Let us find the solution for:
-(x – 4) + 2 = 6 – X
Solve the equation for x:
-(x – 4) + 2 = 6 – X
Multiply the negative sign in the expresion -(x – 4) = -x + 4
-x + 4 + 2 = 6 – X
-x + 6 = 6 -x
Subtract 6 and sum x in both sides
-x + 6 -6 +x = 6 -x +x -6
-x + x = 6 - 6
0 = 0
The equation is true for every x, which means that x can be any real number
Given that 2x+7=27 and 3x+1=28, does 2x+7= 3x+1? Explain.
No, 2x+7 is not equal to 3x+1.
The value of 2x+7 is 27, where as value of 3x+1 is 28, which is one more than tha value of 2x+7. So the correct equation is.
[tex]\begin{gathered} 2x+7=3x+1-1 \\ 2x+7=3x \end{gathered}[/tex]Hence it can be said that,
[tex]2x+7\ne3x+1[/tex]Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.A. right angle 3 is congruent to right angle 7B. m right angle 7 + m right angle 12 = 180
Situation A.
Angle 3 is congruent with angle 7.
That means that line a and b are parallel, because: Angle 3 and Angle 5 are vertical angles, and if Angle 3 is congruent with Angle 7, then Angle 5 is also congruent with Angle 7, therefore, the lines a an b are parallel.
Situation B.
Angle 7 is supplementary of Angle 12.
Angle 12 is supplementary to Angle 13.
Then Angle 13 and Angle 7 are congruent.
Then a and b are parallel and l and m are parallel.
For each system of linear equation shown below , classify the system as “ consistent dependent ,” or inconsistent . Then , choose the best description of its solution . If the system has one solution , give its solution .
System A : consistent dependent.
System B : no solution.
System C: consistentent independent and its solution is (-3, -2).
STEP - BY - STEP EXPLANATION
What to find?
To tell whether the system given is;
inconsistent, consistent dependent or consistent independent.
Given:
• System A
y = 1/4 x - 4
-x + 4y = -16
• System B
y=2/3 x + 2
y = 2/3 x + 3
• System C
y = -x - 5
y=2x + 4
To be able to decribe the given systems, we will:
• Define the terminologies
,• Observe the given graph
,• Identify the graph.
Inconsistent
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Observe the graph of system B,
The lines are parallel and hence the system has no solution.
Consistent dependent
If a system has at least one solution, it is said to be consistent .
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
Observe the graph of system A, the lines are the same.
Hence, the system of the equation in A is consistent dependent.
Consistent independent
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent . In this case the point of intersection of the line line on the graph is only at one point.
Observe the graph of system C, the line iontercsect at only one point which implies the system has exactly one solution at that point.
Therefore, system C can be decribed as consistent independent
and its solution is (-3, -2).
4 The packing crate below is 3 feet long and 21 feet wide. It is filled completely with 648 boxes that measure a foot on each side. 4 3 ft 21 ft Part A: What is the height, in feet, of the packing crate? Show your work.
Given
Lenght of crate= 3 ft
Width of crate = 2.25 ft
Total number of boxes= 648
and edge of each box is 0.25 ft
Required
We need to find the height of crate and volume of crate.
Explanation
Here volume of each box is
[tex]0.25^3=0.015625\text{ cubic feet}[/tex]Let height of crate be h
Then
[tex]3\times2.25\times h=0.015625\times628=9.8125[/tex]i.e.
[tex]h=\frac{9.8125}{6.75}=1.45[/tex]So height of crate is 1.45 ft
Now volume of crate is
[tex]3\times2.25\times1.45=9.8125\text{ cubic feet}[/tex]This volume is same as that of 648 boxes. So we can either find the volume of crate in this way or alternatively we can find the volume of 648 boxes.
The function f(x) = 2x² - 1 is/has A. neither symmetric about the y-axis nor has order 2 rotational symmetry about the originB. order 2 rotational 2 symmetry about the originC.oddD. symmetry about the y-axis
To determine The function f(x) = 2x² - 1 is/has
Option A is wrong cause it symmetric about y - axis
Option B is wrong cause it is not symmetry mm
Option C is wrong , its an even function
Option D is correct because it is symmetry about the y - axis
Hence the correct answer is Option D
A spinner with the colors purple, red, green, and yellow is spun. What is the theoretical probability of landing on purple? O P(purple) = 20% • O O P(purple) = 50% O P(purple) = 100% O P(purple) = 33.3% - O P(purple) = 25%
Answer:
25%
Explanation:
Probability is the likelihood or chance that an event will occur. Mathematically;
Probability = Expected outcome/Total outcome
Since there are 4 colours to spun (purple, red, green, and yellow)
Total outcome = 4
If purple landed, then the expected outcome = 1
Substitute into the formula;
P(Purple) = 1/4
P(Purple) = 0.25
P(Purple) = 25%
Hence the theoretical probability of landing on purple is 25%
El cuadrado de la suma de dos números
Answer:
Step-by-step explanation:
El Cuadrado de un Número 'a' se representa como a2 y se lee como 'a' al Cuadrado. La Suma de los Cuadrados se obtiene sumando los Cuadrados de los Números.
...
Suma de cuadrados de números:
Suma de cuadrados de dos números g2 + h2 = (g + h)2 - 2 gh
Suma de cuadrados de números pares 2n(n+1)(2n+1)3 2n(n+1)(2n+1)3
Use the formula for finding a z-score to determine the missing value in the following table. Round your answer to two decimal places, if necessary
Explanation
We are given the following:
[tex]\begin{gathered} z=0.64 \\ x=-34.90 \\ \sigma=9.48 \end{gathered}[/tex]We are required to determine the missing value μ.
This is achieved thus:
We know that the formula for z-score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Therefore, we have:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 0.64=\frac{-34.90-\mu}{9.48} \\ \text{ Cross multiply } \\ -34.90-\mu=0.64\times9.48 \\ -34.90-\mu=6.0672 \\ -\mu=6.0672+34.90 \\ -\mu=40.9672 \\ \mu=-40.9672 \\ \mu\approx-40.97 \end{gathered}[/tex]Hence, the answer is:
[tex]\mu\approx-40.97[/tex]Wire the explicit expression that can be used to find the nth term in this sequence 3,7,11,15,19An = What would be the 20th term A20 =
From the sequence given 3,7,11,15,19
first term (a) = 3
common difference(d) = 4
Hence to find the nth term, the expression is given as shown below
[tex]\begin{gathered} T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (n - 1)4} \\ \text{ = 3 + 4n -4} \\ \text{ = 4n - 4+ 3} \\ \text{ = 4n - 1} \end{gathered}[/tex]To find the 20th term, we have
[tex]\begin{gathered} T_n\text{ = a + (n -1)d} \\ a\text{ = 3, d = 4},\text{ n = 20} \\ T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (20 - 1)4} \\ T_{20}\text{ = 3 + (19)4 } \\ T_{20}\text{ = 3 +76} \\ T_{20}\text{ = 79} \end{gathered}[/tex]
Triangle KAB is similar to triangle KML. Find the length of AB.L36B5430K50A
Given the figure in the attached image;
The triangles KAB and KML are similar
[tex]\Delta KAB\text{ \textasciitilde}\Delta KML[/tex]So, the sides of the triangles are proportional.
[tex]\frac{KB}{KL}=\frac{AB}{ML}[/tex]Given in the figure;
[tex]\begin{gathered} KB=30 \\ KL=36 \\ ML=54 \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} \frac{KB}{KL}=\frac{AB}{ML} \\ \frac{30}{36}=\frac{AB}{54} \\ AB=\frac{30\times54}{36} \\ AB=45 \end{gathered}[/tex]Therefore, the length of side AB is;
[tex]45\text{ units}[/tex]StorageBoxCrate Size DimensionsWidth8 feet4 inchesHow many boxesfit along thelength of thiscrate?Height 8 feetLength 40 feet6 inches8 inchesA. 16 boxesB. 2 boxesC. 60 boxesD. 5 boxes
5 boxes fit along the length of the crate (option D)
Explanation:Given:
Length of box = 8 in, width = 4 in, height = 6 in
Length of crate 40 ft, width = 8 ft, height = 8 ft
To find:
The number of boxes that can ft into the length of the crate
To determine the number of boxes that will fit into the length of the crate, we will divide the length of the crate by the length of the box
[tex]\begin{gathered} Number\text{ of boxes on the crate length = }\frac{40\text{ ft}}{8\text{ in}} \\ Number\text{ of boxes on the crate length = 5} \end{gathered}[/tex]5 boxes fit along the length of the crate (option D)
The commutative property of addition says that changing the order of addends does not change the sum.Select one:TrueFalse
TRUE
Explanations:Given two integers A and B according to commutative law, if these two integers are added no matter the arrangement of the integers, the sum of the integers will not be affected.
According to the commutative law;
[tex]A+B=B+A[/tex]For instance, let us assume the integers are 4 and 5 where A = 4 and B = 5. Applying the commutative law to the sum, we will have;
[tex]\begin{gathered} 4+5=9 \\ 5+4=9 \\ \text{Hence, 4 + 5 = 5 + 4 (Commutative law of addition)} \end{gathered}[/tex]Based on the above postulate, we can conclude that the commutative property of addition says that changing the order of addends does not change the sum
Need help solving step by step and graphing Problem number 2
f(x) = |x|
Since the variable x is given with absolute value signs, the function f(x) will always take on positive values for all values (negative or positive) of x.
To solution of a function is the value of the function such that f(x) = 0. The function f(x) = 0 when x = 0 because at every value of x on the graph, y = the same value.
e.g. when x =1, y=1. When x =2, y=2 etc...
This is the graph of f(x) = x (without the absolute value sign):
This is the graph of f(x) = |x| :
There are 53 members on the board of directors for a certain non-profit institution. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? There are _ different slates of candidates possible.please answer the question above.
For this problem the order of selection matter (the first person is the chairperson, the second the first vice chairperson and so on); since this is the case we need to use permutations. The permutation is given by:
[tex]_nP_k=\frac{n!}{(n-k)!}[/tex]we have a total of 53 members and the slates contain 4 people, then we have:
[tex]_{53}P_4=\frac{53!}{(53-4)!}=7027800[/tex]Therefore, there are 7,027,800 different slates of candidates.
I need help with this questionWhich of the graphs below sliced for x in the equation -x^2+2x+6=2x-3?
The equation -x^2+2x+6=2x-3 represents the intersections between a parabola and a line, the equation of the parabola is on the left side of the equation f(x)= -x^2+2x+6 and the equation of the line os on the right side g(x)=2x-3.
The general form of the equation of a parabola is f(x)=ax^2+bx+c, when a is greater than zero (positive) the parabola opens upwards, when it is negative the parabola opens downwards, in this case, a= -1, then the parabola that represents this equation should open downwards, then the answer is either the first or the second graph.
The equation of a line is given by the general form g(x)=mx+b, where m is the slope of the line, when m has a positive value the value of the y-coordinate of the line increases as x increases, between the first and the second option the only graph that has a positive slope line is the second one.
Then, the correct answer is the second option.
I need help with this problem.I will need to send you the picture of the problem because it couldn’t fit into the screenshot
EXPLANATION :
From the problem, we have the radical expression :
[tex]\sqrt{36}+\sqrt{49}-\sqrt{16}[/tex]Note that the given radicals are perfect squares :
36 = 6^2
49 = 7^2
16 = 4^2
Then :
[tex]\begin{gathered} \sqrt{6^2}+\sqrt{7^2}-\sqrt{4^2} \\ =6+7-4 \\ =9 \end{gathered}[/tex]ANSWER :
The answer is 1 only
Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.- 5x + 2y + 6z = -2x + 3y + 4z = - 36x + y – 2z = -1AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O No SolutionO Only One Solution=こ%3DO Infinitely Many Solutions
We are given the following system of linear equations
[tex]\begin{gathered} -5x+2y+6z=-2 \\ x+3y+4z=-3 \\ 6x+y-2z=-1 \end{gathered}[/tex]Let us solve the given system of equations.
First, let us find the determinant.
The determinant is given by
[tex]\begin{gathered} D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5\begin{bmatrix}{3} & {4} \\ 1 & {-2}\end{bmatrix}-2\begin{bmatrix}{1} & {4} \\ {6} & {-2}\end{bmatrix}+6\begin{bmatrix}{1} & {3} \\ {6} & {1}\end{bmatrix} \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(3\cdot-2-4\cdot1)-2(1\cdot-2-4\cdot6)+6(1\cdot1-3\cdot6) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(-6-4)-2(-2-24)+6(1-18) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(-10)-2(-26)+6(-17) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=50+52-102 \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=102-102 \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=0 \end{gathered}[/tex]As you can see, the determinant of the matrix is 0
This means that the given system of equations has no solution.
Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.
Recall that the magnitude and direction of a vector:
[tex]\vec{v}=ai+bj[/tex]are given by the following formulas:
[tex]\begin{gathered} \vec{|v}|=\sqrt{a^2+b^2}, \\ \theta=tan^{-1}(\frac{b}{a}). \end{gathered}[/tex]Substituting
[tex]\begin{gathered} a=2, \\ b=8, \end{gathered}[/tex]in the above formulas, we get:
[tex]\begin{gathered} \vec{|v}|=\sqrt{2^2+8^2}=\sqrt{4+64}=\sqrt{68}. \\ \theta=\tan^{-1}(\frac{8}{2})=\tan^{-1}(4). \end{gathered}[/tex]Finally, we get:
[tex]\begin{gathered} \vec{|v}|=2\sqrt{17}, \\ \theta=75.9638^{\circ}. \end{gathered}[/tex]Answer: (|v|=2√17, θ=75.9638°)
[tex]\begin{gathered} \vec{\lvert\rvert v}\lvert\rvert=2\sqrt{17}, \\ \theta=75.9638^{\operatorname{\circ}}. \end{gathered}[/tex]Find y This is geometry (please start off with solution )
Answer:
Explanation:
Given:
To find:
The value of y
We'll go ahead and use the cosine rule to find the value of y as seen below;
[tex]y^2=e^2+s^2-2es\cos E[/tex][tex]\begin{gathered} y^2=42^2+32^2-2*42*32*\cos78 \\ y^2=1764+1024-558.8666 \\ y^2=2788-558.8666 \\ y=\sqrt{2229.1334} \\ y=47.2\text{ cm} \end{gathered}[/tex]Therefore, the value of y is 47.2 cm
What is 1827 plus 1938?
1 1
1827
+
1938
____
3765
Given the figure below, determine the angle that is a same side exterior angle with respect to1. To answer this question, click on the appropriate angle.
The angle that is a same side exterior angle with respect to <8 is ;
<2
Same side exterior angles are supplementary angles on the same side of the transversal , t , and outside the parallel lines l and m
The answer is : < 2
Valeria has an ambitious goal of biking a 200 kilometer road route in less than 12 hours. The graph below shows the distance she traveled across the 12-hour trip. What was Valeria's average speed during the first 7 hours?During which time period ( F through n show on the graph) was her rate the greatest? how do you know?
The average speed must be, (x = distance, t= time)
[tex]S=\frac{x2-x1}{t2-t1}=\frac{100\text{ km}}{7\text{ h}}=14.3\text{ km/h}[/tex]The time period in which the speed was greatest was n, because the slope of the line is the highest. She biked approximately 50 Km in one hour, in any of the other time periods she did so.
How do i solve it And prove the answer is correct
we have that
Sn=24-6n
For n=1 -----> S1=24-6(1)=18
For n=2 ----> S2=24-6(2)=12
For n=3 ----> S3=24-6(3)=6
For n=4 ----> S4=24-6(4)=0
the first 4 terms are
18,12,6,0
their sum is
18+12+6+0=36
answer is option C
Problem N 2
we have
[tex]\sum ^4_{k\mathop=2}2^k[/tex][tex]\sum ^4_{k\mathop{=}2}2^k=2^2+2^3+2^4=4+8+16=28[/tex]Hudson bought 4 pounds of cantaloupe for $11.25.What is the price, in dollars, of 2 lbs of cantaloupe?
If 4 pounds of cantaloupe cost $11.25
then, 1 pound of cantaloupe will cost
[tex]\frac{11.25}{4}=\text{ \$2}.8125[/tex]if 1 pound of cantaloupe costs $2.8125
then, 2 pounds of cantaloupe will cost $2.8125 x 2
[tex]=\text{ \$5.625}[/tex]The answer is $5.625
If the angles of a triangle are 45°, 45°, and 90°,show that the length of the hypotenuse is 3 times as long as eachleg.V 1. Substitute the side lengths of the triangle into the Pythagoreantheoremq² + ² = 22. Combine like terms.
Acording to pythagoras theorem,
[tex]\text{hypotenuse}^2=base^2+height^2[/tex]Here,
[tex]\begin{gathered} \text{hypotenuse}=c \\ \text{height}=a \\ \text{base}=a \end{gathered}[/tex]Therefore we have,
[tex]\begin{gathered} c^2=a^2+a^2 \\ c^2=2a^2 \\ c=\sqrt[]{2}a \end{gathered}[/tex]Hence the proof.
Which is the image of vertex P after the triangle is rotated 180 degreesabout the origin?
For this case we know that the vertex P has the following coordinates:
[tex]P=(-3,2)[/tex]And we want to find the coordinates after rotate 180 degrees about the origin we assume that the translation is anticlockwise so then we just need to do the following :
[tex]P^{\prime}=(-x,-y)=(3,-2)[/tex]And then the solution ofr this case would be (3,-2)
finding radius of cones base when only given the area of the base
Given
A cone's height is equal to the radius of its base.
And, the base area is 1386 square units.
To find:
The radius and volume of the cone.
Explanation:
It is given that,
A cone's height is equal to the radius of its base.
And, the base area is 1386 square units.
Then,
[tex][/tex]Is the triangles similar? If the triangles are similar then this is the statements that we have to use
When two triangles are similar, their corresponding angles are equal.
So, the first step to solve the exercise is to find the measure of the missing angle in each triangle.
We know that the sum of the interior angles of a triangle is 180. Then, we have:
• Measure of angle R
[tex]\begin{gathered} 54\degree+68\degree+R=180\degree \\ 122\degree+R=180\degree \\ \text{ Subtract 122\degree from both sides} \\ 122\degree+R-122\degree=180\degree-122\degree \\ R=58\degree \end{gathered}[/tex]• Measure of angle U
[tex]\begin{gathered} 54\degree+67\degree+U=180\degree \\ 121\degree+U=180\degree \\ \text{ Subtract 121\degree from both sides} \\ 121\degree+U-121\degree=180\degree-121\degree \\ U=59\degree \end{gathered}[/tex]As we can see, the corresponding angles of the triangles RST and UVW are not equal.
Therefore, the triangles are not similar.
list three ways of apple and banana apple worth 1 dollar and banana worth 0.50 cents it's has to be 3 apple more than banana
Given
Three ways of apple and banana worth 1 dollar
Banana worth 0.5 cents
Procedure
Another combination
Apples: 8
Bananas: 2
Cost of apples: $8
Cost of bananas: $1
Another combination
Apples: 9
Bananas: 0
Cost of apples: $9
Cost of bananas: $0
Find the area of a trapezoid with bases 24 and 36 with 45 base angles
A trapezoid with congruent base angles have the other two sides (that are not the bases) congruent to each other:
And the area A of a trapezoid with bases a and b, and height h is given by:
[tex]A=\frac{a+b}{2}\cdot h[/tex]Thus, we need to find the height h of this trapezoid and then use it to calculate its area.
Step 1
We can find h by using the tangent of 45º. We obtain:
[tex]\begin{gathered} \frac{h}{6}=\tan 45^{\circ} \\ \\ \frac{h}{6}=1 \\ \\ h=1\cdot6 \\ \\ h=6 \end{gathered}[/tex]Step 2
Now, we have:
a = 24
b = 36
h = 6
Thus, the area A of the trapezoid is:
[tex]\begin{gathered} A=\frac{24+36}{2}\cdot6 \\ \\ A=\frac{60}{2}\cdot6 \\ \\ A=30\cdot6 \\ \\ A=180 \end{gathered}[/tex]