Question 4 of 10
Multiple Choice: Please select the best answer and click "submit."
What is the length of the altitude of the equilateral triangle below?
30°
6
09
a
60° 90°
3
60°
3
O A. 1
OB. 6
O C. 313
OD. 3
O E. 6.13
O F. 27

Answer:

g(n)=80*3^(n-1)

Step-by-step explanation:

Scarlett started with 80 ants

That is, first term (a)=80

The ant population tripled every week.

First week: 80×3=240

Second week=240×3=720

Common ratio=720/240=3

Or

240/80=3

Therefore, r=3

G is a geometric sequence

Geometric sequence is given by

g(n)=a*r^(n-1)

Substitute a=80 and r=3 into the equation

g(n)=a*r^(n-1)

g(n)=80*3^(n-1)

The explicit formula for the sequence is

g(n)=80*3^(n-1)

Answer:

(0,-7)

Step-by-step explanation:

If nay point is form (x,y)

x is abscissa can be also called x axis coordinate

y is ordinate can be also called y axis coordinate

ordiantes are points lying on y axis.

For any point lying on y axis, its x-axis coordinate will be 0

given that ordinate is -7. it means that value of y coordinate is -7

Thus,  coordinates of the point is (0,-7)

Answer:

15 ml

Step-by-step explanation:

We are told

Solution A = 15% of water

Solution B = 20% of water

Let's assume, the entire solution = 100ml

We are told that in the beaker we have 10 ml of Solution A already

Mathematically,

100 ml = 15%

10 ml = X

100ml × X = 15 × 10

X = 150/ 100

X = 1.5%

Hence in the beaker, we have 1.5% of water from Solution A

We are asked to find how many ml of solution B must be added to make the solution have 18% of water

Let y = number of ml of solution B

Hence

10 ml × 15%(0.15) = 1.5 ml of water - Equation 1

y ml × 20%( 0.20) = 0.20y ml of water ...... Equation 2

Add up the above equation

10ml + y ml ×18% (0.18) = 1.5 + 0.20y

(10 + y)(0.18) = 1.5 + 0.20y

1.8 + 0.18y = 1.5 + 0.20y

Collect like terms

1.8 - 1.5  = 0.20y - 0.18y

0.3 = 0.02y

y = 0.3/0.02

y = 15ml                              

Therefore,15mL of solution B must be added to the beaker in order to create a mixture that is 18% water

Answer:

Step-by-step explanation:

[tex]D_f=D_g\quad\implies\quad (f-g)(x)=f(x)-g(x)\\\\\\(f-g)(x)=f(x)-g(x)=(3x+5)-(x^2)=-x^2+3x+5[/tex]

Answer:

crystal size and rock texture     D

Step-by-step explanation:

:)

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

What is the texture?

The texture is defined as a tactile quality of an object's surface. It appeals to our sense of touch, which can evoke feelings of pleasure, discomfort, or familiarity.

The texture of an igneous rock is dependent on the rate of cooling of the melt slow cooling allows large crystals to form, fast coolng yields small crystals.

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

To know more about the texture

https://brainly.com/question/14375831

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Answer:

Hey there!

The width is 3 inches, and in real life it would be 90 inches. (3x30)

The length is 5.5 inches, and in real life it would be 165 inches. (5.5x30)

90 inches is 7.5 feet

165 inches is 13.75

13.75 times 7.5 is 103.125, so rounded to the nearest integer, that would be 103 ft^2.

Hope this helps :)

Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

[tex]P + B = 14[/tex] ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

[tex]130P + 150B = 1920[/tex] --- Equation 2

Make P the subject of formula in equation 1

[tex]P = 14 - B[/tex]

Substitute 14 - B for P in equation 2

[tex]130(14 - B) + 150B = 1920[/tex]

Open Bracket

[tex]1820 - 130B + 150B = 1920[/tex]

[tex]1820 + 20B = 1920[/tex]

Subtract 1820 from both sides

[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]

[tex]20B = 100[/tex]

Divide both sides by 20

[tex]\frac{20B}{20} = \frac{100}{20}[/tex]

[tex]B = 5[/tex]

Substitute 5 for B in [tex]P = 14 - B[/tex]

[tex]P = 14 - 5[/tex]

[tex]P = 9[/tex]

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Answer:

9% loss

Step-by-step explanation:

We first can find the amount of money the saree was sold for by multiplying its buy cost, 1,750, by 1.04 (adding 4% to 1)

[tex]1750 \cdot 10.4 = 1820[/tex]

Now, 1820 is definitely less than 2000, so we need to find the percent difference between 2000 and 1820. We can use the formula:

[tex]\frac{higher-lower}{higher} \cdot 100[/tex]

So,

[tex]\frac{2000-1820}{2000} \cdot 100[/tex]

[tex]\frac{180}{2000} \cdot 100[/tex]

[tex]0.09 \cdot 100[/tex]

9

So, the loss percent of this dress is 9%.

Hope this helped!

Answer:

  y -6 = 1/3(x +3)   or   y = 1/3x +7

Step-by-step explanation:

The slope of the line describing the given path is the x-coefficient, -3. The slope of the perpendicular line will be the negative reciprocal of that:

  m = -1/(-3) = 1/3

The point-slope form of the equation for a line can be used to write the equation for the new path:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For m=1/3 and (h, k) = (-3, 6), the new path can be represented by ...

  y -6 = 1/3(x +3) . . . . point-slope form

  y = (1/3)x +7 . . . . . . slope-intercept form

P starts at (-3,5)

Move to the right 2 units and you'll get to (-1,5). We add 2 to the x coordinate here.

Then shift the point up three units to get to (-1,8). We add 3 to the y coordinate.

Finally, reflect over the x axis to get the answer (-1, -8)

Note how the y coordinate flipped in sign but the x coordinate stays the same

Answer:

Step-by-step explanation:

Vertex of f is (-1, -4) so its range is limited to y≥-4

|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0

Answer:

D

Step-by-step explanation:

i just took the test

Answer:

73cm²

Step-by-step explanation:

Area of rectangle=½ length×width

=½×18×7

=63cm²

Area of triangle=½b×h

base=18-13= 5cm

height=11-7 =4cm

½×b×h

½×5×4

=10cm²

Area of total=63+10

73cm²

Answer: 73c2

Step-by-step explanation:

Step-by-step explanation:

[tex] \sqrt{p} = \sqrt[r]{w - {as}^{2} } [/tex]

Find raise each side of the expression to the power of r

That's

we have

Send w to the left of the equation

Divide both sides by - a

We have

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

Y=x(t)(0.06) + x

Y =predicted population

X= population currently

t= number of years

Y= 60000(t) + 1000000

Step-by-step explanation:

Let the current population be x

X= 1000000

The rate of increase= 6% each year

Let the the predicted population= y

If the population is to increase by 6% each year the function predicting the population at the future will be

Y=x(t)(0.06) + x

The only changing value in the above formula is the time.

Y= 1000000(0.06)(t) +1000000

Y= 60000(t) + 1000000

Answer: The actual answer is:

next = now x 1.06, starting at 1,000,000

Answer:

Volume left in the cylinder if all the cone is made full:

[tex]\bold{345.72 \ ml }[/tex]

Step-by-step explanation:

Given

Radius of cylinder = 5 cm

Height of cylinder = 14 cm

Radius of cone = 6 cm

Height of cone = 20 cm

To find:

Liquid remaining in the cylinder if cone is made full from cylinder's liquid.

Solution:

We need to find the volumes of both the containers and find their difference.

Volume of cylinder is given by:

[tex]V_{cyl} = \pi r^2h[/tex]

We have r = 5 cm and

h = 14 cm

[tex]V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3[/tex]

Volume of a cone is given by:

[tex]V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3[/tex]

Volume left in the cylinder if all the cone is made full:

[tex]1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }[/tex]

Answer:

lateral area

Step-by-step explanation:

examble a cube if you remove the base and the top you remain with the vertical faces and lateral means vertical(we remove the top because it has potential to be a base if you turn it) it applies to any side touching the ground e.g in a cuboid

Answer:

A. Lateral area

Step-by-step explanation:

The lateral surface area is the area of the lateral (vertical) surfaces, it excludes the area of the base and top of a 3D shape.

Answer:

  927 cubic inches

Step-by-step explanation:

The area of the octagonal base is ...

  A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

  A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

  V = Bh

where B represents the area of the base, and h is the height.

  V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.

the answer on edg is 927

Answer:

4 meters

Step-by-step explanation:

To do this you would need to know what the area of a rectangle is, it is base times width. So you already know the area so you would just divide it by 5 and you would get the width, which is 4 meters

Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]

Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C

Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C

So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]

Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]

Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]

More for reference : https://brainly.com/question/9405925?referrer=searchResults

here's your answer in the given attachment

Answer:

Solution: {(-1,-8), (0,-6)}

Step-by-step explanation:

y=x^2+3x-6 ............(1)

y=2x-6 ....................(2)

Solution:

by comparison, the right-hand sides of both equations are equal (to y)

x^2+3x-6 = 2x - 6

Transpose and simplify

x^2 -x = 0

x = -1 or x=0

Substitute  x = -1 in (2)

y = 2(-1) -6 = -8  ..............(-1,-8)

substitute x = 0 in (2)

y = 2(0) -6 = -6 ...............(0,-6)

So there are two solutions, corresponding to the intersection of the quadratic and the straight line.

Answer:

[tex]\boxed{m<RUS = 65 \ degrees}\\\boxed{m<STU = 90 \ degrees}[/tex]

Step-by-step explanation:

Given that RU = 50°, So Central Angle ROU = 50° too because the measure of arc is equal to its central angle

Now, Let's assume a triangle ROU. It is an isosceles triangle since RO = RU (Radii of the same circle)

So,

∠ORU ≅ ∠OUR (Angles opposite to equal sides are equal)

So, we can write them as 2(∠RUO)

So,

2(∠RUO)+50 = 180 (Interior angles of a triangle add up to 180)

2(∠RUO) = 180-50

2(∠RUO) = 130

Dividing both sides by 2

∠RUO = 130/2

∠RUO = 65 degrees

m∠RUS = 65 degrees  (Both are the same)

In a semi circle (Given that SU is a diameter) , there must be a 90 degrees angle sin it opposite to the diameter.

So,

m∠STU = 90 degrees

From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°

Given that:

m∠ORU = m∠OUR (isosceles triangle)

m∠ORU + m∠OUR + m∠ROU = 180° (angle in triangle)

50 + 2 * m∠OUR = 180

m∠OUR = 65°

m∠OUR =  m∠RUS = 65°

m∠STU = 90° (angle subtended at circumference by semicircle).

From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°

Find out more on circle theorems at: https://brainly.com/question/17023621

Answer:

see below

Step-by-step explanation:

-3.55 g≤ -28.4

Divide each side by -3.55, remembering to flip the inequality

-3.55 g/-3.55≥ -28.4/-3.55

g≥8

Closed circle at 8 and the line goes to the right

Answer:

x=1 and y=6

Step-by-step explanation:

10x+2y=22

3x-4y=-21

First at all, you have to multiply both sides of this equation of 10x+2y=22, like this,

2(10x+2y)=2*22

*Put the 2 for the both sides.

Then, expand them.

20x+4y=44

When we have 20x+4y=44, we can eliminate with another equation.

20x+4y=44

3x-4y=-21

So, the first equation has +4y and the second equation has -4y, so we can use elimination method to eliminate one variable.

This time we can sum these equation to get one variable to get the answer easily. Like this...

20x+4y=44

3x-4y=-21

to become...

23x=23

x=23/23

x=1

When we get the equation like this, we can divide 23 by 23, so we can get the value of x. So, the value of x is 1.

When we know x is equal to 1, we can do the last part substitute x=1 into the second equation which is 3x-4y=-21.

The following steps is like this:

Substitute x=1 into 3x-4y=-21,

3(1)-4y= -21

3-4y= -21

Move the 3 to the another side, like this;

-4y= -21-3

-4y= -24

y= -24/ -4

y=6

*Be careful! When you calculate -24/-4 , you have to know how to eliminate the negative sign. (-) / (-) = +

Negative number divided by negative number is equal to positive number.

So, here we go! the value of x is 1 and the value of y is 6.

That is my solution and explanation from me. I hope you can understand. Bye!

The distance between the points (0, 10) and (–9, 1) is 12.73 units.

Given the following data;

Points ([tex]x_1, x_2[/tex]) = 0, -9

Points ([tex]y_1, y_2[/tex]) = 10, 1

To find the distance between the points;

In Mathematics, the distance between two points on a plane is calculated by using the formula;

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

Substituting the points into the formula, we have;

[tex]Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}[/tex]

Distance = 12.73 units

Therefore, the distance between the points is 12.73 units.

Find more information: https://brainly.com/question/13272812

Answer:

d. 200%

Step-by-step explanation:

( 800 ÷ 400 ) × 100

Answer:

(-4, 2).

Step-by-step explanation:

8x + 5y=-22

-3x - 5y = 2   Adding the 2 equations:

5x = -20

x = -4.

Substitute x = -4 in the first equation:

8(-4) + 5y = -22

5y = -22 + 32

5y = 10

y = 2.

Answer:

[tex]x=-4,\:\\y=2[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\\frac{-25y}{-25}=\frac{-50}{-25}\\y=2\\[/tex]

[tex]\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15\times\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\\frac{24x}{24}=\frac{-96}{24}\\x=-4\\\\\\x=-4,\:y=2[/tex]

Answer:

A’B’C’

Step-by-step explanation:

Well if triangle ABC is rotated 90 degrees clockwise around the origin it will turn right to create triangle A’B’C’.

Given Information:

Launch angle of projectile = 30°

Initial velocity = V₀ = 30 m/s

Acceleration due to gravity = g = 10 m/s²

Required Information:

Angle with the horizontal after 1.5 sec = ?

Answer:

The angle of the projectile to the horizontal after t = 1.5 seconds is 0°

Step-by-step explanation:

The horizontal component of the velocity is given by

[tex]Vx = V_0 \cos(\theta)[/tex]

Where V₀ is the initial velocity and θ is the launch angle

The vertical component of the velocity is given by

[tex]Vy = V_0 \sin(\theta) - gt[/tex]

Where V₀ is the initial velocity, θ is the launch angle, g is the acceleration due to gravity and t is the time.

So after t = 1.5 sec

The horizontal component of the velocity is

[tex]Vx = V_0 \cos(\theta) \\\\Vx = 30 \cos(\30) \\\\Vx = 30 \times 0.866\\\\Vx = 25.981 \: m/s[/tex]

And the vertical component of the velocity is

[tex]Vy = V_0 \sin(\theta) - gt \\\\Vy = 30 \sin(30) - 10 \times 1.5 \\\\Vy = 30(0.5) - 10 \times 1.5 \\\\Vy = 15 - 15 \\\\Vy = 0 \: m/s \\\\[/tex]

The angel is

[tex]\tan(\theta) = \frac{0}{25.981} \\\\\theta= \tan^{-1}( \frac{0}{25.981}) \\\\\theta= 0[/tex]

Therefore, the angle of the projectile to the horizontal after t = 1.5 seconds is 0°