the coordinates of the vertices of a triangle are A(-4,6) B(4,-2) C(-6,-4). find the length AB, BC, and, AC

The angle from the options given that is shown in the drawing is: D. <LIJ.

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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A parabola has focus (3,-2) and directrix y = 2. The point (a.-8) is on the parabola and its distance from the focus is 6 units.

The distance the point(x,y) from the focus(a, b) can be calculated as

\(\sqrt{(x-a)^2 +(y-b)^2}\)

A parabola has focus (3,-2) and directrix y = 2. The point (a.-8) is on the parabola and its distance from directrix y = 2 will be y − 2

Hence equation would be

\(\sqrt{(a-3)^2 +(-8+2)^2}\\\\\sqrt{(a-3)^2 +(-6)^2}\\\\\sqrt{(3-3)^2 +(36)}\\\\\sqrt{ (36)}\\\\6\)

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Answer:

A. y=x+4

Step-by-step explanation:

I used Desmos to graph all the information and the black line (which is A) goes through all the points. See picture

Without more information about the specific situation (such as the height from which the bottle is dropped, the surface on which it is dropped, and so on), a value for p cannot be determined.

The probability of landing a bottle on the floor on any given try is a fixed value, typically represented by "p".

The probability that he will land the bottle on the floor on the tenth try is then given by:

P(tenth attempt landing) = (1 - p)9 * p

where (1 - p)9 represents the probability that he fails to land the bottle on the floor in the first nine attempts, and p represents the probability that he lands the bottle on the floor on the tenth attempt.

However, without more information about the specific situation (such as the height from which the bottle is dropped, the surface on which it is dropped, and so on), a value for p cannot be determined.

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The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).

In other words,

sec(x) = 1 / cos(x)

The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.

To convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.

We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.

Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.

Now we can find the secant of this angle:

sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638

So the answer is approximately -1.638 degrees.

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The value of F in the formula F=9/5C+32 when c = 25 can be written as F = 32.36.

The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own. The variable that is stated in terms of the other variables is the subject of a formula. Take into account the cylinder's volume formula.

Given that F=9/5C+32

c = 25

\(F= \frac{9}{5C} + 32\)

\(F= \frac{9}{5*25} + 32\)

\(F= \frac{9}{125} + 32\)

\(F = 32.36\)

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complete question;

Use the formals F=9/5C+32 when c = 25, find the value of x

The measure of the two line segments are 36 and 27.

We have,

The secant and tangent rule on a circle.

DC is the tangent and ABC is the secant.

Then,

DC² = (AB + BC) x BC

Now,

Substituting.

(4x + 11)² = (27 + 5x - 11) x (5x - 11)

To solve the given equation (4x + 11)² = (27 + 5x - 11) x (5x - 11) for x, we will expand both sides of the equation and then simplify:

Expanding the left side:

(4x + 11)² = (4x + 11)(4x + 11) = 16x² + 44x + 44x + 121 = 16x² + 88x + 121

Expanding the right side:

(27 + 5x - 11) x (5x - 11) = (16 + 5x)(5x - 11) = 80x² - 176x + 75x - 165 = 80x² - 101x - 165

Setting the left and right sides equal to each other:

16x² + 88x + 121 = 80x² - 101x - 165

Rearranging the equation:

0 = 80x² - 16x² - 101x - 88x - 165 - 121

0 = 64x² - 189x - 286

Now, we have a quadratic equation.

We can solve it by factoring, completing the square, or using the quadratic formula.

Let's use the quadratic formula to find the solutions for x:

x = (-b ± √(b² - 4ac)) / (2a)

In our case, a = 64, b = -189, and c = -286.

Substituting these values into the quadratic formula:

x = (-(-189) ± √((-189)² - 4(64)(-286))) / (2(64))

x = (189 ± √(35721 + 73216)) / 128

x = (189 ± √108937) / 128

Since the discriminant (b² - 4ac) is positive, we have two distinct real solutions. Evaluating the square root:

x = (189 ± 329) / 128

We have two possible solutions for x:

x₁ = (189 + 329) / 128 = 518 / 128 = 4.047 = 4

x₂ = (189 - 329) / 128 = -140 / 128 = -1.094 (rejected)

Now,

The line segments are:

AC = 27 + 5x - 11 = 27 + 5 x 4 - 11 = 27 + 20 - 11 = 36

CD = 4x + 11 = 4 x 4 + 11 = 16 + 11 = 27

Thus,

The measure of the two line segments are 36 and 27.

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The equation of the shifted line is y = x + 2

From the question, we have the following parameters that can be used in our computation:

y = x

Shift left 2 units

To shift the equation y = x to the left by 2 units, we can replace x with (x + 2) in the equation.

i.e. (x. y) = (x + 2, y)

So, we have the new equation to be y = x + 2

This is the same line as the original equation but shifted 2 units to the left.

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Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer:

Sorry po just seen your email and I

Answer:

Sorry po just seen your email and I

The y-intercept of the function is  -9,25

The function is given as:

\(y = -5(.8)^{x - 1} - 3\)

See attachment for the graph of the function

From the graph, we have the following highlights:

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The diameter of the opening of the cone is equal to 4 centimetres.

A cone is a solid, three-dimensional geometric shape having a circular base and a pointed apex at the top. A cone is known to have one face and a vertex.

A cone doesn't have any edges.

Given:

Volume of cone = 12π cubic centimetres.

Height of cone, h = 9 centimetres.

Let radius of cone be = r.

We know volume of cone = 12π

1/3 ×π×r²×h = 12π

⇒ r² = (12 ×π ×3)/9π

⇒ r² = 36π/9π

⇒ r² = 4

⇒ r = 2.

So, diameter = 2 × r

= 2× 2

= 4cm.

Therefore, diameter of the opening of the cone = 4cm.

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The equation of the axis of symmetry of the quadratic function in this problem is given as follows:

x = -4.

The equation of the axis of symmetry of the quadratic function is a vertical line given as follows:

x = xv.

In which xv is the x-coordinate of the vertex of the quadratic function.

The vertex of a quadratic function is the turning point of the quadratic function, hence it has a x-coordinate of 4 and the equation of the axis of symmetry of the quadratic function in this problem is given as follows:

x = -4.

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Answer:

3(1)-4=-1 2(1)+5=7

Answer:

5z+1

Step-by-step explanation:

it was simple

Answer:

m = 25 + 6n

Step-by-step explanation:

To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.

Three different expressions that simplify to x^6​ are

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

Index forms are defined as mathematical expressions used to write numbers too small or large in more convenient forms.

Other names for index forms are standard forms and scientific notations.

Note some rules of indices, they are;

Then, we have;

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

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Answer:

L = 3(4) + 2(3) + 6

Step-by-step explanation:

.........

Answer:

7200

Step-by-step explanation:

7000

200

the seven is in thousand spot and 2 is in hundreds spot

SOH CAH TOA

Opposite is 7

Y is the hypotenuse - longest side

So, x is the adjacent

Find y first, we've got opposite & hypotenuse

=> SOH or Sin

Sin(30) = o/h

Sin(30) = 7/h

x h

h x sin(30) = 7

÷ Sin(30)

H = 14

Pythagoras' Theorem: a^2 + b^2 = c^2

(which I've already rearranged, to find value of x)

Square root of 14^2 - 7^2 = 7 root 3.

Thus, the missing lengths should be 14 and 7 root 3.

The answer is:

y = 14

x = 7 root 3

(root => a square root)

Hope this helps!

$60

Step-by-step explanation:

The unit rate can be determined by dividing $24 by 8 attendees to get

\(\dfrac{\$24}{8\:\text{attendees}} = \$3/\text{attendee}\)

so when 20 people are attending the graduation picnic, his total cost is going to be

\(20\:\text{attendees}×\dfrac{\$3}{\text{attendee}} = \$60\)

The most appropriate for this measurement will be finding the perimeter of your bedroom to hang lights. Then the correct option is D.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

You complete a project and record measurements in feet.

The type of project that would be most appropriate for this measurement will be finding the perimeter of your bedroom to hang lights.

Since, if the error occurs, then the error will increase in finding the area and volume.

Then the correct option is D.

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.

Triangle Proportionality Theorem:

To prove this theorem, we begin by drawing a ΔABC with a line DE parallel to side AB. We then draw lines BD and CE, which intersect the parallel line DE at points F and G, respectively. By the properties of parallel lines, we know that ∠ADE and ∠ABD are congruent, and ∠AED and ∠ADB are congruent. Similarly, ∠CDE and ∠BDC are congruent, and ∠CED and ∠DCB are congruent.

We can then use the properties of similar triangles to show that ΔADE and ΔABC are similar, as are  ΔCDE and ΔACB. This means that the ratios of corresponding side lengths are equal:

BA/DE = CA/CE and CB/DE = AB/BD

We can then substitute CA - BA for CB in the first equation, and BD for AB in the second equation:

BA/DE = (CA - BA)/CE and CB/DE = BD/(CA - BA)

Cross-multiplying both equations, we obtain:

BA * CE = DE * (CA - BA) and CB * DE = BD * (CA - BA)

Adding the two equations, we get:

BA * CE + CB * DE = (DE + CE) * CA

Dividing both sides by CB * DE, we obtain:

BA/CB = (DE + CE)/CE * CA/DE = DE/CD

Thus, we have proven the Triangle Proportionality Theorem.

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Answer:

3.65

Step-by-step explanation:

The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6

Answer:

x=-1

Step-by-step explanation:

4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1

Answer:

\( \sf \: x = - 1\)

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30 ÷ 30

→ [ x = -1 ]

Hence, the value of x is -1.

The input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

Given information:

A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug.

Each rat will be given a different dosage of the drug.

The oncologist will then measure the growth rate of the cancerous tumor.

Now, in the experiment, the oncologist tries to study or calculate the growth rate of a cancerous tumor. So, the output that he/she will get will be the growth rate of the cancerous tumor.

The experiment is done on the rate by giving them a dosage of the drug. The dosage can vary based on the study criterion. So, the amount of dosage of the drug should be the input of the experiment.

Therefore, the input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

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