Answer: Total temperature = -6.66ºF
Step-by-step explanation:
Given data,
First temperature = 1.3ºF
Second temperature = -2.8ºF
Fest = 10.000
So,
We can write,
1.3º x + (-2.8º) x = 10.000
x (1.3º - 2.8º) = 10.000
x (-1.5º) = 10.000
x = 10.000/-1.5º
x = -6.66ºF
Therefore,
Total temperature = -6.66ºF
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What is the common difference in this recursive equation?
GIVING BRAINLIEST
look at the picture i attached :)
The common difference for the recursive equation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5 is 5.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The recursive equation:
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5
and [tex]a_{1}[/tex] = -3
We can find the consecutive term using the recursive equation.
[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + 5 = -3 + 5 = 2
[tex]a_{3} =a_{2}[/tex] + 5 = 2 + 5 = 7
The sequence we get is:
-3, 2, 7, 12,....
The common difference means the differences in between two consecutive terms.
2 - (-3) = 5
7 - 2 = 5
12 - 7 = 5
Thus the common difference is 5.
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is –10 an irrational number?
When a number is decreased by 10% of itself, the result is 81, what is the number?
The number is 90.
What is the number?
Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %. Percentages are a measure of frequency.
When the number is decreased, the number becomes smaller. This means that the original number is larger than 81.
The equation that can be used to represent the information in the question is:
(1 - percentage decrease) initial number = 81
(1 - 0.1)x = 81
0.9x = 81
x = 81 / 0.9
x = 90
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can someone help me pls !!!!!!!
please help If f(x)=sinx, then f′(π/3) =
Answer:
[tex]f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\sin x[/tex]
The differentiation of sin(x) is cos(x).
[tex]\implies f'(x)=\cos x[/tex]
Therefore:
[tex]\implies f' \left(\dfrac{\pi}{3}\right) = \cos \left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]
Simplify each expression.
ln e
ln (e) = 1, by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]
In case of natural logarithm, b = e, i.e., [tex]log_e(a)=x[/tex] = ln (a) = x
In the given expression, a = e
Hence, ln (e) = x
By properties of logarithms, we get that: ln (e) = 1.
Hence, ln (e) = 1, by the properties of logarithm.
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Laura can make six flower arrangements in 25 minutes if she makes a 18 flower arrangements how many minutes will it take her
Answer:
75 flowers
Step-by-step explanation:
she needs to make 18 arrangements, so we divide 18 by 6 and get 3. 3 * 25 is 75 so the answer is 75.
Laura will arrange 18 flowers within 75 minutes of the time.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Laura can make six flower arrangements in 25 minutes if she makes 18 flower arrangements. The time will be calculated as,
Time = ( 25 x 18 ) / 6
Time = 25 x 3
Time = 75 minutes
Hence, it will take 75 minutes to arrange 18 flowers.
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Determine whether the vectors in each pair are normal to each other. (6,-3) and (2,4).
Since their dot product is zero, then (6,-3) and (2,4) are normal to each other.
Step-by-step explanation:
Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.
These two vectors are also called orthogonal to each other.
Let u = (u₁, u₂) and v = (v₁, v₂), then the dot product u . v is defined as:
u . v = u₁v₁ + u₂v₂
To check whether the vectors are normal to each other, let us check their dot product.
The given vectors are: (6,-3) and (2,4).
Let u = (6, -3) and v = (2, 4), then,
u . v = 6 . 2 + (-3) . 4
= 12 + (-12) = 0
Since u.v = 0, then (6,-3) and (2,4) are normal to each other.
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Find the two consecutive asymptotes, the period (in radians), the phase shift (in radians) and the vertical shift of the function: y = 4csc(5θ - 3π/4)
Answer:
Phase shift = [tex]\frac{3\pi }{5}[/tex]
Vertical shift = [tex]0[/tex]
Step-by-step explanation:
Shift Definition
[tex]\text{For\:}f\left(x\right)=A\cdot g\left(Bx-C\right)+D\text{,\:where\:}g\left(x\right)\text{\:is\:one\:of\:the\:basic\:trig\:functions,\:}[/tex] [tex]\frac{C}{B}\text{\:is\:phase\:shift}[/tex], [tex]D\text{\:is\:vertical\:shift}[/tex]
Here we have
[tex]\left(x\right)=4\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
which can be written in the form [tex]g\left(Bx-C\right)=\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
So comparing the two we get [tex]B=\frac{5}{4}, C=\frac{3\pi }{4},\:D=0[/tex]
Phase shift = [tex]\frac{C}{B} = \frac{\frac{3\pi }{4}}{\frac{5}{4}}[/tex] [tex]= \frac{3\pi }{5}[/tex]
Vertical shift [tex]D = 0[/tex]
help me please!!! will mark brainliest!!
Answer:
2
Step-by-step explanation:
(0,2) is the y-intercept
SR = 18cm, Given that SR:CD = 3:4 Find The Value of the Ratio
The value of the ratio is CD = 24 cm
How to Find The Value of the Ratio?The given parameters are
SR : CD = 3 : 4
SR = 18 cm
Substitute SR = 18 cm in the ratio SR : CD = 3 : 4
So, we have
18 cm : CD = 3 : 4
Express the ratio as a fraction
So, we have
18 cm/CD = 3/4
This gives
CD = 18 cm * 4/3
Evaluate
CD = 24 cm
Hence, the value of the ratio is CD = 24 cm
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a. An undefined term is a term that has been given no formal definition. In geometry, there are three undefined terms that form the basis for the subject. What are those three undefined terms? Do your best to define those terms.
The three undefined terms that form the basis for geometry are:
- Point
- Line
- Plane
What is undefined?The term undefined is often used to refer to an expression that is not assigned an interpretation or a value.
The main three undefined terms of geometry are:
- Point
In geometry, a point has no dimension.
A point is represented by a dot.
The point has no length, width, or thickness.
A dot can be very tiny or very large.
- Line
A line is a straight one-dimensional figure that has a length but does not have a thickness, and it extends endlessly in both directions.
A line is made of a set of points that is extended in opposite directions infinitely.
- Plane
A plane, in geometry, prolongs infinitely in two dimensions.
It has zero thickness, zero curvature, infinite width, and infinite length.
It is also known as a two-dimensional surface.
Thus,
The three undefined terms that form the basis for geometry are:
- Point
- Line
- Plane
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What is the measure of line AD
Morgan spent $42 for a jacket. This was $14 less than twice what she spent for a a pair of jeans. How much were the jeans?
Responses
$28
$28
$21
$21
$22
$22
$31
Please help me please help me
SOMEONE PRETTY PLEASE HELP MEE
The value of x in the angles is 14.
How to find angles when parallel lines are cut by transversal?When parallel lines are cut by a transversal, angle relationships are formed.
The angle relationships that are formed includes corresponding angles, alternate angles, vertical angle etc.
Therefore, the value of x can be found as follows;
m∠1 = m∠7 (vertical angles)
Therefore,
m∠7 = m∠15(corresponding angles)
Hence,
m∠1 = m∠15
m∠1 = 8x - 4
m∠15 = 6x + 24
Therefore,
8x - 4 = 6x + 24
8x - 6x = 24 + 4
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
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Simplify the expression to a polynomial in standard form
(x+6)(3x² + 4x − 3)
Answer:
3x^3 -8*x^2 + 8*x + 3
Step-by-step explanation:
The standard form for a plolynomial is:
a*x^n + b*x^(n-1) + c*x^(n - 2) ........
We have:
(x-1)(3x^2-5x-3)
this is equal to:
3*x^3 - 5*x^2 + 3*x - 3*x^2 +5*x + 3
where the thing that i did is distribute the multiplication
this is equal to:
3x^3 -8*x^2 + 8*x + 3
in 2012 the total value of exports from the United States was $2,210,585,000,000 that year sports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012
The required value of sports imports of the United States in 2012 is $2,745,240,000,000.
.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
the total value of exports from the United States in 2012 = $2,210,585,000,000
Now it is also given that,
the total value of exports from the United States in 2012 = $837,965,000,000 more than half of the US imports
Therefore, we can write
the total value of exports from the United States in 2012 = $837,965,000,000 + imports/2
Putting the value of exports we get,
2,210,585,000,000 = 837,965,000,000 + imports/2
Taking alike terms together we get,
Imports/ 2 = 2,210,585,000,000 - 837,965,000,000
Solving we get,
Imports/ 2 = 1,372,620,000,000
Multiplying by 2 both the side by 2 we get,
Imports = 2,745,240,000,000
Thus, the value of imports of the United States in 2012 = $2,745,240,000,000
Thus, the required value of imports of the United States in 2012 is $2,745,240,000,000.
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The correct question is :
in 2012 the total value of exports from the United States was $2,210,585,000,000 that year exports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012
If x^2 + x = 1
what is (x^5 + 8)/ x+1
The value given expression of (x⁵ + 8)/(x + 1) is (x⁶ + 8x).
What is termed as indices/index?In mathematics, an index (indices) is the power but rather exponent raised to the a number or variable. In number 2⁴, for example, 4 is the index of 2. Indexes is the plural form of index. We encounter constants and variables in algebra. A constant is just a value that cannot be altered. A variable quantity, on the other hand, can be assigned such a number or have its value changed.The given expression is-
(x⁵ + 8)/(x + 1) .......equation 1
It is stated that;
x² + x = 1
Taking x common;
x(x + 1) = 1
Bring x on the other side.
(x + 1) = 1/x
Put the value of (x + 1) in equation 1.
= (x⁵ + 8)/(x + 1)
= (x⁵ + 8)/[1/x]
Simplifying;
= (x⁵ + 8)x
Multiplying x on both values;
= x⁵x + 8x
= x⁶ + 8x
Thus, the value of the given expression is (x⁶ + 8x).
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Point G is the center of the small circle. Point X is the center of the large circle. Points G, H, and X are all on line segment GX.
what should be the area of a new circle that has a line segment GX as the diameter
The area of a new circle that has line segment GX as its diameter is 121 pi cm² .
Suppose that,
The radius of the small circle (GH) = 10 cm.
The radius of the big circle (HX) = 12 cm.
We will add the line GH and HX to get the total length of line segment GX.
So, GX = GH + HX
= 10 + 12
GX = 22 cm.
So, the diameter of new circle will be equal to line segment GX as it is given in the question.
Then, the area of new circle = π r² ( r = radius)
Radius = D/2 = 22/2 (D = Diameter)
r = 11
Now, Area = π × 11²
= 121π cm²
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numbers like 2%, 3%, 4% and 6% are often used to represent the grade of a road. such a number tells how steep a road is. 3% grade means that for every horizontal distance of 100 ft, the road rises or descends 3 feet. in each of the following cases, find the road grade to two decimal places.
(a) Grade = 2.86%
(b) Grade = 5.85%
What is the horizontal distance?The projectile's horizontal range is the distance it travels while in flight. Since there is no acceleration in the horizontal direction, the greatest distance traveled in the horizontal direction is what this definition means.Vertical distance is the distance following the direction of gravity, and horizontal distance is the distance along the ground surface. The distance between a building and the observer is an example of a horizontal distance, and the building's height is an example of a vertical distance.Anything that forms a 90-degree angle (right angle) with the horizontal or the horizon is referred to as vertical because it is the opposite of the horizontal. The line that spans from left to right is therefore considered horizontal.By the angle's tangent, multiply the object's height. Let's assume, for the purposes of this illustration, that the item is 150 feet tall. The product of 150 and 1.732 is 86.603. 86.603 feet separate you from the thing horizontally.Find the road grade to two decimal places:
Grade in terms of percentage = (rise/run) * 100%
(a) Grade = (40/1400) * 100% = 2.86%
(b) Grade = 5.85%
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I need help with this
The first 4 terms of the geometric sequence are 12 , 36 , 108 and 324.
In a geometric sequence, each term following the first is found by multiplying the preceding one by a constant, non-zero quantity known as the common ratio.
The nth term of a geometric series with first term a and common ratio r is given by [tex]a_n=ar^{n-1}[/tex] .
Given the first term of the geometric sequence is 12 .
And given [tex]a_n=a_{n-1}\times 3[/tex]
Now using the above formula:
a₂ = a₁ × 3
or, a₂ = 12 × 3 = 36
Again using the above formula:
a₃ = a₂ × 3
or, a₃ = 36×3 = 108
Similarly
a₄ = a₃ × 3
or, a₄ = 108 × 3 = 324
Hence the first four terms of the geometric sequence are 12 , 36 , 108 and 324 .
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You are given that f(x)=x²+4 and g(x)=3 x-1 .
a. What are the domain and range of f(x) and g(x) ?
The domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .
Domain : The set of all the possible values of x is called domain of the function .
Range : The set of all the possible values of y is called the range of the function .
Given : f ( x ) = [tex]x^{2}[/tex] + 4 , g ( x ) = 3 x - 1 .
To find : Domain and Range of functions .
f ( x ) = [tex]x^{2}[/tex] + 4
Domain = R ( real nos. )
Range = y ≥ 4 .
g ( x ) = 3 x - 1
Domain = R ( real nos. )
Range = R ( real nos. )
Therefore , the domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .
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Solve the following radical equations.
√(x+3) = 4√x-2
The solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.
The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
Eliminate the radical on the both sides by squaring on both sides-
Both sides must be raised to the second power.
√(x+3) ²=(4√x-2 )²
After squaring we get
x+3=16(x-2)
Solving the equation-
We get rearranged equation as :
x+3=16x-32
15x=35 x=35/15 which further reduces to 7/3 .
Check if the solution is correct by putting it in original equation-
putting x=7/3 in the equation √(x+3) = 4√x-2
we get √16/3=√16/3
Therefore, the solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.
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Can anybody answer and simply this. (-8) × (-6)-(-5)²
Step-by-step explanation:
[tex] = - 8( - 6) - (25) \\ = 48 - 25 \\ = 23[/tex]
HOPE THIS HELPS!!
18
Kylie recorded the number of pears on a pear tree at the end of every week. The following function represents the number of pears on
the pear tree, where x represents the number of weeks.
Which statement is true?
A. The number of pears on the tree doubles each week.
B.
P(x) = 2(2+x)
O D.
The number of pears on the tree increases by 2 each week.
OC. The number of pears on the tree quadruples each week.
The number of pears on the tree increases by 4 each week.
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Based on the given function on the number of pears on the pear tree, the true statement is that The number of pears on the tree increases by 2 each week.
How to find the meaning of function?A linear regression line takes the form:
y = mx + b
y = number of pears
m = change in the number of pears per week
x = number of weeks
b = number of pears at first week
When the function is converted to a linear regression form, it takes the form:
P(x) = 2(2+x)
P(x) = 4 + 2x
This shows that the change in the number of pears per week is 2. This means that the number of pears on the tree increases by 2 each week
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what is the value of this equation?:
[tex]( \sqrt[3]{9} )^{2} \times ( \sqrt{30} ^{2}[/tex]
Answer:
Step-by-step explanation:
When we apply the exponent rule: [tex](\sqrt[n]{x})^n = x[/tex]
[tex](\sqrt[3]{9})^2 * (\sqrt{20})^2 = 30(\sqrt[3]{9})^2[/tex]
[tex]= \mathrm{Decimal:\quad }\:129.80246\dots[/tex]
Solve each equation.
2y+1=25
Solution of this polynomial equation is y = 12
What is a polynomial ?In mathematics, simply polynomial or polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2y+52 x + 1 =253x² + 5x+19(x-3)³According to question,
2y+1=25
=> 2y +1 -1 = 25-1
=> 2y = 24
=> y = 12
Thus solution for given equation is y=12.
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does anyone know how to do this question?
The diameter of the given sphere is; 39.5 cm
What is the Volume of the Sphere?
The formula for Volume of Sphere is;
V = 4/3 πr³
where;
V is volume
r is radius
We are given; V = 32250 cm³
Thus;
4/3 πr³ = 32250
Make r the subject of the formula to get;
r = ∛((32250 * 3/4)/π)
r = ∛7699.12
r = 19.75 cm
Now, radius * 2 = diameter
Thus; diameter = 2 * 19.75 = 39.5 cm
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Which angles are complementary to each other?
Answer:
C. <3 and<4
Step-by-step explanation:
Complementary angles are angles whose two angles make the sum 90°.
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