What is the length of the side of a right triangle that has a side length of 12 ft and hypotenuse that measures 15 ft
Answer:
9 ft
Step-by-step explanation:
The Pythagorean theorem states
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
Substituting in what we know (one leg is 12 and the hypotenuse is 15)
12^2 +b^2 = 15^2
144+ b^2 = 225
Subtract 144 from each side
144-144 +b^2 = 225-144
b^2 =81
Take the square root of each side
sqrt(b^2) = sqrt(81)
b = 9
the rational roots of a polynomial function f(x) can be written in the form p/q where p is a factor of the leading corfficient of the polynomial and q is a factor of the constant term true or false
False.
The Rational Root theorem states that P is a factor of the constant term and q is a factor of the leading coefficient.
What is the solution to the equation ? 1/2n =8 ? = 4 n = 6 n = 10 n = 16
Answer:
n = 16
Step-by-step explanation:
1/2 n = 8 (multiply both sides by 2)
(1/2) (2) n = 8 (2)
n = 8 (2)
n = 16
please
simplify 7^6 √ 7^2
Answer:
Step-by-step explanation:
The tough part of this question is figuring out what to do with √(7^2). You could do it by expanding the square. √(7^2) = √49
Now what is the square root of 49? Is it not 7?
√49 = 7
7^6 * 7^1
7 ^(6 + 1)
7 ^ 7
Answer:
49
Step-by-step explanation:
The sum of two numbers is 10 the larger number is four times the smaller number this is the system of equations used to represent the scenario is Y equals negative X +10 and Y equals 4X what is the larger number
Answer:
The larger number is 8
Step-by-step explanation:
Let
x -----> the smaller number
y ----> the larger number
we know that
x+y=10
y=10-x -----> equation A
y=4x -----> equation B
Solve by substitution
substitute equation B in equation A and solve for x
4x=10-x
4x+x=10
5x=10
x=2
Find the value of y
y=4x-------> y=4(2)=8
therefore
The smaller number is 2 and the larger number is 8
To find the larger number where the sum of two numbers is 10 and the larger is four times the smaller, the system of equations y = -x + 10 and y = 4x is used, and through solving, the larger number is determined to be 8.
The question entails finding the larger number when two numbers sum to 10, and the larger number is four times the smaller number. The system of equations representing the scenario is y = -x + 10 and y = 4x. To find the larger number, set these two equations equal to each other since they both equal y:
4x = -x + 10
Now, solve for x by adding x to both sides:
5x = 10
Then, divide both sides by 5:
x = 2
Since x is the smaller number, and y is four times larger, compute y:
y = 4x = 4(2) = 8
The larger number (y) in this case is 8.
How many significant figures does this number have? 6,253.862 3 4 7 0
Answer: 7
Step-by-step explanation: Since there are no 0’s, just count the number of digits. There are 7.
The system of equations 3x – 6y = 20 and 2x – 4y = 3 is
A. consistent.
B. inconsistent.
C. independent.
D. dependent.
Answer:
The system is inconsistent because there is no solution.
Step-by-step explanation:
I'm going to put both of these in slope-intercept form (y=mx+b where m is slope and b is y-intercept).
3x-6y=20
Solve for y.
3x-6y=20
Subtract 3x on both sides:
-6y=-3x+20
Divide both sides by -6:
y=(-3/-6)x+(20/-6)
Reduce:
y=(1/2)x+(-10/3)
The slope is 1/2 and the y-intercept is -10/3.
2x-4y=3
Solve for y.
2x-4y=3
Subtract 2x on both sides:
-4y=-2x+3
Divide both sides by -4:
y=(-2/-4)x+(3/-4)
Reduce:
y=(1/2)x+(-3/4)
The slope is 1/2 and the y-intercept is -3/4.
The lines are parallel so they have no intersection. I know they are parallel because they have the same slope and different y-intercept.
The system is inconsistent because there is no solution.
Answer:
B) Inconsistent
Step-by-step explanation:
Step 1: Write both equations
3x - 6y = 20
2x - 4y = 3
Step 2: Find x in terms of y
3x - 6y = 20
x = 20+6y/3
Step 3: Substitute x in one of the equations to find y
2x - 4y = 3
2(20+6y/3) - 5y = 3
40 + 12y - 12y = 9
0 ≠ -31
Therefore, these system of equations have no solution.
Step 4: Choose the option
A) consistent- A consistent system of equations has at least one set of equations. Therefore, this option is incorrect.
B) inconsistent- An inconsistent system of equations has no solution. Therefore, this option is correct.
C) Independent- An independent system of equations has one solution. Therefore, this option is incorrect.
D) Dependent- A dependent system of equations have infinite solutions. Therefore, this option is incorrect.
Option B is the right answer
!!
What is the measure of angle ABC in the circle shown in the picture?
Answer:
45°
Step-by-step explanation:
I think you meant m<ACB, and from what I see here, I took half of 90°, which is 45°.
How many subsets does the set A have? A={-3,-2,-1,0,1,2,3}
Answer:
128
Step-by-step explanation:
You find the number of subsets of a set by using the formula [tex]2^{\text{ number of elements}[/tex].
We have 7 elements so that means we have [tex]2^{7}=128[/tex] subsets.
A set with 7 elements can have 128 subsets, as calculated using the equation 2^n, where n is the number of elements in the set.
Explanation:In Mathematics, a subset is a portion of a set, including the empty set and the set itself. The number of subsets a set can have is calculated using the equation 2^n, where 'n' is the number of elements in the set. In this case, the set A includes 7 elements, therefore applying the equation we get: 2^7=128 subsets, which is the answer to your question.
For example, {-3, -1, 0} would be a subset of set A, as would {0, 1, 2}, {-2, 0, 2}, and so on. The complete set ({-3,-2,-1,0,1,2,3}) is also a subset, as is the empty set ({}).
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The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? A)Both the domain and range of the transformed function are the same as those of the parent function.
B(Neither the domain nor the range of the transformed function are the same as those of the parent function.
C)The range but not the domain of the transformed function is the same as that of the parent function.
D)The domain but not the range of the transformed function is the same as that of the parent function.
Answer:
The domain but not the range of the transformed function is the same as that of the parent function ⇒ answer D
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) translated horizontally to the right by h units,
then the new function g(x) = f(x - h)
- The domain of a function is set of the values of x which make
the function defined
- The range is the set values of y that corresponding with the domain
- The domain of the function f(x) = IxI is the set of all real numbers
∴ The domain of f(x) is {x : x ∈ R}
- The range of the function f(x) = IxI is the set of all real numbers
greater than or equal 0
∴ The range f(x) = {y : y ≥ 0}
∵ f(x) reflected across the x-axis, then it will be change to g(x) = -IxI
∴ All the y-coordinates of the point on the function will be change
from positive values to negative values
∵ The rang of f(x) is {y : y ≥ 0}
∴ The range of g(x) is {y : y ≤ 0}
∵ After the reflection the function translated 6 units to the right
∴ The x will change to x - 6
∴ The function will be h(x) = -Ix - 6I
- There is no values of x make h(x) undefined, then its domain is
set of all real number
∴ The domain of h(x) is {x : x ∈ R}
∵ The domain of f(x) is {x : x ∈ R}
∵ The range of h(x) is the same the range of g(x)
∴ The range of h(x) is {y : y ≤ 0}
- f(x) and h(x) have same domains and different ranges
∴ The correct statement is: The domain but not the range of the
transformed function is the same as that of the parent function
- Look to the attached graph for more understanding
# The red graph is f(x)
# The blue graph is h(x)
Answer:
d
Step-by-step explanation:
consider the polynomial p(x)=32x^5y-2xy^5
part a: What is the complete factorization of p(x)=32x^5y-2x^5 over the integers?
part b: what methods are used to factor p(x)=32x^5y^5?
Select 1 answer for a and one for b.
a- 2xy(2x-y)^2 (2x+y)^2
a-2xy(2x-y)(2x+y)(4x^2+y^2
a-2xy(4x^2-y^2)(x^4-4x^2y^2+y^4
b-repeated differences of squares
b- difference of cubes
b-greatest common factor
b-grouping
Answer:
a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²) ⇒ 2nd answer
b- repeated differences of squares ⇒ 1st answer
Step-by-step explanation:
* Lets explain how to solve the problem
∵ p(x) = 32x^5y - 2xy^5
- The coefficients of the two terms are 32 and 2
∵ 2 is a common factor in 32 and 2
∵ 32 ÷ 2 = 16 and 2 ÷ 2 = 1
∴ p(x) = 2(16x^5y - xy^5)
* Now lets find the common factors of the variables x and y
∵ The common factor is x^5 and x is x
∵ The common factor in y and y^5 is y
∴ the common factors in 16x^5y - xy^5 are xy
∵ 16x^5y ÷ xy = 16x^4
∵ xy^5 ÷ xy = y^4
∴ p(x) = 2xy(16x^4 - y^4)
- Remember that a² - b² is called difference of two squares we
factorize it by distributed into two polynomials have same terms
with different middle sign (a + b)(a - b)
∵ 16x^4 - y^4 is a different of two squares because √(16x^4) = 4x²
and √9y^4) = y²
∴ The factorization of 16x^4 - y^4 is (4x² + y²)(4x² - y²)
∴ p(x) = 2xy[(4x² + y²)(4x² - y²)]
- The bracket 4x² - y² is also different of two squares because
√(4x²) = 2x and √(y²) = y
∴ The factorization of 4x² - y² is (2x - y)(2x + y)
∴ p(x) = 2xy(2x -y)(2x + y)(4x² + y²)
a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²)
b- The methods used to factor p(x) are:
greatest common factor and repeated differences of squares
- But you ask to chose one answer of b so chose repeated
differences of squares
Select the expressions that are equivalent to 6r + 5r.
For this case we have the following expression:
[tex]6r + 5r[/tex]
We can rewrite the expression in different ways.
Form 1:
Adding similar terms:
[tex]6r + 5r = 11r[/tex]
Form 2:
Making common factor we have:
[tex]6r + 5r = (6 + 5) r[/tex]
Answer:
Some equivalent expressions are given by:
[tex]6r + 5r = 11r\\6r + 5r = (6 + 5) r[/tex]
The expression 6r + 5r simplifies to 11r by combining like terms. In this case, the 'like term' is 'r'. When we add the coefficients of the like terms, we get 11r.
Explanation:The student's question involves simplifying the expression 6r + 5r. This is an addition problem in algebra where we are adding like terms. Like terms are terms in an algebraic expression that has the exact same variable(s) to the same power(s). In the given expression '6r + 5r', the like terms are '6r' and '5r' because they both have the same variable 'r'.
To simplify, we add the coefficients of the like terms. The coefficient of 'r' in '6r' is 6 and in '5r' is 5. When we add 6 and 5, we get 11. Therefore, the equivalent expression of '6r + 5r' is '11r'.
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What is cos -1 ( -1/2) in quadrant 1 ?
Answer:
[tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
So here they are asking for one angle that gives you the cosine value is equal to -1/2 while being in quadrant 2.
So you look in quadrant 2 and find x=-1/2 which is at [tex]\frac{2\pi}{3}[/tex].
[tex]\cos^{-1}(\frac{-1}{2})=\frac{2\pi}{3}[/tex] while being in quadrant 2.
Which of these sentences is always true for a parallelogram? A. All sides are congruent.
B. All angles are congruent.
C. The diagonals are congruent.
D. Opposite angles are congruent.
Answer:
The correct option is D.
Step-by-step explanation:
A paralellogram is a flat shape with 4 straight sides and opposite sides are parallel.
There are six important properties of a parallelogram.
1) Opposite sides are congruent.
2) Opposite angels are congruent.
3) Consecutive angles are supplementary.
4) If one angle is right, then all angles are right.
5) The diagonals of a parallelogram bisect each other....
Answer:
its D
Step-by-step explanation:
Neeeed help noww please
Answer:
6
Step-by-step explanation:
f(n+1) = f(n) -2
We know f(1) = 10
Let n=1
f(1+1) = f(1) -2
f(2) = 10-2 =8
We now know f(2)
Let n=2
f(2+1) = f(2)-2
f(3) = 8 -2=6
f(3) =6
Plutonium-240 decays according to the function L where o
represents the quantity remaining after t years and k is the decay constant,
0.00011... How long will it take 24 grams of plutonium-240 to decay to 20
grams?
Answer:
[tex]\boxed{\textbf{1700 yr}}[/tex]
Step-by-step explanation:
[tex]-\dfrac{\text{d}L}{\text{d}t} = kL\\\\\dfrac{dL}{L}=-kdt\\\\\ln L = -kt + C\\\text{At t = 0, L = L$_{0}$, so C = $\ln L_{0}$}\\\ln L = -kt + \ln L_{0}\\\ln L_{0} - \ln L = kt\\\\\ln \dfrac{L_{0}}{L} =kt[/tex]
Data:
L₀ = 24 g
L = 20 g
k = 0.000 11 yr⁻¹
Calculation:
[tex]\ln \dfrac{24}{20} =0.000 11t\\\\\ln 1.2 = 0.000 11t\\\\0.1823 = 0.000 11t\\\\t = \dfrac{0.1823}{0.000 11} = \textbf{1700 yr}\\\\\text{It will take } \boxed{\textbf{1700 yr}}\text{ for the polonium to decay to 20 g}[/tex]
Find the range of 2,7,3.1,4.2,1.9,2.4,and 2.7
Answer:2244.23136
Step-by-step explanation:
The range is the difference between the highest term and the lowest term.
The range of the numbers is 1.1.
GivenThe numbers are 2, 7, 3.1, 4.2, 1.9, 2.4, and 2.7.
What is the range?
The range is the difference between the highest term and the lowest term.
[tex]\rm Range = Highest \ Term - Lowest \ Term[/tex]
Here, the highest term in the numbers = 3.1
And the lowest term = 2
Therefore,
The range is given by,
[tex]\rm Range = Highest \ Term - Lowest \ Term\\\\Range = 3.1-2\\\\Range = 1.1[/tex]
Hence, the range of the numbers is 1.1.
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Express 0.7723 as a fraction.
Answer:
7033/10000
Step-by-step explanation:
You get his answer by times it by 1000 so the decimal point is out of the number
what are terms? how do you combine them? can you give me an example?
A term is any number, variable or combination of a number and a variable in an equation.
Examples:
In 2x + 5y + 8, 2x is one term, 5y is a second term and 8 is a 3rd term.
In the equation 2x + 3 + 5x -2
Combine the like terms 2x and 5x are like terms because they both have x as a variable, there is a plus sign in fron of the 5x, so you would have 2x +5x = 7x
Then 3 and 3 are like terms, because they are just numbers, there is a subtraction sign in front of the 2, so you have 3-2 = 1
The equation then becomes: 2x + 3 + 5x -2 : 7x + 1
Which of the following would be the most logical first step to solving this
quadratic equation?
x2 - 4x + 16 = 2
A. Take the square root of both sides.
B. Subtract 2 from both sides.
ESTATE
C. Factor the left side into a perfect square.
D. Divide both sides by x
Answer:
The correct option is B:
Subtract 2 from both sides
Step-by-step explanation:
We have the equation x²-4x+16=2
The first step to solve this equation is:
Subtract 2 from both sides
We get;
x²-4x+16=2
x²-4x+16-2=2-2
x²-4x+14=0
Now this is the quadratic equation. You can use quadratic formula to solve this equation....
Factor the polynomial completely.
Find a GCF: –2x2 + 2 + 5x3 – 5x
GCF = –2 GCF = 5x
Factor out the GCF: –2(x2 – 1) + 5x(x2 – 1)
Which product of prime polynomials is equivalent to the original polynomial?
(–2 – 5x)(x2 – 1)
(–2 + 5x)(x2 – 1)
(–2 – 5x)(x – 1)(x + 1)
(–2 + 5x)(x – 1)(x + 1)
Answer:
Option D is correct
Step-by-step explanation:
The original polynomial is:
–2x2 + 2 + 5x3 – 5x
Arranging in decreasing power of x:
[tex]5x^3 - 2x^2 -5x+2[/tex]
Factoring the given polynomial by grouping:
[tex]5x^3 - 2x^2 -5x+2\\=5x^3-5x- 2x^2+2\\=5x(x^2-1)-2(x^2-1)\\=(5x-2)(x^2-1)[/tex]
Now, (x^2-1) can be further solved using formula:
(a^2-b^2)=(a-b)(a+b)
Solving:
[tex]=(5x-2)(x^2-1)\\=(5x-2)(x-1)(x+1)[/tex]
So, [tex](5x-2)(x-1)(x+1)[/tex] represents the factors of [tex]-2x2 + 2 + 5x3-5x[/tex]
Hence Option D is correct.
Answer: the answer is D
Step-by-step explanation:
the screen has proof it is correct... also please STOP deleting my answers its all ways the same person and its getting really annoying when im giving you the correct answer, im just trying to help :(
In the right triangle ABC shown to the right, what is the length of
AC?
A) 10
B) 14
C) 13
D) 169
E) NOTA
Answer:
The answer is C) 13.
Step-by-step explanation:
To find the hypotenuse (longest side) of a right triangle, you need to use the Pythagorean Theorem. The formula for the hypotenuse is a^2 + b^2 = c^2.
5^2 (five squared) equals 25, and 12^2 (twelve squared) equals 144.
25 + 144 = 169
Next, find the square root of 169. It is 13. 13 is the length of the hypotenuse.
I hope this helped! :)
In the right triangle ABC, the length of the AC is equal to [tex]13[/tex] units.
What is the right triangle?" Right triangle is defined as a triangle with one of the interior angles with measure equals to [tex]90[/tex] degrees."
Formula used
Pythagoras theorem,
(Hypotenuse)² = ( adjacent side)² + (opposite side)²
According to the question,
In the right triangle ABC,
Adjacent side 'BC' [tex]= 12[/tex] units
Opposite side 'AB' [tex]= 5[/tex] units
'AC' represents the hypotenuse of the right triangle
Substitute the value in the Pythagoras theorem we get,
[tex]AC^{2} = BC^{2} +AB^{2} \\\\\implies AC^{2} = 12^{2} + 5^{2} \\\\\implies AC^{2} = 144 + 25\\\\\implies AC = \sqrt{169} \\\\\implies AC =13units[/tex]
Hence, Option(C) is the correct answer.
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please help me with this parent function
Answer:
[tex]\sqrt[3]{x} -3[/tex]: The parent graph will move 3 units down.
[tex]\sqrt[3]{x-3}[/tex]: The parent graph will move 3 units right.
Step-by-step explanation:
The parent function [tex]\sqrt[3]{x}[/tex] looks like the first image attached.
Using knowledge of transformations, numbers outside the radical move the graph up or down (vertically). A positive number moves the graph up; a negative number moves the graph down.
Numbers inside the radical move the graph left or right (horizontally). A positive number moves the graph left; a negative number moves the graph right.
In the first transformation [tex]\sqrt[3]{x} -3[/tex] the number is outside of the radical, meaning that the graph will move vertically. The 3 is negative, so the graph will move 3 units down.
The first transformation moves the parent graph 3 units down.
In the second transformation [tex]\sqrt[3]{x-3}[/tex] the number is inside the radical so the graph will move horizontally. The 3 is negative so the graph will move 3 units to the right.
The second transformation moves the parent graph 3 units right.
The attached images show:
parent function graphparent function graph moved 3 units downparent function graph moved 3 units rightparent function graph and the two transformationsThe distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 2 to t = 5 represent?\
Answer:
The rate of change determines the average speed of the ball when it is dropped from the building.
Step-by-step explanation:
d(t) = 16t^2
when t = 2
d(t) = 16 (2)²
d(t) = 64
when t = 5
d(t) = 16 (5)²
d(t) = 400
Average speed/rate of change = distance/time = 64/2 = 32 feet
Average speed/rate of change = distance/time = 400/5 = 80 feet
The rate of change determines the average speed of the ball when it is dropped from the building.
!!
The average rate of change of d(t) from [tex]\( t = 2 \) to \( t = 5 \)[/tex] represents that the ball traveled at an average rate of 112 feet per second during this time interval.
The average rate of change of a function over a given interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing by the difference in the independent variable values. In this case, we want to find the average rate of change of the function [tex]\( d(t) = 16t^2 \) from \( t = 2 \) to \( t = 5 \).[/tex]
First, we find the values of the function at the endpoints of the interval:
- At [tex]\( t = 2 \), \( d(2) = 16(2)^2 = 64 \)[/tex] feet.
- At [tex]\( t = 5 \), \( d(5) = 16(5)^2 = 400 \)[/tex] feet.
Then, we calculate the difference in the function values:
[tex]\[ \text{Difference in } d(t) = d(5) - d(2) = 400 - 64 = 336 \text{ feet} \][/tex]
Next, we calculate the difference in the independent variable values:
[tex]\[ \text{Difference in } t = 5 - 2 = 3 \text{ seconds} \][/tex]
Finally, we find the average rate of change by dividing the difference in d(t) by the difference in t:
[tex]\[ \text{Average rate of change} = \frac{\text{Difference in } d(t)}{\text{Difference in } t} = \frac{336}{3} = 112 \text{ feet/second} \][/tex]
What is the common difference or common ratio of the sequence 2,5,8,11...? A. 1 B. 3 C. 5 D. 7
Answer:
B. 3
Step-by-step explanation:
A common difference in an arithmetic sequence is the value the terms in the sequence vary from one to another.You can find one term to another by adding or subtracting the common difference.
In this case, the terms are 2,5,8,11,.....
From the first term to the second term, the difference is, 5-2=3
From the second term to the third term, the difference is, 8-5=3
From the third term to the fourth term the difference is=11-8=3
Hence the common difference in this arithmetic sequence is 3
[tex]\huge{\text{Hey there!}}[/tex]
[tex]\huge\text{We could use the word {difference} in this equation}[/tex]
[tex]\huge\text{The\ difference usually means subtract in math}}[/tex] [tex]\huge\text{terms!}[/tex]
[tex]\huge{\text{So, we subtract the terms to find your answer!}}[/tex]
[tex]\huge\text{5 - 2 = 3. So we know that 3 could be a possible}[/tex] [tex]\huge\text{answer.}[/tex]
[tex]\huge\text{11 - 8 = 3 }[/tex]
[tex]\huge\rightarrow\text{8 - 5 = 3}[/tex]
[tex]\huge\text{The ratio difference = 3!}[/tex]
[tex]\boxed{\boxed{\huge{\text{Answer: B. 3}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:}[/tex]
Find four consecutive even integers with a sum of -52
Final answer:
To find four consecutive even integers with a sum of -52, we denote the smallest integer as x and use the equation x + (x+2) + (x+4) + (x+6) = -52 to find that these integers are -16, -14, -12, and -10.
Explanation:
To find four consecutive even integers with a sum of -52, let's denote the smallest of these integers as x. Consequently, the next three integers can be represented as x+2, x+4, and x+6. The sum of these four integers can be expressed as the equation x + (x+2) + (x+4) + (x+6) = -52.
Combining like terms gives us 4x + 12 = -52. Subtracting 12 from both sides gives 4x = -64, and dividing both sides by 4 yields x = -16. Therefore, the four consecutive even integers are -16, -14, -12, and -10.
The four consecutive even integers with a sum of -52 are -16, -14, -12, and -10.
Let's denote the four consecutive even integers as [tex]\( x \), \( x+2 \), \( x+4 \), and \( x+6 \)[/tex].
According to the problem, their sum is -52. So, we can set up the equation:
[tex]\[ x + (x + 2) + (x + 4) + (x + 6) = -52 \][/tex]
Now, let's solve for \( x \):
[tex]\[ 4x + 12 = -52 \][/tex]
Subtract 12 from both sides:
[tex]\[ 4x = -52 - 12 \][/tex]
[tex]\[ 4x = -64 \][/tex]
Divide both sides by 4:
[tex]\[ x = \frac{-64}{4} \][/tex]
[tex]\[ x = -16 \][/tex]
Now that we've found the value of \( x \), we can find the consecutive even integers:
- First even integer: [tex]\( x = -16 \)[/tex]
- Second even integer: [tex]\( x + 2 = -16 + 2 = -14 \)[/tex]
- Third even integer: [tex]\( x + 4 = -16 + 4 = -12 \)[/tex]
- Fourth even integer: [tex]\( x + 6 = -16 + 6 = -10 \)[/tex]
So, the four consecutive even integers with a sum of -52 are -16, -14, -12, and -10.
complete question given below:
Find four consecutive even integers with a sum of -52.Find the four integeres
Find the measure of the third angle of a triangle given that the first two angles are 44º and 72º.
Show your work.
The sum of the three angles of a triangle need to equal 180
To find the third angle subtract the two known angles from 180.
Third angle = 180 - 44 - 72 = 64 degrees.
Answer:
All angles of a triangle add up to 180. Just subtract. -72 --> 108 - 44. 64
Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at x = 4.
Answer:
Possibility 1: [tex]\frac{(x+1)(x+1)}{(x-4)(x+5)}[/tex]
Possibility 2: [tex]\frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}[/tex]
Possibility 3: [tex]\frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}[/tex]
There are infinitely many more possibilities.
Step-by-step explanation:
So we are looking for a fraction in terms of x.
We have a horizontal asymptote so that means the degree of the top has to equal to degree of the bottom. It is also at y=1 which means the coefficient of the leading term on top and bottom must be the same (but not zero) since the same number divided by the same number is 1.
Now we also have a vertical asymptote at x=4 which means we need a factor of x-4 on bottom.
So there is a lot of possibilities. Here are a few:
Possibility 1: [tex]\frac{(x+1)(x+1)}{(x-4)(x+5)}[/tex]
You have the degrees are the same on top and bottom and the leading coefficients are the same. You also have that factor of (x-4) on bottom.
Possibility 2: [tex]\frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}[/tex]
Possibility 3: [tex]\frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}[/tex]
Now a factor of (x-4) can be canceled here but you still have a factor of (x-4) left on bottom so you still have the vertical asymptote. You also still have the same leading coefficient on top and bottom (-4 in this case) and the same degree.
Which equation can be used to solve for b?
Answer:
The first one
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{b}{8}[/tex]
Multiply both sides by 8
8 × tan30° = b, that is
b = 8tan30°
Answer:
b = (8)tan(30o)
Step-by-step explanation:
(6x^2-2x)+(5x-7)
Add and/or simply
Answer:
6x^2 + 3x - 7.
Step-by-step explanation:
(6x^2 - 2x) + (5x - 7)
= 6x^2 - 2x + 5x - 7 Adding like terms we get:
6x^2 + 3x - 7.
Final answer:
To simplify the algebraic expressions (6x²-2x)+(5x-7), you combine like terms to get the final expression 6x² + 3x - 7.
Explanation:
The student's question involves adding and simplifying algebraic expressions. To add the expressions (6x²-2x)+(5x-7), you need to combine like terms. Like terms are those terms that contain the same variable raised to the same power. Here is the process step-by-step:
Identify like terms in both expressions.Combine like terms by adding their coefficients. For the terms, 6x² and 0x² (the second expression doesn't have an x² term, so it's 0x²), add 6 + 0 = 6. For the terms -2x and 5x, add -2 + 5 = 3.Finally, the constant terms -7 and 0 (again, no constant term in the first expression) are combined by adding -7 + 0 = -7.The resulting simplified expression is 6x² + 3x - 7.