Slope-intercept form:
y=−9x+44y=-9x+44
Point-slope form:
y−8=−9⋅(x−4)
Answer this! Please, I need help!
Part a: f(x) = -|x+ 2| - 1, is the modulus function.
part b: f(x) = 2x² - 5, the graph for each function is plotted along with the points.
Explain the term modulus function?A modulus function is one that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter whatever input was provided to this function, the outcome is always favorable.For the given equation of the polynomial.
Part a: f(x) = -|x+ 2| - 1, is the modulus function.
Put the values for x and find y.
For x = -3, y = 0
For x = -2, y = 1
For x = 0, y = -1
For x = 3, y = -4
Thus, the graph for the obtained points are plotted.
part b: f(x) = 2x² - 5
Put the values for x and find y.
For x = -1.581, y = 0
For x = 1.581, y = 1
For x = 0, y = -5
Thus, the graph for the obtained points are plotted.
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Evaluate the following:
Logn(-n)2 = ?
The value of the logarithm expression logₙ (n)⁻² will be negative 2.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ logₙ (n)⁻²
Simplify the expression, then we have
⇒ logₙ (n)⁻²
⇒ -2 logₙ (n)
⇒ - 2
The value of the logarithm expression logₙ (n)⁻² will be negative 2.
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Factorise the following:
a) x + 3x-4
b) x - 2x - 3
c) x + 2x - 8
By Factorise the equations we get 2 points for each equation:
for a) we get (x+4),(x-1)
for b) we get (x-3),(x+1)
for c) we get (x+4),(x-2)
a) x^2 + 3x-4
for this equation we have to take factors of -4:
x^2+4x-x-4
Taking common in the equation we get:
x(x+4)-1(x-4)
After taking common, Now we get two points:(x+4,)(x-1)
b) x^2 +-2x-3
for this equation we have to take factors of -3:
x^2-3x+x-3
Taking common in the equation we get:
x(x-3)+1(x-3)
After taking common, Now we get two points:(x-3,)(x+1)
c) x^2 + 2x-8
for this equation we have to take factors of -8:
x^2+4x-2x-8
Taking common in the equation we get:
x(x+4)-2(x+4)
After taking common, Now we get two points:(x+4,)(x-2)
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"The correct question is":
Factorise the following:
a) x ^2+ 3x-4
b) x^2 - 2x - 3
c) x ^2+ 2x - 8
What is 7/10 divided by 3.4
Answer: 0.20588235294 or ≈0.21
Step-by-step explanation: First, we should change the 7/10 into a fraction. (Divide numerator by the denominator) You should get .7 or 0.7. Then, when dividing, it would be 0.7 divided by 3.4 and I got 0.20588235294. I rounded it to the nearest hundredth to get ≈0.21. I hope this helped! Please, mark brainliest! (If can)
A school is arranging a field trip to the zoo. The school spends 835.19 dollars on passes for 45 students and 2 teachers.
Answer: $17.77 per pass
Step-by-step explanation:
$835.19 / (45 + 2)
$835.19 / 47
= $17.77 price per pass
ABCD is a square with four congruent sides and four congruent angles. triangle BAD is congruent to
ΔBAD is congruent to ΔBCD by the ASA rule.
What is the ASA congruency of triangles?
If any two angles and sides included between the angles of one triangle are equivalent to the corresponding two angles and sides included between the angles of the second triangle, then the two triangles are said to be congruent by the ASA rule.
In the given figure ABCD is a square.
In ΔBAD and ΔBCD
∠B ≅ ∠B ----Common Angle
∠A ≅ ∠A ------Each of 90° angle
Side BD ≅ Side BD ----Common Side
So we can say that ΔBAD ≅ ΔBCD -----(ASA rule)
Hence, ΔBAD is congruent to ΔBCD by the ASA rule.
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question if a, b, and c are positive integers, what is the range of the five numbers 0, 10, a, b, and c ? (1) a b c < 13 (2) a < b < c < 13
The range of the five numbers 0 , 10 , a , b and c is a + b + c < 13
According to the question,
Statement (1) Its given that a + b + c < 13
Since, a, b and c are positive integers So, a,b,c > 0
Now, note that the maximum value that any one of a, b, c can take is 10
Range will always be = 10 - 0 = 10
Statement (2) a < b < c < 13
There are multiple values of a, b, and c that can be possible.
eg; a = 1, b = 5, c = 12
=> Range = 12 - 0 = 12
or, a = 1, b = 2, c = 3
=> Range = 10 - 0 = 10
which can't possible
Therefore , Statement (1) is correct about range
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200-8.(2x+7)=112
(2x-123):3=33
is it two questions?
if it is then.....
Is answer correct?
A polynomial ppp is graphed.
Choose 1 answer.
Step-by-step explanation:
At x=0, we have a zero and it bounces off so one of our answers must include
x^2.
Our other zeroes have multiplicities of 1, so our anly reasonable answer is A
Simplify:
O
O
O
O
(3) ²
9
4
9
(())
9
< Previous
-12
-7
9
(4)
-3
6help
The simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].
What is simplifying an expression?
To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.
Consider, the given expression,
[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5[/tex]
To simplify this using the exponent rule:
[tex]((a)^b)^c = a^b^.^c[/tex]
⇒
[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^(^-^4^*^-^3)(\frac{4}{9})^-^5\\ ((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^1^2(\frac{4}{9} )^-^5[/tex]
Now use the exponent rule:
[tex]a^ba^c = a^(^b^+^c^)[/tex]
⇒
[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^(^1^2^-^5^)\\((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex]
Hence, the simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].
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The Chess Club wants to raise a total of $150 for a group trip.
They earn $1.25 for each box of pies they sell. They have
already made $16.25. Which equation could be used to find
how many more boxes of pies they must sell?
Answer:
Step-by-step explanation:
The number of boxes of pies that the Chess Club must sell to reach their goal of $150 can be represented by the variable x. We can create the following equation to represent this relationship:
1.25x + 16.25 = 150
To find the number of boxes of pies that the Chess Club must sell, we can solve this equation by subtracting 16.25 from both sides and then dividing both sides by 1.25:
1.25x = 150 - 16.25
1.25x = 133.75
x = 133.75 / 1.25
x = 107.
Therefore, the Chess Club must sell 107 more boxes of pies to reach their goal of $150.
If the discriminant of an equation is positive, which of the following is true of
the equation?
Step-by-step explanation:
For this case suppose that we have a quadratic equation of the form:
The solution to the quadratic recuacion is given by:
Where,
The discriminant is:
When the discriminant is greater than zero, then the root is positive, and therefore, we have two positive real solutions.
Answer:
B. it has two real solutions
A market research company wishes to know how many energy drinks teenagers drink each week. They want to construct a 80% confidence interval with an error of no more than 0.06. A consultant has informed them that a previous study found the mean to be 5.7 energy drinks per week and found the standard deviation to be 0.9. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
The minimum sample size required is 108.
What is the standard deviation?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
To find the minimum sample size required, we can use the formula for the margin of error for a confidence interval for a mean:
margin of error = (z*s) / (√n)
where z is the z-score corresponding to the desired confidence level (in this case, z = 1.28 for an 80% confidence interval), s is the standard deviation of the population, and n is the sample size.
We are given that the margin of error should be no more than 0.06 and that the standard deviation is 0.9. We can solve for n by rearranging the formula and substituting in the given values:
n = [(zs) / margin of error]²
= [(1.280.9) / 0.06]²
= approximately 107.5
Since the sample size must be an integer, we must round up to the next integer, which is 108.
Hence, the minimum sample size required is 108.
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standard deviation for 6,8,10,4?
Standard deviation for 6,8,10,4 will be;
⇒ 2.58
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The data set is,
⇒ 6, 8, 10, 4
Now,
Since, The data set is,
⇒ 6, 8, 10, 4
Hence, Mean = 6 + 8 + 10 + 4 / 4
= 7
So, The standard deviation= √ (6 - 7)² + (8 - 7)² + (10 - 7)² + (4 - 7)² / (4 - 1)
= √20/3
= 2.58
Thus, Standard deviation for 6,8,10,4 will be;
⇒ 2.58
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Jackson has $650 in their account and uses their debit card to take out $40 cash each week. Their card has a $5 ATM fee.
Write an equation to express their balance, y, after x weeks.
What will their balance be after 8 weeks?
After 8 weeks, how much will Jackson have paid in ATM fees alone?
The word problem have the following answers:
y = $650 - $45x is an equation to express their balance, y, after x weeks$290 will their balance be after 8 weeks.After 8 weeks, Jackson would have paid $40 in ATM fees alone.Word problems in mathematicsWord problems are mathematical problems which involves the use ofordinary words, instead of mathematical symbols.
From the question, if y is the balance after x weeks, this implies Johnson took out $45 multiplied by x in total including ATM fees, and their balance will be the equation;
y = $650 - $45x
After 8weeks, their balance will be;
y = $650 - $45(8)
y = $650 - $360
y = $290
After 8 weeks, Jackson will pay in ATM fees alone;
$5 × 8 = $40
Therefore, the equation y = $650 - $45x is to express their balance, y, after x weeks and $290 will be their balance after 8 weeks. While Johnson would have paid in $40 in ATM fees alone after 8 weeks.
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4x-2(3x+7)=____x-_____
Answer: x = -9
Step-by-step explanation: 4
x
+
2
=
3
x
−
7
⇒
4x−3x=−7−2⇒x=−9
The boiling temperature (in degree celsius) of platinum is 199 more than four times the boiling temperature (in degree celsius) of zinc. a. Write an expression that represents the boiling temperature (in degree celsius) of platinum. b. The boiling temperature of zinc is 907 degrees celsius. What is the boiling temperature of platinum.
a) The expression that represents the boiling temperature (in degree celsius) of platinum is of: y = 4x + 199.
b) The boiling temperature of platinum is of 3827 ºC.
How to build the expression?The boiling temperature of the platinum is the output of a function, hence it is represented by the variable y.
The boiling temperature of zinc is the input variable of the function, hence it is represented by variable x.
The boiling temperature of platinum is 199 more than four times the boiling temperature of zinc, hence the expression is given as follows:
y = 4x + 199.
Since the boiling temperature of zing is of 907ºC, the boiling temperature of platinum is obtained as follows:
y = 4(907) + 199 = 3827 ºC.
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Question 1(Multiple Choice Worth 1 points)
(05 04 LC)
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9,2,4,3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1,0, 2, 1, 3.
Which is the best measure of center for first period, and why?
O Mean, because there are no outliers that affect the center
O Median, because there is one outier that affects the center
O
Interquartile range, because there is one outier that affects the center
O Standard deviation, because there are no outliers that affect the center
Answer:uu
Step-by-step explanation:
V.4 Area and circumference of
The area of a circle is 12.56 square kilometers. What is the circle's circumference
Use 3.14 for л.
Submit
kilometers
Answer:
12.56 km
Step-by-step explanation:
The circumference of a circle is given by
[tex]c = 2\pi \: r[/tex]
let's find the radius
the area of a circle is given by
[tex]a = \pi \: {r}^{2} [/tex]
12.56 = 3.14 r²
r² = 12.56/3.14
r² = 4
r = √4
r = 2
let's find the circumference
C = 2πr
C = 2 × 3.14 × 2
C = 12.56 km
I hope this helps
Find all solutions to the equation x3 + 16x – 3x2 = 48.
–4, –3, 4
–4, 3, 4
3, –4i, 4i
–3, –4i, 4i
The solutions of the quadratic equation x³+ 16x -3x² = 48 are 3, –4i, 4i
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation.
We are given the quadratic equation as;
x³+ 16x -3x² = 48
Subtract 48 from both sides;
x³+ 16x -3x² - 48= 48 -48
x³+ 16x -3x² - 48= 0
Factor left side of equation.
(x - 3)( x² + 16) = 0
Therefore, the roots are 3, –4i, 4i
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what is the product to 6.5x9.5
Answer: 61.75
Step-by-step explanation:
Evaluate 15/r -1 when r = 5.
The value of the expression 15/r -1 when r = 5 will be equal to 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 15/r -1. The value of r is 5. The value of the expression at r=5 will be calculated as,
E = 15/r - 1
E = 15 / 5- 1
E = 3 - 1
E = 2
Therefore, the value of the expression 15/r -1 when r = 5 will be equal to 2.
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A soft drink can has a height of 16cm and a radius of 3cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can). Give your answer rounded DOWN to the nearest cm, to ensure it fits inside the can.
In linear equation, 16.27 is the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).
Describe a linear equation using an example.
An equation in which there is only one variable is known as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.
A linear equation in one variable would be 9x + 78 = 18, for instance.
l² = r² + h²
l² = 3² + 16²
l² = 9 + 256
= 265
l = √265
l = 16.27
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Select all true statements if n || m.
Parallel lines M and N cut by two transversals, A B and B C. Along line M, three angles are labeled 2, 3, and 4, which together form a straight angle. Transversal A B forms two angles below line N, one labeled 20 degrees and the other labeled A. Together, these angles form a straight angle. Transversal B C forms two angles below line N, one labeled C and the other labeled 60 degrees. Together, these angles form a straight angle. Angle 1 is vertical to the 60-degree angle and is an alternate interior angle to angle 4. Together, angles 1, 3, and an unlabeled angle that is vertical to the 20-degree angle form a triangle between the two parallel lines.
A. m∠2 = 60°
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
D. m∠2 + m∠3 = 80°
E. m∠2 = 20°
Answer:
Hi, the correct answer is A) m∠2 = 60°.
let me put it in this way.
Step-by-step explanation:
Since parallel lines M and N are cut by transversals A B and B C, corresponding angles are formed. Corresponding angles are pairs of angles that are formed by intersecting lines and are on opposite sides of the transversal. In this case, angles 2 and C are corresponding angles, as are angles 3 and A.
We know that angles 2 and C form a straight angle along line M, and angles C and 60 degrees form a straight angle along line N. Since corresponding angles are congruent (have the same measure), this means that angle 2 must have the same measure as the 60-degree angle
The slope of the line shown below is 3/2. What is the value of a? 2, 3, 5, 6
The solution is Option D.
The value of a from the equation of slope is a = 6
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second poin
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the value to be determined be = a
Now , the slope of the line be = m
The value of m = 3/2
So , Slope m = 3/2
And , the value of a is calculated by
Slope = rise / run
Slope = y/x
Since , the value of x = 4
3/2 = y/4
Multiply by 4 on both sides of the equation , we get
y = 3 x 2
y = 6
Therefore , the value of a = 6
Hence , The value of a from the equation of slope is a = 6
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Could someone help me with my math?? Neville says, "I add because of the words
in all. The answer is 9 pencils." Anthony says,
"I multiply because there are equal groups.
The answer is 18 pencils." Who is correct?
Explain.
From the statement, Anthony is correct because 3*6=18
How to determine the number of pencils she bought?We should know that the problem is to determine the number of pencils he bought
The given parameters are that
You can draw a 3 packages of pencils with 6 pencils in each to represent t package.
Now let us do the following:
For Neville
3*6 = 18
And also,
18÷3 = 6
For Anthony
6*3 =18 and
18÷6 = 3
In conclusion, looking at the two analysis, it seems that Anthony is more correct knowing fully well that each of the multiplications and divisions give us 18 or 6
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Complete question:
Critique Reasoning Neville and Anthony are solving this problem: Barbara bought You can draw a 3 packages of pencils with 6 pencils in each to represent t package. How many pencils did she buy in all? Neville says, “I add because of the words in all. The answer is 9 pencils.” Anthony says, “I multiply because there are equal groups. The answer is 18 pencils.” Who is correct? Explain.
A collection of coins consists of nickels, dimes and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin are in the collection if the total value of the collection is $4.35
Answer:
There are 12 nickels, 9 quarters, and 15 dimes.
I hope this turns out useful for you!
Step-by-step explanation:
Reading the problem repeatedly, I found that the nickels were the value that I could change to find out the values of the other coins and to find the answer. I started with the number of nickels as 20, calculating 20 x 5 (5 as the value of the nickel) = 100 ($1.00). Then, I subtracted three from 20 since the number of quarters was 3 less and got 17. 17 x 25 = a value far too big when we were going to add dimes as well, so 8 lowered the number of nickels a reasonable amount and tried again, following the directions in the problem. It took a bit, but I found a value that worked.
Nickel = $0.05
Quarter = $0.25
Dime = $0.10
My work (though I converted a bit using my sense of money)
12 x 5 = $0.60
12 - 3 = 9
9 x 25 = $2.25
9 + 6 = 15
15 x 10 = $1.50
$0.60 + $2.25 + $1.50 = $4.35
Mike drinks of a litre of juice each day.
Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.
Mike buys enough juice to last for 7 days.
What is the lowest price Mike can pay for this juice?
Show how you decide.
lowest price Mike can pay for this juice is £15.8
What is an integer?
An integer (pronounced IN-tuh-jer) is an integer (not a fraction) that is positive, negative, or zero.
An example of an integer is:
-5, 1, 5, 8, 97, 3,043.
Examples of non-integers are:
-1.43, 1 3/4, 3.14, 0.09, and 5643.1.
The set of integers denoted by Z is formally defined as:
Z = {...,-3,-2,-1,0,1,2,3,...}
It is given that Mike drinks of a litre of juice each day.
Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.
Mike buys enough juice to last for 7 days.
Total litre of milk needed = 7 × 1 = 7 litre
7l = 2l + 2l + 2l + 1l
Lowest cost = 4.40 + 4.40 + 4.40 + 2.60 = 15.8
Therefore, lowest price Mike can pay for this juice is £15.8
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hey please explain in it I stuck there please solve fast
If ( sin x + cosec x ) ² + ( cos x + sec x )² = k + tan² x + cot² x then what is the value of k.
a- 8
b - 7
c- 4
d-3
Don't Spam
Answer:
b) 7
Step-by-step explanation:
Given equation:
[tex](\sin x + \csc x)^2+(\cos x + \sec x)^2=k+\tan^2 x + \cot^2 x[/tex]
Expand the left side of the equation:
[tex]\implies \sin^2x+2 \sin x \csc x + \csc^2x + \cos^2 x + 2 \cos x \sec x + \sec^2 x[/tex]
Simplify:
[tex]\implies \sin^2x+2 \sin x \cdot \dfrac{1}{\sin x} + \csc^2x + \cos^2 x + 2 \cos x \cdot \dfrac{1}{\cos x} + \sec^2 x[/tex]
[tex]\implies \sin^2x+2 + \csc^2x + \cos^2 x + 2 + \sec^2 x[/tex]
[tex]\implies \sec^2 x+\csc^2x+ \sin^2x + \cos^2 x +4[/tex]
Use the identity: sin²x + cos²x = 1
[tex]\implies \sec^2 x+ \csc^2x+1+4[/tex]
[tex]\implies \sec^2 x+ \csc^2x+5[/tex]
Use the identities: sec²x = tan²x + 1 and csc²x = cot²x + 1
[tex]\implies \tan^2x +1 +\cot^2x +1 +5[/tex]
[tex]\implies 7+\tan^2x + \cot^2x[/tex]
Therefore:
[tex](\sin x + \csc x)^2+(\cos x + \sec x)^2=7+\tan^2 x + \cot^2 x[/tex]
[tex] \huge{ \bold{Answer -: }}[/tex]
Option b is correct
Explanation-:[tex] \large \bf{given}[/tex]
[tex] \large{ \sf{ \: (sin \: x \: + cosec \: x) {}^{2} + (cos \: x + sec \: x) {}^{2} }}[/tex]
[tex]\large{ \sf{ = k + { \tan^{2} x + \cot^{2} x}}}[/tex]
[tex] \large{ \sf{\implies \: sin {}^{2} x + cosec {}^{2} x + 2 + {cos}^{2} x + {sec}^{2} x + 2}}[/tex]
[tex]\large{ \sf{ = k + {tan}^{2} x + {cot}^{2} x}}[/tex]
[tex]\large{ \sf{ \implies \: 1 + {cosec}^{2} x - {cot}^{2} x + {sec}^{2} x - {tan}^{2} x + 4 = k}}[/tex]
[tex]\large{ \sf{ \pink{ \implies \: 1 + 1 + 1 + 4 = k \implies \: k = 7}}}[/tex]
[tex] \therefore \: k \: = 7[/tex]
____________________Given the equation four ninths plus h equals eleven over nine, determine the value of h. nine over seven, seven ninths, forty four over eighty one, fifteen over ninetee,n
The required value of h in the equation 4/9 + h = 11/9 is 7/9 or seven ninths.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
4/9 + h = 11/9 (1)
To determine the value of h, solve the equation,
Subtract 4/9 from both the sides,
4/9 + h - 4/9 = 11/9 - 4/9
h = 7/9
The value of h is 7/9 or seven ninths.
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