What are the solutions to the system of equations?



y=x2−5x+6y=−4x+6



(−1, 0) and (0, 6)
(0, 6) and (1, 2)
(−1, 0) and (6, 0)
(0, −1) and (6, 0)

The circumference of the circle is 23.89 ft

The circumference of a circle is the distance around it and it can be calculated by the formula:

Circumference = π x diameter

The circumference is therefore:

= 22/7 x 7.6

= 167.2 / 7

= 23.89 feet

The option given that is closest to 23.89 ft is the right answer.

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Answer:

-1.5

Step-by-step explanation:

The value of x is -3/2 or -1.5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

4x²+12x+9 =0

Now, the solution for the expression is

4x²+12x+9 =0

4x²+6x+ 6x +9 =0

2x( 2x + 3)+ 3 (2x+ 3)= 0

(2x+ 3) (2x+ 3) = 0

x= -3/2, x= -3/2

Hence, the value of x is -3/2 or -1.5.

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Answer:

The annual rate of depreciation of the car is 8.05% or 72.41/9

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Price of the purchase of the car = $ 39,150

Price after 9 years = $ 10,800

2. Determine the rate at which the van depreciates in value.

Let's calculate what is the percentage of depreciation after 9 years, this way:

Percentage of depreciation after 9 years = [1 - (Price after 9 years/Price of the purchase of the car)] * 100

Replacing with the values we know:

Percentage of depreciation after 9 years = [1 - (10,800/39,150)] * 100

Percentage of depreciation after 9 years = [1 - 0.2759] * 100

Percentage of depreciation after 9 years = 72.41%

Annual rate of depreciation = 72.41/9 = 8.05%

So, the given statement is false.

Step-by-step explanation:

Given , Mr. Flores has 100 pictures in a photo album. Of these picture , 20 show his friends , 50 show his family and 30 show his pet dachshund.

Probability formula:

[tex]P(A)=\frac{\textrm{Number of favorable outcomes to A}}{\textrm {Total number of out comes}}[/tex]

Total number of out come = 100

Number of photo of his family = 50

Therefore the probability of Mr. Flores selecting a picture of his family is

[tex]=\frac{50}{100}[/tex] [tex]=\frac{1}{2}[/tex] [tex]= \frac{5}{10}[/tex]

The probability of Mr. Flores selecting a picture of his friend is [tex]=\frac{20}{100}[/tex] [tex]=\frac{1}{5} = \frac{2}{10}[/tex]

The probability of Mr. Flores selecting a picture of his pet dachshund [tex]=\frac{30}{100}[/tex] [tex]=\frac{3}{10}[/tex]

Since [tex]\frac{5}{10}>\frac{3}{10}>\frac{2}{10}[/tex]

Therefore the probability of Mr. Flores randomly selecting a picture of his family is greater than the probability of randomly selecting a picture Frou -Frou.

So, the given statement is false.

15/k

15/3

5

Hope this helps! ;)

Answer:

5

Step-by-step explanation:

Since k=3 you would put 3 under 15. Now the equation would look like this: 15/3 instead of 15/k. Then you would divide 15 by 3 which is 5.

For a system to have no solutions the lines must be parallel (they cannot intersect).

So the answer is the graph on the top right.

Answer: top right and bottom right

Step-by-step explanation:

For there to be a solution the lines have to cross at one time so when they are not touching there is no solution

Answer: y= -2/3+8

Step-by-step explanation:

Answer:

The denominator should be 3.  Hope this helps.

Answer:

x=8

Step-by-step explanation:

we know that

The diagonals of a parallelogram bisect each other. That means, each diagonal cuts the other into two equal parts.

so

[tex]5x=6x-8[/tex]

Solve for x

[tex]6x-5x=8\\x=8[/tex]

would be a 25% decrease or .25

Answer:1. 3 inches

Step-by-step explanation:1 inch =2ft 2x3=6

To find the length of the garden in Micah's model, we need to set up a proportion using the given scale. The scale for the figure on the left to the figure on the right can be determined by comparing corresponding lengths.

1.) To find the length of the garden in Micah's model, we need to use the scale 1 inch: 2 feet. Since the garden has a length of 6 feet, we can set up a proportion:

1 inch / 2 feet = x inches / 6 feet

Cross-multiplying, we get 2 feet * x inches = 1 inch * 6 feet

Simplifying, we have 2x inches = 6 inches, so x = 3 inches.

Therefore, the length of the garden in Micah's model is 3 inches.

2.) The scale of the figure on the left to the figure on the right can be determined by comparing the corresponding lengths. If we measure the lengths of a certain side of the left figure and the right figure, we can find the scale. For example, if the length of a side of the left figure is 2 cm, and the corresponding side on the right figure is 4 cm, the scale is 1 cm: 2 cm.

Therefore, the scale is 1 cm: 2 cm.

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Step-by-step explanation:

We have,

[tex]\log _{a}x[/tex]

To find, the value of [tex]\log _{a}x[/tex] = ?

∴ [tex]\log _{a}x[/tex] , where a, b  and x are positive

a ≠ 1 and b ≠ 1

We know that,

The logarithm identity,

[tex]\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}[/tex]

∴ [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]

Where, b is the common base of logarithm

∴ The value of [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]

Thus, the required option A) [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex] is correct.

Answer: 9%

Step-by-step explanation:

You can just divide 200 in half which gives you 100. And divide 18 in half which gives you 9. 9/100, and since 100 is the percent’s denominator (if percent were viewed in fraction), it would be 9.

Answer:

7/20

Step-by-step explanation:

7/10 * 1/2

By multiplying

7/20

0.35

Answer: 7/20 or .35

Step-by-step explanation: .7 times .5 is .35

Answer:

[tex]\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

Remember SOHCAHTOA

The cosine of an angle in a right triangle is the adjacent sides length divided by the hypotenuses length

In this case, for the angle 30 degrees, the adjacent length is [tex]\sqrt{3}[/tex] and the hypotenuse's length is 2

So, the cosine of the 30 degree angle is the first option:

[tex]\frac{\sqrt{3} }{2}[/tex]

Answer:

f(x).f(x) [tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]

Step-by-step explanation:

Given f(x) is a linear function.

Let f(x)= ax+c

given,f(-2)=0

∴a(-2)+c=0

⇔-2a +c=0

⇔c=2a ..........(1)

Again f(4) = -5

∴a.4+c=-5

⇔4a+c=5

⇔4a +2a=5    [∵ c= 2a]

⇔6a=5

⇔[tex]a=\frac{5}{6}[/tex]

Putting the value of a in equation (1)

[tex]c=2 \times \frac{5}{6}[/tex]

[tex]\Leftrightarrow c= \frac{5}{3}[/tex]

Therefore f(x)  [tex]=\frac{5}{6} x+\frac{5}{3}[/tex]

f(x).f(x)

[tex]=(\frac{5}{6} x+\frac{5}{3})(\frac{5}{6} x+\frac{5}{3})[/tex]

[tex]=(\frac{5}{6} x+\frac{5}{3})^2[/tex]

[tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]

Answer:

x= 3.73737373737......

Step-by-step explanation:

To find x, divide -9.9 to both sides.

-37 = x-9.9

-9.9     -9.9

3.73737373737...= x

This is a repeating decimal.

Answer:

Notebook = $2.75

Pencil = $1.25

Markers = $ 0.50

Step-by-step explanation:

Stan:

n + 3p + 2m = 7.5

Jan:

2n  + 6p + 5m = 15.50

Fran:

n + 2p + 2m = 6.25

Stan - Fran:

p = 1.25

Lets replace p with 1.25

n + 3(1.25)  + 2m  = 7.5

2n + 6(1.25) + 5m = 15.50

n + 2(1.25) + 2m = 6.25

Simplify

n + 3.75 + 2m = 7.5

2n + 7.5  + 5m = 15.50

n + 2.50 + 2m = 6.25

n + 2m = 3.75     stan

2n + 5m = 8       jan

n + 2m = 3.75     fran

stan = fran

jan - 2(stan)

m = 0.5

n = 2.75

Answer: n since that number depends on s, the songs he already had.

Final answer:

The dependent variable in Steve's music player scenario is the total number of songs after buying new songs, represented by T = s + n. As the number of new songs purchased (n) changes, the total (T) changes, demonstrating a linear relationship between n and T.

Explanation:

In the scenario where Steve had s songs on his music player and he bought n new songs, the dependent variable is the total number of songs Steve has after the purchase. To define this in terms of a mathematical relationship, we can express the total number of songs (T) as an equation:

T = s + n

Here, s is the original number of songs, and n is the number of new songs purchased. The dependent variable is T (the total number of songs), which depends on the value of n (the number of songs bought). If we change the independent variable n, the total number of songs T will also change.

To illustrate this with a dataset, suppose Steve originally had 5 songs (s = 5). If he buys:

The relationship between the number of new songs purchased (n) and the total number of songs (T) is linear, as T increases by the same amount that n does.

Answer:

6

Step-by-step explanation:

11x + 7 = 73

     - 7    - 7

     11x = 66

divide 66 by 11 and you get 6

Answer:

x = 6

Step-by-step explanation:

Step 1:  Subtract 7 from both sides

11x + 7 - 7 = 73 - 7

11x = 66

Step 2:  Divide both sides by 11

11x = 66

11x / 11 = 66 / 11

x = 6

Answer:  x = 6

Answer:

Option 3

Step-by-step explanation:

y is less than the y values on the red line and greater than the y values on the blue line.

Equation of the red line:

y-intercept is clearly 3

using (0,3) & (-2,2)

Slope = (y2-y1)/(x2-x1)

= (3-2)/(0-(-2)) = 1/2

y = (1/2)x + 3

Equation of the blue line:

y-intercept is clearly -2

Using (0,-2) & (1,1)

Slope = (1-(-2))/(1-0) = 3/1 = 3

y = 3x - 2

y < (1/2)x + 3 & y > 3x - 2

The graph shows the solution for the following inequalities; C. y ≥ 3x - 2 and y ≤ -1/2(x) + 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

[tex]y - y_1 = m(x - x_1)[/tex]

Where:

First of all, we would determine the slope for the red line by using these points (2, 4) and (0, 3);

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope (m) = (3 - 4)/(0 - 2)

Slope (m) = 1/2

At point (0, 3) and a slope of 1/2, an inequality for this line can be calculated by using the point-slope form as follows:

y - 3= 1/2(x - 0)  

y = 1/2(x) + 3

y ≤ 1/2(x) + 3 (since the solid line is shaded below).

At point (0, -2) and a slope of 3, an inequality for this line can be calculated by using the point-slope form as follows:

y + 2= 1/2(x - 0)  

y = 3(x) - 2

y ≥ 3x - 2 (since the solid line is shaded below).

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Mitchel can transport a 1:1 ratio of goats to calves in his livestock trailer, equating to 11 goats and 11 calves per trip, given their respective average weights of 90 and 360 pounds and the trailer's weight limit of 5000 pounds.

Mitchel has a livestock trailer with a weight limit of 5,000 pounds. Given that each goat weights about 90 pounds and each calf about 360 pounds, we need to calculate how many of each animal the trailer can accommodate within its weight limit, while taking into account their average weights.

Let's look at one possible solution, using goats and calves in a 1:1 ratio. This would be 90 + 360 = 450 pounds per set of goat and calf. To fit within the trailer's weight limit, we then divide the total weight capacity by the weight of one set of animals: 5,000 / 450 = 11.11, which we round down to 11. This tells us that Mitchel can transport 11 goats and 11 calves in his trailer for each trip.

It's important to mention that this distribution can be adjusted according to need, as long as the total weight of the animals is kept below the trailer's weight limit.

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Answer:

3

Step-by-step explanation:

If we already know that 10% of 60 is 6 and that 5% is one half of 10%, we can just divide the 10% value by two to find the 5% of 60.

Answer:

Divide it all by 3, then put it outside the parentheses.

3(2x+5)

Step-by-step explanation:

The requried factors of the given expression are given as 3[x + 5].

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
The distributive property is given as,
a[b + c] = ab + bc

Now,
the given expression performing the distributive property in a way given as,
ab + bc = a[b + c]

Given expression,
= 6x + 15
= 3 × 2x + 3 × 5
= 3 [2x + 5]

Thus, the requried factors of the given expression are given as 3[x + 5].

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Answer:

  (x, y, z) = (1, 12, 15)

Step-by-step explanation:

As with any set of linear equations, there are many possible routes to a solution. We might simplify the notation a bit by writing the coefficients in an augmented matrix. The columns, left to right, represent the coefficients of x, y, and z, in order, and the constant term.

The row operations we'll use are multiplying a row by a value and adding that result to another row, replacing the other row by the sum.

We can make things a little simpler by writing the second equation first. Then the augmented matrix we're starting with is ...

  [tex]\left[\begin{array}{ccc|c}4&-1&1&7\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]

Adding the second row to the first, we get ...

  [tex]\left[\begin{array}{ccc|c}5&0&0&5\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]

Dividing the first row by 5 gives ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]

Subtracting this from the second row, and again from the third row, we are left with ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&-3&2&-6\end{array}\right][/tex]

Multiplying the second row by 3 and adding that to the third row, we get ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&0&-1&-15\end{array}\right][/tex]

Subtracting the third row from the second gives ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&-1&-15\end{array}\right][/tex]

Finally, multiplying the last row by -1, we have the solution:

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&1&15\end{array}\right][/tex]

This matrix corresponds to the equations ...

_____

The purpose of our choice of row operations is to make the diagonal elements 1 and the off-diagonal elements 0. That is how we end up with the final equations shown.

As we said, there are many ways to go about this. In general, one can ...