The value of f –1(13) is 4
How to determine the inverse value?The table of values is given as:
x –4 0 2 5 9 13
f (x) –11 1 7 16 28 40
A linear function is represented as:
y = mx + b
Where b represents the y-intercept and m represents the slope
From the graph, when x = 0, y = 1.
This means that b = 1
So, we have
y = mx + 1
Also from the graph, when x = 2, y = 7.
So, we have:
7 = 2m + 1
Subtract 1 from both sides
7 - 1 = 2m + 1 - 1
Evaluate the difference
6 = 2m
Rewrite the above equation as:
2m = 6
Divide both sides of the equation by 2
m = 3
Substitute m = 3 in y = mx + 1
y = 3x + 1
The notation f –1(13) implies that y = 13
So, we have
13 = 3x + 1
Subtract by 1
3x = 12
Divide by 3
x = 4
Hence, the value of f –1(13) is 4
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2. Find the value of x in the triangle. Round your answer to the nearest tenth of a degree. Show your work.
In the above case which involves a Pythagorean Triangle, using the trigonometric function TOA to solve we get: 61.93°
TOA is the acronnum for:
Tangent (θ) = Opposite /Adjacent
Tangent (θ) = 8/15
θ = Tan⁻¹ 0.5333333333
Thus
θ = 61.93°
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Find the answer for this equation
Consider units digit as u and tens digit as t, so t=1/2 u is the right equation.
What is the answer for the equation?Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.
given : t + u=9
1/2u+u=9 by substituting the value of t
3u=18
u=6.
t=1/2*6=3.
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A triangular prism has a base that is an isosceles right triangle with sides ,9 ,9 and 12.7. The height of the prism is . What is the surface area of this prism
The surface area of the triangular prism is 55.8 units²
What is Triangular PrismA triangular prism is a three-dimensional shape with two triangular faces and three rectangular faces. It is also known as a tetrahedron, which is a type of polyhedron with four faces. The triangular prism has a total of six faces and nine edges.
The formula of surface area of triangular prism is given as;
S.A = 2A + PH
A = Area of triangular baseP = perimeter of triangleH = height of triangleThe base area of the prism is given as;
A = 1/2 (b * h)
A = 1/2 * (9 * 14)
A = 63 units²
The perimeter of the triangle is the sum of all the sides.
This is calculated as P = a + b + c
P = perimeter = 9 + 9 + 12.7 = 30.7 units
Surface Area = 2(63) + 30.7 * 14
Surface Area = 55.8 units²
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Complete Question:
A triangular prism has a base that is an isosceles right triangle with sides 9 ft, 9 ft, and 12.7 ft. The height of the prism is 14 ft. What is the surface area of this prism.
Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use. If the police team stops 30 cars during the first hour, what is the standard deviation?
If Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use. If the police team stops 30 cars during the first hour, the standard deviation is 2.191.
How to find the standard deviation?Using this formula to find the Standard deviation
Standard deviation = √ Sample size × Estimated drivers × (1 - Estimated drivers)
Let plug in the formula
Standard deviation = √ 30 × 0.20 × (1- 0.20)
Standard deviation = √ 30 × 0.20 × 0.80
Standard deviation = √ 4.8
Standard deviation = 2.191
Therefore we can conclude that the standard deviation is 2.191.
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What is an equation of the line that passes through the point (6,-4)(6,−4) and is perpendicular to the line 2x-y=52x−y=5?
The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.
What are straight-line equations?The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).
The variables x and y are related to coordinates on the line in the linear equation y = mx + c.
The formula y = mx + c yields a result for y when we enter a value for x.
As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.
According to our question-
a line equation that is perpendicular to the line 2xy=5 and passes through the point (6, 4)
The slope of the given equation 2x-y=5 is first determined.
The line's equation is y=mx+b. where'm' represents the slope
Hence, The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.
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A computer can do a computation in 6.8 x 10-9 seconds? How many computations can the computer do in 5 minutes
Answer:
≈[tex]4.4117647059\times10^{10}[/tex] computations in five minutes.
Step-by-step explanation:
[tex]\frac{5*60}{6.8\cdot10^{-9}}[/tex] = [tex]4.4117647059\times10^{10}[/tex].
Proof in the image.
Please mark brainliest so I can get to the expert rank (only 10 to go!)
how many groups of 1/4 are in 7
Answer:
28
Step-by-step explanation:
28 groups of 1/4 goes into 7
Answer:
28
Step-by-step explanation:
This is a division problem.
7 ÷ 1/4 =
= 7/1 ÷ 1/4
= 7/1 × 4/1
= 28/1
= 28
Answer: 28
You can also solve it this way.
There are 4 1/4's in 1.
In 7, there must be 7 times as many 1/4's.
7 × 4 = 28
Answer: 28
StarWatch Camping Site
The holiday is just 9 weeks away and they
each plan to save £13 per week from now
Charge per person: £6 per night
until their holiday.
Will they save enough money to cover all
Tent pitch:
≤ 10 mª at £15 per night
their camping site charges?
(ground surface)
If the answer is 'yes' say how much extra
>
10 mª at £18 per night
money they will save.
You must show all your working.
Special offer:
For
every 5 nights you
stay, only pay for 4.
Lila and Wassim are planning a stay
at the StarWatch camping site.
They will:
share a tent between them,
both stay for a total of 10 nights,
use a tent with a rectangular base
measuring 2.3 by 4.2 metres.
Answer:
The total cost of their stay at the StarWatch camping site will be £108. This includes the special offer of 5 nights for the price of 4.
Lila and Wassim have saved £130 by the time of their holiday. This means they have saved £22 extra.
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of d feet below the surface, is given by the following equation:
P = 16+4d/9
If a scientific team uses special equipment to measures the pressure under water and finds it to be 172 pounds per square foot, at what depth is the team
making their measurements?
Answer: The team is measuring at ???? feet below the surface.
Therefore , the solution of given problem of equation comes out to be
P is equal to 12 pounds per square foot.
Define equation.Comparable to a balance scale, an equation. The equation (or scale) is out of balance if we add or subtract variable from one side. We also Must keep the "scale" (or equation) balanced while solving math equations such that both parts are always equal as expression are equal.
Here,
P= p = 12 + 4/9d is the equation that describes the relationship between the pressure,
p, of sea water in some deep ocean regions and the depth, d, below the surface.
Where
In pounds per square foot, p.
in feet is d
1) At a depth, seawater has a pressure of 85 pounds per square foot.
85 = 12 + 4/9d
4.9d/9 = 85 - 12 = 73
By xing it out, it becomes
4.9d = 73 × 9 = 657
d = 657/4.9
d = 134.1 feet
2) At 85 feet just below water's surface, the pressure of saltwater is
p = 12 + 4/9 × 85 = 12 + 4/765
P is equal to 12 pounds per square foot.
Therefore , the solution of given problem of equation comes out to be
P is equal to 12 pounds per square foot.
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11
Stephen is n years old.
Rachel is 10 years older than Stephen
(a) Write an expression for Rachel's age.
Tim is 13 years younger than Stephen.
(b) Write an expression for Tim's age.
Juil
neb
13
12
inotdan ni
(c) Write an expression for the total age of Stephen, Rachel and Tim.
nt
2
Find an explicit formula for the geometric sequence 3\,,\,15\,,\,75\,,\,375,...3,15,75,375,...3, comma, 15, comma, 75, comma, 375, comma, point, point, point.
Note: the first term should be \textit{a(1)}a(1)start text, a, left parenthesis, 1, right parenthesis, end text.
a(n)=a(n)=a, left parenthesis, n, right parenthesis, equals
The explicit formula for this geometric sequence 3, 15, 75, 375... is aₙ = 3(5)ⁿ⁻¹.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Note: The nth term of a geometric sequence is equal to the explicit formula for the geometric sequence.
Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = 15/3
Common ratio, r = 5.
Now, we can calculate the nth term (explicit formula) of this geometric sequence as follows:
aₙ = a₁rⁿ⁻¹
aₙ = 3(5)ⁿ⁻¹
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Complete Question:
Find an explicit formula for the geometric sequence 3, 15, 75, 375...
A student graphed f(x) = x and g(x) = f(x) - 5 on
the same coordinate grid. Which statement
describes how the graphs of f and g are related?
A The graph of f is shifted 5 units up to create the
graph of g.
B The graph of f is steeper than the graph of g.
C The graph of f is shifted 5 units down to create
the graph of g.
D The graph of f is less steep than the graph of g.
The statement (c) describes that the graph of f is shifted 5 units down to create the graph of g. The solution has been obtained using the concept of vertical translation.
What is translation?
Translation is the act of moving a shape or a figure from one position to another. It is classified into two types:
Horizontal Translation: This describes the movement of a function graph to left or right.Vertical Translation: This describes the movement of a function graph upward or downward.Now, for a function f(x) we define a vertical translation of N units as:
g(x) = f(x) + N
If N is positive, the translation is upwards.
if N is negative, the translation is downwards.
We are given g(x) = f(x) - 5
This shows that N is negative and therefore, there is translation of 5 units downwards.
Hence, the graph of f is shifted 5 units down to create
the graph of g.
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Reasoning with linear equations
We can rewrite one side of the given equation using distributive property.
What is distributive property?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each term enclosed in a bracket multiplies the number outside of it, and the results are added.
The given equation is: 3(x + 2) = 18
Simplifying this,
3*x + 3*2 = 18
3x + 6 = 18
Hence, we can rewrite one side of the given equation using distributive property.
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is 6.26 number types
The graph of the function f shown in the figure above has horizontal tangents atx=3 and x=6. Ifg(x)=∫02xf(t)dtwhat is the value ofg′(3)?(A) 0 (B)−1(C)−2(D)−3(E)−6
The horizontal tangents at x=3 and x=6 on the graph of the function f are shown in the given image. If [tex]g(x)=\int\limits^{2x}_0 {f(t)}\;dt[/tex], then g'(3) is -2. Then, option (C) is correct.
A function's zero slopes is indicated by a horizontal tangent line that runs parallel to the x-axis. The given graph of function f has horizontal tangents at x =3 and x = 6. Then, the given function is [tex]g(x)=\int\limits^{2x}_0 {f(t)}\;dt[/tex]. Then, we have to find g'(3). It is clear from the graph that f(3) = -3 and f(6) = -1.
Then, applying the Leibnitz rule for differentiation of the given function, we get,
[tex]\begin{aligned} g(x) &= \int^{2x}_0 f(t)\;dt\\g'(x)&=f(2x)\cdot\frac{d}{dx}(2x)-f(0)\cdot\frac{d}{dx}(0)\\&=2f(2x)\end{aligned}[/tex]
Now, substituting x = 3 in the above equation, we get,
[tex]\begin{aligned}g'(3)&=2f(2\times3)\\&=2f(6)\\&=2\times -1\\&=-2\end{aligned}[/tex]
The required answer is -2.
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How do the interior and exterior angles of a polygon relate? *
They are congruent
O They are supplementary
O They are complementary
There is no relations
The relationship between the interior and exterior angles of a polygon is they are supplementary.
What is a regular polygon?
If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.
Here,
we have to show how the interior and exterior angles of a polygon relate to each other.
A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.
As a result, the interior angles of a regular polygon are all equal to 180 degrees minus the measure of the exterior angle(s).
Hence, the relationship between the interior and exterior angles of a polygon is they are supplementary.
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Determine the total flops as a function of the number of equations n for the decomposition, forward-substitution, and back-substitution phases of the LU decomposition version of Gauss elimination.
The total flops as a function of the number of equations n for the LU decomposition version of Gauss elimination is given by (n^3 + 3n^2)/3.
The LU decomposition version of Gauss elimination involves 3 phases which are :
decomposition forward-substitution back-substitution.The flops in decomposition phase is (n^3)/3, forward-substitution phase is n^2 and back-substitution phase is 2n^2. By adding all the flops for these 3 disinct phases we get (n^3 + 3n^2)/3 as total flops as a function of the number of equations n for the LU decomposition version of Gauss elimination.
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what is the slope of the line -3y=12x+6
Answer:
Step-by-step explanation:
uhh
enter the correct 4 digit code
The code is 4321.
A = 4
B = 3
C = 2
D = 1
a salad dressing recipe uses 10 parts oil,4 parts vinegar,and 2 parts honey.Which of the following sets of ingredients are in a proportional relationship with the recipe?select all that apply.
According to the information, the sets of ingredients that have a proportional relationship with the original recipe are: option A, C and D.
How to check the proportional relationship of the ingredients with the recipe?To check the proportional relationship of the ingredients with the recipe we must carry out the following procedure.
Option A.
First, we need to establish how many times 6 is in 12 because this recipe includes 6 parts oil and the original recipe includes 12 parts oil.
12 / 6 = 2Once we identify this number, we must divide the amounts of the original recipe by 2 to identify if the other values are correct.
3 / 2 = 1.52 / 2 = 1In accordance with the above, option 1 would be proportional to the main recipe. For the other options we must perform the same procedure:
In the case of case C. we identify that 24 is twice 12, so we would have to multiply each ingredient by 2 to check the proportional relationship
3*2=62*2=4In the last case (option D), we identify that the proportion is 3/4 with respect to the original recipe, so we must carry out the same procedure keeping this proportion in mind.
12 / 4 = 33*3=93 / 4 = 0.750.75 * 3 = 2.252 / 4 = 0.50.5 * 3 = 1.5Note: This question is incomplete because there is some information missing. Here is the complete information:
Attached image
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what is the difference from C to D
The difference between points C and D is √289 units.
What is Distance formula?
The distance formula is a mathematical formula used to determine the distance between two points in a plane. The formula is:
d = √((x2 - x1)² + (y2 - y1)²)
"C" and "D" are points in a two-dimensional coordinate system. C is represented by the coordinates (-1, 11) and D is represented by the coordinates (7, -4).
The difference between these two points is the distance between them, which can be calculated using the distance formula:
√((x2 - x1)² + (y2 - y1)²)
Where x1, y1 are the coordinates of point C and x2, y2 are the coordinates of point D.
Substituting the values, we get:
√((7 - (-1))² + (-4 - 11)²) = √((8)² + (-15)²) = √(64 + 225) = √289
Hence, the difference between point C and D is √289 units.
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Hi if anyone can answer that would be great thanks!
The value of GL is 161.We can find by using supplementary angles.
What is supplementary angle with example?Supplementary angles are those angles that sum up to 180 degrees. For example angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.There are a total of two supplementary quantities and their units.
How do you find supplementary angles?The sum of two angles is equal to 180° then they are supplementary angles. Each of the angles is said to be a supplement of another angle. Hence we can determine the supplement of an angle by subtracting it from 180°.
Now
According to supplementary angles
GL + LK =180
GL =180- LK
GL = 180 -19
GL = 161
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Situation: Rocco jogs and then walks at the park. Today, he has already jogged 4 miles.
He then starts counting the miles he walks at a constant rate of 3 miles every
2 hours. What is the total distance Rocco travels at the park?
1) Equation:
Where x is:
Where y is:
2) Fill in all empty cells
in the table of values.
3) Proportional or
nonproportional:
Part 1: Where x is: time in hours. Where y is: distance in miles.
Part 2: The table is filled for the values of time and distance.
Part 3: y/x is fixed equation is proportional.
Explain the term total distance?Total distance refers to the actual travel distance between the origin and destination locations of the material.
The formula for the distance is:
Distance = speed * time
Part 1:
The equation formed for the stated condition is:
y = 3x.
Where x is: time in hours.
Where y is: distance in miles.
Part 2: The table is filled for the values of time and distance.
Part 3:
For the equation.
y = 3x.
x = 1, y = 3 : y/x = 3
x = 2, y = 6 ; y/x = 3
As, y/x is fixed equation is proportional.
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The complete question with table is attached.
A smoking cessation program was organized for 623 employees of a company, and 216 successfully stopping smoking. What was
the approximate ratio of successes to failures?
A) 1 to 2
B) 2 to 3
C) 3 to 1
D) 4 to 2
Answer:
A) 1 to 2
Step-by-step explanation:
Total number of people: 623
Successes: 216
Failures: 623 - 216 = 407
Ratio of successes to failure = 216/407
Since 216 is approximately half of 407, the ratio is approximately 1/2.
Answer: A) 1 to 2
Select each expression that has a difference of 4 3/12 
Answer:
Step-by-step explanation:
9 7/12 - 5 4/12 = 4 3/12
michael and martha run a mechanic shop. in one hour michael can perform eight oil changes or change ten tires. in one hour martha can perform seven oil changes or change fourteen tires. michael and martha have the same amount of resources. given this information which of the following is true?
Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.
Absolute advantage refers to the ability of a country or firm to produce a good or service at a lower cost than another country or firm. It is a concept in international trade and economic theory.
A country or firm has an absolute advantage in a good or service if it can produce that good or service more efficiently than another country or firm.
An individual has a comparative advantage in production if it produces at a lower opportunity cost when compared with other individuals.
The opportunity cost of Michael in the changing of oil = 10/ 8 = 1.25
Opportunity cost of Michael in changing tyres = 8 / 10 = 0.8
The opportunity cost of Martha in the changing of oil = 14 / 7 = 2
The opportunity cost of Martha in the changing of tyres = 7 / 14 = 0.5
Michael has an opportunity cost in changing of oil and Martha has an opportunity cost in changing of tyres.
Absolute advantage is when an individual produces more quantity of a good or service when compared to others.
So, Michael changes more oil (8) than Martha (7). Martha changes more tyres (14) than Michael (7)
Therefore, Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.
The complete question is:
Michael and Martha run a mechanic shop. In one hour Michael can perform eight oil changes or change ten tires. In one hour Martha can perform seven oil changes or change fourteen tires. Given this information which of the following is true?
A) Martha has a comparative advantage in changing oil.
B) Martha has an absolute advantage in changing oil.
C) Michael has a comparative advantage in changing tires.
D)Michael has an absolute advantage in changing tires.
E.) Michael has an absolute and a comparative advantage in changing oil
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Answer the picture below
Jim spent a total of $125.15 for the 130 miles he traveled in one day at the $14.95 base fee.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to signify equivalence. A mathematical statement demonstrating the equality of two mathematical expressions is the definition of an equation in algebra. For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two phrases on either side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.
given
per mile the cost is $0.85
Base fee is 14.95
0.85x+14.95= 125.15
0.85x=125.15 - 14.95
0.85x = 110 . 92
x= 110 . 92 / 0.85
x= 130. 49
Jim spent a total of $125.15 for the 130 miles he traveled in one day at the $14.95 base fee.
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NEED SOMEOEN THAT KNOWS PRE CALC The endpoints of a diameter of a circle are (7,−4) and (−3,2).
What is the equation of the circle in standard form?
Enter your answer by filling in the boxes. Enter any fractions in simplified form.
(x-2)² + ( y + 1)² = 34 is the equation of the circle in standard form.
What is the short definition of a circle?
To put it simply, a circle is a spherical shape without any edges or line segments. In terms of geometry, it has the shape of a closed curve.
The circle's points are set apart from the center by a predetermined amount.
The endpoints of the diameter (7,−4) and (−3,2)
the center of the circle is the midpoint of the diameter.
So, the coordinates of the center
(h,k) = ( 7 + (-3)/2 , -4 +2/2)
= ( 4/2 , -1 )
= ( 2 , -1 )
the radius of the circle is just half of the length of the diameter.
So, r = 1/2√(-3 -7 )² + ( 2 - (-4))²
= 1/2√(10)² + ( 2 +4 )²
= 1/2√100 + 36
= 1/2√136
= √136/2
= 2√34/2
= √34
substitute the values of h, k, and r into the standard equation of the circle
( x-h)² + ( y-k)² = r²
( x - 2)² + ( y -(-1))² = (√34)²
(x-2)² + ( y + 1)² = 34
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Linda bought a washer and dryer from Mill page Laundry Supplies for y dollars. She signed an installment agreement requiring a 15% down payment and monthly payments of dollars for one year.
a) Her down payment algebraically is 0.15y (b). number of monthly payments must Linda make12 months (c) The total amount of the monthly payments algebraically is 12x (d) The first term a
and the common ratio d a1 = 0.15y, d = x (e) The total amount Linda pays for the washer and dryer on the installment plan algebraically is 12x + 0.15y (e) the finance charge algebraically (12x + 0.15y) - y = 12x - 0.85y
How to solve the problems?The given parameters that will help us get the solutions are
If y = cost of washer and dryer
x = cost for one month.
Down payment = 0.15y
Numbers of months = 12months
Amount of monthly payment = 12x
First term and common ratio = a1 = 0.15y and d = x
Total amount for washer and dryer 12x + 0.15y
Finance charge
(12x + 0.15y) - y
12x - 0.85y
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Complete question:
2. Linda bought a washer and dryer from Millpage Laundry Supplies for y dollars. She signed an
installment agreement requiring a 15% down payment and monthly payments of x dollars for one
year.
a. Express her down payment algebraically.
b. How many monthly payments must Linda make?
c. Express the total amount of the monthly payments algebraically.
d. If Linda models her payment plan as an arithmetic sequence, give the first term a
and the common ratio d
e. Express the total amount Linda pays for the washer and dryer on the installment plan
algebraically.
f. Express the finance charge algebraically.
A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S 41° W. From a tree x = 90 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively. Find the distance from the gazebo to the dock. (Round your answer to the nearest whole number.)
Solving the triangle we found the distance between the gazebo and the dock is: 69.34 meters. The answer is explained below:
Solving the triangle:The first thing to know is that to solve any triangle you must know at least one side and two other elements that can be sides or angles, that is, at least three elements of the six that make up a triangle.
Now, in the problem we know the value of one side (90 m) and 3 angles (see attached image), therefore the calculation of the distance (one side) is very easy if we apply the law of sines:
According to the Law of Sines, the ratio of the length of the sides of a triangle (not a rectangle) and their respective opposite angle sines, is the same value. Then:
Unknown variable = distancia (d)Opposite angle = 46°d / sen (46°) = 90 m / sen (69 °)
After, we pass sen (46°) to the second term of the equation.
d= sen(46°)*90 m / sen (69°)
d = 0,7193*90/ 0,9335
d = 69,34 m
To learn more about solving triangles see: https://brainly.com/question/25215131
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