The value of x will be 158. The value of x is obtained by simplifying the equation.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Identity used;
(x+a)(x-a) = x² - a²
Given expression;
3(x-7)(x+7) - (x-1)(3x+2) = 13
Solving the equation step by step;
[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]
Hence, the value of x will be 158.
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When Manny goes on vacation, he boards his dog at a kennel. The kennel charges a flat fee
of $25, plus $15.50 per night.
Write an equation that shows how the cost of a kennel stay, y, depends on the number of
nights, x.
Step-by-step explanation:
y = 25 + 15.5x
it's $25 plus the number of nights times $15.5 per night
Solve for X
130, 40, ?
Answer:
x = 90
Step-by-step explanation:
The other unlabled angle in the triangle forms a 180 degree angle with 130 degrees (because they make a straight line). So it can be found by subtracting 130 from 180, which equals 50.
The sum of all the angles in a triangle is 180.
180 - 50 - 40 = x
90 = x
Hello! My name is Galaxy and I'll be helping you solve this problem. We can split this problem into two steps. Them being Theory and Solving.
I'll go ahead and start with the Theory.
TheoryWe can start off by looking at the image you've provided, we can see a triangle that has 2 angles given of a triangle, and an exterior angle of the triangle.
This being said, we can apply the Exterior Angle Theorem.
We can now begin to solve for the missing angle.
SolvingWe can begin to solve by using our given angles to find the third angle.
According to the Exterior Angle Theorem, we know that the unknown angle along with the [tex]40[/tex]° angle must add up to the [tex]130[/tex]° angle.
Therefore, we can solve for [tex]x[/tex],
[tex]x+40=130\\x=130-40\\x=90[/tex]
After this, we know that angle [tex]x[/tex] is equal to 90°.
Cheers,
Galaxy
If function g has the factors (x − 7) and (x 6), what are the zeros of function g?
In a rectangle the length of diagonal AC is given by (20x+12)&BDis (14x+24)cm find AC&BD
Answer:
52cm, based on my understanding of the question.
Step-by-step explanation:
See attached image. Please confirm my understanding of the question.
Could these triangles be congruent? yes, if ab ≅ de yes, if bc = 7 yes, if ab ≅ ef no, because the hypotenuses must have different lengths
Yes, the triangles are congruent if AB ≅ DE.
Criteria for the Congruency of two Triangles
If two triangles share the same sides and angles, they are said to be congruent triangles.
Triangles are tested for congruence using the following 4 criteria:
1) Angle-side-angle(ASA): Two angles and a side of a triangle are congruent if they are equal to two angles and the corresponding side of another triangle.
2) Side-side-side(SSS): Two triangles make congruent triangles if all three sides of one triangle are equal to three sides of another.
3) Side angle side(SAS): A triangle is congruent if its two sides and any included angles are equivalent to those of another triangle's two sides and corresponding angle.
4) Hypotenuse - leg(HL): If a triangle's hypotenuse and one of its legs are equal, then the triangle's hypotenuse and leg are also equal.
Checking for Congruency in the Given Triangles
ΔDEF and ABC have a equal angles, ∠F=∠B, as well as a pair of equal sides, DF = AC.
Thus, in order to satisfy the SAS criterion of congruent triangles, AB = DE
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Answer:
(D) no, because the hypotenuses must have different lengths
Step-by-step explanation:
Part b how do these functions differ from functions you have used in algebra in the past?
The functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
What is a function?It should be noted that a function simply means an equation where the x that is plugged into the equation will yield exactly on e y from the equation.
In this case, the functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
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whats the answer 2 1/3 x 1 2/5
Answer:
84/5 should be the answer
Step-by-step explanation:
cross multiply
PLEASE HELP ASAP!!!!!!
Right △EFG has its right angle at F, EG=8, and FG=2.
What is the value of the trigonometric ratio of an angle of the triangle?
Drag a value to each box to match the trigonometric ratio with its value.
TanE=
SinG=
SecG=
(4,1/4, 4√15/15, √15/15, √15/4)
(PLEASE ANSWER ASAP, ALSO IF YOU KNOW ANY OF THE OTHER ANSWERS TO THE PRE-CALUCLUS-TRIGONOMETRY SEMESTER TEST 6.04 PLEASE HELP!)
The values of the trigonometric ratio is 1/4 , √15 / 4 , 4 .
What are Trigonometric Ratios ?When a Triangle is a right angled Triangle then the ratios used to determine the sides and the angles of the triangle are called Trigonometric Ratio.
It is given that in triangle EFG , right angled at F ,
EG = 8 , FG = 2
By Pythagoras theorem
The length of EF is
8² = 2² + EF²
EF = √(64-4) = √60 = 2√15
The value of the trigonometric ratios is
sin E = Perpendicular / Hypotenuse
sin E = 2 / 8 = 1/4
sin G = 2√15 / 8 = √15 / 4
sec G = 1 / cos G = Hypotenuse / Base = 8 / 2 = 4
Therefore the values of the trigonometric ratio is 1/4 , √15 / 4 , 4 .
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what is the midpoint between 1 + 9i and 5 - 3i?
Answer:
The midpoint between 1 + 9i and 5 - 3i is 3 + 3iGivenPoints 1 + 9i and 5 - 3iTo find Midpoint between given pointsSolution
Midpoint is the average of the two points. Find it as follows:
(1 + 9i + 5 - 3i)/2 = (6 + 6i)/2 = 3 + 3iWhat is 12x³-9x² - 4x + 3 in factored form?
²-[
po
kx-
-
Answer:
(3x^2 - 1) * (4x - 3)
Step-by-step explanation:
Answer:
[tex]( {3x}^{2} - 1)(4x - 3) \\ [/tex]
One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0).
Which transformations could have taken place? Select two options.
Answer: C & D
Step-by-step explanation: Ro 270, Ro -90
please place the dot for me(20 points will give brainliest!!!)
Answer:
2,
Step-by-step explanation:
The vertex is the very highest or very lowest point. X coordinates are listed first, then Y.
find the surface area of the pyramid
Answer:
145
Step-by-step explanation:
mutiply each 6 and 7 twice and add 7x7 from the bottom
Determine which rotations will map this figure to itself.
The rotations which will map this figure itself are 60°, 120°, and 180°, and these values are given in option i.e. (a) ii, iii, and iv.
We have,
A figure which is on a straight line i.e 180°.
Now,
Find the rotations which it will make,
When a person or figure rotates completely i.e. to reach to its original position or shape it makes an angle of 360°.
So,
In the same way;
After rotaions of this figure to reach it to its original position it has to make an angle of 360°.
So,
That means,
First this figure will make a rotation of 60°.
Then it will make a rotation of 120°.
Then it will make a rotation of 180°.
i.e.
The sum of these angles = 60° + 120° + 180° = 360°.
So,
We have to choose that option, in which the sum of angles is 360°.
i.e.
Option 1. ii, iii, and iv.
Therefore, the rotations which will map this figure itself are 60°, 120°, and 180° and these values are given in option i.e. (a) ii, iii, and iv.
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one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
After 3 months memberships will cost the same.
We have,
Cost of Membership of 1st gym = $ 10 per month
And, the Cost of the sign-up fee for 1st gym = $ 45
And,
Cost of Membership of 2nd gym = $ 25 per month
And, the Cost of the sign-up fee of the 2nd gym = $ 0
Now,
Let the number of months = m
So,
According to the question;
45 + 10m = 25m
⇒
25m - 10m = 45
15m = 45
m=3
So, After 3 months memberships will cost the same.
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About how many people moved away from the great plains states during the depression? 100,000 250,000 2.5 million 10 million
Answer:
the answer is 2.5 million
Step-by-step explanation:
About 2.5 million people moved away from the Great Plains states during the Great Depression.
What is the great depression?The 1930s saw a catastrophic economic collapse known as the Great Depression. It was the twentieth century's longest, most widespread, and deepest depression, affecting countries all over the world. The Great Depression began on October 29, 1929, with a stock market catastrophe in the United States known as "Black Tuesday."
This movement was called the Dust Bowl migration and was caused by a combination of factors including drought, soil erosion, and economic hardship.
Many people left the region in search of better opportunities and living conditions.
Therefore, 250,0000 people moved.
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Which expressions are equivalent to 8(-10x+3.5y-7)? Select two options.
A. -80x + 24.5y - 56
B. -80x + 28y - 56
C. 80x + 28y + 56
D. 4 (-20x + 7y - 14)
E. -4 (-20x + 7y - 14)
Answer:
B, D
Explanation:
8(-10x+3.5y-7)
= -80x + 28y - 56
4 (-20x + 7y - 14)
= 8(-10x+3.5y-7)
= -80x + 28y - 56
Answer:
B) -80x + 28y - 56
D) 4 (-20x + 7y - 14)
Original Expression:
⇒ 8(-10x+3.5y-7)
⇒ -80x + 28y - 56
Now confirmed that option B is correct when the expression is simplified which makes option A and C not applicable.
For option D:
⇒ 4 (-20x + 7y - 14)
⇒ -80x + 28y - 56
Option E is not correct as:
⇒ -4 (-20x + 7y - 14)
⇒ 80x - 28y + 56
identify if each function is a polynomial function. justify your answer.
Functions which are polynomials are y=[tex]5x^{4} +x^{2} -8[/tex] ,y=[tex]7x^{3}[/tex] and y=[tex]6^{x}[/tex]
Given Functions : 1) y=[tex]-x^{2} +1/1-2x[/tex] 2)y=[tex]5x^{4} +x^{2} -8[/tex]. 3) y=[tex]7x^{3}[/tex]and g(x)=[tex]6^{x}[/tex].
We need to find which functions are polynomials. We know that polynomials is an expression consisting of indeterminates and coefficients that involves only the operations of addition, subtraction, multiplication and non negative integers .
First function is y=[tex]-x^{2} +1/1-2x[/tex]
The above function is not a polynomial because it has not a variable containing power in whole number and it is in fraction form. Two different polynomials can form numerator and denominator in a fraction.
Second function is y=[tex]5x^{4} +x^{2} -8[/tex]
The above function is a polynomial as it has a variable having power and it is not in fraction also.
Third function is y=[tex]7x^{3}[/tex]
The above function is also a polynomial for the same reason.
Fourth function is g(x)=[tex]6^{x}[/tex].
The above function is also a polynomial.
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please answer the question no 3
as fast as possible
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The value of the given series is 240.
What is arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
aₙ = a₁ + (n-1)d
where d is the difference and a₁ is the first term of the sequence.
The value of [tex]\log_{a^{\frac12}}(a)[/tex] will be equal to 2. Therefore, the series will become,
series = 2 + 4 + 6 + 8 + 10 + 12 + .... + 30
Now, as it can be observed that the given series is an arithmetic series, therefore, the number of terms in the series are,
30 = 2 + (n-1)1
28 = (n - 1)2
n - 1 = 14
n = 15
Further, the sum of the of the series will be,
sum = (15/2)[2(2) + (15-1)2]
sum = (15/2) [4 + 28]
sum = 240
Hence, the value of the given series is 240.
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Can someone look at the screenshot and help me?
Answer:
[tex]\boxed {A) m < CVB}[/tex]
Step-by-step explanation:
If C is a point inside ∠AVB, then :
⇒ m ∠AVC + m ∠CVB = m ∠AVB
3. Solve the following system of equations. 2v 3w = 16 2u + w = 4 v/6 - u/6 = 1
Answer:
this is what i got
Jamar is attempting to factor the expression 15x^2-16x-15. In his first step, he rewrites the expression as 15x^2-25x+9x-15. Which of the following statements in true about Jamar’s work?
A. Jamar's first step is correct. He should continue to factor the expression.
B. The two middle coefficients add to the correct number, but do not multiply to the correct number.
C. The two middle coefficients multiply to the correct number, but do not add to the correct number.
D. The two middle coefficients do not add or multiply to the correct number.
Jamar's first step is correct. He should continue to factor the expression. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
Jamar is attempting to factor the expression 15x² – 16x – 15.
In his first step, he rewrites the expression as 15x² – 25x + 9x – 15.
Jamar's first step is correct. He should continue to factor the expression.
Then the correct option is A.
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what is the y-intercept of f(x)=(1÷4)
Luis is going to an amusement park. The price of admission into the park is $20, and once he is inside the park, he will have to pay $4 for every ride he rides on. How much money would Luis have to pay in total if he goes on 6 rides? How much would he have to pay if he goes on r rides?
Cost with 6 rides:
Cost with r rides: need answers fast
Using a linear function, it is found that the costs are given as follows:
With 6 rides: $24.With r rides: C(r) = 20 + 4r.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the price of admission and the price per ride, the y-intercept is of 20 and the slope is of 4, the cost for r rides is given by:
C(r) = 20 + 4r.
Hence, for 6 rides, the cost is given by:
C(6) = 20 + 4 x 6 = $44.
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Find the value of x
Answer:
11
Step-by-step explanation:
The lengths of three sides of a trapezoid are shown below:
Side 1: 11z2 − 4z + 2
Side 2: −2z + 3 + 12z2
Side 3: 3 − 3z + 13z2
The perimeter of the trapezoid is 5z3 + 40z2 + 7z − 15.
Part A: What is the total length of sides 1, 2, and 3, of the trapezoid? (4 points)
Part B: What is the length of the fourth side of the trapezoid? (3 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (3 points)
Answer:
Part A = 36z² - 9z + 8
Part B = 5z³ + 4z² + 16z - 23
Part c = Yes.
Step-by-step explanation:
Polynomials : Polynomials are algebraic expressions that consist of variables and coefficients.
Trapezium: A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.
Given the length of sides :
Side 1: 11z² - 4z + 2
Side 2: -2z + 3 + 12z²
Side 3: 3 - 3z + 13z²
and The perimeter of the trapezoid is 5z³ + 40z² + 7z - 15.
PART A:
The total length of sides 1, 2, and 3 of the trapezoid is obtained by the sum of the trapezoid :
11z² - 4z + 2 + (-2z + 3 + 12z²) + 3 - 3z + 13z²
11z² - 4z + 2 - 2z + 3 + 12z² + 3 - 3z + 13z²
36z² - 9z + 8
PART B:
The length of the fourth side of the trapezoid is given by the difference between the perimeter of the trapezoid and the sum of length of sides 1, 2, and 3.
5z³ + 40z² + 7z - 15 - 36z² + 9z - 8
5z³ + 4z² + 16z - 23
PART C:
From part A, we can see that the addition of polynomials results in a polynomial.
Likewise, the subtraction of polynomials results in a polynomial.
Therefore, we can say that the polynomials are closed under addition and subtraction.
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please help me its help.
The answer will be 81.
Step-by-step explanation:
just multiple by 3
Answer:
81
Step-by-step explanation:
the people told secrion has a sequence of multiplyung by 3 if you continue the sequence you will get to 81
The speed of light is a constant and approximately equal to 300,000,000 meters per second.
Green lasers emit light at a wavelength of 532 nm. However, the material that is used to make most green lasers does not emit light at 532 nm. Instead, it emits light at a different wavelength, and the laser then uses a “frequency doubler.” This doubles the frequency of the emitted light, and the resultant light is the green 532 nm that we observe.
1 meter is equal to 1,000,000,000 nanometers.
What is the output light frequency of the material used before doubling?
The output light frequency of the material used before doubling will be 0.056 Hz.
What is the frequency?Frequency is defined as the number of repetitions of a wave occurring waves in 1 second.
Frequency is given by the formula as,
[tex]\rm v = \lambda \times f \\\\\ \rm f = \frac{v}{\lambda} \\\\ \rm f = \frac{3 \times 10^8}{532 \times 10^-9} \\\\ \rm f = 3 \times 10^{12} \\\\ f= 0.056 \ Hz[/tex]
Hence the output light frequency of the material used before doubling will be 0.056 Hz.
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what does y=mx+b equal
Answer:
slope intercept form
Step-by-step explanation:
y=mx+b is slope-intercept form
I hope this helps :)
Evaluate f^3+11g-4hf
3
+11g−4hf, cubed, plus, 11, g, minus, 4, h when f=3f=3f, equals, 3, g=2g=2g, equals, 2 and h=7h=7h, equals, 7.
An expression is defined as a set of numbers, variables, and mathematical operations. The value of f³+11g-4h, when the value of f=3, g=2, and h=7 is 21.
The correct question is:
Evaluate the value of f³+11g-4h, where the value of f is 3, the value of g is 2 and the value of h is 7.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of f³+11g-4h, when the value of f=3, g=2, and h=7 is,
f³+11g-4h
= (3)³ + 11(2) - 4(7)
= 27 + 22 - 28
= 21
Hence, The value of f³+11g-4h, when the value of f=3, g=2, and h=7 is 21.
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Answer:
21
Step-by-step explanation:
