Answer:
k-4.7
Step-by-step explanation:
It is k minus 4.7 because when it says less than it means the number that is stated before the phrase is being subtracted :)
Answer:
k-4.7
Step-by-step explanation:
For writing algebraic expressions, we have translate the words to math.
4.7 less than a number k, means subtraction (notice the word- less)
Thus, we have k-4.7
Hope this helps :)
A zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the male giraffe, how many ways can he feed all the animals?
Answer:
144
Step-by-step explanation:
We will use permutations to solve this problem
There are 4 pairs each having a male and a female.
The total number of sample points is 4! = 4*3*2*1= 24
He chooses the male first then the number of sample space he is left with are 3! = 3*2*1=6
The total number of ways he can select is 4! 3! = 24 * 6= 144
Another way of finding it out is
he has 4 pairs each having a male and a female so he chooses 1st male then he would choose from this
4 female choices*3 male choices * 3 female choices *2 male choices *2 female choices *1 male choices *1 female choices *= 4*3*3*2*2*1*1= 144
The zookeeper can feed all the animals in 144 ways
The number of different animals is given as:
[tex]n = 4[/tex]
The number of ways to feed any of the 4 male animals is:
[tex]Ways = 4![/tex]
Expand
[tex]Ways = 4 \times 3 \times 2 \times 1[/tex]
[tex]Ways = 24[/tex]
From the question, we understand that the female of the particular animal cannot be selected (yet).
So, there are 3 female animals left.
The number of ways to feed any of the 3 female animals is:
[tex]Ways = 3![/tex]
Expand
[tex]Ways = 3 \times 2 \times 1[/tex]
[tex]Ways = 6[/tex]
So, the number (n) of ways to feed all the animals is:
[tex]n = 24 \times 6[/tex]
[tex]n = 144[/tex]
Hence, he can feed all the animals in 144 ways
Read more about permutation at:
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Can someone help me out with this please
Answer:
143.81
Step-by-step explanation:
Trapezoid Area
A = 2b/2 * h
A = 9 + 23/2 * 7
A = 32/2 * 7
A = 16 * 7
A = 112
Semi-circle Area
A = πr²/2
A = π4.5²/2
A = π20.25/2
A = 63.62/2
A = 38.81
Total Area
112 + 38.81
143.81
What is the equivalent expression of 8x3 - 8?
Step-by-step explanation:
[tex]8x^3-8=2^3x^3-2^3=(2x)^3-2^3\\\\\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(2x-2)\bigg((2x)^2+(2x)(2)+2^2\bigg)\\\\=(2x-2)(4x^2+4x+4)\\=2(x-1)(4x^2+4x+4)\\=4(2x-2)(x^2+x+1)\\=8(x-1)(x^2+x+1)[/tex]
The equivalent expression of 8x³ - 8 is 8(x-1) (x² + x +1)
How to arrive at the above expression
8x³ - 8 = 2³ x³ -2³
= (2x)³ - 2³
Using a³ -b³ = (a - b) (a² + ab + b²)
= (2x -2) ((2x)² + (2x) (2) + 2²))
= (2x -2) (4x² + 4x + 4)
= 2(x-1)(4x² + 4x + 4)
= 4(2x -2) (x² + x +1)
= 8 (x-1) (x² + x +1)
Learn more about expression at:
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(1) 10x’y' + 15xy? :
Answer:
factor: 5(2x'y'+3xy)
Step-by-step explanation:
thats for factoring, i didnt know what you needed
Answer:
25xy
Step-by-step explanation:
collect like terms
PLZ HELP ME!!! I WILL NAME BRAINLIEST! (:
Answer:
Options 2, 4, and 5 are correct (from top to bottom)
Step-by-step explanation:
g(0)=0
g(1)=1
g(-1)=1
g(4)≠-2
g(4)=2
g(1)≠-1
g(1)=1
Options 2, 4, and 5 are correct (from top to bottom)
the square root of 169
Answer:
The answer is 13
Step-by-step explanation:
You'll say what will you multiply by itself to give you 169.
It will be 13 times itself and it will be =169.
Find x and y. Give reasons to justify your solution. AB is a straight line.
Answer:
x=8 degrees y=21 degrees
Step-by-step explanation:
There are 6 women and 9 men eligible to be in a committee of 5. Find the expected number of women on the committee given that at least one woman must be on the committee. Round the probabilities of the distribution to four decimal places or keep them as fractions. Round the answer to two decimal places.
Answer:
P = 0.2517
Step-by-step explanation:
In this case we must calculate the probability of event, which would be the number of specific events (that is, at least one woman and the rest men, 4), then it would be to choose 1 of 6 women by 4 of 9 men divided by the number of total events, which would be to choose 5 (committee size) out of 15 (9 men + 6 women, total number of people)
P (at least one woman) = 6C1 * 9C4 / 15C5
we know that nCr = n! / (r! * (n-r)!)
replacing we have:
6C1 = 6! / (1! * (6-1)!) = 6
9C4 = 9! / (4! * (9-4)!) = 126
15C5 = 15! / (5! * (15-5)!) = 3003
Therefore it would be:
P (at least one woman) = 6 * 126/3003
P = 0.2517
That is, approximately 1 out of 4 women.
Alejandra can husk 8 ears of corn in 24 minutes. At this rate, how many ears of corn can she husk in 33 minutes?Jonah bicycled 12 miles in 4 hours. What is the unit rate?
Answer:
Step-by-step explanation:
If she can husk 8 in 24mins
⟩ 8 = 24
Let x = ears of corn in 33mins
⟩ 8 = 24
x = 33
If less more divide
⟩ 24x = 8×33
⟩ x = 264÷24
⟩ x = 11 mins
Find the measure of the unknown acute angle. Round your answer to the nearest degree.
Answer:
d. x° = 27°, y° = 63°
Step-by-step explanation:
To choose the correct answer, you only need to know that the smaller angle is opposite the shorter side. x° is opposite the shorter side so will have a smaller measure than y°.
The correct choice is ...
d. x° = 27°, y° = 63°
_____
If you want to actually go to the trouble to determine the angles exactly, you can use the tangent relation:
Tan = Opposite/Adjacent
tan(x°) = 4/8
x° = arctan(1/2) ≈ 26.56°
x° ≈ 27°
y can be computed as the complement of this, or can be computed in similar fashion:
tan(y°) = 8/4
y° = arctan(2) ≈ 63.43°
y° ≈ 63°
help me answer this question please with full working
Answer:
A y=1/2x(powerof)2+5
B 17.5
C x=√42 or x=−√42
Step-by-step explanation:
Answer:
a. y = x^2 + 10
b. when x=5, y = 35
c. when y = 26, x = +4 or -4
Step-by-step explanation:
Given
y = k (x^2/2 + 5), and
(2,14) is on the curve.
Solution:
Substitute x=2 and y=14 in the above equation
14 = k (2^2/2 + 5)
14 = k (2+5)
14 = 7k
k = 14/7 = 2
a. equation connecting x and y is
y = 2 (x^2/2 + 5), or
y = x^2 + 10
b. when x=5
y = 5^2 + 10 = 25 + 10 = 35
c. when y = 26
26 = x^2 + 10
x^2 = 26-10 = 16
x= sqrt(16) = +4 or -4
Find the slope of the line that passes through (–7, 1) and (7, 8)
Answer:
slope= 1/2x
Step-by-step explanation:
For this line, you can count it going up 7 and to the right 14. Next, to calculate the slope, you take the change in y over the change in x, and you take those numbers (7 and 14) and divide 7 by 14 to get the slope, which simplifies to 1/2x, the slope.
Answer:
1/2
Step-by-step explanation:
The slope formula is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
where (x1,y1) and (x1, y2) are 2 points the line passes through.
We are given the points:
(-7,1) and (7,8). Match the corresponding variables with the points.
x1= -7
y1= 1
x2= 7
y2= 8
Substitute these values into the formula.
[tex]m=\frac{8-1 }{7--7 }[/tex]
Solve the numerator first. Subtract 1 from 8.
[tex]m=\frac{7 }{7--7 }[/tex]
Now solve the denominator. Subtract -7 from 7, or add 7 and 7.
[tex]m=\frac{7}{7+7}[/tex]
[tex]m=\frac{7}{14}[/tex]
This fraction can be simplified. Both 7 and 14 can be divided evenly by 7.
[tex]m= \frac{(7/7)}{(14/7)}[/tex]
[tex]m=\frac{1}{2}[/tex]
The slope of the line is 1/2.
if C is the midpoint of EF, C has coordinate -8, F has coordinate 4, then find the coordinate of E
==========================================================
Work Shown:
Let x be the location of E on the number line.
Since C is the midpoint of E and F, this means we can find C's location by adding E and F together and dividing that sum by 2
midpoint = (endpoint1 + endpoint2)/2
C = (E+F)/2
Plug in E = x, C = -8 and F = 4. Then solve for x
C = (E+F)/2
-8 = (x+4)/2
(x+4)/2 = -8
x+4 = 2(-8) .... multiplying both sides by 2
x+4 = -16
x = -16-4 .... subtract 4 from both sides
x = -20
The location of point E on the number line is -20
-------------
As a check, lets add E and F to get E+F = -20+4 = -16
Then cut this in half to get -16/2 = -8, which is the proper location of point C
This confirms our answer.
Destiny draws the lagrest circle she can inside of a square. The circle has a diamater of 12 in. The square is 12 in. By 12in. What is the area of the square Not covered by the circle
Answer:
30.96 [tex]in^2[/tex]
Step-by-step explanation:
Given that
Side of square = 12 in
Diameter of circle = 12 in
We know that, radius is half of diameter,
So, r = 6 cm
We have to find the area of square which is not covered by the circle.
i.e. Required Area = Area of Square - Area of Circle
Please refer to the attached to have a better understanding of the given situation.
Formula:
Area of square = [tex](side)^2[/tex]
Area of circle = [tex]\pi r^2[/tex]
Required Area = [tex]12^2[/tex] - [tex]\pi \times 6^{2}[/tex]
[tex]\Rightarrow 144 - 3.14 \times 36\\\Rightarrow 144 - 113.04\\\Rightarrow 30.96\ in^2[/tex]
So, the answer is 30.96 [tex]in^2[/tex].
Find the measure of angle b.
your answer_____
Answer:
b = 131
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
b+49 = 180
Subtract 49 from each side
b = 180-49
b =131
Answer:
Angle b is 131°
Step-by-step explanation:
Angles on a straight line add up to 180°
To find b add 49 and b and equate it to 180°
That's
b + 49 = 180
b= 180 - 49
b = 131°
Hope this helps you
Calculate $\frac{1}{2} \cdot \frac{2}{4} \cdot \frac{3}{6} \cdot \frac{4}{8} \cdot \frac{5}{10} \cdot \frac{6}{12}$
Explanation:
Each fraction reduces to 1/2, so we have six copies of 1/2 being multiplied together. A shortcut to repeated multiplication like this is to use exponents
So you're really computing (1/2)^6 to get
(1/2)^6 = (1^6)/(2^6) = 1/64
Answer:
2.35*2/3=47/30
Step-by-step explanation:
Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. f(x) = −one half(x − 6)2 + three halves f(x) = one half(x − 6)2 + three halves f(x) = −one half(x + three halves)2 + 6 f(x) = one half(x + three halves)2 + 6
Answer:
Second choice.
f(x) = 1/2(x - 6)^2 + 3/2.
Step-by-step explanation:
The distance of a point (x, y) from the focus = the distance of the point from the directrix, so:
(x - 6)^2 + (y - 2)^2 = (y - 1)^2
x^2 - 12x + 36 + y^2 - 4y + 4 = y^2 - 2y + 1
x^2 -12x + 39 = 2y
y = f(x) = 1/2 (x^2 - 12x + 39)
I see you want the answer in vertex for so it is:
f(x) = 1/2 [ (x - 6)^2 - 36) + 39)
f(x) = 1/2(x - 6)^2 + 3)
f(x) = 1/2(x - 6)^2 + 3/2.
A parabola is a plane that is approximately U-shaped.
The equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
The given parameters are:
[tex]\mathbf{Focus = (6,2)}[/tex]
[tex]\mathbf{Directrix: y = 1}[/tex]
First, equate the directrix to 0
[tex]\mathbf{y - 1 = 0}[/tex]
The equation is then calculated as:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = (y- 1)^2}[/tex]
Where:
[tex]\mathbf{(a,b) = (6,2)}[/tex]
So, we have:
[tex]\mathbf{(x - 6)^2 + (y - 2)^2 = (y- 1)^2}[/tex]
Expand
[tex]\mathbf{x^2 - 12x +36 + y^2 - 4y + 4 = y^2 - 2y + 1}[/tex]
Subtract y^2 from both sides
[tex]\mathbf{x^2 - 12x +36 - 4y + 4 =- 2y + 1}[/tex]
Collect like terms
[tex]\mathbf{x^2 - 12x +36 + 4 - 1 =4y - 2y}[/tex]
[tex]\mathbf{x^2 - 12x +39 =2y}[/tex]
Divide through by 2
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +39)}[/tex]
Express 39 as 36 + 3
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36 + 3)}[/tex]
Factor out 3/2
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36) + \frac 32}[/tex]
Expand the bracket
[tex]\mathbf{y = \frac{1}{2}(x^2 - 6x - 6x +36) + \frac 32}[/tex]
Factorize
[tex]\mathbf{y = \frac{1}{2}(x(x - 6) - 6(x -6)) + \frac 32}[/tex]
Factor out x - 6
[tex]\mathbf{y = \frac{1}{2}((x - 6) (x -6)) + \frac 32}[/tex]
Express as squares
[tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
Hence, the equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
Read more about equations of parabola at:
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which term nest describes a figure formed by three segments connecting three noncollinear points?
Answer:
the triangle, its interior , and its exterior best describes it.
Answer:
Hello!
__________________
Your answer would be Triangle.
the term that best describes a figure formed by three segments connecting three non-collinear points is:
Triangle.
___________________
Hope this helped you!
:D
6 more than 3 times a number
Answer:
6+3x
Step-by-step explanation:
Have a good day and stay safe!
Answer:
Let the number be x
The above statement is written as
6 + 3xHope this helps you
What is the explicit formula for this sequence?
5, 10, 20, 40, 80, 160,...
O A. an = 5 + 5(n-1)
O B. an = 2(5)(n-1)
O c. an = 5(2)"
D. an = 5(2)(n = 1)
Step-by-step explanation:
The above sequence is a geometric sequence
For an nth term in a geometric sequence
[tex] a(n) = a ({r})^{n - 1} [/tex]
where
n is the number of terms
a is the first term
r is the common ratio
From the question
a = 5
r = 10/5 = 2
Therefore the explicit formula for this sequence is
[tex]a(n) = 5( {2})^{n - 1} [/tex]
Hope this helps you
is 0.14 rational and irrational
Answer:
Rational.
Step-by-step explanation:
Irrational numbers are real numbers that can't be written as fractions.
One clue is that the decimal goes on forever (doesn't terminate) without repeating. (pi)
.14 can be written as a fraction: 14/100
Answer:
It's rational
Step-by-step explanation:
Because irrational numbers cannot be written s a fraction and rational numbers can
Please help with this 3a² = 27. Find a
Answer:
[tex]a = 3[/tex]
Step-by-step explanation:
[tex]3 {a}^{2} = 27 \\ \frac{3 {a}^{2} }{3} = \frac{27}{3} \\ {a}^{2} = 9 \\ a = \sqrt{9} \\ a = 3[/tex]
Answer: 9
Step-by-step explanation:
First divide both sides by 3
[tex]a^2=9[/tex]
Then root both sides([tex]\sqrt{a^2}=\sqrt{9}[/tex])
a = 9
Hope it helps <3
Edit: :o this is my 250th answer
find the length asap
Answer:
[tex]\boxed{BC = 11.62}[/tex]
Step-by-step explanation:
Tan 54 = [tex]\frac{opposite}{adjacent}[/tex]
Where opposite = 16, Adjacent = BC
1.376 = [tex]\frac{16}{BC}[/tex]
BC = 16/1.376
BC = 11.62
Answer:
11.62468045 or 11.6 to 1 decimal place
Step-by-step explanation:
→ We need to utilise trigonometry. The first step would be to list out the formula triangles
Tan = Opposite ÷ Adjacent
Sin = Opposite ÷ Hypotenuse
Cos = Adjacent ÷ Hypotenuse
→ Now we need to know which triangle to use, we do that by identifying the side or length we are not given in the triangle and then finding a formula without the name of the given side. First let's identify all the sides.
Opposite = AC = 16
Adjacent = BC = We need to find this out
Hypotenuse = AB = No given value
→ Now we look for a formula with hypotenuse
Tan = Opposite ÷ Adjacent
→ The (Tan = Opposite ÷ Adjacent) is the formula we are going to be using. Since we want to find out the adjacent, we have to rearrange to get adjacent as the subject
Adjacent = Opposite ÷ Tan
→ Now we identify the Opposite and the Tan
Opposite = 16
Tan = 54°
Side note ⇒ Sin, cos and tan will always be the angles
→ Substitute in the values in the formula
Adjacent = Opposite ÷ Tan ⇔ Adjacent = 16 ÷ Tan (54) ⇔ Adjacent = 11.6
→ The adjacent is 11.6 to 1 decimal place
Which of the following equations is not linear?
A. 13x - 12y = 82
B. -6x = y
C. 7 = y
D. y = x² - 2
Answer:
I think its A
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The graph would be a curve because of the exponent.
1)How many pinches of salt would be in 24 servings?
2) How many eggs would be needed to serve 18 people?
3) If you only had 33g of flour, how much of the other
ingredients would you need?
4) If 2 eggs were used, how many grams of flour would be
needed?
5) How much flour would be needed if 900ml milk is used?
HELP!!
Answer:
1. 2 pinch of salt
2. 3/2 egg =1.5 eggs
3. 33g of flour=1/3 pinch of salt
33g of flour=1/3 tbsp of oil
33g of flour=1/3 egg
33g of flour=100ml of milk
4. 24 servings
5. 300g of flour
Step-by-step explanation:
12 servings
Plain flour=100g
Salt=a pinch
Oil= 1 tbsp
Egg=1
Milk=300 ml
1. Pinches of salt in 24 servings
24
12 servings=1 pinch of salt
24 servings=24/12*1 pinch of salt
=2*1 pinch of salt
=2 pinch of salt
2. Egg needed for 18 servings
12 servings=1 egg
18 servings=18/12 * 1 egg
=3/2* 1 egg
=3/2 egg
3. If there are 33 grams of flour,
The other ingredients will be
33g/100g=1/3
The other ingredients will be 1/3 of the original measurement
Salt=a pinch
33g of flour=1/3 pinch of salt
Oil= 1 tbsp
33g of flour=1/3 tbsp of oil
Egg=1
33g of flour=1/3 egg
Milk=300 ml
33g of flour=1/3 of 300ml
=1/3*300
=300/3
=100ml of milk
4. If two eggs were used, grams of flour needed is
1 egg =12 servings
2 eggs=2* 12 servings
=24 servings
5. Flour needed if 900ml milk is used
100g flour=300ml of milk
900ml of milk=300ml * 3
Therefore,
900ml of milk=100g of flour *3
900ml of milk=300g of flour
Which of these sets of side lengths are pythagorean triples!
Hey there! :)
Answer:
Choices 1, 4 and 5.
Step-by-step explanation:
To solve, we can go through each answer choice and check if they are Pythagorean Triples using the Pythagorean Theorem:
1) 26² = 10² + 24²
676 = 100 + 576
676 = 676. This is correct.
2) 49² = 14² + 48²
2401 = 196 + 2304
2401 ≠ 2500. This is incorrect.
3)
16² = 12² + 9²
256 = 144 + 81²
256 ≠ 225. This is incorrect.
4)
41² = 40² + 9²
1681 = 1600 + 81
1681 = 1681. This is correct.
5)
25² = 15² + 20²
625 = 225 + 400
625 = 625. This is correct.
Therefore, choices 1, 4 and 5 are correct.
Answer:
A, D, and E.
Step-by-step explanation:
Given that (-1,9) is on the graph of f(x), find the
corresponding point for the function
f(x) + 5
Answer:
I think -1,14
Step-by-step explanation:
Because you add 5
Hi Plato/Edmentum Users!
The other person is correct!
PLEASE HELP ASAP!:
Solve for a and b
6a-b=-5
4a-3b = -8
Answer:
a = -1/2
b = 2
Step-by-step explanation:
Step 1: Rewrite 1st equation
-b = -5 - 6a
b = 5 + 6a
Step 2: Substitution
4a - 3(5 + 6a) = -8
Step 3: Solve
4a - 15 - 18a = -8
-14a - 15 = -8
-14a = 7
a = -1/2
Step 4: Plug in a to find b
6(-1/2) - b = -5
-3 - b = -5
-b = -2
b = 2
Which binomial is a factor of 9x2 - 64?
COM
3x - 8
9x - 32
3x + 32
9x + 8
Answer:
3x - 8
Step-by-step explanation:
9x² - 64 is a perfect square binomial
3x - 8 and 3x + 8 are the factors
First factor the 2nd degree polynomial.
[tex]9x^2-64=(3x-8)(3x+8)[/tex]
We find that polynomial is factored to two binomials:
[tex]3x-8[/tex][tex]3x+8[/tex]Hope this helps.
The triangular prism has a volume of 27 cubic units. A triangular prism. What will be the volume of the prism if each side is dilated by a factor One-third? 1 cubic unit 3 cubic units 8 cubic units 9 cubic units
Answer:
Option (2)
Step-by-step explanation:
Volume of a prism A (preimage) = 27 cubic units
Factor of dilation of the sides of this prism (image) = [tex]\frac{1}{3}[/tex]
Volume scale factor of these prisms = [tex]\frac{\text{Volume of image}}{\text{Volume of preimage}}[/tex]
Since, Volume scale factor = (Scale factor of dilation of the sides)³
= [tex](\frac{1}{3})^3[/tex]
= [tex]\frac{1}{9}[/tex]
Now from the formula of volume scale factor,
[tex]\frac{1}{9}=\frac{\text{Volume of image}}{\text{Volume of preimage}}[/tex]
[tex]\frac{1}{9}=\frac{\text{Volume of image}}{27}[/tex]
Volume of the image prism = [tex]\frac{27}{9}[/tex] = 3 cubic units
Therefore, Option (2) will be the answer.
Answer:
1 cubic unit
Step-by-step explanation: