asked to evaluate [tex]\frac{f(4)-f(0)}{4-0}[/tex].
To do this we will need to find f(0) and f(4).
f(0) means what y-coordinate corresponds to x=0 on the curve. Find x=0, the curve is above there, go straight up and see y=5 there. This means f(0)=5.
f(4) means what y-coordinate corresponds to x=4 on the curve. Find x=4, then curve is above there, go straight up and see y=0 there. This means f(4)=0.
So we have:
[tex]\frac{f(4)-f(0)}{4-0}=\frac{0-5}{4-0}=\frac{-5}{4}[/tex].
Solve this inequality: 36 - 7 < 32
You already did. That is a true statement.
32 > 29 [and vice versa]
I am joyous to assist you anytime.
The inequality 29 < 32 is true.
After calculating 36 - 7 which equals 29, we compare this result to 32. The inequality 29 < 32 holds true, so the original inequality 36 - 7 < 32 is correct.
The student has asked to solve the inequality 36 - 7 < 32. To solve this inequality, we need to perform the subtraction on the left side of the inequality first.
When we calculate 36 - 7, we get 29. Now we can compare this result to 32 to determine if the inequality holds true.
Since we are dealing with an inequality, we know that if a value a is less than a value b, then a is indeed smaller in quantity or value compared to b. Here, 29 is indeed less than 32. Therefore, the inequality 29 < 32 is true.
If Sn=n^2+3 then t10=?
Answer:
T10= -21
Step-by-step explanation:
If Sn=n^2+3 then t10=?
Sn= n²+5
put n=1, 2
S1= T1 = (1)²+5
=1+5 =6
S2= n²+5
S2=(2)²+5
S2=4+5
S2=9
T2 = S2 - S1
T2 = 9-6
T2=3
T10 = a+(n-1)d
where a = 6, d = -3, n=10
T10= 6+(10-1)*-3
T10=6+(9)*-3
T10=6+(-27)
T10=6-27
T10= -21
Therefore T10= -21 ....
What is 7(x+6)=3(x+9)
Answer:
x= -3.75
Step-by-step explanation:
Answer:
x = -15/4
Step-by-step explanation:
7(x+6)=3(x+9)
Distribute
7x+42 = 3x+27
Subtract 3x from each side
7x-3x+42 = 3x-3x+27
4x +42 = 27
Subtract 42 from each side
4x+42-42 = 27-42
4x =-15
Divide each side by 4
4x/4 =-15/4
x = -15/4
Which one of the following equations could describe the graph above?
Answer: A. y=(1/2)^x+6
Step-by-step explanation: If this is the graph you’re talking about-
When “a” is less than one, the graph increases exponentially to the left. The smaller the value of a, the steeper the slope of the line.
There is a vertical shift up 6 as well
7.
chef has 50 pounds of strip Zebra. The trim loss on the strip zebra is
40% and the cooking loss is 60% of the trimmed weight. How many
pounds of trimmed, cooked strip zebra will the chef have left to serve to
his customers?
Answer:
12 pounds
Step-by-step explanation:
After trimming:
50 − 0.40 (50) = 0.60 (50) = 30
After cooking:
30 − 0.60 (30) = 0.40 (30) = 12
in 135 space shuttle missions, there were two failures. Based on these data, what's the probability of a successful mission?
Answer:
98.518 repeating prercent
Step-by-step explanation:
2 out of 135 can also be written as 2/135
2 divided by 135 is 0.014814814814
that number is the percentage of failures
100% in decimal form is 1.00
1.00 subtracted by the percentage of failures is the percentage of successes
which is .98518518518, 518 repeating move the decimal over 2 and you got the percentage 98.518 repeating
In circle O, AD and BE are diameters. What is m? 106° 132° 138° 164°
Answer:
It is 132 just took it
Step-by-step explanation:
Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The measure of ∠AOE is 132°. The correct option is B.
What are vertical angles?Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.
In circle O, AD and BE are diameters. Also, the measure of ∠EOD and ∠AOB will be equal because the two angles are vertically opposite angles. Therefore,
∠EOD = ∠AOB = 3x
As it is given that the measure of ∠AOC is 90°. Therefore, we can write,
∠AOC = ∠AOB + ∠BOC
90 = 3x + 0.5x + 34
56 = 3.5x
x = 16
Now, the measure of ∠EOD will be,
∠EOD = 3x
∠EOD = 3(16°)
∠EOD = 48°
Further, we can write,
∠AOD = ∠AOE + ∠EOD
180° = ∠AOE + 48°
∠AOE = 132°
The complete question is mentioned in the below image.
Learn more about Vertical Angles:
https://brainly.com/question/24460838
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What is the solution to 2x-8 <12?
Answer:
[tex]x < 10[/tex]
Step-by-step explanation:
[tex]2x - 8 < 12 \\ 2x - 8 + 8 < 12 + 8 \\( 2x < 20) \div 2 = x < 10[/tex]
x<10 is the solution to the inequality 2x - 8 < 12
To solve the inequality 2x - 8 < 12, you can follow these steps:
Add 8 to both sides of the inequality:
2x - 8 + 8 < 12 + 8
This simplifies to:
2x < 20
Divide both sides of the inequality by 2:
(2x)/2 < 20/2
This simplifies to:
x < 10
Therefore, the solution to the inequality 2x - 8 < 12 is x < 10.
Learn more about inequalities here:
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Which properties of equality are used to solve the following (in no particular order)?
3(x + 12) - 2 = 50
Addition Property of Equality
Subtraction Property of Equality
Division Property of Equality
Combine Like Terms
Distributive Property
All except combine like terms. Since you only have 1 variable.
Hope this helps.
r3t40
factor: d2 + 16dm + 64m2
Answer:
[tex](d + 8m)^2[/tex]
Step-by-step explanation:
[tex]d^2 + 16dm + 64 m^2 = (d + 8m)^2[/tex]
d^2 + 16dm + 64m^2
64m^2 + 16dm + d^2
Note: This polynomial is already in lowest terms. It cannot be factored. Are you sure that you posted the entire, correct problem?
What is the length of the hypotenuse in the right triangle shown below?
Answer:
C. 6√2.
Step-by-step explanation:
Since this is a right angled isosceles triangle bot legs are 6 units long
So h^2 = 6^2 + 6^2 = 72
h = √72 = 6√2.
Answer:
The correct option is C) 6√2.
Step-by-step explanation:
Consider the provided triangle.
The provided triangle is a right angle triangle, in which two angles are 45° and one is 90°.
As both angles are equal there opposite side must be equal.
Thus, the leg of another side must be 6.
Now find the hypotenuse by using Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute a = 6 and b = 6 in [tex]a^2+b^2=c^2[/tex].
[tex](6)^2+(6)^2=(c)^2[/tex]
[tex]36 + 36=(c)^2[/tex]
[tex]72=(c)^2[/tex]
[tex]6\sqrt{2}=c[/tex]
Hence, the length of the hypotenuse in the right triangle is 6√2.
Therefore, the correct option is C) 6√2.
A group of students and workers entering a metro station
were asked whether they were riding the bus or the
subway. The two-way table shows their answers.
Types of Transportation
Bus
Subway
Students
Workers
Total
166
27 + 42 + 21 + 76 = 166
Need The Answer Plz And Thank You!! I’m Failing
Angle BCA
Step-by-step explanation:
You can see this due to the angle having the name amount of congruent angle marks.
Two tins are geometrically similar. If the ratio of their volume is 27:64 find the ratio of their curved surface area.
Answer:
9 : 16
Step-by-step explanation:
Given 2 similar figures with linear ratio = a : b, then
area ratio = a² : b² and
volume ratio = a³ : b³
Here the volume ratio = 27 : 64, hence
linear ratio = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{64}[/tex] = 3 : 4
Hence area ratio = 3² : 4² = 9 : 16
16. The dimensions of a window are 3x + 10 and 2x + 6. What is the area of the window?
Answer:
Answer in factored form (3x+10)(2x+6)
Answer in standard form 6x^2+38x+60 ( I bet you they want this answer)
Step-by-step explanation:
The assumption is this is a rectangle.
If you have the dimensions of a rectangle are L and W, then the area is equal to L times W.
So here we just need to multiply (3x+10) and (2x+6).
The answer in factored form is (3x+10)(2x+6).
I bet you they want the answer in standard form.
So let's use foil.
First: 3x(2x)=6x^2
Outer: 3x(6)=18x
Inner: 10(2x)=20x
Last: 10(6)=60
----------------Add up!
6x^2+38x+60
The area of the window is 3x² + 19x + 30
The dimension of the window are 3x + 10 and 2x + 6.
The area of the window can be calculated as follows;
area = lw
Therefore,
area = (3x + 10)(2x + 6)
area = 6x² + 18x + 20x + 60
area = 6x² + 38x + 60
area = 3x² + 19x + 30
read more: https://brainly.com/question/3518080?referrer=searchResults
Events A and B are disjointed.
P(A) = 4/11 ; P(B) = 3/11.
Find P(A or B).
*Answer Options*
7/11
4/11
3/11
8/11
Answer:
7/11
Step-by-step explanation:
Two events are disjoint events if they cannot occur at the same time. It is given that A and B are disjointed events, so A and B cannot occur at the same time i.e. the intersection of two disjoint events will be 0.
For two disjoint events A and B:
P(A or B) = P(A) + P(B)
P(A) is given to be 4/11 and P(B) is given to be 3/11. Using these values in the equation, we get:
P(A or B) = [tex]\frac{4}{11}+\frac{3}{11} = \frac{3+4}{11}=\frac{7}{11}[/tex]