Answer:
Step-by-step explanation:
Therefore, the values of
a
1
and r are 2 and -1, respectively.
The values of a₁ and r of the geometric series are 2 and -1 respectively.
What is Geometric Sequence?Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.
We have the series 2, -2, 2, -2, ......
Here, The first term is 2.
and, the Common Ratio = -2 / 2
= 2/(-2)
= -1
So, the first term is 2 and r is -1.
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1. Which of the following results in the difference of two squares?
O (3r-5y) (3x - 5y)
O (5x+3y) (5x-3y)
O 4r²(3r-9)
O (2r-3y)2
The difference of two squares is (5x+3y) (5x-3y)
How to determine the difference of two squares?The difference of two squares of variables a and b is represented as:
(a + b)(a - b) = a^2 - b^2
By comparing the list of options, we have:
(5x+3y) (5x-3y)
This means that
a = 5x and b = 3y
Hence, the difference of two squares is (5x+3y) (5x-3y)
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A line has the equation 32 - 2y = 1 What is the equation of
parallel line going through the point (-6,
- 10)?
The equation is given by Ar + By = C where
Answer:
A = 3; B = -2; C = 2
Step-by-step explanation:
Original line:
3x - 2y = 1
Slope of original line:
-2y = -3x + 1
y = 3/2 x - 1/2
slope = m = 3/2
Parallel lines have equal slopes, so we need the equation of the line with slope 3/2 that passes through the point (-6, -10)
y = mx + b
y = (3/2)x + b
Substitute -6 for x and -10 for y and solve for b.
-10 = (3/2)(-6) + b
-10 + 9 = b
b = -1
Equation: y = (3/2)x - 1
2y = 3x - 2
3x - 2y = 2
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Considering the vertex of the parabola, the correct statement is given by:
The range of the function is all real numbers less than or equal to 9.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point, which means that the range is all real numbers less than or equal to [tex]y_v[/tex].If a > 0, the vertex is a minimum point, which means that the range is all real numbers greater than or equal to [tex]y_v[/tex].In this problem, we have that:
a = -1 < 0, hence the vertex is a maximum point.The vertex is (-2,9).Hence the range is described by:
The range of the function is all real numbers less than or equal to 9.
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Identify the compositions performed on ΔXYZ to map onto ΔX″Y″Z″.
Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle XYZ was translated 2 units left and 1 unit up to form triangle X'Y'Z'. It was then rotated 180° about the origin to form triangle X''Y''Z''
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TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10 , find the value of x
Answer:
x = 35
Step-by-step explanation:
The angle sum theorem can be used to find the congruent vertical angles RET and IEV. The equation relating these can be solved for x.
Missing angleThe missing angle in triangle IVE is found using the angle sum theorem:
∠IVE +∠VIE +∠IEV = 180°
∠IEV = 180° -50° -70° = 60°
Vertical angleVertical angles RET and IEV are congruent:
∠RET = ∠IEV
2x -10 = 60
2x = 70 . . . . . . . . add 10
x = 35 . . . . . . . . divide by 2
The value of x from the given conditions is 35.
The line TV and RI intersect at E.
The measure of IVE=50° and the measure of VIE=70°.
Since, the points V, I and E makes a triangle.
Therefore, the total angle inside the triangle is 180°.
Hence,
∠IVE + ∠VIE + ∠VEI = 180°
50°+70°+ ∠VEI = 180°
∠VEI = 180°-50°-70°
∠VEI = 60°
Also the angles ∠VEI and the angle ∠RET are congruent.
Therefore, ∠VEI = ∠RET
60° = 2x-10
2x = 70
x = 70/2
x = 35.
The lines TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10. Then the value of x = 35.
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In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them?
4x - 2y = 7
3.x - 3y = 15
Answer:
Multiply the top equation by -3 and the bottom equation by 2
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}[/tex]
To solve the given system of equations by addition, make one of the variables in both equations sum to zero. To do this, the chosen variable must have the same coefficient, but it should be negative in one equation and positive in the other, so that when the two equations are added together, the variable is eliminated.
To eliminate the variable y:
Multiply the top equation by -3 to make the coefficient of the y variable 6:
[tex]\implies -3(4x-2y=7) \implies -12x+6y=-21[/tex]
Multiply the bottom equation by 2 to make the coefficient of the y variable -6:
[tex]\implies 2(3x-3y=15) \implies 6x-6y=30[/tex]
Add the two equations together to eliminate y:
[tex]\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}[/tex]
Solve for x:
[tex]\implies -6x=9[/tex]
[tex]\implies x=-\dfrac{9}{6}=-\dfrac{3}{2}[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies 3\left(-\dfrac{3}{2}\right)-3y=15[/tex]
[tex]\implies -\dfrac{9}{2}-3y=15[/tex]
[tex]\implies -3y=\dfrac{39}{2}[/tex]
[tex]\implies y=-\dfrac{39}{2 \cdot 3}[/tex]
[tex]\implies y=-\dfrac{13}{2}[/tex]
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A rectangular vegetable patch is 5 meters long and 4 meters wide. what is the area?
Answer:
20
Step-by-step explanation:
Area of a rectangle = l*w
5*4 = 20
Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation?
because both triangles appear to be equilateral
because∠MNL and ∠ONP are congruent angles
because one pair of congruent corresponding angles is sufficient to determine similar triangles
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
The information is enough because: C. because one pair of congruent corresponding angles is sufficient to determine similar triangles.
What are Similar Triangles?Similar triangles can be formed during dilation. All corresponding angles of similar triangles are usually congruent to each other.
From the image given, the using rotation about point N and then dilation by a scale factor will make both triangles similar. Thus, with the given information, we can determine both triangles are similar because: C. because one pair of congruent corresponding angles is sufficient to determine similar triangles.
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Answer:
C
Step-by-step explanation:
Took the test
19. For which of the following values of x is the function
f(x)=√4-x2 NOT defined as a real number?
[square root]
A. -2
B. 0
C. 2
D. 4
Answer:
D. 4
Step-by-step explanation:
[tex]\sqrt{2-\left( 4\right)^{2} } =\sqrt{2-16} =\sqrt{-12}[/tex]
since ,√(-12) is not a real number
Then
The function f is not defined for x = 4
Answer:
D. 4
Step-by-step explanation:
thank you for your help 4 was the correct answer took the test and got it right
What is the total length of all meteors that are 1 6/8 inches?
A line plot with the title, length of meteors. The data is measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
The total length of all meteors that are 1 6/8 inches is three and four-eighths inches.
What is the total length of all meteors?Given :
Tick 1 exists 2/8 (1 data point)
Tick 2 exists 3/8 (3 data points)
Tick 3 exists 4/8 (2 data points)
Tick 4 exists 5/8 (no points)
Tick 5 exists 6/8 (2 data points)
Tick 6 exists 7/8 (no data points)
Tick 2 exists 3/8 (3 data points)
....
Tick 13 exists [tex]$1\frac{6}{8}[/tex] (2 data points)
Therefore, total length of all meteors that exist [tex]$1\frac{6}{8}[/tex] inches :
Length of meteor = [tex]$1\frac{6}{8}[/tex]
Number of meteors = 2
[tex]$(2 * 1\frac{6}{8}) = 2 * 1\frac{4}{8} = \frac{28}{8} = 3 \frac{3}{8} = 3 \frac{1}{2}[/tex]
Therefore, the correct answer is option A. three and four-eighths inches
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The complete question is :
What is the total length of all meteors that are 1 6/8 inches? A line plot with the title, length of meteors. The data is a measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three-eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five-eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
A) three and four-eighths inches
B) three and five-eighths inches
C) four and seven-eighths inches
D) three and seven-eighths inches
Suppose we want to choose objects, without replacement, from the objects pencil, eraser, desk, and chair.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
The number of ways when the choice is not relevant is 10
How to determine the number of ways?The number of objects are:
Object, n = 5
The object to choose are:
r = 3
Relevant choice
When the choice is relevant, we have:
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^{5}P_3[/tex]
Evaluate
Ways = 60
Hence, the number of ways when the choice is relevant is 60
Not relevant choice
When the choice is not relevant, we have:
[tex]Ways = ^nC_r[/tex]
This gives
[tex]Ways = ^{5}C_3[/tex]
Evaluate
Ways = 10
Hence, the number of ways when the choice is not relevant is 10
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Solve: ( − )( + ) = �
Answer:
+ and - is always equals to -
Hope it helps!
Question for 60 Points
Using the Factor Theorem to find the equation of the parabola, we have that:
[tex]a + b + c = -\frac{48}{7}[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, we have a horizontal parabola, defined as follows:
[tex]f(y) = a(y - y_1)(y - y_2)[/tex].
The roots are [tex]y_1 = -1, y_2 = -7[/tex], hence:
f(y) = a(y + 1)(y + 7)
f(y) = a(y² + 8y + 7).
The x-intercept is of x = -3, hence f(0) = -3, so:
[tex]-3 = 7a[/tex]
[tex]a = -\frac{3}{7}[/tex]
Then the equation is:
[tex]x = -\frac{3}{7}y^2 - \frac{24}{7}x - 3[/tex]
Then the sum of the coefficients is:
[tex]a + b + c = -\frac{3}{7} - \frac{24}{7} - \frac{21}{7} = -\frac{48}{7}[/tex]
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Answer:
Hello!
Step-by-step explanation:
the chairs in a hall are about to be arranged in a row. if i put 6 chairs in a row there will be 4 left if i put 7 chairs in a row there will be 3 short how many chairs are there
Step-by-step explanation:
THERE WILL BE
6+4+3+7= 23
i need the answer to this.
Answer:
56:49 = 8.7 36:48 = 3:448:42 = 8:724:36 = 2:320:30 = 2:324:32 = 3:418:27 = 2:316:14 = 8:79:12 = 3:4hope this helps
f r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to (StartFraction r Over s EndFraction) (6)?
The equivalent expression to [tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{17}{13}}[/tex]
What are the equivalent expressions?Equivalent expressions are similar expressions that may have different forms but when a value is replaced with the variables in the same form provides the same answer.
From the information given, If:
r(x) = 3x - 1s(x) = 2x + 1Then the fractional form can be an expression as:
[tex]\mathbf{(\dfrac{r}{s})(x)= \dfrac{3x-1}{2x+1}}[/tex]
where;
x = 6[tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{3(6)-1}{2(6)+1}}[/tex]
[tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{18-1}{12+1}}[/tex]
[tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{17}{13}}[/tex]
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50 points will give brainliest
The x-coordinates of the vertices of the hyperbola are 11 and -11
How to determine the x-coordinates?The hyperbola is given as:
[tex]\frac{x^2}{121} - \frac{y^2}{49} = 1[/tex]
A hyperbola is represented as:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Where the coordinate of the vertex is:
Vertex = (±a, 0)
By comparing the above equations, we have:
[tex]a^2= 121[/tex]
Take the square of both sides
a = 11
Substitute 11 for a in Vertex = (±a, 0)
Vertex = (±11, 0)
Hence, the x-coordinates of the vertices of the hyperbola are 11 and -11
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3x/2y=11 x+y/2=7 igualacion
Alguien me puede ayudar
La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).
¿Cómo resolver un sistema de ecuaciones linear por igualación?
Los sistemas de ecuaciones basadas en entidades algebraicas se resuelven mediante procedimientos algebraicos. Grosso modo, el método de resolución por igualación consiste en despejar una variable en dos ecuaciones del sistema para eliminarla y reducir el número de ecuaciones lineales y el número de variables.
A continuación, presentamos una aplicación del método de eliminación:
[tex]\frac{3\cdot x}{2\cdot y} = 11[/tex]
[tex]x = \frac{22\cdot y}{3}[/tex]
[tex]x + \frac{y}{2} = 7[/tex]
[tex]x = 7 - \frac{y}{2}[/tex]
[tex]\frac{22\cdot y}{3} = 7 - \frac{y}{2}[/tex]
[tex]\frac{47\cdot y}{6} = 7[/tex]
y = 42/47
[tex]x = 7 - \frac{y}{2}[/tex]
x = 308/47
La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).
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If you vertically compress the exponential function f(x)=2^x by a factor of 5, what is the equation of the new function?
The equation of the new function is:
[tex]g(x) = \frac{2^x}{5}[/tex]
What is the equation of the compressed function?Here we have the function:
[tex]f(x) = 2^x[/tex]
A vertical compression by a factor of 5 is written as:
[tex]g(x) = f(x)/5[/tex]
Replacing the function f(x) we get:
[tex]g(x) = \frac{2^x}{5}[/tex]
That is the equation of the new function.
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would appreciate the help ty!!!
By using the concept of linear progression and some algebraic handling, we conclude that Joe will earn an amount of $ 31 700 in the 14th year.
How to determine the future income of a worker
According to the statement, we have a case of linear progression as income increases at same rate in time. Linear progressions are described by this formula:
c' = c + r · t (1)
Where:
c - Initial amountc' - Current amountr - Increase ratet - TimeFirst, we calculate the increase rate:
r = (29 600 - 22 600)/10
r = 700
Now we proceed to find when Joe will earn an annual income of $ 31 700:
31 700 = 22 600 + 700 · t
t = 13
By using the concept of linear progression and some algebraic handling, we conclude that Joe will earn an amount of $ 31 700 in the 14th year.
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whats the correct answer
Answer:
C
Step-by-step explanation:
The first part of this is to represent the center.
It sits at (1,-1), so the left hand part of the equation is
(x - 1)^2 + (y + 1) = r^2
That means the answer has to be either B or C. D gets knocked out of the running because of the minus sign in the middle. D does not give a circle.
B is wrong because the y value should be plus. So the answer is C. Notice because the question is multiple choice you don't need to solve for r since all answers give r^2 = 36
Select the correct answer. Which chart best represents the following information about student results from a class assignment? Frequency 10 Score Frequency Chart 1 23 2 Frequency 10 24 8 25 4 Chart 2 26 3 27 5 28 4 29 5
The chart that best represents the student results from a class assignment is B. Histogram or bar graph.
What is a histogram or bar graph?Both histograms and bar charts are graphic vertical and horizontal bars that visually display frequencies with columns plotted on a graph.
The frequencies are depicted on the Y-axis (vertical axis).
The X-axis (horizontal axis) represents the measured variable.
Question Completion with Answer Options:A. Frequency table
B. Histogram or bar graph
C. Pareto chart
D. Pictogram
E. Pie chart
Thus, the best chart to represent the student results from a class assignment is B. Histogram or bar graph.
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Which number has a repeating decimal form?
A. √15
B. 11/25
C. 30
D. 2/6
The length of a rectangle is two more than double the width. If the perimeter is 100 inches, find the
dimensions.
Answer:
width = 34 inches
length = 16 inches
Step-by-step explanation:
Given:
1.)The length of a rectangle is two more than double the width
2.)The perimeter is 100 inches
Let's analyze the first part,
The length is 2 more than double the width so if we let x represent the length the width would be 2x + 2
Now the second part,
the perimeter is calculated by the following formula:
2*(w+l)
(w: width, l: length)
2*(x+2x+2) first do inside the parenthesis by adding like terms
x+2x+2 = 3x + 2 now multiply both terms with 2
2*(3x+2) = 6x + 4 this is the perimeter of the rectangle, now write another equation using this
6x + 4 = 100 subtract 4 from both sides
6x = 96 divide both sides by 6
x = 16 this the length and the width would be
2x + 2 = 2*16 + 2 = 34
Find the remainder when f(x)=2x^3-x^2+x+1 is divided by 2x+1
Answer:
0
Step-by-step explanation:
By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.
What is DC to the nearest tenth? I need help, thank you:)
The measure of the length DC to nearest tenth is 24.1 units
Pythagoras theoremIn order to determine the measure of DC from the figure shown, we will use the pythagoras theorem
Determine the measure of BC
BC² = 22² - 15²
BC² = 259
BC = 16.09
Determine the measure of DC
DC² = 259 + 28²
DC = √583
DC = 24.1 units
Hence the measure of the length DC to nearest tenth is 24.1 units
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Assume a firm reports net income of 84,000 prior to making adjusting entries for expired rent $6400, depreciation 7600 and supplies used 3,000
Assume that the entries have not been made What effect do these errors have on the reported net income
Assume that the entries have not been made. The effect that these errors have on the reported net income is: Net income will be overstated by $17,000.
Net incomeUsing this formula
Net income=Expired rent+Depreciation+Supplies
Let plug in the formula
Net income=$6400+$7600+$3000
Net income=$17,000 (Overstated)
Therefore the net income will be overstated by $17,000.
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is {{-12,8),(-15,8),(-5,8),(-12.8}} a function
Answer:
Yes. {(-12, 8), (-15, 8), (-5, 8)} is function because there is no overlap in the x values.
In △ OPQ, OP ≅ QO and m∠O=65∘. Find m∠Q
Answer:
65°
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so both angle Q and angle P are congruent.
Since angles in a triangle add to 180°, angle Q measures (180-50)/2 = 65°
Solve the system of equations by substitution.
2x + y = 3z
x + y = 6z
What is the value for y from the first equation, that could be substituted into the second equation?
A. -2x +3z
B. 3z + 2x
C. -2x - 3z
D. 2x + 3z