The missing side length is 5.7.
What would be themissing side length?The missing side length AB, can be calculated using the Pythagorean Theorem.The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two sides adjacent to the right angle (A and B) is equal to the square of the length of the hypotenuse (C).In other words, AB^2 + BC^2 = AC^2.In this case, AB^2 = AC^2 - BC^2, or AB^2 = 6.7^2 - 3^2, which simplifies to AB^2 = 44.89.Taking the square root of both sides yields AB = 6.7.Therefore, the missing side length, AB, is 6.7.The missing side length of a triangle with sides of lengths a, b, and c is calculated by using the Pythagorean theorem, which states that a^2 + b^2 = c^2. In this case, we are given that side c is 3, and side a is 6.7.Using the Pythagorean theorem, we can solve for side b by rearranging the equation to read b^2 = c^2 - a^2. Plugging in our known values, we get b^2 = 9 - 44.89, or b^2 = -35.89.Since the square root of a negative number is not a real number, this implies that there is no real number solution for b, and therefore the missing side length of the triangle is not possible.
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Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]
Answer:
[tex]\displaystyle x=\frac{1}{5}y^2[/tex]
Step-by-step explanation:
[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]
Polynomial in standard form
1.
7-3x^3+6x^2
2.
2y-3-8y^2
Answer:
[tex]-3x^3+6x^2+7[/tex][tex]-8y^2+2y-3[/tex]Step-by-step explanation:
The terms are ordered from greatest to least degree.
the image point using the translation (x,y) (x + 4, y -1) for the point (3,3) is?
The image of the point (3, 3) after a translation 4 units right and one unit down is (7, 2)
What is transformation?Transformation involves moving an object from its original position to a new position on the coordinate plane. This can be a translation, dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size. Other types of rigid transformation are reflection, and rotation
The translation using the rule (x, y) ⇒ (x + 4, y -1) is a translation 4 units right and 1 unit down.
The image of the point (3, 3) using the rule (x, y) ⇒ (x + 4, y -1) is (7, 2)
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Write the equation of the line shown on graph (-1,-5) and (2,1)
Answer:
y = 2x -3
Step-by-step explanation:
You want the equation of the line through the points (-1, -5) and (2, 1).
SlopeThe slope of the line is given by ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-5))/(2 -(-1)) = 6/3 = 2
Y-interceptThe y-intercept of the line can be found from ...
b = y -mx
y = -5 -2(-1) = -3
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . . . line with slope m and y-intercept b
Using our found values, the equation is ...
y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3
a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?
Answer:
Step-by-Step:5 cars and 14 bikes
There are 9 players on a baseball team there are 6 teams in the league how many baseball players are in the league
Answer:
54
Step-by-step explanation:
Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.
9 times 6 = 54
Write an equation
Y=|x| 10 units down
To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .
Write an equation Y=|x| 10 units down?y=|x-10|-3
Inside, is opposite. So therefore, to move it right 10 units, you subtract ten. However, outside of the absolute value, it is normal, so to move it down 3 units, you subtract 3.The number –45.3 is 45.3 units away from zero and the number 10 is 10 units away from zero. Therefore, the absolute value of any number is really a positive number (or zero).As we know that absolute value means remove the negative sign from the number and make it positive. So we get the absolute value of -10 as 10. So we get the absolute value of 10 as 10. Hence absolute value of -10 and 10 is 10 and 10 respectivelyTo know more about units visit:
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Question
Enter a linear equation that models the situation.
A drugstore sells pens for $1.40 each and notebooks for $2 each. The owner would like to sell $40 of these
items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 40.
Answer:
1.40p+2n=40
Step-by-step explanation:
Simplify to a single trig function
On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
here,
(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)
=| -cos(t)+2cosec(t) |
= -cos(t)+2cosec(t)
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Anyone knows the answer ?
The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].
What are double angle formulae?
There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.
The double angle formula for cosine is
Cos 2θ = Cos²θ - Sin²θ
=2Cos²θ – 1
= 1 – 2Sin²θ
Given sinθ = [tex]\frac{4}{5}[/tex]
cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]
Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]
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The solution for the question found using the double angle formula for cosine is -.7/-25
What are double angle formulae?There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.
What is angle?An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.
The double angle formula for cosine is
Cos 2θ = Cos²θ - Sin²θ
=2Cos²θ – 1
= 1 – 2Sin²θ
Given sinθ = 4/5
cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² = 1-32/25 = -7/25
Therefore Cos(2θ) fund using double angle formula is -
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3p-3p+2s-6s+2q-3q+8r-7r
Is it ok to not put the p in this equation as the 3p is minus
Answer:
- 4s - q + r
Step-by-step explanation:
that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-
⇒3p-3p+2s-6s+2q-3q+8r-7r
add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q
⇒0 - 4s - 1q + 1r
⇒- 4s - q + r Answer
hope that helps...
simplify expression: 3f+8(2m-7)
After simplification we got the above expression in the form 3f + 16m -56
What is simplify in mathematics?
The word "simplify" implies to turn something in a simpler form.
In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.
How to simplify the above expression?3f + 8(2m-7)
we rearrange the expression by removing the parenthesis.
we remove the parenthesis by multiplying the factors.
3f + 8 × 2m - 8 × 7
3f + 16m -56
the above expression has no like terms to add or subtract so it is kept in this form.
Hence, 3f + 16m -56 is the simpler form.
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i have been trying to figure this out for hours-
answer choices:
SSS
SAS
ASA
AAS
HL
Not Congruent
Answer: The answer is SAS
TEXT ANSWER
How can you use the unit price to find the cost of 10
pounds of tomatoes? Please help
To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.
What is the unit cost?
The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.
Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
The unitary method is used to find the unit cost of an object.
To find the cost of a unit object, multiply a by unit cost.
Given that, the unit cost of a unit pound of tomatoes.
The cost of 10 pounds of tomatoes is 10 × unit price of tomatoes.
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2. What number is a common multiple of
5 and 9?
Find the measurement of the angle I dictated for each trapezoid.
The measures of missing angles in trapezoids are listed below:
Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°
How to determine the measures of missing angles
In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:
Any pair of angles along one of the two parallel lines and between the other two congruent sides have the same measure. Any pair of angles between two parallel lines are supplementary angles. Two angles are supplementary when the sum of their measures equals 180°.Now we proceed to determine the missing angles in every trapezoid:
Case 5
m ∠ K + m ∠ J = 180°
21 · x + 15 · x = 180°
36 · x = 180°
x = 5
m ∠ J = 15 · x
m ∠ J = 15 · 5
m ∠ J = 75°
Case 7
m ∠ U = m ∠ T
m ∠ T = m ∠ U
m ∠ T = 118°
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Wilmer cashed his paycheck at Check Express. The fee at Check Express is 9% of the amount of the check. His paycheck was $291. How much was the fee for Wilmer to cash his paycheck?
Answer:
$26.19
Step-by-step explanation:
9% as a decimal is 0.09.
So, the fee is [tex](291)(0.09)=\$26.19[/tex].
Answer:
$26.19
Step-by-step explanation:
.09 x 291 = 26.19
is y= 2x3 an exponential function?
Answer:
No it is not an exponential function
Prime numbers are the _______ _______of all numbers
The numbers which have only two factors either 1 and the number itself are called prime numbers.
What is prime numbers?Prime number is a natural number greater than 1 that is not a product of two smaller natural numbers while a natural number greater than 1 that is not prime is called a composite number
Therefore a prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
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One solution.
2x - 1 = ____x - 1
the blank space must be 2 or x must be zero, I don't know what you mean by one solution
the blank must equal 2 because on the right side the coefficient of x is 2 so it must be same
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30)≥20 tell you?
The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Greater than (>).Less than (<).Less than or equal to (≤).How to determine the required function?Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;
g(x) ≥ x
when x = 30, we have;
g(30) ≥ 20
Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.
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Complete Question:
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30) ≥ 20 tell you?
It took at least 20 minutes for Mona to find 30 seashells.
Mona found at least 20 seashells in the first 30 minutes.
It took at least 30 minutes for Mona to find 20 seashells.
Mona found no more than 20 seashells in the first 30 minutes.
PLS HELP ME!!!
COSINE RULE I THINK!!
please explain in some detail and will mark brainliest
Answer:
Step-by-step explanation:
if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then
[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]
B=101
a= 3 cm
b=y
c=1 cm
use formula for cos B
cos 101=cos(90+11)=sin 11
[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]
Answer:
2.16
Step-by-step explanation:
To find the length y:
Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.
Using the cosine formula:
a^2 = b^2 + c^2 - 2bc cos(A)
where b=1, c=3 and A=101
substitute these values in the formula:
a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)
a ^2 = 4.647970...
Square root to find a:
a = √4.647970...
a = 2.16
thus, y = 2.16 to 3sf
Help ASAP PLSSS!! I’d really appreciate it! Thank youuu!
Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2
System of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are
a. y = 5x + 11 and y = 5x
Substitute the y value in first equation
5x=5x+11
So the system of equations y = 5x + 11 and y = 5x has no solution.
b. y = 6x + 3 and y = 3x
Substitute the y value in first equation
3x=6x+3
-3x=3
x=-1
y=-3
The system of equations has one solution
c. x + 4y = 8 and y = -1/4x + 2
x+4(-1/4x + 2)=8
x-x+2=8
The system of equations has one solution has no solution
Hence, system of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
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Which of the following tables represents a linear relationship that is also proportional?
x y
0 3
3 6
6 9
x y
0 4
2 6
4 8
x y
0 0
6 3
12 6
x y
0 3
5 5
10 7
The solution is Option A. , Option C.
The equations which are also proportional is y = 3x and x = 2y
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the values of x = { 0 , 3 , 6 }
Let the values of y = { 3 , 6 , 9 }
Now , the proportional equation is y = 3x
So , the proportionality constant is k = 3
b)
Let the values of x = { 0 , 6 , 12 }
Let the values of y = { 0 , 3 , 6 }
Now , the proportional equation is x = 2y
So , the proportionality constant is k = 2
Hence , the equations are y = 3x and x = 2y
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Answer: The solution is Option A. , Option C.
Step-by-step explanation:
The equations which are also proportional is y = 3x and x = 2y
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the values of x = { 0 , 3 , 6 }
Let the values of y = { 3 , 6 , 9 }
Now , the proportional equation is y = 3x
So , the proportionality constant is k = 3
b)
Let the values of x = { 0 , 6 , 12 }
Let the values of y = { 0 , 3 , 6 }
Now , the proportional equation is x = 2y
So , the proportionality constant is k = 2
Hence , the equations are y = 3x and x = 2y
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Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.
g(t) = t^2 - 27/t
The coordinates of the inflection points are (3, 0) and it concave upwards
How to determine the coordinates of the inflection points.From the question, we have the following parameters that can be used in our computation:
g(t) = t^2 - 27/t
Express properly
So, we have
g(t) = t² - 27/t
Calculate the second derivative
So, we have
g''(t) = 2 - 54/t³
Set the differentiated equation to 0
2 - 54/t³ = 0
So, we have
2t³ = 54
Divide by 2
t³ = 27
Take the cube roots
t = 3
Substitute t = 3 in g(t) = t² - 27/t
g(3) = 3² - 27/3
g(3) = 0
This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)
How to determine the point of concave upward and concave downwardRecall that
g''(t) = 2 - 54/t³
Next, we check if the second derivative exist at t = 0,
g''(0) = 2 - 54/0³
g(0) = undefined
The undefined value implies that the graph has a vertical inflection point at t = 0
And as such, the graph of the function is concave upward
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1/3m = 12-m
Please explain step by step to get marked as brainliest.
Step-by-step explanation:
cross multiply
12-m(3m)= 1
12-3m²-1=0
multiply by -1
3m²+1-12=0
3m²= 11
m²= 11/3
m=√11/3.
I need to know the first and last one
The lines FE and GH are parallel to each orther.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given that
ΔPEI = ΔGHI
here ∠pie = ∠gih
PI =HI
GI=EI
So both triangles are congruent
So the FE║GH.
Hence the lines FE and GH are parallel to each orther.
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Help please! How do I write an equation in standard form using the information on the graph?
Answer:
3x -y = 2
Step-by-step explanation:
You want a standard form equation for the line through the points (0, -2) and (2, 4).
SlopeThe slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...
m = (squares above)/(squares to the right) = 3/1 = 3
If we consider the actual x- and y-values represented by these grid squares, then the slope is ...
m = (4 -(-2))/(2 -0) = 6/2 = 3
InterceptThe point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.
Slope-intercept equationWith this information, we can write the slope-intercept form equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2
Standard formThe standard form of an equation for a line is ...
ax +by = c
where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.
We can rearrange the slope-intercept equation to put it into this form.
y = 3x -2
3x -y -2 = 0 . . . . . subtract y
3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.
100 points please answer
The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C
What are trigonometric identities?Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.
These involve certain functions of one, two or more angles.
They also are different from triangle identities, which involves angles and side lengths of a triangle.
To verify a trigonometric identity, we take the following steps;
Convert the equalities to terms of sine and cosine.Solve the identities at possible timesThen, simplify the left-hand side of the equation, before simplifying the right-hand side.Hence, the best option is C
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