On solving the provided question we can say that here, trigonometry, f(x) = -7cos(1x) + -3 => f(1) = -7
What exactly is trigonometry?Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.
Trigonometry is used here.
f(x) = -7cos(1x) plus -3
f(1) = -7
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the function of G takes a student's first name for its input and gives the number of letters in the first name for its output
Describe the meaning of G(jada)=4
Find the value of G(Diego).
Answer:
Step-by-step explanation:
The meaning of the function notations are
G(Jada) = 4 means that the first name Jada has four letters
C(11-15)= chemistry means that the Monday class for 11-15 is chemistry
How to interpret the function notations?
The meaning of the function G
From the question, we have the following parameters that can be used in our computation:
Function G gives the number of letters in the first name for its output.
Next, we have
G(Jada) = 4
Using the meaning of the function, we have
G(Jada) = 4 means that the first name Jada has four letters
The meaning of the function C
From the question, we have the following parameters that can be used in our computation:
Function C gives a student's Monday class for its output.
Next, we have
C(11-15)= chemistry
Using the meaning of the function, we have
C(11-15)= chemistry means that the Monday class for 11-15 is chemistry
The regular price of an Apple Watch is $199. The watch is on sale for 15% off. Which expression is equal to the sale price in dollars, of the Apple Watch
Answer: $169.15
Step-by-step explanation: 15 percent of 199 is 29.85, and 199-29.85 is 169.15
The radius of a circle is 14 meters. What is the circle's circumference?
Answer: 87.96m
Step-by-step explanation:
Circumference of a circle = 2[tex]\pi[/tex][tex]r^{2}[/tex] --> 2[tex]\pi[/tex]14² = 87.96m
6. Application Juanita, who is 1.82 meters tall, wants to
find the height of a tree in her backyard. From the
tree's base, she walks 12.20 meters along the tree's
shadow to a position where the end of her shadow
exactly overlaps the end of the tree's shadow. She is
now 6.10 meters from the end of the shadows. How
tall is the tree?
The height of tree is 9.9372.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
ΔABC ~ ΔDEF only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.
Given;
Juanita is 1.82 meters tall
From the tree's base, she walks 12.20 meters along the tree's shadow to a position where the end of her shadow.
She is now 6.10 meters from the end of the shadows.
Now,
Let, h be the height of the tree;
Here, ΔABC ~ ΔADE,
So, DE/BC = AD/AB
h/1.82 = (6.10 + 12.20)/6.10
h/1.82= 18.30/6.10
h=33.306/6.10
h=5.46
h = 1.82*5.46
= 9.9372
Therefore, by congruency of triangle the answer will be 9.9372.
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three more than product of 15 and a number n is 153. wright an equation that describes this situation
The equation that describes this situation is, 3 + 15n = 153
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
Given that,
Three more than product of 15,
And a number n is 153.
More than = + (addition)
Product = x (multiplication)
Product of 15 and n = 15 x n = 15n
Therefore, the equation is 3 + 15n = 153.
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Rob loves to run. He set a goal to run more than 390 miles this year.
To date, he has run 127 miles. If he begins to run 18 miles per week,
how long will it take Rob to reach his goal?
Write a two-step inequality, using the values provided in the problem,
that represents this situation. Use x as the variable.
The linear inequality to represent given situation will be 127+18x≥390 where x=no. of weeks and he will take 14.6 weeks to reach his goal.
What is a linear inequality, exactly?
In mathematics, an inequality is a mathematical statement that does not have equal sides. In mathematics, an inequality occurs when a connection results in a non-equal comparison of two expressions or two numbers. In the statement, any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), can be used to replace the equal sign "=". Inequalities are grouped into three forms in mathematics: polynomial inequalities, rational inequalities, and absolute value inequalities.
The symbols " <and >" represent severe disparities, whereas " ≤ and ≥ " represent slack inequalities. A linear inequality resembles a linear equation, but the formula is different.
Now,
Total miles to run=390 mile
He already ran=127 mile
Distance left to run=390-127
=263 mile
Rate of running=18 miles/ week
weeks taken to complete 263 miles=263/18
=14.6 weeks
and given situation can be represented by inequality 127+18x≥390 where x=no. of weeks.
Hence,
The linear inequality to represent given situation will be 127+18x≥390 and he will take 14.6 weeks to reach his goal.
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What is the x-intercept of this equation? 3x + 5y = 9
To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).
What is x-intercept ?
An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.
To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.
So, we have:
3x + 5(0) = 9
3x = 9
x = 3
Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).
To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.
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Sketch an angle θ in standard position such that θ has the least possible positive measure and the point (−3,4) is on the terminal side of θ. Then find the exact values of the six trigonometric functions for θ.
To sketch the angle θ in standard position, you can start by plotting the point ( -3, 4 ) on the coordinate plane. Next, you draw a line from the origin ( 0, 0 ) to the point ( -3, 4 ), which represents the terminal side of the angle.
Now, you can use the six trigonometric functions to find the exact values for θ:
Cosine ( cos θ ) = x / r = -3 / 5
Sine ( sin θ ) = y / r = 4 / 5
Tangent ( tan θ ) = y / x = 4 / -3
Secant ( sec θ ) = 1 / cos θ = -5 / 3
Cosecant ( csc θ ) = 1 / sin θ = -5 / 4
Cotangent ( cot θ ) = 1 / tan θ = -3 / 4
Here, r represents the distance from the origin to the point ( -3, 4 ), which is 5 units. Note that these values are for the least positive measure of the angle, which is in the second quadrant.
Consider the following function.
f(x)= |x+5|, x>-5
Find the inverse function f-¹.
I
f-¹(x) =
State the domain and range of f. (Enter your answers using interval notation.)
domain
range
State the domain and range of f-1. (Enter your answers using interval notation.)
domain
range
Inverse function for the function f(x)= |x+5|, x>-5 is f⁻¹(x) = -5 ± x
What is inverse function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.
Given function,
f(x) = |x + 5| , x>-5
It can be written as
y = |x + 5|
Replacing x with y
x = |y + 5|
Solving for y
y + 5 = ± x
y = -5 ± x
Replacing y with f⁻¹(x)
f⁻¹(x) = -5 ± x
Hence, f⁻¹(x) = -5 ± x is the inverse function for function f(x)= |x+5|, x>-5
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How can using a 'Polygon Family Tree' help you to classify 2D figures into a hierarchy of sets and subsets?
Closed, two-dimensional shapes known as polygons are created by three or more-line segments that only meet at their ends.
What are plane figures?A figure that totally resides in one plane is referred to as a plane figure or a two-dimensional figure. Two-dimensional figures are drawn when you sketch, whether by hand or with a computer programme. Two-dimensional models of actual objects can be found in blueprints.
Closed, two-dimensional shapes known as polygons are created by three or more-line segments that only meet at their ends.
How do you classify 2D figures?Circles, triangles, squares, rectangles, pentagons, quadrilaterals, hexagons, octagons, and other basic 2D shapes include these. All shapes—aside from the circle—are categorized as polygons because they have sides. Regular polygons are those with equal sides and angles on all of their faces.
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2. The area of a garden plot can be represented by
the expression 85.2z - 58.8. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.
The expression that represents the area of each section is 14z-9
How to find the expression?The expression to denote the area of each section would be: 14z -9
Given that,
The expression for the area of plot area 84z -54
The number of equal sections in which it is divided 6
To find,
The expression for each section = ?
The area of each section = (total area of the garden(/number of equal sections
= (84x-54)/6
= 6(14z-9)/6
=14z - 9
Thus, is the expression that would represent every section's area.
One model of cars comes with 4 choices
of audio systems, 2 choices of roof
styles (with or without moon roof), and
3 choices of seat covers (cloth, vinyl, or
leather). How many different car
ala
models does a customer have to choose
from if the customer can choose one
10
type of audio system, one style of roof,
and one type of seat cover
A customer has 4 x 2 x 3 = 24 different car models to choose from if the customer can choose one type of audio system, one style of roof, and one type of seat cover.
Use the general slicing method to find the volume of the following solid.
The solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares.
The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units
The radius of the base = 4 units
The length of the side of the square = 2x
The area of the square = a^2
Where a is side of the square
The area of the square = (2x)^2
= 4x^2
The equation of the circle is
x^2 + y^2 = 16
x^2 = 16 - y^2
The area = 4(16 - y^2 )
= 64 - 4y^2
The volume of the square
V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]
= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]
= 64×4 - 4×(4^3/3)
= 256 - 256/3
= 512/3 cubic units
Therefore, the volume of the solid is 512/3 cubic units
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Graph the following system of inequalities below and shade the feasible region.
y > -1
y≥ x²+ 1
(x-1)²+(y-1)² ≤ 16
(4marks)
The graph of the system of the equation y > -1, y≥ x²+ 1, and (x-1)²+(y-1)² ≤ 16 is attached with the feasible region of each part shaded
How to identify the graphs
The equation y > -1 is a horizontal line drawn at point y = -1 and shaded above the line because the sign is greater than. the line is dashed line line since the equation is not "greater than or equal to".
The equation y ≥ x²+ 1 is a parabolic equation
The equality sign attached to the greater than makes the line a solid line and because it is greater than the shading is inside the curve.
The equation (x - 1)² + (y - 1)² ≤ 16 is a equation of a circle
The equality sign attached to the greater than ("greater than or equal to") makes the line a solid line and because it is greater than the shading is inside the circle
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How do I do these questions ??
50 3/5 ft subtract 48 1/3 =
The substraction of 50 3/5 ft and 48 1/3 can be expressed as34/15.
How can the substraction be determined?The concept that will be used here is substraction. One of the four operations used in mathematics, along with addition, multiplication, and division, is substraction. Removal of items from a collection is represented by the operation of subtraction. For instance, the adjacent image shows 5 2 peaches, which are 5 peaches with 2 peaches subtracted, for a total of 3 peaches.
50 3/5 ft - 48 1/3 =
this mixed numbers can be converted to fractions as
253/5 - 145/3
= 34/15
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8. The ratio of x to y is 7 to 18. If the value of x is 49, then what is the value of y? (A) 25 (B) 56 (C) 90 (D) 96 (E) 126 100 (C)
Answer: B) 56
Step-by-step explanation:
[tex]x:y=7:18[/tex]
[tex]x=49[/tex]
find the value of [tex]y[/tex]
let, [tex]x^2[/tex] [tex]7a[/tex]
and let, [tex]y^2[/tex] [tex]8a[/tex]
A/Q
[tex]x=49[/tex]
[tex]7a=49[/tex], divide both sides by 7 to let the [tex]a[/tex] alone,
[tex]a=7[/tex]
///
[tex]y=8a[/tex], so that we now that [tex]a=7[/tex]
so, [tex]y=8*7[/tex]
[tex]y=56[/tex]
hope you've understanded...
The red triangle is a dilation of the blue triangle, with a scale factor, of k=1.5
Use the hotspots to fill in the missing measurements and similarity statement
The measure of each angle and side is given above.
What is image dilation?An enlargement or reduction of a figure that preserves shape but not size.All dilations are similar to the original figure.Dilations have a center and a scale factor.Given is that the red triangle is a dilation of the blue triangle, with a scale factor of {k} = 1.5.
We can write -
57/RT = 1.5
RT = 57/1.5
RT = 38
LM/20 = 1.5
LM = 20 x 1.5
LM = 30
MN/26 = 1.5
MN = 26 x 1.5
MN = 39
∠2 = 15°
∠1 = 121°
Therefore, the measure of each angle and side is given above.
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Please help!!
In the triangle below, b =______. If necessary, round your answer to two
decimal places.
A
38°
Answer here
8
31.6°
25
SUBMIT
Answer:
Step-by-step explanation:
38.06
Leila is walking from the park at point P to a restaurant at point R. She wants to stop for a break when the distance she has travelled and the distance she has left to travel has a ratio of 3:5, at which point should Leila stop for her break?
Answer: To determine the point where Leila should stop for her break, we need to find the midpoint of the line segment connecting points P and R, since the midpoint will represent equal distances from both points.
Let the distance between points P and R be d, and let's call the point where Leila stops for her break point B.
Since the ratio of the distance travelled to the distance remaining is 3:5, we know that the distance from B to P is 3/8 of the total distance d, and the distance from B to R is 5/8 of the total distance d.
Therefore, point B is the midpoint of line segment PR, and can be found by dividing the distance between P and R by 2.
Step-by-step explanation:
Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
The solution is, the required cost of the used game X= 19.
What is equation?An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
So he bought the $120 game with $82
and 2 equally priced game.
This can be changed to an equation: 120= 82+2X.
The X represents the cost of the used game.
120= 82+2X
-82 -82
——————-
38= 2X
38= 2X
Divide by 2 on both sides
X= 19
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Construction One linear foot of 12-in. I-beam weighs 25.4 lb. What is the length of a beam that weighs 444.5 lb?
Answer:
17.6 feet.
Step-by-step explanation:
The length of the I-beam can be calculated as follows:
Weight = Length * Weight per Foot
Rearranging this equation:
Length = Weight / Weight per Foot
Substituting the given values:
Length = 444.5 lb / 25.4 lb/ft = 17.6 ft
So, the length of the I-beam is 17.6 feet.
4. Reginald created a mosaic from 6" square tiles.
If the completed mosaic was 2 feet by 3 feet, how
many square tiles did he use?
Reginald used 2 square tiles to make the mosaic
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The area is the product of the length and width. Hence:
Area = length * width
Reginald created a mosaic from 6" square tiles. Therefore:
Area of tiles = 6 in * 6 in = 36 in²
If the completed mosaic was 2 feet by 3 feet, Hence:
Area of mosaic = 2 feet * 3 feet = 6 feet
1 feet = 12 in
6 feet = 6 feet * 12 in per feet = 72 in²
Number of tiles = Area of mosaic / area of tiles = 72 in² / 36 in² = 2
Reginald used 2 tiles
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The base of a triangle is 2inches more than 2 times the height. If the area of the triangle is 12 square inches, find the base and height.
Answer:
Base: 8. Height: 3.
Step-by-step explanation:
Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.
Need help quick with this problem!!! [tex]\frac{6x^{-1} y^{-1}}{\sqrt[4]{xy^{4}} }[/tex]
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6}{x^1 y^1 \left( xy^4 \right)^{\frac{1}{4}}}\implies \cfrac{6}{x^1 y^1 \left( x^{\frac{1}{4}}y^1 \right)}\implies \cfrac{6}{x^1x^{\frac{1}{4}} y^1 y^1} \\\\\\ \cfrac{6}{x^{1+\frac{1}{4}} y^{1+1}}\implies \cfrac{6}{x^{\frac{5}{4}} y^2}\implies {\Large \begin{array}{llll} \stackrel{a\quad b \quad ~~ c}{6x^{-\frac{5}{4}}y^{-2}} \end{array}}[/tex]
-9 3/8 as an improper fraction
Answer:the answer is -69/8
Step-by-step explanation:
first you plug -9 into 3/8 and it gives you -72/8+3/8 if you add those together you get -69/8
x = [ √(a+2) + √(a-2) ]/[ √(a+2) - √(a-2) ], then a =? the correct answer is a = x+(1/x). explain
how.
The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)
How to clear a variable in a radical equation
In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.
First, write the original equation:
x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]
Second, rationalize the expression:
x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]
x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]
x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4
x = [a - √(a² - 4)] / 2
2 · x = a - √(a² - 4)
Third, eliminate the square root operator by algebra properties:
√(a² - 4) = a - 2 · x
a² - 4 = (a - 2 · x)²
Fourth, find the solution to the expression:
a² - 4 = a² - 4 · x · a + 4 · x²
- 4 = - 4 · x · a + 4 · x²
1 = x · a - x²
1 + x² = x · a
a = (1 + x²) / x
a = 1 / x + x
a = x + 1 / x
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a lady sells brouses at 1500 ksh each. she make a profit of sh.150 shillings for each brouse how much does she pay for it
Answer: If the lady sells each brouse for 1500 KSH and makes a profit of 150 KSH for each brouse, then the cost price of the brouse is 1500 KSH - 150 KSH = 1350 KSH.
So, the lady pays 1350 KSH for each brouse.
Step-by-step explanation:
Fill in the blank to complete the sentence below.
In a standard deck of 52-cards, there are 13 spades and 4 aces, and thus there are
(Type a whole number.)
cards are neither spades nor aces.
Answer: 35
Step-by-step explanation: 52-13-4
Below is a square based pyramid. Calculate the length of side I
The slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.
What is the Pythagoras ruleThe Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we can observe the right triangle with hypotenuse l, height = 15, and base = 8 {half the pyramid base of 16}
the slant height is calculated as follows:
l² = 15² + 8²
l² = 225 + 64
l² = 289
l = √289 {take square root of both sides}
l = 17.
Therefore, the slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.
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