An equilateral triangle has a median drawn from one angle to the opposite side. What is the measure of each angle formed by the place where the median meets the vertex?

(Step by step pls)

Worth 20 points

Check the picture below.

we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.

Question 4

[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]

Question 5

[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]

The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n)  independent variable.

According to the statement

we have to explain the linear regression method and explain the way by which this method is used to predict the values.

So, For this purpose we know that the

Linear regression is the most basic and commonly used predictive analysis. Regression estimates are used to describe data and to explain the relationship.

And

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

from these definitions it is clear that the there is a presence of two types of variables which are dependent and independent variables.

So, The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n)  independent variable.

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Answer:

2(7x + 2)

Step-by-step explanation:

Perimeter of a Rectangle = 2 x Length + 2 x Width.

Given Length = 4x, Width = 3x + 2,

Perimeter of Rectangle = 2(4x) + 2(3x + 2)

= 8x + 6x + 4

= 14x + 4 (Degree one polynomial)

= 2(7x + 2)

The distance that you run around the track in gym class is considered continuous data.

The variable is given as:

Distance

The distance travelled can take any value between 0 and the length of the track.

Take for instance;

The distance travelled can be 1km and it can also be 1.67 km

This means that the distance is continuous

Hence, the statement that completes the blank is (c) continuous

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Answer:

Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

x = 1

4x - (x + 5) = 4 - 6 = -2

8 - 3x - 3 = 8 - 3 - 3 = 2

Answer:

No real roots

[tex]x = -2 + 4i, x = -2 - 4i[/tex]

Step-by-step explanation:

Hello!

We can solve the quadratic by using the Quadratic Formula.

Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

Quadratic Equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

Given our Equation: [tex]f(x) = x^2 + 4x + 20[/tex]

Set the equation to 0 and solve using the formula.

There are no real roots to the quadratic.

Answer: Read the explanation

Step-by-step explanation:

If the points of a figure are all moved the same, they are congruent.

Point A is moved 9 points right, and 7 points down.

Point B is moved 9 points right, and 7 points down.

Point C is moved 9 points right, and 7 points down.

So, they are congruent.

F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)

A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.

Graphs of quadratic functions

The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.

It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.

We need to find the equation of F(x)

In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct

Hence the equation of F(x) is 2(x-2)^2 + 2

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The image point of (4,-2) after the transformations given is; (2,1).

It follows from the task content that the point given is (4, -2) which first reflects over the y axis and hence, renders the new image to be; (4, 2) after which it undergoes a dilation of with dilation factor, 1/2 and hence, the image point is; (2,1).

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The first table is a quadratic function while the second table is a linear function.

1) For the first table, we have;

x y

0 5

1 0

2 -3

3 -4

4 -3

x = 2  and x = 4 have same value of y = -3  and as such it will be a Quadratic Function.

y = x²  - 6x + 5

2) For the second table, we have;

x y

2 5

5 14

6 17

8 23

10 29

This table is a Linear function because  slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1  

3) For the third table, we have;

x y

-3 8

-2 4

-1 2

0 1

1 0.5

This is an exponential function because equation can be modelled by;

y = 2⁻ˣ

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The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is [tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex].

The last option is correct.

The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.

The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.

From the information given:

[tex]\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}[/tex]

Inverse of [tex]\mathbf{\dfrac{8x +1}{2x -9 }}[/tex] becomes [tex]\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}[/tex]

The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:

[tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex]

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Answer:

[tex]m_{1} =1/2\\m_{2} =5[/tex]

Step-by-step explanation:

[tex]2m^{2} -11m+5=0[/tex]

[tex](2m-1)(m-5)=0[/tex]

[tex]2m-1=0\\2m=1\\m_{1} =1/2[/tex]

[tex]m-5=0\\m_{2} =5[/tex]

Hope this helps

Considering the definition of an inequality, the number of friends admitted must be less than or equal to 8, expressed as p ≤ 8

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "p" the maximum number of people who can go to the amusement park, the inequality that expresses the previous relationship is

39.25 p + 11 ≤ 325

Solving:

39.25 p ≤ 325 -11

39.25 p ≤ 314

p ≤ 314÷ 39.25

p ≤ 8

Finally, the number of friends admitted must be less than or equal to 8, expressed as p ≤ 8

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The values of a and b will be -2 and 22 while the other factor in the function is x - 3/2.

The function is given as:

f(x) = ax³ - x² + bx - 24.

Since (x - 2) and (x - 4) are the factors, they will give functions of 8a + 2b = 28 and -16a - b = 10.

This will be solved by elimination method and the values of a and b will be -2 and 22.

Therefore, f(x) = -2x³ - x² + 22x - 24

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Answer:

7a + b

Step-by-step explanation:

5a + 2a + 3b - 2b

= 7a + 3b - 2b

= 7a + b

Answer:

B, cos(0)=1

Step-by-step explanation:

cos(0)=1

Coordinate A is at point (1,0)

Answer:

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

Step-by-step explanation:

Use the formula f(t)=P(1+b)^t

Plug in the information.

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

The only thing I did in the second equation is I subtract 0.12 from 1.

Hope this helps!

Based on the given parameters, the midpoint of the line segment is (5, 1/2)

The complete question is added as an attachment

From the figure, we have the following coordinates

(5, 4) and (5, -3)

The midpoint of the segment is then calculated using

(x, y) = 0.5 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

(x, y) = 0.5 * (5 + 5, 4 - 3)

Evaluate the sum and the difference

(x, y) = 0.5 * (10, 1)

Evaluate the product

(x, y) = (5, 1/2)

Hence, the midpoint of the line segment is (5, 1/2)

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Answer:

D

Step-by-step explanation:

When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)

Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)

Given f(x) is shifted 3 units right,

the new function, g(x) becomes:

[tex] g(x) = {(x - 3)}^{2} + 5(x - 3) - 1[/tex]

Therefore the answer is D in this case.

Answer:Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

If either a or b equals zero, then the sums would be the same.

Since the square root of 0 is 0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.

Step-by-step explanation:

The statement √a + √b = √(a + b) is not possible since a ≠ b

The operation involving surd is most likely an algebraic expression where in the case of surd the value in the square root are like the alphabets in algebraic expression.

Some surd operations are given as shown below:

Now, let us consider the question given:

Since a and b are not equal, it means

√a + √b ≠ √(a + b)

Thus, we can conclude that the statement √a + √b = √(a + b) is not possible

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What is a Venn Diagram?

Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

How to draw a Venn Diagram?

Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram

What is a venn Diagram mostly used for?

Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.

Set notations: The concepts illustrated in Venn ...

Scaled Venn Diagram: Also called Area Propo...

Reuleaux Triangle: Shape formed from the int...

Intersection: The items that overlap in the sets. ...

Here's some question for Venn Diagrams!

A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html

B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm

C. What does a Venn Diagram looks like?

( Try using those questions to partice more about Venn Diagrams! )

( Also, thank you for the points! )

The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts

An equation is an expression that shows the relationship between two or more number and variables.

The line segment has a length of 6.4 cm. Hence:

Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm

The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts

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Answer:

B

hope this helps :)

Answer:

D

Step-by-step explanation:

to find the zeros, equate f(x) to zero, that is

(x - 7)(x + 8) = 0

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 8 = 0 ⇒ x = - 8

The solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

A fraction represents a part of a whole or, more generally, any number of equal parts.

A fraction  can also be described as how many parts of a certain size there are, in a given whole.

The fraction given can be written as follows;

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16)

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y - 4)(y+4)

-8/(2y - 8)  = [5(y - 4) - (7y + 8)] /(y-4)(y + 4)

-8/(2y - 8)  = (5y - 20 + 7y + 8)/(y-4)(y + 4)

-8/(2y - 8)  = (12y - 12)/(y-4)(y + 4)

cross and multiply both sides of the equation;

-8((y-4)(y + 4)) = (12y - 12)(2y - 8)

-8(y² - 16) = 24y² - 96y - 24y + 96

-8y² + 128 =  24y² - 120y + 96

0 = 32y² - 120y - 32

solve the quadratic equation using formula method;

a = 32, b = -120, c = - 32

y = 4 or -0.25

Thus, the solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

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y=6

for the eqution

[tex]\frac{-8}{2y-8} =\frac{5}{y+4} -\frac{7y+8}{y^{2}-16 } \\[/tex]

Answer:

A' (-15, -5)

B' (10, -10)

C' (-5, -20)

Answer:

A ' (-15, -5)

B ' (10, -10)

C ' (-5, -20)

Step-by-step explanation:

The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.

Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.

Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because  [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].

The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]

As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.

The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true.

It should be noted that an inequality simply means a statement of an order relationship between two numbers and algebraic expressions.

From the information given, the equation illustrated is:

y < -0.2x² + 9x - 7.

63 < 0.2(10)² + (9 × 10) - 7

63 < 20 + 90 - 7.

63 < 103

In this case, the ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true since sixty there is less than one hundred and three.

Therefore, this is true.

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Complete question:

The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. Please select the best answer from the choices provided

True

False

Answer:

B. 82

Step-by-step explanation:

I hope it helps you :)

The value of z in the given figure of circle with two lines dividing it into segments is 100.

We are given that the measures of angles ∠1 and ∠2 are 105° and 120°, respectively.

Step 1: Since the interior angles of a triangle add up to 180°, we know that the measure of ∠3 is 180° - 105° - 120° = 55°.

Step 2: Since ∠3 and ∠z are supplementary angles, we know that m∠3 + m∠z = 180°.

Step 3: Substituting the measures of ∠3 from step 1 into step 2, we get 55° + m∠z = 180°.

Step 4: Subtracting 55° from both sides of the equation in step 3, we get m∠z = 180° - 55° = 125°.

Step 5: Since m∠z = 125°, then z = 125°.

Therefore, the value of z is 100.

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