Lines
AB
and
AC
tangent to circle k(O) at B and C respectively. Find BC, if m∠OAB=30°, and AB=5 cm.

The expressions that illustrate the commutative property are: A, D, E, and F (see attachment below).

Therefore, the expressions that illustrate the commutative property are: A, D, E, and F (see attachment below).

Learn more about commutative property on:

https://brainly.com/question/2475734

Answer:

[tex]\large\boxed{y=(x+5)^2-64}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64[/tex]

Answer:

A. t < –15

Step-by-step explanation:

The temperature has to be less than -15

t < -15

Answer:

12 patties

Step-by-step explanation:

4 ÷ 1/3 = 12

Answer:

1.047

Step-by-step explanation:

60° × π/180 = 1.047rad

or

From the standard conversion factor

360∘ = 2 π r a d

we may use ratio and proportion to obtain that

60 ∘ = π 3 r a d

Answer:

pi/3

Step-by-step explanation:

To convert from degrees to radians, we multiply by pi/180

60 degress * pi/180 =  pi/3

60 degrees is pi/3 radians

Answer:

=2a

Step-by-step explanation:

a-2/5a and a+2/5a cancel each other out and your left with a+a aka 2a

Answer:

x=6.7

Step-by-step explanation:

What you have to do is you have to eliminate y. So you need to make y cancel each other out.

2x+2y=17. I can multiply 2 to the second equation to cancel the y's out.

8x-2y=50.

10x=67.

x=67/10 or 6.7.

The value of x for the system of equations will be x=6.7.

A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.

Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.

Multiply the second equation by 2 and subtract from the first equation,

2x+2y=17.

8x-2y=50.

10x=67.

x= 67/10

x = 6.7.

Therefore, the value of x for the system of equations will be x=6.7.

To know more about the system of equations follow

https://brainly.com/question/25976025

#SPJ2

answer: 11

explanation: just plug in -2 for x. the new problem becomes 5(-2)^2 - 9. Negative two squared is 4. 5 times 4 is 20. 20 minus 9 is 11.

Final answer:

When evaluating the expression 5x^2 - 9 for x = -2, we substitute -2 into the expression and find that the value is 11.

Explanation:

To evaluate the expression 5x2 − 9 when x = −2, we first substitute the value of x into the expression and then perform the calculation:

5(−2)2 − 9
→ 5(4) − 9
→ 20 − 9
→ 11

Therefore, when x = −2, the value of the expression 5x2 − 9 is 11.

Answer: 8

[tex]{10}^{2} = 100 \\ {6}^{2} = 36 \\ 100 - 36 = 64 \\ \sqrt{64} = 8[/tex]

Answer:

8

Step-by-step explanation:

6² + x² = 10²

36 + x² = 100

x² = 64

x² = √64

x = 8

Answer:

C

Step-by-step explanation:

Now there are 6+4+8+1+1=20 dads in the Dads Club.

Fewer than 3 children have

So, 6+4=10 dads have fewer than 3 children.

The probability that the dad of Dads Club has fewer than 3 children is

[tex]Pr=\dfrac{10}{20}=0.5 \text{ or } 50\%.[/tex]

The probability that the next dad to join Dads Club has fewer than 3 children is reasonable to be 50%.

Option: C is the correct answer.

           C.  50%

Let P denotes the probability of an event.

and A denote the event that the next dad has fewer than 3 children.

From the table the total number of dads are: 6+4+8+1+1=20

The number of dad who have less than 3 children are: 6+4=10

Hence, we have

[tex]P(A)=\dfrac{\text{Number\ of\ dad\ with\ less\ than\ 3\ children}}{\text{Total\ number\ of dad}}[/tex]

Hence, we have:

[tex]P(A)=\dfrac{10}{20}=\dfrac{1}{2}[/tex]

which in percentage is given by:

     [tex]P(A)=50\%\\\\(Since,\\\\\dfrac{1}{2}\times 100=50\%)[/tex]

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

From the graph we have the points A(2, 2) and B(-6, 4). Substitute:

[tex]AB=\sqrt{(-6-2)^2+(4-2)^2}=\sqrt{(-8)^2+2^2}=\sqrt{64+4}=\sqrt{68}[/tex]

[tex]AB\approx8.25[/tex]

To model Orlando's population growth, an equation in slope-intercept form is y = 2000x + 175000. The year 2010 is 15 years after 1995, so substituting 15 in for x gives a population of approximately 205,000 residents for Orlando in 2010.

To answer the student's question, first we need to write an equation in slope-intercept form to find Orlando's population for any year. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the starting value when x=0). In this case, the variable y represents Orlando's population, m represents the annual growth rate (2000 people per year), and x represents the number of years since 1995.

Using these variables, our equation becomes y = 2000x + 175000, where x is the number of years since 1995. To find Orlando's population in 2010, we must substitute x with 15, since 2010 is 15 years after 1995.

The calculation would be: y = 2000(15) + 175000, which simplifies to y = 205000.

Therefore, Orlando's population in 2010 was approximately 205,000 residents.

Answer:

y+4=-3/2(x-2) is the answer

Step-by-step explanation:

Again over here just use the y=mx+c

m which is the slope is change in y over change in x which in this case is [tex]\frac{-3}{2}[/tex] so which just that we can cross out the first option for the answer secondly to be able to find C just take literally any point from the graphed line, for instance we take (-2,2), just add it in the equation and solve for C

[tex]2=-\frac{3}{2}(-2)+c\\2=3+c\\0=3-2+c\\c=-1[/tex]

y=-3/2-1

Now all you have to see is which of the three equations is equivalent to the one we just found

y+4=-3/2(x-2) is the answer :)

Answer:

  28

Step-by-step explanation:

It is often convenient to compute the Least Common Multiple (LCM) as the product of the numbers divided by their greatest common factor. In this case, that would be ...

  LCM = (14 × 4)/2 = 28

___

As a check, you can do it by looking at the prime factors of these numbers. The LCM will be the product of the unique factors to their highest powers.

  14 = 2·7

  4 = 2^2

Unique factors are 2 and 7. The highest power of 2 is 2; the highest power of 7 is 1.

  LCM = 2^2·7 = 28

Start by setting up a factor tree for 4 and 14.

4 factors as 2 ·  2 and 14 factors as 7 · 2.

When finding the least common multiple, we're looking for factors that match up and here we have a pair of 2's that matches up.

So our least common multiple is 2 from the 2's that match up × the the 2 that doesn't match up x the 7 from the 7 that doesn't match up.

So we have 2 × 2 × 7 or 4 × 7 which is 28.

On my whiteboard, I have attached my factor tree.

Answer:

L = 8

Step-by-step explanation:

The volume of a rectangular prism is found by V = L*h*w. Substitute V = 120, w = 5 and h =3 then solve for the length.

120 = L*3*5

120 = 15L

8 = L

Final answer:

Tina and Bill will take approximately 2 hours and 55 minutes to finish cutting the lawn when they work together, combining their individual rates of work.

Explanation:

If Tina cuts a lawn by herself, she can finish in 5 hours. If Bill cuts the same lawn by himself it takes him two hours longer than Tina, which means it takes Bill 7 hours. To determine how long it will take both of them working together, we can use the rates at which they work. Tina's rate of work is 1/5 of the lawn per hour, and Bill's rate is 1/7 of the lawn per hour. Working together, their combined rate is the sum of their individual rates, which is (1/5 + 1/7) of the lawn per hour.

To find the combined rate, we calculate:
(1/5) + (1/7) = (7/35) + (5/35) = 12/35 of the lawn per hour. To find out how long it will take them to finish the lawn together, we take the reciprocal of this combined rate. Therefore, 35/12 hours, or 2 hours and 55 minutes, is the amount of time they will need to finish cutting the lawn when working together.

Answer:

87.5%

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2+2x-9=15

x^2+2x=24

x^2+2x+1=24+1

(because what you do to one side you do to the other) ^

(x+1)^2=25

(x+1)^2 -25=0

(25 is a perfect square)

(x+1-5)(x+1+5)

(x-4)(x+6)

x=4,-6

Answer: x=-6; x=4

Step-by-step explanation:

Answer:

The x-intercepts will be, x= 7 or x =9

Step-by-step explanation:

f(x)= x^2 -16x+63

At the x-intercept, f(x) is zero.

Therefore;

x² - 16x + 63 = 0

solving it quadratically;

product = 63

Sum       = -16

x² - 9x - 7x + 63 = 0

x(x-9) - 7( x-9) = 0

(x-7) (x-9) = 0

x = 7 or x = 9

Therefore;

The x-intercepts will be, x= 7 or x =9

Answer:

(7, 0) and (9, 0)

Step-by-step explanation:

The x-intercepts refers to the points where the graph of the function crosses the x-axis, or simply the zeroes of the function. In this case, we can determine these points analytically or graphically. We simply graph the function;

y = x^2 -16x +63 then determine where the function crosses the x-axis; see the attachment below;

The x-intercepts of this function are;

(7, 0) and (9, 0)

Answer:

See explanation below, and see attached photo for graphs

Step-by-step explanation:

To graph 3x + y = 6, find the x and y intercepts.  

We get the x intercept when y = 0, so plug in 0 for y and solve...

3x + 0 = 6

   3x = 6

    x = 2, so the x intercept is at (2, 0)

We get the y intercept when x = 0, so plug in 0 for x and solve...

3(0) + y = 6

   y = 6, so the y intercept is at (0, 6)

Plot those two points and draw a line through them

To graph -3x - 4y = 12, find the x and y intercepts.  

We get the x intercept when y = 0, so plug in 0 for y and solve...

-3x - 4(0) = 12

   -3x = 12

    x = -4, so the x intercept is at (-4, 0)

We get the y intercept when x = 0, so plug in 0 for x and solve...

-3(0) - 4y = 12

       -4y = 12

           y = -3, so the y intercept is at (0, -3)

Plot those two points and draw a line through them

The system of equations 3x + y = 6 and -3x - 4y = 12 is graphed by converting each to slope-intercept form, plotting points, and drawing lines. Intersection is found by solving the equations simultaneously, resulting in the intersecting point (4, -6).

To graph the system of equations consisting of 3x + y = 6 and -3x - 4y = 12, we first need to solve each equation for y to get them into slope-intercept form (y = mx + b). Here are the steps:

Next, we plot the lines on a coordinate plane by finding at least two points for each line based on the equations we've just derived:

After plotting these points for each line, draw straight lines through the points to complete the graph. The coordinates of the intersection of the two lines can be found by setting the two equations for y equal to each other and solving for x:

Therefore, the intersection point is at (4, -6).

Final answer:

In mathematics, to find out how many times 3 goes into 100, we divide 100 by 3, resulting in 33 times with a remainder of 1.

Explanation:

The question posed is concerned with division, which falls under the subject area of mathematics. When we consider how many times 3 goes into 100, we are calculating the number of times the number 3 can be subtracted from 100 until we reach zero or a number less than 3. To solve this problem, we use division.

To divide 100 by 3, you would start by seeing how many groups of 3 are in 100. Performing the division gives us 33 with a remainder of 1, which means that 3 goes into 100 a total of 33 times with 1 left over. Therefore the quotient (the result of division) is 33 and the remainder is 1.

The concept being described in the reference material, which mentions exponents and their use to indicate repeated multiplication of a base number, is not directly related to this question, hence it will not be incorporated in the calculation of the division of 3 into 100.

Answer:

A. -6

Step-by-step explanation:

(2,-2) reflected over X would be (-2,2). Then dilate by 3 which you multiply by 3. So -2 x 3 = -6.  

Answer:

c=9

Step-by-step explanation:

7(c - 12)= -21

Divide each side by 7

7/7(c - 12)= -21/7

c-12=-3

Add 12 to each side

c-12+12 = -3+12

c = 9

Answer: c = 9

Step-by-step explanation:

7(c - 12)= -21

Divide each side by 7

7/7(c - 12)= -21/7

c-12=-3

Add 12 to each side

c-12+12 = -3+12

c = 9  ← Answer

* Hopefully this helps:) Mark me the brainliest:)!!

Answer:

The slope is 5/4

Step-by-step explanation:

This equation is written in slope intercept form

y = mx+b, where m is the slope and b is the y intercept

y = 5/4x -7/4

5/4 is the slope and -7/4 is the y intercept

Answer:

B

Step-by-step explanation:

For each box, there is 1 defective lightbulb. Therefore, a delivery of 4 boxes will have 4 defective lightbulbs. A delivery of 2 boxes has 2 defective lightbulbs. 4 defective lightbulbs subtracted by 2 defective lightbulbs equals 2 more defective lightbulbs in 4 boxes than 2. Therefore, it is B.

[tex]\bf \cfrac{Zak}{Fred}\qquad \cfrac{1.86}{1.6}\implies \cfrac{~~\frac{186}{100}~~}{\frac{16}{10}}\implies \cfrac{186}{100}\cdot \cfrac{10}{16}\implies \cfrac{186}{16}\cdot \cfrac{10}{100}\implies \cfrac{93}{8}\cdot \cfrac{1}{10} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{93}{80}~\hfill[/tex]

To express Zak's height as a fraction of Fred's, divide Zak's height by Fred's height. This will yield a fraction that represents how Zak's height compares to Fred's. The heights need to be provided to calculate the actual fraction.

To write the height of Zak as a fraction of the height of Fred, we need to know both Zak's height and Fred's height. For instance, if Zak's height is 4 feet and Fred's height is 6 feet, the fraction representing Zak's height in relation to Fred's height would be ⅓ (Zak's height) over ⅔ (Fred's height). This is simplified by dividing both the numerator and the denominator by the GCD (Greatest Common Divisor) of Zak's and Fred's height if they are not already in simplest form.

If Zak is shorter than Fred, the fraction will be less than 1, indicating that Zak is shorter than Fred. Conversely, if Zak is taller than Fred, the fraction will be greater than 1, indicating Zak's greater height. In your specific question, it seems the heights are not provided, so please provide them in order to calculate the exact fraction.

Answer:

[tex]h = 227\ ft[/tex]

Step-by-step explanation:

We know that the equation that models the height of a projectile as a function of time is:

[tex]h(t) = -16t ^ 2 +v_0t +h_0[/tex]

Where:

[tex]v_0[/tex] is the initial velocity

[tex]h_0[/tex] is the initial height of the projectile.

In our case, the height of the machine is 2 ft.

Then [tex]h_0 = 2\ ft[/tex]

The initial speed is 120 ft/s.

So the equation of the height for this case is:

[tex]h(t) = -16t ^ 2 + 120t + 2[/tex]

This is a quadratic equation whose main coefficient is negative.

The maximum value of the function is at its vertex.

For a quadratic function of the form:

[tex]at ^ 2 + bt + c[/tex]

the vertex of the equation is given by the expression:

[tex]x =\frac{-b}{2a}[/tex]

[tex]y = f(\frac{-b}{2a})[/tex]

In this case:

[tex]a = -16\\b = 120\\c = 2[/tex]

Then the maximum point occurs instantly:

[tex]t = -\frac{120}{2(-16)}\\\\t = 3.75\ s[/tex]

Finally the maximum atura is:

[tex]h(3.75) = -16(3.75) ^ 2 +120(3.75) + 2[/tex]

[tex]h = 227\ ft[/tex]

Answer:

8

Step-by-step explanation:

Answer:

b) f(x) has no x^2 term

Step-by-step explanation:

The general form of a linear function is:

f(x) = ax + b

Where a and b are constant terms and x is the variable.

Option a:

This statement may or may not be true. We can have a linear function with no constant term for example f(x) = 5x is a linear function with no constant and f(x) = 5x + 5 is a linear function with a constant term. So option a cannot be the answer

Option b:

This statement is true for a linear function. x^2 term can be found in quadratic and higher degree polynomials. In linear function the power of variable must be 1.

Option c:

The function can have terms with coefficients other than 1 e.g f(x) = 5x + 5. So this is not true either

Option d:

f(x) must have x term. So this option is also not correct.

Therefore, the correct answer is option b.

Answer:

The correct statement is (b) which is f(x) has no [tex]x^2[/tex] term

Explanation:

The graph of a linear equation is a straight line. The general form of a linear equation is

ax + by + c = 0

Here, the coefficients a and b can't be zero simultaneously.

The term 'c' is a constant and can be zero.

We can see that the exponent on each variable x and y is 1. So, if the exponent in any variable is not 1 then that will not be a linear equation.

Other than this, the coefficients a and b can be zero at a time.

Therefore, on the basis of these facts, we can conclude that the necessary condition for an equation is to be a linear equation is " it should not have any [tex]x^2[/tex] term"

If we have [tex]x^2[/tex] in our equation then it will be a quadratic equation.

Therefore, option b is correct.

Further Explanation:

Any function which is in the form ax+by+c=0 is called a linear function.

Linear function always represents a straight line.

The slope intercept form of a line is [tex]y=mx+b[/tex]. Here, m is the slope and b is the y-intercept.

The formula for slope of a straight is given by

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

Learn more:

https://brainly.com/question/6108704 (Answered by  SociometricStar)

https://brainly.com/question/7876025 (Answered by Calculista)

Keywords: