Which matrix equation represents this linear system?
[tex]2x-7y=-1\\x+3y=-5[/tex]

Answer:

hello : h =5 and K= 1

Step-by-step explanation:

look this solution :

As per the given quadratic function, the value of the vertex of the graph is written as (5, 1)

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants, and a ≠ 0. However, the given quadratic function is already expressed in the desired form, f(x) = a(x - h)² + k, which is known as vertex form. In this form, (h, k) represents the coordinates of the vertex of the parabola.

Now, let's rewrite the given quadratic function f(x) = 2x² - 20x + 51 in the vertex form. To achieve this, we'll complete the square:

Step 1: Factor out the leading coefficient 'a' from the x² and x terms. f(x) = 2(x² - 10x) + 51

Step 2: Complete the square inside the parentheses by adding and subtracting the square of half of the coefficient of the x-term (in this case, -10/2 = -5, and (-5)² = 25). f(x) = 2(x² - 10x + 25 - 25) + 51

Step 3: Group the perfect square trinomial and the constant term inside the parentheses. f(x) = 2((x - 5)² - 25) + 51

Step 4: Distribute the leading coefficient 'a' back into the parentheses. f(x) = 2(x - 5)² - 50 + 51

Step 5: Combine the constants. f(x) = 2(x - 5)² + 1

Now, the quadratic function is in the form f(x) = a(x - h)² + k, where a = 2, h = 5, and k = 1.

Therefore, the vertex of the parabola is (h, k) = (5, 1).

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Answer:

  9 cm

Step-by-step explanation:

Side lengths of similar triangles are proportional. BC is 1.5 times the length of AC, so EF will be 1.5 times the length of DF:

  1.5·6 cm = 9 cm

A) the graph is a linear and the slope is negative and positive .

B) (-1,-1) is not a solution because that point does not appear in the shaded region, therefore there is no solution.

:D

Answer:

$36.00

Step-by-step explanation:

40% of 60 is 24. Subtract from the origanl amount, you get the price after sale, $36.00. Hope this helps :)

Amber plus 2 family members = 3 total people on the plan.

They share the minutes equally so divide the minutes by 3 to find how many she can use:

720 / 3 = 240 minutes per month.

Now divide the monthly minutes by 30 days:

240 / 30 = 8 minutes per day.

the answer is D) x^2 = 20y

Answer: Option C  

[tex]r ^ 2 = 0.684[/tex]

Step-by-step explanation:

The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.

 If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.

If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.

Then for a  relationship, the coefficient of determination [tex]r ^ 2[/tex] is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.

The coefficient of determination [tex]r ^ 2[/tex] for a linear relationship is calculated as the square of the correlation coefficient.

In this problem we have that the correlation coefficient r is

[tex]r = 0.827[/tex]

then the coefficient of determination is:

[tex]r ^ 2 = 0.827 ^ 2[/tex]

[tex]r ^ 2 = 0.684[/tex]

The answer is option C

Answer:

A

Step-by-step explanation:

Add up all of the numbers:

110+142+120+180+ 151+110+159+173+173+144+110 = 1572

Next you divide by how many number there are (there are 11 numbers)

1572 ÷ 11 = 142.9090909

142.9090909 rounded to the nearest tenth is 142.9

Answer:

A.  142.9

Step-by-step explanation:

There are 11 members in the data set, therefore:

The mean = (110+142+120+180+151+110+159+173+173+144+110) / 11

= 1572/11

= 142.9.

Answer:

Option D. A sector

Step-by-step explanation:

we know that

A circular sector is the portion of the circle enclosed by two radii and an arc

so

In this problem we have a slice of the pizza enclosed by two radii and an arc

therefore

The shape of the slice is a sector

Answer:

Option C is correct: A Sector

Step-by-step explanation:

A-p-e-x :)

Answer with explanation:

Equation of line Passing through two points (a,b) and (c,d) is given by:

         [tex]\frac{y-b}{x-a}=\frac{d-b}{c-a}[/tex]

Equation of line Passing through two points (8,0) and (3,7) is given by:

      [tex]\rightarrow \frac{y-7}{x-3}=\frac{7-0}{3-8}\\\\\rightarrow \frac{y-7}{x-3}=\frac{7}{-5}\\\\\rightarrow -5 y+35=7 x - 21\\\\\rightarrow 5 y= -7 x +35 +21\\\\ y=\frac{-7 x}{5}+\frac{56}{5}\\\\y=-1.4 x +11.2[/tex]

Comparing with slope intercept form of line,

y= m x+c, where , m is slope and c is y intercept.

⇒Y intercept = 11.2

Equation of line Passing through two points (5,5) and (3,7) is given by:

            [tex]\rightarrow \frac{y-7}{x-3}=\frac{7-5}{3-5}\\\\y-7= -1 \times (x-3)\\\\y=7-x+3\\\\y=-x +10[/tex]

Comparing with slope intercept form of line,

y= m x+c, where , m is slope and c is y intercept.

⇒Y intercept = 10

Equation of line is, y= -x +10.

The y-intercept of the line passing through point A (8, 0) and B (3, 7) is 56/5. The equation of the line that passes through these points and point D (5, 5) is y = (-7/5)x + (56/5).

To determine the y-intercept and the equation of a line, we first need to find the slope of the line. The slope (m) is given by the rise over run, which can be calculated using the coordinates of two points on the line. We have point A with coordinates (8, 0) and point B with coordinates (3, 7). The slope is therefore:

m = (Y2 - Y1) / (X2 - X1) = (7 - 0) / (3 - 8) = 7 / (-5) = -7/5

Now, we use the slope-intercept form of a line equation, which is y = mx + b, where b is the y-intercept. We can determine b by substituting the slope and the coordinates of one of the given points (we'll use point A). So:

0 = (-7/5)(8) + b

b = (7/5)(8) = 56/5

Therefore, the y-intercept is 56/5.

Knowing point D with coordinates (5, 5) is also on the line, we can use our slope m and this point to write the equation of the line:

y = (-7/5)x + (56/5)

However, since we know point D lies on this line, we can check if our equation is correct by substituting x = 5 and seeing whether y = 5:

5 = (-7/5)(5) + (56/5)

5 = -7 + 56/5

5 = 5

This confirms that our calculated equation is indeed correct and passes through all given points.

Answer:

[tex] \frac{ {8}^{2} }{ {5}^{2} } = \frac{64}{25} [/tex]

B) 64:25

Step-by-step explanation:

Ratio of Lengths = a/b

Ratio of Areas = a^2/b^2

Ratio of Volumes = a^3/b^3

Answer:

its A

Step-by-step explanation:

Answer:

The capacity of the remaining bottles = 4 pints.

Step-by-step explanation:

6*3 + 6*b = 42

6b = 42 - 18

6b = 24

b = 4.

The required quantity of the remaining 6 bottles is 4 pints.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each.

Let b represent the capacity, in pints, of each of the remaining 6 bottles.,
Now,
42 = 3 × 6 + b × 6
42 = 18 + 6b
6b = 42 - 18
b = 24/6
b = 4

Thus, the required quantity of the remaining 6 bottles is 4 pints.

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Answer:

12. Option A is correct

13. Option A is correct

14. Option C is correct

15. Option D is correct

16. Option A is correct

Step-by-step explanation:

12) Lowest Common Denominator of

[tex]\frac{p+3}{p^2+7p+10} \,\, and \,\, \frac{p+5}{p^2+5p+6}[/tex]

We should find the factors of denominators and then find the LCM of the denominators.Finding LCD is same as finding LCM.

Factors of p^2+7p+10 = p^2 +2p +5p+10 = p(p+2)+5(p+2) = (p+5)(p+2)

Factors of p^2+5p+6 = p^2+2p+3p+6 = p(p+2)+3(p+2) = (p+3) (p+2)

Now, rewriting the above equation with factors and finding the LCM

[tex]\frac{p+3}{(p+5)(p+2)} \,\, and \,\, \frac{p+5}{(p+3)(p+2)}\\[/tex]

LCM of (p+5)(p+2) and (p+3)(p+2) = (p+5)(p+3)(p+2)

The LCD is (p+5)(p+3)(p+2).

So, Option A is correct.

13. Divide

[tex]\frac{40x}{64y} \,\,by\,\, \frac{5x}{8y}[/tex]

by stands for division. The equation can be written as:

[tex]\frac{40x}{64y}\div\frac{5x}{8y}[/tex]

Division sign changed into multiplication, we take reciprocal of second term i.e,

[tex]\frac{40x}{64y}*\frac{8y}{5x}\\\\Solving\\\frac{40x*8y}{64y*5x}\\\\\frac{320xy}{320xy} \\\\1[/tex]

So, Option A is correct.

14. Simplify:

[tex]\frac{x+2}{x^2-6x-16} \div \frac{1}{9x} \\[/tex]

Factors of x^2-6x-16= x^2 -8x +2x -16 = x(x-8)+2(x-8) = (x-8)(x+2)

Putting factors in the above equation and changing division sign with multiplication we get,

[tex]\frac{x+2}{(x-8)(x+2)} * \frac{9x}{1}\\\frac{9x}{x-8}[/tex]

So, Option C is correct.

15. Simplify

[tex]\frac{4}{\frac{1}{4}-\frac{5}{2}}[/tex]

Solving denominator,

Taking LCM of 4 and 2 and subtracting we get

[tex]\frac{4}{\frac{1-(5*2)}{4}}\\\frac{4}{\frac{1-10}{4}}\\\frac{4}{\frac{-9}{4}}\\\frac{4*4}{-9}\\\frac{16}{-9} \,\,or\,\,\\\frac{-16}{9}[/tex]

Option D is correct.

16. Simplify:

[tex]\frac{7x+42}{x^2+13x+42}[/tex]

Making factors of x^2+13x+42= x^2 +6x+7x+42 = x(x+6)+7(x+6) = (x+7)(x+6)

Taking 7 common from numerator and putting factors in denominator we get,

[tex]\frac{7(x+6)}{(x+7)(x+6)}\\\\Cancelling\,\, x+6 \,\, from\,\, numerator \,\, and\,\, \\\\\frac{7}{(x+7)}[/tex]

Option A is correct.

Answer:

The correct answer would be option C

Step-by-step explanation:

x = 90

y = 180 - (90 + 47)

y = 43

Answer:

3 hours

Step-by-step explanation:

3 hours as it takes 3 periods to be 40000

If there are initially 5000 bacteria in a culture,and the number of bacteria doubles each hour. The culture will take around 3 hours to reach 40,000 bacteria.

To determine how long it will take for the culture to grow to 40,000 bacteria, we can use the given formula: N = 5000 * (2^t), where N represents the number of bacteria after t hours.

Substitute N with 40,000 and solve for t:

40,000 = 5000 * (2^t)

Divide both sides by 5000:

8 = 2^t

Since 2^3 = 8 we can conclude that t is equal to 3

Therefore it will take approximately 3 hours for the culture to grow to 40,000 bacteria.

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Answer:

3225

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ]

where a is the first term and d the common difference

here a = 6 and

d = 13 - 6 = 20 - 13 = 7, hence

[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex][ (2 × 6) + (29 × 7) ]

                          = 15(12 + 203) = 15 × 215 = 3225

Answer:

Choice A is correct

Step-by-step explanation:

We have been given the expression;

[tex]x^{\frac{9}{7} }[/tex]

In order to re-write this expression, we shall use some laws of exponents;

[tex]a^{\frac{b}{c} }=(a^{b})^{\frac{1}{c} }[/tex]

Using this law, the expression can be written as;

[tex](x^{9})^{\frac{1}{7}}[/tex]

The next thing we need to remember is that;

[tex]a^{\frac{1}{n} }=\sqrt[n]{a}[/tex]

Therefore, the expression becomes;

[tex]\sqrt[7]{x^{9} }[/tex]

Next,

[tex]x^{9}=x^{7}*x^{2}[/tex]

This implies that;

[tex]\sqrt[7]{x^{9} }=\sqrt[7]{x^{7}*x^{2}}\\=\sqrt[7]{x^{7} }*\sqrt[7]{x^{2} } \\=x\sqrt[7]{x^{2} }[/tex]

ANSWER

A.

[tex]x \sqrt[7]{{x}^{2} } .[/tex]

EXPLANATION

The given expression is

[tex] {x}^{ \frac{9}{7} } [/tex]

We want to rewrite the given expression in radical form:

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

This implies that:

[tex] {x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{9} } [/tex]

[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} \times {x}^{2} } [/tex]

Split the radicals.

[tex]{x}^{ \frac{9}{7} } = \sqrt[7]{ {x}^{7} } \times \sqrt[7]{{x}^{2} } [/tex]

This finally simplifies to:

[tex]{x}^{ \frac{9}{7} }=x \sqrt[7]{{x}^{2} } [/tex]

The correct answer is A.

Answer: 15 cm

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

[tex]A=l*w[/tex]

Where "l" is the lenght and "w" is the width.

You know that the area of this rectangle is 75 square centimeters and the width is 5 centimeters. Then, you can substitute these values into the formula [tex]A=l*w[/tex] and solve for the lenght. Then you get:

[tex]75cm^2=l(5cm)\\\\\frac{75cm^2}{5cm}=l\\\\l=15cm[/tex]

Therefore, the lenght of the rectangle is 15 centimeters.

Answer:

15 centimeters.

Step-by-step explanation:

To find the area of a rectangle, you have to multiply the length by the width.

In this case, the width is 5 centimeters.

So, so find the area, you would have to multiply 5 by the length. Let's call the length "x".

The equation to solve this problem would be:

5x - 75

Now we can solve the equation...

Divide both sides by 5...

5x / 5 = 75 / 5

x = 15

Since x is equal to 15, that means that the length is 15, because we said that the length is equal to x.

Length = x = 15

------------------

Hope this helped!

Answer: 6 outfits

Step-by-step explanation:

She can make 6 outfits out of the clothes given.

(p)=pink dress

(b)=blue dress

(y)=yellow dress

(bl)=black shoes

(w)=white shoes

p can combo with bl and w which makes 2 outfits

b can combo with bl and w which makes 2 outfits

y can combo with bl and w which makes 2 outfits

2+2+2=6 outfits

Answer:

40 cm

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{4x}{x}[/tex] = [tex]\frac{48}{x+2}[/tex], simplifying gives

4 = [tex]\frac{48}{x+2}[/tex]

Multiply both sides by (x + 2)

4(x + 2) = 48 ( divide both sides by 4 )

x + 2 = 12 ( subtract 2 from both sides )

x = 10

Hence

width = 4x = 4 × 10 = 40

Answer

a) 2π

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is periodic.

The function is

f(x) =  3*sin(2*x) + 4*cos(3*x)

Which can be seen in the picture below

We can notice that f(x) is periodic. It has periodic amplitudes, and the function has a period T = 6.283   ≈ 2π

The maximum and minimum values are

Max = 6.695

Min = -6.695

Answer:

Length = 12 meters

Step-by-step explanation:

Rectangle

Perimeter P = 2(L + W)

The length of a rectangle, I, is six meters more than it's width, W.

Then L = W + 6

So

P =  2(W + 6 + W)

P = 2 (2W + 6)

P = 4W + 12

Plug in P = 36 meters

36 = 4W + 12

4W = 36 - 12

4W = 24

 W = 6 meters

L = 6 + 6

L = 12 meters

Answer:

60

Step-by-step explanation:

If you do 25% + 6 * 10 , it gives you 62.5 and you round that and it's 60.

Answer:

60

Step-by-step explanation:

25% + 6 * 10

=62.5

round 62.5

=60.

Give brainliest plz :'D

Answer:

Y=3x(x-4)

Step-by-step explanation:

Answer:

Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten".

Step-by-step explanation:

I think the answer is b. y= -1

Answer:

[tex]A(t)=(100-8t)^{2}[/tex]

Step-by-step explanation:

Let

t-----> the number of years

A-----> the area of the cement parking lot

we know that      

The function that represent this situation is

[tex]A(t)=(100-8t)^{2}[/tex]

Final answer:

The function A(t) = [tex](100-8t)^2[/tex] can be used to calculate the area of the cement parking lot after t years by substituting the side length (100-8t) into the formula for the area of a square.

Explanation:

The function that can be used to calculate the area of the cement parking lot after t years is: A(t) = [tex](100-8t)^2[/tex].

To calculate the area of the square parking lot at any given time t, you substitute the side length (100-8t) into the formula for the area of a square, A = side [tex]length^2[/tex].

For example, after 2 years, the area A(2) would be[tex](100-8(2))^2[/tex] = [tex]84^2[/tex]= 7056 square meters.

Answer:

you are correct

Step-by-step explanation:

p.s the way you worded this was confusing