Answer:
Each book costs $15 dollars
Step-by-step explanation
150-15=135
135/9=15
$15
If the side of an equatorial triangle is L then express the perimeter of the triangle in terms of L.
Answer:
3L
Step-by-step explanation:
Perimeter is the sum of side lengths
Since the triangle is equilateral, it has all sides equal and each has length of L
So perimeter is:
P= L+L+L = 3LIn the triangle below,
y = [ ? ] cm. Round to the
nearest tenth.
Answer:
The answer is
12.3 cmStep-by-step explanation:
Since the triangle is a right angled triangle we can use trigonometric ratios to find y
To find y we use cosine
cos∅ = adjacent / hypotenuse
From the question
y is the adjacent
The hypotenuse is 15
So we have
[tex] \cos(35) = \frac{y}{15} \\ y = 15 \cos( 35 ) \\ y = 12.28728[/tex]
We have the final answer as
12.3 cm to the nearest tenthHope this helps you
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer: 3000 in^2
Explanation:
Jeremy bought $2,500 worth of gold this week. If the price of gold appreciates at the rate of 5.5%
each year, what will his gold be worth in 7 years?
Answer:
$3,636.70
Step-by-step explanation:
Given the following:
Initial price of Gold (A) = $2500
Rate of appreciation (r) = 5.5% = 0.055
Worth of gold in 7 years will be?
Period (p) = 7
Using the compound interest formula :
Let F = final amount
F = A( 1 + r/n)^nt
n = number of times Appreciation occurs per period.
Since rate compounds yearly, then, n = 1
F = $2500( 1 + 0.055/1)^(7*1)
F = $2500(1 + 0.055)^7
F = $2500(1.055)^7
F = $2500(1.454679161133794609375)
F = $3636.6979
Amount in 7 years = $3,636.70
What is the solution to the equation to 0.5x+3.5=6
Answer:
x = 5
Step-by-step explanation:
0.5x + 3.5 = 6
0.5x = 6 - 3.5
0.5x = 2.5
x = 2.5 / 0.5
x = 5
Which equation describes the line graphed above?
Answer:
What lined graph?
Step-by-step explanation:
Answer:
Please give a lined graph. However, if your question is like mine, I may be able to help.
Here, the answer is D. For the slope, remember: Rise over Run. The slope will be a fraction, so let the amount of points between points on the line (If that makes sense) be that fraction. The amount between points vertically is the Numerator (top) of your fraction, and the amount horizontally is the denominator (Bottom). If the Denominator is 1, your fraction is a whole number.
Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to four decimal places.) f(x) = cos x, x1 = 0.7
Answer:
The two iterations of f(x) = 1.5598
Step-by-step explanation:
If we apply Newton's iterations method, we get a new guess of a zero of a function, f(x), xₙ₊₁, using a previous guess of, xₙ.
xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ)
Given;
f(xₙ) = cos x, then f'(xₙ) = - sin x
cos x / - sin x = -cot x
substitute in "-cot x" into the equation
xₙ₊₁ = xₙ - (- cot x)
xₙ₊₁ = xₙ + cot x
x₁ = 0.7
first iteration
x₂ = 0.7 + cot (0.7)
x₂ = 0.7 + 1.18724
x₂ = 1.88724
second iteration
x₃ = 1.88724 + cot (1.88724)
x₃ = 1.88724 - 0.32744
x₃ = 1.5598
To four decimal places = 1.5598
If one cup of soy milk contains 4g total fat then how many grams of total fat are in 2 3/4 cups of soy milk
Answer:
11
Step-by-step explanation:
Just multiply 4 times 2 3/4 and youll get 11
If one cup of soy milk contains 4g total fat then [tex]2\frac{3}{4}[/tex] cups of soy milk contains 11g of total fat.
Cross multiplication: 1 cup contains 4grams of total fat then[tex]2\frac{3}{4}[/tex] cups contains x grams of total fat.
1(x) = 4([tex]2\frac{3}{4}[/tex])⇒ x = 4([tex]\frac{11}{4}[/tex])
⇒ x = 11 grams
Hence 11 grams of total fat is there in [tex]2\frac{3}{4}[/tex] cups of soy milk.
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Let f(x)=5x-13 what ordered pair in f corresponds to the equation f(x)=7 ? Recall y=f(x).
Answer:
(4,7)
Step-by-step explanation:
f(x)=5x-13
Let this equal to 7
7=5x-13
Add 13 to each side
7+13 = 5x-13+13
20 = 5x
Divide by 5
20/5 = 5x/5
4 =x
The ordered pair is
(4,7)
after running 3/5 of a race the runner only has 4 miles left how long was the race
Answer:
10 miles
Step-by-step explanation:
3a/5 + 4 = a
a = race long
4 = a - 3a/5
4 = 5a/5 - 3a/5
4 = 2a/5
4*5/2 = a
a = 10
The length of the entire race is 10 miles.
Let length of race = r
Miles left after running 3/5 of race :
r - 3r/5 = 4We can solve the expression thus :
r - 3r/5 = 4
r - 3r = 4 * -5
r - 3r = -20
-2r = -20
divide both sides by -2 to isolate r
r = 10
Hence, the length of the entire race is 10 miles.
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Which statements are always true regarding the
diagram? Check all that apply.
3
OmZ3+ m 24 = 180°
A
co
On
m2 + m 24+ m26 = 180°
m2 + m 24 = m 25
2
7
m21+ m2 = 90°
m24+ m26 = m22
m22 + m 26 = m25
Answer:
m<3 + m<4:= 180°
m<2 + m<4 + m<6 = 180°
m<2 + m<4 = m<5
Step-by-step explanation:
<3 and <4 are linear pairs. They are angles on a straight line. Angles in a straight line sum up to give 180°. Therefore, the statement "m<3 + m<4:= 180°" is TRUE.
<2, <4, <6 are interior angles of a triangle. The sum of the angles in a ∆ = 180°. Therefore, the statement, "m<2 + m<4 + m<6 = 180°" is TRUE.
<2 and <4 are opposite interior angles of the ∆, while <5 is an exterior angle to the ∆. Based on the external angle theorem of a ∆, the statement, "m<2 + m<4 = m<5" is TRUE.
<1 and <2 are a linear pair, and are angles on a straight line. Their sum cannot give us 90°.
m<4 + m<6 ≠ m<2. Rather, 180 - (m<4 + m<6) = m<2 (sum of angles in a ∆)
m<2 + m<6 ≠ m<5. Rather, m<2 + m<4 = m<5
The correct equations are:
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠5 = m∠4
TriangleTriangle is a polygon with three angles and three sides. The sum of angles in a triangle is 180 degree.
From the diagram:
m∠5 + m∠6 = 180° (angle in a straight line)
But:
m∠2 + m∠3 + m∠5 = 180
m∠2 + m∠3 + m∠5 = m∠5 + m∠6
m∠2 + m∠3 = m∠6
Also:
m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)
But:
m∠3 + m∠4 = 180° (angle in a straight line)
m∠2 + m∠3 + m∠5 = m∠3 + m∠4
m∠2 + m∠5 = m∠4
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Thank you:)
Need help with a,b,c for simplifying
Answer:
6
Step-by-step explanation:
A) f(x+h)=6(x+h)-6
=6x+6h-6
B)(6x+6h-6)-(6x-6)
6x+6h-6-6x+6
=>6h
C=6h/h
C=6
Evaluate the following iterated integral by converting to polar coordinates.
∫8 −8∫0^(64−x^2)1/2 sin(x^2+y^2) dydx
Integration
IntegralsIntegration TechniquesIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Double Integrals
Polar Coordinates Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle x^2 + y^2 = r^2[/tex]Integral Conversion [Polar Coordinates]:
[tex]\displaystyle \iint_T {f(x, y)} \, dA = \iint_R {f(r, \theta)r} \, dr \, d\theta[/tex]
The formatting of the question was thrown off, so I have defined it down below.
We are given an integral and asked to convert to polar coordinates as well as evaluate it:
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx[/tex]
It would be quite difficult to evaluate the given integral using conventional methods, so we apply polar conversion to evaluate the integral. Let's start out by converting the function and the bounds.
[Bounds] Cartesian to Polar:
[tex]\displaystyle \left \{ {{-8 \leq x \leq 8} \atop {0 \leq y \leq \sqrt{64 - x^2}}} \right \longrightarrow \left \{ {{0 \leq r \leq 8} \atop {0 \leq \theta \leq \pi}} \right[/tex]
[Function] Cartesian to Polar:
[tex]\displaystyle f(x ,\ y) = \sin(x^2 + y^2) \longrightarrow f(r ,\ \theta) = \sin r^2[/tex]
Now that we've converted to polar coordinates, we can convert the integral using our integral conversion listed under "Multivariable Calculus":
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx \longrightarrow \int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta[/tex]
We can now evaluate the polar integral using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \int \limits^{\pi}_{0} \underbrace{\int \limits^{8}_{0} r \sin r^2 \, dr \, }_{u = r^2 ,\ du = 2r \, dr} d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{8}_{0} 2r \sin r^2 \, dr \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{r = 8}_{r = 0} \sin u \, du \, d\theta \\\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos u \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos r^2 \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos 64 + 1 \bigg) \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( 1 - \cos 64 \bigg) \, d\theta \\\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \bigg(1 - \cos 64 \bigg) \bigg( \theta \bigg) \bigg| \limits^{\pi}_{0} \\& = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }\end{aligned}[/tex]
∴ the integral equals:
[tex]\displaystyle \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]
___
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Topic: Multivariable Calculus
Unit: Double Integrals
Which equation can pair with X- y=-2 to create a consistent and dependent system?
O 6x + 2y = 15
0 -3x + 3y = 6
O _8x – 3y = 2
O 4x – 4y = 6
List the next three numbers for the sequence: 7, 7 2 , 7 4 , 7 8
Answer:
7/16, 7/32, 7/64
Step-by-step explanation:
7, 7 /2 , 7/ 4 , 7/ 8
We multiply by 1/2 each time
7/8 *1/2 = 7/16
7/16*1/2 = 7/32
7/32 *1/2 = 7/64
The equation $y = -6t^2 + 51t$ describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 108 feet in height?
Answer:
4 OR 4.5 SECONDS
Step-by-step explanation:
the sides of an angle are
Answer:
the vetrex
Step-by-step explanation:
what is equal to -3/2
Answer:
-1.5
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
-1.5
-1 1/2
-6/4
Solve. 3(4x−7)=27 erhtnmdyrshgfwegbrnhtjftdgrsefvgsrdhtfjndbgrsvgrbhdtnjyu
★ Solution :
[tex]:\implies\sf 3(4x - 7) = 27\:\:\:\:\Bigg\lgroup \bf{Given\: Equation}\Bigg\rgroup \\\\\\:\implies\sf 12x - 21 = 27\\\\\\:\implies\sf 12x = 27 + 21\\\\\\:\implies\sf 12x = 48\\\\\\:\implies\sf x = \dfrac{48}{12}\\\\\\:\implies\underline{\boxed{\sf x = 4}}[/tex]
Answer:
Answer :[tex]3(x - 7) = 27[/tex]
[tex]⟹3x - 21 = 27[/tex]
[tex]⟹3x = 27 + 21[/tex]
[tex]⟹3x = 48[/tex]
[tex]⟹x = \frac{48}{3} [/tex]
[tex]⟹x = 16[/tex]
Choose the best description for the real number 2.33663336663333666689...
Irrational, because it is a terminating decimal
O Rational, because it is a repeating decimal
Irrational, because it is non-terminating decimal
O Rational, because it is a terminating decimal
Answer:
Irrational, non-terminating
Step-by-step explanation:
This number is irrational because it is a non-terminating decimal. Notice how it continues with the '...'. <3
What is the solution to the equation by -2(y + 1) = 3(y – 2) + 6?
Answer: y= -2.5
Step-by-step explanation:
Distribute the -2 and 3 into the parentheses. -6 + 6 cancels out so you are left with 3y on the right side. Add 2y to the right side leaving you with -2=5y. Divide both sides by -2
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ y = - 0.4}}}}[/tex]Step-by-step explanation:
[tex] \sf{ - 2(y + 1) = 3(y - 2) + 6}[/tex]
Distribute -2 through the parentheses
Similarly, Distribute 3 through the parentheses
⇒[tex] \sf{ - 2y - 2 = 3y - 6 + 6}[/tex]
Since two opposites add up to zero , remove them
⇒[tex] \sf{ - 2y - 2 = 3y}[/tex]
Move 3y to Left hand side and change it's sign
Similarly, move -1 to right hand side and change it's sign
⇒[tex] \sf{ - 2y - 3y = 2}[/tex]
Collect like term
⇒[tex] \sf{ - 5y = 2}[/tex]
Divide both sides of the equation by -5
⇒[tex] \sf{ \frac{ - 5y}{ -5 } = \frac{2}{ - 5} }[/tex]
Calculate
⇒[tex] \sf{ - 0.4}[/tex]
Hope I helped!
Best regards!
Which type of transformation is shown?
Answer:
Translation
Step-by-step explanation:
The object is only moved, which is what happens when a translation occurs
There are twelve signs of the zodiac. How many people must be present for there to be at least a 50% chance that two or more of them were born under the same sign
Answer:
5
Step-by-step explanation:
Given that each zodiac sign occupies 1/12 of a year.
Then the minimum number of persons for Y[all different signs] < 0.5,
The probability of at least two having the same sign is 1 minus the probability of all having different signs.
This can be represented as A [at least 2 person share the same sign] = 1 - Y[all different signs] must be > 0.5
Therefore we have 1 - 12/12 *11/12 * 10/12 *9/12 *8/12 = 0.38
This implies that the lowest number will be found to be 5
Hence, the correct answer is 5.
To solve the linear equation , the first step is to multiply each side by the least common denominator of all the fractions in the equation. What is the LCD?
Answer:
84
Step-by-step explanation:
The least common denominator of the 7, 6, 12, which are the denominators of the fractions in the given linear equation, is the least expression or number that is divisible by 7, 6, 12.
To find the LCD, express each number as factors of itself as follows:
[tex] 7 = 1*7 [/tex]
[tex] 6 = 2*3 [/tex]
[tex] 12 = 2^2*3 [/tex]
Find the product of the highest terms
The product = LCD = [tex] 1*2^2*3*7 = 84 [/tex]
LCD of 7, 6, 12 = 84
Answer:
84
Step-by-step explanation:
Find (f-g)(x) for the following functions. f(x) = x2-2x-24 g(x) = x+4
Answer:
(f-g)(x) = x² - 3x - 24Step-by-step explanation:
f(x) = x² - 2x - 24
g(x) = x + 4
To find (f-g)(x) subtract g(x) from f(x)
That's
(f-g)(x) = x² - 2x - 24 - ( x + 4)
(f-g)(x) = x² - 2x - 24 - x - 4
Group like terms
We have
(f-g)(x) = x² - 2x - x - 24 - 4
Simplify
We have the final answer as
(f-g)(x) = x² - 3x - 28Hope this helps you
HII PLEASE HELP ME IN THIS
Step-by-step explanation:
(i) Sum the forces at point M in the x direction.
∑F = ma
-T sin 30° − T sin 30° + 5 N = 0
2T sin 30° = 5 N
T = 5 N
(ii) Sum the forces on the ring in the x direction.
∑F = ma
T sin 30° − N = 0
N = 2.5 N
Sum the forces on the ring in the y direction.
∑F = ma
T cos 30° − mg − Nμ = 0
Nμ = T cos 30° − mg
2.5 μ = 5 cos 30° − 2
μ = 0.932
(iii) Sum the forces on the ring in the y direction.
∑F = ma
T cos 30° − m₁g − m₂g + Nμ = 0
m₂g = T cos 30° − m₁g + Nμ
m (10) = 5 cos 30° − 2 + (2.5)(0.932)
m = 0.466 kg
Part A.) in another baseball game division, one team had a winning percentage of 0.444... what fractions of the game did the team win? *with full steps please* Part B.)How do you know what power of 10 to multiply by in the second step at the right?
Answer:
4/9
Step-by-step explanation:
0.4444... can be written as a geometric series with first term 0.4 and common ratio 0.1. Each new digit is 0.1 times the previous digit.
0.4
Then 0.4444... = ------------ = 0.4/0.9 = 4/9
1 - 0.1
You may check this result by dividing 4 by 9 on a calculator.
m and n are both integers. Select all the statements that are true if m and n are also equal to each other. m - n = n - m OR +m (- n) = m - n
OR 0 = m - n OR m + n = 0
Answer:
The true statements are;
(i) m - n = n - m
(ii) +m (-n) = m - n
(iii) 0 = m - n
Step-by-step explanation:
We are given that m and n are both integers and we have to select all the statements that are true if m and n are also equal to each other.
(i) The given situation is: m - n = n - m
LHS = m - n
= m - m {because m and n are equal}
= 0
RHS = n - m
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(ii) The given situation is: +m (- n) = m - n
LHS = +m (- n)
= m - n
= m - m {because m and n are equal}
= 0
RHS = m - n
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iii) The given situation is: 0 = m - n
LHS = 0
RHS = m - n
= m - m {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iv) The given situation is: m + n = 0
RHS = 0
LHS = m + n
= m + m {because m and n are equal}
= 2m
Hence, the given statement is not true because LHS [tex]\neq[/tex] RHS.
#1) m - n = n - m
#2) +m (-n) = m - n
#3) 0 = m - n
hope this HELPS!!!!!!!
can u guys answer this
We have,
∠A0C is a linear pair. [ 180° ]∠AOB = x°∠BOC = 128°Now,
∠AOB + ∠BOC = ∠A0C
⇒ x + 128° = 180°
⇒ x = 180° - 128°
⇒ x = 52°