Answer:
2/3 ÷ 1/6
I hope this helps.
solve the following inequalitie and fin x
5/( + 2)(4 − )< 1
Answer: -1 < x < 3
Step-by-step explanation:
[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]
Step 1 The denominator cannot equal zero:
x + 2 ≠ 0 and 4 - x ≠ 0
x ≠ -2 4 ≠ x
Place these restrictive values on the number line with an OPEN dot:
<----------o-------------------o--------->
-2 4
Step 2 Find the zeros (subtract 1 from both sides and set equal to zero):
[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]
Add the zeros to the number line with an OPEN dot (since it is <):
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 3 Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):
Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive
Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive
Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative
Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive
Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive
+ + - + +
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 4 Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.
Negative values only occur between -1 and 3
So the solution is: -1 < x < 3
A student decided to research primate psychology for their science project. They measured how long it took gorillas to adapt to their new habitat when moved from one zoo to another. They measured how long it took the new gorilla to interact regularly (more than 3 times per day) with the gorillas that already live there. Seven different cases were examined and the data collected. What can be said about the data?
The question is not complete, so i have attached it.
Answer:
Option A - The data may not be reliable because there is an outlier.
Step-by-step explanation:
Looking at the question attached and the number of the gorrila vis - a - vis the time to interact, we can see that majority of the time to interact falls between 2.5 and 3.4.
However, we have a time of 8.3 days which is for gorrila 3.
This 8.3 is far higher than the range of the other values. Thus, we have an outlier because an outlier is a value is much more smaller or larger than most of the other values in a set of given data.
Thus, the data may not be reliable because there is an outlier.
Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3
Answer:
Option (3)
Step-by-step explanation:
This question is not complete; here is the complete question.
Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?
Coordinates of the vertices of the triangle ABC are,
A(-3, 3), B(1, -3) and C(-3, -3)
When triangle ABC is reflected over y = -3
Coordinates of the image triangle A'B'C' will be.
A(-3, 3) → A'(-3, -9)
B(1, -3) → B'(1, -3)
C(-3, -3) → C'(-3, -3)
Further ΔA'B'C' is dilated by a scale factor of 2 about the origin then the new vertices of image triangle A"B"C" will be,
Rule for the dilation will be,
(x, y) → (kx, ky) [where 'k' is the scale factor]
A'(-3, -9) → A"(-6, -18)
B'(1, -3) → B"(2, -6)
C'(-3, -3) → C"(-6, -6)
Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-3-1)^2+(3+3)^2}[/tex]
= [tex]\sqrt{52}[/tex]
= [tex]2\sqrt{13}[/tex]
Length of A"B" = [tex]\sqrt{(-6-2)^2+(-18+6)^2}[/tex]
= [tex]\sqrt{64+144}[/tex]
= [tex]\sqrt{208}[/tex]
= [tex]4\sqrt{13}[/tex]
Therefore, [tex]\frac{\text{AB}}{\text{A"B"}}=\frac{2\sqrt{13}}{4\sqrt{13}}[/tex]
[tex]\frac{\text{AB}}{\text{A"B"}}=\frac{\sqrt{13}}{2\sqrt{13}}[/tex]
[tex]AB(2\sqrt{13})=A"B"(\sqrt{13})[/tex]
Option (3) is the answer.
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
A conveyor belt carries supplies from the first floor to the second floor, which is 21 feet higher. The belt makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?
Hey there! I'm happy to help!
LENGTH OF CONVEYOR BELT
We are going to have to use some trigonometry. Let's think of this as a right triangle. The conveyor belt is the diagonal or the hypotenuse, while the ground is and the height of the room make a right angle as the legs.
We have a sixty degree angle between the conveyor belt and the ground. This is means that the 21 foot height is the opposite side of our right triangle. So, we are dealing with the opposite and the hypotenuse, so we will use the sine. The sine of an angle is equal to the opposite length divided by the hypotenuse length.
We will set up the following equation and solve for the length of our conveyor belt (c).
[tex]sin60=\frac{21}{c}[/tex]
We multiply both sides by c.
[tex]c(sin60)=21[/tex]
We divide both sides by sin60.
[tex]c=\frac{21}{sin60}[/tex]
If we evaluate this with a calculator, we get that c is equal to 24.2487113..., or 24 when rounded to the nearest foot.
So, the supplies travel 24 feet from one end to the other.
DURATION OF TRAVEL
We want to find how long it takes the supplies to move across the conveyor belt. We see that every minute, it moves 75 feet. We want to see how many minutes it will take to move 24 feet, as that is the length of the conveyor belt as we previously solved. Let's set up a proportion.
[tex]\frac{feet}{minute} =\frac{75}{1} =\frac{24}{m}[/tex]
We cross multiply, giving us the following equation.
75m=24
We divide both sides by 75.
m=0.32
We want to round to the nearest tenth of a minute, so it will take 0.3 minutes for the supplies to move to the second floor.
Have a wonderful day! :D
Let f(x) = sin x; Sketch the graph of f^2
Answer: see graph
Step-by-step explanation:
Look at the Unit Circle to see the coordinates of the quadrangles.
Build a sine table for one period (0° - 360°).
x y = sin(x) y² = (sin(x))² (x, y²)
0° sin(0°) = 0 (0)² = 0 (0°, 0)
90° sin(90°) = 1 (1)² = 1 (90°, 1)
180° sin(180°) = 0 (0)² = 0 (180°, 0)
270° sin(270°) = -1 (-1)² = 1 (270°, 1)
360° sin(360°) = 0 (0)² = 0 (360°, 0)
Now plot the (x, y²) coordinates on your graph.
Boomer, the dog, eats 3\2 of dog food each week. How many grams of dog food will Boomer eat in 4weeks?'
Answer:
6 grams
Step-by-step explanation:
(3/2)*4 = 12/2 = 6
Answer:
[tex]\boxed{\sf 6 \ grams \ of \ food}[/tex]
Step-by-step explanation:
1 week = [tex]\frac{3}{2} g\ of \ the \ food[/tex]
Multiplying both sides by 4
4 weeks = [tex]\frac{3}{2} * 4[/tex]
4 weeks = 3 * 2 g of the food
4 weeks = 6 g of food
x-6/2=2x/7 solve the equation
Answer:
x-6/2=2x/7
7x-42=4x
7x-4x=42
3x= 42
X = 42/3
5y-5y^2-5+2+2y+3y^2-1
Answer:
7y - 2y² - 4
Step-by-step explanation:
5y - 5y² - 5 + 2 + 2y + 3y² - 1
5y + 2y - 5y² + 3y² - 5 + 2 - 1 (combine like terms)
7y - 2y² - 4
Please help Describe a way that you can remember the elements of the reflection matrices if you forget where the 1s, -1s, and 0s belong.
Step-by-step explanation:
Multiplying the vertex matrix with the matrix gives us a reflection matrix. The most common matrix reflections are seen as reflection in the x - axis as well as reflection in the y - axis.
It can also be reflect by 90 degree or by 180 degree.
So, one way to remember the elements is by multiplying the given matrix by a unit matrix. And on the other hand you can remember the elements remembering by what degree we are reflecting the matrix. This way makes it easier to remember the elements.
The explanation regarding the elements of the reflection is explained below:
The following information should be considered:
In the case when we Multiply the vertex matrix with the matrix so it provides the reflection matrix. The most common matrix reflections are seen as reflection in the x - axis as well as reflection in the y - axis. It can also be reflect by 90 degree or by 180 degree.Learn more: https://brainly.com/question/17961582?referrer=searchResults
If the initial amount of iodine-131 is 537 grams , how much is left after 10 days?
Answer:
225.78 grams
Step-by-step explanation:
To solve this question, we would be using the formula
P(t) = Po × 2^t/n
Where P(t) = Remaining amount after r hours
Po = Initial amount
t = Time
In the question,
Where P(t) = Remaining amount after r hours = unknown
Po = Initial amount = 537
t = Time = 10 days
P(t) = 537 × 2^(10/)
P(t) = 225.78 grams
Therefore, the amount of iodine-131 left after 10 days = 225.78 grams
Write a number sentence that
illustrates the associative property
of addition,
Please, someone help.
Answer:
ok so
faf
Step-by-step explanation:
Factor 20x2 + 25x – 12x – 15 by grouping.
1. Group terms with common factors.
2. Factor the GCF from each group.
3. Write the polynomial as a product of binomials.
(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(5x – 3)(
x +
)
What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y=-4/3x-1
Answer:
[tex]\displaystyle \boxed{y = -1\frac{1}{3}x + 22}[/tex]
Step-by-step explanation:
Parallel Equations have SIMILAR RATE OF CHANGES [SLOPES], so keep [tex]\displaystyle -\frac{4}{3}[/tex]as is and do this:
14 = −4⁄3[6] + b
14 = −8 + b
+ 8 + 8
_________
[tex]\displaystyle 22 = b \\ \\ y = -1\frac{1}{3}x + 22[/tex]
I am joyous to assist you at any time.
what is the area of the shaded region?
Answer:
330.00cm²
Step-by-step explanation:
find the area of both circles and subtract the smaller one from the bigger one.
area of a circle= πr²
π wasn't given so I will use 22/7
so area of the bigger circle = 22/7 × 11²
=22/7 × 121
=380.28cm²
area of the small circle=22/7 × 4²
= 22/7 × 16
= 50.28cm²
Area of the shaded portion = 380.28 - 50.28
= 330.00cm²
Coherence
5. Simon's teacher asked him to e-mail her a copy of the outline for his essay on American
History: When drafting the e-mail, what level of diction should Simon use?
informal
formal
standard
foundational
Answer:
The correct option is;
Formal
Step-by-step explanation:
The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices
Formal diction is used when when communicating in a situation that is formal
Formal diction uses languages that is devoid of slang and grammatically correct
Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.
Complete the recursive formula of the arithmetic sequence -15, -11, -7, -3,...−15,−11,−7,−3,...minus, 15, comma, minus, 11, comma, minus, 7, comma, minus, 3, comma, point, point, point.
Answer:
c(1) = -15
c(n) = c(n - 1) + 4
Step-by-step explanation:
Given arithmetic sequence is,
-15, -11, -7, -3...........
Common difference between each successive and previous term is,
d = -11 - (-15)
= -11 + 15
= 4
Since recursive formula of the arithmetic sequence is represented by,
a₁ = First term of the sequence
a(n) = a(n - 1) + d
where a(n) is the nth term and a(n-1) is the previous term of the nth term.
Form the given sequence,
c₁ = -15
c(n) = c(n - 1) + 4
Find the conjugate of 2 - 5i and then calculate the product of the given complex number and its conjugate. (1 point)
Answer:
29
Step-by-step explanation:
conjugate of a+ib=a-ib
conjugate of 2-5i=2+5i
(2+5i)(2-5i)=2²-(5i)²=4-25i²=4-25(-1)=4+25=29
Answer:
29
i had the same question and 29 was the right answer
With which set of information can you construct a unique triangle?
OA the measurements of all the angles
ОВ.
the lengths of two sides
OC. the measurements of two angles
OD. the lengths of all the sides
OE the measurement of one angle
Answer:
D
Step-by-step explanation:
This would be using the SSS.
Which means knowing three sides.
The other options do not relate to any of the SSS, SAS, ASA, RHS
Hope that helped!!! k
what are the factors of 47 (cuz im STUPID and i dont feel like doing this cuz im working on geogrophy)
Hey there! I'm happy to help!
The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).
So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.
We cannot divide by 2 because 47 is odd.
We cannot divide by 3 because it gives us 15.6666...
We can't divide by 4 because 47 is odd.
We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.
We can't divide by 6 because 47 is odd.
We can't divide by 7 because it gives us 6.714285....
We can't divide by 8 because 47 is odd.
We can't divide by 9 because it gives us 5.2222
And we obviously can't divide it by 10.
Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.
I hope that this helps! Have a wonderful day! :D
Answer: 47 is a prime number
The exponent of prime number 47 is 1 . Adding 1 to that exponent we get (1+1)=2
Factor of 47: 1, 47
Find the area of the following shape.
Answer:
57 units^2
Step-by-step explanation:
First find the area of the triangle on the left
ABC
It has a base AC which is 9 units and a height of 3 units
A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5
Then find the area of the triangle on the right
DE
It has a base AC which is 6 units and a height of 1 units
A = 1/2 bh = 1/2 ( 6) *1 = 3
Then find the area of the triangle on the top
It has a base AC which is 3 units and a height of 3 units
A = 1/2 bh = 1/2 ( 3) *3 = 9/2 = 4.5
Then find the area of the rectangular region
A = lw = 6*6 = 36
Add them together
13.5+3+4.5+36 =57 units^2
Answer:
Total Area = 57 sq. units
Step-by-step explanation:
will make it simple and short
Total Area = A1 + A2 + A3
A1 = (7 + 6) * 6/2 = 39 sq. units (area of a trapezoid)
A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)
A3 = 1/2 (3 * 3) = 4.5 sq. units (area of a triangle)
Total Area = 39 + 13.5 + 4.5 = 57 sq. units
Help! Will give brainliest.
Answer:
A. You can see which shape the bases are, how many bases there are, how many faces there are, and how many edges there are.
B. The bases are ABC and DEF, and I know because they are two congruent triangles on two opposite sides of the shape.
A bag contains five tokens numbered 2, 3, 6, 7, and 8. Two tokens are taken in succession out of the bag without replacement. A) Create the probability distribution for "x" being the number of odd numbered tokens drawn. B) What is mean and variance of the probability distribution?
Answer and Step-by-step explanation:
A) Probability of taken two odd numbered token without replacement:
P(3) = 2/5 = 0.4
P(7) = 1/4 = 0.25
Construct a probability distribution:
X 3 7
p(X) 0.4 0.25
B) Mean of the probability distribution:
E(X) = ∑xp
E(X) = 3*0.4 + 7*0.25
E(X) = 2.95
Variance of the probability distribution:
V(X) = [tex]\Sigma X^{2}p - [E(X)]^{2}[/tex]
V(X) = [tex]3^{2}*0.4+7^{2}*0.25 - (2.95)^{2}[/tex]
V(X) = 7.1475
Mean and variance of the probability distribution are 2.95 and 7.145, respectively.
How to do this question plz answer me step by step plzz plz
Answer:
4 cm
Step-by-step explanation:
Volume is given by area of cross section * height
_______________________________
For condition 1
height = 12 cm
base for area of cross section is 5*8
that is length 8 cm and width 5 cm
thus area of cross section = 5*8 = 40 cm square
volume of milk = area of cross section* height of milk = 40*12 = 480 cm cube.
_______________________________________________
now milk is turned such that base of area of cross section will
15 by 8
that is length: 15 cm and width : 8 cm
thus area of cross section = 15*8 = 120 cm square
let the depth of milk be x
thus, volume of milk = area of cross section* height of milk = 120*x
= 120x cm cube
Since milk is in the same container , its volume before and after the change of alignment of container will remain same
thus
120x cm cube = 480 cm
=> x = 480/120 = 4
Thus, depth under given situation will be 4 cm.
given the mapping f:x-7x-2, determine f(2)
Answer:
Value of F(2) = 12
Step-by-step explanation:
Given:
F(x) = 7x - 2
Find:
Value of F(2)
Computation:
F(x) = 7x - 2
putting x = 2
f(2) = 7(2) -2
f(2) = 14 - 2
f(2) = 12
So, Value of F(2) = 12
1. Which monomial has the same degree as 6a2b8c? A 18t8 B 12p6q5 C 9a5b3c2 D 6w4x2y3z3
Answer: "B. [tex]12p^6q^5[/tex]
Step-by-step explanation:
The given monomial : [tex]6a^2b^8c[/tex]
Degree of this monomial = Sum of powers of variables=2+8+1= 11
Let's check all the options
A [tex]18t^8[/tex]
Degree = 8
B [tex]12p^6q^5[/tex]
Degree = 6+5 =11
C [tex]9a^5b^3c^2[/tex]
Degree = 5+3+2=10
D [tex]6w^4x^2y^3z^3[/tex]
Degree =4+2+3+3=12
We can see that only option B has degree 11.
So, the monomial has the same degree as [tex]6a^2b^8c[/tex] is "B. [tex]12p^6q^5[/tex] "
Please answer this question now
Answer:
AB = 72°
Step-by-step explanation:
The inscribed angle ADC is half the measure of its intercepted arc, thus
56° = [tex]\frac{1}{2}[/tex] ( m ABC ) ← multiply both sides by 2
112° = ABC
ABC = AB + BC = AB + 40, so
AB + 40 = 112 ( subtract 40 from both sides )
AB = 72°
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
Please help! offering 25 points, 5 stars, and a thanks. Ive asked this 3 times now
Answer:
17 quarters
Step-by-step explanation:
Let q = quarters
n = nickels
.25q + .05n = 5.90
we have 16 more nickels than quarters so add 16 quarters to make them equal
n = q+16
Substitute
.25q + .05( q+16) = 5.90
Distribute
.25q+.5q+.80=5.90
Combine like terms
.30q +.8 = 5.90
Subtract .8 from each side
.30q = 5.10
Divide each side by .3
.3q/.3 = 5.1/.3
q = 17
Answer:
Gisel have:
17
quarters
Step-by-step explanation:
1 nickel = 5 cents
1 quarter = 25 cents
1 dollar = 100 cents
5,90 dollars = 5,9*100 = 590 cents
then:
n = t + 16
5n + 25t = 590
n = quantity of nickels
t = quantity of quarters
5(t+16) + 25t = 590
5*t + 5*16 + 25t = 590
5t + 80 + 25t = 590
30 t = 590 - 80
30 t = 510
t = 510 / 30
t = 17
n = t + 16
n = 17 + 16
n = 33
Check:
5n + 25t = 590
5*33 + 25*17 = 590
165 + 425 = 590
If Y varies directly as x
write down the equation
connecting y and x. If y = 10
when x=5, find the value
of y when x= 16
Answer:
32
Step-by-step explanation:
If y is 2 times as much as x, then 1 = 2
5 x 3 = 15 + 1 = 16
10 x 3 = 30 + 2 = 32, or 16 x 2 = 32
Please tell me if I'm wrong.
Please help me!!! I need this ASAP!!!
Answer:
number ten: x=5
number two: x=5³/5
Step-by-step explanation:
number ten:
4x + 3x - 9 = 26
4x + 3x = 26+9
7x = 35
x = 5
number two:
3x + 2x - 8 = 20
3x + 2x = 20+8
5x = 28
x = 5³/5
