Starting with the given equation F sin(θ) = 24/26, we can use trigonometric identities to find expressions for cos(θ), tan(θ), and sec(θ).
First, we square both sides of the equation to get:
F^2 sin^2(θ) = (24/26)^2
Then, we use the identity sin^2(θ) + cos^2(θ) = 1 to solve for cos(θ):
cos^2(θ) = 1 - sin^2(θ)
cos^2(θ) = 1 - (24/26)^2
cos(θ) = ± √(1 - (24/26)^2)
Since 0 ≤ θ ≤ π/2, we know that cos(θ) must be positive, so we take the positive square root:
cos(θ) = √(1 - (24/26)^2)
Next, we can use the fact that tan(θ) = sin(θ)/cos(θ) to find an expression for tan(θ):
tan(θ) = sin(θ)/cos(θ)
tan(θ) = (F sin(θ))/cos(θ)
tan(θ) = (F sin(θ))/√(1 - (24/26)^2)
Finally, we can use the fact that sec(θ) = 1/cos(θ) to find an expression for sec(θ):
sec(θ) = 1/cos(θ)
sec(θ) = 1/√(1 - (24/26)^2)
So, in summary, we have:
cos(θ) = √(1 - (24/26)^2)
tan(θ) = (F sin(θ))/√(1 - (24/26)^2)
sec(θ) = 1/√(1 - (24/26)^2)
Note that we cannot simplify these expressions any further without more information about the value of F.
To know more about value of F, visit:
https://brainly.com/question/13527898
#SPJ11
Which equations are set up correctly to solve for the unknown side length?
The equations that can be set up correctly to find the length of the unknown side using the Pythagorean theorem are:
6² + x² = 17²
x² + 6² = 17²
What is the Pythagorean Theorem?The Pythagorean Theorem is a statement in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The theorem can be written as an equation:
c² = a² + b², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Using the Pythagorean theorem, the equations that can be set up correctly to find the value of x are:
6² + x² = 17²
x² + 6² = 17²
Learn more about the Pythagorean theorem on:
https://brainly.com/question/343682
#SPJ1
Is any set of ordered pair?
Any set of ordered pair cannot be called as a function , the ordered pairs that in which no two different ordered pairs have the same x coordinate is called as a Function .
What is a Function ?
The set of ordered pair (x,y) is called a function, in which no two different ordered pairs have the same x coordinate. and the equation that produces such a set of ordered pairs can be called as function.
For Example : Let us Consider ordered pairs , F = [tex][(1,5) , (3,6)][/tex] ;
we see that , the element 1 has the image as 5 , and the element 3 has the image as 6 .
So , we can conclude that , the each value of x has exactly only one corresponding value of y .
Therefore , the ordered pair can be called as a function .
The given question is incomplete , the complete question is
Is any set of ordered pair is called a Function ?
Learn more abut Ordered Function here
https://brainly.com/question/28931422
#SPJ4
How do you find a quadratic function with a vertex and a point?
The quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero.
What is quadratic function?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape. In mathematics, a quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring." This terminology comes from the fact that a square's area is equal to its side length multiplied by itself. The Latin term quadratum, which means square, is where the word "quadratic" derives.Three points are used to determine a quadratic function, which has the form f(x) = ax2 + bx + c. A quadratic function can be determined from three points on its graph by finding a, b, and c algebraically. Three equations and three unknowns must be solved in order to do this.
To learn more about quadratic function refer to:
https://brainly.com/question/25841119
#SPJ4
Counting More Pebbles Along the Path page 1 of 2: Look at the pebbles along each part of the path. Fill in the missing numbers. 15 13 16 72 CHALLENGE Hansel and Gretel used a pebble to mark every 10 steps as they walked along the path. How many steps have they taken when they get to the last pebble on this part of the path? ____________Use numbers or words to explair how you know
The missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.
What is the missing number?
Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them.
let's take a look at pebbles along each part of the path, there is 1 number of addition to each pebble number to go on next pebble.
i.e. 12, 13, 14, 15, 16, 17
so, the missing numbers are 14 and 17.
now, as given Hansel and Gretel used a pebble to mark every 10 steps as they walked along the path. How many steps have they taken when they get to the last pebble on this part of the path?
so, to go on next pebble there are 10 steps to walk.
therefore, from starting pebble number 12 to last pebble number 17, there are 50 steps ( difference between two pebbles is 10 steps).
hence, the missing numbers are 14 and 17. there are 50 steps taken to reach the last pebble on this part of the path.
To learn more about missing numbers visit : brainly.com/question/12750881
#SPJ4
How do I know if my cervix is dilating?
Knowing if your cervix is dilating typically involves a physical examination by a healthcare provider.
During labor, a healthcare provider will check the dilation of your cervix by performing a pelvic exam. They will use their fingers to feel the cervix, which is located at the top of the vagina, and determine the degree of dilation.
Cervical dilation is measured in centimeters, and full dilation is considered to be 10 centimeters. Before labor begins, the cervix is typically closed and has a firm consistency. As labor progresses, the cervix will start to soften and thin out, and will eventually open, or dilate.
Some women might experience Braxton Hicks contractions, which are sometimes referred as "false contractions" as they can be mistaken for the start of labor, but Braxton Hicks contractions do not cause cervical dilation.
It's important to note that dilation is just one of the factors that indicate that labor is imminent. It is not the only factor and some women can have a fully dilated cervix for days before going into active labor.
In conclusion, knowing if your cervix is dilating typically involves a physical examination by a healthcare provider, who will perform a pelvic exam to feel the cervix and determine the degree of dilation.
Cervical dilation is measured in centimeters, with full dilation being 10 centimeters. Be aware that dilation is just one of the factors that indicate labor is imminent.
Learn more about dilation at
https://brainly.com/question/28147754
#SPJ4
What type of dilation is formed when the scale factor K is greater than 1 blank options?
An expansion where image size increased is formed when scale factor k is greater than 1
What is Dilation ?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
when the scale factor K is greater than 1 , The image will enlarged
Hence, An expansion will be occur.
To know more about Dilation here
brainly.com/question/13176891
#SPJ4
Which side is opposite of 30 in a 30 − 60 − 90 triangle?
The side opposite the 30-degree angle is called the shorter leg in a 30 − 60 − 90 triangle
A right triangle is any triangle that has a 90-degree angle.
A 30-60-90 triangle is a special type of right triangle that has a 30-degree angle and a 60-degree angle in addition to the right angle.
The side opposite the 30-degree angle is called the shorter leg.
The side opposite the 60-degree angle is called the longer leg.
The side opposite the right angle of 90 degrees is called the hypotenuse.
The hypotenuse is twice the shorter leg.
The longer leg is √3 times the shorter side.
if the length of the shorter leg is given, then these properties are used to find the longer side and the hypotenuse.
However, the 30-60-90 properties hold no matter which side is provided.
If the length of the hypotenuse is given, divide it by 2 for the shorter leg. Then multiply that result by √3 to get the length of the longer leg.
If the length of the longer leg is given, divide it by √3 to get the shorter leg. Then, multiply that result by two to get the length of the hypotenuse.
To know more about right angle triangle visit brainly.com/question/3770177
#SPJ4
Identify the center of dilation.
-8
8
0
-4
ty
-8
8
Answer:The slope of the given line is -4
Step-by-step explanation:
make p subject formula in I=PRT/100
Answer:
P=Ix100/RT
therefore P is made the subject formula
Need Answer desperately pls help
Answer:
7) B.
8) D.
Step-by-step explanation:
What is the range of a function in Mcq?
The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.
What is a function?
A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.
A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.
Learn more about function, Here:
brainly.com/question/21145944
#SPJ4
What is the formula of property?
The formula of commutative property is α + β = β + α or α × β = β × α.
The commutative property is the property that deals with the arithmetic operations of addition and multiplication. So mathematically, if we change the order of the operand and it does not change the result of the arithmetic operation then that particular arithmetic operation is commutative.
If two numbers α and β are given, then the formula of the commutative property of numbers is given as,
α + β = β + α
α × β = β × α
α - β ≠ β - α
α ÷ β ≠ β ÷ α
To know more about commutative property, here
https://brainly.com/question/778086
#SPJ4
G(1) = 50
G(n) = 8 - g (n-1)
G(2) =
The value of G(2) of the given sequence formula is; -42
How to solve Arithmetic sequence?The general formula for the nth term of an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
We have the following parameters;
G(1) = 50
G(n) = 8 - g (n-1)
Thus;
G(2) = 8 - g(2-1)
G(2) = 8 - g(1)
Since (g(1) = 50 ), then we have;
G(2)= 8 - 50
G(2) = -42
Read more about Arithmetic Sequence at; https://brainly.com/question/6561461
#SPJ1
Write an exponential function that models the info below.
An initial value of 1,425 increasing at a rate of 5%.
Answer:
y = 1425 * (1 + 0.05)^x
Step-by-step explanation:
An exponential function of the form y = a * b^x can be used to model exponential growth or decay, where a is the initial value, b is the base (growth or decay factor), and x is the time period. In this case, the initial value is 1,425 and the rate of increase is 5%. We can write this as an exponential function as follows:
y = 1425 * (1 + 0.05)^x
where y is the final value after x time periods, and x is the number of time periods (in years, for example). To find the value of the function after x time periods, you can substitute the value of x into the equation.
How do you find an area example?
Answer:
To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area......
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
PLEASE HURRY IM TAKING EXAM pre algebra
The equation which gives infinite solutions, x-10+x = 8+2x-18.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
For the infinite solution the both side of equation must contain equal quantity.
For example,
x-10+x = 8+2x-18
now, solving for x
x-10+x = 8+2x-18
2x-10 = 2x-10
-2x = -2x
-10 = -10
As, both sides are equal which shows the system of equation.
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ1
At charles school, 15 of the 75 students in seventh grade play in the jazz band. How many seventh graders play in the jazz band?.
The jazz band has 15 seventh graders playing according to the ratio.
What is the ratio?A ratio, which is a number, is a way to represent one quantity as a portion of another. A ratio can only be compared when the two numbers in it have the same unit. To compare two objects, ratios are utilized.
Given One fifth of the 75 seventh graders at Charles School participate in the jazz band.
Presented as a ratio
75 pupils, or 1/5 of them, participate in the jazz band.
75 pupils out of the total play in the jazz band.
15 kids in total participate in the jazz band.
15 seventh graders are therefore playing in the jazz band in accordance with the ratio.
Hence, The jazz band has 15 seventh graders playing according to the ratio.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ4
I need you to solve this
Answer:
Step-by-step explanation:
When dividing like bases (x is our base) we simplify by subtracting the exponents, top minus bottom. Since the exponents are fractions, we need a common denominator.
[tex]\frac{1}{5} -\frac{2}{15}=\frac{3}{15} -\frac{2}{15}=\frac{1}{15}[/tex]
thus, the simplification is [tex]x^\frac{1}{15}[/tex]
Answer:
(x 1/5)/(x 2/15)=.
(x1/5)× 15/2x
=15x/10x
=1.5
What is the slope of the line described by the equation below
Answer: -3
Step-by-step explanation: Y=MX+B
Answer:
−3
Step-by-step explanation:
y-5=-3(x-17)
y=-3x+51+5
y=-3x+56
if we have this function:
y=mx+b
The slope is "m".
In this case, m=-3
Answer: sope -3
- 1 2/7x-1=26
Show work
The expression [tex]$1\frac{2}{7}x -1=26[/tex] gives {x} value as equivalent to 21.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the expression as -
[tex]$1\frac{2}{7}x -1=26[/tex]
We can write the expression as -
(9/7)x - 1 = 26
(9/7)x = 27
x = (27 x 7)/9
x = 3 x 7
x = 21
Therefore, the expression [tex]$1\frac{2}{7}x -1=26[/tex] gives {x} value as equivalent to 21.
To solve more questions on expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
One of the legs of a right triangle measures 7 cm and the other leg measures 17 cm. Find the measure of the hypotenuse. If necessary round to the nearest tenth.
Answer:
[tex]\huge\boxed{\sf H=18.4\ cm}[/tex]
Step-by-step explanation:
Given that,Base = 7 cm
Perpendicular = 17 cm
Hypotenuse = H
Using Pythagoras theorem.[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2\\\\(H)^2=(7)^2+(17)^2\\\\(H)^2=49+289\\\\(H)^2=338\\\\Take \ square\ root \ on \ both\ sides\\\\\sqrt{(H)^2} =\sqrt{338} \\\\H=18.4\ cm\\\\\rule[225]{225}{2}[/tex]
5 students are going on a field trip and 5 students are staying at school. What is the ratio of the number of students who are staying at school to the total number of students?
What are the 3 steps of factoring?
The three steps of factoring include taking the common component out of the polynomial then simplifying the polynomial such that the most simple values are left and finally rearrangement.
If we are provided with the polynomial that is very complex in nature then first thing we have to do in order to solve the problem related to that polynomial is to factorise the polynomial.
The factory of that particular polynomial can be done by taking out the most common component out of the polynomial in a multiplication.
After this we have to simplify the polynomial such that only the simplest values are left in the polynomial and finally we have to rearrange the polynomial because after such operations on that polynomial the polynomial will not be easy to understand in the first look of it.
To know more about factors, visit,
https://brainly.com/question/18187355
#SPJ4
27 5/3 in simplest radical form
The value of 27 5/3 in simplest radical form will be 86 / 3.
How to illustrate the exponent?The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Here the value of 27 5/3 in simplest radical form will be the calculated thus:
(27 × 3) + 5 / 3
= (81 + 5) / 3
= 86 / 3
The value in radical form will be 86 / 3.
Learn more about Fraction on:
https://brainly.com/question/78672
#SPJ1
What is the coefficient of XYZ?
Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression XYZ is 1.
What exactly does expression mean?By substituting each variable with a number and conducting mathematical functions, an algebraic formula must be checked. The solution variable in the previous example is identical to 6 since 79 + 8 = 87. To evaluate the expression, we can replace the variables values with ones we are familiar with.
Here,
Given :
XYZ
To find the coefficient of given expression ,
Thus,
From observing we can see XYZ
can be written as
=>1*XYZ
Where 1 is coefficient.
Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression XYZ is 1.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ4
Which expression is equivalent to -8.2 - 5?
Choose 1 answer:
A
B
5- (-8.2)
-8.2 + 5
8.25
-8.2+(-5)
The expression equivalent to - 8.2 - 5 is - 8.2 + (-5)
What is an expression?
A mathematical expression is a phrase that includes at least two numbers or variables, and at least one arithmetic operation. The mathematical operations used can be addition, subtraction, multiplication or division.
Note ,
- × - = +
- × + = -
+ × + = +
For the expression - 8.2 - 5
In the above expression, we are subtracting positive integer 5 from -8.2
So we get the answer as
-8.2-5 = = -13.2
Now this is the solution we should get while solving the given options.
a) 5 - ( -8.2) = 5 + 8.2 = 13.2
b) -8.2 + 5 = - 3.2
c) -8.2 -5 [tex]\neq[/tex] 8.25 (as seen above)
d) - 8.2 + ( -5) = -8.2 - 5 = -13.2
Comparing the solutions, we get that option(d) matches with the required answer.
Therefore option(d) is the correct expression that gives the same answer.
To learn more about expression, follow the link.
https://brainly.com/question/723406
#SPJ1
An architect has designed two tunnels. Tunnel A is modeled by2+7+30x+56=0, and tunnel B is modeled by 2-3x+15y-55-0, where all measurements
are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work (4 points)
Part C: Determine the maximum height of each tunnel is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your
work. (7 points)
Trucks will be able to pass through tunnel B while tunnel A is destroyed.In light of this, the equations for tunnels A and B are x2 + y2 + 30x + 56 = 0 and x2 - 30x + 16y - 95 = 0, respectively.
What is the standard form of parabola equation?A parabola's general equation is either y = a(x-h)2 + k or x = a(y-k)2 + h, where (h, k) stands for the vertex.
y2==4ax is the typical equation for a normal parabola.
Section A: x2+y2+30x+56=0
On both sides of an equation, add 152.
This is,
x²+30x+15²+y²=-56+15²
⇒ (x+15)²+y²=169⇒ (x+15)²+y²=13²
On both sides of the equation, divide 132.
⇒ (x+15)²/13² + y²/13² =1
Part B:x²-30x+16y-95=0
x2-30x+16y=95 now,
On both sides of an equation, add 152.
In other words, x2-30x+152+16y=95+152
⇒ (x-15)²=320-16y
⇒ (x-15)²=16(20-y) (20-y)
Part C:greatest height:A: 13 feet
B: 20 feet ,8 feet wide
A: x+15=8/2=4 y=12.37<13.5
B: x-15=8/2=4 y=19>13.5
In turn, tunnel A will sustain damage while the truck can travel via tunnel B.
To learn more about parabola refer
https://brainly.com/question/28863741
#SPJ1
At Aaron's Automobile's, Bob made $150,000 total in sales and commission last week. If commission is 20%, how much were Bob's sales?
Last week's sales were $______
Answer: 30,000
Step-by-step explanation:
150,000 x 0.2 = 30,000
Using the constant of proportionality, write an equation for this proportional relationship:
You can buy 14 apples for 28 euros.
Use a to represent number of apples and c to represent the cost in euros. Please write your equation starting with c=
c = 14a/28
This equation represents the proportional relationship between the number of apples (a) and the cost in euros (c). The constant of proportionality is 14/28, which means that for every 14 apples, the cost is 28 euros. By dividing both sides by 14, we can also write the equation as a = c/2. This means that for every 2 euros, you can buy one apple.
Learn more about "constant of proportionality": https://brainly.com/question/29126727
What are the zeros of quadratic function 2x² 7x 3?
The zeros of quadratic function 2x² - 7x + 3 = 0 are 3 and 1/2.
There are several methods for solving a quadratic equation of the form ax² + bx + c = 0. In our case, use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a to find the zeros or the solutions for x.
Plug in the values to the formula and solve for x.
x = (-b ± √(b² - 4ac)) / 2a
x = (--7 ± √(-7² - 4(2)(3))) / 2(2)
x = (7 ± √49 - 24) / 4
x = (7 ± √25) / 4
x = (7 ± 5) / 4
x = 3 ; x = 1/2
Hence, the zeros of quadratic function 2x² - 7x + 3 = 0 are 3 and 1/2.
Learn more about quadratic formula here: https://brainly.com/question/1214333
#SPJ4