What are the values of a₁ and r of the geometric series?
2-2+2-2+2
O
a₁ = 2 and r=-2
O a₁ = -2 and r = 2
O
a₁ = -1 and r = 2
a₁ = 2 and r=-1

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 total length of all meteors that are 1 6/8 inches is three and four-eighths inches.

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

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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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''  

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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The chart that best represents the student results from a class assignment is B. 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.

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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La solución del sistema de ecuaciones es igual a (x, y) = (308/47, 42/47).

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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The difference of two squares is (5x+3y) (5x-3y)

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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The measure of the length DC to nearest tenth is 24.1 units

In 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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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.

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:

First, 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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Step-by-step explanation:

THERE WILL BE

6+4+3+7= 23

The x-coordinates of the vertices of the hyperbola are 11 and -11

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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The equivalent expression to [tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{17}{13}}[/tex]

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:

Then the fractional form can be an expression as:

[tex]\mathbf{(\dfrac{r}{s})(x)= \dfrac{3x-1}{2x+1}}[/tex]

where;

[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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Answer:

0

Step-by-step explanation:

By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.

Answer:

+ and - is always equals to -

Hope it helps!

Answer:

Yes. {(-12, 8), (-15, 8), (-5, 8)} is function because there is no overlap in the x values.

Answer:

hope this helps

The equation of the new function is:

[tex]g(x) = \frac{2^x}{5}[/tex]

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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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

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

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

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.

Using 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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Using the Factor Theorem to find the equation of the parabola, we have that:

[tex]a + b + c = -\frac{48}{7}[/tex]

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:

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.

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:

Considering the coefficient a, we have that:

In this problem, we have that:

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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The number of ways when the choice is not relevant is 10

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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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°

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.

The missing angle in triangle IVE is found using the angle sum theorem:

  ∠IVE +∠VIE +∠IEV = 180°

  ∠IEV = 180° -50° -70° = 60°

Vertical 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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The information is enough because: C. because one pair of congruent corresponding angles is sufficient to determine 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

Answer:

20

Step-by-step explanation:

Area of a rectangle = l*w

5*4 = 20