4x - y = 3
ax + 10y = 6
Solve for y

The number of stone pavers needed to go round the patio is 3.

The first step is to determine the perimeter of the concrete patio.

Perimeter : 12 + 12 + 14 = 38 feet

Number of stone pavers needed to go round the patio : perimeter of the patio / length of each stone paver

38 / 14 = 3

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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:

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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We can see that a and b are parallel, and c and e are parallel, so the correct option is E.

On the diagram, we can see that the angles in the third quadrant of the intersections between a and c, and the intersections between b and c,  are the same angle.

Then, lines a and b must be parallel.

For the intersections with line d, we can see that this time the angle is on the fourth quadrant, so c and d are not parallel.

Finally, for line e, we can see that the known angle is on the first quadrant.

Notice that the angle on the first quadrant will be equal to the angle on the third quadrant.

So for the intersections of a and e, and b and e, on the third quadrant we have the known angle (the same one as in the intersections of a and c, and a and b).

Then c and e are parallel.

Then A and C are true.

Thus, the correct option is E.

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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:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x    (the original)

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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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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°

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 monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.

Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.

A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).

Monthly Payments

Option 1

Loan Amount = $200,000

Number of payments = 30×12 = 360

Monthly interest rate = 10%/12 = 0.008333333

Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]

Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]

Monthly payment=33062.328/18.83739

Monthly payment=$1755.144

Option 2

Loan Amount = $200,000

Number of payments = 15 x 12=180

Monthly interest rate = 9.5%/12=0.00792

Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]

Monthly payment=6553.096/3.137

Monthly payment=$2088.97

Total Payments

Option 1

As we've found out the monthly payments, we now need to multiply it by the number of months.

$1755.144×360 = $631851.84

Option 2

$2088.97×180 = $376014.6

Conclusion

Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.

Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.

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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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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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Answer:

16y1yg1gyyq717177171716161yggqg1g2y2gqgq62g2gtqy2g

1jwjqhwhwjmnbhokmbhiknb

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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Step-by-step explanation:

THERE WILL BE

6+4+3+7= 23

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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The equivalent expression of [tex]\sqrt x + 11 = 15[/tex] is [tex]\sqrt x = 15 - 11[/tex]

The complete question is in the attached image

The expression is given as:

[tex]\sqrt x + 11 = 15[/tex]

Subtract 11 from both sides of the equation

[tex]\sqrt x + 11 - 11= 15 - 11[/tex]

This gives

[tex]\sqrt x = 15 - 11[/tex]

Hence, the equivalent expression of [tex]\sqrt x + 11 = 15[/tex] is [tex]\sqrt x = 15 - 11[/tex]

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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

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:

In question 20

B) the triangles are not similar

Step-by-step explanation:

u can see that 1 triangle length is 14 and other 49 and one triangle breath is 8 and other 28 so how they are same

Answer:

IN question 19

what is your question I can't understand

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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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:

20

Step-by-step explanation:

Area of a rectangle = l*w

5*4 = 20

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

Answer:

40 3/8

Step-by-step explanation:

You can just multiple it on calculator, which 1/8 is 0.125 so convert 40.375 to 40 3/8

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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

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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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