Answer:
The product is the difference of squares is [tex]$$\left(11-b\right)\left(11+b\right)=121-{{b}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (11-b)(11+b).We have to multiply the given expression.Square the first term 11. Square the last term b.[tex]$$\begin{aligned}&(11-b)(11+b)=(11)^{2}-(b)^{2} \\&(11-b)(11+b)=121-b^{2}\end{aligned}$$[/tex]
5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
How to determine the equations?When a linear equation is represented as:
Ax + By = C
The slope (m) is:
m = -A/B
When the linear equation is represented as:
y = mx + c
The slope is m
A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m
Using the above highlights, the equations of the lines are:
6. y = -2x + 5; (2, 7)
The slope is:
m = -2
The perpendicular slope is:
n = 1/2
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/2(x - 2) + 7
Evaluate
y = 1/2x - 1 + 7
This gives
y = 1/2x + 6
7. y = -5; (11, 15)
The slope is:
m = 0
The perpendicular slope is:
n = 1/0 = undefined
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 15
8. Graph ; (-12, 10)
The slope is:
m = (y2 - y1)/(x2 - x1)
Using the points on the graph, we have:
m = (2 - 3)/(3 - 4)
m = 1
The perpendicular slope is:
n = -1
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = -1(x + 12) + 10
y = -x - 12 + 10
Evaluate
y = -x - 2
9. y = -1/6x + 1; (-2, -9)
The slope is:
m = -1/6
The perpendicular slope is:
n = 6
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 6(x + 2) - 9
Evaluate
y = 6x + 12 - 9
This gives
y = 6x + 3
10. 6x + 2y = 14; (12, 0)
The slope is:
m = -6/2
m = -3
The perpendicular slope is:
n = 1/3
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/3(x - 12) + 0
Evaluate
y = 1/3x - 4
Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
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When 1,2504 is written in its simplest radical form, which value remains under the radical?
O 10
O 6
O 5
02
The value that remains under the radical is 2
How to determine the value under the radical?The correct expression in the question is:
1250^4
This can be rewritten as:
[tex]\sqrt[4]{1250}[/tex]
Express 1250 as product
[tex]\sqrt[4]{(2 * 5^4)}[/tex]
Expand the expression
[tex]\sqrt[4]{2} * \sqrt[4]{5^4}[/tex]
Simplify
[tex]\sqrt[4]{2} * 5[/tex]
Evaluate the product
[tex]5\sqrt[4]{2}[/tex]
Hence, the value that remains under the radical is 2
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Sam runs 36 km in 2.5 hours, how many km does he run per hour
Answer:
Sarah runs at 14.4km/h
Step-by-step explanation:
36km = 2.5 hours
/ = per or divide
36km/2.5hours = 36 divided by 2.5 = 14.4km/h
What is the answer to the question below
The distance between the two given points coordinates is; Option C: √85
How to find the distance between two coordinates?Formula for the distance between two coordinates is;
d = √((x₂ - x₁)² + (y₂ - y₁)²)
We are given the coordinates as;
(-2, 3) and (5, -3). Thus;
d = √((-2 - 5)² + (-3 - 3)²)
d = √(49 + 36)
d = √85
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Please help me to find the value of x and y . As fast as possible....
Answer:
Step-by-step explanation:
Answer:
y = 40°
z = 140°
x = 100°
Information:
(i) Sum of interior angles of a triangle sum ups to 180°
(ii) On a straight line, the angles sum up to 180°
(iii) One exterior angle is equal to two opposite interior angles.
Solve for zHere the exterior angle theorem applies.
∠z = 120° + 20°
∠z = 140°
Solve for yFind the angle C. Here angles lie on a straight line.
∠? + 120° = 180°
∠? = 180° - 120° = 60°
80°, 60° and y are interior angles of a triangle.
y + 80°+ 60° = 180°
y = 180° - 140°
y = 40°
Solve for x∠? = 40° (vertically opposite angle)
Now,
y + x + 40° = 180°
40° + x + 40° = 180°
x = 100°
help me please im in a rush
Answer:
390 m^2
Step-by-step explanation:
So let's start by finding the surface area of the two triangles on the side. Generally the area of a triangle can be calculated as: [tex]\frac{1}{2}bh[/tex]. but since there is two of them, we can calculate the area of both of them by simply canceling out the 1/2 to a 1. So the area of both triangles are 12 m * 5m as given in the diagram. This gives you 60m^2 area for both triangles on the side
Now let's calculate the rectangle on the top. It has a width and length of 13 and 11 m. So multiply these together to get: 143 m^2
Now let's calculate the rectangle that's on the bottom, it has the dimensions 11 and 12m and multiplying these together gets you: 132 m^2\
Now calculate the rectangle all the way in the back, it has the dimensions 5 and 11m, multiplying these together gets you 55 m^2.
Now add all these together: 60m^2 + 143m^2 + 132m^2 + 55m^2 = 390m^2
Which graph represents an exponential function?
The first graph is the exponential function.
What is exponential function?The exponential function serves as the positive-valued function with respect to real variable. and the values denoted as X which is exponential is all real numbers.
Analyzing the first graph, moving down the graph, we can see that x value increases.
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Answer:
First Graph
Step-by-step explanation:
Edge
what type of polynomial is -3
Answer:
a monomial, a constant
Step-by-step explanation:
It has only 1 term, so it's a monomial.
Also, the term is a constant.
Please help me figure out where they all belong to
The values of the trigonometric functions are
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{13}{12}[/tex]
Trigonometric functionsFrom the question, we are to determine the values of the given trigonometric functions
From the given information,
[tex]sec \theta =\frac{13}{5}[/tex]
∴ [tex]\frac{1}{cos \theta} =\frac{13}{5}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
Thus,
Adjacent = 5
Hypotenuse = 13
Opposite = ?
Using the Pythagorean theorem
|Opp|² = |Hyp|² - |Adj|²
|Opp|² = 13² - 5²
|Opp|² = 169 - 25
|Opp|² = 144
|Opp| = √144
|Opp| = 12
∴ Opposite = 12
Thus,
By using SOH CAH TOA
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{1}{tan\theta}[/tex]
∴ [tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{1}{sin\theta}[/tex]
∴ [tex]csc\theta = \frac{13}{12}[/tex]
Hence, the values of the trigonometric functions are
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{13}{12}[/tex]
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Two systems of equations are shown:
System A System B
6x + y = 2 2x − 3y = −10
−x − y = −3 −x − y = −3
Which of the following statements is correct about the two systems of equations?
The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.
They will have the same solution because the first equations of both the systems have the same graph.
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical.
The correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D
How to determine the right statement
6x + y = 2 2x − 3y = −10 System A
-x − y = −3 −x − y = −3 System B
Let;s solve for x and y in system A
6x + y = 2
Make 'y' the subject
y = 2-6x
Substitute in the other equation
-x -y = -3
-x - (2-6x) = -3
-x -2+6x = -3
Collect like terms
5x = -3+2
x = -1/5
Substitute in y = 2-6x to find 'y'
y = 2- 6(-1/5)
y = 2+ 6/5
y = [tex]\frac{10+ 6}{5}[/tex]
y = 16/5
For system B
-x-y = -3
Make y subject, we have
-x + 3 = y
y = -x + 3
Substitute in the other equation, we have
2x − 3y = −10
2x - 3(-x+3) = -10
2x + 3x -9 = -10
Collect like terms
5x -9 = -10
5x = -10 + 9
x = 1/5
Substitute into y = -x + 3 to find 'y'
y = -(1) + 3
y = 2
Thus, the correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D
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Which of the following is a valid exclusion for the algebraic fraction 8ab^2x/4a^2b - 8ab^2
A. a=/ 0, b =/ 0, a = / b
B. a = / 0, b =/ 0
C. a =/ 0, b =/ 0, a = / 2b
D. b = / 0, a = / b
The valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
How to determine the valid exclusion?The expression is given as:
8ab^2x/4a^2b - 8ab^2
Set the denominator to 0
4a^2b - 8ab^2 = 0
Divide through by 4ab
a - 2b = 0
Add 2b to both sides
a = 2b
Hence, the valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
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"I am thinking of a number. If you
multiply my number by 4 and then add 3
times my number, you will get 175. What is
my number?"
Answer:
y =25Step-by-step explanation:
y×4+3×y=175 4y+3y=175 7y=175 divide by 7 both side with make value of y y=25. this is my answerWhat are the zeros of this function?
A. X=2 and x=-4
B. x=0 and x=4
C. X=0 and x=2
D. X=0 and x=-4
Answer:
The answer is B: x = 0 and x = 4
Step-by-step explanation:
The zeroes of a function are the x-intercepts, or the x values of the points that are on the x-axis. (The x-axis is the numbered horizontal line.)
One of the zeroes passes through the origin, which is (0,0). The other point is right before the number 5 on the x axis, which means that the point is (0, 4). If you look at the x-values of the ordered pairs of the zeroes, that's the answer.
(x, y)
Question 17 of 25
how many solutions does the following system of equations have?
y=5/2x+2
2y=5x+4
a. zero
b. one
c.infinitely many
d. two
Answer:
c
Step-by-step explanation:
y = [tex]\frac{5}{2}[/tex] x + 2 → (1)
2y = 5x + 4 ( divide through by 2 )
y = [tex]\frac{5}{2}[/tex] x + 2 → (2)
the 2 equations are the same and will have infinitely many solutions
One number is 5 more than 3 times another number.the sum of the numbers is 45. find the numbers
Answer:
35 and 10
Step-by-step explanation:
Let m and n be the numbers
m is 5 more than 3 times n can be written as
m = 3n + 5 ... (1)
Sum of numbers is 45 so m + n = 45 .or
m = 45 - n ... (2)
Equating RHS of (1) and (2) gives us
3n + 5 = 45 - n
Collecting like terms
3n + n = 45 -5
4n = 40
n = 10
Therefore m = 45-10 = 35
Quick Check
In (1) substitute for m and n,
LHS is m = 35
RHS = 3 * 10 + 5 = 35
Given the domain {-2, 1, 5}, what is the range for the relation 4x + y = 3?
Answer:
Step-by-step explanation:
Domain is the set of all possible inputs (x) for the function f(x)
The range is the set of all possible values for that domain
This function is 4x + y = 3 which can be re-written as y = 3-4x
Plug in each of the domain values and you will get the range
For -2 : y = 3-4(-2) = 3 + 8 = 11
For 1: y = 3-4(1) = -1
For 5: y = 3-4(5) = -17
So range is {-17, -1, 11}
which inequality represents all values of x for which the quotient below is defined? sqrt 7x^2 / sqrt3x
Answer:
The Answer is x>0
Geometry question I need help with the true or false
Answer:
See below
Step-by-step explanation:
SAS says the two triangles are congruent
so side 6x-4 = 3x+8 then x = 4
x= 4 true
x = 3 false ( because we just found it = 4)
Pythag theorem says QT
(6x-4)^2 = QT^2 + 12^2
( 6(4)-4)^2 = 12 ^2 + QT^2
400 -144 = QT^2
QT = 16 true
Select the correct answer. Which system of equations is represented by this graph? A graph has two diagonal curves. A curve declines through (negative 1, 5), and (2 point 3, negative 5). A curve declines through (negative 5, negative 2) and (2 point 3, negative 5). Both curves intersect at (2 point 3, negative 5). A. B. C. D.
The system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
How to determine the system of equations?This question will be answered using the attached graph
The curve
The curve is a quadratic function, and it has the following features:
Vertex, (h, k) = (-3, -2)
Point (x, y) = (-1, 2)
A quadratic function is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x + 3)^2 - 2
Substitute (x, y) = (-1, 2)
2 = a(-1 + 3)^2 - 2
This gives
2 = 4a-2
Solve for a
a = 1
Substitute a = 1 in y = a(x + 3)^2 - 2
y = (x + 3)^2 - 2
The line
The line is a linear function, and it has the following features:
Point (x1, y1) = (-1, 2)
Point (x2, y2) = (-6, 7)
The linear function is calculated as:
y = (y2 - y1)/(x2 - x1) *(x- x1) + y1
So, we have:
y = (7 -2)/(-6 +1) *(x + 1) + 2
Evaluate the quotient
y = -1(x + 1) + 2
Expand
y = -x -1 + 2
y = -x + 1
Hence, the system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
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What is the solution to the system of equations?
y = 2/3x + 3
x =-2
[-2, -15/2 ]
[-2, 5/3]
(-2, 11/6
(-2, 13/3)
Answer:
(- 2, [tex]\frac{5}{3}[/tex] )
Step-by-step explanation:
y = [tex]\frac{2}{3}[/tex] x + 3 → (1)
x = - 2
substitute x = - 2 into (1)
y = [tex]\frac{2}{3}[/tex] × - 2 + 3 = - [tex]\frac{4}{3}[/tex] + [tex]\frac{9}{3}[/tex] = [tex]\frac{5}{3}[/tex]
solution is (- 2, [tex]\frac{5}{3}[/tex] )
f(x) = 5x³ – 2r²
g(x) 3r -7
Answer:
-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).
Answer:
k = 18=========
GivenLine 13x - ky + 7 = 0Line 2Passing through the points (4, 3) and (5, - 3)To findThe value of k, if the lines are perpendicularSolutionWe know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.
Find the slope of line 1 by converting the equation into slope-intercept from standard form:
Info:
standard form is ⇒ ax + by + c = 0, slope - intercept form is ⇒ y = mx + b, where m is the slope3x - ky + 7 = 0ky = 3x + 7y = (3/k)x + 7/kIts slope is 3/k.
Find the slope of line 2, using the slope formula:
m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6We have both the slopes now. Find their product:
(3/k)*(- 6) = - 1- 18/k = - 1k = 18So when k is 18, the lines are perpendicular.
Question 1 of 5
Select the correct answer.
Which function has a domain of (-♾, ♾)and a range of (-♾, 4)?
PLEASE HELP
A: f(x) = -x^2 + 4
B: f(x) = 2^x +4
C: f(x) = -4x
D: f(x) = x + 4
Answer: A
Step-by-step explanation:
A) Correct. [tex]x^2 \geq 0 \implies -x^2 \leq 0[/tex]
B) Wrong. [tex]2^x > 0[/tex], so the range is [tex](4, \infty)[/tex]
C) Wrong. Linear functions have a range of all real numbers.
D) Wrong. Same logic as C.
From the diagram below, given the side lengths marked, and if we know that < C is congruent to < E, we can say that ___.
Select one:
a.
the two triangles are similar by SAS
b.
the two triangles are not similar
c.
the two triangles are congruent
d.
the two triangles are similar by AA
Since we know that <C is congruent to <E, we can say that: A. the two triangles are similar by SAS.
The properties of similar triangles.In Geometry, two triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Ratio = BC/AC = 6/3 = 2.
Ratio = FE/DE = 4/2 = 2.
Thus, the ratio of their corresponding sides are equal in magnitude i.e BC/AC ≡ FE/DE.
Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.
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On a coordinate plane, 2 trapezoids are shown. Trapezoid M O N P has points (negative 5, 4), (negative 2, 5), (negative 2, 2), and (negative 5, 3). Trapezoid C D E F has points (3, negative 5), (4, negative 5), (5, negative 2), (2, negative 2).
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. Which congruency statement applies to the trapezoids?
CDEF ≅ NPOM
CDEF ≅ MNPO
CDEF ≅ NMOP
CDEF ≅ MOPN
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The correct option is C.
What is a Trapezoid?A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. The congruency statement that applies to the trapezoids is CDEF ≅ NMOP.
Hence, the correct option is C.
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How many units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$
56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$
Properties of triangles are:
A triangle has three sides and three angles.
The sum of the angles of a triangle is always 180 degrees.
The exterior angles of a triangle always add up to 360 degrees.
The sum of consecutive interior and exterior angle is supplementary.
How to solve?Given:
Height: ha = 7
Height: hb = 24
Height: hc = 25
Sum to sides is:
25 +7 + 24 =56 units.
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At a football match, there were 250 more men than women. The number of children was twice the number of women and the number of men was twice the number of women and children combined. How many people were at the match.
Answer:
450 people were at the match
Step-by-step explanation:
So let's make equation :
W = women
M = Men
C = Children
First equation :
M = W + 250
Second equation :
C = 2W
Third equation :
M = 2(W+C)
Let's substitute the second equation into the third :
M = 2(W + 2W)
M = 2W + 4W
M = 6W
Let's substitute this equation into the first one :
6W = W + 250
5W = 250
W = 50
Now we know that that there were 50 women at the match and can substitute this value for the first equation and then the second :
M = 50 + 250
M = 300
This means that there must have been 300 men at the match.
C = 2(50)
C = 100
This means that there must have been 100 children at the match.
Adding all values together gives us :
50 + 300 + 100 =
450 people were at the match
Hope this helped and have a good day
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
3. 72,162
Answer:
The greatest common factor of 72 and 162 is 18.
Step-by-step explanation:
In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 72 is 2*2*2*3*3, and the prime factorization of 162 is 2*3*3*3*3 (you can make a factor tree for both of these numbers to verify this). The common primes factors for both of these numbers are 2, 3, and 3 (both 72 and 162 have one 2 and at least two 3s). 2*3*3 is 18, which is the greatest common factor.
31. Lefties Find the sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of three percentage points, and use a confidence level of 99%. a. Assume that pn and qn are unknown. b. Assume that based on prior studies, about 10% of Californians are left-handed. c. How do the results from parts (a) and (b) change if the entire United States is used instead of California
a. The required sample size when pn and qn are unknown then n = 1844
b. The required sample size when about 10% of Californians are left-handed is n = 664
c. There would have been no effect on parts a and b if entire US has been chosen
According to statement
a. No estimate of proportion is given so we will assume:
{p} = {q} = 0.5
For 99% confidence, z = 2.576
E = 0.03
Hence, Required sample size
n = (0.5)*(0.5)*(2.576/0.03)^2
n = 1844
b. {p} = 0.10
{q} = 1 - {p}
{q} = 1 - 0.10
{q} = 0.90
For 99% confidence, z = 2.576
E = 0.03
Hence, Required sample size n = (0.1)*(0.9)*(2.576/0.03)^2 = 664
c. There would have been no effect on parts a and b if entire US has been chosen because minimum sample size required is not dependent on population size.
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HELPPPPPPP PLEASEEEEEEE
Find the solutions of the quadratic equation:
Answer:
Answer A is correct
Step-by-step explanation:
Let us use completing square method for this.
[tex]x^{2} -5x -10=0\\\\x^{2} -5x=10\\\\x^{2} -5x+\frac{25}{4}=10+ \frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{10*4}{1*4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40}{4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40+25}{4} \\\\(x+\frac{5}{2}) ^{2} =\frac{65}{4} \\\\(x+\frac{5}{2}) = \±\sqrt{\frac{65}{2} }\\\\(x+\frac{5}{2}) =\±\frac{\sqrt{65}}{4}\\\\x=\±\frac{\sqrt{65}}{4}-\frac{5}{2}[/tex]
∴ [tex]x=-\frac{5}{2} \±\frac{\sqrt{65}}{4}[/tex]