Answer:
1.5
Step-by-step explanation:
Two people enter a whispering gallery and want to know where they should stand so they can hear the other person's whisper. The gallery is 100 feet wide and the vertical distance from their head to the peak of the ceiling is 30 ft.
Answer:
The two people should stand 40 feet from the center so that they can hear each other whisper
Step-by-step explanation:
From the question
Width of the gallery = 100 feet
Width = 2a
a = Width/2
a = 100/2 = 50 feet
Height of the gallery = b = 30 feet
Hence, the distance is
d² = a² - b²
d = √a² - b²
d = √50² - 30²
d = √2500 - 900
d = √1600
d = 40 feet
Hence, the two people should stand 40 feet from the center so that they can hear each other whisper.
Geometric Series (attached image) muiltx choice
WILL GIVE THANKS !!
Answer:
Step-by-step explanation:
(B). - 28.7
iv) a) 4x 10² solve it in decimal
40.0*10 is the answer
actually it is 400 but u want in decimal so it is 40.0*10
Answer:
40.0*10
Step-by-step explanation:
have a good day!
Generate an equivalent expression for:
5(2x+3y)
plz asap also not a like high school answer i need this for a flip grid for class so please awnser quick I WILL GIVE BRAINIEST
Answer:
the answer is equal to 10x+15y
How do you write 7.75 in scientific notation?
i neeeed helps asap!
Answer:
7.75-10°
Step-by-step explanation:
which equation represents a line which is perpendicular to y=0
Answer:
This is not possible. Perpendicular lines are opposite but there are no opposites of 0
Step-by-step explanation:
The table shows the prices of some candy items at a store. Jake selected 1.6 pounds of Fruit Chews and 2.6 pounds of Jelly Beans. The sales tax for his purchase was $0.52. .Item. .Price Per Pound. .Fruit Chews. $4.70 .Jelly Beans. $2.35 .Chocolate. $3.50 .If Jake had $25 to spend at the candy store, how much money did Jake have left after his purchase?
Answer:
The amount of money Jake had left after his purchase is $10.85
Step-by-step explanation:
The amount of Fruit Chews Jake selected = 1.6 pounds
The amount of Jelly Beans Jake selected = 2.6 pounds
The sales tax = $0.52
The amount of money Jake had to spend = $25
The table of values are;
Price Per Pound [tex]{}[/tex]
Fruit Chews = $4.70
Jelly Beans = $2.35
Chocolate = $3.50
The amount of money Jake had to spend $25
The total amount of the candies Jake bought = 1.6 × $4.70 + 2.6 × $2.35 = $13.63
The total amount Jake spent = The total amount of the candies Jake bought + The sales tax
The total amount Jake spent = $13.63 + $0.52 = $14.15
The amount of money Jake had left after his purchase = The amount of money Jake had to spend - The total amount Jake spent
The amount of money Jake had left after his purchase = $25 - $14.15 = $10.85
The amount of money Jake had left after his purchase = $10.85.
Determine whether each trinomial is a perfect square or not.. 1.A2+2a+1 2.4+4a+a2 3.A2-3a+9 4.4a2+24a+36 5.A4-10a+25 6.25a2+20a+9 7.A2b2-14ab+49 8.A2-2a-1 9.16a2+24a+36 10.10+6a+a2
Answer:
1) Perfect square, 2) Perfect square, 3) Not a perfect square, 4) Perfect square, 5) Perfect square, 6) Not a perfect square, 7) Perfect square, 8) Not a perfect square, 9) Not a perfect square, 10) Not a perfect square.
Step-by-step explanation:
From Algebra we must remember that a trinomial is a perfect square if and only if:
[tex](a+b)^{2} = a^{2}+2\cdot a\cdot b + b^{2}[/tex], [tex]\forall \,a,b\in\mathbb{R}[/tex] (Eq. 1)
Now we proceed to prove each trinomial:
1) [tex]a^{2}+2\cdot a +1[/tex]:
If [tex]a^2 =a^2[/tex] and [tex]b^{2} = 1[/tex], then [tex]a = \pm a[/tex] and [tex]b =\pm 1[/tex]. Therefore, [tex]2\cdot a\cdot b = 2\cdot (\pm a)\cdot (\pm 1) = \pm 2\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
2) [tex]4+4\cdot a +a^{2}[/tex]
If [tex]a^{2} = 4[/tex] and [tex]b^{2} = a^{2}[/tex], then [tex]a = \pm 2[/tex] and [tex]b = \pm a[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 2)\cdot (\pm a) = \pm 4\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
3) [tex]a^{2}-3\cdot a +9[/tex]
If [tex]a^{2} = a^{2}[/tex] and [tex]b^{2} = 9[/tex], then [tex]a = \pm a[/tex] and [tex]b = \pm 3[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm a)\cdot (\pm 3) = \pm 6\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
4) [tex]4\cdot a^{2}+24\cdot a + 36[/tex]
If [tex]a^{2} = 4\cdot a^{2}[/tex] and [tex]b^{2} = 36[/tex], then [tex]a = \pm 2\cdot a[/tex] and [tex]b = \pm 6[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 2\cdot a)\cdot (\pm 6) = 24\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
5) [tex]a^{4}-10\cdot a +25[/tex]
If [tex]a^{2} = a^{4}[/tex] and [tex]b^{2} = 25[/tex], then [tex]a = \pm a^{2}[/tex] and [tex]b = \pm 5[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm a^{2})\cdot (\pm 5) = \pm 10\cdot a^{2}[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
6) [tex]25\cdot a^{2}+20\cdot a + 9[/tex]
If [tex]a^{2} = 25\cdot a^{2}[/tex] and [tex]b = 9[/tex], then [tex]a = \pm 5\cdot a[/tex] and [tex]b = \pm 3[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 5\cdot a)\cdot (\pm 3) = \pm 30\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
7) [tex]a^{2}\cdot b^{2}-14\cdot a \cdot b + 49[/tex]
If [tex]a^{2} = a^{2}\cdot b^{2}[/tex] and [tex]b^{2} = 49[/tex], then [tex]a = \pm a\cdot b[/tex] and [tex]b = \pm 7[/tex]. Therefore, [tex]2\cdot a\cdot b = 2\cdot (\pm a\cdot b)\cdot (\pm 7) = \pm 14\cdot a \cdot b[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.
8) [tex]a^{2}-2\cdot a -1[/tex]
If [tex]a^{2} = a^{2}[/tex] and [tex]b^{2} = -1[/tex], then [tex]a = \pm a[/tex] and [tex]b = \pm i[/tex]. Therefore, [tex]2\cdot a \cdot b = \pm 2\cdot a \cdot i[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
9) [tex]16\cdot a^{2} + 24\cdot a +36[/tex]
If [tex]a^{2} = 16\cdot a^{2}[/tex] and [tex]b^{2} = \pm 36[/tex], then [tex]a = \pm 4\cdot a[/tex] and [tex]b = \pm 6[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 4\cdot a)\cdot (\pm 6) = \pm 48\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
10) [tex]10+6\cdot a +a^{2}[/tex]
If [tex]a^{2} = 10[/tex] and [tex]b^{2} = a^{2}[/tex], then [tex]a = \pm\sqrt{10}[/tex] and [tex]b = \pm a[/tex]. Therefore, [tex]2\cdot a \cdot b = \pm 2\cdot \sqrt{10}\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.
solve for b and simplify 12=5/2b
Answer:
b = 24/5
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
12 = 5/2b
Step 2: Solve for b
Rewrite: 5/2b = 12Divide both sides by 5/2: b = 24/5Step 3: Check
Plug in b to verify it's a solution.
Substitute: 12 = 5/2(24/5)Multiply: 12 = 12What is the quotient of x and three increased by 12 = 20
Answer:
x= 24
Step-by-step explanation:
Quotient means divide, increased means add
x/3 + 12 =20
Subtract 12 from each side
x/3 +12-12 = 20-12
x/3=8
Multiply each side by 3
x/3 * 3 =8*3
x= 24
Answer:700 / n, the quotient of 700 and a number. 2w, two times a ... h - 3, three less than a number ... 20 + m, 20 more than a number. x - 12, a number decreased by 12.
Step-by-step explanation:
will give brainliest!
which one is it. plz help
Answer:
A.
Step-by-step explanation:
Answer:
The answer is the first option.
Step-by-step explanation:
4. 6x + 2x - 3
help lol i was absent when we learned this and i’m clueless
Answer:
8x - 3
General Formulas and Concepts:
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define expression
6x + 2x - 3
Step 2: Simplify
Combine like terms: 8x - 3What is the equation of the line that has a slope of -6/5 and goes through the point (5, -4)?
Answer:
Step-by-step explanation:
Given
slope =6/5
point =(5, -4)
So
the equation of the line =
(y-y1)=m(x-x1)
Where X1=5,y1=-4,m=6/5
Put the values
(Y+4)=6/5(x-5)
5(Y+4)=6(x-5)
5y+20=6x-30
5y-6x=-30-20
-6x+5y=-50
6x-5y=50.
So the equation of the line is 6x-5y=50.
Solve x-5>-12.
A. X> -7
B. x < -17
C. x > -17
D. x < -7
PLEASE HELP ME
Answer:
A. X>-7
Step-by-step explanation:
So the equation is
X-5>-12
You add 5 on both sides to get the X by itself. You add it because you have to get rid of the -5 and to get to 0 you would add 5.
Which leaves you with X>-7
Answer:
A.) [tex]x>-7[/tex]
Step-by-step explanation:
Solve this the way you would solve an equation: isolate the variable.
Use inverse operations. Add 5 to both sides:
[tex]x-5+5>-12+5\\\\x>-7[/tex]
Since this can't be simplified further, x is greater than -7.
:Done
This table represents the number of inches, n, a plant grows after m, months in a new pot.
When graphed, all of the points in the table lie on the same line.
What is the slope and y-intercept of the line?
slope=−54, y-intercept = 2
slope=45, y-intercept=−1.6
slope=−45, y-intercept=−1.6
slope=54, y-intercept = 2
Months, m Plant height in inches, n
0 2
2 4.5
4 7
6 9.5
Answer: Slope = 5/4
y-intercept = 2
Step-by-step explanation:
We have the table:
Months, m Plant height in inches, n
0 2
2 4.5
4 7
6 9.5
We want a linear relationship to represent this table.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case we can select any pair of points, for example, i will choose the first two:
(0, 2) and (2, 4.5)
Then the slope is:
a = (4.5 - 2)/(2 - 0) = (2.5/2) = 1.25 = 5/4
Then our line can be written as:
y = (5/4)*x + b
To find the value of b, we can replace the values of any of the points in the equation, for example, i will use the point (0, 2) or x = 0, y = 2.
2 = (5/4)*0 + b
2 = b
Then our equation is:
y = (5/4)*x + 2.
Slope = 5/4
y-intercept = 2
Answer:
d
Step-by-step explanation:
I took the k12 test
The population of Busy Village is 3 X 108, and the population of Boring Town is 6 X 103.
Busy Village is how many times the population of Boring Town?
Express your answer in proper scientific notation.
Answer:
5 × 10^4 timesStep-by-step explanation:
Busy Village: 3 × 10^8Boring Town: 6 × 10^3Busy Village is how many times the population of Boring Town?
3 × 10^8 / 6 × 10^3=30 × 10^7 / 6 × 10^3 =30/6 × 10^(7 - 3) = 5 × 10^4 timesh(n)=2n-1; find h(3y)
Answer:
The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length,
μ
=
mass of string
length of string
=
m
l
.
In this chapter, we consider only string with a constant linear density. If the linear density is constant, then the mass
(
Δ
m
)
of a small length of string
(
Δ
x
)
is
Δ
m
=
μ
Δ
x
.
For example, if the string has a length of 2.00 m and a mass of 0.06 kg, then the linear density is
μ
=
0.06
kg
2.00
m
=
0.03
kg
m
.
If a 1.00-mm section is cut from the string, the mass of the 1.00-mm length is
Δ
m
=
μ
Δ
x
=
(
0.03
kg
m
)
0.001
m
=
3.00
×
10
−
5
kg
.
The guitar also has a method to change the tension of the strings. The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.
Hope it is helpful to you
80/100*4.5 (percentage)
Answer:
0.036%
Step-by-step explanation:
Answer:
0.036%Step-by-step explanation:
80/100 ⋅ 4.5 = 360% because...
80/100 = 80% ( wait that's not the reason. )
Here, 80/100 = 0.8 ⋅ 4.5 = 3.6 and if you move
the decimal point two times to the left, you get 0.036%
Hope this helps! <3
Express in scientific notation. Make sure your answer has the same number of significant figures as the starting value.
0.01325 = _____
1.3 x 10 -2
1.0 x 10 -2
1.325 x 10 -2
Answer:
1.325 x 10 -2
Step-by-step explanation:
That is the answer and I know 100% that it is correct
A school survey asked 120 fifth-graders what they bought to give as gifts for Mothers Day. The results are shown in the circle graph.
How many more fifth-graders bought clothes than bought perfume
Answer:
40
Step-by-step explanation:
Will give Brainlyest answer!
Answer:
c
Step-by-step explanation:
Find the derivative:
f(x)=tan[tex](x^{2} +5)[/tex]
Answer:
[tex] 2x \sec^2 (x^2 + 5) [/tex]
Step-by-step explanation:
[tex] f(x) = \tan (x^2 + 5) [/tex]
[tex] \dfrac{d}{dx} \tan u = \sec^2 u \dfrac{d}{dx} u [/tex]
[tex] \dfrac{d}{dx} \tan (x^2 + 5) = \sec^2 (x^2 + 5) \dfrac{d}{dx} (x^2 + 5) [/tex]
[tex] \dfrac{d}{dx} \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x [/tex]
[tex] \dfrac{d}{dx} \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5) [/tex]
y = 6x + 11
2х - Зу = 7
9514 1404 393
Answer:
(x, y) = (-2.5, -4)
Step-by-step explanation:
Since you are given an expression for y, it is convenient to substitute that into the second equation.
2x -3(6x +11) = 7
2x -18x -33 = 7
-16x = 40 . . . . . . add 33
x = -40/16 = -2.5
Using the equation for y, we find ...
y = 6(-2.5) +11 = -15 +11 = -4
The solution is (x, y) = (-2.5, -4).
de un numero se sabe que si a su cuadrado le restamos su mitad, se obtiene el mismo numero, Cuál es?
Answer:
2
Step-by-step explanation:
el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2
Answer: 2
Step-by-step explanation : el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2 Espero que ayude Ten un día maravilloso :)
help me someone solve this
Whats 9+10? Sjjsmslaisusbemkdd
Answer:
21 jk its 19
Step-by-step explanation:
find the area of the figure. (sides meet at right angles.) 2m 2m 2m 2m 3m 7m 7m 7m
please answer dont just do this for points >:(
Answer:
#1 and # 3 maybe
Soooooooory if this wrong, This is the type of question I would get stuck on... O////O
Factor [tex]3x^2y+28xy^2+32y^3[/tex] completely.
Answer:
y(3x + 4y)(x + 8y)
General Formulas and Concepts:
Alg I
FactoringStep-by-step explanation:
Step 1: Define expression
3x²y + 28xy² + 32y³
Step 2: Simplify
Factor out y: y(3x² + 28xy + 32y²)Factor trinomial: y(3x + 4y)(x + 8y)What multiplies up to 32 adds up to 28 with 3 being multiplied as a coefficient? Numbers are 4 and 8.SOLVING STEPS...
STEP1
FACTOR OUT y FROM THE EXPRESSION
SO ITS
[tex]y \times (3x {}^{2} + 28xy + 32y {}^{2} )[/tex]
STEP2
WRITE 28y AS A SUM
STEP3
FACTOR OUT 3x2 + 24xy
SO IT'S
[tex]y \times (3x \times (x + 8y) + 4xy + 32y {}^{2} )[/tex]
STEP4
FACTOR OUT 4xy + 32y2
SO IT'S
[tex]y \times (3x \times (x + 8y) + 4y \times (x + 8y) \: )[/tex]
STEP5
FACTOR OUT (3x × ( x + 8y ) + 4y × ( x + 8y ) )
SO THE ANSWER IS
[tex]y \times (x + 8y) \times (3x + 4y)[/tex]
GAVE ME THE BRAINLIEST IF MY ANSWER WAS HELPFUL...
How many solutions does the following equation have?
7(y + 3) = 5y +8
Choose 1 answer:
A
No solutions
B
Exactly one solution
Infinitely many solutions