which quadratic equation is equivalent to (x-2)^2+5(x+2)-6=0

Answer:

cluster system

Step-by-step explanation: For edgunity

This process is an example of cluster system.

The following information should be considered:

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Answer:

15+x<_25

Step-by-step explanation:

however much weight the puppy gains (x) can not be greater than 25 but can be equal to 25

Answer:

[tex]15+x\leq 25[/tex]

So, [tex]x\leq 10[/tex]

Step-by-step explanation:

Boston Terriers weigh up to 25 lb.

Suppose a puppy of this breed weighs 15 pounds.

Let the puppy can weigh 'x' pounds more.

So, [tex]x=25-15=10[/tex]

But as it is given the maximum weight can be 25 pounds, so the puppy can weigh a maximum of 10 pounds more.

Given by :

[tex]15+x\leq 25[/tex]

So, [tex]x\leq 10[/tex]

Using the Pythagorean theorem with the length of the ladder as the hypotenuse and the base distance as one side, we calculate the height of the building to be approximately 10.82 feet.

The student's question can be solved using the principles of the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario, the ladder, the building, and the ground form a right triangle.

The ladder serves as the hypotenuse, the height of the building is the opposite side, and the distance from the ladder's base to the building is the adjacent side.

To find the height of the building, we can set up the equation using the Pythagorean theorem as follows:

a2 + b2 = c2

where a is the distance from the base of the ladder to the building (2 feet), b is the height of the building, and c is the length of the ladder (11 feet).

Plugging in the values we have:

22 + b2 = 112,4 + b2 = 121,b2 = 121 - 4,b2 = 117.

Therefore, the height of the building is:

b = √117 ≈ 10.82 feet.

The building is approximately 10.82 feet tall.

Answer:

-7k+21

Step-by-step explanation:

Distributive Property:

    ↓

[tex]A(B+C)=AB+AC[/tex]

A=-7, B=K, and C=3

-7k+7*3

Multiply by the numbers from left to right to find the answer.

7*3=21

-7k+21 is the correct answer.

Answer:

Step-by-step explanation:

Answer x = 0

1 < 0 and 13<0

Answer:

x<1.5

Step-by-step explanation:

The equation is

[tex]f(x)=-x^2+3x+8[/tex]

Use a graphing tool to find the vertex of the parabola.When you get the vertex from the graph, you can now write the increase as ; all x-values less than the x-value of the vertex value in the graph

From the graph, the vertex is at (1.5,10.25), the parabola opens down with maximum value y=10.25

The interval of increase is x<1.5

Answer:

[tex]x \geq \frac{3}{2}[/tex]

Step-by-step explanation:

First, the first derivative of the function is computed to distinguish which interval is increasing.

[tex]f'(x) = -2\cdot x + 3[/tex]

An interval is increasing only if slope is increasing as long as x increases. Then, it is quite evident that curve is increasing for:

[tex]x \geq \frac{3}{2}[/tex]

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =-2\\y_{1} =4\\x_{2} =6\\x_{1} =-2[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{-2 - 4}{6 - (-2)}[/tex]

[tex]\frac{-6}{8}[/tex]

^^^Can be further simplified to...

[tex]\frac{-3}{4}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]{\displaystage\boxed{\frac{-3}{4}}[/tex]

Step-by-step explanation:

Slope formula:

     ↓

[tex]\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystage y_2=(-2)\\\displaystage y_1=4\\\displaystage x_2=6\\\displaystage x_1=(-2)\\[/tex]

[tex]\displaystage \frac{-2-4}{6-(-2)}=\frac{-6}{8}=\frac{-6\div2}{8\div2}=\frac{-3}{4}[/tex]

-3/4 is the correct answer.

I hope this helps you, and have a wonderful day!

The answer is b because the ratio is blondes to brunettes.

Follow below steps;

The student asked which statement about the proportions of blonds and brunettes among their 15 friends is false. Given that the proportion of blonds to brunettes is 6 to 9, let's evaluate the options:

Option a) The ratio of the number of friends to brunettes is 15 to 9. This statement is true since there are 15 friends in total and 9 of them are brunettes.

Option b) The ratio of brunettes to blonds is 6 to 9. This statement is false because the proportion of blonds to brunettes is 6 to 9, so the ratio of brunettes to blonds should be 9 to 6.

Option c) The ratio of blonds to the number of friends is 6 to 15. This statement is true because there are 6 blonds out of 15 friends.

Option d) The ratio of brunettes to the number of friends is 9:15. This statement is also true because there are 9 brunettes out of 15 friends.

Therefore, option b is the false statement as the ratio of brunettes to blonds is incorrectly stated as 6 to 9 instead of the correct ratio 9 to 6.

Answer:

<2 = 97

Step-by-step explanation:

Definition: Supplementary angles are 2 or more angles with the same vertex that add up to 180o

Solution

<1 = 83

<2 = ?

Total = 180o

<1 + <2 = 180                   Substitute for angle 1

83 + <2 = 180                  Subtract 83 from both sides.

83 - 83 + <2 = 180 - 83   Do the subtraction

<2 = 97 degrees

The supplement of an 83-degree angle is the angle that adds up to 180 degrees with it. By subtracting 83 from 180, we find that the supplement of the angle is 97 degrees.

The question is asking for the supplement of an angle that measures 83 degrees. In geometry, the supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. To find the supplement of an 83-degree angle, you subtract 83 from 180.

Step-by-step solution:

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

12/√7+2

Rationalize the denominator

=12/7+2 * √7-2/√7-2

=12√7-24/7-4

=12√7-24/3

By taking common from numerator we get

=12(√7-2)/3

=4√7-8

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

The diameter of the circle is approximately 20.37 cm, the radius is approximately 10.18 cm, and the length of an arc measuring 190 degrees is approximately 33.8 cm.

The subject at hand concerns the properties of a circle, more specifically its circumference, diameter, radius, and arc length.

In this case, we know that the circumference of the circle is 64 cm. The circumference of a circle is calculated by the formula 2πr (where r is the radius), or can also be viewed as πd (where d is the diameter). If we equate 64 = 2πr, we can thus find the radius, r = 64/(2π), resulting in roughly a radius of 10.18 cm. The diameter of the circle is simply twice the radius, hence in this context, it would be roughly 20.37 cm.

The length of an arc is calculated by multiplying the radius by the angle (in radian measure), which is represented as θ = s/r. In this case, the arc length is not given directly but we are given an angle of 190, and this seems to denote 190 degrees. Although it's important to mention that the standard measure for calculating arc length is radians, if we convert 190 degrees into radians, we get about 3.32 rad. Thus the length of this specific arc will be r*θ=10.18*3.32, resulting in an arc length of about 33.8 cm.

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The radius of the circle with a circumference of 64 cm is approximately 10.18 cm, the diameter of the circle is 20.36 cm and the length of an arc of 190 degrees in this circle is approximately 33.78 cm.

The given circumference is 64 cm. In a circle, the circumference is given by the formula 2πr = Circumference, where r is the radius and π is a constant approximately equal to 3.14. We can rearrange this formula to find the radius: r = Circumference / 2π. Substituting the given value of the circumference, we have r = 64 cm / 2π ≈ 10.18 cm. This is the radius of the circle.

The diameter of a circle is twice the radius, hence the diameter of the circle is 2 * 10.18 cm = 20.36 cm.

Now, to find the length of an arc of 190 degrees in this circle, we first understand that the total angle in a circle is 360 degrees. Hence, the length of the arc corresponding to 190 degrees will be the ratio of 190 to 360 times the circumference. Therefore, arc length = (190/360) * 64 cm ≈ 33.78 cm.

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Answer: [tex]\bold{C.\quad \dfrac{26}{9}}}[/tex]

Step-by-step explanation:

[tex]\bigg(\dfrac{2}{5}+\dfrac{4}{3}\bigg)\div\dfrac{3}{5}\\\\\\\text{According to PEMDAS, the parenthesis must be performed first.}\\\\\bigg[\dfrac{2}{5}\bigg(\dfrac{3}{3}\bigg)+\dfrac{4}{3}\bigg(\dfrac{5}{5}\bigg)\bigg]\div\dfrac{3}{5}\\\\\\\bigg(\dfrac{6}{15}+\dfrac{20}{15}\bigg)\div\dfrac{3}{5}\\\\\\\dfrac{26}{15}\div\dfrac{3}{5}\\\\\\\text{Dividing by a fraction is multiplying by its reciprocal.}\\\dfrac{26}{15}\times\dfrac{5}{3}\\\\\\\text{Simplify.}\\\dfrac{26}{3}\times\dfrac{1}{3}[/tex]

[tex]=\large\boxed{\dfrac{26}{9}}[/tex]

[tex]\bf \stackrel{\textit{difference of squares}}{(6+3i)(6-3i)}\implies (6)^2-(3i)^2\implies \stackrel{\textit{recall }i^2=-1}{36-(3^2 i^2)}\implies 36-(9\cdot -1) \\\\\\ 36+9\implies 45[/tex]

Step-by-step explanation:

6*6 - 6*3i + 6*3i -3i*3i

36-18i+18i-9i^2

36-9(-1)= 36+9= 45

b*h/2 is the formula for area

8*h= 24

24*2= 48

48/8= 6

6 is the height/ missing side

The value of x for the given right angle triangle such that its area is 24 units² will be 8.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle,

The area of right angle triangle = (1/2)8 × x

(1/2)8 × x = 24

x = 24/4 = 8

Hence "The value of x for the given right angle triangle such that its area is 24 units² will be 8".

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Answer:

dy/dx=  cos(ln(x))/x

Step-by-step explanation:

y=sin(ln(x)) given

We have to use chain rule to differentiate!

Let u=ln(x) then du/dx=1/x

So we have

if y=sin(ln(x)) then y=sin(u) and dy/dx=dy/du * du/dx=cos(u) *1/x

where again u=ln(x) so

dy/dx=cos(ln(x)) *1/x

dy/dx=cos(ln(x))/x

I hope I have the right intepretation because I do see a ? in between sin and (ln(x)) .

Answer:

0.76

Step-by-step explanation:

The mean of the data including the outlier is:

Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87 + 48.32 + 41.59 + 42.71)/12 = 39.98 seconds.

In this case, the outlier comes to be the data: 48.32. If we don't consider that data point, the mean equals:

Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87  + 41.59 + 42.71)/11 = 39.22

The difference is:  39.98 - 39.22 = 0.76

Answer:

C . 0.76

Step-by-step explanation:

We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:

Jan  40.55 Feb 41.51

March 42.01 Apr 38.76

May 36.32  June 34.28

July 35.38  Aug 37.48

Sept 40.87 Oct 48.32

Nov 41.59 Dec 42.71

We have to find the difference between the mean of the data , including the outlier and excluding the outlier

Outlier: That observation which is different from other observations.

The outlier in the given observations is 48.32 because is different from other observations.

Mean of the data including the outlier

Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]

Mean=[tex]\frac{479.78}{12}[/tex]

Mean=39.982

Mean of the data excluding the outlier

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}

Mean=[tex]\frac{431.46}{11}[/tex]

Mean=39.224

Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758

Difference between mean of the data including the outlier and excluding the outlier=0.76

Answer Answer:

Step-by-step explanation:

We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:

Jan  40.55 Feb 41.51

March 42.01 Apr 38.76

May 36.32  June 34.28

July 35.38  Aug 37.48

Sept 40.87 Oct 48.32

Nov 41.59 Dec 42.71

We have to find the difference between the mean of the data , including the outlier and excluding the outlier

Outlier: That observation which is different from other observations.

The outlier in the given observations is 48.32 because is different from other observations.

Mean of the data including the outlier

Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]

Mean=[tex]\frac{479.78}{12}[/tex]

Mean=39.982

Mean of the data excluding the outlier

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}

Mean=[tex]\frac{431.46}{11}[/tex]

Mean=39.224

Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758

Difference between mean of the data including the outlier and excluding the outlier=0.76

Answer :C . 0.76

ANSWER:

7x + 3

let us break the problem into two smaller equations that match-

5x + 2x = 7x

9 - 6 = 3

this leaves you with 7x + 3.

Answer:

$26

Step-by-step explanation:

To find your answer, simply plug in Francesca's time and Phil's time to your cost equation.

Francesca can be represented by the following equation:

[tex]c=6.5(2)\\c=13[/tex]

Phil can be represented by the following equation:

[tex]c=6.5(6)\\c=39[/tex]

As such, Francesca pays $13 and Phil pays $39. Next, since you want to find how much more Phil paid, all you have to do is subtract 13 from 39. That will give you $26.

Answer:

The linear term is -5x

Step-by-step explanation:

The linear term is the term that has the degree equal to 1.

The given function is

y = 2x^2 − 5x − 12

here 2x^2 = quadratic term i.e having degree 2

-5x = linear term i.e having degree 1

-12 = constant

so, The linear term is -5x

Answer:

9 and -4

Step-by-step explanation:

Find two numbers that multiply to be -36 and add to be -5.

That is -9 and 4.

So the factored form of x^2-5x-36 is (x-9)(x+4)

So the x-intercepts are 9 and -4

Answer: The value of the y-intercept is [tex]-\frac{3}{5}[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

In this case we know that the line passes through point [tex](0.4,-\frac{1}{2})[/tex] and has a slope of [tex]\frac{1}{4}[/tex]. Then we can substitute the following values into  [tex]y=mx+b[/tex]:

[tex]x=0.4\\\\y=-\frac{1}{2}\\\\m=\frac{1}{4}[/tex]

Then:

[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b[/tex]

And finally, we must solve for "b":

[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b\\\\-\frac{1}{2}-\frac{1}{10}=b\\\\b=-\frac{3}{5}[/tex]

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

y: It is the cut point with the "y" axis

They tell us as data that:

[tex]m = \frac {1} {4}[/tex]

So, the equation is:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute the given point to find "b":

[tex]- \frac {1} {2} = \frac {1} {4} (0.4) + b\\- \frac {1} {2} = \frac {0.4} {4} + b\\b = - \frac {1} {2} - \frac {0.4} {4}\\b = -0.5-0.1\\b = -0.6[/tex]

Thus, the cut point with the y axis is -0.6

Answer:

[tex]b = -0.6[/tex]

Answer:

The solution of given equation 5(x - 6) = 2(x + 3) is given by,

x = 12

Step-by-step explanation:

It is given that,

5(x - 6) = 2(x + 3)

To find the solution of given equation

5(x - 6) = 2(x + 3)

5x - (5 * 6) = 2x + (2 * 3)

5x - 30 = 2x + 6

5x - 2x = 6 + 30

3x = 36

x = 36/3

x = 12

Therefore the solution of  given equation is,

x = 12

Answer:

4

Step-by-step explanation:

The integer A^2 will have 9 divisors:

1, p, q, p^2, pq, q^2, p^2q, pq^2, p^2q^2

Of these, the last 4 are greater than A. Hence there will be these 4 values of B.

Answer:

it removed body waste like and instructions

Answer:

x=​5/​4, ​3/10

Answer:B. x=10/3

Step-by-step explanation:

A P E X

Answer:

  A.  Its legs are congruent.

Step-by-step explanation:

It is a parallelogram if ...

Answer:

161 minutes

Step-by-step explanation:

$1827-$7=$11.27

$11.27/.07=161

Answer:

161 minutes

Step-by-step explanation:

Bill pays a monthly fee for his long distance phone service = $7.00

and call charges per minute = 7 cents

1 dollar = 100 cents

Therefore 7 cents = [tex]\frac{7}{100}[/tex] = $0.07

Last month, Bill's long distance bill was $18.27.

Let Bill used the phone service for x minutes

The equation for his uses in minutes :

7.00 +(0.07x) = 18.27

0.07x = 18.27 - 7.00

0.07x = 11.27

x = [tex]\frac{11.27}{0.07}[/tex]

x = 161 minutes

Bill was billed for 161 minutes.

Answer:

three fifths candy bar

Step-by-step explanation:

3/1 ÷ 5/1

3/1 × 1/5 = 3/5

Answer:

3 fiths of a candy bar

Step-by-step explanation:

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

========================================

We have the slope m = -6 and the point (-9, -3).

Substitute:

[tex]y-(-3)=-6(x-(-9))\\\\y+3=-6(x+9)[/tex]

Convert to the slope-intercept form (y = mx + b):

[tex]y+3=-6(x+9)[/tex]           use the distributive property

[tex]y+3=-6x-54[/tex]         subtract 3 from both sides

[tex]y=-6x-57[/tex]

Answer:

The solution is -2/7 not –14.

Answer:

its D

Step-by-step explanation: