Mathematics High School

△ABC ~ △AMN and AM = 6, MB = 4, AN = 8, then what is the value of AC?

Answers

Answer 1

Answer:

AC = 13.3

Make proportional relationship:

[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]

Insert values

[tex]\rightarrow \sf \dfrac{10}{AC} = \dfrac{6}{8}[/tex]

Cross multiply

[tex]\rightarrow \sf AC = \dfrac{10(8)}{6}[/tex]

Simplify

[tex]\rightarrow \sf AC =13.3[/tex]

Related Questions

A cylindrical container is packaged inside a prism-shaped box. the box has a volume of 96 cubic units. if the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? round the answer to two decimal places. a. 20.60 cubic units b. 37.77 cubic units c. 51.27 cubic units d. 75.40 cubic units

Answers

Volume is a three-dimensional scalar quantity. The volume of the empty space is 20.602 units³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the volume of the prism, the box is 96 units³ and the diameter of the cylindrical container is 4 units(Radius=2 units), while the height of the cylinder is 6 units. Therefore, The volume of the empty space is,

The volume of the empty space

= Volume of prism - Volume of the cylindrical container

= 96 units³ - (π×2²×6) units³

= 96 units³ - 75.398 units³

= 20.602 units³

Hence, the volume of the empty space is 20.602 units³.

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The slope of a line is 7/8 The y-intercept of the same line is 4
Complete the slope-intercept form equation

Answers

Answer:

y = -7/8x + 4

Step-by-step explanation:

Slope-intercept form :

y = mx + b

m = slopeb = y-intercept

Hence, the equation formed is :

y = -7/8x + 4

Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?

Answers

The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]

How to determine the point?

The points are given as:

A = (4,-5)

B = (6,-4)

m : n = 1 : 3

The coordinate of the point is then calculated using:

[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]

So, we have:

[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]

Evaluate the sum of product

[tex]P = \frac{1}{4}(18, -19)[/tex]

Evaluate the product

[tex]P = (\frac 92, -\frac{19}4)[/tex]

Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]

Answers

Answer:

[tex]x=-2\\[/tex]

Step-by-step explanation:

[tex]8^x=\frac{1}{64}\\xlog8=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{\log8}\\x=-2[/tex]

First we write the equation given

Next we take the log of both sides. This turns [tex]x[/tex] into a normal term instead of an exponent, but turns [tex]8[/tex] and [tex]64[/tex] into the log version of themselves.

Next we can divide both sides by [tex]log8[/tex] to isolate [tex]x[/tex].

This gives us our answer of [tex]\boxed{-2}[/tex]

Question Progress
Work out the value of 4° x 16°

Answers

Answer:

20°0°0 is the correct answer

Quadrilateral ABCD has the following coordinates: A(-6,3) B(-4,5) C(-1,6) and D(-3,2) and
maps onto A"B"C"D". It will undergo transformations that will consist of a reflection over
the y-axis followed by a translation. Point D" is shown plotted in the plane after the
transformation.

A) Write the translation rule that maps point D' to point D".

B) Write the coordinates of point A"

Answers

The translation rule that maps point D' to D" is (x + 3, y) and the coordinate of point A" is (9,3)

How to determine the translation rule?

The coordinates are given as:

A(-6,3) B(-4,5) C(-1,6) and D(-3,2)

When reflected across the y-axis, the transformation rule is:

(x,y) -> (-x,y)

So, we have:

A' = (6,3)

D' = (3,2)

Point D" on the grid is (6,2).

This means that the translation rule that maps both point is (x + 3, y)

The coordinates of point A

In (a), we have:

A' = (6,3)

Using the translation rule (x + 3, y), we have:

A" = (6 + 3,3)

A" = (9,3)

Hence, the coordinate of point A" is (9,3)

Answers

Answer:

P = 20 cm

Step-by-step explanation:

the perimeter (P) is the sum of the 4 sides (s) of the square

the sides of a square are congruent , then

P = 4s = 4 × 5 = 20 cm

Slope of (-9,-2) and (-9,-6)

Answers

Answer:

Slope is undefined.

Step-by-step explanation:

I will choose brainlyist and 20 POINTS

Answers

Answer:

They are all non triangles, but I'm not in your math class, so I don't know.

Step-by-step explanation:

The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was
Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8
and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4.
Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could
you show the stage manager was incorrect?

Answers

Answer:

The answer is c, hope this helps

Step-by-step explanation:

The diagram shows a regular polygon.
x
What is the value of x?
Write your answer as an integer or as a decimal rounded to the nearest tenth.

Answers

Answer:

To find the value of x, use the formula

(n-2) x 180, where n is the number of sides.

In this case, we have a TRIangle, which has THREE sides.

So, n=3

(3-2) x 180

1 x 180

180

If the total sum of the angles is 180, then the measure of one angle would be 180 divided by 3, which is 60.

Let me know if this helps, or if you got any more questions

A rectangle is 21 meters long and 11 meters wide. what is the perimeter of this rectangle?

Answers

Step-by-step explanation:

the perimeter is simply the distance you would have to walk when going around the whole object once.

so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.

so, the perimeter of a rectangle is

2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m

Which is the equation of the line passing through (0,4) and (8,0)?

Answers

Answer:

[tex]\sf y = -\dfrac{1}{2} x +4[/tex]

Find slope (m):

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m): \dfrac{0-4}{4-0} = -\dfrac{1}{2}[/tex]

Now, find equation:

[tex]\sf y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex]

[tex]\rightarrow \sf y - 4 = -\dfrac{1}{2} (x - 0)[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x +4[/tex]

how can i find area of abd triangle. .............

Answers

Answer:

6 square units

Step-by-step explanation:

The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.

angles

Any right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.

Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.

segments

The fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.

The tangent ratio is ...

Tan = Opposite/Adjacent

Applying that to angle β, we have

tan(β) = OD/AD [eqn 1]

tan(β) = BC/AC [eqn 2]

These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.

area

Equation [eqn 1] tells us ...

AD = OD/tan(β)

Equation [eqn 2] tells us ...

BC = AC·tan(β)

The area of ΔADB is ...

Area = 1/2bh

Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))

Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel

The length of AC is given as 6, and we know OD = 2, so the area is ...

Area = 1/2(2)(6) = 6

The area of triangle ADB is 6 square units.

I dive to 17 metres for 47 minutes. after a 30 minute surface interval i do a second dive to 17 metres. losing track of time, i notice my bottom time is now 25 minutes. according to the general rules, what should i do

Answers

If your bottom time is 25 minutes, general rules recommend that you ascend immediately to 15 feet then remain there for 8 minutes. You should then go to the surface and not dive for 6 hours.

What do general rules on diving say about a 25 minute bottom time?

The recommended bottom time is 24 minutes which means that staying there for 25 minutes will have exceeded this recommendation.

You should immediately ascend to 15 feet or 5 meters, and then wait there for 8 minutes. Then return to the surface and avoid diving for the next 6 hours.

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find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground

Answers

Answer:

107.86 to 2 d.p.

Step-by-step explanation:

makes a triangle. 120 feet is the hypotenuse.

we want to find the opposite so we will use sine.

sin(x) = opp/hyp which means opp = sin(x)hyp.

opp = sin(64)120

opp = 107.86 to 2d.p.

Select the expression that’s is equivalent to (x-1)^2

Answers

Answer:

(x-1)^2

=x^2 - 2x + 1

Step-by-step explanation:

hope this helps

Please help me thank you :3

Answers

Quadrilaterals are angles that has 4 sides and angles. The measure of the angle m<SPQ is 110 degrees

Angles in a quadrilateral

Quadrilaterals are angles that has 4 sides and angles. The given quadrilateral is a rhombus with equal opposite sides.

Given the following angles

m<SPR = 2x + 15

m<QPR = 3x - 5

From the figure

m<SPR = m<QPR

Substitute

2x+ 15 = 3x - 5

2x - 3x = -5 - 15

x = 20

Determine the measure of <SPQ
m<SPQ = 3x - 5 +2x +15

m<SPQ = 5x + 10
m<SPQ =5(20) + 10
m<SPQ = 110 degrees

Hence the measure of the angle m<SPQ is 110 degrees

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Which of the following is the equation of the function below? y=2sec (x+pi/6)+2 y=sec2(x+pi/6)]+2 y=sec[2(x+2)] + pi/6 y=2sec(x+2) + pi/6

Answers

The equation of the function is y = sec(2(x + π/6)) + 2

How to determine the equation of the function?

From the graph, we have the following parameters:

Local maximum = 3Local minimum = 1Period = 2Phase shift = π/6

A secant function is represented as:

y = A sec(b(x + c)) + d

Where:

A = 0.5 * (max - min) = 0.5 * (3 - 1) = 1

b = Period = 2

c = Phase shift = π/6

d = 0.5 * (max + min) = 0.5 * (3 + 1) = 2

So, we have:

y = 1 * sec(2(x + π/6)) + 2

Evaluate

y = sec(2(x + π/6)) + 2

Hence, the equation of the function is y = sec(2(x + π/6)) + 2

Answers

Answer:

43.4%

Step-by-step explanation:

229.99 - 129.99

= 100

The percent reduction is:

100/229.99 * 100

=43.4%

In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. the students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. for one student, it lands tails side up six times. the student will construct a 90% confidence interval for the true proportion of tails up. are the conditions for inference met?

Answers

Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.

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What is the length of the diagonal from vertex J to vertex L in the quadrilateral below?

Answers

Answer: 6.7 units for the diagonal from J to L

Step-by-step explanation:

you can use the Pythagorean theorem to find the diagonal (hypotenuse)

a^2 + b^2 = c^2

by counting units from M to J you have a length of 3 for the "a" value

by counting units from M to L you have a length of 6 for the "b" value

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2

take square root of both sides

6.7 = c

the diagonal is 6.7 units

Points a and b lie on a circle centered at point o. if oa = 5 and what is the area of sector aob? use the value π = 3.14, and choose the closest answer. a. 19.6 square units b. 39.3 square units c. 7.85 square units d. 15.7 square units

Answers

The area of sector AOB whose radius OA 5 units is 19.6 sq. units.

What is the Sector?

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.

Here, Radius of Circle = 5 units

length of arc AB / circumference = 1/4

So, Area of Sector AOB = one fourth of area of circle

= 1/4 X π X r²

= 0.25 X 3.14 X 5²

= 0.25 X 3.14 X 25

= 19.625 sq. units

Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.

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Answer:

19.6

Step-by-step explanation:

I need to know how to solve this

Answers

Answer:

K=-6/11

Step-by-step explanation:

3(k/3+4-2k)=3(-9k)

K+12-6k=-27k

12-5k=-27k

12=-22k

K=-6/11

Choose the expression that represents a linear expression.
6x + 6
O-6x² +8x-9
O8x3 + 9x² - 10x + 11
07x4-8x³+9x² - 10x + 11
Question 3(Multiple Choice Worth 1 points)
(06.01 LC)

Answers

Answer:

6x+6

Step-by-step explanation:

a linear expression has no power attached to the x (the unknown)

The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.

Answers

It is true for multiple reasons

Help!! Also the questions says “Which of the following shows JUST a variable?”

Answers

The answer is (g)

Variables are letters that represent unknown numbers
It can be any letter if the alphabet (a,b,c,d…..)
The others are what we call an (expression )which is basically when we put variables with other numbers

A dog eats 3 cans of dog food in 12 days. Write an equation to represent th
proportional relationship. Then find k, the constant of proportionality.
Let c =
Let d =
Equation:
= k•
k=-

Answers

The equation to represent the proportional relationship is c = 0.25d

How to determine the equation?

Let c = the number of cans

Let d = the number of days

So, we have:

c = kd

Where k represents the constant of proportionality.

From the given parameters, we have:

3 = 12k

Divide both sides by 12

k = 0.25

Substitute k = 0.25 in c = kd

c = 0.25d

Hence, the equation to represent the proportional relationship is c = 0.25d

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what is the distance from (7,0)- (-5,5)

Answers

Answer:

[tex]\frac{5}{-12}[/tex]

Step-by-step explanation:

If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].

(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])

I hope I helped you answer your question, and helped better understand it as well

Factorise completely 12 x³y - 18 xy²

Answers

Answer:

6xy(2x²-3y)

Step-by-step explanation:

factorized completely

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